Engineering of Sport 6: Volume 1: Developments for Sports

The Engineering of Sport 6

Eckehard Fozzy Moritz and Steve Haake (Eds.)

The Engineering of Sport 6 Volume 1: Developments for Sports

~ Springer

Eckehard Fozzy Moritz SportKreativWerkstatt GmbH Herzogstral3e 48 D-80803 Miinchen Germany [email protected] www.SportKreativWerkstatt.de

Steve Haake Centre for Sport and Exercise Science Collegiate Hall Sheffield Hallam University Sheffield S10 2BP UK [email protected]

Library of Congress Control Number: 2006927112 ISBN-tO: 0-387-31773-2 ISBN-13: 978-0387-31773-1 Printed on acid-free paper. © 2006 Springer Science-Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Sciencc+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights.

Printed in the United States of America. 98765432 springer.corn

(EB)

Preface

What you are holding in your hands is probably the best overview of activities in sports engineering available at the time of printing; i.e. the state of the art in summer 2006 . It is the result of so many people's work to whom we are indebted that it is difficult to name them: there are the authors, the scientific advisory board, the scientific committee, the theme patrons, the publisher and printer , the advisors of whatever kind - and, here we have to make an exception, there is Ingo and Amanda. Nobody who has been part of the production of this book could have done without them, at the very least us: they handled issues you wouldn't even believe could turn up with efficiency and charm . Thanks, Ingo Valtingoier; thanks, Amanda Staley . In the accumulation of the contributions and the preparation of the proceedings we encountered one development that we were very happy about: the sports engineering community keeps growing - in the number or researchers and experts involved, but also in the breadth of disciplines and institutions contributing. This should definitely be interpreted as a positive development - even though in the evaluation of contributions this lead to a number of intricate discussions. Is sports engineering primarily science? Is it engineering? Is it science and engineering helping sports? Some reviewers had differing views on that: if it is science , you need method, data, and discussion ; if it is engineering, you need method and an outcome with some demonstrable usefulness, if it is an aide to sports then whatever has been done needs demonstrable relevance. As a consequence, some contributions very well done from an engineering perspective have been turned down by hardcore scientists, and vice versa; in some cases we tried to intermediate, in others it may have been bad luck for the contributors. We think sports engineering will have to live with this variety of perspectives and interests; it is rather the appeal of this field in the process of finding itself. Openness combined with consistent reasoning will be needed to progress from here; somewhere in-between academic traditions and Feyerabend's famous "Anything goes". As a quick glimpse behind the scene, besides the disciplinary quarrels sketched above some "cultural" clashes could also not be avoided. One German reviewer put his comments in a very direct way that was hard to bear for the British author; some East Asian authors had a hard time in focusing their writing on the most interesting results and were thus bluntly thrown out; some well-known members in one community have seen their abstract turned down by experts from another area who did not know about the writer 's fame .. . these anecdotes point to just a couple of more issues the sports engineering community will have get to grips with in the not too distant future .

vi

Preface

As the result of various influences in these proceedings you will find a number of new topic areas indirectly related to but important to sports engineering. One area of concern we like to especially highlight here is the topic of sustainability, which may serve as an important yardstick for the future development of sports engineering and hopefully other industrial activities. Furthermore, you will find contributions on trends, cultural influences, human factors and on neural network modeling. Finally, according to the special emphasis of this conference we were successful in seeking a large number of papers in the area of innovation and design, including economic perspectives and proposals for novel design approaches. To our regret, even though we had tried hard we could get no contributions on industrial design - this area with so much relevance to sports equipment apparently is still a step-child in our community. In the assembly of these proceedings we have endeavored to realize some novel approaches. First of all, we used "theme patrons" for different topic areas who not only helped acquire contributions but were also asked to write a synopsis of the contributions in "their" fields. This will hopefully increase the use value for readers, who by just reading the synopses can have a basic idea about developments in certain fields, and can then scan contributions on a much better knowledge basis. This is a first step towards converting the proceedings into a sort of handbook which hopefully will be taken up by future editors. Then, as we tried to increase the relevance of sports engineering to sports, we have asked authors to take special care to illustrate the respective relevance, and to put their contribution into a sports-related category rather than a discipline-oriented category. Therefore, one volume of these proceedings has been named "developments for sports"; it is the biggest and could have even been bigger. The second volume is termed "developments in disciplines", which consists mainly·of contributions focusing on modeling and measurements. A third volume has been named "developments for innovation", a tribute to this special focus of this conference (being organized by a center for innovation in sports), and to the fact that we could accumulate an amazing number of contributions in this field. Finally, we hope that the reader will appreciate the outcome, and we' ll be very happy to receive comments of whatever kind, be it criticism, proposals for improvement or grappa casks and flower arrangements. Eckehard Fozzy Moritz Stephen Haake Editors July 2006

Contents 1 Baseball

Synopsis

3

Alan M. Nathan

An Experimental Investigation of Baseball Bat Durability

5

Patrick 1. Drane, James A. Sherwood. Rebecca H. Shaw

Bending Modes, Damping, and the Sensation of Sting in Baseball Bats

II

Daniel A. Russell

Experimental Investigations of the Relationship of Baseball Bat Properties on Battered-Ball Performance

17

Rebecca H. Shaw , James A. Sherwood

The Effect of Spin on the Flight of a Baseball

23

Alan M. Nathan, Joe Hopkins. Lance Chong. Hank Kaczmarski

Rigid Wall Effects on Softball Coefficientof Restitution Measurements

29

Lloyd Smith. Aaron Ison

The Effect of Holding Methods on a Baseball Bat Performance Estimation System

35

Hiroyuki Kagawa , Takeshi Yoneyama, Masaya Takahashi

2 Climbing - Instrumentation And Testing OfEquipment

Synopsis

43

Franz Konstantin Fuss

An Estimation of the Load Rate Imparted to a Climbing Anchor During Fall Arrest

45

Dave Custer

Dynamicsof Speed Climbing

51

Franz Konstantin Fuss , Gunther Niegl

Instrumented Climbing Holds and Dynamics of Sport Climbing

57

Franz Konstantin Fuss. Gunther Niegl

Forces Generated in a Climbing Rope During a Fall Andrew Phillips , Jeff Vogwell, Alan Bramley

63

viii

Contents

Rock Climbing Belay Device Analysis, Experiments and Modelling Lionel Manin, Matthieu Richard, Jean-Daniel Brabant, Marc Bissuel

69

3 Cycling Synopsis Martin Strangwood

77

Thermo-mechanical Modification Techniques for Structural Foams used in Racing Bicycle Wheels . Catherine Caton, Mike Jenkins, Martin Strangwood

79

The Effect of a Non Circular Chainring on Cycling Performance Nicolas Horvais , Pierre Samozino, Frederique Hintzy

85

Dynamic Characteristics of Modem Mountain Bikes Rear Linkages Angelo Tempia, Aleksandar Subic , Ricardo M Pagliarella

91

An Ambient Intelligence System to Assist Team Training and Competition in Cycling lngmar Fliege, Alexander Geraldy, Reinhard Gotzhein, Thomas Jaitner, Thomas Kuhn, Christian Webel

97

Indoor-Simulation of Team Training in Cycling Thomas Jaitner, Marcus Trapp. Dirk Niebhur, Jan Koch

103

A Bond Graph Model of a Full-Suspension Mountain Bicycle Rear Shock Robin Redfield, Cory Sutela

109

Track Cycling: An Analytical Model Richard Lukes, Matt Carre, Stephen Haake

I 15

Forces During Cycling After Total Knee Arthoplasty Maximilian Mueller , Veit Senner, Markus Wimmer

121

A Study of Aerodynamic Drag and Thermal Efficiency of a Series of Bicycle Helmets Firoz Alam, Aleksandar Subic , Simon Watkins

127

4 Golf Synopsis Steve Mather

135

Contents

ix

An Instrumented Grip Handle for Golf Clubs to Measure Forces and Moments Exerted by Each Hand During Swing Motion S. Koike. H. Iida, H. Shiraki, M Ae

137

The Aerodynamic Influenceof Dimple Design on Flying Golf Ball T. Sajima, T. Yamaguchi. M Yabu, M Tsunoda

143

Experimental Verification of Trajectory Analysis of Golf Ball Under Atmospheric Boundary Layer

149

Takeshi Naruo, Taketo Mizota

Validation of Accelerometers And Gyroscopes to Provide Real-Time Kinematic Data for Golf Analysis

155

K. Fitzpatrick. R. Anderson

Investigation of Wrist Release During the Golf Swing by Using a Golf Swing Robot

161

Yohei Hoshino, Yukinori Kobayashi. Soichiro Suzuki

Segmental Sequencingof Kinetic Energy in the Golf Swing

167

Brady C. Anderson. Ian C. Wright. Darren 1. Stefanyshyn

5 Gymnastics Synopsis

175

David G. Kerwin

Effect of Shoulder Compliance on Peak High Bar Forces During the Giant Swing Alison L. Sheets. Mont Hubbard

177

Effects of Horizontal Surface Complianceon Balance Strategies

183

Wendy Kimmel. Mont Hubbard

Predicting High Bar Forces in the Longswing

189

David Kerwin. Gareth Irwin

Musculoskeletal Work in the Longswing on High Bar

195

Gareth Irwin. David G Kerwin

6 Lawn Sports

Synopsis Matt Carre

203

x

Contents

Quantification of the Cricket Bowling Delivery; a Study of Elite Players to Gauge Variability and Controllability Laura Justham, Andrew West. Andy Harland. Alex Cox

205

Ball Launch Characteristics for Elite Rugby Union Players Christopher Holmes . Roy Jones. Andy Harland. Jon Petz ing

211

A Novel Quantitative Method for the Determination of Wear in an Installed Synthetic Turf System Andrew McLeod, lain James. Kim Blackburn. Gavin Wood

217

Multi-Optimization of Three Kicks in Rugby Kazuya Seo , Osamu Kobayashi. Masahide Murakami

223

The Mechanical Behaviour of Cricket Soils During Preparation by Rolling Pete r Shipton . lain James. Alex Vickers

229

Studies on the Oblique Impact of a Cricket Ball on a Cricket Pitch David James. Matt Carre . Stephen Haake

235

Test Devices for the Evaluation of Synthetic Turf Pitches for Field Hockey Colin Young. Paul Fleming. Neil Dixon

241

7 Skiing, Snowboarding and Ski Jumping

Synopsis Veit Senner

249

Laboratory Device for Measuring the Friction Between Ski-Base Materials and Ice or Snow Mathieu Fauve, Lukas Bdurle, Hansueli Rhyner

251

Biomechanical Instrumentation of the BergIsel Jumping Hill in Innsbruck and Exemplary Analysese Kurt Schindelwig. Werner Nachbauer

257

Dynamic Properties of Materials for Alpine Skis Christian Fischer. Mathieu Fauve, Etienne Combaz. Pierre-Etienne Bourban, Veronique Michaud. Christopher J. G. Plummer. Hansueli Rhyner. JanAnders E. Manson ,

263

Calculation of Friction and Reaction Forces During an Alpine World Cup Downhill Race M. Schie stl, P. Kaps, M. Mossner, W. Nachbauer

269

Contents Measurement of Jumper's Body Motion in Ski Jumping

xi 275

Yuji Ohgi, Kazuya Seo, Nobuyuki Hirai. Masahide Murakami

Riding on Air: A New Theory for Lift Mechanicsof Downhill Skiing and Snowboarding

281

Qianhong Wu. Yesim Igci, Yiannis Andreopoulos, Sheldon Weinbaum

Subjective Evaluation of the Performance of Alpine Skis and Correlations with Mechanical Ski Properties

287

Peter Federo/f. Mirco Auer. Mathieu Fauve, Anton Luthi. Hansueli Rhyner

Timing of Force Applicationand Joint Angles During a Long Ski Turn

293

Takeshi Yoneyama , Nathan Scott. Hiroyuki Kagawa

Effect of Bindingsand Plates on Ski Mechanical Properties and Carving Performance

299

Anton Luthi. Peter Federo/f. Mathieu Fauve, Hansueli Rhyner

Development of a Prototype that Measures the Coefficientof Friction Between Skis and Snow

305

Paul Miller . Andy Hytjan , Matthew Weber. Miles Wheeler. Jack Zable, Andy Walshe , Alan Ashley

8 Football

Synopsis

313

Matt Carre

An Investigation into the Link BetweenSoil Physical Conditions and the Playing Quality of Winter Sports Pitch Rootzones

315

Marke Jennings- Temple . Peter Leeds-Harrison. lain Jam es

Measuringand Modelling the Goalkeeper's Diving Envelope in a Penalty Kick

321

David G. Kerwin. Ken Bray

Flow Visualization on a Real Flight Non-spinning And Spinning Soccer Ball

327

Takeshi Asai, Kazuya Seo, Osamu Kobayashi. Reiko Sakashita

Gaze Point Analysis in Movement Prediction of Soccer Players By Image Processing

333

Yuusuke Hiramatsu, Shigemichi Ohshima, Atsumi Ohtsuki

Traction Testing of Soccer Boots Under Game Relevant LoadingConditions Thomas Grund. Veit Senner

339

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Contents

Correlation between Support Foot Placementand Goal Accuracy for Instep Kicks in the Soccer Field

345

Giuseppe Marcolin, Nicola Petrone, Claudio Robazza

Analysis of the Influenceof Rubber Infill on the Mechanical Performance of Artificial Turf Surfaces for Soccer

351

Enrique Alcantara, David Rosa, Javi er Gamez , Antonio Martinez. Mario Comin. Maria Jos e Such, Pedro Vera.Jaime Prat

Soccer Ball Modal Analysis Using a Scanning Laser Doppler Vibrometer (SLDV)

357

Jouni Ronkainen, Andy Harland

9 Tennis

Synopsis

365

Stuart Miller

Normal Impact of Hollow Balls on Flat Surfaces

367

Yoshihisa Honda

Factors in Tennis Ball Wear

373

Carolyn Steele. Roy Jones. Paul Leaney

Measuring Ball Spin off a Tennis Racket

379

Simon Goodwill. Jamie Douglas. Stuart Miller. Stephen Haak e

3D Player Testing in Tennis

385

Simon Choppin , Simon Goodwill. Steph en Haake

An Extended Study Investigating the Effects of Tennis Rackets with Active DampingTechnology on The Symptoms of Tennis Elbow

391

Robert Cottey , Johan Kotze , Herfried Lammer, Werner Zirngibl

10 Water Sports

Synopsis

399

Jani Macari Pallis

Computational Fluid Dynamic Analysis ofa Water Ski Jumper

401

John Hart. David Curtis. Stephen Haake

Feedback Systems in Rowing Arnold Baca, Philipp Kornfe ind, Mario Heller

407

Contents

xiii

Biomechanical Analysi s of Olympic Kayak Athletes During Indoor Paddling Nicola Petron e, Andrea Isotti, Guglielmo Guerrini

413

So you think you know the ropes? White Water Rescue Ropes and Techniques Matt Bark er

419

Computational Modelling of Surfboard Fins for Enhanced Performance Dave Carswe ll, Nicholas Lavery, Steve Brown

425

Development of Swimming Prosthet ic for Physically Disabled (Optimal Design for One Side of Above-Elbow Amputation) Keiko Yoneyama, Motomu Nakashima

431

Author Index

437

Subje ct Index

441

Contributors

Simon C. Adelmann University of Birmingham, UK Michiyoshi Ae University of Tsukuba, Japan UzomaAjoku Loughborough Univers ity, UK Shinichiro Akiyama Toyota Motor Corporation, Japan Firoz Alam Royal Melbourne Institute of Technology Pdr-Anders Albinsson Swedish Defence Research Agency, Sweden

Enrique Alcantara Universitat Politecnica de Valencia, Spain Brady C. Anderson University of Calgary, Canad a Lauren Anderson Loughborough University, UK

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Contributors

Ross Anderson University of Limerick, UK Dennis Andersson Swedish Defence Research Agency, Sweden Yiannis Andreopoulos The City College of New York, USA Ali Ansarifar Loughborough University, UK Ayako Aoyama Tokyo Institute of Technology Takeshi Asai Yamagata University, Japan Andrew Ashcroft University of Cambridge, UK Alan Ashley United States Ski Association, USA MircoAuer Swiss Federal Institute for Snow and Avalanche Research Davos, Switzerland Andreas Avgerinos Democritus University ofThrace, Greece Arnold Baca University of Vienna, Austria Sarah Barber University of Sheffield, UK Franck Barbier Universite de Valenciennes, France Matthew R. Barker Auckland University of Technology, New Zealand

Contributors Joseph Beck

United States Air Force Academy, USA Nicolas Belluy e

Decathlon, France Alexey, Belyaev

Perm State Technical University, Russia Goran Berglund

Sandvik Material Technology, Sweden Nils Betzler

Otto von Guericke University Magdeburg, Germany Marc Bissuel

INSA Lyon, France Kim Blackburn

Cranfield University, UK Jane R. Blackford

University of Edinburgh, UK Kim B. Blair

Massachusetts Institute of Technology, USA Stephan Boerboom

Technische Universitat Miinchen, Germany Harald Bohm

Technische Universitat Miinchen, Germany Robert Bordas

Otto von Guericke University Magdeburg, Germany Pierre-Etienne Bourban

Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland Jean-Dan iel Brabant

INSA Lyon, France

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Contributors

Alan N. Bramley

University of Bath, UK Ken Bray

Universityof Bath, UK Desmond Brown

University of Ulster, UK Steve Brown

Universityof Wales Swansea, UK Mark-Paul Buckingham

Universityof Edinburgh, UK Jeremy Burn

Bristol University, UK Mike P. Caine

Loughborough University, UK Matt J. Carre

University of Sheffield, UK David 1. Carswell

University of Wales Swansea, UK Catherine J. Caton

University of Birmingham, UK Chaochao Chen

Kochi Universityof Technology, Japan Lance Chong

Universityof Illinois, USA Simon Choppin

Universityof Sheffield, UK Jeffrey 1. Chu

Simbex, USA

Contributors Steffen Clement AUm Sport, Germany Etienne Combaz Ecole Polytechnique Federalede Lausanne (EPFL), Switzerland Mario Comin Universitat Politecnica de Valencia, Spain Alex Cork Loughborough University, UK James Cornish University of Birmingham, UK Robert Cottey HEAD Sport AG, Austria Aimee C. Cubitt University of Bath, UK Kieran F. Culligan Massachusetts Instituteof Technology, USA David Curtis Sheffield Hallam University, UK Dave Custer Massachusetts Instituteof Technology, USA Tim Deans Bristol University, UK Jeroen Dethmers Universiteit Maastricht, Netherlands Neil Dixon Loughborough University, UK Sharon1. Dixon University of Exeter, UK

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Contributors

Jamie Douglas

International Tennis Federation, UK Patrick 1. Drane

University of Massachusetts Lowell, USA Melan ie Dumm

Technische Universitat Munchen, Germany Juan Vicente Dura

Universitat Politecnicade Valencia, Spain Colin Eames

United States Air Force Academy, USA Markus Eckelt

Universityof Applied Sciences Technikum Wien, Austria Jiirgen Edelmann-Nusser

Otto von Guericke University Magdeburg, Germany Frank Einwag

Klinik fur Orthopadische Chirurgie und Unfallchirurgie Bamberg, Germany Carl F. Ettlinger

Vermont Safety Research, USA Paul Ewart

University ofWaikato, New Zealand Emanuela Faggiano

University of Padova, Italy Mathieu Fauve

Swiss Federal Institute for Snow and Avalanche Research Davos, Switzerland Owen R. Fauvel

University of Calgary, Canada

Contributors Peter Federolf

University of Salzburg, Austria Monika Fikus

University of Bremen, Germany Christian Fischer

Ecole Polytechnique Federale de Lausanne(EPFL), Switzerland Peter R. Fischer

University of Augsburg, Germany Keith Fitzpatrick

Universityof Limerick, UK Paul Fleming

Loughborough University, UK lngmar Fliege

Technical University Kaiserslautem Matthieu Foissac

Decathlon, France Kathryn Franklin

University of Glamorgan, UK Philippe Freychat

Decathlon, France Piergiuseppe Fumei

University of Padova, Italy Franz Konstantin Fuss

Nanyang Technological University, Singapore Javier Gamez

Universitat Politecnica de Valencia, Spain

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Contributors

Nico Ganter

Otto von Guericke UniversityMagdeburg, Germany Paul Gebhard

Technische Universitat Miinchen, Germany Alexander Geraldy

Technical UniversityKaiserslautem Anton Gerrits

TNO, Netherlands Alexandros Giannakis

CSEM - Swiss Center for Electronics and Microtechnology, Switzerland Maria Giannousi

Democritus University of Thrace, Greece Paul J. Gibbs

Loughborough University, UK Christophe Gillet

Universite de Valenciennes, France Juan Carlos Gonzales

Universitat Politecnica de Valencia, Spain Simon Goodwill

University of Sheffield,UK Philippe Gorce

Toulon University, France Rae. Gordon

University of Glamorgan, UK Reinhard Gotzhein

Technical University Kaiserslautem Richard M. Greenwald

Simbex, USA

Contributors Thomas Grund

Technische Universitat Miinchen, Germany Guglielmo Guerrini

Italian Kayak Federation, Italy Jose Maria Gutierrez

UniversitatPolitecnicade Valencia, Spain Stephen J. Haake

Sheffield Hallam University, UK Christian Hainzlmai er

Technische Universitat Miinchen, Germany Nick Hamilton

Sheffield Hallam University, UK Dong Chul Han

Seoul National University, Korea R. Keith Hanna

Fluent Europe Ltd., UK Andy R. Harland

Loughborough University, UK John Hart

Sheffield Hallam University, UK Thomas Hartel

Chemnitz University of Technology, Germany Ulrich Hartmann

Technische Universitat Miinchen, Germany Andreas Hasenknopj

MLD, Germany Dieter Heinrich

University Innsbruck, Austria

xxiii

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Contributors

Ben Heller

Sheffield Hallam University, UK Mario Heller

Universityof Vienna, Austria Christian Henneke

SportKreativWerkstattGmbH, Germany Martin Herbert

Bristol University, UK Falk Hildebrand

Institute for Applied Training Science (IAT) Leipzig, Germany Norbert Himmel

Institut fur Verbundwerkstoffe GmbH, Germany Frederique Hintzy

Laboratoirede Modelisation des Activites Sportives, France Nobuyuki Hirai

Universityof Tsukuba, Japan Yuusuke Hiramat su

Meijo University, Japan Philip Hodgk ins

Loughborough University, UK Martin Hofmann

Otto von Guericke University Magdeburg, Germany Frank Hoisl

Technische Universitat Miinchen, Germany Christopher E. Holmes

Loughborough University, UK Yoshihisa Honda

Kinki University, Japan

Contributors Joe Hopkins Western Michigan University, USA Neil Hopkinson Loughborough University, UK Nicolas Horvais Laboratoire de Modelisation des Activites Sportives, France Yohei Hoshino Hokkaido University, Japan Kenji Hosokawa Chubu University, Japan Mont Hubbard University of California, Davis, USA Andrew Hytjan University of Colorado at Boulder , USA Yesim Igci Princeton University, USA Hiroshi /ida Polytechnic University Kagawa , Japan Yoshio Inoue Kochi University of Technology, Japan Carl Johan Irander Sandvik Material Technology, Sweden Jon Iriberri Berrostegieta Performance Enhancement Centre, Basque Government, Spain Gareth Irwin University of Wales Cardiff, UK Aaron Ison Cascade Engineering, USA

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Contributors

Andrea Isotti

University of Padova, Italy Koji Ito

Japan Instituteof Sport Sciences,Japan Takuzo Iwatsubo

Kansai University, Japan Thomas Jaitner

Technical University Kaiserslautem Daniel A. James

Griffith University, Australia David M Jam es

Universityof Sheffield, UK la in James

Cranfield University, UK Mike J. Jenkins

Universityof Birmingham, UK Marke Jenn ings-Temple

Cranfield University, UK Alexander W. Jessiman

Simbex, USA Tomohiko Jin

Toyota Motor Corporation, Japan Robert 1. Johnson

University of Vermont, USA Clifton R. Johnston

University of Calgary, Canada Roy Jones

Loughborough University, UK

Contributors Andre Jordan Otto von Guericke University Magdeburg, Germany LauraJus/ham Loughborough University, UK Hank Kaczmarski University of Illinois, USA HiroyukiKagawa Kanazawa University, Japan Michael Kaiser Institut fitr Verbundwerkstoffe GmbH, Germany Nico Kamperman TNO, Netherlands Peter Kaps University Innsbruck, Austria Shozo Kawamura Toyohashi University of Technology, Japan Ian C. Kenny University of Ulster, UK David G. Kerwin University of Wales Cardiff, UK Andreas Kiefmann Technische Universitat Miinchen, Germany Cheal Kim Kyungpook National University, Korea Moo Sun Kim Seoul National University, Korea Sun Jin Kim Seoul National University, Korea

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Contributors

Wendy Kimmel University of California, Davis, USA Efthimis Kioumourtzoglou Democritus University ofThrace, Greece Bob Kirk University of Sheffield, UK Sebastian Klee

Isabella Klopfer Technische Universitat Munchen, Germany Karin Knoll Institute for Applied Training Science (IAT) Leipzig, Germany Klaus Knoll Institute for Applied Training Science (IAT) Leipzig, Germany Ted Knox Wright Patterson Air Force Base, USA Cheolwoong Ko University of Iowa, USA Osamu Kobayashi Tokai University, Japan Yukinori Kobayashi Hokkaido University, Japan Jan Koch Technical University Kaiserslautern Hannes Kogler Fischer GmbH, Austria Sekiya Koike University of Tsukuba, Japan

Contributors

Philipp Kornfeind University of Vienna, Austria Giorgos Kotrotsios CSEM - Swiss Center for Electronics and Microtechnology, Switzerland Johan Kotze HEAD Sport AG, Austria Christian Kramer Technische Universitat Munchen, Germany Maximilian Krinninger Technische Universitat Munchen, Germany Michael Krohn Hochschule fur Gestaltung und Kunst ZUrich, Switzerland AndreasKruger Otto von Guericke University Magdeburg, Germany Thomas Kuhn Technical University Kaiserslautem HerfriedLammer HEAD Sport AG, Austria Nicholas Lavery University of Wales Swansea,UK Paul Leaney Loughborough University, UK Manryung Lee Kyungin Women's College, Korea Woo Il Lee Seoul National University, Korea Peter Leeds-Harrison Cranfield University, UK

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Contributors

Sebastien Leteneur

Universite de Valenciennes, France Chris Lewis-Jones

Delcam pic, UK Udo Lindemann

Technische Universitat Munchen, Germany Daniel Low

Universityof Exeter, UK Peter Lugner

Vienna University of Technology, Austria Richard Lukes

University of Sheffield, UK Anton Liithi

Swiss Federal Institute for Snow and Avalanche Research Davos, Switzerland Reiner Liitzeler

RWTH Aachen University, Germany Jani Macari Pal/is

Cislunar Aerospace Inc., USA Lionel Manin

INSA Lyon, France Graeme Manson

University of Sheffield, UK

Jan-Anders E. Manson Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland Giuseppe Marcolin

Universityof Padova, Italy Brett A. Marmo

University of Edinburgh, UK

Contributors Antonio Martinez Universitat Politecnicade Valencia, Spain Natividad Martinez Universitat Politecnica de Valencia, Spain Tom Mase Michigan State University, USA Steve Mather University of Nottingham, UK Sean Maw University of Calgary, Canada Alex J. McCloy University of Ulster, UK Mark McHutchon University of Sheffield, UK Andrew McLeod Cranfield University, UK Hossain Md.Zahid Toyohashi University of Technology, Japan Kenneth Meijer Universiteit Maastricht, Netherlands Daniel Memmert University of Heidelberg, Germany Roberto Meneghello University of Padova, Italy Imke K. Meyer University of Bremen, Germany Michael Michailov National Sports Academy, Bulgaria

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Contributors

Veronique Michaud

Ecole Polytechnique Federale de Lausanne(EPFL), Switzerland Thomas Milani

Chemnitz Universityof Technology, Germany Paul Miller

University of Colorado at Boulder, USA Stuart Miller

International Tennis Federation, UK Guillaume Millet

Universite Jean Monnet Saint-Etienne, France Hirofumi Minamoto

Toyohashi Universityof Technology, Japan Sean R. Mitchell

Loughborough University, UK Chikara Miyaji

Japan Institute of Sport Sciences, Japan Yusuke Miyazaki

Tokyo Institute of Technology, Japan Taketo Mizota

Fukuoka Institute of Technology, Japan Stuart Monk

University of Birmingham, UK Ana Montaner

Universitat Politecnicade Valencia, Spain John Morgan

Bristol University, UK Eckehard Fozzy Moritz

SportKreativWerkstatt GmbH, Germany

Contributors Rhys Morris

University of Wales Cardiff, UK Martin Mossner

University Innsbruck, Austria Maximilian Muller

Technische Universitat Munchen, Germany Masahide Murakami

University of Tsukuba,Japan Werner Nachbauer

University Innsbruck, Austria Daiki Nakajima

Kansai University, Japan Motomu Nakashima

Tokyo Institute of Technology, Japan Takeshi Naruo

Mizuno Corporation, Japan Alan M Nathan

University of Illinois, USA Dirk Niebhur

Technical University Kaiserslautem Gunther Niegl

University ofYienna , Austria Christian Nolte

University of Augsburg, Germany Claudius Nowoisky

Otto von Guericke University Magdeburg, Germany Wubbo Ocke/s

Delft Universityof Technology, Netherlands

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Contributors

Stephan Odenwald Chemnitz University of Technology, Germany Yuji Ohgi Keio University, Japan Shigemichi Ohshima Meijo University, Japan Atsumi Ohtsuki Meijo University, Japan Hiroki Okubo National Defense Academy, Japan Steve R. Otto R&A Rules Limited, UK Riccardo M Pagliarella Royal Melbourne Institute of Technology, Australia Jiirgen Perl University of Mainz , Germany Stephane Perrey Universite de Montpellier, France Christiane Peters Technische Universitat Munchen, Germany Nicola Petrone University of Padova, Italy Neil Pettican Cranfield University, UK Jon Petzing Loughborough University, UK Andrew Phillips University of Bath, UK

Contributors John Plaga

Wright Patterson Air Force Base, USA Christopher J.G. Plummer

Ecole Polytechnique Federale de Lausanne(EPFL), Switzerland Alexander Romanovich Podgaets

Delft University of Technology, Netherlands Jaime Prat

UniversitatPolitecnica de Valencia, Spain Celine Puyaubreau

Decathlon, France Franck Quaine

UniversiteJoseph Fourier Grenoble, France Jose Ramiro

Universitat Politecnica de Valencia, Spain Robin Redfield

United States Air Force Academy, USA Martin Reichel

Universityof Applied Sciences Technikum Wien, Austria Hansueli Rhyner

Swiss Federal Institute for Snow and Avalanche Research Davos, Switzerland Matthieu Richard

PETZL, France Claudio Robazza

University of Padova, Italy Bryan C. Roberts

Loughborough University, UK Jonathan Roberts

Loughborough University, UK

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Contributors

Markus A. Rohde

University ofSiegen, Germany Jouni A. Ronkainen

Loughborough University, UK David Rosa

Universitat Politecnica de Valencia, Spain Steve Rothberg

Loughborough University, UK Maxime Roux

Decathlon, France Daniel Russell

Kettering University, USA Anton Sabo

University of Applied Sciences Technikum Wien, Austria Takahiro Sajima

SRI Sports Limited, Japan Reiko Sakashita

Kumamoto University, Japan Toshiyuki Sakata

Chubu University, Japan Pierre Samozino

Laboratoire de Modelisation des Activites Sportives, France Yu Sato

Chubu University, Japan Nicholas Savage

Royal Melbourne Institute of Technology, Australia Hans Savelberg

Universiteit Maastricht, Netherlands

Contributors Michael Schiestl

University Innsbruck, Austria David Schill

United States Air Force Academy, USA Kurt Schindelwig

University Innsbruck, Austria Erin Schmidt

Loughborough University, UK Heinz-Bodo Schmiedmayer

Vienna University of Technology, Austria Alexander Schneider

Tum Till Bum GmbH, Switzerland Isabelle SchOffl

University of Erlangen-Nuremberg, Germany Volker R. Schoffl

Klinik fiir Orthopadische Chirurgie und Unfallchirurgie Bamberg,Germany Stefan Schonberger

Technische Universitat Munchen, Germany Herwig Schretter

HTM Tyrolia, Austria Andreas Schweizer

Kantonsspital Aarau, Switzerland Carsten Schwi ewagner

Technische Universitat Munchen, Germany Nathan Scott

The University of Western Australia, Australia Brian P. Self

United States Air Force Academy, USA

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xxxviii

Contributors

Terry Senior

Sheffield Hallam University, UK Veit Senner

Technische Universitat Munchen, Germany Kazuya Seo

Yamagata University, Japan Sonali Shah

University of Illinoisat Urbana-Champaign, USA Rebecca H. Shaw

University of Massachusetts Lowell, USA Jasper Shealy

RochesterInstituteof Technology, USA Alison L. Sheets

Universityof California, Davis, USA James A. Sherwood

Universityof Massachusetts Lowell, USA Kyoko Shibata

Kochi University of Technology, Japan Jun Shimizu

Japan Instituteof Sport Sciences,Japan Peter Shipton

Cranfield University, UK

Hitoshi Shiraki

University of Tsukuba,Japan Anton Shumihin

Perm State Technical University, Russia Gerard Sierksma

University of Groningen, Netherlands

Contributors Lloyd Smith Washington State University, USA Peter Spitzenpjeil Technische Universitat Miinchen , Germany Carolyn Steele Loughborough University, UK Darren J. Stejanyshyn University of Calgary, Canada Gunnar Stevens University of Siegen, Germany Victoria H. Stiles University of Exeter, UK Valeriy Stolbov Perm State Technical University, Russia Martin Strangwood University of Birmingham, UK WolfStrecker Klinik fur Orthopadische Chirurgie und Unfallchirurgie Bamberg, Germany Martin Strehler SportKreativWerkstatt GmbH, Germany Claude Stricker AISTS - International Academy of Sports Science and Technology, Switzerland William 1. Stronge University of Cambridge, UK Aleksandar Subic Royal Melbourne Institute of Technology, Australia Maria Jose Such Universitat Politecnica de Valencia, Spain

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xl

Contributors

Cory Sutela

SRAM Corporation, USA Soich iro Suzuki

Kitami Institute of Technology, Japan Masaya Takahashi

Sumitomo Light Metal, Japan Hironuri Takihara

Toyohashi University of Technology, Japan Ming Adin Tan

Nanyang Technological University, Singapore Angelo Tempia

Royal Melbourne Institute of Technology, Australia Eva Tenan

Universityof Padova, Italy Dominique Thevenin

Otto von Guericke University Magdeburg, Germany Mark Timms

Hot Stix Technologies, USA Daniel Toon

Loughborough University, UK Marcus Trapp

Technical University Kaiserslautern Masaya Tsunoda

SRI Sports Limited,Japan Sadayuki Ujihashi

Tokyo Institute of Technology, Japan Sandor Vajna

Otto von Guericke University Magdeburg, Germany

Contributors Rafael Valero

AIJU, Technological Institute of Toys, Spain Sergey Vasilenko

JSC Aviadvigatel - Penn Engine Company, Russia Pedro Vera

Universitat Politecnicade Valencia, Spain . Johan Verbeek

University ofWaikato, New Zealand Nicholas Vernadakis

Democritus University ofThrace, Greece Alex Vickers

Cranfield University, UK Laurant Vigouroux

Universite Joseph Fourier Grenoble, France Jeff Vogwell

University of Bath, UK Jorg F. Wagner

University Stuttgart, Germany Klaus Wagner

Institute for Applied Training Science (lAT) Leipzig, Germany David Walfisch

Massachusetts Institute of Technology, USA Eric S. Wallace University of Ulster, UK Tom Waller

Loughborough University, UK Andy Walshe

United States Ski Association, USA

xli

xlii

Contributors

Simon Watkins Royal Melbourne Institute of Technology, Australia PekChee We Royal Melbourne Institute of Technology, Australia Christian Webef Technical University Kaiserslautern Matthew Weber University of Colorado at Boulder, USA Sheldon Weinbaum The City College of New York , USA Andrew West Loughborough University, UK Cory West Hot Stix Technologies, USA Miles Wheeler University of Colorado at Boulder, USA Josef Wiemeyer Technische Universitat Darmstadt Germany Bart Wijers Terra Sports Technology, Netherlands Paul Willems Univers iteit Maastricht, Netherlands Simon Williams University of Glamorgan, UK Markus A. Wimmer Rush University Medical Center Chicago, USA Erich Wintermantel Technische Universitat Munchen , Germany

Contributors Clive Wishart

Bristol University, UK Kerstin Witte

Otto von Guericke University Magdeburg, Germany Gavin Wood

Cranfield University, UK Ian C. Wright TaylorMade-adidas Golf Company, USA Qianhong Wu

Villanova University, USA Volker Wulf

University of Siegen, Germany Bernd Wunderlich

Otto von Guericke University Magdeburg, Germany Masanori Yabu

SRI Sports Limited,Japan Tetsuo Yamaguchi

SRI Sports Limited,Japan Connie Yang

Loughborough University, UK Keiko Yoneyama

Tokyo Institute of Technology, Japan Takeshi Yoneyama

Kanazawa University,Japan Colin Young

Loughborough University, UK Allen Yuen

University of Calgary, Canada

xliii

xliv

Contributors

Jack Zable University of Colorado at Boulder, USA

Michael F. Ziih Techn ische Universitat Miinchen, Germany Eleni Zetou Democritu s University ofThrace, Greece

Andreas Zimmermann University of Siegen, Germany

Werner Zirngiebl Praxiskl inik fur Orthopadie und Sportmedizin, Miinchen , Germany

1 Baseball

Synopsis of Current Developments: Baseball Alan M. Nathan University of Illinois at Urbana-Champaign, [email protected]

Introduction Five papers specifically dealing with the science or engineering of baseball were submitted to the conference. Four of these papers deal with topics associated with issues related to the ball-bat collision. The fifth paper deals with the aerodynamics of a baseball in flight. All of the submitted papers address issues of practical importance to the game of baseball. What follows is a brief summary of each paper, followed by a synopsis of other activity in the field not reported at this conference .

Synopsis of Submitted Papers The contribution of Smith and Ison investigates the effects of wall rigidity in measurements of the ball coefficient of restitution (COR), one of the important parameters affecting bat performance. The COR is measured by impacting the ball against a flat rigid surface and is equal to the ratio of rebound to incident speed. The paper, "Rigid Wall Effects on Softball Coefficient of Restitution Measurements," investigates the effect of wall compliance on the measured COR by impacting softballs against thin clamped plates of known thickness. The COR was generally found to increase with decreasing plate thickness, in agreement with FEA simulations also reported in the paper and with expectations based on a simple model of the trampoline effect. These results will be useful in setting specifications for the compliance of surfaces used for COR measurements. Also reported in the paper is a potentially novel technique for measuring the drag coefficient on a baseball in flight. In the paper "Experimental Investigations of the Relationship of Baseball Bat Properties on Batted-Ball Performance," Shaw and Sherwood investigate the effects of barrel compression and bat moment of inertia (MOl) on bat performance, using bats specifically designed to isolate one of these two properties. The experiment involves static measurements of the barrel compression, modal analysis to determine the frequency of the lowest hoop modes, and high-speed ball-bat collisions to measure the collision efficiency eA- They find that for the bats selected, the MOl contributed more to eA than did the barrel compression . However, using a particular

4

Alan M. Nathan

swing speed formula, it was found that both properties contributed similarly to field performance. Russell 's contribution, "Bending Modes, Damping, and the Sensation of Sting in Baseball Bats," uses modal analysis to determine the frequency and damping rates of the lowest two bending modes in youth baseball bats . He provides evidence that damping reduces the sting felt in the top hand of the batter when the contact occurs off the sweet spot and shows that a novel dynamic absorber tuned to damp the second bending mode greatly reduces the sting . He concludes that the sting is mainly due to the vibrations of the second bending modes, an important practical finding. Drane , et al. in "An Experimental Investigation of Baseball Bat Durability" describe a new impact machine for use in the study of bat durability. The machine uses an air cannon to fire baseballs at high speed and high repetition rate at a bat which is suspended vertically from a support system. Accelerometer and strain gage data are used to investigate various methods for gripping the bat in the machine in order to find the one that best replicates the gripping method used by players. The machine is demonstrated to replicate the type s of bat failure s that is experienced in field use as well as the gripping method used by players. In the contribution "The Effect of Spin on the Flight of a Baseball," Nathan, et al. report the results of new measurements of the lift on a spinning baseball in the range of speeds and spins relevant for the game of baseball. The experimental technique involves the use of high-speed motion capture cameras to track the trajectory of the baseball and measure the spin . The lift coefficients determined from the data help resolve a discrepancy in the literature between two different parametrizations.

Synopsis of Related Activities The relatively small number of baseball-related papers submitted to this conference is not an accurate measure of the activity in the field . A variety of new investigations are in progress but not yet at the stage where they can be reported at ISEA2006. These include the following studies: the effect of ball COR, dynamic stiffness, and compression on bat performance with the goal of normalizing bat performance to these properties of the ball ; oblique ball-bat collisions to learn about the ability of a batter to put backspin on a batted ball; indirect metrics for baseball bat performance and their correlation with direct measures of performance; the effect of different grip methods on baseball bat performance; the visual characteristics observed by a batter that are related to the spin axis of a pitched baseball; measurements of the effect of backspin on the distance and optimum takeoff angle of a long fly ball; and refinement of FEA models of hollow bats to include plasticity, with the goal of predicting denting. With such a large level of research activity, we can expect great things at the ISEA2008 conference.

An Experimental Investigation of Baseball Bat Durability Patrick J. Drane, James A. Sherwood and Rebecca H. Shaw Univers ity of Massachusetts Lowell, [email protected]

Abstract. The service life of a baseball bat is a function of its durability. All wood bats crack, and ash bats exhibit flaking of the barrel due to repeated impacts. In aluminum and composite bats, repeated impacts can cause a change in the material properties, which in tum can lead to dents and microcracks that ultimately coalesce to form macrocracks. A test machine for simulating essentially any field condition for batlball impacts has been developed to study bat durability. The system uses an air cannon capable of firing a baseball at speeds up to 180 mph at a stationary bat which is supported in a grip that replicates a player's hands. This paper will describe the system, present some supporting analysis of the gripping method, and present results of tests from wood and aluminum bats.

1 Introduction Baseball bat durability is a topic of importance to baseball players, teams and governing bodies and bat manufacturers. Players want a bat that is durable with respect to reliable batted-ball performance, teams want durability with respect to controlling operating expenses , manufacturers are interested in minimizing warranty claims, and everyone is concerned about durability with respect to injuries . What bat properties are important with respect to durability is one question that engineers, players and fans of the game try to answer. For wood bats, the important properties may be straightness of the grain, growth -ring density, mass density, color, moisture content, drying method, or the particular forest that makes wood good for baseball bats. For aluminum bats, the important properties may be the alloy, heat treatment, forming process, and wall thickness variation. For composite bats, the important properties may be the material choices for the resin and the fiber reinforcement , orientations of the respective layers, and wall thickness variation For any bat, the durability probably depends on a combination of many of these factors and, in addition , the bat profile . Durability testing can be accomplished using players for field testing or battingcage studies or using a laboratory hitting machine . Field testing can take a long time and can be very subjective. Batting-cage studies can be less time consuming, but require a rotating supply of fresh hitters for every five hits. Of the currently available bat-performance testing machines, none is practical for doing durability testing as it can take a long time to obtain the required number of impacts , and the gripping

6

Patrick1. Drane, James A. Sherwood and RebeccaH. Shaw

Fig. 1. DurabilityTest System

method may not exert forces and constraints on the bat similar to those experienced in field use. The testing system described in this paper and operational at the UMass-Lowell Baseball Research Center is capable of gripping the bat similar to that of a player, getting a number of hits along the profile of the bat in a timely manner, and providing data for quantitatively comparing the durability of baseball bats.

2 Testing System The testing system used for performing the durability testing was developed by Automated Design Corporation in Romeoville, Illinois in collaboration with the Baseball Research Center. The system, shown in Fig. 1, operates with an automatic loading air cannon that fires baseballs into the test chamber. The cannon is capable of firing baseballs at speeds up to 180 mph. After the ball is fired, it is fed back into the magazine by an elevator on the back of the chamber. The bat hangs vertically inside the chamber and is able to pivot about an axis at the handle of the bat when impacted. The automated air cannon for firing baseballs allows for getting repeatable impacts on a bat and for completing durability testing in a relatively short time. Using the computer software, a range of hit locations and impact speeds can be prescribed to run without operator intervention . The time between hits can be as short as 5 seconds, thereby allowing for even the most durable bat to be tested to failure within a few hours. The bat is mounted in the chamber in such a way that the ball is fired at the desired location on the bat, and the bat then rotates vertically from the impact. The bat can be moved up or down between each hit to impact different locations along the bat. The bat can also be rotated, referred to as clocking the bat, so that different locations around the barrel can be impacted. Both clocking and moving the bat up or down to different locations will lengthen the process, but are often well worth the extra time. Clocking is a critical component of testing composite and aluminum bats as they are impacted on different sides in field use and the bat surfaces, especially with aluminum, can be prone to denting. For the testing of wood bats, the bat is not rotated, because in field use the bat should always be impacted parallel to the grain direction . The grip fixtures for mounting the bat into the machine are shown in Fig. 2 (canister grip typically for aluminum and composite bats and roller grip typically for wood bats).

An Experimental Investigation of Baseball Bat Durability

7

Fig. 2. CanisterGrip (left)and RollerGrip (right)

Free-Free Hand-Held Loose Hand-Held Tight Roller-Grip Tight Roller-Grip Loose Canister Grip

3 Evaluation of the Gripping Method One concern when investigating baseball bats in a simulated hitting scenario is ensuring that the test replicates the field use of the baseball bat (Shaw and Sherwood 2006) . For baseball bat durability testing, the impact speed and the method of gripping the handle need to be realistic . The air cannon can easily duplicate the batlball relative impact speed. To investigate how well the gripping methods in the durability machine replicate a player's hands, several studies using strain-gages, accelerometers, and different gripping strengths were preformed in the durability test system and with players. These studies quantified how well the machine grip actually replicates that of a player. Two accelerometers placed along the length of a bat were used to determine the first two bending natural frequencies . Experimental data were collected using five different grip configurations for both fixtures shown in Fig. 2, a player's hands, and free-free. The results are shown in Table 1. All of the accelerometer data for this modal investigation were taken with the bat held stationary (i.e., not swinging). The roller-grip-tight method shows a significant increase in the first natural frequency when compared to the free-free and hand-held conditions. The roller-griploose method (bottom roller loosely touching bat handle) and the canister-grip method both have natural frequencies only slightly higher than the person-held grips for the first bending mode. The results for the second bending mode show slightly more separation between the person-held bat and the machine-gripped bats. Just as with the first bending mode, the roller grip more closely represents a player's hands when the bottom set of rollers is left loose. The canister grip raises the natural fre-

8

Patrick J. Drane,James A. Sherwood and Rebecca H. Shaw

quency of the second bending mode by about the same amount as the roller-grip tight. The roller-grip-tight method and the canister-grip method both constrain the deflection of the bat at two points on the handle, thus changing the effective length of the bat and thereby changing the second bending mode . The roller-grip-loose method allows some deflection within the lower pair of rollers, much like a player's hands would. From these modal data, the roller-grip-loose method and the canistergrip method are concluded to be good representations in the lab of a player-held bat in the field. Strain gage data were collected for several hits from three college players using the same bat, and the respective impact locations were marked after each hit. The same bat was then loaded into the durability machine, and the bat was impacted at the same locations as the field hits using each of the three gripping methods. The impact speeds were varied to match the amplitudes of the peak strain and the shapes of the response with those observed in the field-test data. Estimates for pitch speeds and player swing speeds were used for comparison. Fig. 3 shows the strain-gage response for one of the gages to a hit off live pitching for one of the college players. The strain response is also shown for a similar impact in each of the three gripping methods used in the durability machine. In the strain response from the live hit, there are clearly two modes present right after impact, and then the second mode damps out leaving only the first bending mode in the response . A similar response is seen in each of the grips in the durability machine. However, there is less overall damping present in the durability-machine responses-implying a player's hands absorb more of the vibration than the rubber rollers used in the machine grips . The peak strain seen in a field hit where the impact occurred about 9 in. from the end of the barrel was matched in each of the three machine grips with impacts of - 100 mph . The strain results for each of these hits are shown in Fig. 3. The shape of the strain response is matched closely for all of the grips, but is best matched by the canister grip for the aluminum bat used in this study . The accelerometer and strain gage data support the conclusion that the machine can be a good simulation of field-service conditions for durability testing in a lab environment. Of the three grips tested, the roller-grip-loose method and the canistergrip method are good representations of a player's hands . Based on experience, the roller-grip-loose method is less time-consuming to load a bat than is the canister-grip method . When testing wood bats, which can crack in the handle region and after only a few hits, the roller-grip-loose method is the preferred gripping method in comparison to the canister grip, because a bat can be loaded and unloaded relatively quickly and a crack in the handl e can be easily observed. When testing aluminum or composite bats, which tend to fail in the barrel region of the bat, the canister grip is the preferred gripping method as it allows the bat to be rotated between impacts as the bat would be in the field .

An Experimental Investigation of Baseball Bat Durability

'I

I ;.

• II,

n

9

1111

Iii'

~

Fig. 3. Straingage measurements for four different grips duringimpacts

4 Durability Testing Methodologies The baseball bat durability testing requires a protocol to ensure that the collected data are comparable and sufficiently comprehensive for making conclusions with respect to absolute and relative durability of the tested bats. An example routine that would be programmed for testing an aluminum or compos ite baseball bat may include impacting different locations along the length of the bat as well as different locations around the barrel and varying the speed of the impact. The motors in the durability machine can be controlled so that the testing could begin , for example , with several impact s at the 6-in. location (measured from the end of the barrel) , then several impacts at the 4-in. location and then move to impact the bat several times at the 8-in. location . The clocking device is often programmed to rotate the bat 1/4-, 1/4-, 1/4-, and 3/8-tum after each impact allowing eight consecutive hits to impact the bat on eight evenly spaced locations around the barrel. These rotations are typically an important part of not unfairly causing premature denting of the surface . Another aspect of the programming will adjust the firing velocity , by adjusting the cannon pressure . The speed of impact, for example , can be adjusted to account for the change in velocity of the swing speed of a bat as the impact location is adjusted along the length of the bat. These example routine components allow for considerable flexibility when testing baseball bats, and depending on the routine , different results will be atta ined.

10

Patrick 1. Drane, James A. Sherwood and Rebecca H. Shaw

Fig. 4. Wood bat broken in the durability machine with high-speed camera view

Fig. 5. Wood bats broken in two pieces

Fig. 6. Aluminum samples cracked and dented

5 Results Baseball bats break many different ways as a result of field use, and Figs. 4, 5 and 6 show that similarly diverse results can be obtained from testing in the durability testing system.

6 Conclusions The durability testing system described in this paper and operational at the Baseball Research Center is capable of replicating the types of failures that baseball bats experience during field use. The gripping methods used in the machine replicate a player's grip.

References Shaw, R. H. and Sherwood, 1. A. (2006) Exploring the Crack of the Bat in the Lab : Performance and Durability", IMAC XXIV Conference Proceedings.

Bending Modes, Damping, and the Sensation of Sting in Baseball Bats Daniel A. Russell Science and Mathematics Department, Kettering University, Flint, MI drussell @kettering.edu

Abstract. The painful sensation of sting in the top hand of a player holding a baseball or softball bat may be a deterrent to enjoying the game , especially for young players. Several mechanisms for reducing the vibration of bending modes have been implemented in youth baseball bats in order to reduce sting. One method of assessing the effectiveness of these mechani sms is to compare the damping rate they provide for the first two or three bending modes in a bat. Damping rates are compared for several wood, aluminum, composite, and two-piece construction baseball bats, in addition to several bats with special damping control mech anisms . Experimental evidence suggests that damping mechanism s which reduce the vibration of the second bending mode are preferred by players. A novel dynamic absorber in the knob is shown to effe ctively reduce the vibration of the second bending mode and minimize the painful sting felt in the top hand .

1 The Problem of Hand Sting The problem of sting is often a deterrent to young players who are learning how to swing a baseball bat. When they do make contact with a pitched ball, young players often hit the ball in the taper region or at the very end of the barrel. The painful sting result ing from such poor impacts can be very frustrating, and can discourage young players from continuing on in the sport. The problem of sting is not limited to young players, however, and accomplished adult players will still occa sionally hit the ball badly resulting in painful sting in the hands . Discussions with players reveal that impacts near the taper region in the bat often result in a sharp pain in the fleshy region between the thumb and forefinger of the top hand. This pain is significant enough to sometimes cause bruising, and can persist for several days afterwards. Aluminum bats tend to sting more than wood bats, and while the development of specially designed padded batting gloves and special thick rubber grips on the handles of aluminum bats has improved the sensation of feel somewhat, the problem of sting still remains. Several means of reducing vibration have been implemented. Because the problem of hand sting is more pronounced at the youth level, many of vibration reduction mechanisms only appear in youth baseball bat models . These include inserting a dynamic absorber (tuned-mass-damper) in the taper region of the barrel , inserting an elastomer plug into the knob in the handle , a two-piece construction in which the

12

Russell

First BendingMode Q)

"0

~ 0..

---- .. -

E

ex:

"0

.~

iii

E o

z

o

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 32 Distance from Barrel End (inches)

Fig. 1. Mode shapes for the first two bending vibrational modes in a 32-inch youth baseball bat. Barrel end is at the left and handle is at the right.

handle and barrel are separate pieces connected by a rubber joint, and the injection of foam into the hollow handle.

2 Bending Modes and Hand Location All baseball and softball bats exhibit a family of bending vibrations , similar to what one would find in a free-free beam, with nodes (locations of zero displacement) on the barrel and handle and antinodes (locations of maximum displacement) between nodes. Most of the research published on the issue of sting has focused either on the impact location relative to the nodes of the first two bending modes of vibration (Noble and Walker 1994; Cross 2001) or on the frequencies of the lowest two bending modes (Noble, Walker and Ponte 1996). Figure 1 shows the mode shapes for the first two bending modes for a typical 32inch youth baseball bat. The mode shapes were obtained by performing an experimental modal analysis measurement. Two features of this graph are relevant to the discussion of sting. First is the location of the nodes at the barrel end of the bat. The first bending mode has a node approximately 7-inches from the end of the barrel, and the second bending mode has a node approximately 5-inches from the barrel end. An impact at a node will prevent the corresponding mode shape from contributing to the resulting vibration of the bat. The region between 5-7 inches from the barrel end is often referred to as the "sweet zone" due to the fact that impacts within this region result in minimal vibration in the handle (Cross 1999; Cross 2001). Of greater importance to the perception of sting is the location of the nodes and anti-nodes at the handle end of the bat. The bottom hand is centered on a node for the second bending mode and the fleshy part at the base of the bottom hand is at an antinode for the first bending mode. This would suggest that, if sting is the result of bending vibrations, the bottom hand should be more responsive to the first bending mode but not affected much by the vibration of the second bending mode. The top hand, meanwhile , is centered on a node for the first bending mode and the region between the thumb and forefinger of the top hand is located at an antinode for the second bending mode. This would suggest that the top hand is most responsive to

Bending Modes, Damping, and the Sensation of Sting in Baseball Bats

13

vibration of the second bending mode, and less to the vibration of the first bending mode. Cross argued that the sting is the result of the impulse from the bat-ball collision traveling to the player's hands rather than the result of the bat vibrating in its various free modes of vibration (Cross 1998). However, he does point out that the impulse is indistinguishable from the vibration of the second bending mode.

3 Damping Rates for Bending Modes It has been shown (Brody 1986) that the natural frequencies of a baseball bat are not

significantly altered when the bat is gripped in the hands, thus allowing the handheld bat to be modeled as a free-free bat (Nathan 2000). The hands do, however, add a huge amount of damping so that the natural vibrations of the bat decay very quickly. What is not known, however, is exactly how much damping the hands provide nor how much damping is inherently present in the bat itself. There are very little published data showing measured damping rates for the bending modes of baseball bats. The data that do exist suggest that damping rates for aluminum bats are roughly half those of wood bats (Collier 1992; Naruo and Sato 1998). There are no data available for composite bats, nor for youth bats with vibration reduction mechanisms. One of the aims of this paper is to provide some damping rate data. The damping rate for a particular mode of vibration is one of the modal parameters (mode shapes, frequencies, and damping) that may be determined by curve fitting the frequency response functions (FRF) collected in a modal analysis experiment (Gade, Herlufsen and Konstantin-Hansen 2002). The analytical function used to perform the curve fitting assumes that the structure may be modeled as a 2nd order time invariantsystem with an impulse response function of the form

L [R~.~)le-ak l sin(2Jifkt + ¢~.~»)] , 11

hrs(t) =

(I)

k=l

where hrlt) is the impulse response at location r due to an excitation at location s, and Rn(k) is the residue (mode shape) at location r due to excitation at location s for mode k. Equation (I) indicates that the vibration resulting from an impulse is the superposition of sinusoidal oscillations, each at their own natural frequency j, and exponential damping rate (Jk. The quantity of interest in the present analysis is the modal damping rate c, for the first two bending modes. Most experimental modal analysis software packages report the modal damping in terms of a non-dimensional critical damping ratio ~k' usually expressed as a percentage. The critical damping ratio is related to the modal frequency and modal damping coefficient by (Formenti 1999)

c; -

(7k

k - ~(71 + (2Jifk)2

.

(2)

In our laboratory we extract the damping rate by suspending a baseball bat vertically from the knob using rubber bands. An accelerometer is attached to the knob, and the bat is impacted with a force hammer at the barrel end. The Frequency Response Function consisting of the ratio of acceleration/force is obtained using a two-channel

14

Russell

FFT analyzer and curve fitted to extract the critical damping ratio Sk. The damping rate (h is determined from Eq.(2). Damp ing rates for the first two bending mode s of a sampl ing of youth baseball bats of varying construction are shown in Tab le I. The data show that aluminum bats have very little inherent damping. Wood and composite bats have similar damping rates , both having damp ing rates that are approximately an order of magnitude greater than aluminum bats. The aluminum bats marked with ,*, include a vibration reduction mechanism which significantly increases the damping of either the first and/or the second bending mode . Table I. Damping rates for wood, aluminum and compo site youth baseball bats. marked with' *, include a vibration reduction mechanism. First Bending Mode Damping Frequency Damping Rate f(H z) Ratio I; o (s- I)

Bat Type wood - ash wood - ash wood - maple Aluminum Aluminum Aluminum Alum inum Alum inum Aluminum Composite Composite Composite

* * *

187 212 175 229 190 201

3.368e-3 3.9 I6e-3 6.7 13e-3 4.654e-4 8A 28e-4

163 2 11 197 168 105

1.326e-3 1.112e-2 1.757e-2 6A 3ge-2 3.966e-3 6A33e-3

3.96 5.22 7.38 0.67 1.01 1.67 11.39 23.30 79.87 4.19 4.24

137

6.038e-3

5.20

Bats

Second Bending Mode Damp ing Frequency Damping Rate f(H z) Ratio ]; o (s-') 5.00ge-3 691 21.7 1.20ge-3 663 50A 4.278e-3 15.6 580 763 7.844e-4 3.8 1.01ge-3 4A 690 8.224e-4 780 4.0 559 752 697 6 15 405

2.092e-2 2.2 13e-3 2.30ge-3 3.593e-3 5.702e-3

73.5 10.5 10.1 13.9 14.5

529

6.837c-3

22.7

4 Evidence that Damping Reduces Sting A prelimi nary correlatio n between dampi ng and the perception of sting came from an opportunity to test three youth baseball bats for a manufacturer. Bat A was brand new (still in plastic wrapper) and served as a control while bats Band C had been modified in an attempt to reduce sting, and had eac h been hit by 70 players . The source providing the bats informed us that every sing le player preferred the same bat because it felt better, but we were not told which bat was preferred. We were asked to try to identify the preferred bat and explain why . Modal testing revealed that all three bats had nearly identical bending and hoop frequen cies. The only difference between the bats was in the amount of damping for the first and second bend ing modes . Thi s was immediately apparent by gripp ing the bat barrel light ly at the "sweet spot" and tapp ing the barrel. The vibrat ion from bat C died out immed iately while bat B and the control bat A rang for several seconds. Measured damping rates , shown in Table 2, show that the preferred bat (bat C) had rough ly 6-8

Bending Modes, Damping, and the Sensationof Sting in Baseball Bats

15

times more damping for the first bending mode , and 20-30 times greater damping for the second bending mode . Table 2. Damping rates for three identical youth baseball bats, with bat C being preferred unanimously by 70 different players.

Bat

First Bending Mode Damping Frequency f(Hz) Rate (J (5- 1) 173 172 167

A B C

0.58 0.74 4.82

Second BendingMode Damping Frequency f(H z) Rate (J (s-') 643 2.8 641 3.6 623 82.4

A second correlation between sting and the damping rate of the second bending mode is currently being investigated with the implementation of a novel dynamic absorber (Albin 2004) into the knob of aluminum baseball and softball bats . This vibration absorber may be tuned to reduce the vibration at a specific frequency by adjusting the mass of the plug and/or the stiffness of the rubber support. The knob with the absorber is larger than a normal bat handle knob, and the combined mass of the knob and absorber lowers the frequenc ies of the first two bending modes . Table 3 lists the damping rates for a 32-inch (81.3cm) youth senior league baseball bat without the damper and with the damper tuned to the first and second bending modes . When the vibration absorber is tuned to the frequency of either bending mode, the amount of damping for that mode is huge, while the damping rate for the other mode is not significantly altered. Table 3. Damping rates for a baseball bat with and without a dynamic absorber in the knob that has been tuned to the first and second bending mode.

Bat No damper With damper I With damper 2

First BendingMode Damping Rate (J (s-I) f(Hz) 162 1.75 146 124.6 142 1.52

Frequency

Second Bending Mode Damping Rate (J (S-I) f(Hz) 582 3.3 547 8.5 573 182.0

Frequency

Preliminary field tests, using bats with this absorber in the knob , indicate that the painful sting in the top hand resulting from an impact near the taper region of the bat can be greatly reduced by tuning the absorber to the second bending mode of vibration . In an attempt to further quantify the relative importance of the damping for the first and second bending modes, we have instrumented a bat, with the tunable absorber in the knob, with strain gauges on the handle in order to measure the force under the hands during and following an impact with a ball. Adjusting the tuning of the absorber allows variation of the damping rates of the first and second bending modes, to compare how either or both influence the perception of feel. This further study was still in progress at the time this paper was submitted. As a final demonstration of how increased damping might improve the feel of a bat, Fig. 2 shows the frequency response curve of the vibration amplitude at the location of the top hand for the baseball bat in Table 3. The dashed curve is for the

16

Russell 60 - - - Normal Bat With Damper in Knob

55 50

CD ~ Ql

'"c0 a. '" a:

"

35

" ,," ,, , , ,, , , ,, ,

.. ...

32dB

25 20

>0

15

Ql ::J

\

" " "

30

Ql

c:

,,

45 40

10

0-

~

U.

0 -5 · 10 -15

-20 0

100

200

300

400

500

600

700

800

900 1000 1100 1200 1300 1400 1500 1600

Frequency (Hz)

Fig. 2. Frequency response function for a baseball bat with a tuned-mass damper in the knob. Tuning the damper to the frequency of the second bending mode effectively removes that mode from the resulting vibration of the bat.

bat without the absorber, and the solid curve is for the bat with the damper inserted and tuned to the second bending mode. The dynamic absorber reduces the vibration amplitude of the second bending mode by approximately 32 dB, effectively removing this mode from the vibration of the bat following an impact with a ball away from the sweet spot.

References

u.s.

Albin,1. N. (2004) Patent No.6.709.352. Washington, DC: U.S. Patent and Trademark Office. Collier, R. D. (1992) Material and structural dynamic properties of wood and wood composite professional baseball bats. Proceedings Z" Int. Congress on Recent Developm ents in Air and Structure Borne Sound and Vibration, Auburn University, Auburn, AL, pp. 197-204 . Cross, R. (1998) The sweet spot of a baseball bat. Am. 1. Phys . 66(9), 772-779 _ Cross, R. (200 I) Response to "Comment on 'The sweet spot of a baseball bat. " Am . 1. Phys . 69(2), 231-232 . Gade, S., Herlufsen H. and Konstantin-Hansen, H. (2002) How to Determine the Modal Parameters of Simple Structures. Sound & Vib . 36( I), 72-73 . Formenti, D. (1999) The Relationship Between % of Critical and Actual Damping in a Structure. Sound & Vib. 33(4) ,14-18. Nathan, A. (2000) Dynamics of the baseball-bat collision. Am. 1. Phys. 68(11), 979-990. Naruo, T. and Sato F. (1998) An experimental study of baseball bat performance. In: Haake, S. (Ed .), Engineering a/Sport - Design and Development. Blackwell Pub., pp.46-52. Noble, L. and Walker, H. (1994) Baseball Bat Inertial and Vibrational Characteristics and Discomfort Following Ball-Bat Impacts. 1. Appl. Biomechanics. 10. 132-144 . Noble, L., Walker, H. and Ponte, M. (1996) The effect of softball bat vibration frequency on annoyance ratings . Proceedings of the 14th International Symposium on Biomechanics in Sport, Funchal, Portugal. 371-374.

Experimental Investigations of the Relationship of Baseball Bat Properties on Batted-Ball Performance Rebecca H. Shaw and James A. Sherwood University of Massachusetts Lowell, becky@baseballrc .eng.uml.edu

Abstract. Laboratory tests are used to investigate the relationship between baseball bat performance and two bat properties: moment of inertia (MOl) and barrel stiffness for aluminum and composite bats. Each bat used in the current study is specifically designed and manufactured to isolate a particular property. Static tests, e.g. three-point bend and barrel compression, are used to characterize the properties of each bat. The natural frequencies of the bat are measured using modal techniques. Dynamic performance testing is done using an air cannon capable of throwing a baseball at collision speeds equal to those seen in field play. For the bats studied, variation in MOl contributed more to performance in the lab than did barrel stiffness. However, the changes in predicted field performance due to the two properties were similar.

1 Introduction The Ball Exit Speed Ratio (BESR) is the metric currently used to quantify the performance of nonwood baseball bats. This research examines two bat properties, barrel stiffness and mass moment of inertia (MOJ), and their relationship to performance. For this paper, performance is the speed of the ball as it leaves the batball collision as measured in the lab and predicted in the field. Static nondestructive tests are used to measure the barrel stiffness and handle stiffness of each bat before performance testing. Modal tests are used to determine the first two bending natural frequencies and the first hoop frequency. Each bat was manufactured to isolate a singe property as closely as possible, e.g. all properties equal except for MOl. Laboratory tests are used to determine the performance of each bat, and the results are compared to predictions using the BESR. All testing is done using an air cannon following the NCAA (2005) baseball bat certification protocol.

2 Background One metric used to measure baseball bat performance is the BESR (Carroll 2000), V BESR = .2..+0.5 (I) VI

18 Rebecca H. Shawand James A. Sherwood . 1changes In . MOl . 1ab and fireIdbatted-baII speeds due to changes In T a hIe 1. Theoretica MOl Class

MOl (ozin2)

BESR

Lab BBS (mph)

Low Med High

9000 11000 13000

0.701 0.750 0.786

93.4 100.0 104.9

Relative Lab BBS Diff. (mph) -6.6 0 +4.9

Relative Change in Swing Speed (mph) 3.5 0.0 -3.4

Field BBS (mph) 97.6 100.0 100.6

Relative Field BBS Diff. (mph) -2.4 0.0 0.6

where V I is the ball inbound speed and V R is the ball rebound speed for a collision with a stationary bat. The BESR equation can also be written as, BESR = 1+ 2e -

.

.u *

2(1 + .u*)

(2)

where e is the bat-ball coefficien t of restitution (COR) and, 2

.u* = -mbx

(3) I where I is the mass moment of inertia (MOl) measured about the axis of rotation (6 inches from the knob end of the bat), mb is the mass of the ball and x is the distance from the axis of rotation to the impact location. Using Eqs. I, 2 and 3, the variation in BESR due to MOl can be calculated assuming the bat-ball CO R (coefficient of restitution) remain s constant. If it is assumed that a medium MOl bat has a BESR of 0.750, then high and low MOl bats will have BESR values as shown in Table I. These calculations are all done assuming impact at the 6-in. location (as measured from the tip of the barrel). The differences in performance as quantified by the batted-ball speed (BBS) can be found using, BBS = v(BESR-0.5) + V (BESR + 0.5) (4) where v is the ball pitch speed (mph) and V is the bat swing speed (mph). For these calculations, a 70-mph pitch speed and a 66-mph swing speed are assumed . For bats in this MOl range, the high MOl bats are expected to hit - 5 mph faster than the medium MOl bats and - 11.5 mph faster than the low MOl bats in the lab. These calculations do not account for changes in player swing speed due to MOl. Swing speed is known to be inversely proportional to MOl. Therefore, using one swing speed for all bats in the lab is not a true representation of field performance. A atting cage study by Crisco and Greenwa ld (1999) analyzed the swing speeds of .layers for different bats. The data from this study were analyzed by Nathan (200 1, 003), and the relationship between bat swing speed and MOl was found to be .2 x 10.3 mph/oz-irr', where swing speed is measured 6 inches from the end of the arrel and MOl is measured about the knob. The results for batted-ball speed adjusted for swing speed are presented in the last three columns of Tab le 1. Adjusting for change in player swing speed brings the predicted field performance (Field BBS) of the three bats much closer together than the Lab BBS values.

Investigations of the Relationship of BasebalI Bat Propertieson Batted-Ball Performance 1112 100

I

m

98 SI6

94 92 8tXlJ

Fig. I.

19

-:> ;'

/'

/

""

----~

- --

e -o.9D

- - - 1=0.52'1

10:00

l200J

MOl (oo:·itt)

14(1))

16300

Batted-ball speed vs. MOl adjusting for changes in swing speed

Eq. 2 can be combined with the swing speed model to determine the "ideal" MOl for maximum batted-ball speed at a particular impact location. The results are shown in Fig . 1. For these calculations, it is assumed that the MOl about the knob varies linearly with MOl about the axis of rotation. It is also assumed that the average college player swings a medium MOl bat with a speed of 66 mph. These calculations do not consider movement of the sweet spot due to changes in MOl. This sweet spot vs. MOl relationship will be discussed later in this paper. Figure 1 shows two different curves for BBS vs. MOl, one assuming e=0.529 and one assuming e=0.500. Both curves reach a peak at ~12600 oz-in' indicating that the ideal MOl is not dependant on e. This peak represents the ideal MOl for maximum batted-ball speed for impacts at the 6-in . location. An empirical model relating hoop frequency to softball bat performance was developed by Russell (2004). The maximum efficiency was shown to be at a hoop frequency of just less than 1000 Hz. Because the bat-ball collision time is approximately 0.001 s, a frequency of 1000 Hz would correspond to the barrel moving in and out in harmony with the ball contacting the bat, thus minimizing the collision energy lost to ball deformation. It is assumed that the relationship between baseball bat performance and hoop frequency would be similar to that of the softball bat model. However, the maximum performance would occur at a slightly different hoop frequency due to differences in the collision time between softball and baseball.

3 Results 3.1 Barrel Stiffness Three bats were manufactured to have all properties equal except for the barrel stiffness. Barrel stiffness was measured two ways , with a barrel compression test at 5 in. from the end of the barrel and with a hoop frequency measurement. The hoop frequencies for the bats used in this study range from 2360 to 3950 Hz. Based on Russell's observations, a dramatic change in performance due to hoop frequency is not expected for these bats. However, the batted-ball performance should increase slightly as hoop frequency decreases. For a dramatic change due to hoop frequency, it is expected the bats would need to be in the range of 1000 to 2000 Hz. The results

20 Rebecca H. Shaw and James A. Sherwood T a hIe 2. BarreI str'ffiness an.d pe rfiorrnance resuIts f!or tree h b at s of di1ffierent stiffinesses

Barrel Stiffness Class

MOl (oz-irr')

Barrel Compression 5-in. Avg. (lbs)

Low Med High

10106 10007 10923

723 873 1239

Hoop Freq . (Hz)

Sweet Spot Locat ion (in.)

2360 2670 3950

4.5 4.0 5.0

Lab BBS at the sweet spot (mph) 98.2 96 .6 96.5

e at the sweet spot location 0.528 0.513 0.490

, MOl nusted f!or diff 1 erences In T ahIe 3 . BarreI stiiffness per orrnance resuIts adi

Hoop Freq . (Hz) 2360 2670 3950

MOl (oz-irr')

Sweet Spot Location (in.)

e at the swee t spot location

10000 10000 10000

4.5 4.0 5.0

0.528 0.513 0.490

Predicted Field BBS at the sweet spot (mph) 97.8 96.5 93.2

BBS Diff (mph) 1.3 0.0 -3.3

for these tests along with the experimental performance results are shown in Table 2. All bats were tested per the 2005 NCAA Bat Certifi cation Protocol. The performance results follow the expected trend-as stiffness decreases JiBS increa ses. The stiffness measurements show the low- and medium-stiffness bats to be much closer in stiffnes s than the medium- and high-stiffness bats. It would therefore be expected that the low- and medium-stiffness bats would have similar performance results, and the high-stiffness bat would have a much lower perform ance. However, the performance test results show the high- and mediumstiffness bat s to be very similar. The reason for the differen ce in performance from the expected performance is the MOl difference between the bats. The low- and medium-stiffness bats only differ in MOl by about 100 oz-irr', but the high-stiffness bats are about 900 oz-irr' higher than the medium-stiffness bats . The increase in MOl would cause an increas e in performance. Thus , the high -stiffness bats are higher performing than they would be if they had the same MOl as the other bats. Using Eqs. 2 and 3, the e value in the BESR term can be backcalculated. The e term represents the "bat-ball COR", or the performance due to all factors other than MOl. It is expected that the values for e at the sweet spot location will increa se as the stiffne ss decreases. These results are shown in Table 2. Look ing at the results using e shows a larger difference between the medium and high stiffness bats-as was expected. In addition, the BBS values can be adjusted for MOl using Eqs. 2 through 4. Table 3 shows field-use BBS values for each bat adjusted to an MOl of 100000z-in 2• As was expected, the low- and medium-stiffness bats have similar performance values, and the high-stiffness bat is relat ively low perform ing.

Investigations of the Relationship of Baseball Bat Properties on Batted-Ball Performance

21

Table 4. Performance results for bats with different MOl values MOl

(oz-irr') 9218 9259 10912 11199 12810 12722

Hoop Frequency (Hz) 2470 2500 2530 2560 2920 2910

Barrel Compression 5-in. Avg. (lbs) 821 843 808 762 827 800

Sweet Spot Location 5.0 5.0 4.5 4.5 4.0 4.0

Lab BBS at the sweet spot (mph) 91.9 92.8 100.9 100.7 105.7 104.6

e at the sweet spot 0.503 0.510 0.528 0.518 0.519 0.511

T a ble 5. Battc db ' for the tree h bat rno deIs WIt. h diff I erent MOl va ues - aII speed caIcuIauons MOl

Class Low Med. High

Avg. MOl

(oz-irr') 9239 11056 12766

Sweet Spot Location (in.) 5.0 4.5 4.0

Avg. Lab BBS

(mph) 92.3 100.8 105.1

Relative Lab BBS Diff. (mph) -8.5 0.0 4.3

Predicted Field BBS (mph) 96.1 100.6 101.0

Predicted Field BBS Diff. (mph) -4.5 0.0 0.4

3.2 Moment of Inertia Six bats were manufactured with three different values for MOl, classified as low (handle-loaded), medium (balanced), and high (end-loaded). The MOl values and performance results are shown in Table 4. The range of barrel compression values seen here is small compared to the range considered in Section 3.1 . The performance results in Table 4 show a clear increase in performance with an increase in MOl. The BESR equation (Eq. 2) can be used to separate the MOl term from the "bat-ball COR" term, e, as discussed previously. If each of these bats had identical properties except for MOl, then each would have the same value for e. The values for e at the sweet spot locations are presented in the last column of Table 4. The values for e range from 0.503 to 0.528, and there does not appear to be any correlation between MOl and e- indicating that the differences in e are due to properties other than MOl. The variation in e seen here is similar to that between the low- and high-stiffness bats discussed in Section 3.1. It was seen earlier that for bats with the same MOl a difference in e of 0.038 resulted in a difference in maximum lab or field BBS of 4.6 mph. As a result, a difference in e of 0.025 as seen here would result in a difference of about 3 mph in BBS. The difference in maximum lab BBS between the handle-loaded bats and the end-loaded bats is 12.8 mph. Therefore, the variation in lab BBS due to the variation in e is small compared to the variation in lab BBS due to MOl. The BBS values of the two bats for each MOl class were averaged, and the results are presented in Table 5. Table 5 shows a batted-ball speed difference of 12.8 mph for a difference in MOl of 3527 oz-irr'. The predicted difference was 11.5 mph for an MOl difference of 4000 oz-irr', assuming the sweet spot to be at the 6-in. location. The balanced bats

22

Rebecca H. Shaw andJames A. Sherwood

had the highest values for e, which resulted in the balanced bats having a slightly higher BBS than predicted-shifting them farther from the handle-loaded bats and closer to the end-loaded bats. The total difference is also slightly increased due to the fact that the sweet spot is not at the 6-in. location. Moving the sweet spot out to the 4.5-in. location for the predicted calculations increases the difference due to MOl slightly. For these bats, the sweet spot moves closer to the barrel end as MOl increases. As discussed previously, changes in MOl have a direct effect on player swing speed. Using the swing speed model developed by Nathan (200 I, 2003), the predicted field BBS values were calculated and are presented in the last two columns of Table 5. Adjusting for player swing speed brings the performance of the low- and highMOl bats to within 5 mph of each other. The change in field performance due to MOl (-5 mph) is similar to the change in performance due to barrel stiffness seen in Section 3.1 (-4.6 mph) for the range of properties studied.

4 Conclusion The equation for BESR states that baseball bat performance is dependent on two factors: moment of inertia and bat-ball COR, or e. Experimental data from bats of varying MOl correlate well with results predicted using the BESR equation. Increasing MOl increases performance in the lab, but it also makes the bat more difficult for a player to swing in the field. Variation in swing speed due to MOl is currently not considered in the lab test protocol. As a result, changes in MOl appear to have a larger effect on performance in the lab than would be seen in the field. Bat-ball COR is dependent on several factors, one of which is barrel stiffness. The data from the bats of varying barrel stiffness show an increase in bat-ball COR with a decrease in barrel stiffness. For the bats studied, predicted changes in field performance due to MOl and barrel stiffness were similar.

References Carroll, M.M . (2000) Assessment andregulation of baseball batperformance, Symposium on Trends in the Application of Mathematics to Mechanics, edited by P.E. O'Donoghuc and J.N. Flavin (Elsevier, Amsterdam). Crisco, J.1., Greenwald, R.M., Penna, L.H. (1999) Baseball BatPerformance: A Batting Cage Study, Draft Report, July 14, 1999. http://www.nisss.org/BBSPEED6a.html. Nathan, Alan M. (200 I) Baseball and Bat Performance Standards, Presentation to theNCAA Research Committee, June 13, 2001. Nathan, Alan M. (2003), Characterizing the Performance of Baseball Bats, Am. 1. Phys.lL pp. 134-143 (2003). NCAA (2005) Baseball Bat Certification Protocol. Russell, D.A. (2004) Hoop frequency as a predictor of performance for softball bats, The Engineering ofSport 5, Vol. 2, pp. 641-647 edited by M. Hubbard, R.D. Mehta, J.M. Pallis.

The Effect of Spin on the Flight of a Baseball Alan M. Nathan', Joe Hopkins', Lance Chong', and Hank Kaczmarski' I

2

University of Illinois, [email protected] Western Michigan University

Abstract. New measurements are presented of the lift on a spinning baseball forspeeds in the range 50-110 mph and spins 1500-4500 rpm . The experiment utilizes a pitching machine to project the baseball horizontally; a high-speed motion capture system to measure the initial velocity and angular velocity and to track the trajectory over - 5 m of flight; and a ruler to measure the total distance traversed by the ball. The lift coefficients are extracted from the data andcompared to with previous measurements or parametrizations.

1 Introduction to the Problem In a recent paper, Sawicki et al. (Sawicki, Hubbard, and Stronge 2003) report a study of the optimum bat-swing parameters that produce the maximum range on a batted baseball. Using a model for the ball-bat collision and recent experimental data for the lift and drag coefficients, they tracked the ball from collision to landing. For given initial speed, angle, and spin of the pitched baseball, the bat swing angle and undercut distance were varied to maximize the range. The study found the surprising result that an optimally hit curveball travels some 12 ft. farther than an optimally hit fastball, despite the higher pitched-ball speed of the fastball. The essential physics underlying this result has to do the with the aerodynamic lift force on a baseball projected with backspin. In general, a baseball will travel farther if it projected with backspin. It will also travel farther if is projected with higher speed. In general a fastball will be hit with a higher speed. However, a curveball will be hit with larger backspin. The reason is that a curveball is incident with topspin and hence is already spinning in the right direction to exit with backspin. A fastball is incident with backspin so the spin direction needs to reverse to exit with backspin. It then becomes a quantitative question as to which effect wins: the higher speed of the fastball or the larger backspin of the curveball. According to Sawicki et aI., hereafter referred to as SHS, the latter effect wins and the curveball travels farther. The conclusion of SHS depends critically on the size of the lift force on a spinning baseball. SHS used a particular model for the lift based largely on experimental data that will be reviewed in the next section. That model and the conclusions that follow have been criticized by Adair (Adair 2005), who claims that SHS grossly overestimate the effect of spin on the flight of a baseball. The goal of the present paper is to resolve the disagreement between SHS and Adair, hereafter referred to as RKA, by performing new measurements of the effect of spin on the flight of a baseball.

24

Alan M. Nathan et al.

2 Previous Determinations of Lift When a spinning baseball travels through the atmo sphere, it experiences the force of gra vity in addition to the aerodynam ic forces of drag and lift, FD and FL. Convention ally the lift force is parametrized as FL= Y2C LpAv 2 where A is the cro ss sectional area of the ball, v is the speed, p is the air dens ity, and C L is the lift coefficient. In the SHS parametrization, C L depends only on the spin parameter S=RwN and is a rough fit to the data of Alaw ays (Alaways 1998; Alaways and Hubbard 200 I) and Watt s and Ferrer (Watts and Ferrer 1987). Alaways used a mot ion capture technique 5 to determ ine C L for speeds up to approximately 75 mph (Re <1.6 x 10 ) and for 0.1<S<0.5. Watts and Ferrer measured C Lin a wind tunnel experiment for speeds up to 37 mph (Re<0 .8 x 105) and 0.4<S<1.0 . RKA uses a parametrization (Adair 2002) which follows from the argument that the lift on a spinning ball is related to the difference in drag between two side s of the ball. Thi s prescription leads to lift values that are in good agreement with the Watts and Ferrer data and with SHS at low speeds . RKA argues that extending this prescription to higher speeds lead s to predictions in reasonable agreement with observations from the game itself (Adair 2002), such as the maximum break of a pitched curveball. It is at the high speeds that are typ ical of pitched or hit baseballs that the differences between SHS and RKA are most pronounced . For example, at 100 mph and w=1800 rpm , the SHS lift is about three times larger the RKA lift. Thi s will have dramatic implications for the distance traversed by a long fly ball.

3 Description of the Experiment The essential technique is to project the ball approximately hor izont ally with back spin or topspin and to use a motion-capture sys tem to measure the initial velocity and angular velocity and track the trajectory over approximately five meters of flight. Under such conditions, the vertica l motion is particularly sensitive to the lift force, which lead s to a downward acceleration smaller or larger than g when the ball has back spin or topspin, respectively. Additional information is obtained by mea suring the total distance traversed by the baseball before hitting the floor, which is approximately 1.5 m above the init ial height. The projection device was an ATEC two-wheel pitching machine, which was operated in the range V=50-11 0 mph and w=1500-4500 rpm , corresponding to S=0.1-0.6 and Re=( 1.1-2.4) x 105. A total of 22 pitches were analyzed , all in the "two-seam" orientation. To measure the initial velocity and angular velocity of the ball, a motion analysis sys tem was used. The system, manufactured by Motion Analysis Corporation, consisted of 10 Eagle-4 cameras operating at 700 frames per second and 1/2000 second shutter speed and the EVaRT4.0 recon stru ction software. Each camera shines red LED light onto the ball , attached to which is circular dot of retro-reflecti ve tape. The tape reflects the light back at the cameras, which then record the coo rdinates of the dot in the CCD arra y. The reconstruction software determ ines the spatial coordinates in a global coordinate sys tem by using triangulation among the 10 cameras. The cameras were positioned at various heights along a line approxi mately parall el to and

TheLifton a Spinning Baseball

25

six meters from the line-of-flight of the ball. In order to accomplish the triangulation, the precise position and lens distortions of each camera must be determined from an elaborate calibration scheme. The global coordinate system is defined by positioning an L-shaped rod in the viewing volume of the 10 cameras simultaneously. The rod has four reflective dots located at precise relative locations to each other. With these distances, the software determines a first approximation to the location of each camera. These distances are further refined and the lens distortions determined by waving a wand throughout the tracking volume of the cameras. The wand has three reflective dots at known relative distances. Although the particular calibration software is proprietary, it almost surely uses some variation of the direct linear transformation technique described by Heikkila and Silven (Heikkila and Silven 1997). A typical root-mean-square (rms) precision for tracking a single dot is 1.3 mm. Additional calibrations and consistency checks were performed. A plumb line was used to establish that the y-axis of global coordinate system made an angle of 0.16° with the vertical. The clock of the motion capture system was checked against a precisely calibrated strobe light and found to be consistent within 0.5%. A non-spinning baseball was tossed lightly in the tracking volume and the vertical acceleration was measured to be g to within 1.5%. The setup for this experiment is similar in many respects to that used in the pioneering experiment of Alaways (Alaways 1998) but different is some key respects. One difference concerns the deployment of cameras. Alaways used two sets of motion capture cameras. One set tracked the ball over the first 1.2 m of flight and was used to establish the initial conditions; a second set tracked the center-of-mass trajectory over the last 4 m of flight, starting approximately 13 m downstream from the initial position. This allowed a very long "lever arm" over which to determine the acceleration but a short lever arm for determining the initial spin. In the present setup, we used only one set of cameras distributed spatially so to track over the largest distance possible, approximately 5 m. The same set of cameras determined both the initial conditions and the acceleration. Tracking over a larger distance is useful for measuring the spin at small S, since the angle through which the ball rotates over distance D is proportional to SD. For all of the pitches analyzed in the current experiment, the ball completed at least one complete revolution over the tracking region. We gained some redundant information by measuring the total distance R traversed by the baseball while falling through a height of 1.5 m. The sec ond difference concerns the deployment of reflective markers. Alaways utilized 4 dots on the ball with precisely known relative positions. This allowed him to determine both the initial orientation of the ball and the direction of the spin axis. We experienced great difficulty in tracking more than one dot and therefore used only a single dot, offset from the spin axis by approximately IS°. We were not able to measure the spin axis but simply assumed it was constrained by the pitching machine to lie in the horizontal plane, perpendicular to the direction of motion. New measurements are planned for early 2006 using multiple dots and those results will be reported at the conference.

26

Alan M. Nathanet al. 3000

1520

2000

1500

1000

E

.s

1480

0

1460

-1000

1440

N

=32 m/s <0=522 rad/s

-2000 -3000 0.00

0.04

0.08

t (s)

-c

3' 3

1420

0.12

0.16

1400

Fig. 1. Trajectory data for one of the pitches projected. For clarity, the plot for the z coordinate displays every other point. The inset shows the coordinate system. The ball is projected in the +z direction with topspin. The curvesare least-squares fits to the data. A plot ofy(t) and z(t) for one of the pitches is shown in Fig. 1, where y and z are the vertical and horizontal coordinates, respectively, of the reflective marker. Standard nonlinear least-squares fitting algorithms were used to fit these data to functions of the form yet) = Yem(t)+ Asin(oot+, with the +/- sign applying for backspin/topspin. Nine parameters were varied in the fit: the four initial values, the three rotation parameters, and CL and CD, both of were assumed to be constant over the 5 m flight path . CL and CD are primarily determined by the curvature ofy(t) and z(t), respectively, where the latter is nearly completely masked by the large linear term. The rms deviation of the fit from the data in Fig. 1 is 0.4 mm for yet) and 12.7 mm for z(t), which values are typical of the fits for the other pitches. The inferred values of CL , the primary result of the experiment, are presented in Fig. 2. The error bars on the values are estimates based on the rms deviation of the data from the fit and the calibration tests .

4 Results and Discussion Our results for CL are shown in Fig. 2. Also shown are the SHS parametrizaton and the earlier results upon which the SHS parametrization is based, including the data of Alaways, Watts and Ferrer, and Briggs (Briggs 1959), as corrected by Hubbard

The Lift on a Spinning Baseball

a6 ~ .

0.5 -...

•

present

-~--------

-----l..

[_.. rp; ~j. ~.'.'tf _ !~ . : .j o !

~f

0.2 ---..~~ ~ --- -0.1 } -

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Alaways 2-Seam ._. ._ ... 0_ .. . ; .. 0 Alaways 4-Seam :' ... '" ': ... 0 o Watts & Ferrer t> Briggs ...... -a..-... ~~ ..... Q-- ---- -- .. -----SHS : ... '" 0 0

. , _"'oi 0.4 --·········..···:------------..··d · · >~Q ··~·-:- - - 0.3 __

27

~

n

: -- -r---

t>:

f

--- ---..- [

--.."['--

L..

. · · · ··.. ·i····----------0

0

.__ __.;._.. ..----. : :

·f

--------

"['

--------

0.0 ........~...L....Jl.-.L. -'----.L......l. ~~L......1...~ --'---'---'--~~....J 0.0 0.2 0.4 0.6 1.0 0.8

s

Fig. 2. Results for CL from the present and previous experiments , along with the parametrization of SHS.

(Sawicki et al. 2005) . In the region S0.5 do our results start to deviate from SHS, which is constrained primarily by the high-S data of Watts and Ferrer, most of which were taken at low Re, below 0.6 x 105 (v<25 mph). Interestingly, the present data near S=0.5 agree with Alawa ys and are below the general trend of the Watts and Ferrer data. Perhaps this is an indication of a dependence of CL on Re, for a fixed S. On the other hand , in the range S=0.15-0.30 the values of CL measured in the present experiment are tightly clustered around 0.20, despite a variation in Re in the range (1.1-2.4) x 105 . This seems to suggest only a weak depend ence of CL on v, at least in that regime. For v= 100 mph and (0==1 800 rpm (S=0.154), the present result for C L is in the range 0.20-0.22, the SHS paramet erization is 0.18, and the RKA prescription is cons iderably smaller at 0.06. We conclude that the present data support SHS and do not supportRKA.

5 Summary and Conclusions An experiment has been performed utilizing high-speed motion capture to determine the effect of spin on the trajectory of a baseball. From these data , CL is extracted with good precision over the range 5070 mph.

28

Alan M. Nathan et a\.

References Adair, R. K. (2002) The Physics ofBaseball, 3rd Edition. HarperCollins, New York. Adair, R. K. (2005) Comment on "How to hit home runs: Optimum baseball bat swing parameters for maximumrange trajectories." Am. J. Phys. 73,184-185 . Alaways, L. W. (1998) Aerodynamics of the Curve Ball: An Investigationof the Effects of Angular Velocity on Baseball Trajectories. Ph.D. thesis, University of California, Davis. Alaways, L. W., Mish, S. P., and Hubbard, M. (2001) Identificationof release conditions and aerodynamic forces in pitched-baseball trajectories. 1. App\. Biomech. 17, 63-76. Alaways, L. W. and Hubbard, M. (2001) Experimental determination of baseball spin and lift. 1. Sports Sci. 19, 349-358. Briggs, L. 1. (1959) Effects of spin and speed on the lateral deflection (curve) of a baseball and the Magnus effect for smooth spheres. Am. 1. Phys. 27, 589-596. Heikkila, 1. and Silven, O. (1997) A four-step camera calibrationprocedure with implicit image correction. Proc. CVPR '97, IEEE, 1997, 1106-1112. Sawicki, G. S., Hubbard,M. and Stronge, W. (2003) How to hit home runs: Optimum baseball bat swing parameters for maximumrange trajectories. Am. J. Phys. 71, 1152-1162; Am. 1. Phys. 73,185-189 . Watts, R. G. and Ferrer, R. (1987) The lateral force on a spinning sphere: Aerodynamicsof curve ball. Am. 1. Phys. 55,40-44 .

Rigid Wall Effects on Softball Coefficient of Restitution Measurements Lloyd Smith I and Aaron lsorr' 1

Washington State University, [email protected] Casecade Engine

Abstract The coefficient of restitution (COR) is often measured by impacting a ballagainst a rigid wall. The ball COR is used to regulate performance in many sports. In the case of ball impact sports, such as baseball and softball, the ball COR also contributes to bat performance. Understanding the accuracy of the ball COR has received greater scrutiny as bat performance tests have been refined and performance limits lowered. The effect of the idealized rigid wall surface wasconsidered in this studyby impacting softballs against flat surfaces of controlled stiffness. The ball COR was generally observed to decrease as the impact surface stiffness increased. An exception to this observation was found for the thinnest impact plate (6 mm) which provided the lowest COR value in this study. Onlyimpact surfaces of relatively large compliance wereobserved to affect the measured ball COR. The affect of the distance of the rigid wall from the speed measurement due to drag was also considered. The common distance of 450 mm was shown to report a ball COR that is approximately 0.005 lower than would be obtained by measuring the ball speed at the impact surface.

1 Introduction The coefficient of restitution (COR) of two col1iding objects is defined as the ratio of their relative speed after and before impact, respectively (Beer and Johnston, 1997). The ball COR, independent of the object being impacted, is often desired. To this end bal1s are impacted against a flat rigid wall. Accordingly, the bal1 COR is taken as the ratio of the ball speed after to before impact. The rigid wall ball COR is used by a number of governing associations to certify balls and bats for softball and baseball. Little has been done, however, to define or quantify a rigid wall. ASTM 1887 defines a rigid wall "as cinder block or concrete, minimally 20-cm (8-in.) thick." It is unclear whether this definition is sufficient or unnecessarily conservative . The motivation to understand the effect of a rigid wall on ball COR is two-fold. First, obtaining uniform ball COR measurements from laboratory round-robin studies has been surprisingly difficult. It is possible that differences in respective laboratory rigid wal1 impact surfaces contribute to this problem. Second, most bal1 and bat manufacturers design their products near the allowed performance limits. Reducing the variation in ball COR measurements wil1 allow manufacturers to design their products closer to the allowed limit.

30

Lloyd Smith and Aaron Ison

The effect of impact surface stiffness will be examin ed by impacting plate s supported near. their edges as a function of plate thickne ss. Plate displacement and ball COR will be examined as a function of thickness.

2 Experiment Softballs nominall y 300 mm ( 12 in) in circumference were projected toward a flat impact surface at 27 m/s (60 mph). The balls were delivered using an air cannon as described in ASTM 2219 striking the impact surface without rotation. The balls were impacted sequentially on the four surfaces with the widest distance between the stitches. The impact plate was nominally 300 mm (12 in) in diameter. Six impact plates were studied ranging in thicknes s from 13 to 44 mm (0.5 to 1.75 in) in 6 mm (0.25 in) increments. The impact plate was attached to a support structure through 12 equally spaced 19 mm (0.75 in) bolt s arranged on a 240 rom (9.5 in) diameter circle. Twelve spacers measuring 32 mm (1.25 in) in diameter were placed between the impact plate and support structure to allow free motion of the center of the impact plate . A 25 mm (I in) diameter hole was drilled through the support structure which allowed a non-contact laser vibrometer (Polytec OFV -511 Fiber Interferometer with a Polytec OFV -5000 Controller) to measure the surface motion of the impact plate as depict ed in Fig. I.

3 Numerical Simulation The effect of impact plate stiffness was studied numerically using a finite element simulation. The model consi sted of nearly 30,000 elements and is shown in Fig. 2. The ball was meshed using 8 noded brick elements while the plate was meshed using 4 noded plate clements. Symmet ry conditi ons were appl ied to the sectioned edges of the model. The round holes in the plate represent the edg es of the spacers which were constrained in the direction of the impending ball motion. The ball was modeled as a viscoelastic material whose propert ies were tuned to match the nomin al ball density, COR , and stiffness as described elsewhere (Shenoy, Smith , Axtell 200 I).

SUPPORT STRUCTURE VIBROMETER

6

SPACERS SPEED \

u~~6 ........... IMPACT PLATE

Fig, 1. Schematic of impac t plate stiffness study.

Rigid Wall Effects on Softball Coefficient of RestitutionMeasurements

31

4 Results The average COR was found for 6 softballs impacted 6 times against each of the impact plates, as shown in Fig. 3. (The exper iment was repeated with 24 balls with similar results .) The error bars represent the standard deviation of the mean for each thickness. The COR was observed to decrease with increasing plate thickness. This trend is analogous to the so-call trampoline effect from which thin walled hollow bats derive their performance. The balls were also impacted aga inst a reinforced concrete wall, labeled "Fixed" in the figure . The results suggest that wall compliance must be relatively large to affect the measured ball COR. The results from the FEA model are also presented in Fig. 3, and show good agreement with experiment. The plate clamping condition was observed to have a large effect on the numerical results. Pinned supports at the outside edge of the plate, for instance, produced a much larger change in ball COR with plate thickness than was observed experimentally; while clamped supports at the fastener holes resulted in a smaller change in ball COR with plate thickness than was observed experimentally. For the results presented in Fig. 3, the plate was pinned at the hole circle radius since mechanical fasteners are not able to produ ce a true clamped boundary condition. The model also considered a 6 mm (0.25 in.) thick plate . The ball COR with this plate decreased sharply (0.291). The FEA model of the plate was linear elastic and did not consider yielding, which would have occurred for a 6 mm plate. The reason for the low COR using the 6 mm thick plate is likely related to its high compliance and low natural frequen cy (-300 Hz). The contact time between the ball and plate is of order I ms. The 6 mm thick plate continued to deform while the ball was recoiling. Th is is an example of an elastic mechanism of impact energy loss, and show s that decreasing rigid wall compliance may not always reduce the measured ball COR. The vibrometer was used to measure the displacement of the impact plates . Unfortunately the results of these measurements did provide a reliable description of the plate motion . The displacement rate of the thinner plates exceeded the capacity of the vibrometer, while the motion of the millbase, used to support the impact plates , affected the displacement of the thicker plates . Although the millbase motion appeared to be relatively small during the ball contact (-0.0 I mm), its contribution was difficult to

Fig. 2. Mesh of the simulated ball-plate impact.

32

Lloyd Smith and Aaron Ison

separate from the plate motion . The results of the numerical simulation were used, therefore, to describe the effect of rigid wall motion on COR . Ball COR is shown as a function of the plate displacement in Fig . 4. The ball COR appears relatively constant for plate displacements below 0.1 mm. A peak COR occurred for plate displacements near OJ mm before decreasing sharply with larger plate displacements (i.e . the 6 mm thick plate) . It should be noted that displacement magnitude alone may not be sufficient to describe rigid wall compliance. Plate speed may also play a roll if the ball contact duration changes appreciably with plate compliance. For the case at hand the contact duration was relatively constant resulting in comparable speed and displacement trends with COR, where the speed ranged from 6 to 0.04 m/s. The effect of air resistance is often neglected when measuring the ball COR. The short flight distance of the ball and a misconception that the effect of drag approximately cancels in the COR calculation have been cited to discount drag effects. For a nonrotating sphere (which is the ease with the air cannon used for this work) traveling at a speed , V, the drag force, F, may be found from (White 1986)

F -- "2' pC IJ V2 A

(I)

where CD, o, and A are the drag coefficient, air density, and sphere cross sectional area, respectively. Over the range of speeds common to softball (below 110 mph), CD falls between 0.5 and OJ (Adair, 2002) . The ratio of the measured speeds, v/v;, may be found as

0.475

'r-- - - - - - - - - - - - - - ---,

0.470

o Experiment oFEA

0.465

a::

8

0.460

f

0.455 0.450

13

19

25

32

38

44

Plate thickness (mm)

Fig. 3. Average ball COR from

(j

softballs.

Fixed

Rigid Wall Effects on Softball Coefficient of Restitution Measurements

Va =CORa(e- k )

33

(2)

Vi

where CORa is measured at the impact plate and

k=pCDA x

0)

m

where m is the ball mass and x is the distance from the speed sensor to the impact plate. Six balls were impacted against a rigid impact plate at 60 mph six times each. The speed sensors were moved in 125 mm (5 in) increments, where the distance to the impact plate was taken as the center of the speed sensors. The ratio of the after to before impact speeds are presented in Fig. 5 as a function of sensor distance from the impact plate . While the relatively small range of sensor distances considered here have a small effect on the ball COR, the effect is measurab le and outside the range of experimental scatter. For the case of softball and baseball standardized COR measurements, the center of the sensors are 450 mm from the impact plate. This implies that the actual ball COR is on average 0.005 higher than the commonly measured value. For comparison Eq. (2) is also plotted in Fig. 5, which appears to support Cd = 0.5.

5 Summary The foregoing has considered the effect of impact surface compliance and distance in measuring the ball COR. The reinforced concrete wall commonly used as a rigid surface provided a similar COR measure as suspended plates which much larger compliances. 0.5 r - --

a::

0.4

- --

-

-

-

-

-

-

-

---,

~ ---- -----

o

o

0.35

~ ------------

0.3 -1- -

-

-

-

-

-

0.25 +-0.001

-

---r-

-

-

0.01

-

-

-

-

-

..,--

-

-,--

0.1

- \

-

---i

10

Plate Displacement (mm)

Fig. 4. Ball COR as a function of the impact plate displacement from the numerical simulat ion.

34

Lloyd Smith and Aaron Ison

The results of this work suggest that the current practice of using reinforced concrete provides a good approximation of a rigid impact surface and that more compliant impact surfaces can also provide comparable COR values . The distance between the speed sensors and the impact surface was shown to have a small, but measurable effect on the measured ball COR. This distance should be controlled and reported when measuring ball COR. 0.460 , - - - - - - - - - - - - - - - - - ,

0.455

'2

~ z» :0

0.450

~ 0.445

o

Experiment

----Cd

=0.3

- - C d = 0.5

0.440

+------,.-----,-------1 o

500

1000

1500

Distance from rigid wall (mm)

Fig. 5. Ball COR as a function of speed sensor distance from the impact plate .

6 Acknowledgements The authors gratefully acknowledge the American Softball Association and the Sports Science Laboratory at Washington State University whose support made this work possible. The authors also acknowledge the assistance of Nicholas Smith and Ryan Smith whose meticulous experiments greatly benefited this work .

7 References Adair, R. K., (2002) The Physics of Baseball, 3rd Ed., Perennial, New York . Beer, F. P., Johnston, E. R. (1997) Vector Mechanics for Engineers, 6th Ed., McGrawHill. Shenoy, M. M., Smith, L. V., Axtell, J. T., (2001) Performance Assessment of Wood, Metal and Composite Baseball Bats, Composite Structures, 52:397-404. White, F. M. (1986) Fluid Mechanics, 2nd Ed., McGraw-Hill.

The Effect of Holding Methods on a Baseball Bat Performance Estimation System Hiroyuki Kagawa I , Takeshi Yoneyama', and Masaya Takahashi' I Kanazawa University, [email protected] 2Sumitomo Light Metal

Abstract. To obtain a value for the coefficient of restitution or of the trampoline effect for a given baseball bat it is typical to hold the bat in a clamping fixture or robot during simulated hits. This fixture and the structure or mechanism thatconnects the bat to earth form a dynamic system in which thebat is onlyonepart. If wewish to measure some property of the bat alone, therefore, it is important to understand the influence of the clamp method and boundary conditions it imposes. To investigate this matter we have developed an evaluation system for the coefficient of restitution. Bats were held in three different ways while standard baseballs were fired at them using a pitching machine. In this paper we will describe the evaluation method and give examples of the results obtained on some metal bats. We conclude that the fixing method does affect the measured value of the coefficient of restitution, indicating that caution is needed when comparing the results from different test fixtures.

1 Introduction The coefficient of restitution (COR) is often measured by researchers who are studying the performance of baseball bats (for example Tanaka et al. 1992, Nishikawa et al. 1994, Naruo et al. 1997, and Sherwood et al. 2000). These researchers have made many valuable contributions to the development and science of baseball bats. Nathan 2004 and Hongo et al. 2004 introduced the term "trampoline effect" to describe the relationship between stiffness and COR in baseball bats and golf clubs. The position and significance of the "sweet spot" was thoroughly explored by Takagi 1983. However, so far as we know, the effect of the clamp method of the bat on the measured COR has not yet been investigated. In this study we used three types of bat clamp: 1) suspended on soft supports so that the bat was nearly "free"; 2) clamped but allowed to rotate about a fixed axis (fixed pivot); and 3) rigidly clamped. In actual batting we expect the effective "clamp" condition to be somewhere between the "free" and "rigid" conditions because the human batter will usually hold the bat very firmly but his or her body is still a fairly flexible mechanism. The real "clamp" condition, from the point of view of dynamics, will also probably be different for each batter, batting style and so on. We thus considered that it would be interesting to find out how much the clamp condition affects the apparent COR. This paper describes our methods and some results obtained with metal bats.

36

Hiroyuki Kagawa

2 Measuring Equipment Our apparatus consisted of a pitching machine, a ball velocity measuring frame and a bat fixture, arranged as shown in Fig. 1 (a) . The pitching machine was a commercially available general purpose machine with two rotors. It was able to pitch both hard and rubber balls. The machine had the ability to drive the rotors at different rates to produce various amounts of ball spin: however in this work we set the rotor speeds to be equal i.e. to produce little or no spin. The maximum pitching velocity of the machine was about 180 km/hr (50 m/s). The ball velocity measuring frame was a pair of vertical plates with eleven laser sensors. The plates faced each other and the ball passed between them. The sensors were aligned radially about the bat center to detect the ball after impact, even if its path was up to 15° above or below the horizontal, see Fig. 1 (b). The ball velocity was estimated from the displacement of the laser beams and the time between the beam interruption events. The bat was held in one of three fixtures, as described above (Fig. 2). Additional laser beams were placed near the bat to record its velocity. In the case of the free clamp type, six vertical laser beams were used; in the case of the fixed-pivot clamp type, only one beam was used but it could record both edges of the interruption event of an optical shielding plate fixed on the pivot axis. Batting events were filmed using a high-speed camera capturing 20 000 frames per second. The high-speed camera was also used to verify the laser velocity measurement system, to measure the velocity of the bat after the impact, and to record the contact time and elastic behaviour of the ball. Using this equipment described above, the pitching velocity Vo and the hitting velocity VI were measured during experiments. Additionally, in the case of the method shown in Fig.2 (a) the translational velocity Vb and the rotational velocity ro, of the bat around the center of mass G were measured. In the case of holding method shown in Fig.2 (b) the rotational velocity co, of the bat around the grip point A was measured.

P.td"r11 .C~IM

l..-boilY"...",,.

fr..

(a) Simplified general top view of apparatus.

(b) Alignment oflaser sensors (side view)

Fig. 1 Measuring equipment.

The Effect of Holding Methodson a BaseballBat Performance EstimationSystem

mf

A" 'iv.

m

0

s,

7(~- ;P:;-:.-. B:;- -; G- .~--~

YO

7(

P••8 Ch

~

R

R

(b) Clampedbut allowedto rotate about a fixed axis

(c) Rigidly clamped

~-----..,~

f------~ (a) Suspendedon soft supports

37

Fig. 2 Holdingmethodsfor bats

3 Dynamic Relations Let us define: M Mass of the bat m Mass of the ball I Momentof inertia of the bat The value of COR IS then : (a) Suspended on soft supports

R Rb

Distancebetweenhitting point P and grip point A Distance. between hitting point P and the bat center of mass G

COR = v, + Vb + RbOJb

(I)

Vo

(b) Clamped but allowed to rotate about a fixed axis COR = vt +Rwt

(2)

Vo

where

R=~

(3)

m(vo + vt )

(c) Rigidly clamped COR =:J...

(4)

Vo

In the case of (b) not only the COR but also the hitting position can be evaluated from the velocities alone .

4 Experiments The properties of the bat and balls used in this study are summarized in Table 1. The grip position (or pivot position, for case (b) experiments) was chosen as 152mm from the grip end according to ASTM 1998. The bat was very slightly under the regulation weight for Japanese high -school use (O.9kg) because we removed the grip tape.

5 Results Let us first consider clamp condition (b): rigid pivot type . The value of the distance from A to P, i.e. R, as estimated using only the measured velocities, is compared to

38

Hiroyuki Kagawa

Table 1. Summaryof the propertiesof the bat and balls used Baseball bat Material Entire length, L (mm) Weight, M (kg) Moment of inertia, I (kg. rrr' ) Distance between pivot and center of mass, AG (mm) Distance between pivot and center of percussion, AB (mm) Hard ball Diameter, d, (mm) Weight, m, (kg)

Aluminium 842 0.899 0.180 377

700

C>

'"

bOO

°E ~

J:J

'0

c

500

~

"0>

'0. c

400

~ ~

531 71 0.150

Rubber ball Diameter, d, (mm) Weight, rn,(kg)

"

J:J

."S 0

71 0.136

~

~

J:J

ec

300

]

Dist ance between pivot and batt ing point by act ual measurement (nrn )

Fig. 3 Estimation of batting point for the case of rigid pivot type clamping

the actual va lue in Fig. 3 . The solid line in the figure is the diagonal; the dotted lines are an error band of ±20mm. It will be seen that the data points are generally within that error band . It seems that it is possible to estimate the hitting position using only the three velocities vo, v. , and WI. Fig. 4 shows CO Rs for hard ba ll impacts. The solid line shows the position of the center of percussion B, and the dotted line shows the position of the center of mass G. The same pitching velocity setting was used within each clamp experiment type , but a different average velocity setting was used for each clamp type . For clamp method (a) ("free") the pitching velocity was about 172 km/hr; for method (b) (rigid pivot) it was 168 km/hr; and for method (c) ("rigid") it was 150 km/hr. There was some variation in the actual pitching ve locity, cau sed by variabi lity in the pitching machine. According to our previous experiments (Nasu et al. 2005), a higher pitching velocity produces a lower ob served CO R. So it is expected that the order of the COR data for the methods wou ld not be changed by the variations in the pitch velocity. The forces on the bat when it was held in clamp type (c) were at times very high . When the hitting point P was near the ce nter of mass G, we had some cases where the clamp bolts were broken by the impact. Our first expe rimental bat was actually bent near the grip by one impact at the hitti ng end (the top) . Fig. 4 shows that the CO R for clamp types (a) and (b) increased from the grip to the top, and that it was generally a little higher for clamp type (a). However for impacts near the center of percussion the clamp method made little difference to the measured CO R. This may be understood from the expected force s during an impact. In the case of clamp method (b), the rigid pivot type , we expect a force at the pivot that is increased according to the distance between the hitting point P and the center of percussion B. When the point P is inside B, the direction of the force at the pivot becomes backward. On the other hand , the direction becomes forward when P is outside B. If there is a large force at the pivot , it bows the bat and excites slow vib rations.

The Effect of Holding Methods on a Baseball Bat Performance Estimation System

39

We will call this type of bat deformation "reflection". We also expect deformation of the cross-section of the bat, which we will call "hoop" type deformation; however we won't report about that here. Fig. 4 also shows that the COR for clamp type (c) is considerably lower than for the other clamp types . We suspect that this is due to several high-speed-impact phenomena including the mode of vibration excited in the bat, deformation and energy loss in the bat clamp system, and damping in the bat material. All the clamp types allow reflection deformation, but in the rigid clamp case the magnitude of the oscillations after impact was observed to be the greatest. So we expect that it would be more useful than the other clamp types to investigate the effect of bat deformation "reflection".

0.7 c

.£j Db

'B III

~

0.5

"-

o

.'-:0

'-'

.~ Ojj

~

.·0

'!

QI

~ OJ

q,

• Suspended on soft supports, (a)

~ °e

•

~

Clamped but allowed to rotate about a fixed axis, (b)

[]

Rigidly clamped , (c)

\

02 200

300

400

500

700

600

Distance betJ.Ieen pilot and batti"lg pont em m )

Fig. 4. Distribution of the coefficient of restitution along the longitudinal axis of the bat

c

.£j Db

'B III

~

"-

• Rubber ball (about 84km/h) Hard ball (about 132km/h)

0.5

o

'-'

.~ Ojj

~

QI

~ OJ

02

L-_---"_---'----'-_ _- ' - . L - _ - ' - _ - - - l

200

300

400

500

600

700

Distance betJ.Ieen pilot and batti"lg pont em m )

Fig. 5. Distribution of the coefficient of restitution along the longitudinal axis of the bat in the case of the fixed pivot clamp type.

40

Hiroyuki Kagawa

Fig. 5 shows some additional results obtained using a different bat and both hard and rubber balls. There is a significant effect in the case of a very elastic ball like a rubber one because the deformation is so extreme. The high-speed video footage for the rubber ball impacts showed that the ball became almost completely flattened and wrapped around the bat for a brief instant. If we look only at the trend within each set of results, it is interesting that the distribution of COR along the length of the bat, as measured using a rubber ball, was nearly constant - unlike the measurement done with the harder ball. The bat's characteristics were not visible because the elasticity of the ball was so dominant.

5 Conclusions An evaluation system for the coefficient of restitution of baseball bats with three kinds of clamp methods has been developed. (I) In the case of clamping by suspension on soft supports, that is, "free", the coefficient of restitution for impacts with a hard baseball was high. The main deformation in the impact is local change in the circular cross-section of the bat (hoop deformation). (2) In the case of the fixed-pivot clamp type, the coefficient of restitution matched the "free" clamp case but only for impacts near the center of percussion. We found that it was possible to estimate the hitting position from only three velocity measurements. (3) The rigid clamp type produces very high forces on the bat, for a given impact velocity, so the maximum velocity must be restricted to prevent damage to the bat. Also the observed COR for this clamp type tends to be rather low.

References ASTM (1998), Standard Test Method for Measuring Baseball Bat Performance Factor!, F1881 , pp.I-4 . Koening, K. et al. (2004), Engineeringof Sport S, Yol.2, pp.87-93. Hongo, T. et al. (2004), Prepr. of Jpn. Soc. Mech. Eng., No.04-26, pp.162-167. (in Japanese) Nishikawa,et al. (1994), Prepr. of Jpn. Soc. Mech. Eng., No.940-S9, pp.21-2S. (in Japanese) Naruo, T. et al. (1997), Proc. Sth Japan Int. SAMPE Symposium, pp1311-1316. Nasu et al. (200S), Prepr. of Jpn. Soc. Mech. Eng., No.OS-16, pp.9-13. (in Japanese) Nathan, A.M. (2003), AmJ. Phys., Vo1.71, pp.134-143. Nathan, A.M., et al. (2004), Engineeringof Sport S, Yol.2, pp.38-44. Sherwood, lA., et al.(2000), Engineering of Sport 3, pp.377-387. Takagi, R. (1983), Mechanics of Sports, Koudansha. (in Japanese) Tanaka, et al. (1992), J. Jpn.Soc.Mech.Eng., Yol.64, No.623, pp.S9-64. (in Japanese)

2 Climbing - Instrumentation and Testing ofEquipment

Synopsis of Climbing - Instrumentation and Testing of Equipment Franz Konstantin Fuss Division of Bioengineering, School of Chemical and Biomedical Engineering, and SPERT (Sports Engineering ResearchTeam), BioMedical Engineering Research Centre,Nanyang Technological University, Singapore, [email protected]

Design, development, and testing of sports equipment and measurement devices are classical engineering domains, and try to lead an athlete to greater heights . However, unlike other sports disciplines, climbing equipment does not target at gaining additional centiseconds or centimeters, which are rather an equipment factor than directly related to the athlete 's performance. In climbing, equipment concerns safety and prevention of injuries as well as overuse syndromes. Thus, equipment becomes an important legal issue, once more people are involved and interacting, such as lead climber and belayer. Instrumentation of climbing equipment is crucial for understanding and quantifying the mechanical parameters of climbing, which, in tum, is an invaluable tool for measuring the climber's performance and training success, and offers advice to climber in terms of equipment selection and prevention of injuries . The climbing sport, unfortunately not an Olympic discipline so far, is represented by UIAA (International Mountaineering and Climbing Federation, Union Internationa Ie des Associations d ' Alpinisme). UIAA comprises a special Safety Committee, which deals with equipment related safety issues, especially with safety standards. Climbing equipment encompasses belaying devices such as ropes, anchors (screws, cams) , karabiners, helmets, harnesses, crampons, ice-anchors, ice tools, slings, shoes, and grip-enhancing means . Yet, as mentioned above, these kinds of equipment do not increase the climber's performance: a better grip due to higher friction does not necessarily affect the performance. It rather depends on the climber's experience whether to consider all grip parameters involved, such as surface, material, size, shape, sweat, fatigue and weight distribution among all four limbs. The current research and development in the field of equipment testing moved from simple material and structural testing to more sophisticated testing approaches, such as: I) changes of material and structural properties of ropes after consecutive falls, influence of knots, rope length, and fall factor (fall height over rope length) ; 2) impact of load rate and jerk on anchors and anchoring media like rock faces and ice walls 3) development of safety standards for belaying devices (brakes)

44 Konstantin Fuss The results, and the advice for the climber, are quite clear: I) consecutive falls increase the stiffness of a rope ; 2) use low modulus ropes for ice climbing is preferred ; 3) belaying devices with a large breaking coefficient stop a fall more efficiently but also more uncomfortably. These studies are highly essential for the climber, as they provide either practical advice for the climber, or compare and rank different brands of equipment available in the market. The current research and development in the field of instrumented climbing equipment moved from posturographic laboratory studies to more dynamic measurements during training and competition, thereby providing a performance indicator. Usually and conventionally, climbing performance is measured with difficulty scales (UIAA, YDS, French, UK, etc .) either red-point (to lead climb a familiar route without falling or hanging on the rope) or on-sight (to lead a climb without falling or hanging on the rope on the first attempt without any prior information about the route), as well as the World Cup Ranking for top-climbers. Yet, mechanical parameters of climbing proved to provide a more sophisticated kind of measurement, by differentiating between climbing technique and style , experience, and performance related to a single move . The instrumented climbing equipment consists of wall , holds, and force sensors, placed in between, allowing measurement of contact time , forces, impulse, smoothness factor, and friction on a single handhold. Moreover, the force vectors changing with time can be visualised on the hold though vector diagrams. These parameters correlate well with World Cup Rank and training success. Furthermore, they offer advice to the climber in terms of injury prevention. Future equipment developments expected are safety standards and test reports for all kinds of safety gear, recommendation for the climber which equipment to prefer, and to raise the technical standard for these kinds of equipment. Future instrumentation developments will concentrate on fully instrumented climbing walls for performance analysis, by equipping each hold with a 6-DOF transducer; such a wall is currently in development. It is recommended to set up centralised and independent test labs, preferably in collaboration with UIAA , which perform standardised testing of new brands, or newly developed equipment and publishes the main results on the Internet, by comparing them to other existing equipment. This will ensure the availability of data to all climbers.

An Estimation of the Load Rate Imparted to a Climbing Anchor During Fall Arrest Dave Custer Massachusetts Institute of Technology, USA , [email protected]

Abstract. The strengthof ice anchors is, in part, a function of the load rate; increasing the jerk of the decelerating climber reduces anchor strength in brittle ice. To provide a rule of thumb estimate of the load rate imparted to a climbing anchor during fall arrest, a simple, algebraic formula for load rate is derived. As a first approximation, the load rate is proportional to both the rope modulus and the square root of the fall factor and is inversely proportional to the square root of the length of rope between the belayer and the falling climber. Load rate considerations suggest that ice climbers should use low modulus ropes and avoid high fall factor falls close to the anchor.

1 Introduction Load rate, the time derivative of force, is unimportant in most climbing situations because the components of the safety system are not affected by changes in load rate over the range of values that can occur during fall arrest. For example, metal equipment is expected to be slightly stronger at higher loading rates (Newby 1985). Further, the strength of granite, a rock favored by climbers, also exhib its little change over several orders of magnitude changes in strain rate, and some rock types increase in strength with increased strain rate (Lockner 1995). In contrast, the strength of ice anchors decreases with increasing load rate. While the metal ice screw itself is unaffected, a two order of magnitude increase in strain rate roughly halves the ice strength (Gold 1977). Tests on ice anchors show a similar halving of strength with a: two order of magnitude increase in loading rate (Blair, Custer, Alziati , Bennett 2004) . This phenomenon is complicated by the fact that ductile ice exhibits an increase in strength with increased strain rates . Further complications are the paucity of data and conflict in existing data that pinpoints the brittle /ductile transition at temperatures above -40°C, temperatures at which most ice climbing occurs (Arakawa, Maeno 1997). Nonetheless, the documented decrease in ice and ice anchor strength at higher load rates suggests that climbers need to understand and control the loading rate of ice anchors. To this end, a (very) simple model of a climbing fall is used to derive an algebraic formula to estimate the load rate imparted to a climbing anchor during fall arrest, and this simple model is compared to more realistic models and to existing experimental data .

46

Dave Custer

2 Development of a Simple Estimate of Load Rate The geometry of the roped climbing game determines the load rate that results from a fall. Typically, the belayer is anchored at a stance, and the climber progresses up. The rope connecting the two is clipped into intermediate anchors to reduce the distance the climber would drop in the event of a fall. Should a fall occur, the potential energy of the climber is converted into spring energy in the rope and into heat energy in the rope and at the belayer and the top anchor (Fig. I) . An estimate of the resulting load rate can be developed by equating the potential energy of the falling climber with the spring and heat energy stored in the rope at full extension . Because the resulting model is better suited for spread sheet or finite element analysis than for rule of thumb estimation by climbers, a very simple model (VSM) is developed in which the potential energy of the falling climber is converted only into spring energy. The VSM is then compared to more complicated models that take the various non-spring energies into account. Additionally, the VSM is compared to empirical fall data.

Fig. 1. Where energy goes in the roped climbing game . Figure 1a shows the roped climbing game with a belayer anchored at a stance and the climber above an intermediate anchor . In the event of a fall, the climber falls a distance h, and the rope, length I, will stretch a distance y . Figure Ib shows the situation after the fall when the rope is maximally stretched . The potential energy of the falling climber has been converted to heat energy at the top anchor (d), spring and damping energy imparted to the rope (rsd), and energy lost at the belayer (bb). The inset in Fig. Ib shows the capstan effect of the rope loaded over the carabiner at the top ancho r. Typically, the tension of the rope section between the anchor and the climber is approximately twice that of the rope between the belayer and the anchor (Pavier 1998; McMillan 2003) .

2.1 The Very Simple Model (VSM) of Rope Behavior A simple understanding of rope behavior can be derived by modeling a rope as a spring and by equating the potential energy of the falling climber with kinetic energy as the rope engages; in tum, the kinetic energy is also equated with the energy stored

An Estimation of the Load Rate Imparted to a Climbing Anchor During Fall Arrest

47

in the spring at its maximum extension. Figures 2a-2c show "snapshots" of the falling climber along with the associated quantities and approximations ; Fig. 2d provides an overview of the resulting differential equation, its solutions, and the resulting VSM estimate for load rate. Load rate is proportional to the rope modulus, M, the product of the Young's modulus of the rope material and the rope's cross sectional area (thus, the rope's spring constant, k, is equal to MIl) ; load rate is proportional to the square root of the fall factor, F, the ratio of fall height to rope length, h//; and load rate is inversely proportional to the square root of the rope length, I. This reduction of load rate with increasing rope length may be counterintuitive because everyday experience suggests that longer falls have more severe consequences . Another counterintuitive result is that the load rate is independent of the climber mass. Simple mass/spring oscillation:

f =ky =-my

Boundary conditions :

mgh=±my;"" =±ky;""

m

I

T----------

Solutions:

y =.J2iFi cos(at)

11,-------_ ___ ..1-

Fig.2a.

g/ F . jzm --;w- sm(at) 2

y=

y

w=l

..

... MW cOS()

Y = --;;;Vi /-

_

Fig.2b.

JZ gFM .

Y= - - m- sm(at)

(0/

Load rate:

Fig.2c.

Fig. 2d.

IdJ;'ll =M

[dil

WCOS(at) Vi

Fig. 2. The derivation of the very simple model (VSM) ofjerk during climbing fall arrest. Figure 2a shows the climber just before falling; all the climber 's energy is gravitational potential energy, mgh. Figure 2b shows the climber just as the rope begins to pull taught ; all the energy is kinetic, Y2mi. Figure 2c shows the climber at the maximum rope extension; the fall energy has all been converted to energy stored in the rope spring, Y2k/ (Wexler 1950). Figure 2d develops the equations governing the VSM, culminating in an expression for the load rate.

2.2 Comparison of the VSM to Models that Include Friction Losses and the Potential Energy Produced by Rope Stretch The model developed in 2.1 is quite simple and deserves to be compared to models that include the potential energy due to rope stretch, friction at the carabiner, the damping effect of the rope, and the effects of belayer behavior and energy absorbing systems (EAS). To include the gravitational potential energy of the climber due to rope stretch, y, the development in Fig. 2 needs one modification, the inclusion of an additional potential energy term in the boundary conditions such that the potential energy of both the fall and the stretch equals the energy stored in the spring at maximum extension: mgh+mgymax=Y2kl max' The solution to this quadratic yields the Wexler Equa-

48

DaveCuster

tion, Eq. I, for the tension in the rope. The differential equation itself remains unchanged, so the frequency of oscillation is also unchanged (Wexler 1950). The force predicted by Eq. I is larger than that of the VSM because the addition of the potential energy associated with the spring stretch results in an increase in spring energy and thus force. Equation I predicts load rates slightly (-10%) higher than the VSM predictions, but the load rate remains roughly proportional to the rope modulus, M, and the square root of the fall factor over the rope length, (F/I)I/2 . (I)

Another observation drawn from Eq. I is that the MF/mg term is the product of the energy component proportional to / and the energy component that is independent of y . Thus, Eq. I can be used to estimate forces resulting from situations in which energy is lost due to friction, damping in the rope, and other energy absorbing phenomena such as belayer behavior or EAS. The inclusion of a carabiner at the top anchor has two related effects on the load transmitted to the anchor. The friction at the top anchor affects the load rate by effectively reducing the length of the rope. The extreme cases can be shown by inspection: no friction loss makes the full rope length available to absorb energy, and complete "binding" at the top carabiner reduces the length of rope available to absorb energy to half the fall height. In typical climbing situations, the ratio of rope tensions on either side of the anchor carabiner, y, is about 2:I (McMillan 2004) . Energy is lost to friction proportional both to the difference of tensions in the rope on either side of the top carabiner and to the stretch of the rope section between the belayer and the top anchor . Equation 2 shows the effective rope length as a function of rope length, fall factor, and the ratio of rope tensions across the anchor carabiner. This reduced effective rope length increases the load rate, but does not alter the proportionality of load rate to M or (F/I)1!2.

'effective

=,

(1-~) 2

1

F +-

r

(2)

A spring-dashpot model of the rope has been developed that closely matches empirical data (Pavier 1998). The inclusion of a dash pot in the rope model reduces the maximum force and increases the time it takes to reach the maximum force . Using the values of rope moduli and damping coefficient from Pavier, estimates of the effect of damping on the load rate can be derived by estimating the ratio of energy absorbed by damping to energy absorbed in the spring, which is about I : I. Thus, the MF/mg term in Eq. I is halved, and the maximum force is reduced by a factor of the square root of 2; a I: I ratio of spring to damping energy produces a 45° phase lag that increases rise time by about 50% . While rope damping reduces the load rate, it In does not effect the dependence of load rate on M or (F/I)- .

An Estimation of the LoadRate Imparted to a Climbing Anchor During FallArrest

49

As with rope damping, any energy lost at the belay, by pulling the belayer upwards or by pulling rope through the belay device, can be deducted from the MF/mg term in Eq. 1. Empirical evidence suggests that belayer behavior can increase the maximum force by at most 15% and decrease the maximum force by as much as 30%. The effect of belayer behavior on the time to maximum force is less well documented, though variations of about 15% can be seen in experimental data (Zantoni 2005; Richard 2003). The effects of belayer behavior on the load rate are difficult to estimate or model. The deployment ofEAS can also yield force reductions of up to 30%, and time to maximum force is increased by the duration of EAS deployment, which can be on the order of the rise time without the EAS (Richard 2003).

3 Testing the VSM In this section, the VSM is tested on the fall data available in Helmut Magdefrau's PhD thesis (Magdefrau 1989). The data comprise two subsets large enough to attempt statistical correlation . The single rope subset contains data for 29 falls on an 11 mm (UIAA "single") rope; the half rope subset contains data for 14 falls on a pair of 8.8 mm (UlAA "half') ropes. The belay device used for both subsets is an antzbremse. Force, rope length, fall height, climber mass, duration of loading, and the rope slip through the belay device are recorded. The researchers used themselves as falling climbers, so high fall factor falls are not represented, nor is there any control for belay technique, as evidenced by the variation in rope slippage through the belay device. The VSM model predicts that within subsets the load rate should be proportional to (F/{) 1I2, and that the load rate between the subsets should differ proportionally to the difference in rope moduli. The scatter plots of load rate vs. (F/{)1 12 are shown in Fig. 3. Indeed, the load rates differ between subsets by about 30%, which would be expected if the rope moduli are proportional to the cross sectional area of the half rope pair and the single rope. The correlation coefficient for the single rope data is 0.2, and hypothesis testing suggests there is little certainty of correlation . When the high slip data points are removed, the correlation is 0.6; hypothesis testing gives 90% confidence that there is a correlation . The half rope data have a correlation coefficient of 0.7 and a 98% confidence of correlation . Similar correlation analyses were calculated from the Wexler and Pavier models using the fall scenarios from the Magdefrau single rope data. Additionally , ±15% noise was added to both force and time results from the Wexler model to simulate belayer behavior . The Wexler and Pavier models show correlation coefficients of 0.99 and 0.93 respectively , with almost certain correlation . The noisy Wexler calculations give a correlation coefficient of 0.77.

4 Conclusion The VSM provides a rule of thumb estimate for the jerk and the resulting loading rate, which is approximately proportional to both the rope modulus and the square root of the fall factor and inversely proportion

50

Dave Custer

nal to the square root of rope length. This relationship changes very little when more complicated models that include rope damping and carabiner friction are invoked. The correlation is greatly reduced by belayer behavior. Climbers can control the loading rate through choice of low modulus ropes, judicious anchor placement in proximity to the belay anchor to reduce the fall factor, and use of EAS. 0.30

...ff 0.25

i

e

e

~~ 00 v

00.

00

0.20

=- 0.15

u:

...

.% • •

0 Q<)

':'0

••

~0 .10 tr

Ul

e single rope • half rope pair

0.05 0.00 0.00

10.00

20.00

30.00

40.00

50.00

Load rate (kN/s)

Fig. 3. Scalier plot of load rate vs. square root of (Flf) for Magdcfrau data.

References Arakawa, M., Maeno, N., (1997), Mechanical strength of poly crystaline ice under uniaxial compression, Cold Regions Science & Technology, 26, 215-229 . Blair, K., Custer, D., Alziati, S., and Bennett, W., (2004) The effect ofload rate , placement angle, and ice type on ice screw failure, The Engineering ofSport 5. Volume 2 (ed . M. Hubbard, R.D.Mehta, and J.M. Pall is), International Sports Engineering Association, Sheffield , UK, 283-289 . Gold, L., (1977) Engineering Properties of Fresh-Water Ice, Journal ofGlaciology , 19, 81,

197-211. Lockner, D., (1995) Rock Failure, Rock Physics and Phase Relation s A Handbook ofPhysical Constants . hltp://www.agu.org/reference/rocklllJockner.pdf, Dec. 17,2005 . Magdefrau, H., (1989) Die Belastung des menschlichen Korpers beim Sturz ins Seil und deren Folgen, dissertation, Ludwig-Maximilians University, translated by David LiaBraaten,

1994. McMillan, N., (2003) How Strong Does Your Climbing Gear Need to Be?, British Mountaineering Council Technical Committee. Note 04103. Newby, J., (1985), ASM Handbook . Vol 8, ASM International, Metals Park, Ohio. Pavier, M. (1998) Experimetal and theoretical simulations of climbing falls , Sports Engineering, 1,79-91. Richard, M, (2003) Modelization of the fall in climbing and mountaineering, Annex 21.2003 U1AA Safety Commission Meeting Minutes. Wexler, A. (1950) The theory of belaying, American Alpine Journal. 7,379-405. Zantoni, C, (2005), Presentation, 2005 UIAA Safety Commission Meeting, Chamonix, France.

Dynamics of Speed Climbing Franz Konstant in Fuss! and GUnther Niegl 2 I

2

Nanyang Technological University, Bioengineering, SG, [email protected] University ofYienna, Anthropology, AT,[email protected]

Abstract. This paperaims to provide the first insight into the dynamics of speed climbing. For this purpose, twojug-type climbing holds were manufactured and instrumented with 3D force transducers. At a speed climbing route, three climbers with different experience levels performed four runs at three different speeds (slow, medium, maximal possible speed). The 36 experiments served to analyse the following parameters: contact timeat the hold, magnitude of contact forces and of the shock spike at initial contact, and the climbing velocity between the two holds. In speedclimbing, the higher the climbing speed, the higher are the finger reaction forces at the hold, the higheris the shock spikeat initial contact, and the shorter is the contact time. As speed is a factor of experience, the contact time and the magnitude of forces also correlate with the experience.

1 Introduction As far as lead climbing and bouldering , two of the three sub-disciplines of sport climbing, are concerned, very few literature sources are available . Most of these sources deal mainly with posturographic studies on experimental climbing walls (Quaine et al. 1997ab, 1999, Testa et al. 1999, 2003, Noe et al. 2001) and kinematic studies (Werner et al. 2000, Bursnall and Messenger, 2000). Yet, to date, there is no literature source available on the biomechanics of speed climbing, the third crown discipline of sport climbing . Due to this fact, it was highly challenging to provide insight into the biomechanics of speed climbing for the first time. In speed climbing , i.e., vertical running up the wall, top speed climbers reach a velocity of approximatel y 2 mls. It was the aim of this study, to investigate speed climbing with instrumented climbing holds and to evaluate which mechanical parameters correlate with the climbing speed.

2 Methods Two sloper holds were designed and manufactured for this study (Fig. I). Each of the two holds was connected to a Kistler force sensor (type 9327, Kistler, Winter-

52

FranzKonstantin Fussand GUnther Niegl

thur, Switzerland), placed between the hold and the aluminium frame (Fig. I) . The holds were moulded from a mixture of epoxy resin and sand. The data sampling frequency during the experiment was 500 Hz. The hardware equipment consisted of Kistler amplifiers (DAQ-5040A23), an AID board (National Instruments) and a laptop. We collected the data with DASYLab 5.6 by Datalog. The 3D piezoelectric transducers returned the forces according to the 3 axes of the co-ordinate system . The co-ordinate system was: x - out of the wall , towards the climber; y - upwards (climbing direction); z - to the left. The experiment was carried out at Climb Adventure Pte Ltd Climbing Gym , Singapore . Two factors were considered for the experiment: the experience of climbers (3 climbers with different experience levels , beginner intermediate, and top speed climber), and the speed of ascend (slow, intermediate, and maximal speed) . Each climber performed the runs at the 3 different speeds four times, resulting in a total of 36 experiments. The climbing wall adapted for the speed climbing experiment is shown in Figure 2. The two instrumented holds of a jug type were placed in the middle of the route such that they will be contacted by the right hand . The mechanical parameters calculated from the raw data were: contact time, forces in y- and x-direction (mean and maximum, normalized to body weight), impulse of y-force , ratio of the x-axis to y-axis forces , magnitude of shock spikes, vector diagrams, and climbing speed in the middle of the route. The latter is defined by the distance between the two instrumented holds (1.2 m) over the time taken by the climber to get from the initial contact of the I st instrumented hold to the initial connd tact of the 2 instrumented hold. All the statistical calculations were carried out in SPSS I 1.0 (Statistical Package for Social Sciences). The level of sign ificance was set at p<0.05.

3 Results Figure I shows the typical curves of the resultant forces on the two instrumented handholds. The shapes of these two graphs are basically identical. At the start of the contact on the handhold, there is a force shock spike, followed by a steep increase in forces to a first peak . The force then decreases to a valley and subsequently up to a second peak, which has a lower maximum force. 'A fter the second peak, the contact forces decrease sharply. The most striking result was the existence of shock spikes (Fig . 2) at the initial hold contact. These spikes are apparent in both vertical and horizontal directions and come from the impact of the hand, when it hits the hold.

Dynamics of Speed Climbing

.. .

..

./

53

I·~

I.

i

J•

Fig. 1. Climbing wall for speed climbing experiment (left side; the instrumented jug holds are in position 3 and 5); jug hold and force sensor (middle) ; resultant force - time graphs of the two instrumented holds (right side; climbing speed approximately 0.73 m/s)

o

...

' -1

•i

.. I

I

u _I-I

I

u

,. I

Fig. 2. Shock spikes in x- and y-direction (right side; forces in abso lute values) ; correla tion between contact time at the 1st (a) and 2nd (b) hold and the climbing velocity (right).

The contact time at the hold and the climbing velocity correlate highly. Figure 2 shows the relationship between contact time (t) at the two instrumented holds and the climbing velocity (v). The regressions are non-linear and follow a power fit: hold 1: t = 0.953 V-1.l09, hold 2: t = 1.135 V--{)·887: The correlation coefficients for the 1st (lower) and 2nd (upper) hold are 0.999 and 0.936 respectively. The next significant effect of velocity is on the mean and maximum resultant forces (normalised to body weight) of the two handholds. The p-values range from p

54

Franz Konstantin Fuss and GUnther Niegl

< 0.001 to 0.002 . The various normalised resultant forces are plotted against velocity (Fig. 3). A logarithmic fit provided the best correlation with coefficients between 0.825 and 0.92. The force - velocity relationship can also be seen in the vector diagrams (Fig. 4), which display the resultant force vectors with time on the hold . The resultant shock spikes and the shock spikes in the x-axis direction are also significantly influenced by the velocity of ascend , at p < 0.001. This can be seen from Figure 3, where the shock spikes are plotted against the velocity. The shock spikes in the direction of the x-axis are negative because the direction of the shock spikes is into the wall. The correlation was evaluated with a linear fit. The correlation coefficients are between 0.8 and 0.884. This relationship shows that the higher the speed of ascend , the higher are the shock spikes . Experience of the climber has a significant effect on maximal velocity of ascend (p
66

• II

~

J

I

II

L.

•

•

I ..

L. ..

u _lWoI

OJ

..

..-• .....

0 h

..

..

Y_I-I

rP

"

Fig. 3. Resultant forces (normalized to body weight) vs. velocity (left side; a = maximal value at 151 hold, b = maximal value at 2 nd hold, c = mean value at 151 hold, d = mean value at 2nd hold); shock spikes vs. velocity (right side; e = resultant shock spike at 2nd hold, f = resultant shock spike at 151 hold, g = shock spike in x-direction at 1st hold, h = shock spike in x-direction at 2 nd hold)

Dynamics of SpeedClimbing

a

b

55

c

Fig. 4. Vectordiagrams at different speeds (a: fast, 0.3-0.7 mis, b: medium, 0.7-1.1 mis, c: low, 1.1-1.5 mls); the resultant vectorspointupwards and towards the wall (side view); the vertical bar on the left side corresponds to a force vectorof 500 N.

4 Discussion Speed climbing can be compared to horizontal level walking and running: the higher the velocity, the shorter is the contact time (duration of stance phase in walking and running) , and the higher are the forces (ground reaction forces in walking and running). Furthermore, a shock spike is also present in speed climbing. The spike at the fingers has two components, one in y-direction (upward), the other in x-direction (towards the wall) , which coincide in time. This stands in contrast to walking, where the vertical shock spike at the heel occurs later then the horizontal claw-back spike . It is evident that the maximal speed of a climber depends on his experience and training level. As a short contact time, high finger reaction forces, and high shock spikes correlate with high velocity, it is not further astonishing that these parameters also correlate with experience. At this point, a striking difference becomes apparent: in lead climbers, the better a climber, the smaller are the contact forces at the hold ' (Fuss and Niegl, 2006) ; in speed climbers, the opposite is true, i.e., the better the climber and thus the faster, the higher are the contact forces . In lead climbers , the magnitude of these forces depends on how economical the climbing style is; in speed climbers, the force is a function of speed . Yet, these contact forces do not linearly increase with speed: at higher speeds , the force-velocity function flattens out and increases at a smaller rate than the velocity does (Fig. 3a). This fact does not substantially increase the risk of overuse syndromes and finger injuries , as big velocity differences at higher speeds result into only small force differences. The shock spike, however, increases linearly with speed . Shock spikes are generally know for causing overuse syndromes when experienced at a high frequency over a longer period (e.g., running : chronic knee injuries due to running on hard ground with inadequate shoes; navicular disease in shod horses with a steep fetlock angle) . Speed climbing , how-

56

Franz Konstantin Fuss and GUnther Niegl

ever, is applied only for a couple of seconds (top athletes climb 20 m in about 13 s), hence the risk of overuse syndromes in individual climbs is small and depends on the train ing frequenc y. The contact time at the first instrumented hold correlates perfectly with the velocity by following a power function (line "a" in Fig. 2). The contact time at the second instrumented hold displays the same correlation although the data points are more scattered (line "b" in Fig. 2). The reason for this is that the climbing speed between the two instrumented holds was calculated from the distance in between and the time between the two contacts. As the first contact provides the thrust for cove ring the distance between the two holds, it is the first contact time which show s a higher correlation.

5 Conclusion In speed climbing, the higher the climbing speed , the higher are the finger reaction forces at the hold, the higher is the shock spike at initial contact, and the shorter is the cont act time. Speed climbers should be aware of the fact that big velocity difference s at higher speeds result into small finger force difference s, wh ich in tum doe s not substantially increase the risk of injurie s. The shock spike at initial contact, howe ver, increases linearl y with speed and bears the risk of overuse syndromes, depending on the training frequency.

References Fuss, F. K. and Niegl, G. (2006) Instrumented Climbing Holds and Dynam ics of Sport Climbing. In: E.F. Moritz and S. Haake (Eds), The Engineering ofSport 6. Sprin ger, Munich. Noe, F., Quain, F. and Martin , L. (200 I) Influence of steep gradient supporting walls in rock climbing: biomechan ical analysis. Gait Posture, 13, 86-94. Quaine, F. and Martin, L. (1999 ) A biom echanical study of equilibrium in sport rock climbing. Ga it Posture, 10, 233-239. Qua ine, F., Martin , L. and BIanchi, J.-P . ( 1997a) Effect of a leg movement the organisation of the forces at the hold s in a climbing position: 3-D kinetic analysis. Hum . Mov. Sci., 16, 337-346. Quaine, F., Martin , L. and BIanchi, J.-P. (1997b) The effect of body position and number of supports on wall reaction forces in rock climbing. J. App!. Biomech ., 13, 14-23. Test a, M., Mart in, L. and Debu, B. ( 1999) Effects of the type of holds and movement amplitude on postural control assoc iated with a climbing task. J. Gait Posture, 9, 57-64. Testa , M., Martin , L. and Dcbu, B. (2003) 3D analysis of posturo-kinetic coordin ation associ ated with a climbing task in ch ildre n and teenagers. Ncurosc i. Lett., 336, 45-49. Bursnall J. and Messe nger N. (2000) Analysis of cli mbing techn ique using the ProReflex 3d mot ion analysis sys tem. In: N. Messenger, W. Patterson and D. Brook (Eds.) The Science a/Climbing and Mountaineering. Human Kinet ics Software, Champaign, IL, C D-RO M. Werner I., Gebert W. and Kauer B. (2000). Three dim ension al analysis of rock climbing techniques. In: N. Messenger, W. Patterson and D. Brook (Eds.) The Science a/Climbing and Mountaineering. Human Kinetics Softw are , Champaign, IL, CD-ROM.

Instrumented Climbing Holds and Dynamics of Sport Climbing Franz Konstantin Fu ss' and Gunther Niegf , Nanyang Technological University, Bioengineering, SG, [email protected] University of Vienna, Anthropology, AT, [email protected]

2

Abstract. This paper gives an overview of usage of instrumented climbing holds (equipped with force sensors) for assessing the performance of a climber, be it during training or competition, as well as assessment of training progress and success, gripping techniques, and value of equipment (e.g., chalk). The experience of the climber is expressed by a short contact time, a lower force at the handhold, a low impulse, and high friction. During training, the contact time, mean force, maximal force, and impulse decrease whereas the mean and maximal friction and the smoothness factor increase. There is no difference between dry hand and liquidchalked hands, between dry and wet hands, and between powder-chalked hand on a clean surface and dry hand on a messy surface. However, powder chalk is far better than liquid chalk or a dry hand, and on messy surfaces, a dry hand is better than a powder-chalked hand. The higher a climber jumps during double-dynoing, and the more fatigued he is during bouldering, the lower are the finger reaction forces and thus the injury risk.

1 Introduction The research group at University of Grenoble, France (Quaine, Martin and Bianchi, 1997a, 1997b ; Quaine and Martin, 1999 ; Noe, Quaine and Martin, 2001 ; Testa, Martin and Debu, 1999,2003) has used instrumented climbing holds for posturographic studies on experimental laboratory climbing walls. These used sterile standard conditions, equipped with strain-gauged holds for analysis of the weight shift, and load distribution, from 4-limb contact to 3-limb contact when moving upward. In addition, the overall acceleration, and after subsequent integrations, the velocity as well as displacement of the centre of mass of the body are obtained. Qu aine, Vigouroux and Martin (2003) investigated individual forces applied by the fingers in different crimp positions. The data for the finger tip force s were collected in a seated posture (and not during climbing) in which the test subjects exerted a horizontal force on the force sensors in three different finger postures: extended crimp, opened crimp and closed crimp without the usage of the thumb. Li, Margetts and Fowler (2001) calculated the static friction coefficient between the hand and different rock surfaces by measuring the normal and tangential forces with stra in gauges and detecting slippage with a potentiometer. Non-chalk contact

58

Franz Konstantin Fuss and GUnther Nicgl

between hand and rock produced a friction coefficient of 3 whereas chalk reduced the coefficient to 2.5. Consequently, Li et al. (200I) considered 'chalking' a myth. The goal of the present studies was to apply instrumented climbing holds to real sport climbing situations (competition and training; difficult climbing and bouldering) rather than to laboratory conditions, as well as to reinvestigate the influence of chalking. Eight different studies have been carried out so far, related to (I) mechanical parameters of climbing during competition, (2) influence of experience on the mechanical parameters of climbing during competition, (3) training influence on the mechanics of climbing, (4) friction between hand and climbing hold under different conditions, (5) mechanics of the double dyno technique, (6) mechanics of the pinch grip, (7) finger load distribution during climbing, and (8) fatigue influence on the mechanical parametersof climbing.

2 Methods For all instrumented holds used, the forces were measured with from 1-4 Kistler force sensors per hold (type 9317 and 9327, Kistler, Winterthur, Switzerland), placed between the wall and one handhold. The data sampling frequency was 100-200 Hz. The hardware equipment consisted of Kistler amplifiers (DAQ-5040A23), an AID board (National Instruments) and a laptop. The data was collected with DASYLab 5.6 (Datalog). The 3D piezoelectric transducers returned the forces in the 3 axes of the co-ordinate system. The co-ordinate system was: x out of the wall, towards the climber; y upwards (climbing direction); z to the left. The usage of two force sensors in the y-direction allowed calculation of the moment about the z-axis, and the centre of pressure (COP, origin of the force vector) in the xy-plane on the hold surface. For this task, the surface of the hold was digitised in the xy-plane and a lSI, 3'd, 9th, or io" order polynomial regression function was determined with respect to the original sensor co-ordinate system, depending on the nature of the curvature. Thus, the y-coordinateof the COP (Y eop) is a function of X coP. Yc OP = f (XCOf

»

(I)

The moment equilibrium, calculated from Fx and F , (external forces applied to the handhold, calculated from the sensor forces measured), Mz (the moment about the z-axis), Ycop and Xeo? , becomes

Mz - Fx Yco? + FrXcop = 0

(2)

After substituting Eq. (I) into Eq. (2), the resulting equation was solved for Xcop with Matlab (MathWorks). In the case of more than one root, the selection of the correct root was based on a continuous COP movement. The vector diagrams together with the handhold surface were reconstructed in AutoCAD 2000 (Autodesk). The vectors (Fig. 2) thereby were positioned on the hold, yet they were directed towards the hand, comparable to standard vector diagrams in clinical gait analysis (Pedotti or butterfly diagrams). The mechanical parameters of handhold-hand interaction, calculated subsequently with respect to time were: I) contact time, 2) force in y-direction (vertical

Instrumented Climbing Holds and Dynamics of Sport Climbing

59

force), 3) force in x-direction (sagittal force) , 4) resultant force,S) angle of the resultant force (in the xy-plane), 6) position of the resultant force (COP), 7) impulse of the y-force , 8) instantaneous friction (I'i), 9) smoothness factor (SF), and 10) vector diagram (20 in the xy-plane). The instantaneous friction (I'i) is the tangential force divided by the normal force, by converting x- and y-forces into normal and tangential components according to the position of the COP and the slope at the COP (first derivative of Eq. I). The instantaneous friction (I'i) changes with time and is not related to the static or dynamic friction coefficient, as during climbing, u, occurs usually before impending slippage. The dimensionless smoothness factor (SF) is the body weight divided by the mean of the absolute difference (in N) between the yforce-time graph and a parabolic curve of the same impulse . The parabolic curve serves as a model for the ideal force time graph of the handhold contact. The closer the y-force-time graph approaches a parabolic curve, the smoother is the force application , and the higher the SF. The parabolic force(F)-time(t) graph was calculated from Eq. 3, in which T is the total handhold-hand contact time, and J is the impulse of the actual y-force-time graph . F=(t/T-(t/7)2) (6J/7)

(3)

Fig. 1. Differentinstrumented holds (see below)

The events and instrumented holds at the 8 different studies were : (I) Mechanical parameters of climbing during competition: National Climbing Championship of Singapore, men's semifinal (n=30), at the National Rock Climbing Centre, SAFRA Yishun Country Club, on 17 August 2002 ; jug type hold (Fig. I-a) . (2) Influence of experience on the mechanical parameters of climbing during competition: UIAA-ICC Sport Climbing World Cup, ladies ' quarter-final (n=23 ; all top-6 climbers and 15 of the top-25 climbers of the then current world rank list), Singapore EXPO, 24 August 2002; curved sloper (Fig . I-b,c), at a 15° overhang. (3) Training influence on the mechanics of climbing: training session at National Rock Climbing Centre, Singapore, 17 mm deep edge (Fig. I-d ,e), self-manufactured. (4) Friction between hand and climbing hold under different conditions: Nanyang Technological University, Singapore; self-manufactured horizontal hold with surface of an artificial climbing hold and under different conditions (see results) (5) Mechanics of the double dyno technique: training session at National Rock Climbing Centre , Singapore; self-manufactured jug type (Fig. I-f) .

60

FranzKonstantin Fuss and GUnther Niegl

(6) Mechanics of the pinch grip : training session at National Rock Climbing Centre, Singapore; self-manufactured CNC-machined pinch grip type (Fig . I-g ,h,i) with 4 force sensors for independent measurement of finger and thumb forces. (7) Finger load distribution during climbing: training session at Climb Adventure Pte Ltd Gym, Keppel Towers, Singapore; self-manufactured CNC -machined edge (Fig . I-j,k) with 4 force sensors for independent measurement of all 4 fingers. (8) Fatigue influence on the mechanical parameters of climbing: bouldering session at Climb Adventure Pte Ltd Gym, Keppel Towers , Singapore; 4 selfmanufactured edges, 15 mm - 50 mm deep (Fig . I-I).

3 Results (I) Mechanical parameters of climbing during competition: the contact time was 7.93 ± 2.89 s (mean ± standard dev), the mean resultant force 117.0 ± 30.6 N, the impulse 897 ± 296 Ns, the mean friction 0.316 ± 0.129, the maximal friction 0.608 ± 0.210, and the smoothness factor was 24.6 ± 10.4. The force applied during the setup phase is still low, about 30 N on average (Fig. 2a,b). The beginning of the crank phase is marked by a sudden rise of the force, which reaches 163 N on average. The force during the lock-off phase is 62 N on average, and the friction is far higher (0.34) than during the first two phases (0.05). (2) Influence of experience on the mechanical parameters of climbing during competition: the contact time was 8.24±5.03 s, the mean resultant force 100.0±30.1 N, the impulse 786±435Ns, the mean friction 0.40 I±0.189 , the maximal friction 0.626±0.225 , and the smoothness factor was 18.1±8.0. Generally, the experience of a climber is expressed by a short contact time , a lower force at the handhold, a low impulse , and a high friction (greater inclination of force vectors; Fig. 2c,d) . The better the climber is, the higher is the rate of reaching a high friction . The climbers were divided into three groups, according to the world rank list after updating the World Cup results of Singapore. The percentage of the climbers per group, producing a mean friction > 0.5 was : group I (rank <30): 42% >0.5; group 2 (rank 30-60): 33% >0.5; group 3 (rank >60): 20% >0.5. Thus, it appears that better climbers can produce a higher friction, even if there is no need to do so. A high positive correlation could be found between smoothness factor and friction (r = 0.916) . (3) Training influence on the mechanics of climbing: the climbers had to climb a route eight times. The mechanical parameters were tested as to a significant difference (p :S 0.05) between first and last 2, 3, and 4 climbs . The contact time, mean force, maximal force, and impulse decreased significantly from first to last 2, 3, and 4 climbs . The mean and maximal friction and the smoothness factor increased significantly from first to last 4 climbs . Thus, the mechanical parameters behaved as expected and the training effect could be proven . (4) Friction between hand and climbing hold under different conditions (static friction coefficient in parentheses): I) dry hand (0.722 ± 0.087), 2) wet hand (0.675 ± 0.164),3) hand covered with powder chalk (chalk bag, MgC0 3 ; 0.958 ± 0.145) , 4) hand covered with liquid chalk and left to dry (,Pure Grip ' liquid chalk , by Beal , Vienne, France; 0.763 ± 0.155), 5) dry hand on messy surface (covered with liquid

Instrumented Climbing Holds and Dynamics ofSport Climbing

61

chalk; 0.925 ± 0.072),6) hand covered with powder chalk on messy surface (0.650 ± 0.089). The moving COP indicated the onset of slippage; the static friction coefficient was determined on the graphs displaying friction (tangential force over normal force) versus displacement of the COP; the static friction coefficient is marked by a sharp bend of the graph. The results revealed that there is no significant difference between dry hand and liquid-chalked hand, between dry and wet hand and between powder-chalked hand on clean surface and dry hand on messy surface. However, powder chalk is far better than liquid chalk or a dry hand, and on messy (polluted with chalk) surfaces, a dry hand is better than a powder-chalked hand. (5) Mechanics of the double dyno technique: from the forces at the lower handhold and the two footholds, the take-off velocity and the jumping height were calculated. The results showed that in unsuccessful jumps, the take-off velocity is too low. In successfuljumps the climber jumps higher than required and lunges for the upper hold far before the dead point. Furthermore, the closer to the dead point the climber latches the upper handhold, the higher is the peak reaction force at the fingers. The advice for the climber is to jump higher than necessary, and to grab the handhold as early as possible (before the dead point). This results into a high success rate and a minimal finger injury risk. (6) Mechanics of the pinch grip: in the pinch grip, the force of the thumb is about 1/5 - 1/4 of the finger force (Fig. 2e,t). The friction at the thumb is 2-3 times higher than that of the fingers. Friction and forces on fingers and thumb increase with the wall inclination; the finger forces increase more than the thumb forces do. Finger mean resultant force (in multiples of the body weight) at 5° and 30° wall inclination: 0.275±0.047 and 0.395±0.038. Thumb force at 5° and 30°: 0.067±0.012 and 0.077±0.016. Finger friction at 5° and 30°: 0.222±0.066 and 0.376±0.062. Thumb friction at 5° and 30°: 0.460±0.099 and 0.657±0.232. (7) Finger load distribution during climbing: we compared three different grip types: closed crimp, open crimp, and open-hand grip. The greater force was applied by the index finger in the closed crimp whereas the middle finger applied the significant force in comparison with the index and the ring finger for both open crimp and open-hand grip. The latter 2 have a similar force distribution shape, but the closed crimp has a descending distribution with the index having maximum force to the little finger with the minimum force. The force distribution of the closed crimp correlates to the previous works. The normal mean force (downward vertical force) of the 4 fingers, index, middle, ring, and little, during the closed crimp was 34.1 %, 28.8%,22.4%, 14.6% respectively, during the open crimp 23.6%, 30.1%, 25.6%, 20.8%, and during the open hand grip 24.0%, 30.3%, 26.8%, 18.8%. The distribution of the horizontal mean force (out of the wall towards the climber) was: closed crimp - 42.8%, 24.0%, 21.6%, 11.6%, open crimp - 28.0%, 30.6%, 24.5%, 16.1 %, open hand grip - 25.1 %, 34.2%, 25.5%, 15.1 %. (8) Fatigue influence on the mechanical parameters of climbing: finger reaction forces were measured with instrumented holds during climbing a difficult bouldering route. The fatigue level of the participants was assessed according to the Borg scale. The mechanical parameters were correlated to the fatigue level. Once fatigue sets in, the force at the holds drops more than 10% between two groups of Borg < 5.5 and

62

Franz Konstantin Fuss and Gunther Niegl

Borg > 5.5 . This indicates that a fatiguing climber exert less force on the handholds, which, in tum, leads to a lower injury risk during fatigue. 2

2

2

b

Fig. 2. Different vector diagrams; a, b: National Championship (\ =set-up, 2=crank, 3=lockoft); c, d: World Cup (c is more experienced than d); e, f: pinch grip at 5° and 30° wall.

4 Discussion and Conclusion Instrumented climbing holds provide a useful tool for assessing the performance of a climber, be it during training or competition, as well as training progress and success, gripping techniques, equipment, and result in feedback advice for climbers, e.g., lower injury risk while fatiguing, and higher risk for perfect dead-pointing. Specifically, the results of Li et al. (200 I) could not be verified: chalk is not a 'myth' as it provides higher friction than a dry hand. However, on messy ('chalked') surfaces, a dry hand is significantly better than a powder-chalked hand. The latter fact is important for competitions, as this indicates a clear disadvantage of climbers who start first, even if the route setters clean the holds during the competition. A hold cannot be cleaned perfectly by a brush and gets messy faster than a washed hold.

References Li, F. X., Margetts, S. and Fowler, I. (2001) Use of ,chalk' in rock climbing: sine qua non or myth? 1 Sports Sci., 19,427-432. Noe, F., Quain, F. and Martin, L. (2001) Influence of steep gradient supporting walls in rock climbing: biomechanical analysis. Gait Posture, 13,86-94. Quaine, F. and Martin, L. (1999) A biomechanical study of equilibrium in sport rock climbing. Gait Posture, 10,233-239. Quaine, F., Martin, L. and BIanchi, l-P. (\ 997a) Effect of a leg movement the organisation of the forces at the holds in a climbing position. Hum. Mov. Sci., 16,337-346. Quaine, F., Martin, L. and Bianchi, l-P. (\997b) The effect of body position and number of supports on wall reaction forces in rock climbing. J. Appl. Biomech., 13, 14-23. Quaine, F., Vigouroux, L. and Martin, L. (2003) Effect of simulated rock climbing finger postures on force sharing among the fingers. Clin. Biomech. 18,385-388. Testa, M., Martin, L. and Debu, B. (\999) Effects of the type of holds and movement amplitude on postural control associated with a climbing task. J. Gait Posture, 9, 57-64. Testa, M., Martin, L. and Debu, B. (2003) 3D analysis ofposturo-kinetic coordination associated with a climbing task in children and teenagers. Neurosci. Lett., 336,45--49.

Forces Generated in a Climbing Rope During a Fall Andrew Phillips', Jeff Vogwell' , Alan Bramley' 'University of Bath, UK, Department of Mechanical Engineering. UK, Department of Mechanical Engineering. lVogw [email protected] 3University of Bath, UK, Department of Mechanical [email protected] 2University of Bath,

Abstract. The use of micro-protection is key to thedevelopment of the sport of rock climbing as harder, blanker rock faces arc attempted. However in many situations the force of a fall will be severe enough to injure a climber or exceed the strength of this equipment and so an improved understanding of the factors affecting maximum impact force and subsequent minimisation of this force is essential for the safe use of micro-protection. A laboratory scale rig has been designed to measure the impact forces generated during simulated simple climbing falls. The results show an increase in force with subsequent falls on the same rope due to irreversible damage, however this effect becomes saturated after a certain number of falls . A simple analysis using a linear rope stiffness is described and its predictions compared with the experimental results. The theoretical forceequation is generally found to be valid.

1 Introduction Rock climbing as a sport has been in existence for over ISO years during which time there have been major improvements in the safety equipment used. From rudimentary beginnings modem equipment is now based on sound scientific principles and has greatly reduced the risks involved (Smith 1998). Standards and popularity have risen phenomenally over the last 50 years and for the average climber the sport is now considered relatively safe. For those pushing the limits however the risks are still significant and a thorough understanding of the capabilities and limitations of their equipment is essential. The principles of traditional rock climbing involve the ascent of a rock face using only natural features and technical climbing ability. Safety equipment is used to guard against the consequences of a slip or fall rather than a direct mechanical aid. The behaviour of the rope is therefore crucial and this paper is concerned with the validation of a simple analysis for the rope forces generated in a fall, the effect of the knot used to attach the rope and the effect of repeated falls and associated rest periods on the magnitude of these forces. An earlier theoretical analysis of this situation has been provided (Pavier 1998)

2 Analysis The forces generated in the climbing rope during a simple fall can be determined by considering the conversion of the potential energy of the falling climber into strain energy of the extending rope. A simple analysis can be derived by assuming linear elasticity of the rope which in reality will be visco-elastic. The model used is shown in Fig 1. A climber runs out a length of rope I above the second (the belayer) who is

64

Andrew Phillips, JeffVogwell, Alan Bramley

at a distance h/2 when a fall occurs. After falling a distance h the rope starts to provide a restriction. This conversion of potential energ y into strain energ y is given by Eq. I . " [F ORI: "'AI.I .

A.fTF.R FAL l.

Second

Flg.I , Geometry of simple climbing fall

EAt52 mgh+mgt5=-(I ) 21 where E is the tensile elastic modulu s of the rope and A its cross sectional area . The force F generated in the rope is given by Hooke ' s law as

F = EAI5

(2)

I

Solv ing Eq.1 for

Substituting for

0 0

gives

from Eq.2 gives

s = mgl [1+ 1+ 2AEh ] EA

mgl

2AEh] F=mg 1+ 1+-[ mgl

(3)

(4)

Thu s for a climber of weight mg using a rope of stiffness EAII, the maximum theoretical tens ion generated in the rope is dependent on the ratio hi/. This ratio, often referred to as the "fall factor" by climber s enables an assessment of the integrity of the safety chain in any given situation .

Forces Generated in a Climbing Rope During a Fall

65

3 Experiments A simple rig was constructed to enable drop weight test to be performed on a suspended rope up to a maximum drop height of 790 mm. Instrumentation was provided to measure the forces generated in the rope. Static tests were used to determine the nominal stiffness values of the rope The rope used throughout the tests was 9 mm Edelris Rocky Half. The typical behaviourof the rope during a drop test at maximum length is shown in Fig. 2. The weight used was a 55 kg mass and this corresponds to the recorded force (-0.5 kN) as the mass is suspended from the load measuring device. The maximum force recorded of 3 kN corresponds to about six times the static weight. 3.5 3

-:::Z

....

2. 2

II;

Q

t.z.

1.5

0.5 0

0

'f\.,,-lL . .J..... 2

3

4

5

Tim e ( ) Fig .2. Typical force time relation during a drop test with a rope length of 855 mm, a drop

height of 790 mm and a falling mass of 55 kg.

The effects of various rest periods on maximum impact force generated was investigated with the rope knotted to the mass carrier and using the mass of 55 kg. An initial drop test was carried out on three new rope samples from the maximum height of 790mm and total length of 855mm. In each case the mass was then left to hang statically on the rope for 5 minutes before being raised to the release position. For the first rope sample a second drop was carried out after a rest period of 5 minutes, for the second sample the second drop occurred after a rest period of 30 minutes and for the third sample the rest period was 60 hours. At the beginning of each rest period the knot was loosened and reset to its original dimensions. The results are shown in Fig.3. Each of the initial drops occurred under identical conditions so these results have been averaged. Despite minor variation, rest period appears to have little effect on the impact force of a subsequent drop or fall under these conditions. These conditions are clearly sufficient to cause permanent damage and the resultant increased impact force, being greater than mg is significant. This

66

Andrew Phillips, JeffVogwell, Alan Bramley

supports recommendations that ropes be disposed of if subject to fall factors of I or above . Clearly, however, the increase in stiffness due to the tightening of the knot during a fall is much less than that occurring as a result of permanent damage. -15

r-----------------.,

Average Ma imum Imp C1 Force of First Drop

-I

3S

Z

3

~ u

I"'

• Imp

25

~ 0

"-

o Imp

IS

t Force of cond drop w ith untightened knot

0.5 0

C1 Force of

ond Drop

2

SOlin

30min

60hr

Rest Period

Fig. 3. Effect of rest period on maximum impact force.

The effect of rapid consecutive drops on maximum impact force was investigated. The rope attached to the mass carrier with a knot and using the full mass of 55 kg, an initial drop test was carried out on one new rope sample of total length of 855mm from the maximum height of 790mm and. This remained under a static load for 5 minutes before being raised to the release position. After a 5 minute rest period a second drop was carried out. Maintaini ng the same intermediate static load and rest period a total of six consecutive drops were carried out. A total rope length of 855mm was again used. This series of tests was then repeated but excluding the knot. The results are shown in Fig 4. The results suggest that the increasing stiffness from repeating drops appears to saturate. It is also apparent that the increased force reduces the safety margin available for the climber. 6

~

4

""';;'

3

Z

eo

....... IncludingKnot __ Excluding Knot

"- 2

O l.-.._ _.L..-_ _.l..-_ _....L..._ _....L..._ _....L.._ _....L.._ _....J

o

2

4

6

7

Drop No.

Fig. 4. Variation of impact force with consecutive drop tests

The effect of varying the Fall Factor was investigated used a rope attached but excluding a knot and a falling mass of 55kg . Using the full rope length of 855mm, 5 new samples were tested each with a different drop height from 790mm to 190mm in steps of l50mm corresponding to a reduction in fall factor from 0.92 to 0.22. Each sample is only subject to one test. Using the linear tensile modulus (hence stiffness)

Forces Generated in a Climbing Rope During a Fall

67

value calculated from the earlier static tests Eq. 4 can be evaluated to give predicted impact forces for a range of fall factors. This is shown in Fig.5 along with the actual experimental results obtained by varying drop height with a constant rope length. As can be seen there is good correlation between the experimental and theoretical data in terms of the shape of the curve the experimental data is at a lower force than the theoretical. This suggests two things; EqA is potentially valid for this situation, but the empirical stiffness value is possibly inaccurate resulting in the higher theoretical values. Alternatively friction at the sliding interfaces reduces the maximum kinetic energy of the mass. 3.5

Z

"'';;'" ~

2.5

2

~ 1.5

• -

0.5

ExperimentalData Theoretical databasedon empiricallinear stiffnessvalue

o'--_ _--'-_ _ ----'-_ _---'

0.00

0.40

0.20

..L-_ _- '

0.80

0.60

1.00

Fall Factor, hit

Fig. 5. Variation offorce with fall factor

The variation of rope length at a constant fall factor was investigated using a rope attached without a knot and a full mass of 55kg. The rope length varied from 855mm to 255mm in steps of l50mm with a new sample being used for each test. 3.5

•

2.5

~

•

•

•

•

2

u

•

~ 1.5

Experimental Data

u,

-

0.5 200

400

600

Theoretical data

basedon empirical linearstiffness value 800

1000

Rope Lent h (mm)

Fig. 6. Effect of rope length with a constant Fall Factor on the force generated in the rope

4 Conclusions An initial impact force of approximately 3kN corresponding to a fall factor of 0.92, is sufficient to cause permanent damage and a resultant increase in stiffness. This does not reduce within the maximum rest period considered of 60 hours and results in a significant increase in the force during a subsequent drop of approximately 25%. Eq. 4 is generally valid within the context of these tests and for un-knotted rope samples stiffness may be represented linearly, ignoring the initial less steep section of the force-extension graph. The inclusion of the knot (as is the case in practice) reduces impact force due to reduced stiffness. The stiffness of a knotted rope sample

68

Andrew Phillips, JeffYogwell, Alan Bramley

is directly related to the percentage of the overall rope length occupied by the knot. Consequently at short rope lengths force is not constant for a given fall factor (hiT) . As rope length increases the knot has a lesser effect on stiffness. These results may be of particular relevance to climbers attempting rock climbs requiring the use of micro-protection, aiming to minimise the impact force in order to maximise their safety margin. The inclusion of one or more additional knots close to the harness attachment may be of benefit although this will obviously dictate that the climber must always be at least a minimum rope length away from the nearest runner as the knots will not pass through the karabiner. Furthermore; these results show that, with respect to the rope, for those climbers operating at lower standards (who are always using protection devices with the maximum strength rating and with the experience to identify good placements), there are no consequences of a fall that will significantly compromise their safety margin in a subsequent fall.

Acknowledgements The authors acknowledge the University of Bath for the provision of facilities for this work.

References Pavier , MJ. (1998) . Failure of climbing ropes resulting from multiple leader falls. nd Proceedings ofthe 2 International Conference on Engoneering ofSport (ed. S J Haake) Blackwell Science, Oxford. Smith, R. (1998). The development of equipment to reduce risk in rock climbing. Journal ofSports Engineering. 1,27-39.

Rock Climbing Belay Device Analysis, Experiments and Modeling Lionel Manin' , Matthieu Richard', Jean-Daniel Brabant', and Marc Bissuel' !

INSA Lyon, France, [email protected] France

2 PETZL,

Abstract. Amazingly no standard exists for belay devices used in rock or ice climbing. This paper presents an analysis performed on several belay devices that permits their comparison in terms of characteristics and efficiency. The belay device characterization consists in testing the brakes in the case of a given fall arrest in a testing room. Here, a belay device is characterized by its braking coefficient, the rope slip through the brake till the arrest of the fall and the impact load on the last runner. The braking coefficient is the ratio between the rope tensions on the tight and slack sides of the belay device. A device called "virtual hand" has been developed, ittries to reproduce the belayer hand action on the rope during the fall arrest, and it also enables the measurement of the load on the brake and the control of the rope tension on the belayer hand side. The fall arrest intensity or brutality is evaluated from the measurements of the rope slip in the brake and the load on the last runner. The analysis of the three measured characteristics enables the comparison of the six belay devices tested. It appears that these three quantities are related, indeed the larger the braking coefficient the lower the rope slip and the higher the impact load. The energy of the fall is absorbed over a shorter time period for belay device having a high braking coefficient. Therefore, an efficient braking gives way to a high impact force on the climber and a more brutal arrest of the fall. A basic model for the brake has been implemented in an already developed climber fall arrest model. Comparison of experimental and numerical results is made and is satisfactorily.

1 Introduction Rock climbing material has considerably developed this two last decades. Many technological innovations have been created for karabiners and belay device or brake, they aim at getting products that are lighter, safer, more ergonomic and efficient, and that also respect international standards (Smith 1996; Blackford and Maycock 2001) . Surprisingly, no standard exists for belay device (also called brake or descender), it is only the manufacturer know-how and the climber experience that are used as reference or base for new development and design. In order to be able to compare several types of brake and to build a database for the brake characteristics, an experimental and numerical study has been conducted. The objectives are to characterize and to classify the brakes. This study is part of a larger project that aims at simulating the climber fall arrest dynamics taking into account fall parameters, rope route, anchor points and material characteristics

70

Manin, Richard, Brabant, Bissuel

(Manin, Mahfoudh, Jauffres and Richard 2005). In this project, a numerical model has been developed and the brake characteristics are needed for the fall arrest simulation. To accomplish this work, Petzl manufacturer of rock climbing material and the French university lNSA-Lyon have collaborated. Here the purpose is not to discuss about belaying techniques and safe use of belay devices, but to describe a characterization method that can give way to a classification of the brakes. Previous works have studied the factors affecting the various belaying techniques (Schad 2000; Smith 1996; Zanantoni 2000): use of twin or half ropes, slip ratio, type of device, position and weight of the belayer, length of slipping rope, amount of friction along the rope. The major aim is the evaluation of the impact load on the last runner and the rope slip depending on the belay device used. These two quantities give indications on the brutality of the fall arrest and on the brake efficiency . Several models have been developed and they perform satisfactorily (Bedogni 2002; Pavier 1998; Manin et al. 2005), however few work has been done on descenders.

2 Belay Device Experimental Analysis The presence of a large amount of friction in practically all real falls is a great advantage in mountaineering, but it conceals a number of basic factors which are fundamental for the analysis of the dynamic belay process (Zanantoni 2000), and it does not permit to see the contribution of the belay device in the fall arrest. Moreover, the behaviors of belayers when stopping a fall are very different, and even with the same operator repeatability is difficult to obtain. Therefore, in order to test in the same way all the belay devices considered, it was necessary to have a fall easily reproducible with a fixed configuration and a minimum number of perturbing factors. The tests have been realized in Petzl test room equipped with a fall tower and a specific device called "virtual hand" to which the brake is attached. The virtual hand plays the role of the second and insures an almost identical braking action for each fall arrest.

2.1 Test Rig Description The fall configuration used to test the belay devices is very simple (Fig. 1): only one karabiner (the last runner) in the rope route except at the return anchor. The "virtual hand" (bottom right of Fig. 1) has been developed to reproduce the belayer hand action on the rope during the fall arrest, and it also enables the measurement of the load on the brake and the rope tension on the belayer hand side. The "v irtual hand" uses a torque limiter coupled with a barrel on which the rope is coiled to apply an almost constant retaining load on the rope as the belayer hand does. The torque limiter has been adjusted so that it resists to a rope tension smaller or equal to 160 N, over that limit the barrel rotates and the rope slips through the descender. The value of l60N has been determined from the measurement of the maximum load applied to a rope a hand could retain. A torquemeter placed between the torque limiter and the barrel permits to measure the torque on the barrel and therefore the rope tension on

Rock Climbing Belaying Device Analysis, Experiments and Modeling

71

the slack side of the belay device. Load sensors are placed at the last runner and at the brake. All sensors are connected to a computer via a data acquisition board .

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2.2 Belay Device Measured Characteristics and Results Three characteristics have been measured for the six brakes tested: the impact load on the last runner, the braking coefficient and the final rope slip in the brake. The braking coefficient Pi is defined as the ratio between the rope tensions on the tight span (T J) and the slack span (Fmax_hand) of the brake :

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Figure 2 shows the evolution of all the measured quantities versus time during a fall arrest done by the virtual hand for two different brakes. T2 is the rope tension on the mass side. It can be seen that the type of belay device used has great influence on force magnitudes and displacements . For the two cases of Fig.2, differences of lkN for the impact force and 1.5m for the displacement are observed . This points out, regarding the climber potential injury, that the force supported by the climber and the rope slip through the brake during a fall arrest can be very different depending on the belay device used. The arrest of a given fall can therefore be progressive or brutal. The braking coefficient is not constant during a fall arrest (Fig. 3), it increases during the slowing of the fall until the start of the rope slip in the belay device and then it remains almost constant until fall is stopped (about 1.3s) and then slightly decreases. It is this constant value that is considered. The measured belay device

72

Manin, Richard, Brabant, Bissuel

characteristics are summarized in Table I, they correspo nd to mean values obtained from at least three tests. A good reproducibility of the test was observed . Reverso

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RockClimbing Belaying Device Analysis, Experiments and Modeling

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to a small rope slip in the descender . Regarding the efficiency of stopping a fall, brakes with large braking coefficient perform better as they stop the fall quicker than brakes with smaller braking coefficient. However, the energy of the fall being absorbed on a shorter time, the brutality of the fall arrest is higher. Note that the values presented are for a given fall in a test room with a fixed belayer role played by the virtual hand. ,....------- - - - - 14 - - FigU'e 8

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3 Brake Modeling and Comparison with Experiments A basic modeling of the belay device has been implemented in our model (Manin et al. 2005). Here the brake is considered as a force multiplier (Bedogni 2002). It helps retaining a rope tension by amplifying the load applied by the belayer's hand on the rope. Slip occurs at the belay if the tension on the tight side of the brake divided by the braking coefficient f3J is equal or larger to a critical value (Pavier 1998). The critical value corresponds to the maximum rope tension a hand can hold (160N for results presented on FigA), it can be adjusted in the model. Figure 4 shows simulation results (thin line) compared to measurements (bold line) obtained for two different brakes used for the arrest of the same fall. The agreement between calculations and measurements is good, it is better for the mass displacement and the virtual hand force than for the last runner and brake loads where the calculated and measured shapes of the load evolution differ. Some discontinuities are observed for the calculated last runner load at the start of the rope ten-

74

Manin, Richard, Brabant, Bissuel

sioning phase. It is due to the time incremental numerical scheme used, that point is being improved.

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4 Conclusion A method for characterizing belay de vices has been presented, it permits to compare sev era l des igns from the determination of three parameters. Impact load, rope slip in the brake an braking coefficient observed for each brake are related and the ir analysis enables the estimation of the brutality of a fall arrest. Regarding the comfort of the cl imber, a descender with a large braking coefficient will stop his fall efficiently but uncomfortably.

References Bedogni, V. (2002) Computer mathematical models in belaying techniques, Report, Italian Alpin e Club. Blackford, J., Maycock, E. (2001) Mountaineering Equipment - Ropes Harnesses, Karabiners and Anchors, Materials World Vol. 9 no. 8, pp. 8-12 Special European Supplement. Manin, L., Mahfoudh, 1., Jauffres, D., Richard, M. (2005) Modeling the climber fall arrest dynamics, 5th International Conference on Multibody Systems. Nonlinear Dynamics. and Control. ASME, Long Beach, USA, Sept. . Pavier, M. (1996) Derivation of a rope behavior model for the analysis of forces developed during a rock climbing leader fall, The Engineering ofSport , Haake S., pp.271-279. Pavier, M. (1998) Experimental and theoretical simulations of climbing falls, Sports Engineering , pp. 79-91. Schad, R. (2000) Analysis of climbing accident, Accident Analysis & Prevention, Volume 32, Issue 3, pp. 391-396. Smith, R. (1996), The development of protection systems for rock climbing, The Engineering of Sport, Haake S., 1996, pp229-238. Zanantoni, C. (2000), Analysis of belaying techniques: A typical UIAA Activity, World Mountain eering and Climbing, The Journal of the UIAA, no. 3, pp. 7-11.

3 Cycling

Synopsis of Current Developments: Cycling Martin Strangwood Sports Materials Research Group , The University of Birmingham, Department of Metallurgy and Material s, m.strangwood @bham .ac.uk

Scope of the sport Cycling , as a sport, encompasses a range of types from the reproducible conditions prevailing in indoor velodrome track cycling through road racing to the very variable conditions experienced in mountain or all-terrain biking. All of these aspects of the sport are represented by the papers presented in this section of the conference. Indeed, by covering the performance of helmets the paper by Alam et al. is also relevant to everyday commuting by bicycle. The papers presented also cover a number of aspects involved in circular development from design through performance to improved design, with a strong concentration on sensor development and analysi s to optimi se performance and training .

Equipment design - mechanics and sensors The need to maximise mechanical efficiency in cycling equipment has long been an area of research and innovation and this continues in the papers presented here, which cover all three disciplines noted above . One method of increasing the specific stiffness of a bicycle and its components comes from the use of improved ('advanced') materials in traditional and more innovative designs. In recent years titanium- magnesium- and aluminium-based (e.g. AILi) alloys have been introduced to the frames of road bikes, whilst track bikes have made increasing use of carbon-fibre composites. The effective use of these new, and generally less forgiving , materials requires greater understanding of the operating conditions of the equipment and hence more optimized design and manufacture. The paper by Caton et al. is an example of this where a composite-skinned foam sandwich structure, which has been used for many years for disc wheels, has been modified in its manufacture to reduce weight and maintain stiffness and strength. The use of more specialized materials, such as polymer and metal matrix composites and high strength steels is likely to see greater use of composite structures such as these in giving a mix of propert ies. Whilst the design of road bikes is fairly traditional, innovations can occur in components, which are exemplified by Horvais et al. who have assessed the force evolution

78

Martin Strangwood

from non-circular chainring and related this to triathlete performance. This is a good example of linking theoretical mechanical advantages with what can actually be achieved by athletes using the equipment. At the same time any reaction forces must be within acceptable limits for the athlete' s physiolog y and, whilst Hervais et al. concentrate on optimizing performance, Muller et al. address the issue of measuring reaction forces for cycling after total knee replacement. Research using these methods and in this area could be expanded to physiotherapy for cyclists after injury and an optimization of their return to full fitness levels, minimizing the risk of aggravating the injury. Greater design innovation is associated with mountain biking and this is shown by the various suspension designs studied by Tempia et al.. The dynamic response of suspension systems is crucial to both performance and athlete 'feel' and this requires careful monitoring. Tampia et al. have modeled the suspension travel, whilst Redfield and Sutela have modelled and dynamically measured the response of a rear shock to give its force / velocity characteristics. Greater development of systems to dynamically measure the response of cycling equipment in use will be seen in future and should lead to greater athlete / equipment optimization when used to verify models on readily accessible code such as Matlab and Mathematica.

Sensors and training As well as sensor development for the mechanical response of the equipment, then increased use of sensors is being seen in assessing the performance of athletes in competition and during training . The two submissions by Jaitner and co-workers describe the development of sensing systems and protocol s to allow coaches to optimize the training of individuals in a group environment. Validation of these approaches should open up this approach to a range of other sports and is an interesting development.

Aerodynamics and safety In common with other vehicles, aerodynamics is an important parameter influencing performance and 'feel' . The relatively controlled atmosphere of indoor track cycling lends itself to both measurement and modelling of aerodynamic parameters, which form part of an optimization program for cycling [Lukes et al.] along with power output and frictional forces. The verification of this approach should allow forms of cycling in more varied conditions , e.g. road racing , to be modelled and linked to variations in equipment , such as those noted above . Finally, and most importantly, it is necessary for sport to be safe for the participants and this is covered by Alam et al.s contribution on cycling helmets , which would be pertinent to all forms of cycling. The need to balance comfort, i.e. cooling , with performance, i.e. low drag, is a common problem in many sports and one where quantitati ve study is needed along with determination of the athlete' s perception.

Thermo-mechanical Modification Techniques for Structural Foams used in Racing Bicycle Wheels Catherine Caton, Mike Jenkins and Martin Strangwood Sports Materials Research Group, The University of Birmingham, Department of Metallurgy and Materials, m.strangwood@bham .ac.uk

Abstract. The effects of a range of thermo-mechanical treatments on closed cell polyrnethacrylimide foam have been quantified in terms of surface roughness, closed cell dimensions at the surface and in the bulk, and cell wall thickness . These have been carried out for a range of specimen sizes and have led to the determination of optimal conditions to balance expansion of closed sub-surface cells and collapse of cell walls for the open surface open cells for smaller foam samples, where the modification is constrained to the surface regions and leaves the bulk compressive and shear properties of the foam unaffected . Surface modification in this manner reduces the uptake of resin by the foam during manufacture of sandwich beams and discs. Application of the surface modification to larger samples resulted in excessive thermal gradients and bulk pore formation highlighting the need for edge constraint.

1 Introduction Composite sandwich disc wheels are frequently used in track racing where low weight and low aerodynamic drag are required whilst providing a wheel of high stiffness and strength . Disc wheel structures comprise a high shear strength, low density polymer core, surrounded by high modulus carbon fibre composite skins . Production of sandwich beams uses of an adhesive resin layer to produce a coherent bond between skin and foam core. Due to the cellular structure of the foam, this leads to a significant amount of resin uptake into the core, so increasing the mass and inertia of the structure, important factors in wheel design and performance. Previous work [Caton et al., 2004] investigated a thermo-mechanical surface modification process to prevent resin uptake into a polymethacrylimide (PMI) closed cellular core . Using a matrix of time, temperature and pressure conditions, lcrn' cube specimens were heat treated in air on a hot plate to determine optimum thermal treatment conditions of 212 °C for 5 minutes under a pressure of 491 Pa, which did not affect the bulk material, but reduced resin ingress by 14% when manufactured as carbon fibre/PMI sandwich beams . Mechanically stiffness was found to be the same as in beams with untreated cores and all failed through the foam in the near interfa-

80

Catherine Caton et al.

cial region showing no reduction in the interfacial bond with surface modification, but this needs to be investigated for larger structures.

2 Experimental Procedure Scaling up was achieved in two stages; initially 'small' (sm) foam samples (40mm2 surface area, 7mm in depth) of Rohacell PMI 511G density (p.) of 52 kg/rrr' were treated thermo-mechanically on one face in air on a hotplate at temperatures between 185 and 240°C; 1159 - 1465 Pa pressure and for times between I and 3 minutes. 51 IG [Roehm, 2004] softens at around 180°C. Top surface and centre temperature profiles for the 200°C and 240°C, 1465 Pa pressure and 2 minutes schedules were recorded using Type-K thermocouples. 'Large' (I) sized specimen, 125 x 262.5 mrn/ surface area, (7mm depth, 51 IG), were thermo-mechanically treated on both faces simultaneously using two heated AI platens in an oven for the same conditions as above. An edge-constrained specimen, using a steel ring and the sample was circular (15 mm radius and 10 mm thick) was also investigated (185°C, 1465 Pa, 2 minutes). Surface-modified sm samples were impregnated with ACG VTA260 PK13 epoxy adhesive under vacuum (pressure under 20 mm Hg) following a cure cycle of 0.5°C/min heating ramp rate, 2 hour dwell at 100 °C and 2°C/min cooling rate. Modified surfaces were gold coated and observed in a Jeol 6060 scanning electron microscope (SEM) operating at 20 kV. Bulk and ingress samples were sectioned normal to the top face using a slow speed diamond saw to minimise damage, gold coated (bulk) or cold mounted in Epofix (ingress), ground to 500 grit and polished to a 1 urn finish, and examined by SEM (bulk) or optically (ingress). Axiovision 4.0 image analysis software was used to characterise cell and pore areas, lengths and breadths along with cell wall thicknesses. Resin ingress depths were measured directly from an optical microscope fitted with KS300 image analysis software, whilst sectioned surface images were measured to give R, roughness values.

3 Results And Discussion The sm samples resulted in a significant temperature variation through thickness, Fig. 1 (a), which was not seen in the I samples (heated from both sides), Fig. 1 (b). This results in distortion (buckling) of the foam with strains limited at low temperature; increasing through-thickness direction as temperature increased. Table 1, which indicates that greater (gas) expansion of the cells, without permeation occurs. The use of dual-sided heating for the I samples reduced the curvature, but at the expense of large central pore formation, Fig. 2. The size of the pores was larger at lower temperatures, Table I, which corresponded to greater strains suggesting that, at higher temperatures compression of the sample through thickness combated the gas expansion. Pore formation was associated with audible signals from cracking along the centre-line and this occurred within the first 30 seconds of the heat treat-

Thermo-mechanical Modification Techniques for Structural Foams

81

ment, which corresponds to the initial steep temperature rise noted in thermal profiles, Fig. I (b). The steel ring constraint eliminated the central pores at 18S°C.

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The roughness of thermo-mechanically treated surfaces varied with time, temperature and pressure, but not in any simple, monotonic manner, Fig. 3. Lower treatment temperatures, e.g. Fig. 3 (a), generally show the lowest R, values at low applied pressure increasing again at the intermediate pressure level before being reduced at the highest pressure level. This order is followed over the time range studied, but an initially high R, is reduced from 1 to 2 minutes exposure, but then increases up to 3 minutes exposure . With increasing temperature then R, increased to maximum values at 21aoe except for higher pressures and longer times, when the R, maximum is

82

Catherine Caton et al.

shifted to 220°C. At 230°C and above the R, values showed a decrease, Fig. 3 (b), which was largely time-independent at low pressure but varied at higher pressures . The heat-treated sm sample surfaces showed collapse of the original surface cell walls causing a reduction in R, values. Heating of the sub-surface cell walls softens them whilst the gas inside expands leading to an increase in cell volume and bulging at the surface tending to increase R, values, Fig. 4 (a). The variation in R, with pressure and time at low temperatures would be consistent with high local stresses on the surface (open) cell walls giving rise to rapid plastic collapse . This would increase the contact area reducing the local stresses with time, coupled with increased heat transfer causing later temperature rises and gas expansion so that R, increases again .

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Increased treatment temperature reduces the failure stress of the surface cell walls leading to more rapid collapse of the surface cell walls, but also easier flattening of the tops of the expanding sub-surface cells so that the surface is flatter overall with evidence of greater elevated temperature material flow, Fig. 4 (b). A cyclic variation of surface roughness may be expected with temperature/time increase as the greater expansion of the enclosed gas in sub-surface cells increases R, until cell wall strength is reduced and rupture occurs to increase R, further, only to be followed by cell wall collapse reducing R, and leading to bulging of a lower layer of closed cells.

Thermo-mechanical Modification Techniques for Structural Foams

83

In the un-heat-treated condition the open surface cells tended to fill with resin from any adhesive layer resulting in ingress to an average depth of 339 urn (between 282 and 410 urn [Caton et aI., 2004]) . In the sm samples, closure of the surface cells has resulted in a much more uniform ingress depth, which was temperaturedependent, but largely time- and pressure-independent. At 210 DC, all three pressures and times gave resin ingress between 148 and 188 urn, i.e. a 50 % reduction. Single-sided heat treatment of sm samples gave satisfactory surface modification and resin ingress reduction, but bowing of the sheets resulted in local variations in pressure and temperature and inhomogeneous behaviour. Dual-sided heat treatment of the I samples overcomes the bowing problem, but introduces central pores . Pores were larger for lower temperature heat treatments, Table I, when significant expansion of the sample took place ; increasing the holding time at the lowest temperature reduced the pore size, but did not reduce the overall expansion of the samples. Increasing the treatment temperature reduced both the pore size and sample expansion, with the highest temperature resulting in overall shrinkage, but pores did not re-heal . Individual pores showed size variation, which may result from size and gas content variations in the original foam ; this still needs confirmation. Pore imaging by SEM shows both spherical and elliptical (higher temperature) expansion of cells . Examination of the ruptured cell walls associated with the central pores reveals the presence of buckling and shear fracture , Fig. 5 (a), akin to that seen in room temperature shear testing of the unmodified foam, Fig. 5 (b). These features would be consistent with shear loading of the cell walls to failure before they have been heated sufficiently to deform plastically; consistent with early pore formation .

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Determination of cell sizes for the variously heat treated PMI 5 I IG foam samples indicates a large scatter, as expected from foamed material, but, importantly samples showing large pores have larger cells to the edge of the specimen, but this is reversed (smaller edge cells) for samples showing limited pore formation . The variation in cell structure in the bulk and at the surface above is consistent with collapse of the open surface cell walls initially as the high local stresses combined with elevated temperature cause plastic flow. Heating of sub-surface and lower cells follows softening their walls with internal gas expansion and wall thinning, in extreme cases leading to cell wall rupture . Poor foam thermal conductivity causes the

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Catherine Caton et al.

centre to be cooler than the surfaces, which means that the cell walls are still brittle whilst any heated surface is expanding so that the gas in the centre cells is being compres sed shearing the vertical (cool) cell wall s. Dual-sided heat ing increase s shearing to expansion from above and below and can exceed the fracture stress of the walls to cause the failure feature s noted in Fig. 5. Lower treatment temperatures result in longer times for cell wall heating and plasticity so that pore expansion can occur to the large dimensions noted in Table I. Once formed , pores open up on unloading to give expan sion of the sample in the thickne ss direction, Fig. 2. Hence, extended time at 185°C would not be expected to reduce the pore size suggesting that the trend shown in Table I may represent statistical variations in the starting material. Increasing treatment temperature increases thermal gradi ents resulting in greater thermal flux and so a faster temperature rise in the centre so that the cell walls are more plastic and can accommodate increased gas pressure without fracture . On unloading the still intact cell walls will relax and contract so that the overall sample dimensions show less through thickness expansion, Table I. Thermally activated gas perme ation and diffusion should also occur. This is easier for higher cell wall temperatures, so that, for lower temperatures, higher internal closed cell gas pressures occur , further enhancing cell wall fractur e. Intact cells will be larger at lower temperatures due to higher internal pressure without permeation relief. The use of a steel ring for edge constraint may not have prevented gas loss, but have accelerated it by providing a high conductivity path to heat the edge cells to reduce the stresses caused by gas expansion in the un-constrained I samples. The use of a non-conductive constraint needs to be carried out to confirm this. Thu s indicate controlled heating rates balanc ing of expansion and heat transfer may be needed.

4 Conclusions and Further Work Thermo-mechanical treatments leading to surface modification of PMI 51IG such that resin ingress is decreased by 50% have been identified. The beha viour of the foam is based on a balance of heat transfer, thermal softening, gas expansion and diffu sion, and plastic flow, which has not allowed scaling up of the treatment without pore format ion. Identification of a work ing hypothesis for pore formation has indicated that greater control of thermal transfer is likely to be a successful approach.

References Caton, C.1., Jenkins, M.1., Strangwood, M., (2004), The Engineering of Sport 5. Eds M.Hubbard, R.D.Mehta & J.M .Pall is, ISEA, Sheffield, pp 22 7-233. G ibson L.J., (1984), Optimizat ion of stiffness in sandw ich beams with rigid foam cores, Materials Science and Engineering. 67 125-135 . Roehm (2004) www .roehm .com

The Effect of a Non-Circular Chainring on Cycling Performance Nicolas Horvai s, Pierre Samozino, Frederique Hintzy Laboratoire de Modelisation des Activites Sportives, Bourget du Lac, France , nicolas .horvais@etu .univ-savoie.fr Abstract. The aim of this work was to analyse the effect of a non-circular chainring during sub and supra-maximal cycling conditions on physiological, mechanical and muscular data . Results showed that the use of the non-circular chainring was beneficial during top and bottom dead centres by decreasing the effective force for a same external force for sub-maximal condition and by increasing the crank angular velocity for supra-maximal condition. However, this non-circular chainring was without effect during the pedal downstroke.

I Introduction Cycling propulsion only result from forces applied to the pedals . The study of pedal forces application could help to understand the cycling performance since Ericson and Nisell (1988) showed that the effective force applied to the pedal (tangential force) was maximal during the downstroke at 90° and minimal at the top and bottom dead centres. This effective force was transmitted to the chain via the crank and the chainring. Thus, an improvement performance could then be realized by modification on chainring. Traditionally, chainring were circular. Recently, a non-circular chainring called Osymetric chainr ing (OC) has been manufactured on the no constant force applic ation principle throughout the pedal crank revolution (Fig. 2). Indeed, the OC radius described a sinusoid curve similar to the effective force evolution during the pedal crank (Fig . I), i.e. large radius when the effective force was maximal and inversely . Theoretically, OC would allow facilitat ing the foot path around the top and bottom dead centres by a lower radius than a standard circular chainring (CC) . In order to keep the same development, it was necessary to increase the radius chainring in another zone . In order to minimi ze the negative effect of this radius increase , this one has been placed where the effective force applied to the pedals is the most important (i.e. at 90°). To our knowledge, only one study tried to compare the oxygen consumption between OC with CC in sub-maximal cond ition (Ratel, Duche, Hautier , Williams and Bedu 2004) and did not show a significant. It could be explained by a no muscular pattern modific ation . However, the muscular activity was not measured.

86

Nicolas Horvais, Pierre Samozino, Frederique Hintzy

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Figure J: Radius of a circular chainring (CC) and an Osymetric chainring (OC) for 52 teeth chainrings during a pedal revolution

Figure 2: Geometry of the Osymetric chainring.

The aim of our study was then to compare and analyse mechanical, physiological and muscular data obtained during endurance and anaerobic fatiguing Wingate tests using OC and CC. 2 Materials and methods 2. 1 Subjects 12 male triathletes volunteered to participate in this study . Their age was 32.0 ± 6.7 years , height was 179.3 ± 5.2 cm, weight was 77.5 ± 10.2 kg and fat mass percentage was 16.8 ± 4.6 %. 2.2 Experiment protocol Each subject participated in randomized two sessions (OC and CC sessions) separated of 24h recovery. During the two sessions, subjects realised: - a 8 min sub-maximal test at of 100 and 200 W (4 min per power output in an ascending order) at a constant pedalling rate fixed at 80 rpm. - a supra-maximal test corresponding of a 30 s Wingate test against a friction load of 0.834 N .kg'l body mass. The starting position was standardized with the right foot placed at 45° . At the signal given by the experimenter, subjects were vigorously encouraged to sprint maximally (i.e. from zero to maximal velocity) and to maintain this maximal effort during 30 s. During each test, subjects had to stay seated on the saddle . The handlebar and the saddle height were adjusted to height's subjects and remained constant for all tests and sessions . Feet of subjects were not fixed on the pedals in order to avoid a traction phase during the upstroke. 2.3 Material and data analysis Mechanical data analysis A typical friction -loaded cycle ergometer was used for this study (Monark 818E, Stockholm, Sweden), specifically equipped with strain gauge (Interface MFG type ,

The effect of a non circular chainringon cycling performance

87

Scottsdale, Az, USA) for the friction force measurement and with optical encoder (Hengstler type RIS IPSO, Aldingen, Germany) for the flywheel measurement, (Arsac, Belli and Lacour 1996). Flywheel angular displacement and brake belt force were sampled at 50 Hz. The cycle ergometer has been modified by the addition of a 52 teeth CC and a 52 teeth Oc. Instantaneous external force (Fex! in N) produced by subjects was determined as the sum of frictional force (measured by the strain gauge) and inertia force (dependent on the acceleration of the flywheel) (Arsac et al. 1996). Moreover, the effective force (Feffee in N) applied to the pedals was calculated from the instantaneous external force (Cavanagh and Sanderson 1986). During the sub-maximal test, instantaneous maximal and minimal external and effective force (Fexl-max. Fexl-min, Feffee-max and Feffee-min), pedalling rate and power output were recorded over each pedal downstroke, which was limited between the two minimal values of instantaneous power output corresponding to top and bottom dead centres, and were analysed between OC and Cc. During the 30 s Wingate test, power output was averaged during the first 5 s (Pmean 0 - 5 s), the last 5 s (Pmean 25 - 30 s) and during the entire test (Pmean 0 - 30 s). The rate of decrease of power output during the test, i.e. the fatigue index, was obtained by the ratio between the Pmean 25 - 30 s and the Pmean0 - 5 s. Physiological data analysis Oxygen consumption (V;'02) and carbon dioxide production (V;C0 2) were measured breath to breath with an automatic gas analyser system (Cosmed K4b2 , Rome, Italy). Both O2 and CO2 fraction were calibrated with know reference gas mixture (room air and a standard certified commercial gas preparation). The expired gas volume flow rate calibration was performedby mean of 31 syringe (Hans Rudolph). During the sub-maximal test, V; O2 and V; CO2 have been measured continuously and averaged over the last 30 s of each power output. Gross efficiency (GE) was obtained by the ratio of mechanical energy to energy expenditure. Musculardata analysis Electromyographic surface signal (EMG) was collected at 1000 Hz during all tests using an eight ways system (Mega-ME3000P8, Mega Electronics, Finland). Bipolar electrodes were placed on the skin (spaces of 2.5 ern) over the gluteus maximus (Gmax), the biceps femoris (BF), the rectus femoris (RF), the vastus lateralis (VL), the tibialis anterior (TA) and the gastrocnemius (GAS) muscles of the right lower limb for both tests. The skin at each electrode site was shaved and cleaned with an alcohol-ether mixture. The EMG signals were amplified (x 600) and filtered and the treatment was carried out thanks to the software Megawin (Mega Electronics Ltd, Finland). The raw EMG data were full-wave rectified and smoothed using a 50 ms moving averaging windows. From the raw EMG, averaged EMG (aEMG) has been chosen for analysis.

88

Nicolas Horvais, Pierre Samozino, Frederique Hintzy

During the sub-maximal test, aEMG was averaged during the last 10 pedalling cycles of each power output. aEMG was normalized to the maximum value observed during one burst across the Wingate test for each individual muscle (%). The averaged total EMG (aEMGT in %) was averaged from the 6 muscles studied. During the 30 s Wingate test, aEMG was averaged during the first 5 s and the last 5 s and during all the 30 s of the test. aEMG was normalized (i) to the maximum value observed during one burst across the Wingate test for each individual muscle and (ii) to the power output realised (%.W-I ) . The averaged total EMG (aEMGT in (%.W,)) was calculated with the 6 muscles studied. The rate of decrease of aEMG during the test, i.e. the fatigue index was obtained by the ratio between the aEMG of the last 5 s and the aEMG of the first 5 s. Statistics Results were presented as mean ± standard deviation (SO) values. Comparison of data between CC and OC were realised using a Wilcoxon test. The limit for statistical significance was set at P < 0.05. 3 Results

Concerning the sub-maximal test, data were presented in table I. No significant difference appeared in all data between OC and CC except for F effee-max in both powers output and for F effee-min at 100 W (Feffec-rnax with OC significantly higher than CC and F effee-min OC were significantly lower on CC). Concerning the Wingate test, data were presented in table 2. There was no significant difference in both mechanical and muscular studied data between the use of OC and Cc. 100W

Sub m aom er t est Phys iologic al

data Mecha nic al dat a (N)

OC

cc

GE

13 9 :t 17

13 5:t 0 9

15 4 ± 1 8

14 8 t 14

F... ~.

227 . 3 7

23 5 " 6 37 . , 4 2779. ,92

382 .39 10 4 . 3 2 4171 t 42 2

37 1 t 139

113 9 t 351

360 . 3 2 9 5.25 4500 .382 93 8. 25 1

139 :l: 4 9

12 0 t 6 0

11 7 ± 5 0

99 :t 7 6

100.5 6

126:1:109 10 6 t 8 7

F,..,.,..,..,

42t 14

F . II~ ."" .

248 0t40 4

F. n K ....... EMGT Gmax

40 9 ± 15 3

SF

aEMG(%)

200 w

CC

14 1 t 7 1 9 2t5 1

76 . 5 3 11 3 t 7 0

VL

RF

235 . 100

GAS TA

18 1 t 11 8

'4 2. ,23

* *

9 7

t

*

OC

10 4 t 9 8

77

g8 t 4! 189 . 103 13 7 . 122 63.3 6

9 1 :t5 5

12 5 %8 2 21 5:t 11 6

19 5 . 9 2 122 . 9 2 99 .93

221 :t 21 1 9 1. 6 7

Table 1: Values (mean ± SO) of data measured during the sub-maximal condi-

tion in two conditions: circular chainring (CC) and Osymetric chainring (OC). *: significantly difference between CC and OC (P < 0.05). wmqare test Mechanical p data (W kg"l)

,..,.. .

.EM G

aEMG, Gmax SF

(% W ' )

: GAS TA

0 · 5 second

CC 6 5 ."

OC 79. , 5

25. 30 second CC OC

52.0 7

0 13 .0 03 0 14. 00 3 0 19 .003 0 14 .004 0 16 .003 021 . 005 014 .0030 16 . 0030 19.0 05

o · l) second

Fatigue Index

CC

OC

CC

OC

47 .06

67.07

6 1. , 1

36 7 . 6 4

397 . 6 3

0 21 . 0 03 0 23 . 003 020 .0 04

0 16 .003 01 7 . 004 0 17 . 003

0 16 .003 0 16 .0 02 0 16. 0 03

534 " 6 5 621 .415 373 . ,96

5C0 .24 0 52 1 . 325 28 4 .,96

~:~ :~~~ ~ :~ :~~~ ~~ :~ ~: ~ ;; : ~ ~~ ~ ~~ :~~~ ~ :~ :~~; :~::~ ~~ :;;;

01 4 . 00 3 0 13 . 0 03

0 16 . 003 0 13 .003

016.0 03 0 16. 0 03

0 16 .003 0 16 .005

0 16. 003 0 16.0 03

0 16 .003 017.003

36 6 .3 12 376 .23 1

274 .229 323 .23 3

Table 2: Values (mean ± SO) of data measured during the Wingate test with two

chainrings: circular chainring (CC) and Osymetric chainring (OC).

The effect of a non circular chainringon cycling performance

89

4 Discussion Sub-maximal condition did not show significant difference on efficiency when using OC versus Cc. This result was in line with Ratel et al. (2004) who explained that the physiological demand associated to the moving lower limbs at the top and bottom dead centres and the production of higher force for a larger part of the downstroke was insignificant in relation to the total physiological demand. Theoretically, OC would first permit to facilitate the foot path at the top and bottom dead centres. This theoretical assumption has been verified in the present study by the analysis of the effective force applied to the pedals. Indeed, Feffee-min (i.e. the effective force at top and bottom dead centres) was significantly lower with the use of OC versus CC (table I). Moreover, with a smaller Feffee.min on OC versus CC, Fext.min (i.e. the external force developed to the driving wheel) was identical between OC and Cc. These results confirmed a facilitated foot path during the top and bottom dead centres. Since OC facilitated the foot path during the top and bottom dead centres, it would be expected to observe a lower muscular activity (level and / or burst duration) permitting the top and bottom dead centres foot path as RF and BF. In the present study, anal ysis of RF and BF level and burst duration did not show significant difference between the use of OC and Cc. Two hypotheses could be proposed. First, this result could be due to the bi-articular function of both muscles who participated also to the pedal downstroke for RF and to the pedal upstroke for BF; and secondly, this result could be due to important SO, them even due to important inter-individual differences on muscular activity. The second theoretical assumption was the minimizing effect of the radius increased during the downstroke since the effecti ve force applied to the pedal at 90° was important. Result s of table I showed that Fext-max was identical between OC and Cc. This result was logical since power output and pedalling rate were similar and fixed for both OC and Cc. Howe ver, to produce the same Fext-max with OC and CC, subjects should have produced more Feffee-max with OC than cc. This result was significant at 100 Wand a tendency appeared at 200 W. Since OC constrained subjects to produce more Feffee.max. it would be logical to find more muscular activity on muscles permitting the pedal downstroke as GAS , VL and G max. The muscles anal ysis permitting the pedal downstroke did not show significant difference between the use of OC and Cc. Consequently, the cycling muscular pattern of subjects had not been modified with Oc. This result could be positive since there was an increase of Feffcc-rnax without increase of the muscular activity responsible of the Fcffccmax ' Thus, sub-maximal results seemed shown that the use of OC was beneficial during the top and bottom dead centres but without effect during the downstroke. Identical result on GE could be due to this result since , like suggested by Ratel et al. (2004), the phy siological demand associated to the moving lower limb at the top and bottom dead centres was insignificant in relation to the total phy siological demand . Nevertheless, an increase of power output would have allowed a significant difference on GE since the physiological demand associated to the moving lower limb at the top and bottom dead centres increase with power output. Similar results on GE could also come by a lack of adaptation to Oc. It would be interesting to realise a learning period of OC use.

90

Nicolas Horvais , Pierre Sarnozino , Frederique Hintzy

Concerning the Wingate test , there was no significant difference between the use of OC and CC on mechanical and muscular parameters studied. An increase of Pmean could have appeared if subjects would have succeeded to increa se their pedalling rate. Indeed , the friction force being fixed, the only solution to increase power output was to increase pedalling rate. Therefore, it would seem that subjects did not succeed to increase their pedalling rate. Yet, according to sub-maximal condition results, the OC use would lead to an increa se of crank angular velocity during the top and bottom dead centres foot path if the same effective force was applied to the pedal. It would mean that the crank angular velocit y during the pedal downstroke was lower with the use of OC than Cc. Unfortunately, the method used in this study did not permit to verify theses hypotheses since velocity was measured at the flywheel and that it evolution was influenced by the inertia . However, the no significant difference between muscular OC and CC data permitted to give an answer to the non improvement of Pmean during the Wingate test. It would seem that the muscular force applied on the pedal with OC was not sufficient to keep a crank angular velocity permitting to produce higher power output. It would seem therefore that the use ofOC would be beneficial for subjects having an important muscular capacity. It was the result of the study of Hintzy, Belli, Rouillon, Grappe (2000) where sprint specialist subjects had improved their maximal power output with OC vs. CC while increasing their pedalling rate for sprints of 8 s. In conclusion, results of this study indicated that theoretical benefits brought by OC did not significantly improve performance whatever the cycling condition for subjects studied. Th is result could partly be due to a lack of adaptation to OC design.

References Arsac, LM. Belli, A. Lacour, 1.R. (1996) Muscle function during brief maximal exercise: accurate measurements on a friction-loaded cycle ergometer. Eur. 1. Appl. Physiol. 74, 100-106. Cavanagh, P.R. Sanderson, 1.S. (1986) The biomechanics of cycling: Studie s of the pedaling mechanics of elite pursuit riders . In: Burke , E.R. (Eds .), Science ofcycling. Human Kinetics, Champaign, Illinois , pp. 90-122 . Ericson, M.O. Nisell, R. (1988) Efficiency of pedal forces during ergometer cycling. Int. 1. Sports Med. 9, 118-122. Hintzy , F. Belli, A. Rouillon , J.D . Grappe F. (2000) Effects of non circular chainweel on force-velocity relationship during sprinting on a cycle ergometer (in French) . Sci. Mot. 40, 42-47 . Ratel , S. Duche, P. Hautier C.A. Williams C.A . Bedu, M. (2004) Physiological responses during cycling with "harmonic" and circular chainrings. Eur. .I. Appl. Physiol. 91, 100104.

Dynamic Characteristics of Modern Mountain Bikes Rear Linkages Angelo Tempia, Aleksandar Subic , Riccardo M. Pagliarella [email protected] .au

Abstract. Recent years have seen a tremendous development of full-suspended mountain bikes, especially for downhill and free-ride market. These mountain bikes strongly rely on the ability of the rear suspension shock absorber to manage extremely large forces and wheel travel. Wheel travel is generally achieved through the geometry of the suspension linkage ; whereby forces are counterbalanced by the shock hydraulic and spring . The Sports Engineering Research Group (SERG) at the School of Aerospace , Mechanical and Manufacturing Engineering, RMIT University has investigated the dynamic characteristics of different rear linkages suspension geometry. The kinematic analysis has been performed using different programs . A customised Matlab" code has been developed to analyse in detail the kinematic of the linkages , a MSC.Adams™ simulation has been conducted to better understand the kinematic and kinetic behaviour. After-market shock absorbers are becoming more and more popular but how their performance is influenced by the rear linkage geometries is often underestimated or not even considered. The results of this research aim to investigate and compare the dynamic characteristics of rear linkage of modem full-suspended mountain bikes .

1 Introduction Mountain biking is a relatively new sport that can be seen as an evolution of cyclocross. This sport came popular in the early 1980's in California and has continued to grow in popularity to a point where it was introduced as an Olympic sport in 1996. This exposure has driven bicycle manufacturers to develop an ever increasing number of model claming increasing performances. The use of suspension on off-ride bicycles has proliferated in the past few years. Although such a proliferation may be partially attributed to fashion (Sasaki, 200 I), bicycle suspension has technical merits and interests. Bicycles equipped with suspension result in increased rider comfort, enhanced wheel contact and control, and they also allow riders to manage the high jumps and the heavy landings that have made this sport popular among youngsters and sportive from other disciplines. In this paper a Downhill and a Cross Country rear suspension configurations of two of the most popular mountain bikes in Australia are analysed in their kinematic behaviour.

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Angelo Tcmpia et al.

2 Mountain bike Rear Suspension The primary design consideration for suspension systems has to be inserted in the context of the bicycles use. Cross Country mountain bikes need a suspension system that responds to bumps but does not respond to rider induced forces , so that the input of the rider is not wasted into modifying the geometry of the rear end of the bike . If the suspension responds to the rider's forces, energy is used to compress the suspension instead of propel the rider. Free-Ride and Downhill mountain bikes , instead, require a huge amount of travel in order to manage high drops and big jumps typical of these disciplines, but the interaction between pedalling and the rear suspension it is not of a prior importance. The most important design parameters of a mountain bike rear suspension system include the various torques and forces that are imposed on the suspension kinematic by the rider and the terrain . These forces can be classified in 3 main categories. Pedal induced forces compel all current rear suspension configurations to either compress or extend the rear geometry. They act through drive chain and wheel drive load . A design that causes the rear suspension to move under pedal induced forces, wastes some of the rider input power into either heat energy (shock compression) or forcing the mass of the rider to lift (negative sag) interacting with reaction to bumps . Braking induced forces may cause a jacking force on the rear linkage. These forces can cause the suspension to lose its effectiveness under heavy braking loads. The easiest way to overcome this problem is to use floating brakes ; however, this solution increases both weight and cost Terrain induced forces are the responsible in the first instance for the adoption of suspension on a mountain bike. These forces are received through the contact between the ground and the rear wheel, and are transmitted to the shock absorber through the suspension linkages . Many typical rear suspension designs have the rear wheel follow an arc-like path when a bump is encountered. This forces the wheel to be displaced in a forward and upward direction. As a result of this, there occurs the undesirable situation of the wheel compressing uphill when climbing instead of the wheel following the curvature of the terrain . This increases the bump shock force transmitted to the sprung mass of the bicycle because the wheel is not moving perpendicular to the bump . The perfect kinetic solution would be a suspension that is able to respond only to terrain induced forces and not to pedal and braking induced forces .

2.1 Centre of Curvature Being a series of linkages bond together and forced to move around fixed points, motion of suspensions can be analysed using the instantaneous centre of rotation. This point identifies the point the linkages are moving around. This point, being centre of rotation, can be seen as the point where if a force is appl ied it produces no moment. The suspension mechanism is needed in order to be able to create some sort of suspension ratio, but since its centre of rotation moves with the movement of the linkages it becomes difficult to understand the wheel path. The Centre of Curvature

Dynamic Characteristics of Modem Mountain Bikes Rear Linkages

93

1 _

1

••sIng

1

1

..

1 1

o

U.

•

",

-

:" ..

Docrooslng

~

/ "1 1

1

Fig. 1. Typical suspension motion ratio instead is the parameter that can easily identify the wheel path . This point can be calculated as analysing two consecutive different instants of motion .

3 Rear Suspension Geometry The final aim for a rear suspension varies from context to context; some times it is required to increased comfort, other times it is required to increase the contact between the tyre and the ground, other times it is used to absorb a great amount of energy. For these reason nowadays it is possible to have many different configuration for a rear suspension design, but they all can be divided in major categories: • Mono-shock and Cantilever Beam Designs • Four Bar Linkage Design s • Unified Rear Triangle (URT) Designs • McPherson Strut (Macstrut) Designs • Lawwill Linkage Designs • Bottom Bracket Pivot Designs • GT I-Drive

3.1 Suspension Motion Ratio The motion ratio of a rear suspension is critical to proper suspension operation. Current bicycle design incorporate motion rations in the range from rapidly rising to rapidly falling . Rapidly rising rates can cause the suspension to be too soft and acti ve in the initial part of the wheel travel, mainly cau sing a pedalling energy waste; this can also create problem with the travel of the suspension that might become no compliant. A falling rate also involves negative aspects. A falling rate suspension is initially stiff and gets softer as the suspension travel along; this might cause again the suspension to become non complaint. All rear suspension geometries can achieve almost any suspension rates , Fig . I. The rate of a bicycle suspension is composed of the internal rate of the shock and the rate inherent in the suspension geometry, hence suspension rate is to be considered

94

Angelo Tempia et al.

Fig. 2. Specialized StumpJumper Expert

Fig. 3. Kana Stab Deluxe

when design or choosing the appropriate shock absorbers, which generally have different internal rates. Pairing a falling rate frame with a linear coil shock or an extremely rising rate frame with an air shock might not have acceptable results. The accepted suspension component used on most production bicycles is either coil spring and oiled damper combination or an air spring shock absorber. Coil springs tend to have more linear rates, while air springs tend to have rising rates. All frames may be fitted with a range of shocks, which these days generally have one of two lengths and standard mounts . The contribution to rate from suspension geometry is determined by the way in which the shock mounts, front and rear wheel axles, and main triangle move relative to one another. The front wheel axle establishes frame orientation to the ground but generally may be neglected , since bottom brackets are almost universall y at the same distance from the ground without rider.

4 Analyses The rear suspensions of a Specialized StumpJumper Expert and a Kona Stab Deluxe have been analysed. The StumpJumper design features a four bar linkages with a very short upper linkage; the Stab Deluxe instead has a Lawwill Linkage Designs with the wheel attached to the lower linkage. An analysis of suspension ratios and wheel paths was conducted using a Matlab" code customised for each particular suspension. The four bar linkages of the Specialized showed an unexpected very lightly decreasing linear behaviour. This characteristic suits well the original air shock absorber, but it is not the best solution for a coil over shock. The path of the rear the wheel followed a trajectory very close to a circumference, due to the fact that the centre of curvature did not move much during the whole motion of the suspension. The wheel path is widely curved and it is running slightly up and back, as it is believed that this configuration is the best solution, Fig 4-6. The Lawwill Linkage design of the Kona showed an again unexpected very lightly decreasing linear behaviour. Even though it some reckon that a linear behaviour is the best way to cope with drops, the Kona suspension characteristic, together with the original coil over shock absorber, results in a slightly decreasing suspension rate, that is not ideal for Downhill mountain bikes. In this case the path of the rear

Dynam ic Characteristics of Modem Mountain Bikes Rear Linkages

95

e: .2

U .~

"0

......- """"'-"

N

-----_~~ S •

Y direction

Fig. 4. Specialized StumpJumper Expert Centre ofInstant Rotation (circle) and wheel path (dots)

»

•

M

Wheel travel

•

~

Fig. 5. Specialized StumpJumper Expert suspension ratio

~.

E

~.

8, '0

8. e:

~

0 " 'I

II

..

.'!-

..

..

vvneel travel

.

Fig. 6. Specialized StumpJumper Expert Centre of curvature distance from pivoting point

•

Y direction

.'

Fig. 7. Kona Stab Deluxe Centre ofInstant Rotation (circle) and wheel path (dots)

the wheel follows a circumference, due to the fact that the centre of curvature coincides with one of the pivoting points of the linkages, The wheel path is widely curved and it is running slightly up and back, as it is believed that this configuration is the best solution. Fig 7-8

5 Conclusions A bicycle suspension has many input forces, but in order to limit the analysis we only considered the kinematic implication of the movement of the rear linkages. This approach simulates sudden compression by the ground either through wheel contact with an obstacle such as a rock or from the impact of a drop-off. In general, it is believed that a widely curved rear axle path running slightly up and back is the best solution (Sasaki 2001), In the case of an obstacle, the bump force will be up and back relative to the frame, so the initial tangent should be up and back. The direction of the force will tum more vertical as the bike clears objects of "ride-able" size, so a

96

Angelo Tempia et ai.

..r----~----~---__,

..

c " .2

~" Q.

E

8"

"

..

..

Wheel travel

..

•oo

...

Fig. 5. Kona Stab Deluxe suspension ratio

widely curving path turning slightly upward should be ideal. This configuration also allows the wheel base to increase and the wheel to follow the asperities. Tight curves are generally inferior for shock absorption . Having a widely curved rear axle path is sometimes difficult to achieve with a linkage with a fixed pivoting point; 4-bars linkages represent a better solution that often allows the tight curve deficiency to be mitigated to some degree by having the path tangent tilting backward through all or most of travel Even though a 4-bar linkage solution allows for more freedom in the design, it is difficult, if not impossible to clearly identify what suspension solution represents the optimum. Clearly for cross country competition a kinematic that minimises the negative drag and the energy lost during pedalling, would be the best choice; this can be achieved with a configuration whose centre of instantaneous rotation is not moving to much (as it can be seen for the Specialized suspension) . In downhill, it would be preferable a high travel suspension. When the ultimate design target is travel, it is sometimes impossible to obtain a restricted space frame fro the centre of instantaneous rotation, as it can be seen for the Kona configuration . Rising rates benefit short travel designs, since this will allow better initial compliance, while reducing the probability of hard bottom-outs; a linear suspension ratio will offer the smoothest , most consistent compliance in the event of a drop-off. Both mountain bike object of the research showed good design geometry even though the Lawwill Linkage highlighted a slightly decreasing suspension ratio, leaving some doubts regarding the optimal choice of the shock absorber that can be associated with the suspension. It would be interesting to have the possibility to modify the anchor point for the shock absorber on the linkages in order to vary the suspension ratio.

References Dla, H. (2000) MTB Suspension Tuning and Technology http ://www .math .chalmers .se/-olahe/Bike/index .htmi. Herath, P. (2004) Design and Analysis ofa Mountain Bike Rear Suspension System . Mechanical Engineer ing Thesis , RMIT. Sasaki , K. (2001) A Bicycle Rear Suspension Analys is Method . http://www .mtbcomprador.com/conten t/category13/671105/.

An Ambient Intelligence System to Assist Team Training and Competition in Cycling Ingmar Fliege, Alexander Geraldy, Reinhard Gotzhein, Thomas Jaitner, Thomas Kuhn, Christian Webel Technical University Kaiserslautem, [email protected]

Abstract. Teamwork in cycling plays an important role, notonly during competition to push a cyclist, but also in training to maximize individual training effects. In this paper, we present a fully operational prototype of the Assisted Bicycl e Trainer, a distributed ambient intelligence system to enhance outdoor group training of cyclists. The prototype is designed to run on different hardware platforms and communication technologies, in particular, embedded PC communicating via WLAN and Bluetooth, and light-weight micro controllers using ZigBee for inter-bicycle communication. A focus of the paper is on the tailored communication solutions anddifferent broadcast schemes.

t Introduction Ambient Intelligence (AmI) is a vision where we will be surrounded by unobtrusive electronic devices, sensitive and responsive to people and objects, seamlessly embedded into the environment, and interconnected through wireless ad-hoc networks ' [I] . AmI systems will provide ubiquitous services that enhance human capabilities and the quality of life. It is expected that AmI systems will have an impact on all spheres of our life, including professional work, leisure activities, public health, transportation, communication, and sports. In this contribution, we present a specialized Ami system to support outdoor bicycle group training. Even though cycling is primarily known as an individual sport, teams play an important role in training and competition. In particular, the team time trial is an outstanding event in a major competition like the Tour de France. Even more, road cycling in groups is common in training. In typical team training, a group of cyclists covers a distance of up to 200 km, with a varying road profile. For best training effects, each cyclist should ride with an individual exercise intensity that depends on various conditions such as physical capabilities and skills of the cyclist, speed, road incline, head wind and temperature. In Section 2, we describe the Assisted Bicycle Trainer (ABT), a distributed AmI system that enhances the outdoor training of a group of cyclists, and survey the implementation of our fully operational prototype. Tailored communication solutions of the ABT are addressed in Section 3. We conclude with a brief outlook in Section 4.

98

I. Fliege, A. Geraldy, R. Gotzhein, T. Jaitner, T. Kuhn, C. Webel

2 The Assisted Bicycle Trainer The objective of the Assisted Bicycle Trainer (ABT) is to improve the training effects such that each cyclist is as close to his individual exercise intensity as possible. To achieve this objective, the ABT dynamically collects status data of each cyclist, and displays a summary of these data to the human trainer accompanying the group of cyclists by car. Based on this information, the trainer may adjust training parameters, for instance, by ordering the group to change speed, or by ordering a particular cyclist to take the lead, exposing him to the headwind, while all others can exploit the slipstream and thus need less pedal power. Orders of the trainer are shown on small displays attached to each bicycle. The ABT is a self-organizing system, supporting, in particular, dynamic group formation and mobility. Communication among cyclists and human trainer is performed via a wireless ad-hoc network. Currently, the Assisted Bicycle Trainer supports two outdoor training modes: individual training, where every cyclist can monitor the recorded sensor data during the training session, and group training, where the training of every cyclist is controlled by software and directed by the human trainer. In a typical training session, a group of cyclists covers a large distance. While the speed of the whole group must be the same to avoid partitioning, the position of the individual cyclists within the group can be used to control the power that every cyclist requires to hold the group speed. The Assisted Bicycle Trainer measures and collects various data of each cyclist and uses this information to calculate the group speed and the position of every cyclist within the group to enhance the outcome of the training. Depending on the availability of sensors, a variety of data may be used for controlling the training. Examples are the road profile , the slope, the wind speed and the power output of each cyclist. Our Assisted Bicycle Trainer consists of three main components: • ABT application . The distributed ABT application has been designed for supporting outdoor bicycle training with a varying number of cyclists. It consists of a cyclist application running on every bicycle system, and of a trainer application that runs on the trainer laptop . The cyclist application interacts with the cyclist by a combination of a graphical user interface (GUI) and voice output. • Communication middleware. The communication middleware controls interbicycle communication for the acquisition of sensor data and GUI management as well as the intra-bicycle communication. The middleware is divided into an application specific and into a generic part . The generic part handles communication tasks that appear in every distributed application, such as media access and multi-hop routing. The application-specific middleware provides serv ices that have been tailored for the ABT application. These services include sensor data acquisition and distribution as well as determining the current number of cyclists and detection of field partitioning. The communication middleware is running on all nodes of the ABT system. • Hardware platform . Currently, there exist two hardware platforms for the assisted bicycle trainer. The first platform is an embedded-PC solution using WLAN for inter-bicycle communication and Bluetooth for intra-bicycle communication. The second platform is a small, ultra low power solution

An Ambient Intelligence System to Assist Team Training and Competition in Cycling

99

that is based on MicaZ motes [3], manufactured by Crossbow Technologies. The MicaZ motes mainly consist of a micro controller, and communicate using ZigBee, a low power wireless technology.

Fig. 2 Crossbow MicaZmote (OEMedition) Fig. 1 The Wireless LAN solution for the Assisted Bicycle Trainer

Figur e I shows the embedded-PC solution, installed on a bicycle . The embedded PC, WLAN stick, Bluetooth adapter, a pulse rate receiver, and batteries are mounted on the carrier. A PDA showing the current driver status (e.g., pulse rate, actual speed) and the trainer's orders (e.g., required speed, position changes) is attached to the handle bar. The cyclist carries a transmitter belt that detects the pulse rate and sends it to the pulse rate receiver. The trainer system (not shown in Figure I) is installed on a laptop, with a sophisticated graphical interface to monitor and direct the training. Intra-bicycle communication between PDA and embedded PC is by Bluetooth, wireless LAN is used for inter-bicycle data exchange. Figure 2 shows a MicaZ mote, which has the size of a stamp, and which replaces the embedd ed PC and the wireless LAN communication of the embedded-PC platform. In comparison to the embedd ed-PC platform , the micro controller solution is preferable due to its low weight and low power consumption. To validate the technical function ing of the embedded-PC solution , we have run several outdoor training sessions with one cycli st and a trainer accompanying the cycli st in a car. Sensor values were communicated via WLAN up to a distance of 120m. On the trainer laptop , the heart rate values of the cyclist were recorded. A sample taken during a short training run is shown in Fig. 3.

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3 Communication Middleware The main task of the communication middleware is the provision of inter-bicycle and intra-bicycle communication. We have developed a middleware that serves as a hardware abstraction layer to the application , and that can be adapted to the specific needs of different configurations. When developing distributed systems based on wireless ad-hoc networks , routing across multiple hops is of particular importance . The ABT requires a broadcast service - every message should be received by every node including the trainer laptop. Here, we can distinguish two different types of broadcasts : • Local broadcasts are transmitted by a node and received by every node that is within range of the transmitter. In this case, no routing protocol is required. Local broadcast can be used in scenarios where the range of the transmission technology is high enough to reach all other nodes. • Global broadcasts are transmitted through the entire network, regardless of the transmitter's range, as long as the network is not partitioned. If some nodes are not within range of the transmitter, this requires multi-hop routing. Depending on the implementation of the routing protocol , the reliability and the overhead of the global broadcast may vary. For inter-bicycle communication of the ABT, we have tailored two communication systems, supporting local broadcast and global broadcast, respectively. Global broadca st is realized by NXP/MPR [5], which uses a selective flooding strategy to save bandwidth. Both protocols have been specified with SDL [2], a formal, standardized language for the design of distributed systems and protocols.

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101

To compare protocol performance, we have performed extensive simulations, using ns+SDL [4], our network simulator for SDL systems. One simulation scenario consisted of a field of 20 cyclists and a trainer. At simulation times 150 and 550, a group of cyclists separates from the field, resulting in the partitioning of the networks when using local broadcasts. Figure 4 gives an idea of this situation . Here, the remaining field consists of cyclists I, 2, and 3, with cyclist 4 of the separated group still being within their communication range. Thus, when using local broadcast, the other nodes can not communicate with the trainer, who stays close to the main field. This situation is improved by NXP/MPR, where messages are forwarded across multiple hops. 25

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Simulation results for the scenario are shown in Figure 5. With local broadcast, network connectivity goes down when a group of cyclists separates from the field until the field is reunited. With global broadcast based on NX P/MPR, there is full network connectivity most of the time. However, there are short periods of time during which some nodes can not be reached, which is due to node mobility, frame collisions, and signal interference. Whether local or global broadcasts are used should be transparent for the ABT application. In the case of a communication system that supports local broadcasts only, the ABT application is notified about the cyclists currently within reach. This would also be the case for a communication system using global broadcasts when two groups of cyclists are too far away from each other for the communication system to establish a connection between these two groups.

102 I. Fliege, A. Geraldy, R . Gotzhein, T. Jaitner, T. Kuhn, C. Webel

4 Conclusion In this paper, we have presented a fully operational prototype of the Assisted Bicycle Trainer (ABT), a distributed ambient intelligence system to enhance outdoor group train ing of cyclists, and have demonstrated its technical functioning . In particular, we have described the tailored communication solution of the ABT , supporting different types of broadcasts, and the advantages and drawbacks of these broadcast schemes. Future work includes the incorporation of additional sensors into the ABT, the conception and implementation of sophisticated control algorithms for optimizing training effects , and the application of the ABT during regular group training sessions.

References E. Aarts, R. Harwig, M. Schuunnans. Ambient intelligence. The invisible future: the seamless integrat ion of technology into everyday life, Mc-Graw Hill, 2002 . International Telecommunications Union . Specification and Description Language (SDL). ITU-T Recommendation Z.100, August 2002 . Crossbow. Micaz wireless measurement system. http ://www.xbow .com/Products/ Produ ctpdf', files/WirelessJldf/M lCAz _Datasheet.pdf. T. Kuhn , A. Geraldy, R. Gotzhein, and F. Rothlander. ns+SDL - The Network Simulato r f or SDL System s. In A. Prinz, R. Reed, and 1. Reed , editors, SDL 2005, Lecture Notes in Computer Science (LNCS) 3530, pages 103- 116. Springer, 2005 . I. Fliege, A. Geraldy: NXPIMPR - An Optimized Ad-Hoc Flooding Algorithm, Technical Report 343/05, Computer Science Department, University of Kaiserslautern, Germany, 2005

Indoor-Simulation of Team Training in Cycling Thomas Jaitner, Marcus Trapp, Dirk Niebuhr, Jan Koch TU Kaiserslautem, [email protected]

Abstract. For the single cyclist performance parameters such as power, speed, or heart rate can be monitored during training and competition. Although cycling is primarily a single sport, riding in groups is a very common in training. An ambient intelligence system has been developed for the training of a group of cyclists. The objective of this system is to improve team training such that each cyclist is as close to his individual exercise intensity as possible. Besides physiological and biomechanical data, subjective sensations are also considered. The focus of this paper is on feedback training. Based on the comparison of dynamically collected status data and set values, the feedback training system adjusts training parameters, for instance by advising the group to change the orderor the formation, to increase or decrease the speed, or to split the group. In a final version, the system should rununder outdoor conditions. As an intermediate step, a prototype forindoor training wasestablished.

1 Introduction Cycling in groups is a very common method in training especially for long lasting training sessions (Gregor and Conconi, 2000). For best training effects, each cyclist of a group should ride with his predetermined exercise intensity that at least will slightly differ between athletes due to individual physical capabilities and skills,. While the speed for all cyclists must be the same, the power output depends on the position within the group. Because of the head wind the power output of the leading cyclist is up to 36% higher than the power output of subsequent cyclists (Neumann, 2000). In consequence, cardiocirculatory and metabolic effort of subsequent cyclists will be lower. To improve team training the cyclists might regularly change positions, adjust the speed of the whole group or arrange their positions according to individual differences in exercise intensities. Besides physiological and biornechanical parameters the subjective sensations are considered as reliable and highly relevant indicator to determine the appropriate exercise intensity (Gregor and Conconi, 2000). However, subject's sensations are normally not monitored by technological measurement systems in cycling. A promising approach for the evaluation of physical exertion during training is offered by the RPE scale (Borg, 1998) An ambient intelligence system has been developed for the training of a group of cyclists (Litz et al., 2004). The objective of this system is (I) to improve training for

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Thomas Jaitner, Marcus Trapp, Dirk Niebuhr, Jan Koch

the single athlete considering physiological and biomechanical data as well as subjective sensations and (2) to improve team training such that each cyclist is as close to his individual predetermined exercise intensity as possible. The system consists of three major parts : data acquisition, communication between multiple bicycles, monitoring training data and feedback training . The focus of this paper is on feedback training. In a final version, the system should run under outdoor conditions. As an intermediate step , a prototype for indoor training was established that consists of 4 bicycles and 4 ergometers. The ergometer data are processed by a simulator, which calculates the power each cyclist must generate for a given speed considering head wind, lee and road profile . Simulated power, speed, cadence as well as the heart rate are transmitted to each cyclist.

2 Prototype of the Bicycle Trainer 2.1 Hardware Setting and Software Architecture Four bicycles were mounted on ergometers (Tacx Tl680 FLOW) and equipped each with a Sony Vaio U-7 I micro laptop with a touch screen as user interface. All micro laptops are connected among each other using Wi-Fi technology forming an ad-hoc network . The control software running on this micro laptop uses the current speed, the current cadence, the current pedal power, and the current heart rate of each cyclist as sensory input data. This can be seen in Fig. I exemplarily for only two bicycles . The sensors are connected wireless or alternatively by wire to a proprietary sensor board which delivers the sensor values to our control software using the RS232 serial interface (Wahl, 2004) . A standard pulse belt was used as pulse sensor. Processing of real sensor values as well as conversion of control variables of the brake current as result of the force information from the simulation is done on another control board . They are connected via CAN-Bus. This separation between two different boards is done since the system can be easily used outdoor just by removing the simulator board circuits, the simulator and the ergometer. The hardware setting (Fig . I) is supported by a software system that allows various flexible hardware configurations without changing or replacing the software system. Therefore, a Service Oriented Architecture was chosen (Bartelt et al., 2005) where services are identified only by their software interfaces enabling the easy use of different hardware. By service we refer to the software representation of devices (e.g. sensors) as well as to software units (e.g. single training control functionality) which are executed on a device with computation capacity. This is necessary since it cannot be assumed, for instance, that all cyclists use the same sensors or the same set of sensors. Additionally, by using this software architecture, the number of cyclist that can addend group training is not bounded above or below. The architecture is based on a Configuration Service , where each service registers together with different configuration sets of needed services, which allows more flexibility at runtime . Thus, it is possible to select another configuration at runtime- e.g. introduce a new sensor, switch from single training to group training, and so on - without changing the software or even restarting the system. For example, the single training control service registers at the configuration service stating that it needs a pulse sensor ser-

Indoor-Simulation of TeamTraining in Cycling

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Fig. 1: Hardware architecture of the indoor prototype

vice, a power sensor service and many services more in order to be run. When it notifies the Configuration service, that it wants to be run, the best set of services is determined by the Configuration Service, based on quality of service descriptions and contextual information. After determining the best required services, they are handed over to the single training control service which can then start working.

2.3 Simulation of head wind and road profile The power generated by the cyclist can only be gathered indirectly with knowledge of speed and the imposed force or moment of crank torque, respectively. The power is derived from the torque and the speed while the torque is calculated by the force and the wheel radius . The moment of torque which is the force normalized to the radius is assumed to be approximately equal at crank and rear wheel. Hence the power can be determined by the adjustable brake of the ergometer. For a more realistic training in the indoor environment, the properties of a dynamic world were simulated by a simplified model (Palm, 2005). The brake forces of each ergometer were adjusted considering dynamic friction, wind resistance, and slope dependent lift forces : (2) The single components of the brake force therefore are determined as follows (Eq.3) :

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FG=m·g·sin(a)

(3) FW=Y2'p'cw 'A(v+v w )2

with mass of cyclist and bicycle m, acceleration of gravity g, slope a at current position, coefficient of friction C R, density of air p, air drag coefficient c w, front surface A, wind velocity in counter direction vw• Air drag coefficient as well as front surface were approximated according to Gressmann (2003). The exploitation of the slipstream by cyclists on subsequent positions is considered by a linear reduction of the wind resistance depending on the velocity and the distance to previous cyclists. This approximation is based on calculations by Gressmann (2003) and Neumann (2000).

3. Feedback training control 3.1 Single training An individual training plan serves as initial input for the feedback control of the single cyclist. The exercise intensity is described by target power, ' corresponding heart rate and cadence for given time intervals. The primary task of the system is to control the cyclist's heart rate by adjusting the target power. When a cyclist's heart rate is above the upper bound of the tolerance range for a certain time the preset power will decrease. This procedure will be repeated until the cyclists heart rate will remain in the range of tolerance . Additionally, a limit for the decrease of power has been defined, which cannot be underrun by the feedback control. The system reacts in the opposite way every time the cyclist stays 30 seconds below the lower bound of the heart rate corridor. All control parameters can be adjusted individually. The initial settings are a range of ±3 beats for the heart rate, a time period of 30 s and a decrease rate of 10%.

3.2 Influence of Subjective Sensations During the whole training the system asks the cyclist regularly to enter the actual rating of perceived exertion as feedback about the current subjective sensations using the RPE scale (Borg, 1998). On a scale from 6-20 , values between 10 and 14 are presumed as adequate exercise intensity, whereas lower or higher values are considered as non-adequate exercise intensity. The subjective sensations influence the feedback control in the way that the tolerance range of the heart rate will be mod ified by low as well as high rating .

3.3 Group training The group training control is based on the single training control as described above . Two or more cyclist can form a training group . During the training the group control

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maximizes the training effect of every single cyclist while keeping the group together. Therefore, the optimal group speed is calculated by minimizing the sum of differences for all cyclists between the target values of their initial training plans and the new target values of the group. Moreo ver, a formation is calculated which determines the position of each cyclist. If the cyclist's sensor values are not within the tolerance corridor, the following means are taken for optimization in the given order : I. Changing position s with in the group 2. Changing the formation of group 3.Adjusting speed 4. Splitting the group All data gathered during the single or group training is stored persistentl y and can be used for evaluations afterwards.

4 Evaluation of the indoor simulation prototype So far, several training sessions were run successfully. Fig. 2 shows exemplarily the heart rates of two cyclists during a simulated team training. The training was started with preset lead ing intervals of 90 seconds and individuall y determined heart rate boundaries. Grey bars indicate the leading intervals of cyclist I (solid line). Leading intervals of cyclist 2 (dotted lines) are marked in white . 110 ..-.....--

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In the third leading interval of cyclist 2, the heart rate exceeds the tolerance range . Therefore, the cyclist are instructed to change position , before the preset time target is reached . Due to the feedback control mechanism, all subsequent leading interval s of this cyclist are reduces. In Fig. I, this can be observed by varying amplitudes of the white bars. Cyclist I is able to maintain the preset time target s up to the third last

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Thomas Jaitner, Marcus Trapp , Dirk Niebuhr, Jan Koch

leading interval. A change of positions is initiated after 60 seconds due to a transgression of the individual heart rate boundary. In this case, the intervention of the feedback control mechanism was accompanied by a higher rating of the subjective sensation, which results in a decrease of the upper heart rate boundary.

5 Conclusion According to the preliminary results, the indoor simulator as well as the implemented feedback control system seem to be an effective aid for cycling training . The established communication structure is reliable under indoor conditions. By a set of training experiments tolerance ranges for cyclists of different levels of performance are determined to optimize the feedback control algorithms. While the system should run under outdoor conditions, parallel and future work will focus on the integration of different sensors (e.g. force sensors at the crank, GPS) as well as on the optimization of the communication structure.

Acknowledgements This work was supported by the Research Center Ambient Intelligence of the University of Kaiserslautern.

References Bartelt, c., Fischer, T., Niebuhr, D., Rausch, A., Seidl , F., Trapp, M. (2005) Dynamic Integration of Heterogeneous Mobile Devices . In: Proceedings of the Work shop in Design and Evolution of Autonomic Application Software (DEAS), ICSE 2005 , S1. Louis Borg , G. (1998) Borg's Perceived Exertion and Pain Scales . Human Kinetics, Champaign Gregor, RJ., Conconi, F. (2000) Road Cycling. Blackwell Science,Oxford Gressmann, M. (2003) Fahrradphysik und Biomechanik. Delius Klasing , Bielefeld Litz, L.. Wehn, N. and Schuermann, B. (2004) Research Center "Ambient Intelligence" at the University of Kaiserslautem. VDE Kongress 2004, I, 19-24, VDE , Berlin Neumann, G. (2000) Physiologische Grundlagen des Radsports. D1. Zeitschrift f. Sportmedizin, 5, 169-175 Palm, S. (2005) Realisierung eines Simulators filr den Fahrraddemonstrator BicMon . Unpublished work , University of Kaiserslautem. Wahl, 1. (2004) Dokumentation der programmierten Anwendung fur das Sensor-Board des BicMon-Demonstrators. Unpublished work, University of Kaiser slautem.

A Bond Graph Model of a Full-Suspension Mountain Bicycle Rear Shock Robin Redfield l and Cory Sutela/ J

Departm ent of Engineering Mechanics, United States Air Force Academy , Colorado Springs , CO, USA, rob.redfield @usafa .af.mil SRAM Corporation, Colorado Spring s, CO, USA

Abstract. As the sport of mountain biking matures , equipm ent continually evol ves to afford better biking performance, enjoyment, and safety. In the arena of suspension systems, mountain bikes have moved from rigid suspensions with large, knobby tires to front fork suspensions, and finally full suspensions. Suspensions have gone from elastomeri c compl iance to air and coil springs with adjustable travel. Damping has progressed from fixed to adjustable rebound , compression, and lockout. The current trend is to add force or frequency dependent damping to minimize response of a suspension from pedal input. A bond graph model of a mountain bike rear shock is developed incorpora ting adjustable rebound /low- speed compre ssion, high-speed compression, and adjustable, compression damping initiation. An air shock with a nitrogen charge is modeled with velocity across the shock as input. The dynamic equations that come from a bond graph model are simulated to predict key responses. Experimental response of the modeled shock is acquired subject to periodic velocity inputs. The experimental response is used to tune the design parameters of the model and for validation . Future use of the model is to better understand the physics and performance of the mountain bike shock and to relate performance to the requirements of expert mountain bikers .

1 Introduction The popularity of full suspension mountain bicycles continues to increase as new designs allow users to ride increasing technical terrain with more control. Today's all-purpose trail riding frames are designed to perform reliably in harsh downhill conditions without adding unnecessary weight that would compromise climbing performance. Suspension elements (forks and rear shocks) must provide isolation from large impacts, attenuation of high frequency bump s, and dissipation of kinetic energy, while adding the least weight possible. A relatively new development in mount ain bike forks and rear shocks is a regressive damping configuration: the so called "stable platform" or compression initiation control (cc) system . The cc system provides increased efficiency during climbing and hard pedaling by reducing or preventing suspension movement. In the ideal embodiment of this system , the suspension system becomes fully active immediately upon encountering an impact force greater than some threshold size. Analyzing the behavior of cc damping systems is challenging because there is a wide range of conditions relating to force, position, and velocity to which the shock is subjected. The most popular approach to assessing rear shock performance is the

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Robin Redfield and Cory Sutela

test ride - a qualitative technique which necessarily contains a degree of subjectivity . Shock dynamometer curves (plots of force with displacement and force with velocity) are also used, but these are complex and difficult to interpret. Previous research relating to mountain bicycle suspension performance includes both experimental and theoretical analyses of complete bicycles (Sutela (2004) references a selection of research examples). Redfield (2005a and b) used a bond graph/conservation of energy approach to model a front only and full suspension bicycle coupled to a rider to predict system performance for a bike/rider exposed to changes in terrain. Until now, a detailed model of mountain bike rear shock behavior has not been described . The goals of this research are to reduce the design cycle time for rear shocks by : Creating a mathematical model of a modem bicycle rear shock, including consideration of a cc system. The model must reflect the physical behavior of the system so that once it is validated it can be used to guide the performance optimization that is possible by adjusting geometry and operating pressures . Measuring the physical performance of the modeled shock. The experimental results can be used to validate the model. Adjusting model parameters to identify which physical parameters inside the shock most strongly influence its performance .

2 Methods 2.1 Rear Shock Model Mountain bike rear shocks control relative motion between the sprung mass (main frame, mf) and the unsprung rear triangle (rt). Fig. 1 is a schematic of a shock assembly that incorporates a damper body that moves over a piston containing oil flow ports. These ports are essentially fitted with 2 check valves (one user tuned) and a user adjustable orifice. One check valve is factory set for high speed compression relief; the other is set for compression initiation control, the shock force necessary to initiate compression . The orifice controls rebound and low-speed compression damping. The piston is supported by the air pressure, PA, and is contained also by the seal head and shock body. The shock also contains a sealed volume of pressurized nitrogen, N], which acts on the floating piston (jp) volume to maintain positive pressure within the damping oil chambers at all times, preventing oil vaporization during shock movement. Vrt and Vmf represent the axial components of the main frame and rear triangle velocities . The damper body is divided into 2 chambers (1 and 2) which are both completely full of oil. The size of chambers I and 2 depends on the position of the piston within the damper body. The piston itself is hollow and contains a rebound/low-speed compression port and high speed compression relief on one side, and a cc valve on the other. The ports are modeled representing a flow proportional to the square-root of the oil pressure drop, while the high speed relief valve limits the

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2.2 Experimental Setup A shock of the type described in the model was subjected to a prescribed input velocity sine wave of the mfeyelet (rt eyelet fixed), using an MTS 24.11 dual servo-valve hydraulic load. The actuator contains an integral LVOT and is fitted with a calibrated Interface 1210 ACK-5K-B load cell (measuring the mf eyelet force). The shock was subjected to displacement sine waves of varying frequency , with peak-topeak stroke length of 25mm. The MTS damper test software (V3 .5.3) produces

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Force vs. Displacement and Force vs. Velocity curves. Results are given for 1Hz and 5Hz sine waves, and in each case the graph represents the 2nd of 3 sequential sine waves at a given frequency .

3 Results Figure 4 shows the eyelet force predicted by the shock model under 3 distinct damper settings in addition to one cycle of test data, all in response to a typical IHz sinusoidal displacement input. Geometric data and initial fluid pressures are taken from the tested rear shock.

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...... - 2 000 I:...!!::::::::::::::=:.:..:JL:.:..::.._ -.L_ _-l_~-l - 4 00 - 200 0 200 400 Velocity, mm/ 6 Fig. S. 5 Hz test data and model prediction

5 Conclusions A model, based on fluid pressure and flow through orifices in a production mountain bicycle shock, was created using the bond graph technique. The model was calibrated at an operating frequency of I Hz by adjusting model parameters that relate to design choices that could be physically implemented in the shock. The calibrated model was applied to a 5Hz operating frequency, demonstrating good agreement with measured data. Deviations from the test data might be related to friction inside the shock body , inertia of the fluid, or the thermodynamic conditions during compression of the N 2 chamber, although these were not investigated in this work. The model can be applied by design engineers to identify the physical parameters which most significantly affect the measured performance of the shock, and how these are manifested in the damper curves. This will ultimately result in reduced design cycle time as new shocks are developed.

References Sutela, C. (2004), Measurement of suspension efficiency in mountain bicycles during hill climbing, The Engin eering ofSport 5 - Procedings ofthe International Sports Engineering Association (ISEA), Vol. 1, pp. 487-493. Karnopp, D., Margolis, D., and Rosenberg, R. (2006), System Dynamics; Modeling and Simulation ofMechatronic Systems. 4th ed., Wiley InterScience, New York. Redfield Robin (2005),"Large Motionmountainbiking dynamics," Vehicle System Dynamics, Vol. 43, No. 12, pp. 845-865. Redfield, Robin C. (2005), "Planar, Large Excursion BondGraph Model for Full Suspension MountainBiking," Proceedings ofthe ASME Dynamic Systems and Control Division2005, ASME International Mechanical Engineering Congressand Exposition, 2005.

Track Cycling: An Analytical Model Richard Lukes', Matt Carre' and Stephen Haake

, Sports Engineering Research Group, University of Sheffield, [email protected] Sports Engineering, CSES, Sheffield Hallam University

2

Abstract. This paper presents an analytical model of track cycling the purpose of which is to provide a tool that allows subtle changes to be made to the bike, rider or environment and a corresponding change in performance realised. The model has been derived specifically for track cycling, and considers the implications of riding in a velodrome. Various inputs are required by the model, such as; rider power, atmospheric conditions, tyre properties, velodrome geometry, aerodynamic properties and bike and rider characteristics. A fundamental principle of the model is that the centre of mass travels a shorter distance in the bends than the wheels. An application is demonstrated by examining Chris Boardman's 4 km individual pursuit world record ride. The predicted completion time shows excellent agreement with the record, however assumptions regarding atmospheric conditions and equipment dictate that further validation is necessary. Examining the output demonstrates three fundamental principles of track cycling; (I) aerodynamic resistance is highly dominant, (2) the bike accelerates in the bends and decelerates in the straights and (3) the rolling resistance increases in the bends. A graphical-user-interface is to be produced for the model providing coaches and researchers with an accessible and practical investigative tool.

1 Introduction In the sport of cycling margins of victory are often extremely small, particularly in track cycling. As a result equipment selection in track cycling is always of paramount importance. The choice of equipment is often governed by an educated reckoning that one piece of equipment will improve performance over another. The actual performance difference of selecting one piece of equipment over another is not often realised. This paper presents an analytical model for track cycling which provides a tool that allows the difference in equipment to be quantified in terms of overall performance. Analytical models of cycling are by no means a new concept. A number of authors have produced equations of motion for the purpose of examining particular aspects of cycling (van Ingen Schenau 1988; aids, Norton, Lowe, Olive, Reay and Ly 1995; Bassett, Kyle, Passfield, Broker and Burke 1999). Where this analytical model aims to further previous understanding is in the derivation of a model specifically for track cycling.

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Richard Lukes , Malt Carre and Stephen Haake

2 Model Formulation The model is too length y to show the entire formulation, howe ver the fundamental principles will be presented. The basis of the model is that there are two states of riding; one in the straights and one in the bends. The force s that dictate the rider' s motion arc hown in Fig. I.

Fig. I . The dominant forces on a bike

FD is the drag force , FA is the acceleration force , FR is the rolling resistance, FlY is the contact force, F w is the weight and F T is the tran sferred force . Resol ving these force s in the direction of motion gives the governing equat ion, F 4 = rna = FT

-

FD

-

FR

(I)

In the straights the rider is travelling in a straight line and therefore not tipp ing, leadin g to the simple free-bod y diagram shown in Fig. 2(a). In the bend s the change in velocity results in an angular acceleration and the addit ion of a centripetal force (Fig. 2(b )). To maintain balance the bike tips , moving the centre of mass in towards the track centre. The shift of mass is an important principle in the analytical model as it is assumed the work of the rider is used to propel the centre of mass around the track . In the bends the centre of mass trave ls less distance than the base of the wheel. Therefore the movement of the centre of mas s effectively cuts the comer, re ulting in acceleration at thc base of the wheel for a con tant power input.

Fw

(a) Straights

(b) Bends

Fig . 2. The forces on the bike in the straight (a) and in the bend (b)

An Analytical Model for Track Cycling

117

Angle fJ is the banking angle of the track, a is the tipping angle of the bike , F F is the lateral friction force at the wheel, Fe is the centripetal force, rw is the radius of the wheel-to-track contact point and rm is the radius of the centre of mass. To continue the model derivation the forces shall be examined individually.

2.1 Transferred Force The transferred force , F T, is the force propelling the rider along. In this model F T accounts for the internal losses within the bike, occurring mostly due to chain inefficiency and frame and component deflection and is given by,

(2) where, '7 is the bike efficiency, P is the rider power and v is the bike velocity.

2.2 Rolling Resistance The rolling resistance, FR, is proportional to normal contact force and rolling resistance coefficient, !1R. (3) The term in the bracket in Eq. 3 is the normal contact force accounting for its increase in the bends . The term C, a coefficient that accounts for the increased rolling resistance due to 'scrubbing' . Scrubbing occurs when the bike is not perpendicular to the track and the rider has to steer the front wheel into the slope . This small angle of steering causes the front wheel to skid or 'scrub' as well as roll along the surface leading to increased rolling resistance, as demonstrated in Fig. 3. The scrubbing coefficient, C" has been determined using data reported by Kyle (2003) and is dependent upon the angle of the bike relative to the track.

1

Direct ion of mot ion is identical in bo th cases

Rolling Resistance

Difference in rolling resistance du e to 'scrubbing'

(a) Flat track: Rolling

t

(b) Banked track: Scrubbing

Fig. 3. Comparing flat and banked tracks illustrating scrubbing

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Richard Lukes, Matt Carre and Stephen Haake

2.3 Aerodynamic Drag Aerodynamic drag is the major contributor to the cyclist's resistance. The aerodynamic drag force, FD, is calculated using,

(4) where CD is the drag coefficient, A is the frontal area and p is the air density. Drag coefficients and frontal areas have been obtained from CFD simulations.

2.4 Completed Equation Putting the terms from Eqs. 2-4 back in Eq. I gives the governing equation for the model, Eq. 5. rna = (

~ :J-( CdA~ pv' J-[(m ;: cosa+ mgsina }l C, J R

(5)

3 Using the Model 3.1 Solution Procedure The model uses the following procedure at a finite number of time steps to provide a solution. START From power profile and governing equation calculate distance travelled by centre of mass Resolve forces in the bends to determine tipping angle and radius of centre of mass Use ratioof radii (wheels to centre of mass) to calculate the distance travelled by the wheels

Fig. 4. Thesolution procedure The model has been created for a I km time trail or 4 km individual pursuit. Generic power profiles for each event have been created, however the model allows the use of power profiles extracted from an SRMTM power measuring crank. Once all the input parameters for the specific event have been selected the model can calculate the forces throughout the event, tipping angles and split times.

An Analytical Model for Track Cycling

119

3.2 Example Application To demonstrate the model a 4 km pursuit shall be examined. In 1996 Chris Boardman set the world record for this event, covering the distance in 4 m I I.I s. The model has been used to replicate this performance. A power profile for this event has been constructed using the work of Broker, Kyle and Burke (1999), who stated that Chris Boardman averaged 520 W over the entire event and 474 W once cycling at a constant speed. The drag coefficient area (CoA) has been taken from Hill (1993), who examined the same rider on a slightly earlier version of the bike in a wind tunnel. The frontal area has been calculated based on the rider's height and weight using the method presented in Bassett et al. (1999), giving a CD of 0.52. Values for rolling resistance, bike efficiency and climate conditions have been selected to mimic the actual conditions as closely as possible. Using these conditions the model predicted a completion time of 4 minutes 10.7 s, which is a good approximation of the actual event. However it must be stated that this does not serve as a strict validation due to the approximate nature of the input parameters. The output of forces and velocity are shown in Fig. 5, illustrating some interesting aspects. Firstly, the dominance of aerodynamic resistance is highly apparent. Secondly, the fundamental concept that the movement of the centre of mass accelerates the bike in the comer is demonstrated by examining the velocity profile. In the model, the bike's velocity in the bends increases by approximately 0.4 m/s, a sensation felt by experienced riders. Thirdly, the rolling resistance noticeably increases in the bends due to the far greater contact force as the bike turns. ~

~

40

-10

o

60

120

Time (s)

180

Fig. 5. The force and velocity output from the model

The model can also be used for comparative analyses. Hill (1993) also reported the CoA of a conventional track bike with a rear disc wheel, giving a CD of 0.62. Using the model to compare the conventional track bike to the previous LotusSport bike shows that Chris Boardman would have completed the 4 km event 13.9 s slower, highlighting the efficiency of the LotusSport bike and the use of the model.

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4 Discussion Continuation of this analysis will involve some improvements to the model, mostly involving a more detailed representation of the track geometry. In addition to modifications, validation will be carried out whereby SRM power data is used as the input and actual split times are compared to the model output. Once these steps are complete a user interface will be created, providing coaches and researchers with an accessible and practical tool for future investigations. One such further investigation would be comparing the use of large and small sprockets. Large sprockets are more efficient than small ones (Burgess 1998), however are disadvantaged in terms of weight and aerodynamics. Once sufficient data has been obtained the model would provide an ideal tool for this and similar comparative analyses.

5 Conclusions The fundamental principles of an analytical model for track cycling have been presented . It has been demonstrated that this model can be used to scrutinise various track cycling events . The output from the model has been shown to give the forces and split times for the event. The application of such a model as both a research and training tool can be greatly beneficial to give a fuller understanding of the event in search of a performance advantage, which is of course the ultimate aim .

6 Acknowledgements Many thanks to Dr Simon Goodwill for offering time to code the model.

References Bassett , D.R.J., Kyle, CR., Passfield , L., Broker, J.P. and Burke, E.R. (1999) Comparing cycling world hour record s, 1967-1996 : modelling with empirical data. Med. and Sci. in Sports and Exercise , 31(II), 1665-1676. Broker, J.P., Kyle , CR. and Burke, E.R. (1999). Racing cyclist power requirements in the 4000 m individual and team pursuits. Med. and Sci. in Sports and Exercise, 31(II), 16771685. Burge ss, S. C (1998). Improving cycling performance with large sprockets . Sports Engine ering, I, 107-113 . Hill, R.D. (1993) Design and development of the LotusSport pursuit bicycle. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 207(4),285-294. Kyle, CR. (2003). Selecting Cycling Equipment. In: E.R. Burke (Ed .), High-Tech Cycling: The science ofriding faster. Human Kinetics, Colorado, pp. 1-48. aids, T.S., Norton , K.I., Lowe, E.L.A., Olive, S., Reay , F. and Ly, S. (1995) Modelling roadcycling performance. Journal of appl ied physiology , 78(4), 1596-1611. van Ingen Schenau, G.J. (1988) Cycle power: a predictive model. Endea vour , 12(1),44-47.

Forces During Cycling After Total Knee Arthoplasty Maximilian Muller', Veit Senner', Markus Wimmer 1 Technische 2

Universitat Munchen, Germany, [email protected] Rush University Medical Center Chicago, USA

Abstract. Recreational sport activity after total knee replacement (TKR) is of growing interest to patients . Therefore , the purpose of this study was to evaluate dynamic loads acting on artificial and normal knees during cycling. A force measurement system has been developed and was installed to evaluate the external loads on the pedals of a stationary bicycle. To analyze the data, different evaluation algorithms were programmed to calculate pedal force levels of the subjects during cycling.

1 Introduction Recreational sport activity after total knee replacement (TKR) is of growing interest to patients . In particular, cycling is one of those hobbies with up to 50% of TKR patients riding a bicycle during leisure times (Kuster et al. 2000). The specific contact mechanics of the tibiofemoral joint is well known for walking; however, there is limited information for cycling activities (in particular for TKR joints). Thus, the purpose of this study was to evaluate knee kinematics and kinetics acting on artificial and normal knees during cycling.

2 Methods 2.1 Overview The determination of knee loads in cycling using an inverse dynamics approach requires the contact forces at the pedals as well as precise data on the joint kinematics (Fig. 1). This presentation focuses on the design of a force measurement system and on the determination of the contact forces at the pedals as well as on the measurement of knee kinematics . External Loads + Kinematics

D

InverseDynamics

D

Internal Loading

Fig. 1. Calculation of internal loading by inverse dynamics

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Maximilian MUller

The following model was considered on how to obtain knee loads (internal loading) from the contact forces at the pedals later on and therefore served as a basis for the design of the measurement system in terms of the required load components and reference frames . In a system of segments inverse dynamics is usually started at the point next to the one of interest concerning the loads. For the present study this is the contact point at the pedal (Fig . 2). The reactive knee forces can be calculated by Newton mechanics which is cut to a 2-dimensional case for the example.

m.a =

LF=

F'contact

+ F'g + F'knee

( 1)

F kncc is the wanted knee force. To obtain reactive muscle moments, the principle of conservation of angular momentum is used as follows

e . ~ =L M =

F'kncc X r kncc

+ 1\1 muscle + F'contact X rconta ct + 1\1 contact

(2)

The left side of the equation is known from the kinematics analysis and while all other parts of the right side are given from equation (I) or from the anthropometric data Mmuscle can be calculated by solving the equation. hip

femoral

IZi Feoee

knee joint shank

IZi

fool

IZi

9 F c.ontacl

Fpedal

Fig. 2. Model of leg segments for inverse dynamic s

2.2 Force Measurement System The force measurement system for the pedal loads was integrated into the crank shafts and is based on strain gauge technology. For all load types Wheatstone fullbridge arrangements were used to minimize the influence of temperature changes and cross-sensitivity. The cells were designed to measure the three forces in space on both pedals . The magnitude of loads was adjusted to expected values of elderly people on stationary bicycles. Therefore, the max imum pedal force was set to a load of 500 N. The axial forces were read out directly by strain gauge bridges, the radial and lateral forces were determined by separate bridges determining bending moments (taking the lever arms into account) . The data transmission from the cranks to the acquisition equipment as well as the power supply of the load cells were realized by collector rings mounted to the cranks and the bicycle frame respectively. Miniature

Power and Forces During Cycling After Total Knee Arthoplasty

123

voltage amplifiers were put directly onto the load cells to avoid deterioration of the signals during the transmission (Fig . 3).

Fig. 3. Load cel1 with on board voltage amplifiers

2.3 Kinematics Analysis 3D-motion data of the lower extremity segments were obtained by a video based camera system with passive markers placed on the skin. Data were recorded at 120 Hz with four cameras (Qualysis, Sweden). As skin movement relative to the underlying bone is a primary factor limiting the resolution of detailed joint movement using skin-based systems, in this study, the cyclist's legs were equipped with an advanced marker set to conduct the so-called 'Point Cluster Technique' (Andriacchi et al. 1998) . Twenty-one markers, distributed on shank and thigh , reduce the influence of non-rigid body motion artefacts during human motion testing. Two additional markers were placed on the cranks and on the pedals to obtain the dynamic crank angle that is essential to relate the force data to the motion data .

2.4 Post-Processing Calibration matrix - The load cells are designed to measure strain by a generalized load Q which is applied to the cell. During calibration the load cell's voltage signals were related to actual applied loads . This was accomplished by applying known static loads in various combinations. Cross sensitivity between the different sensor signals was diminished by displaying the signals from cross sensitivity along with the main signal from the applied load type . In order to obtain a valid linear regression, seven different loads of every load type were applied. Finally, the linear coefficients were determined, relating the applied load Q to the voltage response V of the load cell as follows

V=a* Q

(3)

Presuming that every load type is represented by the signals of a separate strain gauge full bridge a calibration matrix [C] was generated which related every single generalized load to a voltage signal by means of the linear coefficient. [V] and [Q] are column vectors and the equation is given by

[V] = [C] x [Q]

(4)

124

Maximilian MUlier

The value of a calibration matrix grounds in the fact that it can be inverted to produce a sensitivity matrix [Cmv] . The latter can be used to determine unknown loads. Equation (4) may be rewritten as

[Cinv] x [V] = [Q]

(5)

This step was performed for every set of the 120 data sets total by a MatLab® software routine . Calculation of forces - The loads initially are seen by the load cells at the position of the strain gauges, namely the measurement plane M (Fig . 4). In order to calculate the forces acting on the bicycle pedals they have to be translated to the point of load incidence P by cutting the accordant part free and setting the mechanical equilibrium equations with the corresponding geometric parameters. Furthermore, the loads currently are displayed in the local coordinate system of the turning crank and have to be transformed to a fixed coordinate system in order to facilitate interpretation of the data . This was accomplished by accounting the dynamic crank angle with a transformation matrix for the loads.

J.

Fig. 4. Translation of loads to the point of load incidence at the pedal (P)

2.5 Setup of the System Figure 5 shows the setup of the load cell at the crank of the stationary bicycle that was used for the study .

Fig. 5. Setup of the load cell at the crank

Powerand Forces DuringCycling After Total Knee Arthoplasty

125

Figure 6 shows the overall setup of the testing equipment with the stationary bicycle, the camera system and the data acquisition computer prepared for the study.

Fig. 6. Overall setup of the testing equipment

2.6 Study Design Thirty subjects with an average age of 57.4 yrs . were included into the study. 10 subjects (av. age 64,5yrs.) had a total knee prosthesis with a constrained tibiofemoral articulation (i.e . internal-external and frontal plane rotations were limited with this design); 10 subj ects (av . age 53.lyrs.) had a total knee prosthesis with similar des ign but a mobile bearing allowing unconstrained internal-external rotation; 10 subjects (av. age 54.5yrs .) had a normal (natural) knee joint and served as agematched controls. Patients were tested at 2 levels of resistance with 5 seconds of acquisition time each. Before every testing, the patients would undergo a personal survey and examination conducted by the medical doctor assigned to the project.

3 Results and Discussion In the following the specific results of a normal subject are exemplarily presented. The range of flexion during cycling was 41°_126° . With increasing flexion angle the epicondylar axis of the femur rotated 37° internally and translated II mm posterior (based on a fixed tibia reference frame) . The forces measured at the contact between foot and pedal were analyzed in vertical (left foot: max. -I ON/min .-120N), horizontal (lOON/ 35N) and lateral (30N /-15N) direction (displayed in a fixed reference frame) to compare them with the anterior-posterior translation and internal/external rotation of the knee (Fig . 7.). As has been reported by others, the forces during biking were relatively low; however, the knee joint underwent considerable internal/external rotation and anterior-posterior translation. Total knee arthroplasty designs are typically optimized for walking and not for deep flexion maneuvers. Therefore, despite the overall low forces, generated movements at the articulation can still be troublesome causing wear and/or increased constraint forces at the tibia plateau and fixation .

126

Maximilian Muller

I

)"1---

~~~:....AL· i·f -

~~~----

P_ fOtcn. Loft _

.- ...... Fig. 7. AP-translation and internal rotation (upper row), pedal forces (below) of a normal

4 Conclusions To our knowledge this is one of the first studies who aim to compare force generation in patients after total knee arthroplasty . The measurement system was validated and the study with TKR patients is finished. Now, the data has to be processed to obtain information about effects of TKR on cycling activity. In addition to the pedal loads, however, we also acquired the contact forces at the saddle and at the handlebar to preserve the possibility to build and validate a forward simulation model of the whole cyclist which is the content of a future project.

References Andriacchi, T., et al. (1998) A Point Cluster Method for In Vivo Motion Analysis: Applied to a Study of Knee Kinematics . J Biomech Eng. 120(6):743-9. Kuster, M., et al. (2000) Knee endoprosthesis: sports orthopedi cs possibilities and limitations . Orthopade 29(8) :739-45. Raskulinecz, (1980) Design and Construction of an Anthropometric Dummy of the Alpine Skier. Case Western Reserve University, Ohio. Wimmer, M.A. (1999) Wear of the Polyethylene Component created by Rolling Motion of the Artificial Knee Joint. Shaker, Aachen .

A Study of Aerodynamic Drag and Thermal Efficiency of a Series of Bicycle Helmets Firoz Alam, Aleksandar Subic and Simon Watkins RMIT University, [email protected]

Abstract. The primary objective of a helmet is to provide head protection during fall or accident, however, thermal comfort and aerodynamic efficiency are becoming important design criteria. Helmet with venting generally increases thermal comfort but decreases aerodynamic efficiency. Therefore, an optimal design for helmet is very important in order to satisfy both aerodynamic and thermal efficiency. The primary objective of this work is to study the aerodynamic efficiency and thermal comfort of a series of current production helmets available in Australia. Aerodynamic drag and thermal comfort was measured under a range wind speeds, yaw andpitch angles andcompared.

1 Introduction Bicycle helmets are mandatory for recreational or professional bicycle riders in many countries including Australia. Although the primary objective of a helmet is to provide head protection during fall or accident, thermal comfort and aerodynamic efficiency are becoming important design criteria (Alam et al. 2005, Bruhwiler 2003, Reid and Wang 2000). Most bicycle helmets are made of foam that holds up heat, generated by the rider' s head during cycling. Humidity and high ambient temperature make the situation worse as trapped heat causes significant discomfort (sweating, stickiness etc). Helmets with venting can minimise this problem. However, venting generally increases aerodynamic drag. Therefore, an optimal design for helmet is very important in order to satisfy both aerodynamic and thermal efficiency. The primary objective of this work is to study the aerodynamic efficiency and thermal comfort of a series of current production helmets available in Australia for recreational users. Each helmet was tested for their aerodynamic efficiency and heat dissipation characteristics under a range wind speeds, yaw and pitch angles in the RMIT University Industrial Wind Tunnel. Descriptions about RMIT Industrial Wind Tunnel and other equipment were given in Section 2. Helmets were ranked according to their aerodynamic efficiency and thermal comfort.

128

Firoz Alam, Aleksandar Subic and Simon Watkins

2 Test Procedures and Helmet Descriptions The aerodynamic efficiency in terms of drag and heat dissipation characteristics for five helmets were experimentally measured under a range of speeds (20, 30, 40, 50 and 60 km/h wind speeds), yaw angles (0, ±30°, ±60° and ±900) and pitch angles (90, 60, 30 and 0 from horizontal axis). The aerodynamic drag was measured using a six component force sensor. The thermal efficiency in terms of heat dissipation (temperature drop) was measured using a heat pad on the dummy head. Seven thermo couples were attached with the heat pad located around the head under the helmet. An instrumented dummy head with the heat pad, thermo couples and helmet is shown in Figure 3. All five helmets are different in terms of venting holes and structural geometry . All five helmets were new and manufactured by Rosebank Australia. These helmets are: Blast, Mamba, Nitro, Summit and Vert (see Fig 1). In order to understand the effects of venting, the Vert helmet was modified (venting blanked off) and tested twice as standard and modified configurations, see Fig 1f.

a) Nitro Helmet

d) Vert helmet

b) Mamba helmet

f) Vert helmet modified (simply blanked off)

e) Blast

Fig. 1: A bird's eye view of all helmets

Fig. 2: Experimental setup in the test section with a dummy head

Fig. 3: Experimental setup for thermal testing (dummy head, heat pad and helmet)

A studyof aerodynamic drag and thermal efficiency of a series of bicyclehelmets

129

3 Results and Discussion Each helmet was tested with and without the head assembly (dummy head and mounting device) for all speeds, yaw angles and pitch angles; and the aerodynamic forces due to helmets were determined. All forces were converted to their nondimensional parameters and only the drag force coefficient (Cd) is presented in this work. Thermal efficiency was measured by heating up the heat pad at 60°C which was selected arbitrarily . A thermostat was used to keep the temperature constant on the heat pad. Seven thermocouples were attached on the heat pad under the helmet to monitor the temperature drop around the head. Two thermocouples were attached at the front of the head, two on each side (left & right), two on the rear of the head and one thermocouple at the centre of the head in order to obtain a comprehensive temperature distribution (see Fig 3). The temperature drop was monitored for 5 minutes at all wind speeds. The temperature readings from all seven thermocouples were averaged and presented in this paper . The results for zero yaw angles are presented here. The drag coefficient as a function of Reynolds numbers and pitch angles and the average temperature drop for the Mamba, Nitro and Vert helmets are shown in Figs. 4-9. The results for other helmets are not shown here. The drag coefficient (Cd) is relatively independent of Reynolds numbers for all helmets at 90° and 60° pitch angles except at very low speeds. However , minor Reynolds number dependency for all helmets was noted at other pitch angles (30° and 0°). The pitch angle was measured from the horizontal. The airflow at 30° pitch angles becomes complex due to the interaction of the flow separation from the local venting and fitting strips. The highest aerodynamic drag was found at 0° pitch angles for all helmets except the Vert helmet with and without venting. With an increase of pitch angles, the projected frontal area of the helmet reduces and the airflow becomes more streamlined. The Vert helmet has minimum venting and it produces relatively lower aerodynamic drag compared to other helmets. No significant variat ion in drag coefficient of the unmodified and modified Vert helmets was noted . The Vert helmet generates the lowest drag at over 30 km/h and 90° pitch angles . On the other hand, the Nitro and Summit helmets produce higher drag at the same speeds and pitch angles . The pitch angle has virtually no impact on the drag coefficient for the Vert helmet (see Fig 6). Cd Var iation with

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FIg. 5: Drag coefficient as a function of Reynolds number and pitch angles (Nitro helmet, 0° Yaw)

130

Firoz Alam, Aleksandar Subic and Simon Watkins

The temperature drop is evident for all helmets with the increase of Reynolds number. The pitch angle has negligible effects on temperature drops for the Blast, Mamba, Nitro and modified Vert helmets. However, a significant variation in temperature drops due to pitch angles is noted for the unmodified Vert helmet. Additionally, a small variation in temperature drops was noted between 90° and other pitch angles for the Summit helmet. The lowest temperature drop was noted for the modified helmet as expected due to no venting (not shown here). The highest temperature drop was evident for the Mamba helmet. Although the Vert helmet was aerodynamically more efficient, it is the worst performer in terms of thermal efficiency. On the other hand, the Nitro and Summit had relatively higher aerodynamic drag at 90° pitch angle and generate significant temperature drops. However, the Mamba helmet is the optimal helmet for its aerodynam ic and thermal efficiency as it produces the highest temperature drops at all pitch angles and low aerodynamic drag (second lowest drag). The number of venting, venting geometry and venting location play an important role in temperature drops. However, they also can generate more aerodynamic drag. Cd variatlOI1With R. ynold. num b.r s (V, rt helm st, 0 Yaw, Vario us Pilch angle . )

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Average Terrperature (Nitro, 0 Yaw . various Ri ch angles)

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100000

RBy nolds f\Urrbe r

FIg. 6: Drag coefficient as a function of Reynold s number and pitch angles (Vert helmet, 0° Yaw)

~

-.-30 Ric h ~ OAtc h

~- - --

40

300000

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0

50000

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150000

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250000

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FIg. 9: Temperature vananon With Reynolds numbers as a function of pitch angles (0° yaw), Vert helmet

A study of aerodynamic drag and thermal efficiency of a series of bicycle helmets

131

4 Conclusions The drag coefficient is relatively independent of Reynolds numbers at high speed s under 90° and 60° pitch angle s for all helmet s. The Vert helmet produces the lowest aerodynamic drag but worst performer for heat dissipation. The Nitro and Summit generate higher aerodynamic drag but perform well in heat dissipation. The pitch angles have significant effects on aerodynamic drag, however less effects on heat dissipation . The Mamba is the optimal helmet for its aerodynamic and thermal efficiency. The number of venting, venting geometry and venting location on the helmet play the key role for the thermal and aerod ynamic efficiency.

5 Acknowledgments The authors are very grateful to Anthony Resta and Rhys Solomons for their assistance with the testing and data analysis. We are also indebted to Rosebank Australia for providing the helmets .

References Alam, F., Watk ins, S. and Subic, A. (2005) Aerodynami c efficien cy and thermal comfort of bicycle helmets , Proc. ofthe 6'h International Confe rence on Mechanical Engineering (ICME2005). TH-3 2 (1-6), ISBN 984-32-2846-4, 28-30 Decemb er, Dhaka , Bangladesh. Bruhw iler, P. A. (2003) Heated, perspiring manikin headform for the measurement of headgear ventilation characteristics, Meas. Sci. Technol. 14: 2\7-227 . Reid,1. and Wang, E. L. (2000) A system for quanti fying the cooling effectiveness of bicycle helmets , J Biomech Eng. \22 (4): 475-460

4 Golf

Synopsis of Current Developments: Golf Steve Mather University of Nottingham, UK, [email protected] The main challenge in the golf industry is to design equipment which can be used by the 95% of golfers who do not play the game well. This is where the market lies. Unfortunately, the trend appears to be to design clubs for the professional and better amateur golfers and then allow for small changes in mass distribution or shaft flexibility to aid those with poor swings. The first step in the building block process of redesigning clubs must be to understand the nature of all swings, particularly the major differences between the good and poor swing. Some of the papers in this category of the proceedingsoffer building blocks for researchers to use in studying the golf swing, and are therefore very useful additions to the current situation. We must not lose sight of the fact that the elite end of the sport is still the shop window for golf clubs. It is interesting to note from one of the papers that even with first class golfers, the variations from swing to swing can be marked. Perhaps these athletes can take advantage of some of the latest technology. There is no doubt that much of the distance gained and accuracy attained in the game of golf comes from the technology applied to the design of the golf ball. The effect of ball construction on performance was first brought to public attention in papers at golf conferences 10 years ago. Since then, the market has made huge strides in applying the technology to marketable balls. However there is still room for matching the ball to the club design, or perhaps more relevantly, changing the club design to match the technology offered by the ball. Much data is therefore needed on the spin generation mechanisms and the aerodynamics of the flight of spinning spheres. One paper in this category deals with the variation of Lift and Drag coefficients during the fight of the ball.

An Instrumented Grip Handle for Golf Clubs to Measure Forces and Moments Exerted by Each Hand During Swing Motion

S. Koike', H. Iida

2

,

l

H. Shiraki and M. Ae'

I

Instituteof Health and Sports Sciences, UniversityofTsukuba, Ibaraki, Japan, [email protected]

2

Machine and Control Department, Polytechnic University, Kanagawa, Japan

Abstract. An instrumented grip handle was designed to simultaneously measure the forces and moments exerted by each hand on the handle during golf swing. Eleven pairs of strain gages were attached on the surface of an aluminum bar inserted under separated grip covers. The device was calibratedunder static conditionsand revealedgood agreementbetweenapplied and calculated loads. The output of the sensors was converted into forces and moments by resolving static equilibriumequations. A professional golf player participated in this study and performed golf swings with several clubs. Reflective-markers on the body segment endpoints and on the clubs were captured by VICON motion system with 8 cameras operatingat 250Hz. The results obtained in this study were: (1) long axial load of shaft affected the sensor coefficients of the device, and (2) internal forces and moments that do not cause the motion of the club were observed in the swings.

t Introduction In golf swing, the upper limbs and the golf club form a closed multi-segment loop. Due to the kinetic redundancy caused by the closed loop, it is impossible to determine the forces and moments exerted by each hand on the grip handle of the club with only visual information. The only way to obtain such information is to measure it directly . Previous research on the kinetics of golf swing have investigated single hand models (Milne and Davis , 1992; Sprigings and Neal, 2000) . The purpose of this study was to propose an instrumented grip handle for golf clubs capable of obtaining kinetic information of each hand during swing motion .

138

SekiyaKoike, Hiroshi Iida, Hitoshi Shiraki and Michiyoshi Ae

2 Methods 2.1 Structure of the Club Figure 1 shows the fully assembled club and the definition of the club coordinate system (oe-xeYeze). Two spherical markers with negligible-mass shafts were attached on the club for the purpose of measuring the orientation of the moving club. Figure 2 shows the structure of the instrumented grip handle . The grip handle consists of an aluminum alloy bar and two sets of aluminum covers . Eleven pairs of strain gages were attached on the bar to calculate : I) the torsional moment acting around the grip axis between the hands; 2) the bending moments; and 3) the tensile and compressive axial forces.

Sphere markers for measurcment= :::----{;> of position and orientation

c onnector) Head side grip In~trumented Butt side grip gnp handle

Fig. 1. The fully assembled golf club.

Fig. 2. The structure of the instrumented grip handle .

2.2 Device Calibration Each strain gage was calibrated under various static load conditions with an aluminum

An Instrumented Grip Handle for Golf Clubs

139

calibration rod attached to the grip handle by a connector. For loading and unloading conditions, calibration was carried out under long axial tensile load exerted by string 6 and two-a xial transversal forces exerted by strings 1-4 as shown in Figure 3(a). The transversal forces were measured by the load-cell 1. For the purpo se of studying various long axial tens ile load conditions, which are due to mainly the centrifugal forces that result from the rotational movement of the club, calibration of the strain gages for bending moments was completed using several axial-load cond itions. The tensile loads were applied by hanging weights with a string attached to the end of the calibration rod and passed through a simple pulle y system. The value was detected with load-cell 2 and was changed with the positioning of the weight s on a rail as shown in Figure 3(b).

2.3 Calculation of Forces and Moments Although the forces and moments exerted by each hand on the club are distributed all over the handle area, these loads were represented by vectors , assuming that they act at the fixed points of the hands in swing motion. The inertial forces of the handle pieces were neglected. From equations und er static force/moment equilibrium conditions (Koike et al, 2004) , the forces and moments are derived as follows:

N head N butt F head

»:

La =A-1

LC Ld Lf

A=

I

I

I

I

0 0

I I

[crh,head - rsa) X] [Crhbutt - rsa) X [Crhhead-rsJx] [crh,butt - rsc) X] 0 [crhbutt - rsd)X] 0 [Cr hbutt -rSf) x]

(1)

where vectors F, and N, indicate the vectors of force and moment for the {h location, the subscripts head and butt stand for the values at the head-side and butt-side hand s, and the vectors r h,head and r h.butt represent the position vectors of the fixed points of the head-side and butt- side hands, and the vectors 'Zk and r sk indicate mom ent and position vectors at the Jlhsensors, respecti vely.

(a). The calibration device.

(b) . The loading device .

Fig. 3. The setup for the calibration.

140

SekiyaKoike, Hiroshi Iida, Hitoshi Shiraki and Michiyoshi Ae

0% - 50%

(a). The swinging club coordinate system.

50% - 100% (b). Forward swing motion.

Fig. 4. Stick diagrams of the coordinate system and the forward swing motion.

2.4 Swing Motion Analysis The forces and moments exerted by each hand were expressed according to the swinging coordinate system using a plane named "swing plane". The plane was approximately calculated so as to involve the head and butt positions of the club from the moment the head of club was highest to impact with the ball. Figure 4(a) shows stick diagrams of the swing plane and the orientation of the swinging club coordinate system . A professional golf player volunteered to participate in this study. The player performed swings with driver, fifth iron and sand wedge clubs. Markers on the body segment endpoints and on the clubs were captured by VICON motion system with 8 cameras operating at 250Hz . A personal computer was used to store the strain gage signals, which were amplified by dynamic strain amplifiers. The sampling frequency of the data collection was 500Hz. The forward swing motion was defined from the top of swing to impact. Figure 4(b) shows examples of stick pictures of standardized forward swing motion.

3 Results Figure 5(a) shows the plots between sensor output voltages and applied y-axial moments with respect to the sensors 'tf,x and 'tfJ' under various loading conditions. From the calibration results of the sensors for bending moments, the relationships showed very good linearity and little crosstalk in terms of the moments acting about other axes at each loading condition. Since the tensile loads affected the relationship, the gradients of linearity were calculated by using interpolating functions with respect to the tensile loads as shown in Fig. 5(b). Figure 6 shows an example of the curve patterns of actual and calculated values of the forces applied atxswc-axis under axial load of about 150N. The curves show good agreement. Figures 7 (a), (b) and (c) show the forces at xswc-axis, Y swc -axis and the moments around Zswc axis in the forward swing with fifth iron club. Solid and dashed lines represent the components of head- and butt-side hand, respectively. These values were expressed in the swinging club coordinate system, and were normalized to forward

An Instrumented GripHandle for Golf Clubs

141

swing phase . The duration of the phase was OJ sec.

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Fig. 6. Curve patterns of actual and calculated forces . The xswc-axial forces of the hands showed approximate reverse patterns . The couple force that accelerate the angular motion of the club decreased gradually until 25% of the motion normalized time, increased until 70% time, and then decreased rapidly toward impact. Large internal forces were observed between the hands alongyswc-axis until 70% and the resultant force along the axis increased toward the impact reaching large positive values . Although the moment of the butt side hand around zswc-axis showed negative values during the forward swing phase, the moment of the head side hand showed positive values until 80% of the motion normalized time. Since the magnitudes of the forces of the head side hand were greater than those of the butt side hand until 80% time, the resultant moment acted as an angular accelerative torque around the axis up to 80% time.

4. Discussion Since the sensors were located in the grip handle attached to the club shaft with the connector, it was possible to obtain kinetic information of each upper limb during golf

142

Sekiya Koike, Hiroshi lida, Hitoshi Shiraki and Michiyoshi Ae

swing with several types of clubs . As is the case with an instrumented baseball bat (Koike at el, 2004), the output voltages of the strain gages for the bending moments were affected by the long axial forces, which were mainly caused by centrifugal forces and tensile forces . Because of that, it was necessary to calibrate the sensor device under various relatively high axial forces . In hitting motions with the hands , infinite combinations of forces and moments can be exerted by each hand to realize the same motion of the hitting tool due to the kinetic redundancy of the closed segments loop . From the results obtained in this study, forces and moments of head side and of the butt side hands canceled each other out. Hence, it is necessary to obtain kinetic information of each hand by using the device to realize complete understanding of golf swing mechanism.

5. Conclusions An instrumented grip handle capable of measuring forces and moments exerted by each hand was proposed to achieve a kinetic analysis of each hand in golf swing. The merit of the grip handle type device is that kinetic information about various types of clubs can be obtained by exchanging shafts via the connector. The ability to quantify acting forces and moments of each hand in golf swing has the potential to (I) understand the mechanics of swings and to (2) evaluate technique skills of increasing head speed for golfers .

20 ~

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is ~

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j .c ;

100 (%]

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Fig. 7. The forces and moments expressed by the swung club coordinate system .

References S. Koike, H. lida, T. Kawamura, N. Fujii and M. Ae. (2004) An instrumented bat for simultaneous measurement of forces and moments exerted by the hands during batting . The Engineering of Sport 5, 2, 194-199. R.D.Milne and J.P.Davis. (1992) The Role of the shaft in the golf swing , Journal of Biornechnics, Vol.25, No.9, 975-983 . E.J.Sprigings and R.J.Neal. (2000) An insight into the importance of wrist torque in driving the golfball : A simulation study, Journal of Applied Biomechanics, Vol.16, 356-366.

The Aerodynamic Influence of Dimple Design on Flying Golf Ball

T.Sajima', T'Yamaguchi', M.Yabu' and M.Tsunoda2 'SRI Sports Ltd., Hyogo, Japan 2SRI Research and Development Ltd., Hyogo, Japan

Abstract: The dimples on the golf ball surface affect the aerodynamic force while flying. They are designed for this effect with various sizes, depths, contours and shapes; those are combined and distributed on the surface. In this study, the aerodynamic influence of the dimple design on drag and lift force is investigated by analyzing the result of the indoor and outdoor ball launchertests that measure CD, CL, trajectoryand flyingdistance.

1 Introduction The flying performance of a golf ball is changed by the dimples on the surface of golf ball. In other words, the drag force and lift force are changed by size, depth, contour and shape of dimple. In this study, the dimple depths are selected for the analysis and the relationship between the depth and CD (drag coefficient) and CL (lift coefficient) while golf ball is flying is investigated with the numerical analysis for the indoor launcher test and the outdoor launcher test. Aoki, Oike and Nonaka (2002) and Ting (2005) clarified change of CD and CL that the rotating ball with different dimple depth. However, the level of depth is not suitable for the recent trend of golf ball and numerical analysis and experiment is not performed in the condition of the driver hitting of average golfer. Then dimple depth in our study is designed within the depth of recent golf balls. Carry distance and trajectory are measured with the outdoor test under average golfers' initial launchcondition.

2 Design of test balls Specifications of the dimples are shown in Fig. I and Table I. And the pattern of dimples is shown in Table 2. This study adopts same dimple pattern and different dimple depth for each sample. The difference of depth makes difference of the total dimple volume and the curvature of cross-section on the surface of samples. Depth d is distance from a dimple outline plane to the central deepest part and volume V is capacity of the part below the dimple outline plane. Diameter D of dimple is 4.07mm and number of dimples N are 300. The dimple pattern on golf ball surface is completed by connection of two hemispheres shown in Table 2. Test balls are made of ionomer resin cover and rubber core by the injection molding. The diameter of the balls is 42.7mm and the cover thickness is 2.3mm. However, as several pins for core holding and air vent is arranged around the pole of cavity for injection molding, twelve

144

Takahiro Saj ima

dimples made by these pins are added to above 300 dimpl es. Finally, 3 12dimples are arranged on all the balls. Though golf balls are usually painted after injection molding, in this study, samples are prepared without painting. The dimension of these real balls fit in CA D model for the numerical analysis.

v

Fig.1. Sectional-view of Dimple Sampl!

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,

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LonqillJde (deal

(dea) a

b

c

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240 1440 2640 1016 790 905 720 840 970 720 862 995 1440 895 1800 1440 1800

360 1560 2760 11411 1370 1255 1080 1320 1190 1080 1298 1165 2160 1265 2520 216 0 2520

48 0 1680 2880 1736 1510 1625 1440 1560 1690 1440 1582 1715 2880 1615 3240 2880 3240

720

1440

2160

2880

600 1800 3000 18611 2090 1975 1800 2040 1910 1800 2018 1885

72 0 1920 3120 2456 2230 2345 2160 2280 2410 2160 2302 2435

840 2040 3240 25811 2810 2695 2520 2760 2630 2520 2738 2605

960 2160 3360 3176 2950 3065 2880 3000 3130 2880 3022 3155

1080 2280 3480 33011 3530 3415 3240 3480 3350 3240 3458 3325

1985

2335

2705

3055

3425

Table 2. Coordinates of Dimples (hemisphere)

The Aerodynamic Influence of Dimple Design on Flying Golf Ball

145

3 The analysis of the initial launch condition for golfers

3.1 Condition for analysis CD and CL of flying golf ball are changing from moment to moment and these variations make a big influence on distance and trajectory. In particular, it is important to know CD and CL at the initial launch condition for longer distance. Then CD, CL analysis is performed under initial launch condition of average golfers. Ball speed (equal to flow velocity given in simulation) and Back spin rate are set up with 58rn/s and 2400rpm by the result of our research.

3.2 Results CAD models those have a difference of dimple depth are designed by SolidWorks 2003. The design of these models is similar to current golf balls on sale. Numerical analysis is performed by the fluid analysis software FLUENT using DES model and making 6,000,000 cells in mesh. This analysis shows that as dimple depth becomes deeper, CD becomes greater and CL becomes smaller. The indoor test to know CD and CL is carried out using ITR that was developed by USGA . The technical structure and procedure is described in "The Indoor Test Range (ITR) Technical Description and Operation Manual Revision 2.0" edited by United States Golf Association Research and Test Center. Figure 2 shows comparison between numerical analysis and experimental result at indoor test range . CD and CL of the numerical analysis are average value between t=0.003 and t=0.01285 (t: analyzing time). Subscript (S) shows the result of simulation and subscript (1) shows the result of indoor test. Analysis shows as dimple depth becomes deeper, CD becomes greater and CL becomes smaller. Though the value difference of CD is about 0.02, the tendency is similar to numerical analysis. From CD analysis, shallower dimple will be more advantageous than deeper dimple for flying distance. Nevertheless, it is important to consider the balance of CD and CL for flying distance as CL tendency towards dimple depth is opposite to CD. 028 -J 026 ....,

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146

Takahiro Sajima

4 Indoor and outdoor launcher test 4.1 Indoor launcher test The detail of USGA for overall distance and symmetry test is described in "ACTUAL LAUNCH CONDITIONS OVERALL DISTANCE AND SYMMETRY TEST PROCEDURE (PHASE 2) Revision 1" edited by United States Golf Association and Royal and Ancient Golf Club of St. Andrews. Figure 3 shows conditions of the test. These conditions are set within the bounds of ball speed and back spin rate on flying ball hit with driver club. CD and CL under these conditions are measured by ITR and CD, CL while flying are identified by software (USGA ITR DATA ANALYSIS ver.2.0.0). CD and CL on flying of three samples are identified by this procedure under the initial condition of typical Japanese average golfer (Initial ball speed: 58m/s, Back spin rate: 2400rpm, Launch angle: 12deg). Figure 4 and 5 shows the result of CD and CL simulation. As dimple depth becomes deeper, CD becomes greater from Oyd to about 80yd after test ball fired. But the tendency becomes opposite after that. As dimple depth becomes deeper, CL becomes smaller in all flying. 3400 . - - --

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The Aerodynamic Influence of Dimple Design on Flying Golf Ball

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4.2 Outdoor test by ball launcher Test balls are launched outside to measure actual carry distance and trajectory under same initial condition as indoor test (Initial ball speed: 58m/s, Back spin rate: 2400rpm, Launch angle: 12deg). Measurement is carried out by TRACKMAN. TRACKMAN is the flying ball following system with milIi-wave radar. Six balls of each sample are launched. In addition, while testing wind is against the balls and temperature is 5degees centigrade. Figure 6 shows the side view of actual trajectory. Radar unit is located 4yds in front of ball launcher. Actual carry distance is shown in Figure 6 is the distance between TRACKMAN and the landing point of ball. As dimple depth becomes shallower, carry distance becomes greater and apex of trajectory becomes higher. The difference of carry distance is about 3 or 4 yards amongst test balls.

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200

148

Takahiro Sajima

5 Conclusion The analysis under initial launch condition of typical average golfer shows that as dimple depth becomes deeper , CD becomes greater and CL becomes smaller. If dimple depth is changed in the dimple design , carry distance and trajectory will be changed. From CL analysis , as dimple depth becomes deeper , trajectory will become lower, and as dimple depth becomes shallower, trajectory will become higher. It is important to understand the balance of CD and CL for distance and feedback the results to dimple design . The tendency of numerical analysis results is similar to experimental indoor test results. To control carry distance and trajectory with dimple design, it is important to understand not only tendency of initial launch condition but also values of CD, CL change all over the trajectory . In this study, as dimple depth becomes deeper, CD becomes greater from Oyd to about 80yd after fired but the tendency Results of outdoor becomes opposite after that by the identification of USGA software . test clarifies the difference of actual carry distance and trajectory while all flying among different dimple depths. As dimple depth becomes shallower, carry distance becomes greater. This result is concerned with the difference of CD on flying ball. As dimple depth is shallower, trajectory before the apex becomes higher. This result is concerned with the difference of CL on flying ball. The difference of dimple depth is only about 0.0 Imm among each sample, but the little difference makes great difference of carry distance .

References Aoki, K., Oike, A., Nonaka, M. (2002) The Effect of dimple number on the flying characteristics of a golf ball. The engineering a/Sport 4. (Ed. By S.Ujihashi and SJ.Haake), pp330-336. Ting, L.L. (2005) GOLF BALL AERODYNAMIC BEHAVIOR AS AFFECTED BY THE DIMPLE DEPTH AND DIMPLE SHAPE CHANGES. The Impact a/Technology on Sport. (Ed. By A.Subic and S.Ujihashi) , pp234-239. Zagarola, M.V., Lieberman, B., Smits, AJ. (1994) An indoor testing Range to measure the aerodynamic performance of golf balls. Science and GolfII. (Ed. By AJ.Cochran and M.R.Farrally), 53, pp348-354.

Experimental Verification of Trajectory Analysis of Golf Ball under Atmospheric Boundary Layer Takeshi Naruo' and Taketo Mizota' Mizuno Corporation, Osaka, Japan, [email protected] Fukuoka Institute of Technology, Fukuoka, Japan

Abstract. Aerodynamic forces and torque acting on the ball were measured under various

flight conditions in a wind tunnel. Using the aerodynamic force coefficients, mathematical calculation of flight trajectory was made by time integral calculus. Three-dimensional flight trajectory, changes in velocity as well as rotation velocity were obtained. Furthermore the logarithmic law was applied to trajectory formation of a golf ball in order to include influence of atmospheric boundary layer. Moreover, an experiment was conducted in order to verify the logarithmic law and the trajectory formulation. Wind velocity distribution in the vertical direction was measured. As a result, the measured result almost matched the logarithmic law. Golf balls were hit under various initial launch conditions by a professional golfer using various golf clubs. Initial launch conditions of the golf balls were measured and wind velocity distribution in the golf ball direction was also measured. The golf ball trajectory under atmospheric boundary layer was calculated by using measured initial launch conditions and wind velocity distribution. The calculated drop positions by trajectory analysis agreed with the actual measured results.

1 Introduction A maximum flight velocity of 80 mls and a maximum spin rate of 10,000 rev/min may be reached in a golf drive, but since the velocity and spin rate are high, aerodynamic measurements under actual conditions are difficult. Furthermore, the golf ball is strongly affected by the wind during its flight ; however, previous studies have not taken this into account. A device to rotate an actual golf ball stably at a maximum of 10,000 rev/min in an air flow of 80ml s was developed. Using the device, drag, lift, and aerodynamic momentum acting on the ball were measured under real flight conditions. Trajectory analysis was made by time integral calculus by the measured aerodynamic coefficients. To consider the effect by the wind, a flight analysis method was taken in which the atmospheric boundary layer effect was included in the 3-dimensional flight trajectory equation. According to these measured wind direction and wind velocity, the flight trajectory analysis with the logarithmic law and a comparison of analysis results with actual measurements were conducted.

150

Takeshi Naruo and Taketo Mizota

2 Results of Aerodynamic Forces Measurement The golf ball-rotating device consists of a square frame structure with a D.C. motor mounted on the top center of the frame. The ball was positioned at the center of the frame with the steel wire passing through the center of the ball and fastened to the ball. With this device, it became possible to rotate a golf ball stably at a high spin rate of 10,000 rev/min. The Skyway SD432 ball (made by Bridgestone) was used for the experiments. The rotating device is mounted on sliding air bearings and balanced by pulling the springs in both the positive and negative directions of the force to be detected. Figure 1 shows the relationship between spin rate parameter Sp, drag coefficient CD and lift coefficient CL. The experiment results of Bearman et af. are shown respectively in solid lines. In this experiment, Sp is made to change over a wide range . During this time, the Reynolds Number is also changed but together with the results of CD and CL, can be roughly expressed by one curved line. 06

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3 Method of 3-D Trajectory Analysis of Golf Ball 3.1 Method of Trajectory Analysis The force working on the ball during a certain time t is shown by the equations (1) to (3). Fx(t)= -l/2(CD(t)cosacos~+CL(t)(sinacose+cosasin~sine))pAU(t)2

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151

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Also, during flight, aerodynamic torque reacts on the golf ball to decay spin number. The decrease of spin number by aerodynamic torque may be shown by formula (4). N(t+~t)=-pAdCm(t)U(t)2~tI(4rrl)N(t)

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Where a:Launch angle, p:Side deviation angle, UiVelocity, d.Diarneter, A:Cross section area, p:Density of air, N:Spin rate, I:Momentof inertia Figure 2 shows the wind velocity vertical distribution diagram used to embrace the effects of the atmospheric boundary layer. Here, the logarithmic law is applied. This logarithmic law closely matches the experimental value in the wind tunnel boundary layer and it is said that it also coincides with the observation results in surface boundary layer having smooth surfaces like those of grasslands. Where V0 is the velocity at a height of 10mabove ground, Vy is the average velocity at a height of Y, V* is the friction velocity, and to is the shearing stress at ground suru, c. V =.JT::IP AI . K . h . lace,' " . so, K IS annan constant Wit an approximate value of 0.4, while Y' is the roughness constant, but here 0.09 is used assuming that the periphery of the course I consists of thick grown grass. H is the average height of . to" obstructions. To embrace the effect of the wind in trajectory analysis, the components of the wind are calculated from the angle A of the velocity components (clockwise direction from ~z X axis considered as +). The aerodynamic force applied on the ball is obtained from the relative speed of the ball and air Fig. 2. Wind velocity current, while the position of the ball is obtained from the vertical distribution absolute speed. This is repeated until the ball lands on the ground.

3.2 Confirmation of Logarithmic Law The distribution of wind direction and wind velocity was measured in the vertical direction to continn whether the logarithmic law could be applied. The measurements were made at the Shingu Coast of Fukuoka Prefecture where the ejection experiment was conducted. Five vane anemometers were installed vertically from the height of 1.5m to 5.5m at Im intervals. The wind velocity was measured 5 times at I-minute intervals for 10 minutes and the average value was obtained. The appropriateness of the logarithmic law by these measurements was continned as shown in Fig. 3. Here, U* is the wind velocity measured at a height of 5.5m. By dividing wind velocity U by U*, the horizontal axis is shown as dimensionless expression. Wind velocity U was 4 - 6m/s. From the result, the wind velocities from the height of Om to 30m that was maximum height of golf ball flight by using a logarithmic law based on the wind velocity at 5.5m was calculated.

152

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4 Ejection Experiment and Trajectory Analysis with Study of the Wind Effect 4.1 Method of Wind Direction and Wind Velocity Measurement A golf ball flies the maximum 270m in approximately 6 seconds. It is therefore necessary to understand how wind velocity and wind direction vary with time and position . First, 5 poles were set at every 50m from the reference point to 250m, and the wind velocity and the direction were checked at 5.5m high. The measurements were conducted over approx . 3 hours to take 50 sets of data. The difference in wind velocity depending on position was measured. From the result , it was confirmed that wind was blowing at a constant wind velocity, even at the point 250m away. The time change barely affected the wind direction . Moreover, there was no change in the wind direction by place s, and the wind was mostl y from south. From this test result , while the ball flies a maximum of 270m in approx . 6 seconds, there was no difference in the wind velocity and wind direction by time or location, and it was found that flight trajectory analysis could be made, assuming that wind velocity and wind direction are constant during the flight.

4.2 Method of Ejection Experiment Four poles equipped with vanes anemometers at the height of 5.5m were installed at every 50m from the hitting position towards the flight direction . The wind direction and the velocity were measured when the ball passed by the poles , and the average values measured at four positions were used as the average of wind velocity and wind direction. The test was made for which the ball direction was changed 30 degrees to have cross wind. In regard to the launching ball , the initial values of launch angle II ,side deviation angle p, ball velocity Uo, spin rate No, and the rotating axis inclination e were measured by the launch monitor "Pythagoras (made by Mizuno)." In order to check under

Experimental Verification of Trajectory Analysis of Golf Ball

153

various initial conditions, driver, 5 iron, 7 iron, 9 iron and pitching wedge were used. All shots were taken by a profes sional golfer.

4.3 Results of Experiment and Analysis with Study of the Wind Effect Two exa mples of the results are shown. The initial cond itions of the ball , wind dire ction and wind velocity are show n in Table I. Figure 4 shows the flight trajectory analy sis result of example I with the use of a driver. The flight trajectory was calculated using initial conditi ons, and the broken line indicates the case where the wind was not con sidered while the solid line indicates the case where the measured wind direct ion and wind veloc ity were considered . The wind direction is shown on the graph by an arrow . The solid circle mark show s the ball landing position measured. Becau se of the tail wind , the analysis result which considered the wind showed a 5m longer flight distance than the result which did not consider the wind . By considering the wind, it was found that the landing point could be adjusted to the actually mea sured landing point. Figure 5 show the test and anal ysis results of example 2 with the use of a pitching wedge . The wind is roughl y at a right angle to the direction of flight , and compared with the case where the wind is not con sidered, it is seen that the ball deviates approx. 5m to the left from the ball direction in case the wind is considered. Moreover, the flight distanc e is about 3m longer. Also in this result, the ca lculated result s in con sideration of the wind meet the actually measured value. Figure 6 shows a comp arison of the actual measurements and the calculated values of flight distance . The measurement s with con sidering the wind are shown by the solid square, while the results without con sideration of the wind are shown by circle. When the actual measurement and the calcul ated value coincide, the data is app eared on y=x. When minimum square approximation is conducted on the result in which wind is not considered, y=O.945x is obtained, but when the wind is considered, the result becomes y=O.98 1x, i.e. it approaches y=x. Figure 7 shows the comparison between the measurement of side deviat ion and calcul ated value. The measurement with consideration for the wind is indicated by a solid square mark , while the measurement without con sideration for the wind is indicated by a circle. It is found that the data of the square appro ache s y=x more than that of the circle. However the slight dispersion is seen. The follow ing reason can be thought of. The actual wind changes for the appro x. 6 seconds during ball flying but we calculated assuming that there was no change in wind direction and wind velocity during the flight , which might cause the difference. Table. 1. Results of ejection experiment a

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5 Conclusions By applying the logarithmic law, trajectory formulation of a golf ball under atmospheric boundary layer was shown. And the logarithmic law was verified by measuring of wind velocity distribution to the vertical direction. Comparison of flight distance was made with numerical analysis results and actual measured values and an extremely favorable matching of results was seen. Thus the validity of the trajectory formulation of a golfball under atmospheric boundary layer was verified

References Bearman P.W. and Harvey 1.K. (1976) Golfball aerodynamics. Aeronautical Quarterly, 27, pp.112-122. Naruo, T. and Mizota, 1. (2005) Trajectory analysis of golf ball under atmospheric boundary layer. The Impact on Technology on Sport, Melbourne, pp. 253- 260.

Validation of Accelerometers and Gyroscopes to Provide Real-time Kinematic Data for Golf Analysis Fitzpatrick, K. and Anderson, R. University of Limerick, UK, [email protected] Abstract. Golfers continually demand more information about their performance and require immediate feedback on their swing . This research attempts to measure the pitch «(I)) and yaw ('P) angle of the clubhead at ball-contact and compare this to the same angle at shot set-up. Acceleration of the clubhead at ball-contact is also measured. These three variables have been linked to golfing performance in the literature. For the research two gyroscopes and one dual axis accelerometer were incorporated with a putter head. One gyroscope was positioned on the head of the club to measure deviations occurring between the yaw angle at set-up and the yaw angle at ball contact (~(I)). A second gyroscope was positioned to measure deviations between the pitch angle at shot set-up and the pitch angle at ball contact (~'P) . Each gyroscope also provides angular velocities of the club throughout the swing . To measure the clubhead acceleration (a) an accelerometer was positioned on the clubhead parallel to the movement. The system and methodology has been verified and tested for both accuracy and reliability in the field, it is those results that are presented here . Several testing techniques were used to ensure the data obtained from the sensors was accurate and compared well with kinematic data obtained from a motion analysis system . The reported RMSD error existing between the angle data 0 obtained from the sensors (~'P & ~'P) and the motion analysis system was 0.2 for both the yaw and pitch angle over any two second period (sufficient for a golf stroke) . The accelerometers illustrated potential benefit for use as feedback tool but proved to be inadequate as a method for deriving velocities or displacements. The output from the gyroscopes and accelerometer may be displayed in a manor such that it is a feasible means for giving valuable feedback to a golfer.

1 Introduction Many golfers in their post win interviews will hail their putting prowess in the tournament while the loser will often lament poor putting as the cause of their less than heroic performance. With 50% of prescribed shots in the golf allotted to putting it is critical that, if a golfer is to succeed, this aspect of the game is performed to a higher degree than any other. The literature emphasises the necessity to maintain the club-

156

Fitzpatrick K and Anderson R.

face perpendicular to the intended direction of ball at point of contact to propel the ball in the intended direction (Brooks 2002; Pelz 2000; Rosburg 1963; Werner and Greig 200 I). It is also clear from the literature that the golf ball should be putted with the ball being hit slightly upwards (Pelz 2000; Werner et al. 2001). This upward action allows for the ball to begin rolling quicker and avoid skidding across the green (Pelz 2000). The literature also states that the clubhead should be accelerated through the ball at contact (Foston 2001; Newell et al. 2004; Pelz 2000; Rosburg 1963). To provide information on these variables it is vital to measure the pitch (tD) and yaw (If) of the clubhead and the clubhead acceleration . By combining MicroElectro-Mechanical Systems (MEMS) technology with golf clubs (specifically gyroscopes and accelerometers) golfers can acquire accurate and relevant information regarding their golf swing. Gyroscopes have many industrial applications and are used in the automotive industry and image stabilisation. The basic principle of a rate gyroscope is it operates on the vibratory principle of a single proof mass suspended by flexures anchored to the substrate. The flexures serve as the bendable suspension between the proof mass and the substrate, allowing the mass to oscillate freely in two orthogonal directions (Acar and Shkel 200 I). If the gyroscope is subjected to any angular rotation, the Coriolis force is induced, the resulting oscillation amplitude is proportional to the Coriolis force, and thus to the angular velocity to be measured as an electrical output. Accelerometers are small, inexpensive, have low power requirements and are relatively robust sensors that measure changes in acceleration . They have applications in industry, in as diverse action as the release of airbags in cars to laptop hard drive impact and theft protection. Many different types of accelerometer exist, strain gauge, piezoresistive, piezoelectric and inductive, or in more recent times the move has been towards capacitive . A centre sensor layer is built for the actual pendulous mass and is bonded between two other silicon layers that form capacitive sensing layers. The differential capacitor structure is decoded using phase sensitive demodulators or other approaches on a separate chip. Using this technique, accelerometers can be built that have excellent performance characteristics (AnalogDevices 2006). The rate gyroscope is designed to measure the angular velocity of the clubhead through out the putting stroke. The actual angle, calculated by integrating the angular velocity, can be used to determine the angle of the clubhead at any particular phase of the putt and also provide results relating to the yaw and pitch angle at point of contact. The data obtained from the accelerometer may be used to demonstrate the acceleration pattern throughout the swing and indicate if the putter head is accelerating at ball contact. One of the most common improvement methods used by golfers is video based feedback . This method of feedback, based on your swing kinematics, offers the golfer an opportunity to view his/her swing. It can be relatively expensive, difficult to set up and often may involve the use of complicated computer editing. The software may give an option to view the swing slowed down or compared to another swing. One of the major draw backs of video analysis is it requires a trained or experienced person to pin point aspects of the swing that need to be adjusted . It is usually the coach that offers this advice. This can be an added expense and requires the coach to be present, which can often mean sessions must be arranged around the

Validation of Accelerometers andGyroscopes to Provide Real-time Kinematic Data

157

coach's availability . It is anticipated to use the data from the MEMS to give meaningful feedback to the golfer. The system in intended to be incorporated in a training tool. The data from the MEMS could be displayed to the golfer in an attempt to improve putting performance or identify flaws in the stroke. The data could potentially be displayed in a means that is easily interpreted by the golfer or could be used as an assistance to the coach. It could be used to identify flaws in the swing not visible to the naked eye or so minute that detecting their occurrence may not be possible.

2 Methods and Results

2.1 Attachment of sensors The gyroscope chosen was the Analog Devices ADRXS 150EB (Analog Devices, Massachusetts) . It was chosen because it was small, light weight, low cost, low power supply required and could measure up to 150 degrees per second. The volume of the sensor itself measures less than 0.15cc, weighs less than half a gram (Analog Devices2004) . The gyroscopes were positioned on a perspex board, which could be easily attached to the putter head (see figure I) . and yaw Gyroscope A was setup to measure the yaw angle ('I') and gyroscope B was setup to measure pitch angle (<1» . The accelerometer chosen was the dual-axis Analog Devices ADXL202 (Analog Devices, Massachusetts) . It was chosen because it was small, light weight, low cost, low power supply required and could measure up to 2g in two perpendicular directions. The sensor measures 5mm x 5mm x 2mm. One axis of the accelerometer is arranged to measure acceleration along the aim line of the putt, at point of contact (the x axis). The second axis of the accelerometer is aligned perpendicular to the aim line in a lateral direction the z axis; see Figure 2.

Fig 1: The MEMS attached to the Perspex board that can slotted into a receiver on the putter head (Right) and illustration of the axes that the dual axis accelerometer measures (Left)

158

Fitzpatrick K and Anderson R.

A perspex board was attached to the sensors and could be fixed to the head of the putter. The junction box on the perspex board slotted into a receiver that transmitted the reading from the sensors along a series of wires up the shaft of putter, as shown in figure 2. The sensor array was then connected to a computer (Powerlab, New Zealand) to display and record the output from the sensors.

2.2 Compatibility of the Gyroscopes Prior to the system being used in the field the limitations of its accuracy and reliability must be assessed. The accuracy and reliability of the actual gyroscopes is reported in the manufacturers data sheet (ADRXS 150EB, Analog Devices, Massachusetts) . To assess the accuracy of the gyroscopes in conjunction with the proposed system a rig was designed to securely hold the golf club . The rig allowed the swing rate of the club to be controlled and also restricted movement of the club-head to one plane . Therefore data for both pitch angle or yaw angle could be obtained. Data was acquired from the sensor array and also from a Peak Motus motion analysis system (Peak Technologies, Colorado, USA) capturing kinematic data at 50Hz . Retro reflective markers were placed at either side of the clubface, representing the putter face and, post calculation, the yaw angle (the movement specifically measured by gyroscope A). Retro reflective markers were also placed at either end of the shaft representing the pitch angle post-calculation (the movement specifically measured by gyroscope B),. When obtaining data related to the yaw angle the camera was placed above the putter pointing towards the floor (i.e focused on the x-z plane) . This enabled the motion analysis system to calculate the angle between the clubface and the x-y plane projected onto x-z plane (i.e the yaw angle) . The second setup, with the camera focused onto the x-y plane enable the acquisition of the the angle between the shaft and the x-z plane projected onto the x-y plane (i.e the pitch angle) . Initial pilot work was undertaken and compared the data obtained from the gyroscopes to the data obtained from the motion analysis. The movement of the club was recorded using a 50Hz S-VHS video camera (Panasonic AGDP800, Matsushita Electrical Industrial, Japan) . The video images were digitised using motion analysis software (Peak Motus 2000) . The resultant coordinate data was filtered using a Jackson Knee optimised Butterworth filter. During this data was acquired from the sensors via a PowerLab data acquisition system (AD Instruments, New Zealand). Pilot work and subsequent analysis of the angular velocity data identified that the gyroscopes reached a plateau at certain stages throughout the movement. This can be attributed to the movement velocity being greater than the range of the gyroscope (150 degs .s'). Integration of angular velocity curves, which exceeded this maximum of ISO degs .s' led to inaccuracies in the angle data . Further trials were conducted at an angular velocity below 150 degs .s' (more representative of a 10ft golf putt) to eliminate these shortcomings of the sensor. The RMSD, between the integrated gyroscope data and the motion analysis angle values was reported at 2°. At closer inspection of the angle data it was obvious that the largest variance between the sensor data and motion analysis data occurs at the turning points of the curve. This notable divergence in two lines was inflating the

Validationof Accelerometers and Gyroscopes to Provide Real-time Kinematic Data

159

RMSD values artificially. This divergence was decreased by fine-tuning the sensitivity values of the gyroscopes within the ± 10% range stated on the sensor data sheet (stated sensitivity is 12.5 mV f ls ± 10%). For the two gyro scopes used in this research the optimal sensitivity was calculated as being 11.9 mV f ls. Final tests of compatibility of the gyroscopes were completed over a number of durations to examine the effect, if any , of drift on the accuracy of the data. The results (illustrated in table I) identify that the RMSD existing between the motion analysis data and the sensor data was minimal. At the 2 s range (the typical length of a golf putt) the RMSD was 0.21°. In summary the gyroscopes can offer accurate angular velocity data when embedded in the club, this data can subsequently be used in a feedback system. Duration RMSD

of

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2.3 Compatibility of the Accelerometers As the system does not use absolute acceleration values, just the relative magnitude and the time based curve that are created throughout a movement pattern , a true calibration of the system is not required. The gravity based calibration procedure for the accelerometers is outlined in the manufacturers data sheet and will not be discussed here (Analog, 2004) . The accelerometers could adequately represent acceleration and therefore the change in acceleration patterns pre and post ball contact.

3 Discussion In conclusion the sensor array presented here has been shown to be both accurate and reliable and can offer the information required for a feedback mechanism for golf putting. The yaw angle is crucial in insuring that the ball is putted in the intended direction. Any deviation in the yaw angle results in ball being struck off line and the likelihood of a missed putt is increased. The pitch angle insures that the control over the putt is maxim ised. By striking the ball in a slightly upward direction, topspin is created and the ball tends to skid less. Integration of the gyroscope's angular velocity output, gives sufficient accuracy to determine the yaw and pitch angle. This information could be used as a valuable tool for coaches and golfers. Accelerometers can be of benefit to the putting stroke. They are capable of indicating the presence of acceleration in the putt i.e. changes in acceleration can be demonstrated. Therefore it is possible to demonstrate if the golfer accelerated at point of contact with the ball or not. At this point quantifying the acceleration is not possible, but accelerometers can be used to demonstrate the presence of acceleration. Also it is feasible to use the acceleration data to represent a movement pattern .

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Fitzpatrick K and Anderson R.

Accelerometers have been shown to be a reliable tool in trying to replicate a movement pattern (Foerster et aI. 1999). This can be utilised in developing an ideal movement pattern and then attempts could be made to replicate this. This in tum could lead to a more consistent putting stroke. Initial results utilising the system proposed herewith have proved positive on improving the putting performance of novice golfers . However statistical data was not available at time of going to press . Gyroscopes have been proven as a means of giving accurate and meaningful kinematic data on a golf putt. Accelerometers can be used to give meaningful indication of kinematic movement. The ability to train with a club that can assess movement patterns and movement patterns in real-time, is an exciting prospect.

Acknowledgements Funding for this research is provided by the Irish Research Council for Science, Engineering and Technology: funded by the National Development Plan of Ireland .

References Acar, c., and Shkel, A. (200 I). A design approach for robustnes s of rate gyro scopes. Modeling and simulation of microsystems, 80-83 . AnalogDevices (2004). +/J 000/, single chip yaw rate gyro with signal conditioning, Vol. 2005. Analog Devices. AnalogDevices (2006). Using iMEMS Accelerometers in Instrumentation Applications. Analog Devices. Brooks, R. J. (2002). Is it a pendulum, is it a plane ? - Mathematical models of putting, Science and GolflV Proceedings from the World Scientific Congress of Golf, pp. 127-141. Foerster, F., Smeja, M., and Fahrenberg, J. (1999). Detection of posture and motion by accel erometry: a validation stud y in ambulatory mon itoring. Computers in Human Behaviour 15,571-583. Foston, P. (2001). The complete encyclopidia of golf techniques. Running press book publishers, Penn sylvania . Newell , S., Foston, P., and Atha , A. (2004). The complete golfer, 3 ed. Annes publishing limited, London . Pelz, D. (2000). Dave Pelz's Putting Bible. Doubleday, New York . Rosburg, B. (1963) . The putter book, Vol. 3. Nicholas Kaye Ltd, London. Werner, F. D., and Greig , R. C. (200 I) . Better Golf from New Research. Orig in Inc, Jackson.

Investigation of Wrist Release During the Golf Swing by Using a Golf Swing Robot 1

Yohei Hoshino ', Yukinori Kobayashi/ and Soichiro Suzuki· J

2

Hokkaido University, Graduate School of Engineering, [email protected] Hokkaido University, Graduate School of Engineering, [email protected] Kitami Institute of Technology, Faculty of Engineering, zuki@ mai l.kitami -it.ac.jp

Abstract. In this study, skill of the wrist release during golf swing is investigated by using a golf swing robot. A torque plan of the shoulder joint of the robot is assumed as a two-steps modulation torque that is a simplification of the acceleration torque induced by the weight shift, rotation of torso and the shoulder of a golfer. Relationship between the torque plan and the skill of the wrist release, such as natural release and late hitting , is investigated by using the golf swing robot.

1 Introduction Characteristics of swing style of professional and expert golfers appear in the wrist release as a ' natural' or 'late' release. There have been studies on the effect of delayed wrist turn (Jorgensen 1970) and the wrist turn in the down swing by the threedimensional nature of the forces and torques applied to the club (Vaughan 1981; Neal and Wilson 1985). The effect of ' natural release' and ' late hit' was investigated numerically by using a two dimensional rigid double pendulum model (Pickering and Vickers 1999). The skill of the wrist release in the down swing was analyzed by using a three-dimensional dynamic model based on the double pendulum including the effect of supination of a forearm and three-dimensional shaft vibration (Suzuki, Haake and Heller 2005). In this study, skill of the wrist release during golf swing is investigated by using a golf swing robot (Hoshino, Kobayashi and Yamada 2005). The golf swing robot consists of wrist and shoulder joints, two rigid links and a golf club. Although the golf robot does not have a cubital joint and cannot rotate the golf shaft around the axis of the shaft, the robot has a hook mechanism to lock the wrist joint. The hook mechanism is important to evaluate the relationship between the wrist release and torque plans for the shoulder joint. The swing robot pulls up the golf club (backswing) and then swings it in a swing plane. The backswing action is performed by a digital servo controller. Feed-forward torque is applied only to the shoulder joint during the downswing. A linear quadratic regulator (LQR) in consideration of the vibration of the club shaft is employed to stop the robot during the follow-through action after the impact for decreasing the degree of shock due to abrupt slowdown. Since it is difficult to measure all of the state variables, a state observer is employed for the state feedback control system.

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The torque plan of the shoulder joint is assumed as a two-steps modulation torque that is a simplification of the acceleration torque that is induced by the weight shift, rotation of torso and the shoulder of a golfer (Suzuki, Haake and Heller 2005). Relationship between the torque plan and the skill of the wrist release , such as natural release and late hitting, is investigated by using the golf swing robot.

2 Equation of Motion of the Golf Swing Robot

Ball

f e Golf club
wlOg plane

Fig. 1. Swingplane of the golf swing The swing robot and the system of orthogonal axes (x, y, z) are shown in Fig. 1, and the robot swings a golf club in the swing plane o-xy. The angle between the direction of gravity and the x-axis is a. The robot has two joints and two rigid links that are modeled on the arm of the golfer and the grip of the club . The simplified governing equation of the system is needed to construct the control system of the robot. The golf club is modeled as a flexible beam in consideration of bending and torsional stiffness and in consideration of eccentricity of the center of gravity of the club head on the shaft axis. Properties of the club are as follows: a uniform crosssectional area A 3, diameter d-, length L3 , Young's modulus £3, area moment of inertia h, mass per unit volume P3 and eccentricity of the center of gravity of the club head L 4 Figure 2 shows the coordinate system in the xy-plane . Angles 8\ and are the absolute rotating angles of the first joint and the second joint, respectively. The club shaft is assumed homogeneous and initially straight along the C:;raxis shown in Fig . 2. The masses of the first link, the second link and the clubhead mass, respectively, are mb mi . and m4 , and the mass moments of inertia of the first link and the second link are J 1 and Ji. respectively. The mass moments of inertia of the club head mass around the axes C:;4, '14 and (4 are J4/;, J4q and J4i;' respectively. Tables I to 4 show parameters of the swing robot and golf club . In these tables, parameters L, fJ and c denote the length of link, the position of the center of gravity , the coefficient of friction and Young 's modulus of the golf club, respectively . Deflection of the flexible link along the '12 axis is denoted by vq and torsion angle of the flexible link is rp. A mathematical model of the golf robot is derived by Hamilton's principle in consideration of bending and torsional stiffness and in consideration of eccentricity of the center of gravity of the club head on the shaft axis. Natural frequencies and the 0

e

Investigation of Wrist Release During the GolfSwing

163

/

Hook

x

Fig. 2. Coordinate system of theswing robot Table 1. Parameters of the first link ml [kg) 2.92 J 1 [kg -rrr'] 0.201 Lllm)

PI CI

[N vrn -s/rad]

0.310 0.774 0.151

Table 3. Parameters of the club shaft P3 [kg/ml] 1.50x 10' A 3 [m 2] 13 [m4 ] L3 [m) £ 3 [GPa)

5.66x 10.5 3.18xlO· IO 0.83 100

Table 2. Parameters of the second link m-. [kg) 0.650 4 h [kg' m2) 2.0x 10. L2 1m] [N r m-s/rad]

C2

0.050 0.102

Table 4. Parameters of theclubhead m4 [kg) 0.210

Jd kg' m 2)

J4'1 [kg-rn"] J 4d k g' m 2J L4 [m]

4.5xI0-4 4 I.OxlO4 2.0xlO4.00xI0· 2

vibration modes are obtained by numerical and experimental modal analyses. Using a time function q(t) == sin on , we assume the bending displacement v~ and the torsional angle lfJ to be 00

00

vf/(q,t) == Lqi(t)T/fi(q) , qXq,t) == Lqi (t)T91 (q) . ;= 1

(I)

;= 1

where T" i and r qJi, respectively, are the i-th mode shapes of bending displacement and torsional angle, and OJ is the circular frequency. An approximate system of finite dimensional equations is obtained using a finite number of modes in Eq. (1). Considering first two modes, the non-linear equations of motion are obtained as J(x)x + Dx + Kx +h(x,x)+ g(x) == pu + IJ~ (2) where X =[01 O2 ql q2Y,U==[r1 f zr , p == [12x2 02x2Y ' is the generalized force vector applied to the center of gravity of the club

and II: head. J, D and K are inertia, damping and rigidity matrices, respectively, and h, g and u are nonlinear force, gravity and input vectors, respectively. The nonlinear force vector h includes these constraint forces.

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Yohei Hoshino et al.

3 Controller Design The swing robot pulls up the golf club (backswing) and then swings it in a swing plane . The backswing action is performed by a digital servo controller. Feed-forward torque is applied only to the shoulder joint during the down swing . A linear quadratic regulator (LQR) in consideration of the vibrat ion of the club shaft is employed to stop the robot during the follow-through action after the impact for decreasing the degree of shock due to abrupt slowdown. Since it is difficult to measure all of the state variables, a state observer is employed for the state feedback control system. Ignoring the gravity in Eq. (2) and linearizing Eq. (2) around x = 0, we can obtain the linear equations of motion as

Ji+Dx+Kx = pu+d

(3)

where d is the equivalent disturbance vector, and K is the rigidity matrix . Equation (3) can be rewritten as the state variable equation, X = AX + Bu + Ed (4) where

x=k

x Tr, A=[

°

-r:«

I ] , B=[

-i 't:

°]

rip

and E=[ 0] l .

r

The discrete-time system of Eq. (4) is given as

X k+,=A"X k+B"uk+E"dk

(5)

Control model of the backswing action is constructed on the system of Eq. (5) . Here , the output equation is

Y=[OI 02Y=C pX ,C p = [ I 2x2 02x2 :02x2 02X2]

(6)

Then we employ a type I digital servo system of the rotating angles OJ and ~ for the system of Eqs. (5) and (6). The state variables except for OJ and ~ are estimated by a state observer based on a type I digital servo system . The structure of this observer is similar to that of a steady-state disturbance observer (Ho shino et al. 2005). The robot also has a hook mechanism to lock the wrist joint for emul ating the wrist cocking action of a golfer (Suzuki and Inooka 1998). The hook can achieve wrist cock action in the downswing.

4 Torque Plan and Wrist Release Difference of swing motions between experts and beginners remarkably appears in the wrist release. It is important to utilize strain energy of a shaft and potential energy of an arm for fast head speed with natural and late wrist release in an actual swing motion . Delay of the zero-crossing point where the shaft is straight and the wrists then release is a way to achieve the fast head speed. We can evalu ate the proficiency degree of the swing motion by using an efficiency index rthat is calculated by ratio of kinetic energy of the head to work of the shoulder (Suzuki , Haake and Heller 2005).

Investigation of Wrist Release During theGolfSwing

~ z

~ z <)

::l

2' ~

o (a)

165

<)

Torso

" ,

.

"

Input time [sec] Composite acceleration torque of whole body motion

~

::l

...0cr'

01""

E-

o

Input time [sec] (b) Simplified two-steps modulation torque

Fig. 3. Acceleration of theshoulder joint

r;

Te

~

Z

'"

<)

::l

~ -e

r:T

01

(; E-

O

Input time [sec] (a) Triangular torque

0

Input time [sec) (b)Trapezoidal torque

Fig.4. Triangular torque and trapezoidal torque In order to delay the zero-crossing point, torque input of the shoulder joint has to increase during the acceleration of the arm. The acceleration torque of the experts is assumed to consist of weight shift, rotation of a torso and shoulder as shown in Fig. 3(a). Then, the acceleration torque was simplified to two-steps modulation torque as shown in Fig. 3(b) to investigate the relationship between the zero-crossing point and torque patterns. Validity of this torque function for delaying zero-crossing point was examined by comparing with simple trapezoidal and triangular function as shown in Fig. 4(a) and (b), respectively. Figure 5 shows the simulation results in the case of the golf swing robot. Figure 5(a) shows the relationship between a shoulder joint angle at the wrist release Or [deg) and QMAX [N·m] for three types of the function under the same condition of the shoulder work. Figure 5(b) shows relationship between T and head speed at impact Vh [m/sec]. We can know the position of the arm at the zero-crossing point from On because the wrist is always released at the zero-crossing point by 'natural release' . Although values of QMAX are not so large because of the restriction of the maximum torque of the robot, results of two-steps modulation torque give latest wrist release for all values of Q",f.4x, Therefore, the acceleration torque with whole body motion can delay the zero-crossing point and achieve fast head speed efficiently. Figure 6 shows the experimental results in the case of the golf swing robot. The qualitative tendencies of the experimental results are agree with those of the simulation. Therefore, the golf swing robot can emulate the human skill of 'natural release' and 'late hitting' by actuating with two-steps modulation torque.

166

Yohei Hoshino et al.

......-.

r

.. ...... -) 0 -4 0

-50

I .

-

~

........-...

~ -7 0

>.

g

"

• .0 .0.0.0·0·0·0

-90ldegl

- KO -YO

3 .1

.5

- . - 2 steps lTt<X!ulatirn - - - - Triangular - 0 - Trapezoidal

~ -60

--------Zl-:rr-Oo&O·e:Q:--------j

";:j t:

U3

2.7

Q,•• ,OC·O~·.::. O·...... O_·O_·O_~_~ _ _~_ _

-100 10

12

14

16

IK

2 .9

2.5

20

L-_~_~~_~_~_----J

13.2

13.0

Q_. ,IN' ml

(a)

13.4

13.6 V'Im/sec l

Ll .K

14.0

(b) Comparison of efficiency index

Comparison of a shoulder joint angle at the wrist release

Fig. S. Results of the wrist release and efficiency index in the case of golf swing robot

r

-)0

·40

_

t4 .50.-

_ .._

~ ·6 0

-

_

_ ._ ._ ._. - ._ .

-KO

~

:·~~·_T~~:':

_

" ~

UJ

12

14

16

IK

Q_.,IN·m!

Comparison of a shoulder joint angle at the wrist release

20

•••••••• 2 stepsmodulation

0 .5 0 .0

10

::::·::.:.;;:.:~::::::::i:=.:.:::::::~::::::.:.~::.:..

15

e-,

htepsrm d ulmioo

:~l~

.

2 .0 ~-~--~----~-~ ~

g r.u

-_.-

.90 (a)

I

_ .....

_ - - - - - . -.--

'" ·70

-100

_

... _

.• Triangu lar

L-_~

IJ

14

_ _~ _ ~_ _~_....J

15

16

17

IK

V·lm/sec l

(b) Comparison of efficiency index

Fig. 6. Experimental results of the wrist release and efficiency index

References Hoshino, Y., Kobayashi, Y. and Yamada, G. (2005) Vibration control using a state observer that considers disturbances of a golf swing robot. JSME International Journal, 48, pp. 6069. Jorgensen, T. ( 1970) On the dynamics of the swing of a golf club. American Journal of Physics, 38, pp.644-651. Neal, R.J. and Wilson, B.D. (1985) 3D kinematics and kinetics of the golf swing. lnternational Journal ofSports Biomechanics, I , pp. 221-232. Pickering, W.M. and Vickers, G.T. (1999) On the double pendulum model of the golf swing. Sports Engineering , 2, pp. 161-172. Suzuki, S. and Inooka, H. (1998) A new golf-swing robot model utilizing shaft elasticity. Journal ofSound and Vibration, 217, pp.17-31. Suzuki, S. (1999) Torque planning for a new golf swing-robot emulating golfer's skill. Proc. ofthe JSME Sympo sium, No.99-41 (in Japanese), pp.44-47. Suzuki, S., Haake, S. and Heller, B. (2005) Skill analysis of the wrist release in golf swing to utilize shaft elasticity. The Impact of Technology on Sport (edited by Subic and Ujihashi), Australian Sports Technology Alliance Pty Ltd, pp.188-193. Vaughan, CL. (1981) A three-dimensional analysis of the forces and torques applied by a golfer during the downswing, Biomechanics VII-B (edited by Morecki et al.), Polish Scientific Publishers, Warsaw, pp_325-331.

Segmental Sequencing of Kinetic Energy in the Golf Swing Brady C. Anderson', Ian C. Wright 2 and Darren 1. Stefanyshyn' I

University of Calgary , Canada, [email protected] Golf Company, USA

2 TaylorMade-adidas

Abstract. This paperinvestigates the sequential transfer of kinetic energy from proximal to distal segments in the golf swing. Forty five male, scratch golfers performed driver swings before a multi-camera motion analysis system. Position data recorded from the trials wereused to scale and update the movement of a kinematic golf model. The rigid bodies of the golf model were assigned basic, homogenous, geometries with known inertial properties. The rigid bodies of the human-golf club system were subdivided into 4 linked segments. Translational, remote rotational and local rotational kinetic energy was calculated for each segment throughout the swing. It was found that the peak magnitudes of total kinetic energy increased sequentially from proximal to distal segments, while the timing of these peaks did not follow a sequential pattern. This paper describes the useof a novel method of kinetic energy calculation in thegolfswing. and itsapplication in club head speed generation.

1 Introduction In order to generate a fast swing, a golfer interacts with the ground via his feet. Through . a series of hip, torso and arm rotations, he generates both a translational and rotational impulse at his hands on the club grip. Many studies have looked at how club head speed at impact is generated by the kinetics of different segments of the golfer (Jorgensen 1994; Sprigings, Marshall, Elliot and Jennings 1994; Nesbit 2005). To date, there is still no explanation available as to the transfer of speed between segments. The summation of speed principal (Bunn, 1972; Putnam, 1993) has been an influential concept in the literature, as a means of explaining how both angular and translational velocities can be transferred in a linked system. This principal states that the system will achieve an optimum end point velocity if the link velocities peak sequentially. A link will begin motion at the instant its proximal neighbor achieves a peak velocity, and so forth along the line. The distal end point of each link should then increase sequentially along the system. In opposition to sequential peaking of velocity, Van Gheluwe and Hebbelinek (1985) have proposed the principal of optimal coordination of partial momenta (Putnam, 1993). This states that optimal distal end velocity of a linked system is reached when the angular velocities of the links peak simultaneously. Putnam (1993), has argued that this

168

Brady C. Anderson, Ian C. Wright and Darren J. Stcfanyshyn

principal may not work in kinetic applications since the inertial properties of the links cause interactions which work against simultaneous peaking. At present, it is not known how different segments contribute to impact speed in golf. The purpose of this investigation was to explore the transfer of speed from the feet to the club head. Kinetic Energy (KE) takes the inertial properties of the links in account, and is independent of direction, so there was no need to place constraints on the kinematics of segments. These motion constraints have been shown to lead to errors in calculations of end point velocity; ie. Constraining long-ax is rotation (Marshall and Elliot, 1999).

2 Methods Forty five male scratch golfers were used as subjects in this study . Kinematic data were collected on the MATT motion analysis system (TaylorMade-adidas Golf, Carlsbad CA) . Subject motion was tracked using retro-reflective markers, placed on anatomical landmarks and fixed to the subjects clothing. Position data from the markers were collected at 110Hz and used to scale and update a kinematic golf model designed by Motion Reality Inc. (Marietta, GA) . The volume of the kinematic model was scaled to the size of each human golfer. Truncated cones and ellipsoids were used as the general geometric shapes to be fitted to the golf model rigid bodies. These shapes were modeled to be homogenous, and of known volume and inertial properties. An example of the geometric shapes applied to model the human golfer can be seen in figure I. The shapes were given a density of 1.03 x 103 kg/rrr', as reported to be that of the human body , by Clauser, McConville and Young (1969) . Body mass was self reported by a subset of21 male subjects. The se1freported mass was on average 2.1% lower than the mass calculated by the model with a standard deviation of 8.2% body mass . In order to ensure that our calculated mass was not statistically different from our reported whole body mass, a student t-test was employed to test if the difference found was significantly different than zero. A p-value of 0.8819 showed that the measured and modeled body masses were not significantly different. The kinematic golf model was split into four segments, 10 explore the possibility of proximal to distal peak energy sequencing. Each of the segments contained a number of rigid bodies . The Hips segment contained the feet, the legs, and the pelvis . The Torso segment included seven independent sections of the thorax, two sections of the neck, and the head. The Arms segment consisted of the shoulders, arms , hands, and fingers . The club segment consisted of a grip, 8 shaft sections, and the club head. The mass and moments of inertia of these rigid club hodies were measured directly previously.

Segmental Sequencing of Kinetic Energy in theGolfSwing

169

Fig. 1. Example of the rigid body geometries applied to the kinematic golf model.

The total KE for each segment was calculated as the sum of the rotational and translational kinetic energies of those segments (eq.l). The translational KE was found about the center of mass of each segment as a whole (eq.2), where the mass of the segment was found as the sum of masses of the bodies comprising the segment (eq.3). The velocity of the center of mass of each segment was calculated as the time derivative of the position vector of the segment centroid (eqA) . This position vector is a mass normalizedsum of the positions of all the segment's rigid bodies (eq.5). KEtolal

=KEtranslational + KErotational

(I)

KEtranslational

=Lm

i

2

v = d~'m dt

n

m segment

- , =-1 mcmV;'m-

(3)

(4)

em

i=1

(2)

n

Lm)~ ~m _....:ci=::..:.I_ _

(5)

mcm

Rotational KE was calculated as the sum of local rotation of the rigid bodies about their own center of mass, and remote rotation of the rigid bodies about each segment center (eq.6). KErotational

= KEbody rotation + KEsegment rotation

o, =

(6)

KEbody rotation

(8)

OJ'"

W/ (3,2)) OJ/ (1, 3)

[W/ (2, 1)

1

- 1-1,U) =-21 OJ. ' ,

= dRi R t dt

'

(7)

(9)

Local rotational KE of the individual bodies was calculating using the angular velocity vectors and moment of inertia tensors for each body (eq.7). The inertial properties of each body were derived from their geometry and the angular velocities of

170

Brady C. Anderson, IanC. Wrightand Darren 1. Stefanyshyn

each body were obtained from the skew-symmetric angular velocity matrix (eq.8). This matrix was calculated by finding the first derivative of the 3x3 rotation transform at each time step and multiplying by the transpose of that rotation transform (eq.9).

~1 v - , KE segment rotation =L..J - mi i ~tan '

(10)

=P;~ -

(12)

~I

p;~lan

2

P;drad

-

dP' ------'!!!.. dP

(II )

=p;u(p;u. p;~ )

(13)

V ~, =-

~

p;l1rad

~

Remote segment rotation energy was found by calculating the tangential velocity of each body i about the segment center of mass. The difference velocity vector V6 is the difference between the velocities of each body minus the velocity of the segment center of mass (eq.II). A radius vector r, from the segment center of mass position to the body center of mass position was found at each time interval. The component of the difference velocity along the radius vector (Vdr ad ) was found as the projection of the velocity on the radius (eq.l3). The tangential component was then found by vector subtraction (eq.12). This difference velocity tangential component vector was then used to calculate remote segment rotational KE (eq.IO). Total KE traces were filtered using a 41h order low pass Wavelet filter at a cutoff of 20 Hz. Statistics were done using a multi-factorial one-way ANOVA test at a significance level u=.05, with a Tukey post hoc analysis.

3 Results Figure 2 shows total KE calculations for each segment during a single swing trial. Ball contact is shown at time-O sec. For this trial, the magnitude of the KE peaks increase starting proximally at the Hips and moving distally to the Club. The Arms, Torso and Hips segments all peaked at approximately the same time, prior to ball contact. The Club segment KE peaked at impact. The total KE for the club segment peaked at roughly 250J.

-. ........

-

.'"

,to

Fig. 2. Total KE for segments throughout the golf swing for a single player during one trial. Time = 0 sec. represents ball contact. KE is shown in joules.

Segmental Sequencing of Kinetic Energy in the GolfSwing

171

3.1 Magnitude of Kinetic Energy Peaks For each player, the segment KE peak magnitudes were expressed relative to the Club KE peak. Figure 3 shows the means of these peaks and their standard deviations. Each segment's KE peak was significantly different from the others. The magnitude of the KE peaks increased sequentially from the proximal to the distal segments.

0.8 0.6

*'

0.4

02 O L..-.l----L._ _L..---L._---J'----'-_----l._

Hps

Torso

ArlT6

.........- .J

Chb

Fig. 3. Relative magnitudes of total KE peaks forgolfer segments throughout a golfswing as

compared to the golfclub peak KE. Error bars represent thestandard deviation. Theasterisk symbolizes statistical difference from allother segments.

3.2 Sequential Timing of Kinetic Energy Peaks The timing of the KE peaks were analyzed in a fashion similar to the peak magnitudes. Timing was expressed relative to total Movement Time (MT) where 0 represents the top of baekswing and I represents ball impact. Figure 4 shows the group mean relative timing for each segment KE peak along with the correspondingstandard deviations. Only the Club segment timing was statistically different from the other three. The three human based segments peaked at approximately the same time while the Club segment, being external to the player, peaked later in the swing. 1.2

r--

*

0.8

-

0.4

o Hips

Torso

Arms

Club

Fig. 4. Relative timing of total KE peaks for golfer segments as a function of Movement Time. MT

at 0 represents thetop of backswing, while MT at 1 represents ball contact. Error bars represent the standard deviation. The asterisk symbolizes statistical difference from theother segments.

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Brady C. Anderson, Ian C. Wright and Darren J. Stefanyshyn

4 Discussion Peak magnitudes of total KE increased sequentially from proximal segments to distal segments in the golf swing. This finding supports the principal of summation of speed. The timing of these peaks however, did not occur sequentially. At approximately 80% MT during the downswing, that the segments belonging to the golfers' bodies peaked simultaneously. Shortly after, the Club segment reached a maximum KE. One would expect that if energy were being transfered sequentially along body scgements, distal links should experience an increase in kinetic energy at the expense of their proximal neighbor. This decrease in proximal kinetic energy only seemed to happen when the Club segment kinetic energy reached a maximal peak.

5 Conclusion Neither the summation of speed principal nor the principal of optimal coordination of partial momenta can fully explain the pattern of kinetic energy transfer observed in this investigation. It was found that the magnitude of kinetic energy increases proximally to distally, but there is an instant during the downswing when the kinetic energy of the segments in the golfers body, tend to peak simultaneously. This leads to a later peak in KE of the most distal link, the golf club, at ball impact.

Acknowledgements We would like to thank the TaylorMade-adidas Golf Company and Biomechanigg Research Inc. for their support of this paper.

References Bunn, J.W. (1972). Scientific Principals o(Coaching. Prentice-Hall Inc., Eaglewood Cliffs, NJ. Clauser, C. E., McConville, J. T., & Young, J. W. (1969). Weight, volume, and center of mass of segments of the human body. AMRL Technical Report (Rep. No. AD 710 622) . WrightPatterson Air Force Base, Ohio: Aerospace National Research Laboratory. Jorgensen, T. P. (1994) . The Physics ofGolf. r' ed. AlP Press, New York, NY Marshall, R. N. & Elliot, B. C. (2000) . Long-axis Rotation: The Missing Link in Proximal-to-distal Segmental Sequencing. Journal of Sports Sciences 18,247-254. Nesbit, S. M. (2005) . A Three Dimensional Kinematic and Kinetic Study of the Golf Swing. Journal of Sports Science and Medicine 4, 499-519. Putnam, C. A. (1993) . Sequential motions of body segments in striking and throwing skills: Descriptionsand explanations. Journal of Biomechanics 26, Suppl.l , 125-135 Sprigings, E., Marshall, R., Elliot, B. & Jennings, L. (1994) . A three- dimensional kinematic method for deterrning the effectiveness of arm segment rotations in producing racquet-head speed. Journal of Biomechanics 27, 245-254. Van Gheluwe, B. and Hehhelinck, M. (19R5). The kinematics of the service movement in tennis: A three-dimensional cinematographical approach. Biomechanics IX-B., (Edited by Winter, D.A., Norman, R.W.. Wells, R.P. Hayes, K.C. and Patla, A.E.). Human Kinetics Publishers Inc., Champaign, lL. 521-526

5 Gymnastics

Synopsis of Current Developments: Gymnastics David G Kerwin Cardiff School of Sport, UWIC , UK, dkerwin @uwic .ac.uk

Background to Recent Research in Gymnastics Modeling has dominated research in gymnastics in the recent past. Peter Bruggemann's Cologne (Germany) based group has concentrated on energetics in high bar circling and release and regrasp skills whilst Fred Yeadon 's Loughborough (UK) group has focussed on momentum rings circling and in the preparation for high bar dismounts (eg Hiley and Yeadon 2005) . Another theme has been ' control' with recent contributions from Jill McNitt Gray's group in California (USA) focussing on strategies for landing from rotating jumps whilst Fred Yeadon and colleagues have addressed questions of control in twisting somersaults and hand balancing. This group have also studied vaulting and tumbling using forward dynamics models to examine both technique and control. A common theme running through many of the recent studies has been the interaction between the gymnast and the equipment and inevitably therefore heightens the impact that engineering can have on research in this sport. Engineering has also been central to many of the gymnastics studies through the appl ication of control theory to the study of human movements and the development of forward dynamics modelling with Dads" and Autolev I1ITM being the preferred option s.

Papers Featured at the Conference Two contributions in the current conference draw on the themes of control theory and forward dynamics model ing. Wendy Kimmel and Mont Hubbard, reporting on balancing on a horizontally compliant surface (trampoline), have developed single and double segment models and showed that knowledge of foot position is not important in the feedback control system whereas segment orientation is necessary to achieve a marginally stable closed loop system. Alison Sheets, also with Mont Hubbard, used Autolev III to develop a forward dynamics model of uneven bar giant circling. This is a combination of experimental and modelling work, first to determine parameter values for the 'shoulder' then to use these to enhance a four segment, rigid linked, planar model of circling. Interestingly they report, no changes to the hand force related slippage limiting factor

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David G Kerwin

(Sheets and Hubbard 2005), but a reduction in flight revolutions as a result of energy dissipation during the swing. Energy exchanges in bar swinging also features in the paper by Gareth Irwin and David Kerwin. Using inverse dynamics, in a similar manner to the study by Arampatzis and Bruggemann (2003), male international gymnasts performing general longswings (giant circles) on a high bar were studied. Customised inertia data for the gymnasts have been combined with video analysis to develop a four segment planar model. Based on observations from the earlier paper, the lack of a compliant shoulder is likely to overestimate total energy, but serves to highlight the critical importance of the functional phase in the longswing. The final paper in this section by David Kerwin and Gareth Irwin revisits the problem of determining high bar forces in competitionand examines the influence of inertia and kinematic data on inverse dynamic determination of bar forces and contrasts this with estimates based on bar deflections.

Future Research Trends Modelling will continue as a central theme of gymnasticsbased research. The control in this environment makes the approach very powerful in examining aspects of technique, investigating control strategies and understanding mechanisms underpinning injury without putting gymnasts at risk. Forward dynamic models which are torque driven tend to be more stable than the angle driven variety, but as with all forward dynamics models, the key challenge remains specificationof the internal parameters. Improvements in technology and the use of remote sensing will encroach more into sport from engineering and the impact of increased volumes of fine grained data will in the future underpin performance profiling, retrospective and prospective studies of injuries and form the core of future coaching knowledge.

References Arampatzis, A., and Bnlggernann, G.P. (2003) Mechanical energeti c proces ses during the giant swing before the Tkatchev exerci se. Journal ofBiomechanics, 34, 505512 . Hiley, MJ. and Yeadon , M.R. (2005) The Margin for Error When Releasing the Asymmetric Bars for Dismounts . Journal ofApplied Biomechanics, 21, 223-235. Sheets, A.L. and Hubbard, M. (2005) Effects oflow bar avoidance and gymnast size on high bar dismount performance. Proceedings ofXXth Congress of International Society of Biomechanics.

Effect of Shoulder Compliance on Peak High Bar Forces During the Giant Swing Alison L. Sheets' and Mont Hubbard' 'University of California, Davis, Mechanical Engineering, [email protected] 2University of California, Davis, Mechanical Engineering, [email protected]

Abstract. When a female gymnast model does not include shoulder compliance, a simulated optimal performanceof a giant swing on the uneven parallel bars is limited by the maximum force that can be exerted on the hands without slipping from the bar (Sheets and Hubbard 2005). To determine the effect of shoulder compliance on hand force, two four-segment gymnast models including an arm, a torso/head and two leg segments are compared: one in which the shoulder is a rigid pin joint, and one which includes shoulder compliance. Experimental values of shoulder stiffness and damping are determined to best describe I-D vertical damped oscillations of the gymnast/bar system. Optimum shoulder and hip motions during the swing are calculated to complete the most dismount flight revolutions prior to the mass center (CM) passing a specified landing height. Optimization constraints include maximum bar/hand force, physiologic joint limitations, low bar avoidance, and minimum landing distance from the bar. Shoulder and hip motions result from time varyingjoint torques that are limited by joint angle, angular velocity, isometric strength, and activation factors. Bar release time and joint torque activations at ten nodes equally spaced throughout the swing are optimized using the downhill simplex method. Joint torque activations at all other times are approximated by cubic splines fit to the ten nodes. Performance limitations due to the slipping constraint are not reduced in the compliant model, even though it is active for a shorter period. The compliant shoulder model also produced fewer flight revolutions than the rigid one, 1.417 vs. 1.478, because the shoulder dissipated energy during the swing and stored it at bar release.

1 Introduction The giant swing (giant) begins and ends in a handstand and allows the gymnast to connect skills, or increase angular velocity to be able to execute more complex dismount or release-regrasp moves (Hiley and Yeadon 2003). Because of the importance in a routine, a giant swing simulation using a rigid four segment gymnast model is created (Sheets and Hubbard 2005). The model's hip and shoulder movements during the swing are optimized to maximize the number of flight revolutions after bar release. The optimal performance is subject to constraints on gymnast joint torque, angular velocity, and ranges of motion. Interestingly, none of these constraints is active when the maximum force that can be exerted on the bar without slipping is limited to 4*mg (Witten 1996). This limitation is important because force is transmitted through the hands and onto the bar to accelerate the Clvl, which occurs when the gymnast changes body configuration to avoid the low bar, transfers angular momentum between segments or increases the system' s mechanical

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Alison Lynn Sheets and Mont Hubbard

energy using muscular work. Therefore, the bar force constraint inherently limits maximum joint angular velocities, possible ranges of joint angles, and the gymnast's ability to do work. It also reduces the influence of increased hip and shoulder strength on performancebecause the gymnast must remain in contact with the bar. It is possible that optimizations performed using a rigid model may overestimate the importance of the slipping constraint. When Brewin et al. (2000) included shoulder compliance in the model of a gymnast performing a giant swing on the men's ring apparatus, the calculated peak shoulder force was reduced; which also reduces hand force on the ring. This paper aims to determine experimentally gymnast shoulder stiffness and damping. These values will be used to ascertain if the rigid shoulder assumption used in previous models overestimated the bar force and thus the bar force constraint's importance. Maximum bar deflection, and maximum number of dismount revolutions are compared to quantify effects of shoulder compliance.

2 Methods 2.1 Gymnast and Uneven Parallel Bar Model Two four-segment models ofa collegiate gymnast (m = 69.3 kg, and h = 2.05 m with arms above head) include head/torso, arm, and two leg segments. Each segment's inertia, mass and eM location is determined using a "stadium solid" model. Both gymnast models assume the hip is a rigid ball and socket, while one shoulder is a rigid pin joint and the other includes a damped linear spring to represent connective tissue. Arm and leg motion is driven by instantaneous torques determined by scaling the maximum isometric joint torque by joint angle dependence, angular velocity dependence, and joint torque activation A(t) (Sheets and Hubbard 2005). The scalar function of time, A(t), varies over the range [-I, I] and is the fraction of the maximum possible torque (created by fully activating all muscles crossing each joint at the current state) applied to cause joint extension and flexion , respectively. The A(t) time histories are approximated by cubic splines fit to ten nodes equally spaced throughout bar contact. The simplex optimization method (Neider and Mead 1965), is used to calculate optimayoint torque activation at the nodc and bar release time.

Fig. 1 Schematic of the compliant shoulder gymnast model

Effect of ShoulderCompliance on Peak High Bar Forces Duringthe Giant Swing

179

The bar is modeled as a massless linearly elastic spring with an experimentally determined stiffness of 15,000 N/m. The coefficient of friction between hands and bar is measured to be j.1 = 0.85. Bar damping is not included because the shoulder accounts for most of the system damping (Hiley and Yeadon 2005) . The state vector defining the compliant gymnast and bar system is composed of seven generalized coordinates (GC) [P, 8" 8hz. ~Y' xi, Yb, y.,] and their time deriv atives (Fig. I) . The rigid model needs only six GC's because there is no shoulder stretch, Ys= O. AutoLEV (Kane and Levinson 2000) is used to derive the equations of motion, which are solved with a Runge-Kutta numerical integration using C.

2.2 Shoulder Stiffness and Damping Coefficients Shoulder stiffness, k.; and damping, b" are experimentally determined by initially displacing a gymnast hanging from the bar and recording the bar and gymnast vertical oscillations. Markers are placed on the bar center between the hands, on each forearm and on the sternum. Ten trials are performed with three different initial conditions . Four trials begin with the gymnast standing on an elevated surface with extended shoulders, then the feet are unloaded and bar loaded . During three trials the gymnast jumps vertically to catch the bar with fully extended shoulders. Finally, three trials begin by hanging from the bar while a large downward force is applied to the feet then released . Three motion analysis cameras film the resulting vertical oscillations of the bar, gymnast forearms and torso at 250 frames/sec . The change in distance from the sternum to the forearm as a function of time is approximated by a damped osc illation and two decaying exponential functions .

FJ =c, sin(aJdt +¢)e-~aJ,,r + c2 e-tlT2 + C3e -tiT]

where OJd

(2)

= ~ OJ; (1- ( 2 ) and the constants CJ, lj>, C2, Cj ,

f4" (,

f 2,

and

fj

are deter-

mined using a least squares fit of the function F J to the experimental data . The calculated system natural frequency f4" damping ratio (, and time constants f 2 and fj are then used to determine k; and b.. Using measured values of bar stiffness kb , bar mass m.; gymnast arm mass m, and remaining gymnast mass mg in the system equations of motion (mh + m a )xh = -khxb + k, (x, - x h) + b, (X.I· - xh) + (mh + ma)g (3) mgx g =-k,(x, -xb)-b,(xs - xh)+mgg

(4)

the system characteristic equation is expressed in terms of the unknowns k, and b;

S4 + 0.17Ib,S3 + (2290 .555 + 0.171ks )S2 + 42.574b,S + 42.574k s = 0 (5) Initial guesses for ks and bs allow calculation of eigenvalues (roots of the characteristic equation). Two real eigenvalues represent time constants, and the pair of complex eigenvalues represent system natural frequency and damping. The values of k, and b, are optimized to minimize the sum of squared differences between the calculated eigenvalues and constants determined by the F J optimization. F2

=(OJn -

OJnopt ) 2

+ (10«( -

(opt»2

+ (f2 -

f 2opt ) 2

+ (f3 -

f 30pt ) 2

(6)

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Alison Lynn Sheets and Mont Hubbard

2.3 Giant Swing Optimization The optimal solution begins (to= 0) with the gymnast in a handstand rotating about the deflected bar with an angular velocity of 1.8 rad/s (Hiley and Yeadon 2003) . It ends at bar release (If) and results in maximum straight body dismount revolution s, with arms above the head, prior to Clvl passing height OAh above ground. lo = (OJ(Jf )6.t[ + r(1f )) /(21f) (7) where oiJf) is release angular velocity, 6.1[ flight time and r(tf) angle shown in Fig. 1. Optimization constraints include limitations on: joint ranges of motion, angular velocity, rate change of muscle activation, bar force and minimum landing distance. Using the optimization criterion in Eq. 7 and including constraints as penalty functions to be subtracted from the objective function lo, the optimal giant swing joint torque time history and release angle are calculated for gymnast models with a rigid and compliant shoulder .

3 Results 3.1 Shoulder Stiffness and Damping Coefficients The experimental data is well approximated by a damped oscillation and two decaying exponential functions (Fig. 2). There is little variation between the calculated natural frequencies , damping coefficients , and time constants using the F[ optimization even though three different initial conditions are used (Table I).

I

OJ!

I

i .,

0

I

-OJ!

-OJ! ·1

0

8

i

OJ!

· 1.60' --'0:"":J!-

...

- '-

- '":" J!-

-:2-

-:' 2 J!

... I I Doc:Io'Iong _ ... ......-

( IIOf

O.

I

0

I

02 0 -02

-0 '

0

OJ!

IJ!

I

2

2 J!

..O'--O....,J!----:-~--:' 1.6 2 2J!

H

I

Fig. 2 A typical result for one of the ten trials using the F] curve-fit optimization

Effect of Shoulder Compliance on Peak High Bar Forces During the Giant Swing

181

Table 1: Natural frequency, damping ratio, and time constants from F, optimizations

Average

fUn

1;

14.713

0.114

t2

rms error (em)

t3

0.239

0.343

0.137

0 .594 0.045 0.078 0.106 0.048 o The coefficients calculated using F, are consistent, meaning the standard deviations (c) are small compared to mean values, but the estimation of k, and b, gives less consistent results. Although there is a large o, the average ks and bs correspond fairly well with those experimentally determined by Hiley and Yeadon (2005) (Table 2). Table 2: Shoulder stiffness and damping calculated using F] optimizations

Average

k, (crk)

Hiley ks

b, (crb)

Hiley bs

22466 (12710)

25261

2432 (1042)

1003

Numerous other methods were tned, varymg bar stiffness and mcludmg bar dampmg, but none produced more consistent results. The average values were used in the giant simulation to quantify the effect of shoulder stiffness on bar force.

3.2 Giant Swing Performance Effect Due to Shoulder Compliance When the gymnast model includes shoulder compliance, the number of possible flight revolutions following an optimized simulated giant swing is slightly reduced from 1.478 (Sheets and Hubbard 2005) to 1.417. Possible reasons for reduced dismount performance are that the damper dissipates energy when the shoulders stretch (Fig. 4), and that the shoulders are stretched at bar release (Fig. 3) indicating that kinetic energy has been stored and not returned. The total energy during the rigid model's giant swing (Fig. 4) is similar to that measured by Arampatzis and Brueggemann (1999, Fig. 6a) during elite female performances. O.\S

g

.c u

~

0.1

...

O.os

j

>-

'0

"'<5" ~

0

-O.os

·3

.::!

.\ Y

a

(rad]

Fig 3. Shoulder stretch as a function of gymnast angle

·3

·2

·1

0

_y (r3d)

Fig 4. Net energy change for rigid and compliant shoulder models

The performance decrease caused by the bar force constraint was not reduced by the compliant shoulder. Although the constraint is active earlier during the rigid body model 's swing, it still limits both performances when the gymnast's CM is below the bar (Fig. 5). The rigid model's constraint becomes active when the gymnast's legs move to avoid the low bar and the CM is accelerated, whereas the compliant model's shoulders stretch in addition to the bar flexing to produce this motion (Fig. 3).

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Alison Lynn Sheets and Mont Hubbard

. ••

... ... .

. , ...

••

II

Fig 5 Both bar center paths, solid lines, approach bar deflection limits, dotted circle The bar force result is consistent with the findings of Brewin et al. (2000) who de tennined that, although ela sticity of the shoulder and apparatus slightly decreased peak shoulder forces, gymnast technique was far more important. Because the optimized gymnast technique for the rig id and co mpliant models could not vio late the force constraint, it is not surprising that both maximum bar forces we re identical.

4 Conclusions It is possible to determine shoulder stiffness and damping by recording vertical gymnast oscillations on the uneven parallel bars. Although the system natural frequency, damping rat ios and decay time are consistent over all trials, the resulting values of k, and b, varied mo re . The addition of shoulder compliance, using average values, decreased giant swing performance. Energy was dissipated during the sw ing by the damper, and the gymnast releases the bar with energy stored in the compliant shoulder structures. The bar force constraint continued to be active during the swing.

References Arampatzis, A, and Brueggemann, G.P. (1999) Mechanical energetic processes during the giant swing exercise before dismounts and flight elements on the high bar and uneven parallel bars. J of Biomech 32, 811-820. Brewin, M.A., Yeadon, M.R., Kerwin, D.G. (2000) Minimizing peak forces at the shoulders during backward longswings on rings. Human Movement Science 19, 717-736. Hiley, M. J. and Yeadon, M. R. (2003) Optimum technique for generating angular momentum in accelerated backward giant circles prior to dismount. J Appl Biomech, 19(2), 119-130. Hiley, MJ., Yeadon, M.R. (2005) The margin of error when releasing the asymmetric bars for dismount. J Appl Biomech. 21, 223-235. Kane, T. R. and Levinson, D. A. (2000) Dynamics Online: Theory and Implementation with AutoLE V. Online Dynamics, Inc., Sunnyvale, CA. NeIder, J. A. and Mead, R. (1965) Computer Journal. 7,308-313. Sheets, A.L. and Hubbard, M. (2005) Effects of low bar avoidance and gymnast size on high bar dismount performance. Proceedings ofXXth Congress ofInt Soc of Biomechanics. Witten, W. A., Brown, E. W., Witten, C. X., Wells, R. (1996) Kinematic and kinetic analysis of the overgrip giant swing on the uneven parallel bars. J Appl Biomech, 12(4),431 -448.

Effect of Horizontal Surface Compliance on Balance Strategies Wendy Kimmel and Mont Hubbard University of California, Davis, Mechanical and Aeronautical Engineering, [email protected], [email protected]

Abstract. Balancing on a horizontally compliant surface is examined by comparing the task with successively more complex dynamic models. 1,2 and 3D OF systems are used to examine the balance strategies (state feedback control laws) needed to maintain stability. The I and 2 segment systems use a spring attached at the lowest point of the (lower) segment to model horizontal compliance. Velocities are neglected and only position and angular displacement state variables of the system are fed back to achieve balanced , marginally stable closed loop systems. Regions of stability in the feedback gain space are compared using the RouthHurwitz criterion, root locus and other graphical techniques. Boundaries of the stable regions in the feedback gain space are provided by the inequalities satisfied by the gains for positivity of the leading column of the Routh array. Knowledge and feedback of horizontal foot position is not important since it is possible to achieve stability by neglecting it entirely.

1 Introduction Balance is important enough to be leamed early in our lives. It plays a crucial role in posture and bipedal locomotion and is also relevant in many sports tasks. It consists of a dynamic feedback control process, in which the state of the body (orientation, position and their rates of change) is sensed and compensatory muscular torques are applied to restore the body to its inverted pendulum equilibrium position. We are ' balanced' if we are able to return to vertical after a perturbation is applied . Considerable research has occurred on the mechanisms and strategies of the balance task (Pai and Patton 1997; Pai 2003; Patton, Pai and Lee 1998) in standing and locomotion. Virtually all these studies have assumed that the supporting surface is rigid and the horizontal forces induced at the support point are provided by friction between the rigid surface and the foot. Almost no work has yet examined the balance task on a surface with either vertical or horizontal compliance, yet this task is important in some sports activities (e.g. trampoline) . This paper examines balance on horizontall y compliant surfaces by comparing several models of increasing complexity. Active ankle torque determined from a linear feedback control law is applied to the joint between the body and the compliant surface in order to maintain stability of the system.

184

Wendy Kimmel and MontHubbard

2 Methods- Single and Multi-Segment Body Models For each system, the equations of motion are derived using the AutoLev symbolic dynamics computer program (Kane and Levinson 2000). System dynamics are also linearized in AutoLev using Taylor series approximations . The linearized systems are used to derive feedback strategies . The more complex the system, the more states which must be included in the control law for stability. Although full state feedback including velocities as well as position states would allow 'exact placement of closed loop eigenvalues, here only position feedback is considered. Thus the maximum stabilization that is possible with this limited feedback scheme results in marginal stability (closed loop eigenvalues on the imaginary axis). The RouthHurwitz Criterion is used to determine limitations on the feedback gains for stability. Of interest is how stable regions in the feedback gain space are related to those for more complex models with more segments and to those for simpler systems without compliance .

2.1 One Segment Models The simplest balance model including horizontal ground compliance consists of a single uniform segment of length 2L, mass m, and central moment of inertia J, supported by the vertically rigid ground with constant surface stiffness k in the horizontal direction (Fig. Ib). Because the segment can tilt B and its base can translate xfi this system has two degrees offreedom (DOF). A similar single DOF system without horizontal ground compliance , a one segment body with its base fixed on a completely non-compliant surface (Fig. la), is useful for comparison to understand the effects of compliance . This body also rotates through but motion of its base is prevented . In both cases the control variable responsible for achieving balance is a torque T applied between the ground surface and the body, as a model for ankle torque in the human. The system without compliance has linearized equation of motion 18 - mgL B = - T = - K liB. A root locus versus the gain K(J shows that there are

e

two open loop real roots of equal magnitude (mgL/J)lI2, one stable and one unstable. The active torque T= K(J~ that feeds back the angular rotation of the segment, is able to achieve marginal stability when K(J > mgL, that is when the feedback term outweighs the destabilizing effect of gravity. For values of parameters m=60 Kg, g=9.8 m/s" and L=0.8 m, this inequality becomes K(J > 470 N/m. This I DOF, one segment model on a rigid surface without horizontal compliance can be compared to its counterpart on a compliant surface (Fig. Ib). The stabilizing feedback is again in the form of a control torque T= KxXf + K(JBbetween the segment and the surface. In this case it is a function of two position states xf and B, where K, is the gain constant for the changes in the position xf and K(J is the gain constant for changes in the body rotation angle B. Again this torque is similar to an ankle torque.

Effect of Surface Compliance on Balance Strategies 185

Fig. la. 1 OOF, 1 segment, non-compliant surface

b.2 OOF, 1 segment, compliant surface

c.3 OOF, 2 segments , compliant surface

The only other forces acting on the segment include the force of gravity at the center of mass and the spring force acting at the' foot' point f defined as

F;= -kxfi

(1)

where k=24000 N/m is the spring constant. The two linearized equations of motion for the 2 DOF system can be written as mX em = F, (2) I em ij = Fr L + mgL B + T The linearized kinematic relation relating motion of the center of mass and the foot, xcm=xr LB, allows the first of Eqs. 2 to be rewritten in terms of the variable xf . Substituting it and Eq. I into Eqs. 2 yields mx, - mLB = -kx r

(3) IemB=-kx rL+mgLB+Kxxr +KoB After taking the Laplace transform of the differential Eqs. 3, the characteristic equation for the 2 DOF system can be shown to be mls' +(mKe +kI+mk~ +mL~ -m2gL)s+(kKe -mgkI.)=0 (4) First the gain K, for the x foot position was ignored in order to determine whether feedback of only angular position of the body is enough to stabilize the system . A root locus can be used to visualize the effect that feedback of angular rotation of the segment has on stability. When Kx=O, the root locus versus K o indicates that the unstable system can be made marginally stable when the angular position of the body is fed back with a sufficient gain, even when the motion of the foot is neglected. As in the I DOF system, there are two real roots, one stable and one unstable. In addition, there exist two purely imaginary open-loop (OL) poles and a pair of lower frequency purely imaginary OL zeros . Again as in the I DOF system, the root locus indicates that the 2 DOF system cannot achieve full stability in the sense of arbitrary

186

Wendy Kimmel and Mont Hubbard

pole placement, but rather only marginal stability, since the roots lie on the imaginary axis even with infinite gain. Knowing that the system can be stabilized with feedback of only one of the states, the Routh-Hurwitz criterion (Nise 2000) was applied to more fully examine stabilizability by applying it to Eq. 4, the characteristic equation of the 2 DOF system. According to the Routh criterion (Nise 2000), each coefficient in the first column of the Routh array must be positive to guarantee system stability. In general, because each EOM is second order, for an n DOF system the Routh criterion yields 2n-1 inequalities. Each of these inequalities involving the feedback gains, when viewed as an equality, results in an equation for a boundary of the stable region, and the set of gains resulting in a marginally stable system will lie on one side of the boundary. The stable region is then the intersection of the three regions determined by the boundary equations, the equalities related to the three Routh inequalities: x, > -(-m 2gL+kI+me +mLKJ /m x, > ~m2gL-mek-mLKx + kI±2(-k 2Ime -kImLK x) 1m (5) x, >mgL This stable region is shown in Fig. 2. Note that one of the boundaries (Eq. 5c) is identical to the stability requirement for the I DOF system. However, the region of stable gains is further limited by the other two boundaries. The logical intersection of these requirements indicates that the uppermost curved line, which results from Eq. 5b, is the lower boundary of acceptable gains. There is no upper limit on values of either gain. There is no value of K" or any amount of foot positional feedback that can successfully stabilize the system alone. The gain K, can even take on larger negative values for a sufficiently large Ke. But for any positive K" as long as K, is greater than the constant mentioned earlier, the system can be stabilized.

,

2 x 10

0

"",

"~

* *

Region of Stability

~*

-2

'Jt,.

-4

* * * * * * * *

..

*~

:2

-6

-8 -10 -12

-5

0

".

-,

-,

".

-,

". ".

-,

"-,

".

".

"-, -,

c:

Ke

-, 10 x 10'

Fig. 2. Acceptable region in the Ke, K, feedback gain space for a stable 2 DOF system

Effectof SurfaceCompliance on BalanceStrategies 187

2.4 Two Segment Body Model The next level of complexity involves the addition of a second segment (Fig. lc) by splitting the body at the hip into legs (mJ= 26 Kg, 2LJ= 0.9 m) and a torso (m2= 36 Kg, 2L2= 0.8 m) Again the system is unstable without control , requiring an active ankle torque between the lower segment and the surface that feeds back , in general, all 3 position states ; xI, (}j and ()2. (6) Analogous to the procedure used above , the Routh-Hurwitz criterion for the characteristic equation is used to derive five inequalities from positivity of the first column of the Routh array, the satisfaction of which is necessary for stability. The complexity of the inequalities motivates that this be done by computer using a symbolic manipulator; we used Autolev. The boundaries are now 2-D surfaces in the 3-D gain space. For the numerical values above , three of these inequalities (7a, b, c) are K OI > 651.40 - 0.57965k - 0.70360K x + 0.49796Koz K Ol > -0.453k + 498.89 + 0.498Ko2 - 0.704K x ± (-1310 .7k 2 -5.560e-38k-3512.8kK oz -1906.3kK x

-

(7)

1.927e8 -1.520e6K oz - 3.977e5K x K 0 1 > (51007k + O.6483Kx + 1.15ge - 3kK oz ) / k Although one of the other two inequalities (7d) is too lengthy to be shown here, the last one (7e) is identical to the first (7a) above. Again a reasonable choice for parameters allows numerical visualization of the five boundary surfaces and the stable region in the gain space that satisfies the above boundary equations (7a, b, c) (and the two not listed) . Since they are difficult to portray on paper we choose not to present the surfaces and stable regions in 3-space here , electing rather to show sections of these surfaces. One such interesting section is that corresponding to Kx=O. In Figs . 3a and 3b below, the stable subsection of marginal stability for this section is illustrated by the diamond shapes bounded by several of the inequalities (other inequalities are irrelevant for these parameters and Kx=O) . Thus as in the 2 DOF case, it is possible to neglect foot position entirely and, with the appropriate choice of gains K eJ and Ke:a feeding back only segment orientation is sufficient for stability. The inequality (7d) not shown above has been plotted with the' - -' shape in Fig. 3b, an enlarged portion of Fig. 3a that allows the complexity of the inequality to be seen. For this particular inequality (7d), as K e2 varies, K el has either I, 3 or 5 real roots, resulting in I, 3 or 5 branches of the surface seen in Fig. 3b.

188

Wendy Kimmel and Mont Hubbard 5

X 10 0.5 ,..:-.:."-------,-----,..,,--

-

1

s

-1

-1.5 -2

/

0.5

o -0.5

X 10·

oi

-1

o~

-1.5 -2

0

-2.5

Fig. 3a. Section of 3 DOF system stability.

I

o

-3 5 10

0\ o

-3

*

!

o

~

0 Kfll

/

-0.5

s

~:

a,e!

0 0 0 0 00 00 0 0 00 0 000 000 0000 0000 00 00 00000 00000 00 0000 000000 000000 000 000 0 00000 0 0 00 0 0000

/

-2

j

0 K61

X 10·

3b. Exploded region in Fig. 3a.

3 Conclusions It is possible to examine regions of gain space for I and 2 segment systems on a non-compliant surface in order to determine the necessary feedback control to maintain marginal stability. For the two simplest dynamic systems representing balance , and for the realistic parameters chosen, no account needs to be taken of foot position in the feedback law. Only feedback of segment orientation is necessary to achieve a marginally stable closed loop system. Further extensions of these systems to include more segments and surface compliance in the vertical as well as horizontal planar dimensions will allow closer comparisons to realistic human- sport surface interactions.

Refer ences Kane , T.R. and Levinson , D.A. (2000) Dynamics Online: Theory and Implementation with AutoL ev. OnLine Dynamic s, Inc., Sunnyvale, California. Nise, N.S. (2000) Control Systems Engineering. John WiIcy, New York . Pai, Y. and Patton, 1. (1997) Center of mass velocity- position predictions for balance control. Journa l of Biomechanics 30 (4), 347-354 . Pai, Y. (2003) Movement termination and stability in standing. Exercise and Sport Sciences Reviews 31 (1), 19-25. Patton, 1.L., Pai, Y., and Lee, W.A. (1999 ) Evaluation ofa model that determines the stability limits of dynamic balance . Gait and Posture 9, 38-49.

Predicting High Bar Forces in the Longswing David Kerwin and Gareth Irwin University of Wales Institute, Cardiff, [email protected]

Abstract. The longswing on high bar in men's artistic gymnastics is the core skill within all competitive routines. The forces applied to the bar by the gymnast are important when studying a performer's technique or when examining injury mechanisms. Previous studies have used video measurements of the bar's motion to predict bar forces to within 7% of the range of directly recorded forces. Also, by assuming zero external forces at the gymnast 's feet, inverse dynamics have been used to predict bar forces, but previously this method has resulted in errors greater than 20% . A study , employing 20 DLT technique s and customized inertia data for four elite male gymnasts performing three longswings on a strain gauged high bar, was conducted to enable the two methods for estimating bar forces to be directly compared. Digital video images were recorded at 50Hz from which the bar centre, head centre and the nearest wrist, elbow , shoulder, hip, knee, ankle and toe were digitized, starting before the gymnast reached the handstand, continuing throughout one revolution and ending once the gymnast passed beyond the handstand (-400°). All video and force data (1000Hz) were interpolated within a single 360° longswing at 1° intervals and root mean squared differences (rmsd) between the measured bar forces and those predicted by bar deformation and inverse dynamics were compared. Tracking the motion of the bar in 20 was poor in comparison to the 8% rmsd when using inverse dynamics. In the latter technique, deliberately swapping inertia data sets between the subjects increased errors. Inverse dynamics data were sensitive to kinematic and inertia data errors but the use of the 20 DLT and the inclusion of personalized body segment parameters contributed to an overall reduction in error compared to previously reported data. When direct bar force measurement cannot be obtained, the bar deformation technique is recommended providing that 3D video is used with a pre calibrated bar. Alternatively, with appropriate inertia data and DLT processing, the inverse dynamics technique can be employed, albeit with a slight loss of overall accuracy in predicting the precise profile of the high bar forces.

1 Introduction The longswing on high bar in men's artistic gymnastics is the core skill within all competitive routines. The forces applied to the bar by the gymnast are important when studying a performer's technique or when examining injury mechanisms. The longswing has been a subject of much research but studies dealing specifically with the bar forces are limited . Kopp and Reid (1980) used a strain gauged bar to measure the forces directly. Okamoto, Sakurai, Ikegami and Yabe (1987) and Irwin and Ker-

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win (2006) described the kinematic and kinetic profiles of the hip and shoulderjoints through an inverse dynamics approach of the longswing and more recently Arampatzis and Brilggemann (1998) and Yeadon and Hiley (2000) have made detailed studies of 'general' and 'accelerated' longswings using forward dynamics. A study using video measurements of the bar's motion to predict bar forces to within 7% of the range of directly recorded forces was reported by Kerwin and Hiley (2003). Also, by assuming zero external forces at the gymnast's feet, inverse dynamics have been used to predict bar forces, but previously this method has resulted in errors greater than 20% (Gervais 1993). Challis and Kerwin (1996) analysed the sources of error in inverse dynamics analyses and highlighted the influence of the kinematics and in particular the treatment of the raw digitizer data when determining segmental accelerations. During gymnastic competitions, direct measurement of the bar forces is difficult although not impossible. However, there are many occasions when video data are available but without force measurements. The bar in a competition can be calibrated in the 'field' as described by Kerwin et al. (2003) and used by Hiley and Yeadon (2005), but there are many occasions where these data are not available. The purpose of this study was to revisit the use of inverse dynamics as a method for predicting high bar forces in comparison to the values obtained by measuring the displacement of the bar. Both data sets were evaluated against directly measured forces using a strain gauged high bar.

2 Method 2.1 Data Collection All testing was performed in a gymnastic arena on a standard competition high bar (Continental Sports, Huddersfield, UK). Four men from the National Gymnastics Squad participated in this study (age = 22.5 ± 4.I yrs, mass = 66.4 ± 7.2 kg, and height = 1.69 ± 0.05 m). Customized body segment inertia parameters were developed for each gymnast using the methods of Yeadon (1990). A digital camcorder (Sony DSR-PDI 100AP, 3-CCD, Japan) was located approximately 40 m from the centre of the high bar and angled at 800 to the plane of motion to avoid viewing the gymnast's hands and bar centre through the bar supports. (The normal orthogonal alignment requirement was negated by the use of 20 DLT procedures). Images of a single calibration pole of height 5.176 m were recorded as it was sequentially placed at three locations to create a vertical plane approximately 5 m x 5 m. Four equally spaced spherical markers (diameter 0.10 m) were centered on the pole creating 12 known points within the field of view. Reaction forces on the bar were recorded (1000 Hz) using strain gauges (CEA/09/280UW/120, UK) bonded in pairs to the bar's surface. The bar had been pre-calibrated up to 3 kN and then back to 0 N in each dimension and the two bar stiffness values (Kz and Ky) determined using linear regression between the known loads and the bar's deflection.

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Each gymnast performed three series of five longswings. Images in the sagittal plane were recorded at 50 fields per second with the electronic shutter set to 1/300 s. Synchronization of the force and video data was achieved through the use of 20 LEDs (Wee Beasty Electronics, Loughborough, Leicestershire, UK) in the field of view of the camera. A single trigger initiated force data capture and began a sequential illumination of the LEDs at I ms intervals. By identifying the single image in which more than one and less than 20 LEDs were illuminated it was possible to synchronize the data to an accuracy of - 3 ms.

2.2 Data Processing All digitizing was completed using the TARGET high resolution system (Kerwin 1995). Following six repeat digitizations of the calibration images, three of each gymnast's longswings from the three sequences were selected for analysis. The longswing begins with the gymnast in a handstand on top of the bar and ends when he has rotated through 360° and is back in the handstand position. For a gymnast in a sequence of swings, the gymnast passes through rather than holds the handstand position, and so images ten fields before 0° until ten fields after 360° were digitised. In each field, the bar's centre, gymnast's head centre and his wrist, elbow, shoulder, hip, knee, ankle, and toe on his right side (nearest the camera) were digitized. Data reconstruction was achieved using an eight parameter, 2D direct linear transfonnation (DLT) algorithm (Kwon 1999). A low pass digital filter with cutoff frequency set to 6 Hz was used for all data. Later residual analysis (Winter 2005) was used to customize cutoff frequencies for each trial and for selected data points. Each gymnast was modelled as a pin-jointed four link system comprising arms (including hands), trunk, thighs and shanks (including feet). Customized segmental inertia profiles of mass and centre of mass location for each gymnast were produced. These were based on volumes estimated from the anthropometric measures for the individual gymnasts and intrinsic density data for each segment. Minor proportional adjustments were made to the segment mass values so that the predicted and measured whole body mass values agreed. The recorded strain gauge data were converted to force units using the predetermined calibration coefficients to produce the measured force values (Fz and Fy). All subsequent calculations were completed in Mathcad 13™ (Adeptscientific, UK). For inter and intra subject comparative purposes all data were interpolated at 1° intervals from 0° to 360°. Bar deflections were combined with the stiffness coefficients (Kz and Ky) to predict the vertical and horizontal bar forces . External forces at the toes were assumed to be zero and inverse dynamics applied to estimate the forces at the knees, hips, shoulders and finally the handslbar interface. Quantification of the level of agreement between the directly measured forces and the two sets of estimated forces was developed around two scores; the root mean squared differences (nnsd) between the measured vertical and horizontal force profiles, and the differences at the peaks of the measured forces. Finally perturbations to the inertia data and the data filtering procedures were made to check the sensitivity of the analyses.

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3 Results and Discussion The DLT reconstruction errors for the calibration points were ±0.004 m (y) and ±0.003 m (z). The ranges of forces determined directly from the strain gauge measurements were -1991 N to +1993 N horizontally and -340 N to 2760 N vertically . Table 1 shows the percentage root mean squared differences between the measured forces and those predicted from the 2D bar displacement to range from 10 to 15% (y) and from 12 to 17% (z). The percentage rmsd values for the inverse dynamics data were from 4 to 5% (y) and from 5 to 8% (z). Table 1. Differences between the measured force data and values predicted from bar deflections and inverse dynamics analys is as rmsd (%) and peak forces (%) Bar Deflection Inverse Dynamics Gymnast rmsd(Fy) rmsd(Fz) rmsd(Fy) rmsd(Fz)

A B

C D A B

C D

15.0 (2.5) 10.2 (2.0) 12.4 (0.5) 14.8 (1.0) peak(Fy) 32.5 (3.4) 23.7 (7.1) 17.7 (10.0) 13.4 (16.6)

13.8 (0.8) 12.1 (1.6) 13.2 (3.3) 17.0 (4.5) peak(Fz) 4.3 (1.6) 17.7 (3.8) 15.5 (7.0) 7.0 (14.9)

3.9 (0.4) 5.2 (1.2) 3.6 (0.8) 4.7 (1.5) peak(Fy) 1.3 (5.5) - 1.9 (4.1) -1.6 (4.4) -0.3 (7.3)

8.0(2.1) 7.7 (0.9) 5.3 (0.6) 6.7 (1.3) peak(Fz) -6.0 (6.5) 13.4 (2.6) 5.8 (1.7) 4.0 (1.2)

The corresponding comparisons for the differences in peak values were from 18 to 33% (y) and from 4 to 18% (z) for bar deflection forces and from -2 to 1% (y) and from -6 to 13% (z) for bar forces derived via inverse dynamics.

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Figure 1 shows that the overall match between inverse dynamics data and the strain gauge data was consistently superior to that for the bar deflection data. In a previous study by Kerwin et al (2003) very close agreement was found between bar

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deflection data and the measured forces and so it would appear that difficulties in digitizing the bar centre from the oblique camera view, even with the inclusion of the DLT procedures, resulted in data of poor quality . The inverse dynamics data generated from this 2D analysis produced a better match to the measured forces than had previously been reported and in all cases showed rmsd agreement of 8% or less. Peak values did not agree as closely in time or magnitude with the measured data, with bar deflection peaks varying from 13 to 33% (y) and from 4 to 18% (z). With inverse dynamics these values were lower ; from 0 to 2% (y) and from -6 to 13% (z). Thus , although the overall level of agreement appears to be better than the previously reported 20% of the range, the subtleties of the fluctuations in the forces, particularly around 1800 of rotation, were masked . The sensitivity of the inverse dynamics analyses was investigated through varying the segmental inertia profiles and manipulating the cutoff frequencies. Three of the gymnasts used were of similar size (70.39, 70.03 and 68.45 kg) whilst the fourth was smaller (55.56 kg). The respective custom ized inertia data sets were swapped within the inverse dynamics calculations and when the kinematics for the largest subject were used with his own inertia data, the differences with respect to the measured forces were 3.6% (rmsdy) and 7.2% (rmsdz) . Almost identical values were observed for the two other gymnasts of similar masses, but for the smallest gymnast, the corresponding differences increased to 6.5% and 12.7% respectively. The corresponding differences in the peak force values changed from 4% to 15% (y) and -13% to 8% (z) when the small gymnast' s inertia data were included . Changing the cutoff frequencies in the Butterworth filter for the bar deflection data from 1 Hz to 20 Hz, altered the level of agreement between the measured and predicted forces with the residual analysis indicating an optimized cutoff frequency of 4.5 Hz. Similar tuning of the movement data within the inverse dynamics analyses resulted in cutoff frequencies ranging from 3.6 Hz (y and z) at the wrists to 6.9 Hz (y) and 7.6 Hz (z) at the toes, but had minimal influence on the level of agreement between the predicted and measured bar forces .

4 Conclusions Predicting high bar forces using video analysi s of bar displacement has previously been shown to produce good results in circumstances when the bar has been appropriately calibrated. Digitized data from a single camera view, even allowing for the 2D DLT analyses, was unable to reproduce data of the quality previously reported when using 3D image data . Inverse dynamics analysis does not require knowledge of the characteristics of the apparatus and so could be very useful in competitions, but does rely on knowledge of subject inertia data to determine segment masses, mass centre locations and hence , by differentiation, segmental accelerations. Poor levels of agreement (-20%) have previousl y been reported for bar forces determined by inverse dynamics. Careful selection of customized inertia profiles and tuning of filtering procedures has been shown to improve the overall agreement between measured and predicted forces to 8%. Peak forces also appeared to be predicted better by in-

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verse dynamics analyses. Comparisons of the time histories revealed that neither method could be used to replicate the fine changes in the bar forces which were particularly evident as the gymnast was passing under the bar. If the overall magnitude and general shape of the force profile is required, inverse dynamics is suitable for predicting bar forces . When more detailed tracking of small bar force fluctuations is required, particularly for example in detailed technique analyses; computer simulation model evaluation or when considering injury potential , then either the forces need to be measured directly or very precise 3D bar displacement time histories need to be obtained.

References Arampatzis, A., and Bruggemann, G.P. (1998) A mathematical high bar- human body model for analysing and interpreting mechanic al- energetic processes on the high bar. Journal of Biomechani cs, 31, 1083-1092 . Challis, lH . and Kerwin , D.G. (1996) Quantification of the uncertainties in resultant joint moment s computed in a dynamic activity. Journal of Sports Sciences, 14,219-231. Federation International de Gymnastique (FIG) (200 I) Code ofPoints. artistic gy mnastic/ or men, Switzerland. Gervais, P. (1993) Calculation of reaction forces at the hands on the horizontal bar from positional data . In S. Bouisset , S. Metral and H. Monod , (Eds.) Proceedings ofthe XIVth Congress ofthe International Society ofBiomechanic s, 468-469 . University of South Paris, Paris, France . th Irwin G. and Kerwin, D.G. (2006) Musculoskeletal work in the longswing on high bar. 6 Interantional Sports Engineering Conference, Munich , Germany. Kerwin , D.G. (1995) Apex/Target high-resolution video digitising system . In J. Watkins (Eds .) Proceedings ofthe Sports Biomechanics section ofthe British Association ofSports and Exercise Sciences, Leeds, UK. pp. 1-4. Kopp, P.M. and Reid, J.G . (1980) A force and torque analysis of giant swings on the horizontal bar. Canadian Journal of Applied Sport Science , 5, 98-102. Kwon, Y.H. (1999) 2D Object plane deformation due to refraction in two-dimensional underwater motion analysi s. Journal of Applied Biomechanics, 15, 396-403 . Okamoto, A., Sakurai , S., Ikegam i, Y., and Yabe, K. (1987) The changes in mechanical energy during the giant swing backward on the horizontal bar. In In L. Tsarouchas, J. Terauds, 8. A. Gowitzke, & L. E. Holt (Eds.) Biomechanics XIB. International Series on Biomechanics, Amsterdam: Free University Press, pp. 338-345 . Winter, D.A. (2005) Biomechanics and motor control ofhuman movement, Third Edition, Wiley Science , Hoboken , New Jersey. Yeadon , M.R. (1990) The simulation of aerial movement. Part II: A mathematical inertia model of the human body. Journal of Biomechanics, 23, 67-74 . Yeadon , M.R., and Hiley, MJ. (2000) The mechanics of the backward giant circle on the high bar. Human Movement Science, 19, 153-173. Hiley, MJ . and Yeadon , M.R. (2005) The margin for error when releasing the asymmetric bars for dismounts. Journal of Applied Biomechanics, 21, 223-235 .

Musculoskeletal Work in the Longswing on High Bar Gareth Irwin and David G Kerwin UWIC, Cardiff School of Sport, Cardiff, Wales, [email protected], dkerwimgmwic.ac.uk

Abstract. The aims of this study were to determine the contributions of the gymnast's musculoskeletal system during the execution of a general longswing on high bar and to evaluate the overall interaction between the gymnast and the elastic bar. Images of four international gymnasts were recorded (50Hz) performing three series of four longswings on a strain gauged high bar (1000Hz). Real world coordinates were reconstructed using 20 OLT and synchronized with the force data. Inverse dynamic analyses were employed to determinejoint kinetics during each longswing. Analyses were performed on the whole longswing and on the hip and shoulder ' functional phases' defined as maximum extension to flexion at the hips and maximum flexion to extension at the shoulders respectively. The muscle moments and powers at the shoulders were consistently found to be dominant, with maximum values at the shoulders being 4.5 ± 1.70 Nm-kg' & 14.4 ± 6.7 W.kg- I and 2.3 ± 0.5 Nmkg' & 6.0 ± 1.7 W.kg-I for the hips. In all cases the peak values within the muscle moment profiles occurred within the functional phases highlighting the importance of these active phases to the overall skill. The corresponding muscular work profiles highlighted that an average of 71% ± 6% of the total work occurred during the functional phases of the longswing. Quantification of bar strain energy, based on bar deformation, enabled an energy deficit to be determined. This deficit arose from frictional losses at the hand bar interface, air resistance and bar hysteresis and hence defined the minimum work that the gymnast needed to contribute to complete the circle successfully. These analyses highlighted the dominance of the contribution made by the gymnast between 2000 and 2400 of rotation, during a successfullongswing.

1 Introduction Longswings on the high bar fall into two categories the 'general' and the ' accelerated' . The general longswing is learned before the accelerated and is used to link other skills . The accelerated longswing precedes complex release and re-grasp skills and dismounts. Over the last two decades the majority of high bar related research in sports biomechanics and engineering has focused on the accelerated longswing. Since 1990 this has been dominated by two research groups, in Loughborough (Yeadon and Hiley 2000 ; Hiley and Yeadon 2003) using a forward dynamics approach to investigate optimizing the longswing and in Cologne (Arampatzis and Briiggemann 1998; 1999) using an energetic approach to explain the interaction between the gymnast and the elastic bar during the longswing. These groups provided kinematic and kinetic descriptions of the hip and shoulder joints during the

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accelerated longswing and identified the characteristics of optimum technique (Yeadon et al. 2000). Okamoto, Sakurai, Ikegami, and Yabe (1987) described the kinematic and kinetic profiles of the hip and shoulder joints through an inverse dynamics approach of the general longswing but there has been little recent research into the general longswing, particularly considering the number of changes in the rules, the apparatus and the skill levels of gymnasts (FIG 200I). The early work on the general (Okamoto et al. 1987) and the later work on the accelerated longswing (Yeadon et al. 2000; Arampatzis et al. 1998; 1999) established the importance of the hips and shoulders, particularly as the gymnast passes under the bar. This phase of the skill is characterized by a rapid hyper extension to flexion of the hips and hyper flexion to extension of the shoulders. Quantifying the specific musculoskeletal demands on current performers during the general longswing would provide useful information for the development of this skill and may subsequently inform the development accelerated longswing. Therefore, the aims of this study were to determine the contributions of the musculoskeletal system during the performance of the general longswing and explain the overall interaction between the gymnast and the elastic bar.

2 Method 2.1 Data Collection Four members of the Men's UK National Gymnastics Squad participated in this study (age = 22.5 ± 4.I yrs, mass = 66.4 ± 7.2 kg, and stature = 1.69 ± 0.05 m). Anthropometric data were collected for use with a geometric inertia model (Yeadon 1990) to obtain subject specific body segment inertia parameters. All testing was performed in a gymnastic arena on a standard competition high bar (Continental Sports, Huddersfield, UK). Each gymnast performed three series of four general longswings. Images in the sagittal plane were recorded using a digital camcorder (Sony DSR-PDI IOOAP, 3-CCD, Japan) placed approximately 40m from the centre of the activity at a height of 5 m with its optical axis at 80° to the plane of motion. This provided a clear image of the functional phases of the longswing and particularly limited the obstruction of the support upright of the high bar as the gymnast passed the lower vertical. The camera was operated at 50 fields per second with the electronic shutter set to I1300 s. Calibration of the performance area was achieved by placing a single calibration pole of height of 5.I76 m, containing four O.10m spherical markers, at three pre-marked locations to form a vertical plane of approximately 5 m x 5 m. Reaction forces on the bar were recorded (1000 Hz) using strain gauges bonded in pairs to the bar's surface. Calibration was performed by loading and unloading the bar with known loads and recording the average voltages for each loading condition. Vertical and horizontal bar stiffness (K, and Ky ) were used in combination with linear regression equations to predict vertical (Fz) and horizontal (Fy) bar forces (Kerwin and Irwin 2006). Synchronization of the force and video data

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was achieved through the use of 20 LEDs (Wee Beasty Electronics, Loughborough, Leicestershire, UK) in the field of view of the camera which were sequentially illuminated at lms intervals . The force data capture and the LEDs were triggered simultaneously, enabling the force and video data to be matched to within 3 ms.

2.2 Data Processing The images of the calibration object and the gymnast were digitized using the high resolution TARGET motion analysis system (Kerwin 1995). Camera calibration was achieved using an 8 parameter direct linear transformation (D LT) algorithm (Kwon 1999). In each field the centre of the bar, the centre of the gymnast's head and his right wrist, elbow, shoulder, hip, knee, ankle, and toe were digitized. Based on Winter's (1990) residual analysis, a digital low pass filter (6 Hz) was used to remove random error from the reconstructed co-ordinates. Joint kinetics were determined through the application of Newton 's 2nd law of motion. The human performer was modelled as a pin-jointed four link system comprising arms, trunk, thighs and shanks. In order to minimize the propagation of errors, the closest known forces were used to calculate the internal joint forces. As such a combined approach of 'bar down' to calculate the shoulder and hip forces and a 'toe up' to calculate the knee and hip forces was used. The average of the two estimated hip forces was used throughout the subsequent analyses . Muscle power (MP) was calculated as the product of the muscle moments (MM) and angular velocity (0)) providing a measure of the rate of work done. The mechanical work was calculated from the time integral of the MP profiles for each joint and enabled the type of muscle action at each joint to be specified. Muscle moments, powers and work done at the shoulders and hips were calculated for each long swing . The total biomechanical energetic processes of the gymnast performing the long swing were calculated using the relationship shown in (Eq. 1). Equation 1 incorporates three major components including bar energy (Eq. 2), gymnast energy (Eq. 3) and by subtracting the combined bar and gymnast energy, a value of net energy was calculated. For the gymnast in the handstand position on top of the bar, the angle between his mass centre (CM) and the bar was set at 0°. To compare within and between trials all data sets were interpolated in 1° intervals from 0° to 360° using a cubic 'Ispline' function, (Mathcad 2001i, MathSoft Engineering, Inc. Surrey , UK) . I 2 I E total = -1 CO + mgh + - m v

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Gareth Irwin and David G Kewin

3 Results and Discussion During the initial 90° of the descent, minimal muscular activity at any joint was found, which corresponds to the findings of Okamoto et al. (1987). From 90°, an extension-to-flexion moment at the hip joint precedes the ascending phase, which is also reflected in the muscle power (Fig. 1.) This pattern concurs with Arampatzis et al. (1998) although the magnitudes of their values are higher due to the fact they investigated the accelerated longswing. In all cases the shoulders played a dominate role particularly in the ascending phase. The peak hip moment was 48% of the peak shoulder moment whilst the dominance of the shoulders was further emphasized with the hips generating40% of the peak muscular power at the shoulders (Fig. I.). 5 .,

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Fig. 1. Average Muscle Moment (MM) and Power (MP) at the hip(h)and shoulder (s)during the general longswing on high bar. The large extension (positive) moment at the shoulders (4.5 ± 1.7 Nm -kg") and corresponding large positive powers demonstrate a concentric contraction around the joint. Similar joint kinetics were reported by Arampatzis et al. (1998), but compared to the study by Okamoto et al. (1987) the current study reports values 42% higher which may reflect differences in modem technique and equipment. The majority of work done by the performer occurred in the ascending phase with peak values of 0.81 ± 0.10 Lkg" and 1.56 ± 0.76 ].kg'l at the hips and shoulders respectively. The total energy of the bar-gymnast system is illustrated in Fig. 2.a. The maximum energy is achieved at approximately 160° with a value of 19 ± 4.1 Lkg which is comparable in magnitude to that reported by Arampatzis et al. (1999). The difference in the total energy at the start (0°) and end (360°) of the longswing provides an indication of the success of the skill. Based on the conservation of mechanical energy the difference must be equal to or greater than zero in order for the performer to return to the handstand position.

Musculoskeletal Work in theLongswing on High Bar 23

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Fig.2. (a)Average Total Energy andNetEnergy (Enet) of the gymnast-bar system. (b)Averageenergy contributed by the gymnast's (Egymnast) musculoskeletal system. Incorporated into the total energy profile (Fig. 2.a) is the strain energy at the bar, the gymnast's musculoskeletal energy (Fig. 2.b) and the net energy that the swinging gymnast possesses due to previous motion about the bar (Enel) . The findings of this study show that 70% of the work contributed by the gymnast occurs relatively late in the ascending phase.

4 Conclusions This study has shown the gymnast's physical input into the longswing is a fundamental component of successful performance. The joint kinetics playa vital role in understanding these variables and provides technical information relating to the muscle actions and hence the physical demands placed on the gymnast. The gymnast's energy is required to compensate for friction at the bar hand interface, air resistance and losses of energy due to the bar not being perfectly elastic. In addition, minor changes in timing of hip and shoulder actions, as explained by Hiley et al. (2000), can remove energy from the system. The key active phase for the general longswing for the shoulder and hip joints occurs consistently between 200 0 and 240 0 of rotation about the bar.

References Ararnpatzis, A., andBruggernann, G.P. (1999) Mechanical energetic processes during the giant swing exercise before dismounts and flight elements onthehigh barandtheuneven parallel bars. Journal of Biomechanics. 32, 811-820. Arampatzis, A., and Bruggemann, G.P. (1998) A mathematical high bar-human body model foranalysing andinterpreting mechanical- energetic processes onthehigh bar. Journal of Biomechanics. 31,1083-1092. Federation International de Gymnastique (FIG) (2001) Code ofPoints, artistic gymnastics/or men. Switzerland. Hiley, MJ ., andYeadon, M.R. (2003) The margin forerrorwhen releasing thehigh barfor dismounts. Journal of Biomechanics. 36, 313-319.

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Kerwin , D.G. (1995) Apex/Target high-resolution video digitising system . In 1. Watkins (Eds.) Proceedings of the Sports Biomechanics section of the British Association of Sports and Exercise Sciences. Leeds, UK. pp. 1-4. Kerwin, D.G., and Irwin, G. (2006) Predicting high bar forces in the longswing. 6th International Sports Engineering Association Conference, Munich , Germany . Kwon, Y.H. (1999) 20 Object plane deformation due to refraction in two-dimensional underwater motion analysis. Journal of Applied Biomechanics. 15,396-403 . Okamoto, A., Sakurai, S., Ikegami , Y., and Yabc, K. (1987) The changes in mechanical energy during the giant swing backward on the horizontal bar. In In L. Tsarouchas, 1. Terauds , B. A. Gowitzke, & L. E. Holt (Eds .) Biomechanics XIB, International Series on Biomechanics. Amsterdam : Free University Press, pp. 338-345 . Readhead, L. (1997) Men 's Gymnastics Coaching Manual . Huddersfield, UK. Yeadon, M.R. (1990) The simulation of aerial movement. Part II: A mathematical inertia model of the human body. Journal of Biomechanics. 23, 67-74 . Yeadon, M.R., and Hiley, M.J. (2000) The mechanics of the backward giant circle on the high bar. Human Movement Science . 19, 153-173.

6 Lawn Sports

Synopsis of Current Developments: Lawn Sports Matt Carre Sports Engineering Research Group, University of Sheffield, [email protected]

The topic of lawn sports could arguably include any sport that is played on natural or synthetic turf, including those as diverse as lawn bowls, tennis and American football. The sports that are included in this section are related to only three : cricket, field hockey and rugby football, as the subject of soccer has generated enough papers to warrant its own section . However, the research areas covered in this section demonstrate the wide variety of expertise applied in the field of sports engineering, including soil mechanics, impact modelling and optimisation, amongst others. The one factor that all lawn sports have in common, of course, is the lawn (or . turf) itself. Four papers in the following section concentrate on improving the understanding of the performance of turf surfaces. The paper by McLeod et al. examines a new method for quantifying the amount of wear in synthetic turf surfaces . In recent years, synthetic surfaces have seen increased use, due to advances in technology as well as changing lifestyles . Great effort is concentrated on designing the complex systems that make up these surfaces, as well as applying the experience required to install a quality product. However, less is known about how different designs of surface degrade over time, both through repeated use and exposure to the elements . A better understanding of these issues will undoubtedly be improved by a measurement technique such as the one proposed here. Young and Fleming also discuss measurements of synthetic turf, in this case, the type designed specifically for world-class field hockey, water-based pitches . Their paper contains an in-depth critique of the test devices used to predict playing performance of such a surface, including player and ball interactions and conclude with some sound recommendations for future study . The behaviour of natural turf, is equally as complex as a layered, synthetic system, but requires a different kind of expertise . In the case of a cricket pitch, the playing surface is designed mainly for interaction with the ball, providing a hard, consolidated surface which would appear alien to players from most other sports that use turf. However, the performance of the pitch has huge implications for the way a game of cricket is played . The paper by Shipton et at. examines how the mechanical behaviour of soil changes through repeated rolling; one of the key elements in pitch preparation. This fundamental research is vital to lead to a better understanding of cricket pitch performance. James et at. also examine cricket pitch performance, but their study is related directly to the interaction between ball and surface . Their paper describes a model of oblique impact that can be used in conjunction with two relatively simple tests, to

204 Matt Carre predict how a cricket ball rebounds off the surface; or in cricketing parlance, 'pace' and 'bounce' . It is hoped that this knowledge and technology can be used to aid groundsmen in their preparation of quality pitches. The remaining three papers are less concerned with what happens at the surface, but rather what happens to the ball during play . Still on the theme of cricket, Justham et al. discuss the quantification of a bowling delivery, one of the key factors in the game . Using data collected during the thrilling Ashes series in 2005 , fought between England and Australia, they examine key aspects of professional deliveries and use this information to aid the design and manufacture of a bowling machine. Rugby football is the subject of the paper by Holmes et aI., which again uses measurements taken from professional sportsmen, but in this case a range of kicks and passes are studied, which are all important in an actual game situation. This . study results in the generation of an extensive data set of flight characteristics, immediately after ball launch (velocity, spin and angle) which will serve as being very useful for future studies of ball aerodynamics, ball-boot interaction and ball handling . Seo et al. examine the flight of a rugby ball after being kicked, for three different kicking scenarios. They use multi-optimisation techniques to predict the best conditions to be adopted in each kick, to obtain the desired results . This kind of research has great implications for providing strategies that can be used by coaches and players alike. In summary, this section demonstrates the wide variety of expertise, knowledge and understanding in different areas of sports engineering. Once applied, this will have a very positive impact on a range of exciting lawn sports .

Quantification of the Cricket Bowling Delivery; a Study of Elite Players to Gauge Variability and Controllability Laura Justharn, Andrew West, Andy Harland, Alex Cork Loughborough University, UK, [email protected]

Abstract. The bowling delivery has been recognized as an important factor in cricket. The batsman faces each delivery and attempts to read the bowler's actions to predict the type of delivery and to avoid making an error in judgment which could cost the game. Numerous studies have been carried out to investigate factors such as the biomechanic and kinematic aspects of the bowling delivery and what information the batsman is able to pick up from the delivery sequence. However the factors which constitute the bowling delivery, the mechanisms adopted to bowl the ball and how a subtle variation in the ball release affects the delivery, have not been studied in such detail. This research is focused on understanding how the bowler is able to control and vary their delivery patterns. Using performance analysis data collected from the second Ashes test held between England and Australia in August 2005 two bowlers have been studied over a six overbowling spell. Information regarding the variability within each overhasbeen analyzed to help quantify the mechanics of the bowling delivery.

1 Introduction The bowler is a key player in any cricket match as they can alter the outcome simply by the way they deliver the ball. The mechanisms involved with creating a bowling delivery have been investigated in terms of kinetic, kinematic, biomechanic, physiological and anthropomorphic factors but not in tenns of what the bowler actually does to create the delivery or how consistently they are able to bowl over a prolonged period (Elliott 1986; Elliott 1993; Bartlett 1996; Glazier 2000; Noakes 2000). Coaching manuals mention a Correct grip, economical run-up, balanced delivery stride at the crease and a fluent follow through but they omit to mention how to construct a delivery from them. (Khan 1989; Ferguson 1992). Generally the bowling delivery is classified by the speed of the ball at release, as shown in Table I, with a recognized range of speeds for each bowling type. Any further generalized classification is avoided due to the unique features of each bowler. A fast paced bowling delivery reaches the batsman in less then half a second, which does not give him long enough to view the ball, work out his shot selection and move in preparation. He must supplement the information available from the ball's flight with information provided by the bowler during the preparatory stages of the delivery. The batsman watches for variations in the length of the run-up, the position and angle of the ann and hand as the ball is released and the grip on the ball

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as each of these have an effect on the delivery characteristics (Abernethy 1984; Penrose 1995; Renshaw 2000). Bowlers will practice to make the difference between their stock delivery and any variations as small and undetectable as possible. It is therefore not simply the speed of the ball or the mechanism of ball release which constitutes the complete bowling delivery. There are a number of other factors to consider which combine to formulate the complete delivery sequence. The purpose of this research is to begin the process of understanding and quantifying the unique and common ball release characteristics of elite cricket bowlers . Bowler Classification Fast Medium Spin

Transit time (ms) 528-396 660-528 988-660

Ball velocity (mph) 75-100 60-75 40-60

Ball velocity (m/s) 33.5-44 .7 26.8-33 .5 17.9-26.8

Table 1. A classification of bowling with respect to the speed of delivery. The transit time is the time taken from ball release to reaching the batsman (I7.7m)

2 Experimental Procedure Player Performance analysis is becoming increasingly important in all sports. The Hawk-Eye ball tracking system is used as a television commentary tool and also as a performance analysis tool. It uses three orthogonal cameras to track the ball from the moment of release to just before it impacts the bat. The speed of the ball and its trajectory is recorded so the position of where the ball bounces and any swing or deviation in the flight path may be calculated. This can show how the bowler's performance changes over a prolonged period and under the pressures associated with a match. Feedback Cricket is a video based analysis tool. From each delivery the area of the pitch where the ball bounces, the shot selected by the batsman, where the ball was hit and any runs scored from the ball are recorded. The Ashes is a biennial series of 5-day test matches taking place between Australia and England. Access has been granted to data collected from the second test match of the series, which was held at the Edgbaston ground in Birmingham, England from Thursday 4 th to Monday 8th August 2005. Data collected from the HawkEye and Feedback cricket systems have been analyzed for two right handed fast bowlers over a six over spell in the first innings of the match to understand the variability and controllability that each player possesses.

3 Results Hawk-Eye is a valuable tool, used here to compare the average delivery characteristics of each bowler for every over in the bowling spell. Figure I shows the average speed of the ball release with respect to the length at which it pitched during the delivery. The speed of the ball at release seems to be well controlled by both bowl-

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ers. Bowler I bowls with a speed range of ±3 mph for every over except over 6 when he bowls one much slower ball. This slower ball is a deliberate variation on the stock delivery and is used in an attempt to wrong-foot the batsman. Bowler 2 is more consistent and bowls with a speed range of ±2 mph except during over 5 when he bowls two slightly quicker balls as a variation to his stock delivery . There is not any noticeable drop off in consistency of the speed of delivery over the course of the bowling spell. Figure 1 shows that bowler 1 tends to bowl slightly more quickly than bowler 2, but most deliveries are clustered around the same speed of 84 mph to 86 mph (37.6 mls to 38.4 mls) for both bowlers .

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Variations to the stock delivery come in many forms and the bowler practices to make every delivery sequence as similar as possible in a bid to prevent the batsman being able to perceive any difference in the delivery until the ball is released. The major variations are in the pitching length and the speed at which the ball is released . Often a quicker ball will be pitched shorter such that it will bounce up towards the batsman more aggressively . Bowler 1 bowls at a consistent speed whilst altering the pitching length of the ball much more frequently, for example in over 3 the speed is consistent to within 2.6 mph (1.16 mls) but the pitching position varies between 4.13 yards to 12.63 yards (3.78 m and 11.55 m). Throughout the bowling spell both bowlers were predominantly bowling to right handed batsmen . Figure 2 shows that they consistently pitched the ball on the off side of the batsman. The variability in pitching length and line are larger due to external effects acting on the ball during flight, for example airflow around the ball. Bowler I varies the pitching length regularly and variations up to 8.5 yards (7.8 m) in the pitching length and 0.6 yards (0.55 m) in the width are seen. For Bowler 2 the pitching length varies by up to 6.6 yards (6.0 m) with the same variation in pitching

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line as Bowler 1. Figure 3 contains images from the Hawk-Eye virtual environment and shows how Bowler 1 and 2 vary in their deliveries . The images show over 3 of the bowling spell, whereby bowler I varies the length of the ball considerably and bowler 2 maintains as much consistency as possible .

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Fig . 3. Images from the Hawk-Eye virtual environment which shows the third over bowled in the spell. Bowler I is on the left and bowler 2 is on the right. Feedback cricket can be used to understand how the bowler creates their delivery and the variations resulting from any alterations. The basic actions of both bowlers are the same. They are right handed with a long run up, a front-on delivery action and a pronounced follow through to dissipate excess momentum . The bowling arm is kept very straight throughout the delivery process and the ball is released close to the apex of the curve of the arm. Bowler 1 tends to vary the release position of the ball from the apex of the curve to just following it which results in the large variations in

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pitching positions. A ball which is released later will pitch shorter than a ball released earlier. Bowler 2 tends to release the ball as close to the apex of the ann curve as possibl e, resulting in the slightly more consistent pitching length. The reaction of the batsman for each bowling deli very and how many runs were scored is also recorded using Feedback Cricket. A shorter bowled del ivery will generall y force the batsman to playoff the back foot and a more fully bowled delivery will allow the batsman to come forward and playoff the front foot. A good length ball is one which cause s the most indecision about whether to play forwards or backwards. Figure 2 shows that both bowlers pitched the ball between 5 yards (4.6 m) and 9 yards (8.2 m) from the batsman's stumps and from the data collected from feedba ck cricket this sho ws that the ball was pitched at a good length to slightl y short of a length .

4 Discussion

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Fig . 4. The novel bowling machine has been designed and developed using information gathered about real bowling spell s to ensure a realistic training environment. Key aspects of both bowlers' deliveries have been con sidered using Hawk-Eye and Feedb ack Cricket. The speed of ball release remains con sistent throughout the bowling spell with variations being observed in an attempt to take a wicket. The position where the ball pitches has greater variation due to factor s outside of the bowler's control such as the motion of the ball through the air betw een being released and impacting the pitch . The bowler tries to wrong foot the batsman and force them to make errors with every delivery. However the Hawk -Eye anal ysis has shown that the bowler doe s not appear to aim for the batsman's stumps, rather for the batsman them selves, which entices them to attempt to play each delivery . Even on a small scale it is very difficult to quantitatively analyze bowling deli veries. Each bowler subtlety varies each deli very and therefore unkno wn factors are con tinually at play throughout any match . The bowler considers the sco re line, the

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batsman who is facing him, the positioning of the fielders , the time of the day , how many overs he has already bowled or is likely to still need to bowl"and many other critical aspects unique to the individual match . Th is initial study has shown that modem bowlers, who have a similar playing history and coach ing input, will maintain common playing techn iques but will develop personal method s to vary the delivery, decei ve the batsm an into misjudging their movement s and take wickets. Modem players must be successful tacticians to reach international standard. Further work must be carried out looking more in depth at specific aspects of the bowler' s delivery under more controlled conditions before further conclusions may be drawn . Knowledge and under standing about the deli very of elite level cricket bowlers has aided the manufacture of a bowling mach ine system at Loughborough University which is able to recreate realistic delivery patterns as shown in Fig. 4. Existing bowling machines may simulate bowling deliveries but they do not have the integrity of the additional background knowledge from the studies undertaken to understand the bowling delivery. This analy sis has enabled a better understanding of the ranges of capabilities required in the novel bowling system as well as the variations which would generally be observed throughout an individual over or bowling spell.

Acknowledgements The authors would like to ackno wledge the financial support of the Engineering and Physical Scien ces Research Coun cil of Great Britain (EPSRC) and the IMCRC at Loughborough University. The y would also like to thank the players and coaches at the ECB- NCC at Loughborough University.

References Abernethy, B., Russell , D.G. (198 4) . "Adva nce cue utili sation by skilled cricket batsmen ." Australian Journal of Science and Medicine in Sport 16(2): 2- 10. Bartl ett, R. M., Stockill, N.P., Elliott, B.C., Burnett, A.F. (1996). "Th e biomechanics of fast bowlin g in men' s cricket: a review ." Journal o f Sports Science s 14(5 ): 403 -424. Elliott, B., Baker, 1., Foster, D. ( 1993) . "The kinematics and kinetic s of the off-drive and ondrive in cricket." Austr alian Journ al of Science and Medi cine in Sport 25(2): 48-54 . Elliott, B. C, Foster, D.H., Gray, S. (19 86) . "Biomechan ical and phy sical factors influencing fast bowling." Australian Journal of Sc ience and Medicine in Sport 18( I) : 16-21 . Fergu son, D. (1992). Cricket: Technique. Tactics. Training, The Crowood Pres s Ltd. Glazier, P. S., Paradisis, G.P., Coo per, S-M . (2000). "Anthropometric and kinematic influences on rele ase speed in men' s fast-medium bowling." Journal of Sports Scienc es 18( 12): 1013- 1021. Khan, K. ( 1989). lmran Khan's cricket skills, Th e Haml yn Publ ishin g Group. Noakes, T. D., Durandt 1.1. (2000). "Physiologic al requ irem ents of cricket. " Journal of Sports Sciences 18( 12): 9 19-929. Penr ose, J. M. T., Roach , N.K. ( 1995). "Deci sion mak ing and adva nced cue util isation by cricket batsmen." Journal of Hum an Movem ent Studies 29(5): 199-218. Renshaw , 1., Fairweather, M.M . (2000). "Cric ket bow ling deli veries and the discrim ination abi lity of pro fessional and ama teur batters." Journal of Sp orts Sc iences 18( 12): 951-957.

Ball Launch Characteristics for Elite Rugby Union Players Christopher Holmes , Roy Jone s, Andy Harland and Jon Petzing Loughborough University, c.e.holmes @lboro.ac.uk

Abstract. The role played by a team ' s kicker in determining the outcome of a rugby union match is becoming increasingl y important. However , unlike in other sports, there is no existing data regarding the kicking and passing abilities of elite rugby players . The objecti ve of this study was to determine the launch characteristics of a place kick, drop kick, spiral kick (kick to touch) and spin pass. Testing was carried out at senior English League rugby union clubs, and data from 14 elite kickers were evaluated including current international players . The subjects were asked to perform the different kicks on a specially marked rugby ball at a distance of 60 m from the posts. Each skill was performed until they had achieved five 'good' strikes or passes . A high speed camera (NAC 500), operating at 500 frames per second was used to record the ball velocity , spin and launch angle . The data presented shows that players are able to achieve velocitie s of 38.1 m!s whilst imparting 405 rpm to a rugby ball (drop kick). The maximum spin rates seen in the other types of kick are considerably lower. The study of the spin pass has shown that whilst players impart considerably lower levels of velocit y to the ball (18.3 m!s), they are capable of achieving spin rates similar to those seen for a place and spiral kick.

1 Introduction The specification for a 'match ball' (rugby) is defined by the governing body, the International Rugby Board (lRB). The ovoid ball specification falls into three main categories, the dimensions of the ball, weight of the ball and pressure of the ball at the start of play . The parameters defined are all static values, and dynamic ball performance is not measured. This is similar to the majority of other ball sports, however the balls behaviour during play is of importance and other governing bodies are introducing dynamic performance criteria . In order to develop dynamic ball assessment procedures it is necessary to appreciate the capabilities of elite players. This data can then be used to define the parameters for the dynamic ball tests. The aim of this study was to obtain the ball launch characteristics of a spin pass and three different types of kick, using professional players from senior English League rugby union clubs. The three kick types selected are the place kick, drop kick and spiral kick . There is currently no literature detailing the initial launch characteristics of a rugby ball during various types of kicks or passes . Macmillian (1975) used three

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skilled footballers to perform three different types of kicks seen in Australian Rules football. The drop punt and drop kick are similar to the spiral and drop kick investigated during this study. A high speed camera operating at 400 frames per second with a shutter speed of 1/1200s was used during the testing. Ball velocities of 24.9 and 27.2m1s were stated for the drop kick and punt respectively. Hartschuh (2002) studied the ball launch characteristics during an American football punt. 13 punts were filmed using a 30 frames per second video camera. A ball velocity of 24.5±0.6m1s and an angle of 49.4±1.5° were stated. A number of studies have examined ball velocities achieved during the kicking of a soccer ball. Neilson (2003) carried out a comprehensive study of 25 professional players, at five senior English football clubs. A high speed camera operating at 500 frames per second with a shutter speed set to 1I1000s captured the initial trajectory of the ball after impact. A maximum-recorded velocity of 33.1mls was stated for a full power kick, with a maximum ball spin of 833rpm achieved during an instep and outstep swerve kick. The velocities stated by Neilson (2003) were similar to the maximum measured during a study by Asami and Notle (1983), 34.0 mls. Ofsignificance is that the majority of studies do not include spin data. The study aims to obtain comprehensive launch data which can be used for further scientific study.

2 Method Player testing was carried out at six professional English rugby clubs, with data from 14 players analysed and presented. All players were established kickers and had international representative honours, including four full internationals. The clubs consisted of five English Premiership clubs and a national division one club. The testing procedure was carried out on natural turf training pitch environments. Seven unbranded ' match balls' were used, to help negate any player brand bias that may exist. The unbranded balls were marked with a series of constant and dashed lines to enable the accurate determination of spin during the digitising process, "Fig I". The subjects were requested to perform three different types of kick at full power, enabling maximum velocity to be achieved, at a distance 60m from a set of posts. The first kick was a place kick, the second a drop kick and the third a spiral kick. The subjects were asked to perform each skill until they had achieved five 'good' strikes or passes. The test players all wore their own boots and supplied kicking tees. Only one player analysed during the study kicked with their left foot. The player details are shown in "Table 1". Table l. Mean (±SD) test subject data (n=14 )

Age (years) Body mass (kg) Body height (m) Boot size

25± 3.74 88.06 ± 5.72 1.78 ± 0.03 9.71 ± 1.14

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The test procedure was approved by the University Ethics Committee and players were informed of the test procedure and their rights prior to testing. The initial movement of the ball after impact or throw was captured using a highspeed camera (NAC 500) operating at 500 frames per second with a shutter speed of 1/IOOOs. A composite high-speed video image can be seen in "Fig I" . The highspeed camera footage was digitised using Image Pro Plus software, and the ball velocity and launch angle numerically calculated. The software allows the displacement of the centre of the ball to be calculated, over a given time interval.

Fig 1. Composite image of place kick

The uncertainty of the measurement, Q TOTAL, can be defined using Eq I. The uncertainty of the device, Q DEVICE, is assumed to be very small by comparison to other uncertainty that exists within the measurement procedure. The uncertainty of the setup, Q SETUP, is attributed to the ball flight not being perpendicular to the camera placement. Q SETUP, is difficult to measure and was controlled by accurate alignment of the cameras position, and requesting players to strike the ball along a given trajectory. Uncertainty of the analysis, Q ANALYSIS, can be described as a measure of repeatability. The repeatability of the analysis was calculated and defined for velocity as ±1.33m!s (95% confidence) and for launch angle ±O.29° (95% confidence). Q TOTAL = Q SETUP + Q

DEVICE

+ Q ANALYSIS

(I)

Eqs I. Uncertainty of the measurement procedure

The measurement of spin has been analysed by evaluating the number of frames required for a quarter rotation of the ball. The spin defined for the place and drop kick is tumble axis backspin, whilst rifle spin is the main component of a spiral kick and spin pass. The distance to the first bounce of each of the kicks is measured using the Bushnell Yardage Pro 1000 laser range finder to an accuracy of ± Im.

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3 Results and Discussion The test results are summarised in table 2 and shown in graphical form in "Figs 2-4". Table 2. Mean (±SD) test results for all kicking and passing data Kick / Pass

Velocity (m/s)

Ball Spin (rpm)

Launch Angle (0)

Distance (m)

Place

26.44 ± 2.97 25.60 ± 3.77 28.06 ± 3.70 13.79 ± 1.48

238.10 ± 44.92 234.25 ± 66.57 216.41 ±46.11 219.09 ±32.98

30.22 ± 4.41 35.76 ± 4.28 43.91 ± 4.55 12.19 ±5.26

53.74 ± 5.72 51.30 ± 5.70 55.42 ± 7.22

Drop Spiral Spin Pass

The average ball velocities achieved during the different types of kicks were similar. A maximum recorded velocity of 38.1m/s was achieved during a drop kick. Macmillan (1975) stated a mean velocity of 27.2m/s (89.2 ftls) during an Australian rules drop kick. This lower value could be due to the differences between the types of balls investigated, and an increase in player development. The maximum recorded velocity for the spiral and place kick were similar, 33.6 and 33.5 m/s respectively. The maximum velocities recorded were 5m/s higher than the full power soccer kick recorded by Neilson (2003). The differences between these values could be due to the differences between balls being kicked and the greater mass of the rugby players. The average velocity value for the spin pass was considerably lower than the kicking actions, but the low standard deviation illustrates the repeatability of the simple action. A maximum velocity of 18.3 m/s was recorded for the pass.

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Ball Launch Characteristics for Elite Rugby Union Players

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The average ball spin produced during a spiral kick was lower than that of a drop or place kick. This maybe attributed to the fact that the spiral kick had a higher velocity. During the natural kicking motion of a drop or place kick, tumble axis spin is imparted onto the ball as it is struck below centre. Large amounts of rifle spin could be imparted onto a spiral kick, but this would cause the player to kick across the ball, reducing the velocity and overall distance . The maximum spin value of 405rpm was recorded during a drop kick. The average rifle spin imparted onto a ball during a pass is larger than that of a spiral kick. The maximum ball spin for a spiral kick and spin pass were 341 and 288rpm respectively.

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The lowest angle recorded was for the place kick. During a drop and spiral kick the ball is dropped before contact with the foot, which may account for this increase .

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The increase in launch angle between a spiral and drop kick was noted by Macmillan (1975) whose results state that the launch angle of a spiral kick was 7° greater than that of a drop kick. The maximum distance achieved during any kicking action was 71m (spiral kick) . During the investigation players found the spiral kick the most difficult kicking motion to replicate, which accounts for the increased standard deviation. The maximum distances for the place and drop kick were 63 and 60m respectively.

4 Conclusion The present study provides the first comprehensive data for launch characteristics of elite rugby players . The mean initial velocity for the three types of kicks ranges between 25.60 and 28.06 mis, depending upon kick type . The mean velocity for the spin pass was significantly lower at 13.79 mls. Maximum velocities of 38.05 and 18.30 mls were recorded for a kicking action (drop kick) and spin pass respectively. The maximum spin rate obtained by a professional player in this study was 405 rpm (drop goal), which was considerably higher than data recorded for the pass (288 rpm) . The launch angle increased during a drop goal to 43.91± 4.55°, in comparison to the other kicking actions, which compares to results stated by Macmillian (1975) . The most difficult skill to replicate during the testing procedure was the spiral kick . This accounts for the higher standard deviation when examining the distance measurement. The maximum distance measured was 71m (spiral kick) to the first bounce. The data from this study can be used to define the parameters of any dynamic tests that are to be developed in the future. The study used elite players , which ensures that the values obtained are close to the maximum achievable.

Acknowledgements The authors would like to thank the rugby clubs, and players who agreed to participate in this study, and would also like to thank adidas for supplying the balls . Thanks also to the EPSRC Advance Instrument Pool for the use of the high speed camera

References Asami, T and Nolte, V (1983) . "An alysis of Powerful Ball Kicking". Biomechanics VIII-B,675-700 Hartschuh, R. (2002) . "Physics of Punting a Football." http r//www. wooster.edu/physics/JrIS/Files /Ryan .pdf (Accessed - 07/07/05) Macmillian, M. (1975) . "Determinants of the Flight of the Kicked Football." Research Quartley 46 : 48. Neilson, P.N. (2003) . "Dynamic Soccer Ball Performance Measurement." 5th World Congress ofScience and Football (Lisbon, Portugal, 11-15 April)

A Novel Quantitative Method for the Determination of Wear in an Installed Synthetic Turf System Andy McLeod, lain James, Kim Blackburn and Gavin Wood Cranfield University, UK, a.j.mcleod.sO [email protected]

Abstract. This study focuses on the initial development of an image analysis methodology for quantifying the wear and degradation of synthetic sports turf, post installation, where the carpe t/in fill system is subjected to systemic abrasion and wear from play and maintenance. The pilot study images the surface of polypropylene fibres, which have been agitated with differing sand infill types, with a scanning electron microscope. The resultant image s were analysed to determine the degradation of the extrusion features evident in virgin fibre, and it was found that there was significant, quantifiable wear of the turf fibres after seven days with all test sands . The image data for fibres between 7 and 28 days was dependent upon sand type . Further development of the technique is required for determining the next stage of wear - characterized by pitting of the fibre surface by the sand .

1 Introduction The use of a quantitative model of fibre wear within a synthetic sports turf system will enable identification of the main cause s of wear and, by a change of material s and management techn iques , will allow sign ificant advance s in the financial sustainability of synthetic turf surfaces. At present, within the sports industry, the measurement of the resistance to wear of synthetic turf sports surfaces is carried out pre-in stallation. Normal testing of the integrity of the carpet system is carried out by measuring the tensile properties of individual fibres, the effect of ultra violet light and aging . Further fibre is subjected to simulated wear by metal blades , abrasive wheels and the reproduced action of football studs (FIF A, 2005 ; BS7044, 1990). These methodologies were designed for testing the compliance of a product with the relevant specifications for installation and performance; such approaches to testing do not characterize the wear mechanism of the whole system of polymer carpet fibres and infill materials in the field environment The usual method for wear quantification is by mass loss measurements, which is suitable when the worn material components are detached from the main sample. Due to the low mass of the worn turf fibre components there is a loss of resolution when weighing, even on a high precision balance, which makes this method less effect ive for use with synthetic sports turf. In addition, this method provides no information on the distribution of wear over the component and will not show the level of wear in areas of fibre structural failure (Gahlin & Jacobsen, 1998).

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This paper will show the results of a pilot study for a field assessment method, in development, which aims to objectively quantify the ' degree of wear ' of fibre samples and identify the processes causing the wear of the fibre, using surface image analysis techn iques. The aim of this experiment was to quantify the effect of sand infill abrasion on the fibres of an artificial turf surface .

2 Materials and Methods 2.1 Test Materials The fibres used were from a stock roll of 4 mm wide, extruded monofilament polypropylene used in the manufacture of synthetic sportsturf. Fibre s were cut by scalpel to a length of 23 mm. The infill materials comprised two rounded sands commonly used in sand filled (2nd generation) synthetic turf surfaces in the UK, with the trade names 'No 21' and '2EW' ; in addition a sharp sand was used as a contrast.

2.2 Test Method 50 g of each sand was placed with three of the 23 mm long fibres specimens into a 250 ml polypropylene screw capped bottle . The bottles were placed on an over-andunder shaker and rotated through their long axis at 28 rpm. Treatment periods were 7, 14, 21 and 28 days, with an untreated control. Each treatment combination of sand and period was replicated five times . On removal from the shaker the fibre samples were washed gently with distilled water to remove sand particles and allowed to air dry .

2.2 Fibre imaging technique Initial investigations of images recorded with high power optical microscopy, using transmitted and reflected light, determined that such techniques were not appropriate for quantification of the degree of wear. Subsequently, the fibres were imaged using an FEI XL30 SFEG scanning electron microscope (SEM) to investigate the pattern of abrasion and how this contributed to surface deformation and ultimately plastic and brittle failure of the turf fibres. Before the fibres were viewed using the SEM they were sputter coated with a gold/palladium (80/20) mix, to increase the conductivity of the sample . The SEM method ensured consistent resolution, magnification (x200) and luminous flux density among the replicates of each treatment. Images were captured from each replicate. Output images were 256 grey scale , 712 x 484 pixel in tagged image file format.

A Novel Quantitative Method for the Determination of Wear

219

Fi g. 1. SEM images of the control and after 7 and 28 days of continuous agitation with the 2EW sand 10000

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2.3 Image analysis Initial visual inspection of the images determined that the linear patterns on the virgin fibre, resulting from the extrusion process were degraded into random pattern orientations with increased wear period (Fig.l). In extremis this resulted in punctured fibres with point defects that were related to fibrillation in SEM images of field samples of synthetic turf of 5 years age.

220

McLeod et al.

To determine objectively whether this pattern of degradation was related to sand type and wear period, a filtering process was used to quantify 'linearity' in each image using the Leica Erdas Imagine v8.7 image analysis software. The filter comprised two 7 x 7 matrices that measured horizontal and vertical continuity in each image. The resultant of each component was determined as an angle, and a frequency distribution of pixels within 2° classes, between 0 and 90° determined. Images with a high linearity were characterized by a distinct peak at an angle between 2 and 4° (the specific angle is an artefact of fibre alignment on the SEM, it is the peak that is significant, see Fig. 2). Images with less linearity were characterized by a more uniform distribution of pixels between 0 and 90° (see Fig. 2). To quantify this characterization, the ratio of the maximum frequency to the total number of pixels within the distribution was determined, referred to as the peak ratio (PR). It was hypothesized that PR would decrease with increasingwear period.

3 Results Table I. Mean peak ratio of linearity in SEM images of synthetic turf fibres subjected to wear by three sands for four wear periods

7

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For all treatments, PR reduced significantly after 7 days of wear, compared to the control (p
A Novel Quantitative Method for the Determination of Wear

221

an anomalously low PR value at day 7 and no significant difference between days 14 - 28 (Fig. 3). The sharp sand followed a similar pattern to the 2EW except for an outlier at 21 days.

4 Discussion The results of this trial illustrate the potential of the SEM image analysis methodology for the quantification of wear of synthetic turf in field samples of different ages . A clear effect of abrasion by sand infill material has been shown and quantified. For application in field samples, however, more development is required. In this experiment the effect of abrasion on this PR index of 'linearity' was immediate. The PR value measured the abrasion of the linear extrusion features on the fibre surface, it did not reflect the severe 'pitting' of the surface at 28 days, which is not linear and more irregular - further image processing techniques are being investigated to identify these features as they are believed to be critical in creating point defects in the fibre. Further work will also include a quantification of wear and an investigation of wear mechanisms in the field for fibre collected from field sites of different usage and maintenance. The final objective is to characterize and quantify the effect of maintenance equipment on turf fibre and surface performance.

5 Conclusion A directional filter image processing technique was successfully applied to scanning electron microscope image of synthetic turf fibres following increasing periods of wear with different sands used in the infill of sand filled synthetic turf surfaces. Significant wear of the turf fibres was identified after seven days with all three sands . Over a 7 to 28 day period, further wear was identified with the 2EW and sharp sands; this effect was not observed with the No 21 sand . Further development of the technique is required for determining the next stage of wear - characterized by pitting of the fibre surface by the sand .

Acknowledgements The authors gratefully acknowledge that this research was funded by the Engineering and Physical Sciences Research Council of the UK and the Institute of Groundsmanship.

References Adachi, K., Hutchings, I.M. (2005) Sensitivityof wear rates in the micro-scaleabrasion test to test conditionsand material hardness. Wear. 258, 318-321 BS7044 (1990). BS 7044-2.3:1990: Artificial sports surfaces methods of test: methods for detcnnination of durability. British Standards Institution, London, UK FIFA (2005) FIFA Quality concept: Handbook of test methods and requirements for artificial football turf. FIFA Marketing& TV AG, Switzerland.

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Gahlin, R. & Jacobsen, S. (1998) A novel method to map and quantify wear on a micro-scale. VVear. 222, 93-102 Hertzberg, R.VV. (1983) Deformation and Fracture Mechanics ofEnginee ring Materials. John Wiley & Sons, New York, 826 pp

Multi-optimization of Three Kicks in Rugby Kazuya Seal , Osamu Kobayashi and Masahide Murakami) I

2

3

Yamagata University, [email protected] Tokai University University of Tsukuba

Abstract. What are the features of theoptimal kicks in rugby? What is the bestway to achieve satisfactory kicks? The objective of this paper is to provide the answers to these questions by optimizingthe initial velocity and angular velocity vectors for three kinds of kick - the punted kick, the kick into touch andthekick for goal.

1 Introduction There are three kinds of kick in rugby, the punted kick (the ball not spinning), the kick into touch (the ball spinning on its longitudinal axis) and the kick for goal (spinning on its transverse axis). We have measured the aerodynamic forces for each of these cases (Seo, Kobayashi, Gotsu and Murakami 2003) (Seo, Sakamoto, Kobayashi and Murakami 2005), and the results can be summarized as follows. In the case of the non-spinning ball, the drag increases with increasing angle of attack, a, which is the angle between the longitudinal axis and the flight path. The lift increases up to about a = 60°, when the effects of aerodynamic stalling occur. The pitching moment has positive values (nose-up) except when a = 0 or 90°. The side force depends on the position of the lace since the flow around the ball, which is affected by the lace and the 4 seams of the ball, is asymmetric. Therefore, it is considered that a punted kick rotating at lower spin rates fluctuates in the lateral direction during the flight. The rolling moment and the yawing moment are assumed to be 0 (Seo, Kobayashi and Murakami 2004) . In the case of a ball spinning on its longitudinal axis, the drag, the lift and the pitching moment are almost same as the non-spinning case, though there is a slight quantitative difference for CD. The side force increases with increasing w because of the Magnus force except when a = 0°. In the case of a ball spinning on its transverse axis, the lift increases with increasing co because of the Magnus force. The Magnus force is at its maximum when the spinning (transverse) axis is perpendicular to the flight direction. The side force depends on the angle between the spinning axis and the direction of flight. The side force is a maximum when this angle is 45°, while it is 0 at 90°. In order to optimize the three kicks, the flight trajectories need to be simulated. This can be solved by integrating the full nonlinear six-degrees-of-freedom equations of motion numerically (Seo, Kobayashi and Murakami 2006) on the basis of an aerodynamic database constructed from wind tunnel test data. What are the best

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Kazuya Seo

kicks to use? The objective of this paper is to calculate the features of the optimal kicks in each case.

2 Modeling The inertial coordinate system is shown in Fig.l . The origin is defined by the intersection between the player's own goal line and the left touch line, with the XE-axis along the touch line towards the opponents half, the Y E-axis along the goal line towards the goal posts and the ZE-axis vertically downwards. T a bIe 1 Cantra parameters Control parameters Abbr. Velocity vector Vo Flight path angle Yo Azimuth angle Yo Angular velocity vector roo Elevation angle of roo 10 Azimuth angle of roo Ko Yaw angle 'Po Pitch angle 80 Roll angle <1>0

Fig. 1. Internal coordinate system XI;

Fig. 2. Velocityvector (Angular velocity vector)

XI;

Fig. 3. Euler angles

The control parameters for optimization are the initial conditions, which are the magnitude of the velocity, the direction of the velocity, the magnitude of the angular velocity, the direction of the angular velocity and the Euler angles as shown in Table 1. Figure 2 shows the velocity vector as well as the angular velocity vector and figure 3 shows the Euler angles. The coordinate system in the frame of the ball is denoted by Xb,Yb, and z, with the origin at the center of gravity of the ball. The x, axis is along the longitudinal axis, while the Yb and Zb axes are along transverse axes with

Multi-optimization of Three kicks in Rugby

225

the zb-axis in the direction of the valve. The sequence of rotations conventionally used to describe the instantaneous attitude with respect to an inertial coordinate system is shown in Fig.3 (Stevens , 1992). Starting with the inertial coordinate system the following sequence is followed; 1. Rotate about the ZE axis, nose right (positive yaw 'P), 2. Rotate about the Yl axis, nose up (positive pitch 8), 3. Rotate about the x, axis, right wing down (positive roll <1».

3 Multi-optimization of the Punted Kick The punted kick rotating at low spin rates fluctuates during flight. The objective here is to achieve the maximum number of extreme positions in the X E and YEdirections as well as the longest hang time. This makes it more difficult for the opposition to catch the fluctuating ball. A long hang time reduces the chances of the opposition being able to mount a counter-attack by tackling them just after the catch . 70 60

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The punted kick from the center of the field is optimized. The initial position is assumed to be (XE, YE, ZE) = (50, 35, -0.5). The ranges of the nine control parameters in Table 1 are defined as follows : 15
<8 0< 90°, & a <<1>0< 360°. Three object ive functions are considered, two of which are the number of extrema in the Xj-axis and the YE-axis. The third objective function is the hang time. For optimiz ation all the objective function s must be maximized. Since there are three objective functions , the problem is a multi-optimization problem. To carry out optimization, the elitist multi-objective genetic algorithm was applied (Deb, 2003) . The optimum flight trajectory is shown in Figs 4 & 5. The optimal initial conditions were found to be Ivo 1=25m/s, Yo =80 °, YJJ=-2.7°, liill=0.94rps, \{)=99°, Ko=-128°, 0 %=85°,80=-84 °, & <1>0=7.7°. The hang time is 5.4 seconds . The number of extrema

226

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in the Xj-axis is 3, and that in the Yj -axis, 13. If the velocity vector is not included in the XE-ZE plane, there are extremas in the Xj-axis because of the side force. Figure 5 is the catcher's view. The amplitude of the fluctuations is from several to ten centimeters. Since it must be difficult for the opposition to catch this kind of punted kick, it becomes a powerful weapon in the game.

4 Multi-optimization of the Kick into Touch Two kicks into touch from the behind the 22m line are optimized. Two images of the flight trajectory are shown as I & II in Fig.6. The spin direction is assumed to be clockwise as viewed from behind. This spin direction is normally given by the leftfooted kicker. The initial positions are assumed to be (X E, Yb ZE) = (20, 50, -0.5) for I and (XE, YE, Zd = (20, 20, -0.5) for II. The flight time is denoted by tr and two objective functions are considered, one of which is the distance achieved in the forward direction at the end of the flight time, tr , and the other is the absolute value of the difference in YE between the ball and the touch line at tr, i.e., the distance between the touch line and the ball when it lands on the ground. Although there are nine control parameters in Table I, only six of these are taken into account. Since the longitudinal axis coincides with the spinning axis, Iu & Ko are automatically determined from the Euler angles. Moreover, the initial roll angle <1>0 is unimportant and is assumed to be 0° in this case. The results are shown in Figs.7 & 8. The data for I are shown by the open circles, and those for II are shown by the open triangles. The two objective functions are shown in Fig.7. The flight distance in the forward direction, XE-20, increases as the absolute value of the difference in YE between the ball and the touch line, fJ. YE, increases. Although the ideal situation is given by the largest flight distance in the direction of XE and the smallest value of fJ. Yb it is impossible for these conditions to be satisfied simultaneously. It can be seen that the flight distance of II is longer than that of I; that is, the optimal kick made using the leg nearest the touch line produces a greater distance than that made using the leg furthest from the touch line. However, the range of optimal solutions for II is narrower. The relationship between the optimal Yo and the optimal 8 0 is shown in Fig.8, with the solid line showing 8 0 = Yo. It was found that 8 0 is comparable with Yo in the case of I, while 8 0 is slightly greater than Yo in the case of II. The condition where 8 0 = Yo means that there is no precession at t = Os. In the case of 8 0 > Yo for II, there is precession owing to the difference in angle between the velocity and angular velocity vectors, and the precession is clockwise around the velocity vector from the kicker's point of view. This helps prevent any lateral movement in the negative YE direction in the very primary phase.

227

Multi-optimization of Three kicks in Rugby

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5 Multi-optimization of the Kick for Goal The kick for goal from 45° on the 22 meter line is optimized. The initial position is assumed to be (XE, Y E, ZE) = (78, 13, -0.145) and the time at which the ball passes over the crossbar is denoted by tf. Two objective functions are considered. One is the absolute value of the lateral deviation of the ball from the center of the goalposts at tf, and the other is the difference in height between the ball and the crossbar at tf. Since the transverse axis coincides with the spinning axis, \;) & !Co are automatically determined from the Euler angles . Therefore, seven of the nine control parameters in Table 1 are taken into account for this optimization. Two objective functions are shown in Fig.9. Although the smallest lateral deviation and the largest height difference give the ideal situation , it is impossible for these conditions to be satisfied simultaneously. The left limit solution in Fig.9 is that in which the deviation is almost 0 (the ideal situation), but the height difference is relatively small. The flight trajectory in this case is shown in Fig.10. The optimal initial conditions are IVo I =25m/s, Yo =41 0 , Xo=45°, I%I = IOLp.S, '1'0 =51 0 , 0 0 =90°, & <1>0 =6°. It can be seen that the projection of the flight path onto the surface of the

pitch is a straight line without any hook. The optimal Yo and optimal Xo should be in the ranges of 41.2 < Yo < 42.5 ° and 41.9 < Xo < 45.0°. The deviation is almost 0, when Xo = 45.0°. This means that the direction of the velocity vector points toward the center of the goalposts, and no side force acts on the ball. If the ball tends to hook because of a side force, it has to travel a greater distance and loses altitude . It can be concluded that the angular velocity should be perpendicular to the velocity as well as the longitudinal axis in order to meet the optimal conditions.

228

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5 Conclusions We have carried out a multi-optimization study of th ree kinds of kick in rugby. The features of the optimal solutions are : 1.

2.

3.

In the case of the opt imal punted kick , the number of extrema in the lateral direction s is more than 10, and the amplitude of the fluctuations is from several to ten centimeters. In the case of the kick into touch, the optimal kick made using the leg nearest the touch line produces a greater flight distance than the optimal kick made using the leg furthest from the to uch lin e. However, the initial window is narrower. In the case of the optimal kick for goal, the angular velocity should be perpendicular to the velocity and also to the longitudinal axis of the ball.

References Deb, K. (2002) Multi-Objective Optimization using Evolutionary Algorithms. Wiley, New York. Seo, K., Kobayashi, O. Gotsu, A. and Murakami, M. (2003) Aerodynamic force data on a rugby football. Sports Dynam ics Discovery and Application, pp.289-294. Seo, K., Kobayashi, O. and Murakami, M. (2004) Regular and irregular motion of a rugby football during flight. The Engineering 0/Sport 5, YoU , pp.567-573. Seo, K., Sakamoto, S., Kobayashi, O. and Murakami, M. (2005) The initial window of a successful kick for goal of rugby football. The Impact a/Technology on Sport, pp. 280285. Seo, K., Kobayashi, O. and Murakami, M. (2006) Flight dynamics of the screw kick in Rugby. Spo rts Engineering, Submitted for publication. Stevens, B.L. and Lewis, F.L. (1992) Aircraft Control and Simulation, Wiley, New York.

The Mechanical Behaviour of Cricket Soils During Preparation by Rolling Peter Shipton, lain James and Alex Vickers Cranfield Centre for Sports Surfaces, Cranfield University, UK, [email protected]

Abstract. The nature of the ball - surface interaction in cricket has been identified as critical to the quality and safety of the sport . The requirement for even ball bounce and good pace from a clay loam soil cricket pitch has been successfully characterized and has been observed to be related to soil properties such as dry bulk density , moisture content and organic carbon content. To achieve the required mechanical properties, practitioners manage the compaction of a cricket pitch through the use of smooth steel-wheeled rollers. The relationship between moisture content and the compaction and shear strength was determined for a typical clay loam soil and was found to be significant. The effect of subsequent passes of 4.75 and 5.71 kN on soil dry bulk density was also determined in the soil dynamics laboratory. Maximum dry bulk density was achieved after 20 and 10 passes of each roller, respectively. The roller did not have a significant effect on dry bulk density below 50 mm in the profile .

1 Introduction There are few sports where the ballistics of ball trajectory prior to, during and post interaction with the surface are as critical for the quality and safety of playas in cricket. The two key parameters, describing this interaction are known within the sport as 'pace' and 'bounce'; defined by James, Carre, and Haake, (2004) as the velocity and trajectory of the ball post impact with surface. For both the batting and fielding side to have an equal chance in the game , and for batsman safety, variation in pace and bounce of pitch should be 'predictable' i.e. within acceptable limits of play. Whilst these limits are subjective in their nature, the effect of adverse ball surface interaction is apparent to players, officials and spectators of the game and will result in low scores, shortened games and risk of injury . Further, complete uniformity in pace and bounce will favour the batting team , desirable in short versions of the game where a result is guaranteed but less so in 4 and 5 day games where a result is dependent upon completed innings. Variation in pace and bounce was studied by James et ai, (2004) who developed methods of measuring and predicting variation in pace and bounce in UK cricket. The relationships among pace and bounce and soil physical/chemical parameters such as particle size distribution, dry bulk density (the oven-dry mass of soil in a known volume) and organic matter content were reported by Baker et al (2003), who determined that there was a positive correlation between pace and the dry bulk density and sand content of a soil, but there was a negative correlation between pace and moisture content, silt content and organic matter. Whilst established relationships of

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Shipton et al.

this type exist, these relationships observe the pitch in its 'match-ready condition', i.e. they do not inform the pitch construction or preparation process beyond the required final physical condition of the surface . Furthermore, these relationships are based upon soil-physical rather than soil-mechanical properties. To achieve the required uniformity of surface mechanical properties, the soil is compacted using a steel smooth-wheeled roller. This aims to increase bulk density and shear strength through compaction and to produce a level, smooth surface. Whilst in a compacted, dry state a clay soil provides high mechanical stiffness and shear strength (a key property for resistance to wear), the shear strength of a clay soil is known to be highly sensitive to moisture content (Henkel, 1959). Therefore, during play, soil moisture content must be kept to a minimum. To achieve drying of the complete soil profile, grass growth and deep rooting are essential as water is removed through transpiration. Therefore bulk density and shear strength must not exceed critical values which prevent grass growth for extended periods of time. The requirements of a surface are bounded by a lower limit of sufficient surface shear strength and stiffness for pace, bounce and wear resistance , and an upper limit of shear strength for grass growth. To translate any mechanical model into practical guidelines for the practitioner, the optimum soil moisture and duration for rolling, and how rolling practices affect surface mechanics must be investigated. This forms the key aim of a four year study by the authors to model the mechanical behaviour of cricket soils during preparation. This paper reports on the first year of this project which aimed to determine key mechanical properties of a typical soil used in cricket pitch construction in the UK and the behaviour of these soils during construction and compaction by a steel smooth-wheeled roller.

2 Materials and Methods 2.1 Test Soil Characterization and Selection The soil (labelled el30 here) was sourced from Essex, UK and had a particle size distribution of 30% sand, 40% silt, 30% clay. It is typical of soils used at elite and well resourced recreational levels of the game .

2.2 Determination of the Optimum Moisture Content for Compaction of Each Soil All moisture contents in this paper are reported on a gravimetric (mass) basis. The optimum moisture content for compaction of the soils was determined using the 'Proctor Test' (Proctor, 1933). Soil specimens of a fixed bulk volume 929 ml, were prepared at a range of gravimetric moisture contents between 5 and 30% . Each specimen was constructed in 3 layers, each layer receiving 27 blows from a 4.5 kg hammer, dropped from a height of 450 mm. The resultant dry bulk density (Pb) of each specimen was determined by measuring the oven dry mass of the soil in a known volume . The proctor optimum moisture content for compaction was determined as the peak of the moisture content - dry bulk density curve .

The Mechanical Behaviour of Cricket Soils During Preparation by Rolling

231

2.2 Determination of the Shear Strength Shear strength, the shear stress at failure of a test specimen was determined using two methods: the translational shear box and the quick, undrained triaxial shear test. For the translational shear box, specimens were prepared at 6% and 18% moisture content. The 60 x 60 x 20 mm samples were then placed in the translational shear box and subjected to an incremental strain at a rate of 1.25 mm/min. The shear stress at failure was determined for a range of normal stresses between 15.7 kN/m2 and 70.2 kN/m2. For the quick, undrained triaxial shear test, 38 mm diameter x 72 mm length cylindrical samples were failed in shear at total confining stresses of 35, 69, 103 and 138 kN/m2, at a strain rate of 1.5 mm/min. Samples were prepared at 15, 18 and 23% and tests were conducted in triplicate. In both methods, dry bulk density was constant at 1500 kg m,3. Linear models of soil failure at a shear stress (r, kN m") , as a function of normal stress (o , kN m,2) were determined by the Coulomb theory of soil failure (Lamb & Whitman, 1969). t>

c + otan¢>

(I)

This model, described in Eq. I, was determined by linear regression in the translational shear box test and by the construction of Mohr's circles for the triaxial test. Mean values of cohesion (c, kN m") and internal angle of friction ( ¢>, degrees) were analyzed by ANOVA.

2.3 The Effect of Successive Passes of a Roller on Dry Bulk Density A test surface of C130 soil (10m length, 1.8 m width, 0.2 m depth) was constructed in the Cranfield University Soil Dynamics Laboratory in 50 mm compacted layers. Initial Ph was 1200 kg m' at a moisture content of 20.5%. A smooth steel-wheeled roller, typical of those used in the preparation on cricket pitches (diameter 0.3 m, width 1.2 m), was towed at two speeds, 0.28 and 0.56 m S,I over the soil surface. The experiment was conducted at roller weights of 4.75 and 7.51 kN. Pb was measured for subsequent passes of the roller at 50, 100 and 150 mm depths within the profile. The effect of roller weight on bulk density at each depth was determined by ANOVA.

3 Results 3.1 Compaction and Moisture Content In the compaction test, there was a characteristic increase to a maximum, and then decrease in dry bulk density as moisture content was increased (Fig. 1). A significantly greater maximum p, was achieved with the heavier hammer (1850 kg m' at a moisture content of 15%) than with the lighter hammer (1650 kg m" at 20%). The difference between hammers was expected due to the increased work done on the

232

Shipton et al.

soil from the greater mass and this is typical of proctor test results. Beyond maximum Pb, compaction was limited by the pore water in the soil and thus the curves were similar from 20% moisture content. 1900 ,

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3.2 Shear Strength Parameters Table 1. Mohr-Coulomb shear strength parameters for the Cl3D soil Soil

Gravi metric moisture content, 0/0

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3.3 Th e Effect of Subsequent Passes of a Roller on Soil Bulk Density Rolling increased Pb significantly in the first 0-50 mm of the profile. At 50-150 mm there was no consistent pattern of p, increase with successive passes of either roller. The increase in p, at 0-50 m with subsequent passes of a roller was characterized by an increase to a maximum for the first passes and then a plateau for subsequent

The Mechanical Behaviour of Cricket Soils During Preparation by Rolling

233

passes. For the 4.75 kN roller this peak occurred at 1470 kg m" after 20 passes; for the 7.51 kN roller the peak was 1540 kg m-3 after 10 passes. 1700

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Fig. 2. Mean drybulk density of C/30 at 0-150 mm depth, following successive passes of a 4.75 kN (a)and 7.51 kN (b) smooth steel wheeled roller at 20% gravimetric moisture content. Error bars represent the LSD at p=0.05

4 Discussion The results of both the compaction and shear strength analyses illustrate the sensitivity of both properties to moisture content. Depending upon the magnitude of the load applied, there is an optimum moisture content for the compaction of the soil and a maximum bulk density that can be produced. For effective rolling of cricket pitches soils should be as close to the optimum moisture content for the load being applied. In compaction, an increase in moisture content eventually reduces the effect of normal stresses due to the low compressibility of water. In shear, an increase in moisture content was shown to initially increase shear strength due to an increase in cohesion caused by the interaction between clay particles and thin films of water. As soil moisture content increased above 15%, however, cohesion did not increase but friction between soil particles reduced significantly, reducing soil strength. When rolling cricket pitches the shear strength of the soil has to be exceeded by the rolling stresses for compaction to be achieved. Whilst the principal objective is normal loading of the soil, horizontal stresses are inevitable and are considerable in driven rollers where torque can cause wheel slip in excess of shear strength. In these conditions the soil is at significant risk of undesirable surface damage that could have an adverse effect on ball pace and bounce. The data in Fig. I showed that maximum compaction occurred with the greater load at 15%, which coincides with the maximum shear strength of the soils in Table I. The data in Fig. 2, however, showed that even the heaviest roller (some rollers currently in use in the field may exceed this weight) did not cause compaction beyond 1540 kg m", less than the maximum with the lighter hammer in Fig. I at similar moisture contents. Field data have shown that p, can reach the 1850 kg m' observed in Fig. I due to consolidation from removal of water over longer periods of

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Shipton et al.

time. At such a value of Ph, air filled porosity can be as low as 5%, to reduce porosity further will limit grass growth and the effect of grass on both moisture content and shear strength by root reinforcement has not been considered here. It is also important to note that maximum compaction was achieved after only 20 passes of a 4.75 kN roller and 10 passes of a 7.51 kN roller. If this result is observed in similar experiments with grass surfaces, currently in progress, then it will have a significant effect in reducing the time spent rolling cricket pitches in practice. Also, the roller was only effective in compacting the first 50 mm of the profile. This has direct implications for the construction of cricket pitches where it is apparent that only consolidation will increase the bulk density of the soil below 50 mm depth. It should be noted that the critical compacted surface depth for ball interaction is not well understood or quantified in the literature.

5 Conclusion The maximum dry bulk density (Ph) in a proctor compaction test of a typical soil used in first class cricket in the UK, was 1850 kg m' at 15% gravimetric moisture content using a 4.5 kg hammer and 1650 kg m" at 20% using a 2.5 kg hammer. The shear strength of the soil was greater at 15% than 18 and 23%. As soil moisture content increased from 8 to 15 %, cohesion increased significantly, but was not significantly different from 15 to 23%. Internal friction decreased significantly from 8 to 23% due to lubrication of soil particles by water. It was shown that after 20 passes of a 4.75 kN roller, typical of the type used in cricket pitch preparation, Ph increased significantly from 1200 to 1470 kg m" but that there was no significant increase for subsequent passes. Likewise, for a 7.51 kN roller, a maximum bulk density of 1540 kg m" was achieved after only 10 passes. These data form part of the development of a model to improve the construction and preparation of cricket pitches.

Acknowledgements The authors gratefully acknowledge that this research was funded by the UK EPSRC and the England and Wales Cricket Board. Thanks to R. 1. Godwin, M Freeman, R Newland, S Stranks and R Swatland for their input and assistance.

References Baker, S.W., Hammond, L.K.F., Owen, A.G. and Adams, W.A. (2003) . Soil physical properties of first class cricket pitches in England and Wales. 2. Influence of soil type and pitch preparation on playing quality. Journal of the Sports TurfResearch Institute, 79, 13-21. Henkel, DJ. (1959) . The relationship between the strength, pore-water pressure and volumechange characteristics of saturated clays. Geotechnique, 9, 119-135. James, D. M., Carre, M. 1., Haake, S. 1. (2004) . Theplaying performance of county cricket pitches. Sports Engineering. 7(1): p. 1-14 Lamb, T.W., Whitman, R.Y. (1969) Soil Mechanics . John Wiley & Sons, New York. Proctor, R.R. (1933). The design and construction of rolled earth dams. Engineering NewsRec, III (9), 245-248

Studies on the Oblique Impact of a Cricket Ball on a Cricket Pitch David James, Matt Carre and Stephen Haake Sports Engineering, CSES , Sheffield Hallam University, [email protected] Abstract. The cricket pitch is a carefully prepared strip of natural turf of fundamental importance to the play of the game , yet the understanding of the factors that lead to good pitch construction remains limited. In order to ascertain why some cricket pitches are perceived to perform well whilst others cause difficulties, the mechanics of the oblique impact of the ball on the pitch have been explored. This study presents the development of a normal impact model to the oblique impact scenario . A coefficient of dynamic friction and an analysis of the pitch crater were used to predict the ball's rebound dynamics. Model parameters were determined from simple surface testing procedures and model predictions were found to be within an acceptable range of divergence from experimental impact measurements.

1 Introduction Previous attempts at modelling sports ball-surface interactions have generally assumed that either the ball or the surface could be considered rigid, due to the difference in stiffness of the two parts . For instance, studies of tennis ball-court interactions have assumed the surface to be rigid whilst the ball deforms in a non-linear elastic way (Haake et al., 2005) . In these models, the surface simply acts to allow a frictional force to develop on contact. In other impact situations, such as golf ball/green, the ball has been assumed to be rigid compared with the surface (Haake, 1989). Modelling of a cricket ball-pitch interaction is complex due to the fact that both the ball and the surface deform to some degree. Carre et al. (2004) developed a spring-damper normal impact model of a cricket ball impacting on a rigid surface using experimental data . The model was then used to predict oblique impacts by including a coefficient of friction . The model predictions compared well with experimental data for rebound speed and spin generation, but not with rebound angle . More recently, James et al . (2006) showed that it is possible to predict the 'pace' ofa cricket pitch (oblique rebound speed) by combining two simple measurements of restitution and friction in a rigid-body model. However, similar to Carre et al. (2004) the model was unable to predict the angle of rebound. It is believed that deformation of the pitch can cause a steeper rebound than one might expect due to the ball impacting on the front of the depression that it has made (Carre et al ., 1999) .

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David James, Matt Carre and Stephen Haake

2 Normal Impact Model James et at. (2004) described the normal impact of cricket ball on a cricket pitch by suggesting a two degree of freedom system that allowed for both deformations of the ball and the pitch . This paper will use their suggested normal impact model as a basis for understanding the more complex oblique impact.

m " cricket ball mass k b - ball stiffness parameter

C.

Cb"

ball damping parameter

kp " pitch stiffness parameter C.

T Y.

c po

pitch damping parameter

Yb" displacement of ball's centre of mass Y»: displacement of pitch

Fig. 1. A two degree of freedom spring damper model of a normal ball impact.

Figure I shows a schematic of the normal impact model. Since the force acting on the ball and the pitch are equal , the impact force can be determined at any time interval , t, during impact using Eqs. 1-3. (Fr ) , = m( h)t (I)

=(kh)t-I'.,(Yh - Yp )t + (ch)t-I'.,CYh (F, .), =(k p)t _I'.' (Y,,), + (c,,)t - l'.tCY,,), (FI')'

yp ),

(2)

(3)

The force equations assume that both pairs of stiffness and damping coefficients change during impact. Howe ver, their values at each time interval , t, are based on the ball conditions at the previous time interval , t-Si. In this way, the model can be solved using the finite-difference method. However, the displacement of the pitch, Y", is unknown and a further relationship is required to define it. Combining Eqs. 2 and 3 and using finite difference definitions,

(y ) = (kh)t-6J(Yh), + (ch)t -6J + (Yp)t-6Jl
(kp)'_6J + (kh)t-6J + [(ch)t-6J + (cp),_6J ]

~-l

1

(4)

Equation 4 can describe the displacement of the pitch in relation to the motion of the ball's centre of mass if all stiffness and damping parameters are known. Parameters were determined by dropping a cricket ball onto a rigid load cell, and then dropping a rigid impact hammer onto a cricket pitch (James et al., 2004) .

3 Oblique Impact Model The two degree-of-freedom normal impact model was extended to describe the oblique impact. Notably, the interact ion between the front face of the deformed ball and the crater that is formed during impact was considered.

Studies on the Oblique Impact of a Cricket Ball on a Cricket Pitch

237

Fig. 2. A schematic of the forces acting on a cricket ball during impact.

A schematic of the forces acting on the cricket ball during impact with a deformable pitch is shown in Fig . 2. The normal reaction force, F norm, is calculated using the same method as for the normal impact model (Fy in Eq. 1) and the corresponding frictional force is the product of the normal reaction force and a coefficient of friction, 11. This was measured using a weighted sledge supported by three cricket balls that was pulled along the pitch surface using a constant torque motor (see James et al., 2006) . As shown in Fig. 2, the ball impact produces a crater in the pitch that generates an additional resultant force, Fdej> accompanied by a corresponding perpendicular frictional force, f.1F'deJ. The direction and position of these forces can be calculated by considering the variation in force acting over the ball/crater contact surface. The oblique impact model assumes the area of contact between the ball and pitch crater to be represented by the geometry shown in Fig. 3 (i.e. the truncated base of the deformed ball plus the front half of a slice of the ball with a depth equal to that of the pitch deformation), Experimental results using the SERG impact hammer showed the cricket pitch to have a slow recovery from deformation (James et al. 2004) . The back half of the ball was therefore considered to be free from contact with the pitch.

(a)

(b)

Fig. 3. The area of contact between the ball and pitch during an oblique impact (deformations are exagger ated for clarity) with (a), the reaction force from one segment of the sphere 's annulus, (Fder)9. And (b), the resultant force, Fdef calculated by integrat ion over the contact area.

An estimation of the magnitude of the force, F deJ was taken as the damping force produced by the area of material in front of the ball. Difficulties arise if a stiffness parameter is also incorporated in this part of the model due to the large horizontal

238

DavidJames, Matt Carre and StephenHaake

deflections. During impact, the size of the area in front of the ball changes, as does the ball's velocity . The oblique reaction force, Fdej, is therefore time dependent and was approximated by;

(Fdej) / =

W1lr(YP)/~(Xb 2 + Y;)/

(5) i.e. the product of a pitch damping coefficient, w (determined from impact hammer tests), the area of pitch in front of the ball and the ball's absolute velocity. In order to calculate the position from where, the resultant force, Fdej acted , a general force, (Fdej)e, for a small segment of the sphere 's annulus was considered (see Fig . 3(a)). Since the direction of this reaction force is dependent on the location of the segment it was necessary to determine the combined effect of the reaction forces from all segments within the half annulus. This general reaction force located at an angle, B, and at time, t, can be estimated as follows:

(Fdej )0,/ = wr(y p)/ 8B~(.Xb + yh . 2

(6)

It follows that the reaction force from all segments can be spilt into components in the x, y and z directions (shown in Fig. 3(a)) by considering the angles of Band A.

(FXdej )0,/ = -wr(Yp)/8B~(.Xb2 + y;)/

cOSBCOSA

(7)

(FYdej )0,/ =

wr(Yp)/8B~(.x/ + y;)/ sin A

(8)

(Fz dej )0,/ =

wr(Yp)/8B~(.x/ + y;)/ sin Bsin A-.

(9)

The combined effect of the oblique reaction force in each of the x, Y, and z directions can be determined by integrating Eqs. 7-9 with respect to Bbetween tr/2 and tr/2, so that:

(FXdej)/

=-2wr(yp)/~(X/+y;)/ COsA

(10)

1lWr(Yp)/~(Xb 2 + y;)/ sin A

(11)

(FYdej)/ =

(Fz dej)/ = 0

(12)

Fig. 3(b) shows the direction and location of the resultant reaction force, Fdefi due to the combined reaction forces from all segments of the front of the pitch crater. The angle at which the combined oblique reaction force , Fdej, acts to the horizontal was determined by comparing the magn itude of its horizontal and vertical components (Fxdefi Fydej)' Defining this angle as r(see Fig . 3(b)), it can be shown that;

r=Tan-1[;TanA]

(13)

This angle changes throughout impact but can be calculated by considering the deformation of the ball and the pitch, thus;

A=Tan-1

r-Yb+ 0.5y p

~r2 -(r- Yb+0.5Y p)2

.

(14)

Studies on the Oblique Impactof a Cricket Ball on a Cricket Pitch

239

This analytical description shows the combined oblique reaction force Fdef> to always act at a point two thirds of the horizontal distance between the centre line of the ball and its leading surface. With the direction and magnitude of all forces known (Fnorm, tJFnorm' F dej , tJFdej) the model was set to run with a time interval of 1 us. The resultant vertical and horizontal forces on the ball were calculated at each time interval along with displacement, velocity and acceleration of the original geometric centre of the ball and the pitch surface. The ball's angular velocity was also calculated at each time interval by considering Eq 15. (w) = (Fx)J-(Yb\]Llt +(w) (

(/)(

(-!it

(15)

The moment of inertia of the ball was assumed to vary due to deformation and was approximated as a solid sphere with a reduced radius so that: (/)( =

Xm[r- (Yb )iiT

(16)

The directions of the frictional forces (tJFnorm , tJFdej) were made to switch direction when the ball was deemed to be rolling on the surface. For the force tJFnorm' the direction switched when the equatorial velocity of the truncated section of the ball exceeded that of the horizontal velocity of the ball's centre . The oblique impact was considered to end when the ball and pitch lost all physical contact. It was found that the normal reaction force, F norm' returned to zero before the end of impact. From this point onwards, forces F llorm and tJFllorm were switched off and the ball's trajectory was solely affected by forces Fderand tJFde!'

4 Experimental Verification Validation data for the oblique impact model was gathered by projecting cricket balls obliquely onto a test plot of a professionally maintained cricket pitch . The impacts were recorded using high speed video at 400 frames per second . A bowling machine was set to simulate a range of bowler deliveries and the impact footage was analysed using bespoke software. Model parameters for the cricket ball were considered to be the same as those found by Carre et al. (2004) . Model parameters for the pitch were found by using the SERG impact hammer in the same method as described by James et al. (2004) . The coefficient of friction between the ball and pitch was determined by using friction sledge apparatus as discussed in James et al. (2006) . Figure 4 shows the model predictions to be in a generally good agreement with the experiment data. An equal ratio line is shown on both plots and it can be seen that the model is able to predict rebound speed with a high degree of accuracy, whilst predictions of rebound angle are more scattered. The model over-predicts the balls' rebound angles to some degree, but it provides a significant improvement on previous models (Carre et al., 2004 ; James et al., 2006) . It is also worthy to note that the rebound angles of cricket balls are inherently variable . The model 's predictions of rebound spin rate were found to be in good agreement with the experimental results (data not shown) .

240

David James , Matt Carr e and Stephen Haake

.

JO

~

-

I

25

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20

-e

.ll

~

..

!

Actual rebound speed (ms')

(a)

25

30

-

• ..... ..... . .. .

.

-'• "e•-

-

------.",

.

- -- -

----- -- - '--------------1

.e

-

:'~I'

-. . -

15

.':

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20

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-e

JL---_--_ - -~-_______l

-

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.8

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.!!

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5 -jL--~--~--~-~ ______i

5

10

15

20

25

30

Actual rebound angle (degr.e s)

(b)

Fig. 4. Compari sons between high speed video measurements of the cricket ball rebound and the corresponding model so lutions for; (a) rebound speed and (b) rebound angle .

5 Conclusions The model for a normal impact of a cricket ball on a pitch was developed to the oblique impact scenario. The perform ance of the new model was evaluated by comparing experimental impact data to model predictions. The new model was shown to perform generally well, and in the case of predicting rebound angle , it performed significantly better than previous models. The new model provides the ground work for a metho d of predi cting the playing performance of cricket pitches; a tool which would be a valuable asset to Ground Staff.

References Carre, M.J., Baker, S.W., Newell, A.J. & Haake S.J. (1999). The Dynam ic Behaviour of cricket balls durin g impact and variations due to grass and soil type. Sports Engineering, 3,1 45-160. Carre, M.J., James, D.M. & Haake, S.J., (2004). Impact ofa non-homogen ous sphere on a rigid surface. Proc. Instn. Mech Engrs. Part C: Journal 0/ Mechanical Engi neering Science, 218, 273-281 Haake, S.J . (19 89). Apparatus and test Methods for measuring the impact of golf balls on turf and their application in the field . PhD thesis, The Univer sity of Aston in Birmingham. Haake, S.J., Carre, M.J., Kirk R. and Goodwill, S.R. (2005) Oblique impact of thick walled pressurized spheres as used in tennis. Proceedings / or the Institution 0/ Mechanical Engineers, 219 (c), 1179-11 89. James, D.M., Carre, M.J. and Haake, S.J. (2004) Th e normal impact of a cricket ball on a cricket pitch. In: The Engineering ofSport 5: Proceedings ofthe 5th International Conference on the Engineering ofSpor t (eds M. Hubbard, R.D. Mehta & J.M. Pallis) Vol 2, pp. 66-72, ISEA, UK. Jame s, D.M., Carre, M.J. and Haake , S.J. (2006) Pred icting the playing characteristics of cricket pitches. Sports Engineering (In press).

Test Devices for the Evaluation of Synthetic Turf Pitches for Field Hockey Colin Young, Paul Flem ing and Neil Dixon Loughborou gh University, [email protected]

Abstract. Many existing tests for field hockey can be categorized into; how the ball, and how a person interacts with the surface. Interactions durin g sporting activities can significantl y influence how a game is played from both a technical and tactical perspecti ve. Understanding interaction s of this nature and ident ifying factor s that can influence and control their performance is essential to comprehend the mech anical beha vior of a sports surface. Howe ver, synthetic turf pitche s are complex structures, comprising several layers, all of which contribute to their comp osite behavior. Therefore, the mechanical response of the surface to interactions is difficult to measure. It has been argued by many researchers that mechanical tests are inappropriate to simulate in-game conditi ons and their suitability has been brought into quest ion. Furtherm ore, there is a lack of good qual ity peer reviewed data on the mechanical behavior of synthetic turf pitche s. Test data are collected by accredited laboratories for the relevant sports gove rning body, with the data remaining unpubli shed , thus there is no way to validate or recomm end impro vements to these standards. Consequentl y, this paper presents results from a comprehensive program of testing on six world class synthetic turf pitches used for field hockey. Current test equ ipment and methods employed by the governing body for field hockey (FIH) were validated and recomm endations were formul ated for their suitability. It was found that impact tests, includ ing the Berlin Artificial Athlete, provided a simple mean s to classify one pitc h against another and gave a significant difference between the six pitche s. A review of ball interaction tests, including vertica l ball rebound , and ball roll were found to be significantly influenc ed by environmental factors such as moisture and wind, which highligh ted the importance of careful mon itoring dur ing testing to ensure pitche s were evaluated in appro ved cond itions. In conclusion, current mechanical tests provide a simple and effective way to classify one pitch directl y against another. However, their use for determin ing how the surface beha ves in a ' rea l' gam e situation and the mechan ical inform ation obtained is considered limited

1 Introduction Synthetic turf pitches are complex structures with several layers , all of which contribute to their composite behavior. Therefore, the mechanical response of the surface to interactions from players, balls and sports equipment are difficult to assess. Impacts involving sports objects , such as a ball or the player and the surface, can

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Colin Young, Paul Flemingand Neil Dixon

affect the technique and tactics of a sports performer and the way in which the game is played. The Federation De Internationale Hockey (FIH) produced a list of requirements to which a playing surface must adhere to in order to be used for sanct ioned competitions . These standards are published in the 'handbook of performance requirements and test procedures for synthetic hockey pitches - outdoor' (FIH, 1999). The objectives of the standards are to ensure that field hockey competitions are played on pitches which ; provide a proper reflection of team merit , allow players to display and develop their skills , offer comfort and limit risk to players, and extend playability in adverse weather conditions. The handbook has three tiers of standards for different levels of ability/competition: global, standard and starter. The 'global' standard is the most stringent and is compulsory for international competitions and only unfilled (or water based) systems can obtain this standard. However, there is still a large range of acceptability even at this tier and there is a lack of any good quality peer reviewed research on pitch accreditation to validate the approach (Young, 2006) . The most common device for measuring impact behavior on sports surfaces is the Berlin Artificial Athlete. The Berlin is currently used by the FIH as a measure of impact response. The peak impact force is measured, and surface cushioning (F j ) is presented as the percentage reduction compared with a rigid (normally concrete Fe)' surface. Force Reduction = (Fe - Fj)/F e

(1)

There are two tests specified by the FIH to measure ball/surface interactions. The first ball rebound (or rebound resilience) is a measure of the energy lost during impact with the surface from a vertical drop. The second is a measure of the frictional resistance of the ball as it rolls across the surface and is called ball roll distance (or ball roll resistance). The roll resistance is defined as the force acting at the point of contact between the ball and surface. This paper presents results from a comprehensive program of testing on six 'global' standard field hockey pitches. Several of the current tests methods are evaluated for their suitability to measure the behavior of synthetic turf pitches and factors that influence the measurement are also assessed, including the effect of surface water/irrigation and construction specification.

2 Methodology This section outlines the test methods/equipment used to evaluate the behavior of six 'global' standard water based field hockey pitches. Pitch selection was based on several criteria. Firstly, feedback given by players during interviews and questionnaires (Young. 2006) were analyzed and a shortlist of suitable pitches were identified based on perceived playing characteristics. The shortlist was then reduced to pitches that conformed to FIH 'global ' standard accreditation. From the remaining list priority was given to the pitches with available construction specification to facilitate understanding of the effects of different constructions. From the above criteria six

Test Devices forthe Evaluation of Synthetic TurfPitches for Field Hockey

243

pitches were highlighted for field testing, due to data protection the pitches can not be identified and henceforth shall be labeled pitches A to F. Details of the six pitches are illustrated in Table I. Pitch

Subbase Thickness Asphalt Thickness Shockpad Type Shockpad Thickness Pile Material Pile Height

Table

A 250mm

450mm

C 200mm

250mm

E 200mm

250mm

65mm

65mm

70mm

65mm

65mm

65mm

In-situ & Integral 15mm'

In-situ & Integral 15 mm'

Integral

In-situ

Integral

In-situ

8mm

15 mm

6mm

15 mm

Nylon

Nylon

Nylon

Polypropylene

Nylon

Polypropylene

B

D

F

12 mm 12mm II mm 15mm II mm 13mm Note: 'combinationof 12 mm in-situ and 3 mm integralshockpads 1. Construction details of the six synthetic turf field hockey pitches

Prior to testing each pitch was applied with a full irrigation cycle to ensure it was tested under similar conditions to what players experience during a game. This was repeated every 40 minutes as would be standard during a game of field hockey. To ensure that a good global coverage of the pitch was achieved during testing a grid system was produced with 25 test locations evenly spread across the entire playing area, this provided comprehensive coverageof each pitch. The FIH outlines many tests for the accreditation of field hockey pitches, however, given this size and context of this paper three test methods are presented within, these are described below.

2.1 Berlin Artificial Athlete The Berlin Artificial Athlete consists of a falling mass of 20 kg that is electronically released from a height of 55 mm onto a spring with a stiffness of2000 kN/m-' that is connected to a test foot of 70 mm diameter. The peak impact force is measured three times, and surface cushioning is presented as the average percentage reduction of the second and third drops compared with a rigid (normally concrete) surface, as described in the FIH handbook (1999). The requirement for 'global' standard pitches is between 40 - 65 % force reduction.

2.2 Ball Roll Distance Ball roll distance, was measured by rolling a ball down a standard inclined plane or ramp. The ball (approved by the FIH) should roll a prescribed distance within a maximum deviation of3° from the straight line. The test was repeated in the opposite direction and results were averaged, thus reducing the possible effects of wind, slope, wear, pile bias and smoothness. The test follows the procedure outlined in the FIH handbook of performance requirements (1999). The requirements outlined by the FIH for' global' standard pitches is between 9 m - )5 m ± ) 0 % of the mean.

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Colin Young, Paul Flemingand Neil Dixon

2.3 Ball Rebound Height To determine the ball rebound resilience a vertical drop test was used . The test followed the procedure of the FIH standard (1999). It consisted of releasing a ball from a height of 1.5 m (surface to underside of ball) on to the test surface. The height of rebound for 'global' standard pitches should be between 100 mm and 250 mm with a maximum deviation of 20 % from the mean . The FIH specify that the test should be ' wet' and an approved hockey ball be used .

Pitch Test Device Berlin Artificial Athlete (%) Ball Rebound Height (em) Ball Roll Distance (m)

Mean SO COY Mean SO COY Mean SO COY

A 60.4 3.0 5.0 32 .8 2.4 7.2 14.5 1.0 7.2

8

C

D

E

61.8 3.8 6.1 36.8 3.2 8.6 13.6 2.1 15.6

43 .6 1.7 4.0 20.7 5.2 25.0 15.4 1.8 11.8

55.5 3.5 6.3 41.1 1.0 2.5 15.1 1.6 10.3

45.4 2.1 4 .6 26.2 0.7 2.8 14.0 1.1 8.1

F 52.7 4 .2 7.9 32 .2 2.2 6.8 15.5 3.1 20.0

Note : SO = standard deviation, COY = coefficient of variance

Table 2. An overview of the results from six synthetic turf field hockey pitches

3 Results The following section presents the results from the data collection on six 'global ' standard synthetic turf field hockey pitches. An overview of the results is presented in Table 2.

3.1 Berlin Artificial Athlete Measurements with the Berlin identified pitch C as the hardest pitch with a force reduction of 43 .6 %. Pitch B was measured as the softest pitch with a force reduction of 61 .8 %. Table 2 illustrates the force reduction for all six pitches. From the 25 test locations it was found that pitch C had the least variability with a COY (coefficient of variance, standard deviation / mean) of 4.0 % compared with pitch F which had the most at 7.9 %.

3.2 Ball Roll Distance A small difference was measured between the six pitches with the ball roll test. Pitch B had the shortest measured distance of 13.6 m and Pitch F had the longest with 15.5 m. Three of the pitches (C, E & F) fell narrowly outside the FIH 'global' specification . A large directional difference was noticed during testing, on pitch B there was a difference from 11.84 m (north to south) to 18.12 m (south to north). This difference was attributed to the influence of the wind .

Test Devices for the Evaluat ion of Synthetic Turf Pitches for Field Hockey

245

50 ,------ - - - - - - - - - - - - - - - - - - - - - ------,

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10

e Match Conditions a Saturated O -tTTTTTTTTTTTTTTrTT1rTT1-rnTTTTTTTTTTTTTTTTTTrrn-rnTTTTTTTTTTTTTTTTTTrTT1crrr1 ~NW~~~NW~~~NW~~~NW~~~NW~~ mmmmm~~~~~ooooo~~~~~rororororo

Location

Fig 1. The influence of moisture of ball rebound height on pitch A

3.3 Ball Rebound Height A large spread of measurements were taken from the ball rebound height tests. Pitch C had the lowest mean rebound height of 20.7 ern compared with pitch D 41.1 em which was the highest. Five of the six pitches rebound height fell outside the FIR guidelines for rebound height. It was noticed whilst testing that the degree of water on the surface significantly influence the rebound behavior of the ball. Hence, pitch A was tested under three different levels of saturation (dry, match and saturated). Figure I illustrates the magnitude of difference for each of these conditions .

4 Discussion The amount of water on the pitch was shown to significantly influence the behavior of the ball during impact. Thus the uniformity of the watering system to apply a even application of water to the whole playing area is vital to ensure the behavior of the pitch is consistent. The surface water appears to dissipate the impact energy of the ball resulting in less energy being returned to the ball and hence a lower rebound height. The Berlin and ball roll tests did not measure a difference for each moisture level. The impact behavior of the surface measured with the Berlin was most dependent on the shockpad and carpet layers. It was found that the pitches evaluated with a

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Colin Young, Paul Fleming and Neil Dixon

relatively thin integral system (C & E) had a much higher stiffness than the pitches with an in-situ shockpad system. From these data there was no obvious link between subbase and asphalt layers and pitch behavior, it can therefore be assumed that the carpe t/shockpad combination are more influential to pitch performance. The six pitches fell within the FIH specifications for impact behavior. Howe ver, for ball behavior three pitche s failed roll distance and five pitches failed the ball rebound test. This suggest s that the pitches are outside the requ irement s of the FIH and hence not suitable for ' elite' field hockey. Howe ver, all of the six pitches initially passed the accred itation process. It is unclear if the pitches beha vior have changed over time (between the accreditation testing and this testing) or if the equ ipment/methodology used was different. This raises the issue of regular reaccreditation to ensure pitche s remain within the required standards. In the past it has been argued that these mechanical tests do not fully represent what a player or ball experiences during a game situation and that to fully understand the complex mechanism of pitch behavior test methods are required that more closely simulate these conditions. However, given that the existing test methods are a suitable way to index/clas sify pitche s, for the purpose of surface accreditation, they are considered appropriate.

5 Conclusions Measurements from these test devices have established that large differ ences exist between pitches. These differences can be attributed to their construction specifications and environmental influences. Future measurements are requ ired to determine the influence of 'ageing' and how the pitches perform ance changes over time. This can also be linked to the maintenance of the pitch which should be investigated. A more fundament al study into the precise influenc e of water is required to better understand its effect s. Similarl y, the rate of drainage/evapor ation of water from the surface can influen ce the pitches behavior during the course of a game, especi ally in warm weather conditions and this problem needs to be evaluated.

References Dixon, S. 1., Batt, M. E. and Collop, A. C (1999) Artificial Playing Surfaces Research: A Review of the Medical, Engineering and Biomechanical Aspects. International Journal of Sports Medicine 20, 209-21 8. Handbook ofPerf ormance Requirements - Outdoor (1999) Federation Intemationale de Hockey, Brussels, Belgium. Young, C (2006) Mechanical and Perceived behavior ofsynthetic turf pitches forfield hockey . Unpublished PhD Thesis, Loughborough University.

7 Skiing, Snowboarding and Ski Jumping

Synopsis of Current Developments: Skiing, Snowboarding and Ski Jumping Veit Senner Technische Universitat Miinchen, Department Sport Equipment and Materials, [email protected] .A total of 11 contributions demonstrate the diversity of research in the field of skiing, snowboarding and ski jumping. This shows how engineering methods can help to better understand the complex interaction between equipment and athlete and to better describe the physical phenomena behind these sports.

Snow Friction and Skiing Four research groups address the topic of ski snow tribology : Paul MILLER et al. (USA) discuss the development of a system for measuring the kinetic coefficient of friction between the bottom surface of a ski and snow. A large-scale laboratory tribometer, which measures the friction of a small ski sample on ice or snow was built and validated by Mathieu FAUVE (Switzerland) . The scientists in the group of Qianhong WU (USA) present a simplified mathematical model to describe lift mechanics due to both the transiently trapped air and the compressed snow crystals. An interesting camera-DL T-based method to determine friction and reaction forces in competition skiing without interfering with the athlete is proposed by Michael SCHIESTL and his co-workers (Austria).

Ski Design and Performance Mechanical properties of the ski are focused in three contributions coming all from Switzerland. The investigation of Anton LUTHI and his colleagues is dealing with the effect of different bindings and plates on the mechanical behaviour of the ski. Combining their laboratory measurements with performance tests on the slope they were able to perform correlation analysis between subjective tester ratings and the measured physical characteristics. A similar question is treated by Peter FEDEROLF et al. whose study underlines considerable differences in the subjective assessment of the ski's performance. Nevertheless some correlation between subjective tester ratings and the bending and torsional stiffness of the ski were found.

250 Veit Senner Finally the dynamic response of the ski as a function of temperature is examined by Christian FISCHER and his colleagues. The researchers attribute increased damping of a ski to the existence of the polyamide top layer which seems to be most effective at temperatures around 0 "C.

Skiing and Ski Jumping Motion The long turn of an expert skier is examined in the Japanese - Australian coproduction of Takeshi YaNEYAMA and Nathan SCOTT . They determine vertical binding forces and plantar foot pressure and combine this data with joint angle measurements and video recordings. Two research groups present their work on ski jumping: Kurt SCHINDELWIG and Werner NACHBAUER (Austria) analyse the accuracy of an instrumented jumping hill in Innsbruck. Satisfying accuracy was obtained for the joint angles; improvements are needed regarding velocity calculation of the centre of mass . Another approach to flight dynamics of ski jumping is proposed by a Japanese researcher group around Yuji OHGI. Their method uses a tri-axial accelerometer and a single axial gyroscope attached to the jumper's body . Comparing these measurements to the results of high speed video-grammetry the authors conclude that their method was suitable to derive accurate enough motion data for the entire jump action .

Equipment Related Safety Aspects in Skiing and Snowboarding Equipment related safety aspects in Skiing and Snowboarding are addressed in three contributions. Jasper SHEALY (USA) examines the distribution of stated primary cause of death as a function of helmet utilization for the last five winter seasons in U.S. His results suggest that while helmets may be effective at preventing minor injuries , they have not been shown to reduce the overall incidence of fatality in skiing and snowboarding. (Please note: This paper is printed in the "Safety Section" of these Proceedings). Richard GREENWALD and colleagues (USA) present and validate a novel brace for preventing wrist fractures in snowboarding. With impact testing they compared the stabilizing effects of their prototype to those of a commercially available wrist guard . (This paper is also printed in the "Safety Section" of these Proceedings). An overview of 15 years of work in the field of skiing equipment is given by SENNER and co-workers (Germany). They present their approaches to prevent knee injuries, deal with the problem of ski bindings' inadvertent release and show some aspects regarding the interaction between binding function and ski design . Future prospects on ski equipment research are summarizing their contribution.

Laboratory Device for Measuring the Friction Between Ski-Base Materials and Ice or Snow Mathieu Fauve, Lukas Baurle, Hansueli Rhyner WSL, Institute for Snow and Avalanche Research (SLF), Davos, Switzerland, [email protected]

Abstract Today's knowledge of ski friction is mainly based on experience from field testing

with real skis. A systematic investigation of ski frict ion in field conditions however, is difficult, since snow properties and weather conditions can vary rapidly during outdoor tests. An efficient field test conducted with an accurate and continuous snow characterization is both time consuming and expensive. In order to avoid the high uncertainties of field testing, a large-scale laboratory tribometer, which measures the friction of a small ski sample on ice or snow was built. The sample is attached to the measuring arm which is placed on a revolving rink of ice or snow. Additional weights can be mounted on the arm to vary the load. The operating temperature can be set between -20°C and O°c. Velocity at the position of the sample can be varied between 0.5ms· 1 and 20ms· l • Infrared sensors measure the temperature evolution of the track over time during the friction tests. In addition, procedures were developed to create different ice roughness and snow hardness. Preliminary results show a good correlation between the field and laboratory measurements. This device allows for more accurate, faster and cheaper testing of ski-base materials or surface treatments.

1 Introduction Sliding on snow has been studied for a long time. Yet it was only 1939 when Bowden and Hughes showed that the water film that enables low kinetic friction is caused by frictional melting. The influence of snow characteristics on the sliding friction was analysed by several researchers (Eriksson 1955; Colbeck 1992; Nachbauer 1996; Moldestad 1999; Buhl, Fauve and Rhyner 200 I; Fauve et al. 2005). Most of these studies rely on results of field testing. However, field testing remains time consuming, is relatively expensive , and can lead to false judgement if conducted without proper snow and weather characterisation during the testing (Fauve et al. 2005) . Some groups have therefore set up experiments to study under laboratory conditions the friction between different materials and ice or snow (Bowden and Hughes 1939; Lethovaara 1987; Buhl et al. 2001; Ducret et al. 2004) . It was recognized early that the warming of the ice/snow track, as well as the vibrations of the device can present a problem . Thus small tribometers using low sliding velocities, which are not representative of actual skiing conditions , were often used. Our aim was therefore to built a laboratory device which can measure friction at velocities

252

Mathieu Fauve, LukasBaurle, Hansueli Rhyner

encountered in real skiing while at the same time measuring the track surface temperature . The device should also be accurate enough to measure low differences between current ski-base preparations. In order to analyse the adequacy of the device and to optimise its development, comparative tests between field and laboratory measurements were made.

2 Experimental Set-Up 2.1 General Description of the Tribometer The tribometer consists of a 1.80m diameter rotating table filled with ice or snow, of one arm for holding the sample and measuring the friction force and of another arm for fixing snow and ice preparation tools (Fig. I).

Fig. 1. Ice and snowtribometer

In order to avoid undesired vibrations, the table is directly attached to the concrete ground. Normal force can be varied by applying dead loads of 10,20 and 30N. Frictional force is measured at a frequency of maximum 100Hz via a strain gauge load cell. The relative velocity at the location of the sample can be varied between 0.5ms· 1 and 20ms· l • The rotational speed of the tribometer is measured continuously using a magnet encoder.

Laboratory Measuring Device of the Friction Between Ski and Ice or Snow

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The device is placed in a cold room whose temperature can be set between -20°C and O°e. The humidity in the cold chamber oscillates between 60% and 80%. Infrared temperature sensors measure the temperature of the track in front of and behind the sample (fig. 2).

2.2 Sample Preparation The samples consist of aluminium plates onto which different materials are glued (Fig . 2). The size of the sample can vary between 40 to 200mm (length) and 5 to 70mm (width). A soft foam rubber is placed between the sample and the force sensor in order to assure a flat, parallel contact and to damp the small unevenness of the track and vibrations. A special equipment enables to grind the small size samples using a traditional ski grinding machine .

Fig. 2. Sample fixed to the friction force sensor of the measuring arm with infrared surface temperature sensors in front of and behind the sample .

2.3 Ice and Snow Preparation A steel bar is used to cut a perfectly flat ice surface (Fig. I). For the experiments, an elevated track is created, in order to avoid the slider to cut into the ice. Special cylinders with given surface roughness can be mounted to roll on the ice track and produce a defined ice surface topography. For measurements on snow , special procedures were developed in order to obtain homogeneous and sufficient hard snow.

254

Mathieu Fauve, Lukas Haurie, Hansueli Rhyner

3 Results In order to verify the usefulness and accuracy to the tribometer, tests were carried out in the laboratory and on the field with the same sliding materials. During theses comparative tests, three different polymer base materials, denominated A, Band C, were tested on three downhill skis as well as on three 70mm x 20mm laboratory samples . Skis and samples were grinded and waxed the same way .

3.1 Testing Conditions The downhill skis were tested in summer 2005 in Kaunertal, Austria during two test days . The snow was hard and coarse grained on both days. The snow surface temperature was constant at -8°C +/- 0.5°C during the first day and increased from 2°C to O°C and was slightly wet at the end of the second day. The air humidity was around 65% on both days . A top level skier tested the skis three times during each day. The average gliding time was around 19.5 seconds on the first day and 21.1 seconds on the second day. In order to analyze both days independently of the gliding times, the parameter DifCTime was introduced. This parameter corresponds to the time difference per second of sliding between one ski and the mean sliding time for all skis. The laboratory tests were carried out on the tribometer at a speed of 7ms· 1 at -1°C and -10°C on a flat ice surface . The pressure applied on the small samples was 30kPa, which corresponds to the static pressure applied by a 80kg skier on a downhill ski. The air humidity in the cold room was 70%. The friction tests with the small samples were repeated three times for each temperature. After a run-in period of 30 s, the friction coefficient was measured for 10 seconds and averaged. The measured coefficients offriction were between 0.026 and 0.082 . The parameter Diff, COF was introduced in order to minimize the influence of different ice surface preparations on the coefficient of friction . The parameter Diff-COF corresponds to the difference in percent between the friction coefficient measured for one sample and the mean friction coefficient for all samples at a given temperature.

3.2 Comparison Between Field and Laboratory Measurements The results of the field tests show a big difference in the sliding properties of the three ski-base materials (Fig.3). Skis with the base material B were the fastest for both cold and wet conditions (a negative value of Diff" Time indicating a faster ski than the mean ski). Base material C was the slowest especially for cold conditions. Figure 4 displays the results of the laboratory tests which show the same trend as observed during the field tests. The field and laboratory testing conditions were not exactly identical , nevertheless, the correlation coefficient between these tests for warm and cold conditions is 0.93 and 0.84, respectively, which suggests very good correlation.

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4 Conclusions The tribometer enables an accurate measurement of the friction coefficient of different ski-base materials on ice and snow at high sliding velocity with a good control of the track temperature. Such testing at constant conditions presents a major advantage in comparison to field testing, where to many factors can influence the results . The comparison between field and laboratory tests shows a very good agreement. Nevertheless, more comparative tests should be conducted on other snow conditions in order to be able to reproduce other real conditions in the laboratory. The tribometer can be very useful for the selection of the best ski-base surface treatment for specific snow conditions. It can also be used for the testing of new base materials or surface treatments. Apart from ski bases , other equipments like ski edges or skins for back-country skiing can also be tested with the tribometer. In parallel to such comparative tests, the device is also being used for fundamental research with the aim of developing a snow and ice friction model (to be published).

Acknowledgment Authors would like to thank the companies Stockli Skis and Toko for the good collaboration during this project and the Commission for Technology and Innovation (CTI) for its financial support .

References Bowden, F.P., Hughes, T.P. (1939) The mechanics of sliding on ice and snow . Proc. R. Soc. London, Ser A 2117, 280-298. Buhl, D., Fauve, M., Rhyner, H.U. (2001) The kinetic friction of polyethylene on snow: the influence of the snow temperature and the load. Cold Regions Science and Technology 33, 133-140. Colbeck, S.c. (1992) A review of the processes that control snow friction. CRREL Monograph 92-2, U.S. Army Regions Research and Engineering Laboratory, Hanover. Ducret, S. et al. (2004) Friction and abrasive wear ofUHMWPE sliding on ice. Wear. Res. 99, 110-118. Eriksson, R. (1955) Friction of runners on snow and ice. SIPRE Report TL 44, Meddelande 34/35, 1-63. Fauve, M. et at. (2005) Influence of snow and weather characteristics on the gliding properties of skis. Science and Skiing 3, 401-410. Kuroiwa , D. (1977) The kinetic friction on snow and ice. Journal of Glaciology 19 (81), 141152. Lethovaraa, A. (1987) Influence of vibration on the kinetic friction between plastics and ice. Wear 115, 131-138 Moldestad, D.A. (1999) Some aspects of ski base sliding friction and ski base structure. PhD . Thesis Norwegian University of Science and Technology. Nachbauer, W. et al. (1996) Effects of snow and air conditions on ski friction . Skiing Trauma and Safety : Tenth Volume , ASTM STP 1266, 178-185.

Biomechanical Instrumentation of the BergIsel Jumping Hill in Innsbruck and Exemplary Analyses

Kurt Schindelwig, Werner Nachbauer University Innsbruck, Austria, kurt.schindelwig@uibk .ac.at Abstract. During the rebuilding of the BergIsel ski jumping hill, a new biomechanical measurement system was installed . The system consists of seven force platforms which were placed about 10.5 m along the jumping table and six high speed cameras to film the take-off and the flight phase s. Five elite ski jumpers, each with three training jumps, were analyzed. In order to assess the accuracy of the measuring systems, velocity of the centre of mass during take-off was calculated from the kinematically and dynamically measured data and then compared. Additionally, each jump was digitized three times by two different persons to determine the error of semimanual digitizing. The results showed that the velocity of the centre of mass differed by an average of 5 % with a maximum difference of 30 %. The maximum difference between the repeated digitized data of the joint angles was three degrees. From the results we concluded that the data are good enough for prec ise describing j umping movement of elite ski jumpers. However, the large differences between the two methods of calculating velocities of the centre of mass must be further examined.

1 Introduction The most recent studies of ski jumping describe the correlation between special parameters such as take-off velocity or rotation impulse at take-off and the jumping distance (e.g. Arndt et al., 1995; Schwameder & MUller, 1995; MUller et al., 1996; lost et al., 1997, 1998; Virmavirta et al., 2005). Before this project, a ski jumping hill equipped with a kinematic and dynamic measuring system did .not exist in Austria . The aim of this work was to develop a measurement system allowing precise and rapid determination of kinematic and dynamic parameters at the BergIsel jumping hill. Comparisons of the velocity of the centre of mass calculated by the kinematic and dynamic measuring data were used to assess the accuracy of the measuring and analysis system .

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Kurt Schindelwig

2 Methods 2.1 Measurement Devices For kinematic recording of take-off, a field of view of 7 m be fore to 2 m behind the jumping table was filmed with two high speed cam eras with a sampling frequenc y of 230 Hz and a resolution of 1024 x 512 pixel (Vosskiihler, Typ HCC-IOOO CMOS) (Fig 1.1). For the flight phase, four high speed cameras with a sampling frequ ency of 60 Hz and a resolution of 1280 x 5 12 pixel (ISG LightWi se, Typ LW-I.3-G-1 394 ) were mounted (Fig. 1.2). Three photoelectric beams were installed at the position 10.5 m, 6.5 m and 0 m on the jumping table (Fig. 1.3). They were used for triggering the kinematic and dynamic mea suring system s and determining the horizontal velocity. Th e three force components were sampled (1000 Hz) by seven force platforms (KISTL ER, Typ Z 1840 1-100) , whi ch were fixed about 10.5 m along the jumping table (Fig. 1.4). Two wind gauge s were installed next to the jumping table .

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Biomechanical Instrumentation of the Berglsel Jumping Hill

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2.2 Data Collection Five elite Austrian ski jumpers were recorded during three training jumps under windless conditions (speed of wind less than 0.5 m/s). The force data were smoothed with cubic splines . A special software program using Labview 7.1 (National Instruments) was developed in order to digitize the image coordinates of the joint points. The software permits automatic tracking with manual correction . From the image coordinates the 2-d coordinates of the joint points were determined by the DLTmethod. The 2-d coordinates were smoothed with quintic splines. Every jump was digitized three times by two different persons . The velocity of the centre of mass was determined in two different ways. In the first method, a six segment model of the ski jumper's body was used to compute the centre of gravity and its velocity was determined from the first derivative of the smoothed coordinates . In the second method the measured force normal to the jumping table was integrated numerically. The dynamic calculation did not include the aero dynamical lift.

3 Results The maximum difference between the repeated digitized data of the joint angles was three degrees (Fig. 2). The maximum velocity difference of the centre of mass between the multiple digitalisations was 0.15 m/s. maomsm differ ence

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4 Discussion The results show that the system described precise the angles of the body segments during ski jumping. However, the large differences between the two methods of calculating velocities of the centre of gravity must be further examined . One possibility is the large influence of the angle of trunk inclination on lift. The influence of lift will be determined through wind tunnel readings in future projects .

References Arndt, A., Briiggemann , G.-P., Virmavirta, M., Komi, P.V. (1995) Techniques used by Olympic ski jumpers in the transition from take-off to early flight. Journal of Applied Biomechanics 11,224-237. Jost, B. Kugovnik, 0 ., Strojnik, V., Colja, I. (1997) Analysis of kinema tic variables and their relation to the performance of ski jumpers at the World Championship in ski flights at Planica in 1994. Kinesiology 29 (I), 35-44 . Jost, B. Vaverka , F., Kugovnik, 0 ., Coh, M. (1998) Differences in selected kinematic flight parameters of the most and the least succesful ski jumpers of the 1996 World Cup competit ion in Innsbruck. Biology of Sport 15 (4),245-251.

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Muller, W., Platzer, D., Schmeltzer, B. (1996) Dynamics of human flight on skis: improvements in safety and fairness in ski jumping. Journal of Biomechanics 29, 1061-1068. Schwameder, H., Muller, E. (1995) Biomechanische Beschreibung und Analyseder VTechnik im Skispringen. Spectrum I, 5-36. Virmavirta, M., Isolehto, 1., Komi, P., Bruggemann, G-P., Muller, E., Schwameder, H. (2005) Characteristics of the early flight phase in the Olympicski jumping competition. Journal of Biomechanics 38, 2157-2163

Dynamic Properties of Materials for Alpine Skis Christian Fischer', Mathieu Fauve", Etienne Combaz':", Pierre-Etienne Bourban ' .Veronique Michaud', Christopher J.G . Plummer', Hansueli Rhyner' and Jan-Anders E. Manson! Laboratoire de Technologic des Compositeset Polyrneres (LTC), Ecole Polytechnique Federalede Lausanne(EPFL), Switzerland, [email protected] 2 WSL, Institute for Snow and Avalanche Research (SLF), Davos,Switzerland !

Abstract. The aim of the present research has been to quantify the influenceof different materials on the global dynamic response of a ski. The properties of the individual constituent materials were characterized as a function of temperature and frequency using dynamic mechanical analysis. At the same time, the dynamic behavior of skis with different designs was investigated in a cold room at between -15 and 25°C using specially developed apparatus. The results indicated the overall behavior to be influenced significantly by the polymeric topsheet, which showed a strong damping peak at about 0 "C. Elasticity-based FEA accounted well for the experimental results for the two first flexural vibrational modes of the skis. For higher modes, however, the viscoelastic nature of the polymeric components led to significant discrepancies betweenthe predicted and observed behaviors.

1 Introduction A principal aim of ski manufacturers in recent years has been to reduce vibration in various ways . Skis completely devoid of vibration nevertheless do not procure good sensations for the athlete, so that it is crucial to discriminate between those frequencies that should be damped to increase performance, and those that are important for the skier 's "feel". New test methods have therefore been developed to analyze the dynamic properties of skis . Understanding how skiers apply forces and how vibration patterns affect the feel of a snowboard or a ski should allow a more rational approach to design and improve overall performance. The dynamic properties of skis were first investigated systematically in 1972 (Piziali and Mote 1973). G1enne et al. (Glenne, Jorgensen and Chalupnik 1994) subsequently compared different measurement devices, showing that small amplitude tests such as the ISO test may not be representative of field conditions. More recently, various groups have integrated the boot/binding system into their analyses so as to reproduce real skiing conditions more accurately (Glenne, DeRocco and Foss

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Christian Fischer et al.

1999; Casey 200 I). Comparison of the results with results obtained from freesuspension tests demonstrated the important role of the boot and binding in cutting off high frequencies . The behavior of skis on snow has also been studied in situ using accelerometers (Nemec 200 I), leading to the conclusion that carving skis result in less vibration during turns by preventing skidding. Nevertheless, resonance may still occur and is often detrimental to performance in that it reduces ground contact, so that the skier is no longer able to continue the carved tum . Highamplitude deformations at low frequencies are of particular concern in this respect. Comparatively little attention has so far been paid to the influence of the constituent materials on the dynamic response of skis, although it is known that they may playa significant role (Scherrer, Bidaux, Kim, Manson and Gottardt 1999). The aim of the present work has been to investigate the contribution of selected components to the global behavior, with emphasis on its temperature dependence. To this end, the mechanical properties of the different materials that constitute the ski have been characterized independently and then linked explicitly to experimental results for the vibrational properties of the entire ski by finite element analysis (FEA).

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2 Materials and Methods A schematic of the cross-section of a competition ski is given in Fig. 1. Each part of the sandwich structure has a specific function . The topsheet is intended as a protective layer. The wood core, which has a non-uniform thickness, giving a smooth bending profile, plays an important role in stiffness and damping. The glued aluminum alloy /composite (usually a glass fiber-epoxy laminate) stack that constitutes the upper and lower faces of the ski determines stiffness in bending and torsion. The only material whose characteristics are essentially identical in different skis is the aluminum alloy, specifically developed for ski applications and said to show an optimum combination of stiffness and weight. In the course of the present investigation, skis with various types of sandwich structure were considered, differing in the construction of the upper and lower faces, the face thicknesses and presence or ab-

Dynamic Properties of Materials for Alpine Skis

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sence of the polyamide topsheet. However, the following discussion will concentrate on the influence of the topsheet and the structure of the upper face. The ski with the topsheet is referred to as ski A, and an identical ski without the topsheet (replaced by a simple powder surface coating), is referred to as ski B. Ski C contained an additional layer of cured epoxy impregnated glass fiber mat glued to the aluminum layer of the upper face. Ski D was identical to ski C without the additional composite layer.

2.2 Dynamic Mechanical Analysis (DMA) Specimens from the topsheet were clamped at both ends and subjected to dynamic deformation in torsion, using a strain-controlled Rheometries ARES rheometer. The remaining materials, which were significantly stiffer than the topsheet, were tested in three-point bending using a Rheometric Solids Analyzer (RSA). 52 x 12 mrrr' specimens were used throughout, but their thickness varied according to the material.

2.3 Ski Testing The Skitester 2004 is a device specifically developed for dynamic testing of whole skis and snowboards. The principle is to measure the acceleration after a standardized shock imparted to a ski clamped at the position of the binding. A small hammer hits the front of the ski, close to its edge, exciting both torsional and flexural vibrational modes. The corresponding displacements are measured by laser reflection. The experiments were performed at temperatures ranging from -15 to 25 °C.

2.4 Finite Element Analysis (FEA) Elasticity-based FEA (Ansys 8.1) was used to verify the measurement technique and the experimental results. The ski was represented by a multi-layer mesh incorporating elastic material parameters extracted from DMA measurements at room temperature and a frequency of 1.5 Hz. It was composed of perfectly bonded 3D elements whose thickness corresponded to that of the thinnest layer of the structure.

3 Results and Discussion 3.1 Vibrational Modes and FEA The first five resonance frequencies for ski A obtained experimentally at 25 °C and calculated using FEA are shown in Table I. The agreement between the calculated and observed behavior for the first two vibrational modes was good. For higher modes, however, it was poorer. This was due to the viscoelastic nature of the polymer-based materials in the sandwich structure (glues, composite laminates, wood, the topsheet). Viscoelastic effects have not so far been incorporated into the calculations, but become increasingly importantas the frequency increases.

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3.2 Influence of the Topsheet Fig. 2 shows the I st resonant frequencies of ski A and ski B at different temperatures, showing consistently lower values for ski A than for ski B. This was attributed to the increased damping of the ski from the polyamide topsheet, this generally tending to reduce the resonant frequency (Balachandran and Magrab 2004) . The resonant frequency of ski B decreas ed monotonically with increasing temperature. However, ski A showed a signifi cant minimum at 0 "C. Table 1. Resonant frequencies for ski A at 25 °C determined experim entally and predicted using FEA . Mode

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Fig. 2. Comparis on of the I st resonant frequen cy of ski A (left) and ski B (right) at different temperatures. These measurements were carried out using accelerometers placed on the ski rather than laser reflect ion. The added weight of the accelerometer also reduced the resonance frequencies somewhat (cf. Table I), but had no effect on the relative influence of the topsheet.

The mechanical response of viscoel astic materials is sensitive not only to temperature but also to strain rate. This is illustrated in Fig. 3(a) , which show s taniivs. temperature for the topsheet at different constant angular frequencies , OJ. The tanO values reflect the damping capacity of a material and are equi valent to the loss factor, 7], at low damping levels (Graesser 1992). The results in Fig. 3(a) clearl y show the damping peak , associated with the glass transition in polyamides, to shift to higher temperatures as OJ is increased. Th is peak dominates the temperature regime charac-

Dynamic Propertie s of Materials for Alpine Skis

267

teristic of service conditions for an alpine ski, which explains the minimum in the resonant frequency for ski A at 0 °C (cf. Fig. 2). To gain an idea of the dynamic properties of viscoelastic materials at frequencies beyond those that are directly accessible experimentally, time-temperature superposition is often used (Ferry 1980). Fig. 3(b) shows time-temperature superposition of the elastic modulus G ', the loss modulus G", and tand for a reference temperature of o"C. The damping peak appeared at OJ in the range 10 - 90 radls ((between about 1.5 and 15 Hz) . This was consistent with the dynamic behavior of the skis in Fig. 2. Ski A, with the topsheet, showed a maximum loss factor at 0 °C for the first resonant frequency (84.2 radls or 13.4 Hz), whereas ski B, without the topsheet, showed a continuous decrease in loss factor as the temperature decreased from 25 to -20 °C. .[0.,--

'ET

- - - --

-

-

-

-

--,

F--:::-...--_.,......_.,......-..--_.....-l''"'-l

001

01

10

100

1000

frequency. .. (nodi.)

Fig. 3. (a) Evolution of the main damping peak of the polyamide topsheet as a function of applied frequency and (b) time-temperature superposition for a reference temperature of 0 "C. 008 '0' '02

r:: i

OS

c::J 2S' C _ O'C _ ·20"C

(a)

001

c::J 2S' C O'C _ ·2O"C

lbl

006 :';005

~00' II

,i003

j

0 02 00' 000

Fig. 4. (a) l" resonant frequencies of ski C and ski D at different temperatures and (b) the corresponding damping properties.

3.3 Influence of Variations in the Structure of the Upper Face The influence of the additional epoxy-glass fiber mat in the upper face of ski C is shown in Fig. 4, which also give results for ski D. In this case, although the increase

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Christian Fischer et al.

in stiffness associated with the presence of the additional glass mat clearly increa sed the structure' s I st resonance frequency (Fig. 4(a » , it had relativel y little influence on damping behavior (cf. Fig 4(b» . The stiffne ss could also be increa sed by using thicker alum inum plates for the sandwich faces . Howe ver, this led to an undesirable increase in the overall weight of the ski and to significantly decre ased damp ing.

4 Conclusions The influence of the constituent materials properties on the overall dynamic behavior of skis has been investigated. The results indicated the overall behavior to be influenced significantly by the polym eric topsheet, which showed a strong damping peak at about 0 "C. Elasticit y-based FEA accounted well for the experimental results for the first two flexural vibrational modes of the skis . For higher modes, however, the viscoelastic nature of the polymeric components led to increasing divergence between the predicted and observed behaviors. In future work , it will therefore be necessary to introduce more complex model s that take into account these effect s.

Acknowledgements The authors gratefull y ackno wledge the Stockli Ski Comp any for materials and skis, the Interstate University of Applied Sciences of Technology Buchs for designing the Skitester 2004, and the Sport s and" Rehab ilitation Engine ering (SRE) program of the EPFL for financial support.

References Balachandran, B. and Magrab, E.8. (200 4) Vibrations. Brook s Cole, Pacific Gro ve, CA. Casey, H. (200 1). Materials in ski design and developm ent. In: Materials and Science in Sports, Froes, F.H. and Haake, SJ. (Eds.), TMS, Warr endale , PA, pp. 11-17. Ferry, J.D . (1980) Viscoelastic Properties ofPolym ers, Wiley, New York. Glenne, B., DeRocco , A. and Foss, G. ( 1999). Ski and Snowboard Vibration. Sound Vib. 33(1), 30-33. Glcnne , 8. , Jorgensen , J.E. and Chalupnik, J.D . ( 1994) Ski Vibration s and Damping. Exp. Techniques 18(6), 19-22. Graesser, EJ. and Wong , C.R. (1992) The Relationship of Traditional Dampin g Measures for Materials with High Damping Capacity: A review. In: lvtD: Mechanics and Mechanisms of Material Damping , Kinra, W. and Wolfenden, A. (Eds.), ASTM , Philadelphia, pp. 316343. Nemec, 8. , Kugovnik, 0 ., Supej , M. (200 1) Influence of the Ski Side Cut on Vibration s in Alpine Skiing. Sci. and Skiing II, 232-24 1. Pizial i, R.L. and Mote, C.D. (1973). Snow Ski as a Dynamic System. Mech. Eng. 95(2), 5252. Scherrer, P., Bidaux, J.-E., Kim, A., Manson, J.-A.E. and Gottardt, R. ( 1999) Passive vibration Dampin g in an Alpine Ski by Integration of Shape Memory Alloys. J. Phys.I V 9, 393400.

Calculation of Friction and Reaction Forces During an Alpine World Cup Downhill Race Michael Sch iestl', Peter Kaps ', Martin Messner', Werner Nachbauer' University ofI nnsbruck, Department of Engineering Mathem atic s, Geometry, and Computer Science, Michael @Schiestl.name 2 University of Innsbruck, Department of Sport Science , [email protected] I

Abstract. Understanding friction and reaction forces involved in Alpine Skiing is of great theoretical importance for sport science. We have developed a method to analyze a skier's motion during a downhill race from video data taken by a single camera. This may help to compare the technical equipment and the skills of different skier s.

1 Introduction In the following we will present a method to reconstruct the trajectory of a skier from motion pictures taken by a single camera. This will allow us to set up the equations of motion on the measured path in order to calculate the friction and reaction forces . Finally, we will present the results of the analysis for Stefan Eberharter' s downhill race during the Alpine World Cup in Kitzbuhel in 2002 .

2 Method 2.1 Surface generation The calculation of an object's position visible on just a single picture requires the object to be located on a known surface - in our case the skiing slope. Therefore, the first kilometer of the famou s skiing slope Streif in Kitzbuhel was geodetically surveyed by measuring the position of approx. 550 terrain points with a theodolite. Then, a mesh describing the snow surface was generated by triangulation of the terrain points (see Fig. I) . To guarantee realistic results it is of importance that the skier's trajectory is reconstructed on a preferably smooth surface or - more precisely - on a surface with continuous first derivatives, also called Gl-surface. In our case the terrain points were distributed irregularly - a fact that restricts the possible methods. We chose the Clough-Tocher algorithm which generates a G I-surface from any given triangulation

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(Hugentobler 2004). This way we obtained a parameterization of the snow surface of the form z = z(x , y ) with (x,y ) being the horizontal , and z the vertical Cartesian coordinate (terrain altitude).

2.2 The DLT The direct linear transformation (DLT) is a well known photogrammetric method for reconstructing an object's position from image data. However, the calculation of 3-D coordinates of a moving object is only possible if either multiple pictures are available which are simultaneou sly taken by several cameras or the object is located on a known surface. Furthermore , a minimum number - depending on the type of algorithm - of visible pass points with measured position coordinates is required. Generally, the more pass points on an image the better the precision of the result. We have modified the DLT algorithm as described e.g. by Kwon (1998) in two respects: Firstly, we solved the DLT equations on the Clough-Tocher G'<surface describing the skiing slope. Secondly, we improved the DLT' s precision by exploiting the fact that when a series of pictures is taken by the same camera , e.g. during a motion video, several camera parameters remain constant and do not have to be recalculated every frame. This way - if e.g. the camera ' s position is known - fewer pass points are required and the precision of the measured data is improved. This advance could be achieved by transforming the II DLT parameters describing the camera projection into a new set of paramet ers which can be interpreted in a more useful way, namely the camera ' s position and orientation as well as zoom and distortion factors. This way situation-specific equations could be derived that can be used to improve the accuracy of the measurement in many cases (SchiestI2005).

2.3 Reconstruction of the Trajectory The positions of the left and right ski binding were reconstructed on large parts of the surveyed track. The images taken at a frame rate of 25 picture s per second allowed a sufficiently precise reconstruction of the skier's motion during a time period of 10 seconds on the whole. The mean value of the left and right ski was taken as an approximation of skier 's center of mass. We received the trajectory by smoothing the data during three different steps: • The image coordinates of the pass points and ski bindings were slightly smoothed. • The reconstructed positions x(t;), yeti) and Z(ti) were smoothed as a function of time. Cubic spline function s were used to approximate the data points. • For each data point calculated in step 2 the curve length l, was determined. Then the set of data points (ti,!;) was taken to evaluate smoothed curve lengths L; at the same times ti. Finally, the data points (X(ti),Y(ti),Z(t;)) having the smoothed curve length L, were calculated . Any further analysis resorts to the curve fitting these positions.

Calculation of Friction and Reaction Forces Duringan Alpine Downhill Race

271

Note that the third step does not change the shape of the trajectory, however it smoothes the accelerations along the path.

2.4 Calculation of Friction and Reaction Forces Let the measured trajectory be a curve

;:(1):=(x(I), Y(I ). Z(IWparameterized

time t. From Newton' s Law the skier' s equation of motion can be written as mF(1) = Fx + FJ + F;. with m being the skier' s mass, F<:= (0. O.- mg

r

the gravity force ,

F;.

by the (I)

being any

energy cons ervati ve force and FI repre sent ing non con servative resistance forces such as kinetic and air friction as well as the resistance in tangential direction due to the snow spray of the carving edges (Hirano and Tada 1996). Note that F;. arises from the constraint of ;:(1) being restricted to values on the measured trajectory - in

F;. can be regarded as the reaction force . F;. doe s not perform work, hence F;. must be orthogonal to the skier's velocity vector t . in other word s f: . F;. = 0 . Analogously, the friction force is other word s

By definition

parallel to the velocity:

IIFf II= FJ . f: 111f:11.

Let iJ := mF - Ff( ' Then dot-multiplying Eq. I with

Fr

=

(0 .;')F/II FI1

2

F gives : F;. =iJ-Ff

(2)

3 Results In the following we will present the results for Stefan Eberharter's run during the Alp ine World Cup downhill race in Kitzbiihel 2002 . Thre e parts of the section known as "Mausefalle" as well as the " Steilhang" were succe ssfull y recon structed and analy zed, in Fig. 2-5 the second and third part of the Mausefalle are shown . The prec ision of the measured traject ory strongly depends on the number and the quality of the pass points. In favorable parts of the track the accuracy can be expected to be just a few centimeters and less. The accuracy of the reaction and friction forces is worse (approximately +/- 20 %) due to the second derivatives involved in the calculation. Also keep in mind that the reaction force includes the skier's body weight of 100 daN.

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... .. .........

.,.

"

X (m)

Fig. 1. The triangulated starting area of the Streif

Fig. 2. The reconstructed trajectory Mausefalle part 2

""'I

...

'SO

'''~ f ~

~~~

--=:::::::

so Incoon Iote- IdaN)

.. .. ,

r_'I_1

.. .. ..

Fig, 3, Results Mausefalle part 2

Calculation of Friction and Reaction Forces During an Alpine Downhill Race

70

eo 50

I

>

30

20 10

o - 10

- 20

eo

o

20

-eo

- 20

X(m)

Fig. 4. The reconstructed trajectory Mausefalle part 3

250 ,....---r--,.--~--,----.-- -~-~--~---,

200

'50 100

50

- 50 - 100 - 150 _2OOL---'-_ _ 8~

9~

'0

ios

11

T,meI [sec]

Fig. 5. Results Mausefalle part 3

12~

13

273

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Michael Schiestl et al.

4 Discussion The reaction force curve assume s values up to 240 daN. Thu s, the forces acting on the leg exten sion muscles of a skier can reach critical values dur ing short periods of time . Friction value s of 50 daN and larger are fairly high and might be reduced by better equ ipment and skiing technique. The calculated friction consists of the air res istance and the tangential resistan ce between ski and snow. For straight running or traversing the snow friction can be modeled as Coulomb friction (Kaps et al 1996). Yet, it seems that during turn s other friction mechanisms have to be considered, e.g. the tangential resistance due to the snow spray of the carving edge s. Attempts to calculate drag and friction coefficients ceY4 and J1 without such effect s failed. However, the development of more advanced friction models might require the measurement of parameters such as the angle between ski axis and ski velocity which plays an important role for skidding. To determine this angle the accuracy of the measurements has to be improved.

5 Conclusion This study show s that the friction and reaction force s act ing on a skier can be measured during a competition without interfering with the athlete. By using better cameras and more pass point s one could impro ve the accuracy of the measurement greatly allowing a refined anal ysis of friction model s in future studies using this method .

References Hirano, Y., Tad a, N. ( 1996) , Numerical simulation a/a turning alpine ski during recreational skiing, Med icine and Science in Sports and Exercise, Vo l. 28, pp. 1209-1213 . Hugcntobl er M. (2004), Terrain Modelling with Triangle Based Free-Form Surfaces , PhD Thesis, University of Zurich, Mathem atical Facult y. Kaps P., Nachbauer W., and Mossner M. ( 1996). Determination ofKinetic Friction and Drag Area in Alpine Skiing. Skiing Trauma and Safety: Tenth Volume, ASTM STP 1266, Mote C. D., et al., Ameri can Society for Testing and Materials, pp. 165-177. Kwon Y.H. (1998), DLT Method, http ://kwon3d.com/theory/dlt/dlt.html. Schi estl M. (2005), DLT Data Reconstruction on Clough- Tocher Interpolated G' -Surfacesfor Simulation in Alpin e Skiing. Diplom a The sis, University of Innsbruck, Mathematical Faculty , http ://Michael .Schiestl .name /publications.

Measurement of Jumper's Body Motion in Ski Jumping

Yuji Ohgi ', Kazuya Se0 2, Nobuyuki Hirai' , Masahide Murakami 3 Graduate School of Media and Governance, Keio University, Japan, ohgi@sfc .keio.ac.jp of Education, Art and Science, Yamagata University, Yamagata, Japan 3 Graduate School of System and Information Engineering, University of Tsukuba, lbaraki, Japan J

2 Faculty

Abstract. The authors propose motion analysis of ski j umping by data logging method using inertia sensors. A tri-axial accelerometer and a single axial gyroscop e were attached onto the j umper's body. Simultaneously, high speed cameras were equipped for the image capturing in order to obtain the jumper's motion from the take-off and the middle phase of the flight. The characteristic s of the ski jumper during whole phases were identified by using the inertia sensors.

1 Introduction Flight dynamics of ski jumping through the whole phases has not been explained. As for the biomechanical aspect, kinematical and kinetical methods were applied in the field studies (Babiel, Hartmann, Spitzenpfeil and Mester 1997; Kaps, Schwameder and Engstler 1997; Kom i and Virmavirta 1997; Yamanobe and Watanabe 1999). Aerodynamic approaches were also examined for the steady flight phase (Seo, Watanabe and Murkami 2004a ; Seo, Murakami and Yoshida 2004b). Most of these studies were conducted for the motion either on the slope or in the air. Total kinematical data measurement from the start, inrun , take-off, steady flight to landing was not reported. The purpose of this study was a kinematical measurement of ski jumping through all phases by using inertia sensors and high speed video cameras. Then authors intended to analyse a relationship between the sensor information and the jumper' s motion based on the video anal ysis.

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Yuji Ohgi et. al.

2 Methods 2.1 Field Measurement Figure 1 shows the schematic illustration of our experimental equipment. The authors applied a tri-axial accelerometer (Hitachi Metals Inc., H480A-2G5VR) and a single axial gyroscope sensor (Murata Corp ., ENC-03J) . For the data acquisition, a PDA (TOSHIBA GENIO, WindowsCE 2003) and compact flush AID converter (CCubed Ltd., Dataq CF2) were used . The sensor unit and PDA were located on jumper's low back at L5. Data sampling was taken on 256Hz. A local coordinate system was defined on the jumper's trunk . As for the gyroscope sensor, it rotated around y-axis of the local coordinate system (Fig. 2). Positive sign of the angular velocity means that the jumper takes forward tilting motion and negative corresponds to the backward tilting , vice versa . In the field measurement at Hakuba Ski Jumping Stadium, a high speed videography was also taken on the large hill slope . Three high speed video cameras were equipped from both side of the large hill slope . Two of those cameras (Photron Inc., Fastcam-R2, 250Hz) were configured from the left side at a distance of 15m to take both pre and post take-off phases . From the apposite right side, at a distance of 40m , another camera (Photron Inc., Fastcam-l024PCI, 500Hz) was set up for the wide range of the flight phase approximately 1.8 s. In this study , the ski jump is assumed to be performed on the sagittal XZ plane on the global coordinate system, which was located on the edge of the slope . Subject was a high school ski jumper (l71.0cm, 55Kg, four years career) . Jumper's head (helmet), hip, knee, ankle, toe, top and tail of the ski were digitized for analysis. Those digitized coordinates were once approximated to the 5th ordered polynomial equations, then reconstructed as the horizontal (X) and vertical (Z) coordinates.

2.2 Flight Dynamics Model of Ski Jumping In Fig. 2, U indicates a velocity vector of the center of gravity of the jumper-ski model. For our convenience, we assumed the hip joint to be a center of gravity in this study . And our sensor unit was also assumed to be attached on this location . In this figure, the jumper's trunk and lower extremities were combined as a single segment and its angle e, a. represented his flight motion in the air. e is the trunk angle to the horizontal plane, a. is angle between trunk and the velocity vector U.

Measurement of Jumper's Body Motion in Ski Jumping

277

Fig. 1 A schematic illustration of the sensor unit and the logging unit

Wy

x-axi al component L cos(7tl2 - 0) - [) cos z-ax ial co mponent L sin(7tl2 - 0) - D in

0. -

0. -

mg sin 0

; mg

mg co. 0

Fig. 2 Local coordinate system of the ski jumper. The gravity and the aerodynamic force exerted to the jumper-ski system were illustrated in figure. Drag and lift forces were disassemble to the sensor axis direction.

3 Results An example of results was shown in Fig. 3. The acceleration and the angular velocity have two different frequency components around the take-off. For that reason, the authors applied 7th ordered adaptive smoothing filter (Kawata-Minami filter), which is applicable to time series with spike peaks or instantaneous transient local peaks. Acceleration on x and z-axis of the sensor unit has large and high frequent vibration at the take-off instance. Similarly, the angular velocity steeply changed negative, then turned into positive again after take-off. After that, you can see that the angular

278

Yuji Ohgi et. al.

velocity indicated positive, which means jumper's forward tilting motion . The result shows that subject tried to do his forward tilting motion at least three times . Because the angular velocity (VI" has three local maximums after his take-off. This multiple tilting attempts of jumper were stable within subject through his all jump trials. Bar graph in Fig. 4 shows that duration time of the forward tilting (FT), steady flight (SF) and backward tilting (BT) phases among successful seven jumps. Forward tilting phase was determined by the interval between take-off transient acceleration peak and the moment when the angular velocity reached 0 deg/s. After forward tilting motion, the jumper kept steady flight phase . Finally, he draws up his upper body to the upright position to prepare his landing. So, backward tilting motion was distinguished by the angular velocity when it became negative. Mean and standard deviation of total flight time were 3.225±O.369s . The initial angle between jumper's trunk and horizontal line Oil and the angle between trunk and the velocity vector all were obtained from the video analysis.

,

e ~

]

~ <

· ID

.:<> .JAJ 1O

.JAJ

~"'1'D

t.o . l:

<

.0:

.'D

I

TI""" I

.:<> . )0

_jJOO f. .~._ _ ~ i I ~

:00 1(10

.JOO

00)'

> ~~-~:

T

IR

TO

LA

·100

<

.:00

TI""" I

10 I

Fig. 3 Acceleration and angular velocity of the ski jumper during whole jump (right), and pre and post take-off phase (left). Start (ST), Inrun (IR), Take-Off (TO) and Landing (LA) are indicated.

Measurement ofJumper's Body Motion in Ski Jumping

279

20

12

3

o

Landing

D

234

56

7

I

Backward tilting ready llight Forward lilting

Take -otT

Trial

Fig. 4 Initial trunk angle (eo), initial velocity (vo) of the jumper and his flight phase time distribution.

4 Discussions On the basis of simple model in Fig. 2, the authors assumed the center of gravity of the jumper-ski system to be located on his hip joint. And the upper trunk and the lower extremities were assumed a straight line. In addition, the ski is also assumed to be same segment with jumper. It is quite simple model of the jumper-ski system. Usually, the aerodynamic forces were taken into account that those act to the CG. Then drag and lift are decomposed to the orthogonal components on parallel and vertical direction to the velocity. However, in this figure, those decomposed forces were decomposed again with respected to the sensor sensitivity axis. Thus, composite forces act on the x and z-axis direction of the local coordinate system, which correspond to the sensor axis are formulated as below. L cos (7[/2-8) - D cosa - m g sine

(1)

L sin (7[/2-e) - D sino. - m g cost)

(2)

Since our used accelerometer is capable to measure static acceleration, so that, when we hold the sensor unit, it detects Ig. However, in case of free fall, it detects no gravitational acceleration on any axis. Therefore, we have to consider that no gravitational components, as terms mgsinil; mgcostl, would be observed. For the calculation of the drag and the lift, we need the time series of both Band 0. . As for e, it can be computed by the integration of the angular velocity w, (Fig.S). On the other hand, a. requires the tracked coordinates of CG and its velocity direction. First of all, we have to prove the integration of the gyroscope data forB. Then, we can carry on the

280

Yuji Ohgi et. al.

calculation of the drag and lift force . An examinat ion of those important aerodynamic forces is now being investigated.

50'

,,-....

401FT [

SF

~30 1

'2, 20 1
lO r

-L_ , ~~_~~=-~-=---.L~

TO

2

Time(s)

3

e,

Fig.S Jumper's trunk angle which was calculated by the integration of the gyroscope data . Initial angle eo was determined by the video analysis at the take-off. Forward tilting (FT) , steady flight (SF) and backward tilting (BT) intervals were indicated in the figure .

5 Conclusions The authors conducted a measurement of jumper's motion in ski jumping by using inertia sensors with the high speed videography. According to the obtained inertia sensors ' data, we could derive jumper's trunk motion during whole jumping phases . Also at the conference, the estimation of the aerodynamics will be presented.

References Babiel, S., Hartmann, U., Spitzenpfeil, P. and Mester, J. (1997) Ground reaction forces in alpine skiing , cross-country skiing and ski jumping., Science and Skiing, MOiler E. et al. (Eds) 200-207 . Kaps, P., Schwameder, H. and Engstler, G. (1997) Inverse dynamic analysis of take-off in ski jumping, Science and Skiing, Science and Skiing , MOiler E. et al. (Eds) 72-83 . Komi, P.V. and Virmavirta, M. (1997) , Ski-jumping take-off performance : Determining factors and methodological advances. Science and Skiing , MOiler E. et al. (Eds) , 3-26 . Seo, K., Watanabe, I. and Murakami , M. (2004a) Aerodynamic force data for a V-style ski jumping flight. Sports Engineering, 7, 31-39. Seo, K., Murakami , M. and Yoshida , K. (2004b) Optimal flight technique for a V-style ski jumping. Sports Engineering, 7, 97-104. Yamanobe, K. and Watanabe, K. (1999) Measurement of take-off forces in ski jumping competition , Japan ese Journal ofBiomechanics in Sports and Exercise , 3, (4), 277-286 .

Riding on Air: A New Theory for Lift Mechanics of Downhill Skiing and Snowboarding Qianhong wu', Yesim Igd, Yiannis Andreopoulos' and Sheldon Weinbaum' I

Villanova University , [email protected] Princeton University The City College of New York

Abstract. A simplified mathematical model is derived to describe the lift mechanics of downhill skiing and snowboarding, where the lift contributions due to both the transiently trapped air and the compressed solid phase (snow crystals) are determined. To our knowledge, this is the first time that anyone has attempted to realistically estimate the relative contribution of the pore air pressure to the total lift in skiing and snowboarding. The model uses Shimizu's empirical relation to predict the local variation in Darcy permeability due to the snow compression . The forces and moments on the skier or snowboarder are used to predict the angle of attack of the planing surface, the penetration depth at the leading edge and the shift in the center of pressure for two typical snow types, fresh and wind-packed snow . Our model predicts that, when there are no edging or turning maneuvers and the velocity of the snow boarder or skier, U = 20 mis, for fine-grained, wind-packed snow approximately 50% of the total lift force is generated by the trapped air for snowboarding and 40% for skiing . For highly permeable fresh powder snow the lift contribution from the pore air pressure drops substantially. The force and moment balance on the planing surface due to the trapped air and the snow crystals are then used to develop a theory for control and stability in response to changes in the center of mass as the individual shifts his/her weight.

1 Introduction Downhill skiing or snowboarding, in its simplest form, refers to the motion of a human sliding down an inclined plane on a porous medium . The extensive classic literature treating the science of skiing and snowboarding is summarized in (Lind and Sanders 1996). A major contribution in this literature is the pioneering work of (Colbeck 1991; 1992; 1994a; 1994b; 1995) on the reduced frictional force that results from the micron-thick fluid film that forms on the underside of the ski or snowboard due to frictional heating. More recently, Feng and Weinbaum (2000), hereafter referred to as F&W, have developed a new lubrication theory for highly compressible porous media which shows a remarkable dynamic similarity between the motion of red blood cells (RBCs) on the endothelial surface layer (ESL) that lines our microvessels and that of a human skier or snowboarder skiing on soft snow powder even though their difference in mass is of order 1015• F&W predict that the excess pore pressure generated by a planing surface moving on any compressible porous media scales as d = h2/K, where h is the layer thickness and K is the permeability,

282

Qianhong Wu et al. (h)

Fig. I. (a) . Schematic illustration of a snowboard or ski compressing a layer of snow powd er. (b) . Forces upon a skier as he/she descend s down the fall line.

and that a is of order 102 or larger for both RBCs gliding on the ESL and humans skiing. Thus, the lift forces generated can be four or more orders of magnitude greater than the classical lubric ation theory. The enhancement in lift ar ises from the fact that, as the porous media compresses, there is a dramatic increase in the lubrication pressure, becau se of the mark ed increase in the hydraulic resistan ce of the fluid as it tries to escape from the confining boundaries of the planing surface through the compressed porou s layer. The princ ipal difference between the tightl y fitting RBC in a capillary and a human skier or snow boarder is the leakage of the excess pressure at the later al edges of the skis, as can be seen from Fig. Ia. F&W theory was first verified qualitatively by the snow compaction ex periments in (Wu, Andreopoulos, and We inbaum 2004; Wu, Andreopoulos, Xanthos and Weinbaum 2005b; Wu 2005). However, this theory has the following major limitations for skiing or snowboarding: (i) the 2-D-fiber-array model in F&W is not appropriate for pred icting the variation of snow permeability due to the wide variety of shapes and sizes of ice crystals (Arons and Colbeck 1995) ; (ii) the assumption that the ice crystals' contribution to the total lift is negligible in F&W is not appropriate based on the experiments in (Wu, et al. 2005b; Wu 2005 ); (iii) the F&W analysis emph asizes lift generation in porou s media, but doe s not treat the other force s and moments acting on the skier or snowboarder as shown in Fig. 1b. In the pre sent study, we shall develop a new theoretical approach to treat these limitations and provide a realistic model for lift mechanics of downhill skiing and snowboarding.

2 Methods The ories to predict the snow perm eability have had limited success (Jordan, Hard y, Perron and Fisk 1999) and the most widely used formula is Shimizu' s (1970) empirical expression, K=O .077exp(-0.0078p,)d\ where p, is the density of snow and d the mean diam eter of the ice crystals. In the current application shown in Fig. la, p, changes due to the motion of the skils nowboard, thu s, K changes as a function of x :

K = 0.077 exp [( 1- (1-1 I k ) ·( I - x l L

r') In ( K~ 1 0.077d~ )J d~

( I)

(Wu, Igci, Andreopoulos and Weinbaum 2006), where I. is the length of the ski/snowboard; k = h2/h" h: and h , are the local thickn ess of the snow layer at the

Ridingon Air: A New Theory for Lift Mechanics of Downhill Skiing and Snowboarding 283

leading (x = L)and trailing (x = 0) edges of the planing surface, respectively; and K z is the permeability beneath the leading edge, K z = O.077exp[(holh z)ln(KoIO.077 et)]et, where ho and K o are the undefonned thickness and permeability of the snow layer, respectively. For a skilsnowboard gliding with velocity U = (Un Un UJ over a snow layer as shown in Fig. la, the trapped air' s velocity in the x direction satisfies Darcy's law (Feng and Weinbaum 2000), u = -(Klj.l)(fJPlfJx) where j.l is the viscosity of the air. The flow in the transverse plane can be viewed, to a first approximation, as a stagnation-point flow in a porous medium (Wu, et al. 2005a), v = -(Klj.l)(fJPlfJy), w=-Az where A is the vertical velocity gradient, A=-U:(x. y . h)lh. Combining with the continuity equation, fJulfJx+fJvlfJy+fJw/fJz = 0, we obtain V 2 P = -j.lA I K -(I I K)Vp ·VK . (2) Equation 2 is the new simplified governing equation for the pore pressure in skiing or snowboarding. The two terms on the right hand side have a simple interpretation. The first terrn proportional to A is the forcing due to the angle of attack and the lateral edging of the ski/snowboard. The second term arises from the variation in permeability due to the compression of the snow layer. If both of them vanish one obtains the potential equation for Darcy flow without any forcing. In the present study, we shall only examine the simple case where there is no lateral tilt, thus, h = h(x) , K = K(x) , A = (Ulh)dhldx where = Un and the pressure distribution in the y direction is parabolic (Feng and Weinbaum 2000; Wu, et al. 2005a). Introducing dimensionless variables, p'> (P-Po )/P o, p.> (Pc-Po)/Po, x'= xlL, y' = yl( WI2), h'= hlh, and K '= KIKz, where Pc(x) is the centerline pressure corresponding to the cross section at the location x, Po is the air pressure at the edge of the planing surface which is very close to the atmospheric pressure, one obtains

u

d

2p;(x')

dx 12

+

I K'( x')

dK'(x') dp;(x')

dx'

dx'

_~ , x' + E

p,( )

BL

=0

K'(x')h'(x')

(3) ,

where e = (WIL)z, Of. =(;11 Po)(Ulhz)(dh ldx)(Lz IKz). Equation 3 subject to the boundary conditions, pc'(O) = p,.'( I) =0, can be solved numericalIy and the 2-D pressure distribution beneath a snowboard/ski surface is determined, p'( x' , y') = (1- y') p,.'(x'). The solid phase (ice crystals) lift force is obtained by measuring the quasi-steady force generated when the snow is subject to incrementally increasing compressive forces (Wu, et al. 2005b; Wu 2005). This force in its dimensionless form is given by P,' (x') = ?'olid (x) I t; = (Pm~ I p). f([ 1- A+ A(I- I1 k) x'] I (G>o- 0.06))

(4)

(Wu, et al. 2006), where P",lid (x) is the local solid phase pressure, Pmg = mgcosze/LW where ah is the angle of the inclined slope,f is the empirical relation obtained in (Wu, et al. 2005b; Wu 2005), G>o is the undefonned porosity of the snow layer, and A. = hzlh o is the compression ratio at the leading edge. Figure Ib shows the representative forces acting on a skier gliding on an inclined snow slope. The weight mg is resolved into two forces, Fs parallel to the slope, and FN nonnal to the slope. The lift force, which refers to the total reaction force of the snow in the skiing community, is in the present analysis the sum of the distributed

284

Qianhong Wu et al.

forces due to the pore air pressure, N. , and the ice crystals' reaction force, N; The skier gliding down the slope has a snow friction force F f = 1]N s where '1 is the coefficient of friction, and a wind resistance or aerodynamic drag force F D, which are directed up the slope. FL is the aerodynamic lift force which is negligible compared with N. and N, (Perla and Glenne 1981). In this figure, the forces are shown at the points at which they act. When a skier has achieved terminal velocity, there is no acceleration and, thus, there is no inertial force, so all the forces as well as the torques shown must sum to zero: mg ccs a , = No + N s' No(xc - x.} + Ffl c = Ns(x s - xc>' (5a, b) where No =

rC:2(p - ~)

dxdy, N s =

r~olid

(x) Wdx ,

t,

is the normal distance of

the CM from the ski surface, xc, X a and X s are the x coordinates of CM, center of N. and center of N; respectively. Equation 5a can also be written aSlair +!solid =1 where lair = Na/mgcosah and !solid = N./mgcosah'

3. Results and Discussion When a skier/snowboarder (m = 80 kg) glides down a slope (a h = 150 , '1 = 0.04) at velocity U, over an undeformed snow layer of thickness, ho = 10 em, and permeability Ko, without changing the location of CM (for skiing, xc'= 0.40; for snowboarding xc'= 0.45), one has to adjust the compression ratios k = h-fh , and A, = h 2/h o, to satisfy the force and moment balance Eqs. 5a and 5b. The lift distribution between the trapped air and the ice crystals strongly depends on the geometry of the planing surface, W/L, the velocity U, and the properties of the snow layer, K o and <1>0. This is reflected on the two dimensionless parameters, e and (}L in Eq. 3. In this paper, we consider two typical snow types, wind-packed( Ko = 5.0xlO-IO rrr', <1>0 = 0.6, d = 0.42 g mm) and fresh snow (Ko = 1.7xlO- m2, <1>0 = 0.8, d = 1.0 mm) which bracket the range of permeability for most skiing conditions (Wu, et al. 2005b; Wu 2005). Because the permeabil ity of fresh snow is roughly 34 times larger than the wind-packed snow, air can not be trapped efficiently. When snowboard ing at a given speed ( U = 20 mls), one needs a much larger compression of the fresh snow layer (h2/ho = 0.38, h /h o=0.31) and a larger contribution from the solid phase (!s olid = 82%) to generate the required lift compared with the case of wind-packed snow (h2/ho = 0.70, h l /h o=0.65 , !solid = 46%), see Fig. 2a. Figure 2a also shows that for a given snow type, an increase in velocity leads to an increase in the trapped air' s contribution to the total lift and a decrease in the compression of the snow layer. This is because as one increases his/her velocity, the contact time of the planing surface with the snow layer decreases, the trapped air has less time to escape before the pore pressure decays and thus, the required snow compression is smaller. Since e for a ski (L = I.7 m, W= 0.1 m) is 1/16 that for a snowboard (L =1.16 m, W= 0.27 m), solutions ofEq. 3 for skiing differ greatly from those for snowboarding. In general, due to the large increase in the pore pressure relaxation at the lateral edges, the required snow compression is larger in skiing than in snowboarding. As shown in Fig. 2b, as one glides

Riding on Air: A New Theory for Lift Mechanics of Downhill Skiing and Snowboarding 285 over a wind-packed snow layer at U =20 mis, for skiing k = h2/h) = 1.3l5,fair = 42%, while for snowboarding, k = 1.072,fair = 54%. (3)

o 024!-

(b)

·········,·--·""c ·

·.........·· ~ 1 0' mfs:treSI1 -snow:·· · -

.0 001 00

U=15nVs,fresh snow ;

·· =··lI?20rn's.fJeshsOOw,....

. .........

20 mis, Ind- ack d srow

-

02

04

,06

0 oo,t- · ········· ·

i

08

... !....

'-----_-'--_---'--_---"_ _-'-------'

10

02

0,0

04

06

08

10

Fig. 2. Centerline pore pres~ure distribution for (a). snowboarding on wind-packed or fresh snow. (b).snowboarding or skiing on wind-packed snow. (a)

00 2

....

1 ......

,

(b)

=u, .

C ··

00 1

p.' 000

1

2

x~'~P3!3a ;

x,·=0.40 - xc'=0r 429 -.<>.7"",'.=0.452... x,'=0465 .' -0- ' x,'=p.473 -iT.

02

•

b

... .... ..

..

-

~

..... ....... .•

i

04

x'

06

0 .8

1.0

Fig. 3 (a) Centerline pore pressure (b) solid phase lift pressure distribution beneath a snowboard surface as one glides over a wind-packed snow layer at U = 20 m/s and shift their position of the CM. The dashed lines crossing the pressure profiles show this shift in .r,.'.

Figure 3 provides the critical insights for snowboard control and stability. A snowboarder can alter his/her CM by shifting their weight from the front to the rear foot (x, decreases). This change is accompanied by a transfer of lift forces from the air to the solid phase and a change in the angle of attack of the snowboard. The dashed lines in Fig. 3a and b crossing the pressure profiles show this shift in x,' . The curves in Fig. 3 apply to a neutral stability condition in which the sum of moments about the CM vanishes. If one shifts their weight (changes x,') without changing their angle of attack (trajectory a-b in Fig. 3), the initial neutral moment balance is broken and an unbalanced pitching moment is generated. In order to maintain stability, one has to input a muscular moment or change the compression ratios of the snow layer (trajectory b-e in Fig. 3) to get back to a new neutral moment balance position. The latter requires no muscular input, and is accompanied by a transfer of lift forces between the trapped air and the solid ice crystals as well as changes of snow compression at the leading and trailing edges. In summary, we have developed a new theoretical analysis of the lift forces generated during downhill skiing or snowboarding, which incorporates the lift contribution from both the transiently trapped air and the compressed ice crystals. This study

286

Qianhong Wu et at.

is an important practical application and extension of the F&W lubrication theory . The results presented herein agree with the more qualitative predictions in (Wu , et al. 2004 ; 2005b) where the pore pressures generated in snow were measured for the first time using a porous-cylinder-piston apparatus. This new theory of lift mechanics of downhill skiing and snowboarding would be invaluable for future snowboard design .

References Arons, E. M., and Colbeck, S. C. (1995) Geometry of heat and mass transfer in dry snow: a review of theory and experiment. Reviews ofGeophysics 33, 463-492, Colbeck, Samuel c., and Warren, G. C. (1991) The thermal response of downhill skis . Journal ofGlaciology 37(126),228-235 . Colbeck, Samuel C. (1994a) A review of the friction of snow skis . Journal ofSports Sciences 12,285-295. Colbeck, Samuel C. Bottom temperatures of skating ski on snow. Medicine and Science in Sports and Exercise 26(2) : 258-262, 1994b. Colbeck, Samuel C. (1995) Electrical charging of skis gliding on snow. Medicine and Science in sports and exercise 27( I) , 136-141 . Feng, 1., and Weinbaum, S. (2000) Lubrication theory in highly compressible porous media: the mechanics of skiing, from red cells to humans. 1. Fluid Mech. 422, 282-317. Jordan, R. E., Hardy, 1. P., Perron, Jr, F. E., and Fisk, D. 1. (1999) Air permeability and capillary rise as measures of the pore structure of snow: an experimental and theoretical study. Hydrol. Process. 13, 1733-1753. Lind, D., and Sanders, S. P. (1996) The Physics of Skiing -Skiing at The Triple Point, Woodbury, New York , pp. 1-268. Perla , R., and Glenne, B. (1981) Skiing In: D. M. Gray and D. H. Male (Eds) , Handbook ofSnow, Pergamon, Toronto, pp . 725 . Shimizu, H. (1970) Air permeability of deposited snow. Institute of Low Temperature Science: Sappora , Japan : Contribution No.1053 , English Translation. Wu, Q., Andreopoulos, Y., and Weinbaum, S. (2004) From red cells to snowboarding: A new concept for a train track . Physical Review letters 93( 19), 194501 194504 . Wu, Q., Weinbaum, S., and Andreopoulos, Y. (2005a) Stagnation point flow in a porous medium. Chemical Engineering Sciences 60, 123-134. Wu, Q., Andreopoulos, Y., Xanthos, S., and Weinbaum, S. (2005b) Dynamic compression of highly compressible porous media with application to snow compaction . Journal ofFluid Mechanics 542, 281-304. Wu, Q. (2005) Lift generation in soft porous media; from red cells to skiing to a new concept for a train track . Doctoral Dissertation. City University of New York, New York, NY, May, 2005 . Wu, Q. Igci, Y., Andreopoulos, Y. and Weinbaum, S. (2006) Lift mechanics of downhill skiing or snowboarding. Medicine and Science in Sports and Exercise. to appear in June .

Subjective Evaluation of the Performance of Alpine Skis and Correlations with Mechanical Ski Properties Peter Federoff":", Mirco Auer', Mathieu Fauve/, Anton Luthi', Hansueli Rhyner' I

Christian-Doppler-Laboratory Biomechanics in Skiing, Department of Sport Science and Kinesiology, University of Salzburg, Austria . peter.federolf@sbg .ac.at WSL Swiss Federal Institute for Snow and Avalanche Research SLF, Davos, Switzerland.

Abstract. The competition between ski and binding manufacturers is very strong . The purchase decision of customers is occasionally based on ski testing by the customer himself, but often the purchase decision mainly relies on published results of commercial ski tests . In this study we analysed evaluation methods and results of five important ski tests for the winter season 2004/2005, whose results were published in skiing related media . All of those tests are very extensive, but they differ strongly in their evaluation methods , in the skiing skill of their testers , and, hence, in the results and purchase recommendations they give. From our point of view it is a shortcoming of all of these ski tests that while they established a very sophisticated testing procedure, they neither evaluated mechanical properties of the tested skis, nor did they record the snow conditions during their tests. Whether a ski exhibits a good performance or not, depends not exclusively on the properties of the ski, but rather on the properties of the whole system athlete-binding-ski and the interaction of this system with the type of snow present during the test. To analyse these interrelations we conducted a ski test with five testers and five pairs of skis. The ski testers were all experienced, sport-orientated skiers . The snow conditions during the tests were hard snow with a good grip. Subsequent to the subjective evaluation of the ski performance in the field tests all ski-binding combinations were tested in the laboratory for their bending and torsional properties. On the one hand, the results of our study underline the strong differences in the subjective assessment of the ski performance. On the other hand indications for correlations between bending and torsional stiffness of the skis and the grades they achieved in the subjective assessment for the specific conditions were found . We also analysed that changing external conditions affect strongly the outcome of the subjective ratings .

1 Introduction The development of new skiing equipment is a fast process and the competition between ski and binding manufacturers is very strong . For most customers it is nowadays virtually impossible to keep an up-to-date overview of progress and trends in the skiing industry . Only a few customers have the opportunity to test a broad range of skis themselves before they buy a new ski, Hence, the purchase decision of skiers who buy a new ski is strongly influenced by reports and promotions published in skiing-related media . The various ski tests annually conducted and published by these media have a very significant impact of the purchase decision . In this study we compared evaluation methods and results of five important "commercial" ski tests published in German-speaking media , which were conducted for

288

Peter Federolf et al.

the winter season 2004/2005. All of these ski tests assess test skis by analyzing the subjective ratings of individual ski testers. All tests have developed a highly sophisticated test procedure and rely on a large number of ski testers and test runs. However, they differ in the skiing skill of their testers, in the task performed by the testers, in their evaluation criterions, and in the evaluation method. As a result, they vary substantially in their ratings of the skis and in the purchase recommendations they give. (for a direct comparison please refer to www.carving-ski.de.i All of the reviewed ski tests strongly concentrated on the skis, paying little attention to other factors, which might have an impact on the results. Whether a ski exhibits a good performance or not, depends not exclusively on the properties of the ski, but rather on the properties of the whole system athlete-binding-ski and the interaction of this system with the type of snow present during the test. Another issue is that skiing equipment comprises not only the ski itself, but also the binding, often an additional riser plate, and the ski boot. It is unquestionable that the ski is the most important component, however, it is obvious that the properties of the other components also have some impact on the performance of the whole system (e.g. Nigg et al. 200I; LUthi et al 2006). Hence, a different rating of the same ski in different ski tests might also be caused by different equipment components. The purpose of this study was to get a general idea to which extent mechanical properties affect the performance characteristics of skis. A second aim was to determine and analyse which factors influence the results of ski tests and might be responsible for the observed discrepancies.

2 Methods Table I lists the selected ski-binding combinations. The Stockli skis were chosen because they were not evaluated in the cited commercial ski tests, which reduced a potential preoccupation of the ski testers' opinion. The fifth ski, the Atomic SL IIM, was selected because it had achieved top grades in all commercial ski tests. Unlike the other skis it was used in a rent ski configuration including binding plate. test ski number

Ski manufacturer

I

Stockli

2 3 4 5

Stockli Stockli Stockli Atomic

Product name Spirit Spirit Spirit Laser SL SL 11M

length [cm] 170 170 170 171 160

Binding Manufacturer Fritschi Atomic Atomic Atomic Atomic

Tab. I. Ski equipment selected for the test.

product name Diamir Race Race Race rent binding

Subjective Evaluation of Skisand Correlations withMechanical Properties

289

For the purpose of this study, the bending and the torsional stiffness of the front and rear sections of the ski-binding combinations were determined subsequent to the ski tests. The bending stiffness was characterized by a characteristic bending value, defined as the load exerted to the ski-binding system divided by the ski's deflection (ONORM 1977). The ski 's torsion value was calculated by dividing the torque by the deflection angle (ONORM 1977). A detailed description of the measurement devices can be found in LUthi et al. (this conference). Five experienced skiers , which have a similar, sport orientated skiing style, but differed in body proportions (body masses between 72 and 95 kg) have conducted the field tests. The evaluation criterions used in our rating of the test skis were defined in a discussion with all testers to ensure that the definitions were clear and equally applied . The definitions contained a detailed description, two extremes between which a ski has to be classified, and suitable test turns . The used evaluation criterions were easiness ofturning, selfsteering, edge grip, stability, and overall impression . th The ski test was conducted on 24 March 2005 between 9.00 and 11 .20 in the Jakobshorn ski area in Davos, Switzerland. For each ski two runs were performed by the testers, during which they individually performed the test turns . Successively, they had to rate the ski on a one-to-five scale for each evaluation criterion. Five represented the optimal, one the worst extreme defined for each test criterion. On the early hours of the test the snow was dry and very hard, but due to machine grooming on the evening before the snow still allowed a good grip. During the course of the tests the snow surface was exposed to the sun and became softer, giving the skis a slightly better grip. To ensure an individual rating, the testers were not allowed to talk about the skis during the test, because an optical neutralization of the test skis was not possible due to the unequal ski-binding combinations. Prior to the test all skis were base and edge grinded and waxed by a local sports store.

3 Results and Discussion The mean rating given by the five testers is shown in Fig. I. Error bars indicate the standard deviation . Not surprisingly, test ski 5, which consisted of matched ski, binding plate, and binding, was rated best in most of the criterions. It performed especially well in the criterion easiness of turning, while it rated less well in the criterion stability . This can be explained by the fact that ski 5 was 10 em shorter than the other skis in this test. Among the results for the other test skis, which all had a similar ski length, the rating of ski 4 differed significantly from the rating of skis I to 3. Obviously, the ski model had a stronger impact on the result of this ski test than the binding model. Ski I, equipped with a different binding mounted on the same ski model, rated similarly as skis 2 and 3. Skis 2 and 3 were similar in construction, but did not obtain the same rating . This might be explained by the fact that, due to different earlier usage , they slightl y differed in their mechanical properties (Fig. 2 and 3).

290

'" t

u; ~

:=;>.

Peter Federolf et al.

o ski 1

o ski:?

o ski 3

• ski 4

a ski 5

easiness of turning

self steering

edge grip

s tability

overall ression

5 4

~

.0

c:

3

~

.zCl ~

2

"0

cg

Cil

c:

""E

1

~

0

Fig. 1. Mean rating of the test skis.

Figures 2 and 3 compare the mean rating of the test skis to the bending and torsion characteristics of the skis. In the specific test conditions (hard snow surface) stiffer skis tended to perform better than softer skis (see Fig. 2). Higher torsional stiffness of the ski shovel seemed to affect the ski negatively , whereas the torsional properties of the ski end did not correlate with the rating (see Fig. 3).

0 +-- ..-- .===:;:::::===;::::::===-1 4.5

5

5.5

6

6.5

7

bending value [N/mm] Fig. 2. Comparison of the skis' bending values with their mean rating in the test.

Subjective Evaluation of Skis andCorrelations with Mechanical Properties

291

5 -r-- - - - - - - - - - ---,

5 -r-- - - - - - - - - - ---,

4

4

••

o

e A

c:

eas iness of turn ing self steering • edge grip stability • overall irrpression ~-~::::;=====;===~

1,5

2

2,5

3

:g 2

easiness of turn ing

E

A self steering

edge grip stability • overall irrpression O +--~===T==::::::;:::=:::::::!..l G

3

3,5

4

4,5

5

t or s ion value s k i en d [tfll /"]

t or s ion value s ho ve l [tfll /"]

Fig. 3. Comparison of theskishovels' andtheski ends' torsion values with the mean rating. The high variances in the individual ratings indicate a limitation of the validity of the results and ask for a closer analysis of equipment-independent factors, which could possibly affect the testers' rating. One such factor are changing external conditions, e.g. changing snow properties. Therefore, a strikt test procedure had been set up, which ensured, that the ski test could be completed within two hours. 4,5

VI

:.:zVI =III

a

4 3,5

01

c:

:Q

r=

3

c:

III

'1l

E

2,5

easiness of turning

self steering

edge grip

stability

overa] irrpression 2 9:20 AM

9:40 AM

10:00 AM

10:25 AM

10:50 AM

approximative lime of the evaluation

Fig.4. Overall ratingof all testersandall test skis independence of time. An indication for changing external conditions affecting the skis' rating is a general trend in the mean rating of all testers for all skis. In fact, a clear trend is visible in the overall rating of the criterion edge grip , which, probably due to the softening

292

Peter Federolf et al.

snow surface, rated more than half a grade better at the end of the test (see Fig. 4). The rating for easiness of turning declined strongly during the first hour, but increased again in the second hour. The rating for stability also showed strong fluctuations . Unfortunately an explanation for the last two effects could not be found .

5 Conclusions In this study the subjective field performance was correlated to mechanical properties of different ski-binding systems. In fact, correlations of bending stiffness and torsional stiffness of the ski shovel to the performance ratings are indicated by the results of our study . Within the scope of this project the geometrical properties of the skis, e.g . the side cut, were not considered. The individual ratings of different ski testers fluctuate strongly. It could be shown , that they are affected by changing external conditions, such as the snow hardness. Hence, further studies with more test skis and testers are needed to obtain a good overall picture of the interrelation between ski properties and performance. Based on the results of this study, we would like to suggest that additionally to the evaluation of the skis in field tests the mechani cal and geometrical properties of the test skis and the external conditions should also be recorded. Correlations between performance and properties of the skis offer the opportunity to give more specific recommendations for customers. They would also provide valuable data for the ski manufacturers to potentially improve their ski models or adapt them for the specific needs of individual target groups of skiers .

References Howe, J. (1983) Skiing Mechanics. Poudrc , LaPorte, CO, USA. Howe , 1. (200 I) The New Skiing Mechanics . Mcintire Publishing, Waterford, ME, USA . Lind D. and Sanders S. (\996) The Physics of Skiing. Springer-Verlag New York, NY, USA. LUthi, A., Federolf, P., Fauve , M., Rhyner H.U. (2006) Effect of Bindings and Plates on Ski Mechanical Properties and Carv ing Performance. This conference. Nigg , 8. M., Schwameder, H., Stefanyshyn D. and Tschamer v. V. (200 I) The Effect of Ski Binding Position on Performance and Comfort in Skiing. In E. MUller, H. Schwarneder, C. Raschncr, S. Lindinger and E. Komexl (Eds .), Science and Skiing II, Verlag Dr. Kovac , Hamburg, Germ any , pp. 3-13 . Onorm (1977) Alpinski, Elastische Eigenschaften, Labormessverfahren. Austrian Standart Organisation (Osterr eichisches Normungs instituti , Vienn a, Austria .

Timing of Force Application and Joint Angles During a Long Ski Turn Takeshi Yoneyama' , Nathan Scotr' and Hiroyuki Kagawa) ) Kanazawa Univer sity, [email protected] The University of Western Australia

2

Abstract. Using a measuring system which is described in detail in another paper in this conference, the load on the ski, sole pressure, leg joint motion , and tum direction have been measured during a long tum of an expert skier. The instant of tum change was associated with a change in the sign of the force moment about the ski direction. The total force on the outside ski was generally about double that on the inside ski, while both loads instantly decreased at the tum change. Foot pressure increased at the heel area during the steering process. The center of the pressure was always kept in the rear part near the heel, but it moved forward at the tum change. The main motion of the leg was a combination of flexion-extension of the hip joint, knee joint and ankle joint. The outside leg was kept extended angle during the steering process, while the inside leg gradually flexed and extended. The trajectory of the body was estimated from the data of a magnetic compass at the backpack. The forces, foot pressure, joint motion and body trajectory were compared with the video image of the skier. This comparison showed that the skier made the tum change earlier than the centerline of the tum trajectory. During the tum change process, the skier first extended the previous inside leg without flexing the outside leg. Next, he shifted the main load from the previous outside leg to the other leg; at this time the force moment also changed. Then he flexed the new inside leg. We think that the timing of these motions is the main factor determining the downhill speed achieved.

1 Measurement The measurements reported here were made using equipment that is described in another paper in these proceedings (Scott et al 2006) . An expert skier who was a test player for a ski company wore the measuring apparatus as shown in Fig.l . The equipment consisted of load cells between the binding plate and the ski, foot pressure pad between the foot and the inside of the boot, Measurand ShapeTape" to measure leg joint angles, a magnetic compass and mechanical gyrocompass to measure the backpack angle, and a data logger in the backpack. The side curve of the ski was 21m. The athlete was 185cm tall and weighed about 90kg . The experiments were done at Shiga-kogen, Nagano, in February 2005 . The ski field was planar with slope 20° to the horizontal. The athlete performed four long tum

294

Takeshi Yoneyama, Nathan Scott and Hiroyuki Kagawa

cycles after an initial straight descent. Each cycle took 4 seconds and the distance travelled was 60m in the plane of the snow: the skiing speed was about 60kmlhr. Although the forces and foot sole pressures were measured on both legs, the leg angles were only measured on the left leg. This report is thus mainly to do with the left leg.

M agn':lic cornpa '

D lJJ logger In lhe ba kpac],

Fig. I.

Measurement system

2 Forces on the Ski

- IcoI

lC'ft

lit

ft

'

...

...

j~[fYi, W ~

li

~

17

W

~

Tile ••

Fig. 2.

m nun

lIIII r-r-:-:--:-:--r-~--.--..., Ill!

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.

o H~""'-'--t-Lll""it---+l

...., L.....l..lCol=.J'--_-"'""=~~_~

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11

Forces at the four points of the ski

The load cells detected upward forces at 4 points of the left ski: front right side, front left side, back right side and back left side. By "upward" we mean normal to the plane of the ski. The front points were 180mm in front -of the boot center and the back points were 140mm behind it. The transverse distance between the measurement points was 54mm. The forces measured during two tum cycles are shown in Fig 2. The vertical line marking the tum change instant will be explained below. Note that during the right tum , the right side forces were large while the left side

Timing of Force Application and Joint Angles Duringa Long Ski Tum

295

front force was nearly zero and back force was a little bit negative . In the left tum, the left side back force was larger than the front side force while the right side force was nearly zero. The total upward force on the left ski is shown in Fig. 3. Comparing the loads for the inside and outside period, the load on the outside ski was generally about double that on the inside . However at the instant of the tum change both the inside and outside total forces were small. Left turn Inside leg

z

Right turn Left turn Right turn Outside leg Inside leg Outside leg

_

~::::~ ~ ~ uu _~ _ _ P500 c o -g 0

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-_

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.-

~-

_.-

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16

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19

-

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22

23

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part of the ski cycle where the left leg was outside, the pressure was mainly in the heel area so the center of pressure is also towards the rear. At the tum change the total pressure was quite small and the center of pressure was central. When the left Ileg was on ihe'insit!e, ihe center 01' pressure was again toward ihe rear. •

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This signal was post-processed to produce vectors tangential and normal to the tape. The vectors at the tape attachment points on the left leg were used to estimate the joint angles; the result is shown in Fig.7. The largest angle changes were for hip joint flexion and knee joint flexion. The data of the flexion of the ankle looks too small to fit the hip joint and knee joint motion. Some abduction-adduction, thigh rotation and lower leg motion was also observed. Comparing the motion of hip joint flexion with the tum change time, it can be seen that the hip joint is still extended at the tum change. This means that the skier first extended the previous inside leg while keeping the extension of the outside leg at the tum change. Next, he shifted the main load from the previous outside leg to the other leg and there was a change in the sign of the force moment. After that, he flexed the new 16.5s 17s J7.5a !Xs I X.5s 19s 19.5s 20s 20,5s + - Right tum Len tum _ inside leg. Outside leg Inside leg The flexion and extension posture of the left leg, and upper body angle, Fig.S. Leg posture during the tum are shown using stick figures in Fig.8. Knee joint angles were assigned so that the upper body inclination looked reasonable compared with the video image of the skier. The posture at the tum change was intermediate between the most flexed posture and most extended posture

5 Trajectory A trajectory for the upper body was estimated using the magnetic compass in the backpack and the assumption of constant 60km/hr speed; see Fig. 9. The positions at the tum change times are marked with circles. The radius of the first half part of the turn arc was larger than that of the second half. The tum change point was a little bit before the centerline of the tum curve. From this we infer that the athlete anticipates the tum change as early as possible for the next first half part tum.

6 Comparison Among the Data Foot pressure, forces at 4 points, leg joint posture and video image of the skier are compared in Fig. 10. Forces at four points are expressed as vectors. The timing of these motions must be critical factors in determining the overall downhill speed achieved. We appreciate the cooperation of Ogasaka company.

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References Scott N.W., Yoneya ma, T.,Kagawa,H. & Takahashi, M., Measureme nt of jo int motion and acting forces on a top athlete skiing" Proc. 5th International Engineering of Sport Conf.Davis, Cali fornia, 13-16 Sept. 2004, Vol. 1 pp 394-400. Scott N, Yoneyama T & Kagawa H, " A Unified, Custom-Bui lt Measuring System for a Ski Athlete" , Proc. 6th International Confe rence on the Engineering of Sport, Munich, Aug 2006 (these proceedings).

Effect of Bindings and Plates on Ski Mechanical Properties and Carving Performance Anton Luthi), Peter Federolfl,2, Mathieu Fauve' and Hansueli Rhyner' ) WSL Swiss Federal Institute for Snow and Avalanche Research SLF, Davos , Switzerland,

luethi @slf.ch 2

Christian-Doppler-Laboratory Biomechanics in Skiing, Department of Sport Science and Kinesiology, University of Salzburg, Austria.

Abstract. The carving performance of modem ski equipment is determined by the overall mechanical properties of the whole system composed of ski, binding and binding plate. In the current study the effect of different bindings and plates on the mechani cal properties was determined in the laboratory using different devices . Measured were the shape of the ski when bent , bending and torsional stiffness, as well as the force distribution on the running surface of the ski when pressed again st an array of 26 x 6 strain gauge sensors. The stati stical uncertainty on all quantities determined is lower than 2 %. The performance in carving was evaluated by test skiers according to the criteria : easiness for turning , stability and edge grip . Binding/plate/ski-combinations with high rank ing in the field evaluation were found to have similar mechanical characteristics. Thi s correlation between field tests and laboratory characterisation allowed to give indications on the ideal overall mechanical properties of ski equipment for carving.

1 Introduction Bindings and plates play an increasingly important role in ski equipment design . They do not only significantly affect various ski properties generally discu ssed as being important for performance such as bending and torsional stiffness, as well as vibrational and damping characteristics (Schultes 1978; Lind and Sanders 1996; Howe 200 I) but also affect how the force is transmitted from the skier to the ski. This transmission, together with the ski geometry, the overall bending and torsional properties of the bind ing/plate /ski system and external parameters such as ski loading, edging angle and snow mechanical properties define how the ski is deformed while skiing, what forces act on it and thus how the ski performs. The purpose of the current study was twofold: to determine the effect of different bindings and plates on the ski mechanical properties and on the performance in carving, and to get insight on the ideal properties of ski equipment for carving through the correlation of laboratory and field tests. Such information is scarce in the literature because on the one side, ski manufacturers rarely publish their knowledge and

300

LUthi et a!.

on the other side, the definition of ideal properties is hindered by the fact that they depend on such diverse parameters as ski technique, skiing ability and snow conditions.

2 Measurements The laboratory and field test were carried out for three binding/plate systems (Fig. I) which were all mounted on the same ski model, namely a 161 em long slalom ski of the manufacturer Stockli. The first two systems (A, B) are commercially available, the third system (C) is a prototype design. One of its particularities is that its stiffness can be altered. It can also be fixed to the ski using various screw positions. For the current investigations it was used in two different configurations, namely a stiff one with screw positions 1-3 (C I) and a soft one with screw positions 1-2 (C2).

Fig. I. Tested binding/plate systems. A: Atomic binding with Hangl plate, B: Atomic binding with VIST plate, C 1: Prototype binding/plate stiff, with serew positions 1-3. C2: Prototype binding/platesoft. with screw positions 1-2. For the laboratory measurements the bending and torsion apparatus shown in Fig. 2 and the force distribution device shown in Fig. 3. were used. For the bending tests, the ski was supported 5 em from the tail and 23 em from the front and loaded by a force piston at the center of the binding (located 69.7 ern from the ski end) via a phantom boot ISO 9338 Typ A. During loading, applied load and ski deflection at the location of force application were continuously recorded using a strain gauge force sensor and a distance transducer. From this recording, the bending stiffness was derived. The distance transducer can also be automatically moved along the ski axis and was employed to determine the shape of the ski before and after loading. The difference of the two curves yields the effective ski deformation curve. For the torsion tests, the ski was rigidly fixed at its center via the ISO phantom boot inserted into the binding (Fig. 2) and a torsion moment applied 23 ern from the ski tail. This set up was primarily aimed at determining the torsion stiffness of the binding/plate link between boot and ski. From the continuous recording of the applied torsion

Effect of8indings and Plates on Ski Mechanical Properties

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moment and the torsion angle the torsion stiffness was derived. The force distribution device consists of an array of 26x6 strain gauge force sensors and a force piston to press the ski equipment against it. For the current measurements, the readings of the six force sensors in each array row were summed up to get a two dimensional force distribution along the ski axis. For all binding/plate systems tested all mentioned measurements were repeated at least three times and then averaged, the statistical variation on all quantities determined being lower than 2 %. The performance in carving of the different plate/binding/ski combinations was evaluated in free skiing by five experienced skiers having a similar, sport orientated skiing style. The evaluation criteria were easiness for turning , stability and edge grip. During the tests the snow was hard but not icy. Each tester did two runs with a given combination before noting down his comments and changing to the next one. After the tests, a I to 4 ranking of the four evaluated systems was derived for each tester from his subjective judgements of then the results averaged over all testers .

Fig. 2. Test apparatus in bending (A) and torsion (8) mode .

Fig. 3. Device for measuring the force transmission through the ski to the ground .

3 Results and Discussion The shapes of the bent binding/plate/ski combinations when loaded with 320 N are shown in Fig. 4. The corresponding bending stiffness values are listed in Table 1, which also shows the torsion values and the mean ranking in the field tests. Figure 5 shows the force distribution on the running surface when loaded with 400 N. Con-

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ceming the field tests, all testers felt distinct differences between the tested systems. All testers ranked system A and B superior to systems CI and C2, with system A being the favourite one for four out of five testers.

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The results show that plate and binding significantly affect the mechanical properties of ski equipment. The resulting differences can not only be measured in laboratory but also considerably affect the performance in field tests. When comparing the results of the laboratory and the field tests, it is striking that the two systems superior in the field test, namely A and B, show salient common characteristics. These are a flattening of the bent ski shape in the ski center, a more elongated force distribution on the running ski surface with the force maximum being located in the front part of the ski, and a high torsional rigidity between boot and ski. In general, systems performed the better, the flatter the bending curve, the higher the torsional stiffness, the wider the force distribution and, with the exception of system B, the higher the overall bending stiffness was. The advantage of a high bending stiffness is consistent with the findings of Federolf, Auer, Fauve, Luthi and Rhyner 2006. A flat bending curve translates itself to an increased difference between maximal flexural stiffness at the ski center and minimal stiffness at the ski ends, a finding consistent with Nachbauer, Rainer and Schindelwig 2005. The advantage of a high torsional rigidity between ski boot and ski seems obvious from the viewpoint of a firmer fixation of the ski to the athlete. A more elongated force distribution on the running surface seems to be advantageous from at least two points of view: first the skier supporting portion on the running surface is wider, which decreases the local loading of the snow and hence the risk of snow failure. Thereto, it should be noted that a elongated distribution may be disadvantageous on very hard snow where a very well centred distribution may be required to build a supporting track into snow at all. Second, the force on the ski tail and specially on the ski front is higher which makes the ski more easily controllable. The fact that systems A and B show a rather similar bending stiffness when compared to system C1 but perform significantly better in the field tests suggests that the resulting force distribution on the running surface is an as important system characteristic as the bending stiffness when regarding carving performance. This distribution is affected by the system stiffness but probably to a larger extend by the manner in which binding and plate transmit the high loading forces in carving to the ski. This suggestion is supported by Finite Element calculations of the prototype system (CI, C2) in which the calculated ski shape in the carving situation was found to be more affected by the screw positions (1-2 vs. 1-3) than by its stiffness. Another possible explanation for the performance difference between systems A, Band CI would be the large difference in binding/plate stiffness.

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4 Conclusion The current study shows that bindings and plates significantly affect the overall mechanical properties of ski equipment. The resulting differences can not only be measured in the laboratory but also considerably affect the performance in carving. For carving on hard (but not icy) snow, it was found that ski, plate and binding should be combined in such a way as to obtain a flat bending curve, a wide force distribution on the running surface and a high torsional rigidity of the binding/plate link between ski and ski boot. The results further suggest that more attention should be paid to the force distribution on the running surface as an important parameter when trying to define optimal system properties for carving. For this reason, a new measuring device is currently being put in service which allows to determine this force distribution in the bent ski situation.

References FederolfP., Auer M., Fauve M., Luthi A. and Rhyner , H. (200 6) Subjecti ve evaluation of the performance of alpine skis and correlations with mechanical ski propert ies. Thi s conference. Howe, J. (200 1) The new Skiing Mechanics. Mcintire, Waterford Lind, D. and Sanders, S.P . ( 1996) The Physics ofSkiing . Springe r, New York Nachb auer W., Rainer F. and Sch indelwig K. (2004) Effects of ski stiffness on ski performance. In: M. Hubbard , R.D. Metha and J.M .Pallis (Eds.), The Eng ineering ofSpo rt 5 Vol. I. Central Plains Book, Winfield, pp. 472-478. Schulte s, H. ( 1978) Del' Alpinski . Haller & Jenzer, Burgdorf

Development of a Prototype that Measures the Coefficient of Friction Between Skis and Snow Paul Miller l , Andy Hytjan', Matthew Weber', Miles Wheeler', Jack Zable l , Andy Walshe, Alan Ashley / I

2

Dept. of Mechanical Engineering, University of Colorado at Boulder, [email protected] United States Ski Association

Abstract. This paper discusses the development a system for measuring the kinetic coefficient of friction between the bottom surface of a ski and snow . The prototype for taking these friction measurements has been built and tested . This measurement system contains load cells , accelerometers, data acquisition hardware and software, a laptop, skis, and connecting hardware . The system developed is portable, accurate and can operate at a variety of skiing conditions and skier weights . The kinetic coefficient of friction is calculated by measuring the friction force on the ski and determining the normal force acting on the ski. Data was taken between speeds of 0 to 4 m/s with normal forces of 22 to 82 kgs on an icy surface as well as on surfaces with much higher coefficients of friction . The kinetic coefficient of friction between skis and an icy surface was calculated to be 0.041. The data obtained agreed with previously published results and was quite repeatable .

1 Introduction A prototype device that measures the kinetic coefficient of friction between skis and snow was built and tested to help determine which type of skis, ski waxes and waxing techniques would produce the lowest coefficient of friction on certain snow conditions, including an icy surface . The coefficient of friction between skis and snow can vary significantly depending on the type of ski and wax that is used for a certain type of snow . The temperature and humidity of snow has also been shown to affect the coefficient of friction as well (Spring 1989). Accurate and repeatable measurements have been taken using the current prototype at speeds up to 4 mls. The prototype was designed such that measurements can be taken on site, on actual ski courses, as opposed to using devices where snow has to be packed on to a testing surface (Buhl 200 I and Keinonen 1987). The device takes advantage of commercial ski bindings and can be easily interchanged with different types of skis . The measurement system is basically composed of off-the-shelf equipment. The device is portable, easy to setup, and is designed such that a range of ski velocities can be obtained from 0 to 13.5 mls. This paper will primarily focus on the proof of concept

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of the system to accurately determine the coefficient of friction on icy surfaces . A picture of the measurement system is shown in Fig. I

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2 Experimental Setup The ski module contains all the components of the data acquisition system . It consists of a protective case with a set of cut off ski boots attached to the bottom of the case. These modified ski boots fit into regular commercial ski bindings. Tension in the two opposing cables were measured by load cells (Omega LC20I-IOO and Omega 2511 LCEB-25) that were connected between the respective towing and restraining cables and the protective case shown in Fig I. Inside the black protective case shown in Fig. 1 are the data acquisition components including a laptop computer which ran a LabView data acquisition program.

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Additionally, the case contains a 3 axis accelerometer (Three Analog Devices ADXL05 uni-axial accelerometers) that measured accelerations in the towing and normal directions of movement. Movement of the skis was controlled by manually pulling the ski module via a tow cable. The protective case is rigidly connected into the bindings of the skis.

3 Experimental Procedure The coefficient of friction was measured! calculated on two different surfaces to show proof of concept for the system. The surfaces chosen were such that they represent the extremes for the expected coefficients of friction . The primary goal was to prove that the system was capable of repeatable and accurate measurements. The first set of tests measured the coefficient offriction between the protective case and a polymeric tile floor, or plastic on plastic. The second set of tests was done to calculate the coefficient of friction between skis and ice, with the weight of the module being the variable. Each test was conducted for approximately 30 seconds. Tests were performed by pulling the ski module from speeds of 0 to 4 mis, while approximately maintaining a zero degree angle with respect to the horizontal for the two opposing cables. Typical force data is shown in Fig . 2.

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4 Theoretical Analysis The friction force acting on the skis was calculated by using the output of the load cells to determine the tension in both the tow cable that pulls the ski module across the surface and the opposing restraining cable. Fig . 3 show s a free body diagram of the forces acting on the ski module.

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5 Testing Results 5.1 Plastic on Plastic Friction Testing Results Plastic on plastic friction testing was done by pulling the protective plastic case along a hori zontal plastic surface. The case was dragged at a constant speed of approx imatel y 1.5 mls. After four consecutive tests the coefficient of friction was calculated to be 0.479 . The standard deviation for this coefficient of friction was calculated to 0.023, which shows the systems ability to make repeatable accurate

Development of a Prototype that Measures the Coefficient of Friction

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measurements. This coefficient of friction falls within the plastic on plastic values found on the MatWeb.com online material property database (MatWeb 2005).

5.2 Skis on Ice Friction Testing Results Friction testing was done between skis and a smooth ice surface which was at 17.5° C. The ski module was dragged at speeds up to 4 mls. Weight was added on top of the ski module to simulate the weights of different skiers. The results for the testing are shown in Table I.

Table 1 Results for Testing on Ice Load Weight (kg) 41 61 82 Average Coefficient of friction between skis and ice

Coefficientof Friction 0.0422 0.0415 0.0418 0.0412

As expected the results adhere to Coulomb-Amonton's first law of friction and the coefficient of friction did not significantly change by increasing the weight of the ski module (Persson 1989). Strausky et al had calculated a kinetic coefficient of friction between skis and ice to be around 0.03; however, this was at speeds between 0.005 to 0.0I mls (Strausky 1998). Spring found that the kinetic coefficient of friction increases as the speed increases (Spring 1988). Thus, the kinetic coefficient of friction obtained around .041 is reasonable, since it was taken at speeds up to 4 mls. The coefficient between skis and ice also falls near the coefficient of friction for skis on snow (Buhl 200I). The testing results for all ice tests produced a standard deviation of 0.0019, again showing the good repeatabilityfor this system.

6 Conclusions The calculation method of the coefficient of friction discussed has been proven to be accurate and consistent. Testing results for plastic on plastic and skis on ice, compared well to published results. The method has been shown to work at speeds up to 4 mis, however higher speeds will be tested in the future. This method of calculating the coefficient of friction is advantageous over other methods because it can be used at the actual ski locations as opposed to lab testing. This ability to test at race locations can lead to better predictionsof what type of ski and ski wax should be used for a particular race.

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7 Future Work The current prototype will continually be refined to improve measurement accuracy and precision. Future testing will be done at higher speeds as well as on inclined surfaces; therefore calculated coefficient of friction values will be more closely related to actual racing conditions. One improvement to the current prototype system is to automate the system to allow for testing at higher speeds. The current prototype is manually pulled across the surface while the rear axially opposing cable is also manually pulled on. This significantly limits the possible testing speeds. Design plans are underway to create a motorized system that would pull the ski module to higher speeds. A variable speed motor will be used to allow measurements to be obtained at speeds up to 20 m/s.

The ability to test on inclined surfaces, will allow more flexibility of ski race locations. An inclinometer would be then incorporated into the ski module.

Acknowledgements The team would like to thank Puneet Parish and Brad Dunkin of the University of Colorado Integrated Teaching and Learning Laboratory for all their help and advice with developing our measurement system.

References Buhl 0 , Fauve M, Rhyner H (200 I) The kinetic friction of polyethylen on snow: the influence of the snow temperature and the load. Cold Regions Science and Technology. 22, I33140. Keinonen J. (1978) An experimental device for measuring friction between ski and snow. Acta Polytechnica Sacndinavica. n PH123, 6-11. MatWeb, http i//www.matwcb.corn, 2005 Personn B, Tosatti E (1989) Physics of Sliding Friction. Vol E311. NATO ASI Series, Boston Spring E. (1988) A method for testing the gliding quality of skis. Tribologia. 7 n I, 9-14. Spring E. (1989) Ski Tribology. Acta Polytechnica Sacndinavica, Electrical Engineering Series. N E164, 108-119. Strausky H, Krenn J.R., Leitner A, Aussennegg F.R. (1998) Sliding plastics on icc: fluorescence spectroscopic studies on interfacial water layers in um thickness regime. Applied Physics B (Lasers and Optics). vB66 n5, 599-602.

8 Football

Synopsis of Current Developments: Soccer Matt Carre Sports Engineering Research Group, University of Sheffield, [email protected] Soccer is arguably the biggest sport in the world, in terms of the impact on everyday lives, either through spectating or participation. Indeed, as the conference to which these proceedings are linked begins, we will all still be recovering from the excitement of the 2006 World Cup final that occurred in Berlin a few days previously. A sport that has so much impact, unsurprisingly also generates great research interest, reflected in the number of papers in the following section as well as in other sections of these proceedings. In sports engineering this research is fairly well distributed between four key components of the game: the ball, the pitch, the footwear used and the players themselves. The soccer ball has been re-designed and improved many times over the years and current designs employ a combination of careful material selection and sophisticated manufacturing techniques to produce balls which are impressive in terms of performance, durability and consistency. Ronkainen and Harland describe a technique using laser Doppler vibrometry to carry out modal analysis of a soccer ball. This will be of great use in determining the mechanical response of a ball due to dynamic loading and aid in the further improvement of ball design. Asai et al. concentrate their efforts on the flight of the ball and combine some traditional wind tunnel experiments for spinning and non-spinning soccer balls with a truly innovative method of obtaining flow visualisations for real, kicked balls. The data obtained and findings observed will undoubtedly be of great use to future studies of soccer ball aerodynamics. Two papers in this section are concerned with the performance of the pitch. AIcatara et al. examine synthetic soccer surfaces, in particular those that incorporate an in-fill of sand and rubber granules (known in the industry as 'third-generation pitches') . Their paper compares pitch installations that have a varying size of rubber granule with various measurement indices, to study the effect of rubber infill morphology on mechanical performance. This information can be utilised in the future design of these types of surface. The paper by Jennings-Temple et al. looks at the more traditional surface used in soccer, natural turf, and they investigate the link between physical soil properties and playing quality for player-surface interaction. In many countries, soccer is played during the winter season and the pitch is exposed to harsh weather conditions, which can have a detrimental effect on the game. The findings from this study can be used to improve pitch-management and maintenance strategies, improving the quality of play for players and spectators alike.

314 MattCarre A very important topic of study related to soccer is traction of studded footwear, where there is a need for high player performance, whilst preventing injury. Both these factors become increasingly important at the professional level of the game. Grund and Senner describe the design and development of a new device that can be used to simulate the interaction between a studded boot and a surface, whilst measuring the forces that are produced for different movements . This data can then be fed into a multi-body computer model of the human knee to calculate the resulting anterior cruciate ligament (ACL) tensile forces. This study, combined with the planned future work, has the potential to gain a real understanding of the cause of ACL injuries, with respect to boot-surface interaction, which would be of huge benefit to the health of soccer players. The three remaining papers are related to how players perform under different conditions . Work carried out by Marcolin et al. is also concerned with boot-surface interaction, but in this case the focus is on how the placement of the support foot affects shooting accuracy for different types of instep kick. Findings from this study will be of great interest to coaches and is directly applicable to a training environment. An intriguing study by Hiramatsu and Ohshima analyses how the position of a gaze point (e.g. knee, waist or ankle) is used by defensive players to predict the ensuing movement of attacking players, even in situations where the attacking player is trying to trick the defender by use of ' feint' moves. The accuracy of this prediction for different situations, as analysed by a brain-mimicking function could provide some incredibly useful advice for players and coaches to improve defensive ability. To address the balance, Kerwin and Bray's study could ultimately improve the attacking nature of a side through more successful penalty kicks. Their study first involves a simulated penalty shoot-out between a ball firing machine and real goal keepers, whose movements are monitored using a force platform and video analysis . This information is fed into a computer model which can predict the likelihood of certain shots being successful, with reference to a ' diving envelope' within which the keeper is able to make a save. At the point of writing this, I am hoping that Kerwin and Bray have passed their findings onto the England Football team, who, on past experience, often rely on penalty shoot-outs for the success (or otherwise) of their international matches! Soccer research is clearly moving forward in many areas, leading to greater safety and enjoyment for players, easier monitoring of the rules by FIFA, and better entertainment for spectators .

An Investigation into the Link Between Soil Physical Conditions and the Playing Quality of Winter Sports Pitch Rootzones Ma rke Jenning s-Temple, Peter Leeds-H arrison , lai n James Cranfield Uni versity at Sil soe, m.a.jennings-temple.sOI@cranfi eld .ac.uk

Abstract. Playing quality standard development failed to demonstrate how set targets could be achieved, resulting in Groundsmen being unable to manage pitches to optimize playing quality. This research linked easy-to-measure pitch parameters to the outcome of tests for playersurface interaction quality, to enable this to be monitored in real-time and ensure appropriate pitch management options arc selected. 25 pitches were tested three times over an 18-month period. Tests for surface traction and hardness were conducted, along with a range of soil and grass factors; multiple linear regression was used to generate prediction models. R2 values varied with soil type and weather conditions, although increased sand content generally reduced the reliability of the prediction equations. It was eoneluded that top-dressing may have skewed the data; suggesting more sand-based pitches than actually existed, or that sanddominated rootzones varied little in playing quality. The production of significant regression equations has demonstrated which easily-influenced pitch factors can be manipulated to alter player-surface interaction quality and ultimately, lower the risk of injury.

1 Introduction Shildrick and Dye ( 198 3) identified the need for a code of pra ct ice to assist Groundsmen to make management decisions which would aid the pro vision of high quality sports pitches. Playing qu al ity sta ndards were first proposed by Bell, Baker and Canaway (1985) and the final report from the Natural Turf Pitch Prototypes Advisory Panel was published in 1992 (Ada ms , Gibbs, Baker and Lance 1992 ). The research, spons or ed by the Sp ort s Co uncil and performed by the Sports Turf Research Institute (STRl) failed to produce a code of practice, or man agement plan. The Performance Quality Standards (PQS) document publi shed by the Institute of Groundsmanship (lOG ; lOG 200 I) contains targets for particular test s for pitch quality . Absent are guidelines on how to achieve these numbers. The lack of coherent guidelines to achieve the recommended targets for pitch quality has contributed to football (soccer) being identified as 1000 times more dangerous than high-risk industr ial occupations (Hawkins and Fuller 1999) . A recent rep ort from the Department for Culture, Media and Sport (O CMS 2002) det ailed the aims of the Briti sh Go vernment to use increased sport participation to combat in-

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creasing levels of obesity and associated illnesses . In the document , it is explicitly stated that increased participation rates must not be mirrored by increased injury rates. The aim of this research was to establish a link between easil y measured pitch parameters with the outcome of the two tests for player-surface interaction quality. This would enable Groundsmen to monitor pitches in real-tim e and eventually facilitate the selection of optimum pitch management tools for the production of a safe surface.

2 Materials and Methods Twenty five pitches at fifteen football clubs in England and Scotland were visited three times during January and May 2004 and April 2005. The range of clubs included those in the Premiership and Scottish Premiership, lower league clubs and private schools . Each had a dedicated Groundsman.

2.1 Soil Physical Tests Tests determined gras s cover (%) using a point quadrat, Grass length (mm) using a rising disk , surface evenne ss (mm) measured using a graded wedge and a 2m straight edge and volumetric moisture content (%) was determined in the laboratory from soil cores removed from the pitch . Bulk density (M g/m') was determined for the 0-50mm and 50-100mm core sections. Soil water tension (matric potenti al; kPa) was determined using a bespoke tensiometer. Each of these tests was conducted at 5 location s on each pitch . A full particle size analysis was performed on the combined soil from each of the five cores.

2.2 Pitch Quality Tests Player-surface interaction quality was assessed using two tests; surface hardness and traction. The hardness test used a Clegg hammer, first developed by Clegg (1976) for evaluating pavement base course layers. A 0.5kg hammer was dropped 0.55m onto the surface. A single drop method was used and the reading in g was recorded. Three tests were performed at each location. Traction test equipment was manufactured and operated in accordance with the guidelines presented by Canaway and Bell (1986) and BS 7044 (BSi 1990). A metal disk encompassing six 15mm studs equally spaced at 46mm radii from the centre was loaded with 41kg of steel weights. With the studs fully engaged into the surface , a torque wrench , attached to the disk via a metal shaft was turned and the maximum force at failure was recorded in Nm. Total equipment weight was 45.5 kg. This 'test was performed once at each location .

An Investigation into the Link Between Soil Physical Conditions and the Playing Quality 317 2.3 Pitch test locations

Test locations have varied in previous studies, in general ranging from twelve (Holmes and Bell 1986) to six (Holmes and Bell 1987; Baker and Gibbs 1989). The five test locations displayed in Fig. I included high and low wear areas.

Fig. t . Pitch test locations. This figure was present on data collection sheets and was annotated to ensure each visit used the same test locations. 2.4 Statistical analysis

Using the statistical package Statistica™ (Statsoft Inc., USA), backward stepwise regression eliminated non-significant variables and generated equations to enable the prediction of playing surface quality from a combination of soil and grass factors; all of which can be managed or influenced by the Groundsman. The factors entered into the regression analysis were: Grass length, grass cover, surface evenness, volumetric moisture content, 0-50mm bulk density, 50-100mm bulk density, Log clay content, Log silt content, medium sand content and Log fine sand content. This study avoided using the results of one quality test to predict another and only a regression statistic (R2) >0.5 was deemed acceptable. 3 Results and Discussion

Non- normality in the data was treated by Log transformation. This was necessary for the Clegg hammer readings and the soil constituents: clay, silt, fine sand and coarse sand. 3. t Soil types

Six soil types were identified: clay (n=30), clay loam (n=55), loamy sand (n=35), sand (n=205), sandy loam (n=15) and sandy silt loam (n=15). Tabs. 1-2 demonstrate the regression models for two contrastingsoil types; sand and clay loam.

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3.2 Regression models

Regression models for sand and clay loam pitches under wet and dry conditions are shown in Tabs. 1-2. 'Wet' indicates rain or irrigation within 2 days of the tests.

Sand

Wet Dry

Clay Loam

Wet Dry

St. error 5.57

Traction = 0.31 (grass cover) - 0.29 (grass length) - 9.43 (50-100mm bulk density) + 37.80 Traction = 0.23 (grass cover) - 0.22 5.64 (moisture content) + 1.98 (Log silt content) + 28.79 Traction = 0.17 (grass cover) - 0.54 4.56 (grass length) + 0.86 (evenness) + 31.66 Traction = -0.94 (moisture content) + 7.19 74.68

R2 0.55

p p
0.38

p
0.89

p
0.68

p
Table l. Traction regression equations forsand andclay loam soil types

Sand

Wet Dry

Clay Loam

Wet

Dry

St. error 0.21

Hardness = 0.002 (grass cover) + 0.56 (0-50mm bulk density) + 4.34 Hardness = -0.01 (moisture content) + 0.15 0.23 (50-1 OOmm bulk density) + 4.95 Hardness = -0.0\ (grass length) + 0.04 0.13 (evenness) + 0.71 (0-50mm bulk density) -0.03 (medium sand) - 0.27 (Log fine sand) - 0.98 (Log silt) + 8.64 Hardness = 0.004 (grass length) - 0.16 0.04 (moisture content) - 0.01 (medium sand) + 6.58

R2 0.13

p p
0.39

p
0.76

p
0.91

p
Table 2. Hardness (Log g) regression equations for sand andclay loam soil types Unsurprisingly increased grass cover increased traction on wet and dry sand while increased bulk density increased hardness on wet sand. This relationship was particularly weak however. On wet clay loam soil, grass length reduced traction possibly through reduced friction between the surface and the metal plate, while longer grass may have cushioned the blow of the hammer on the surface. Importantly, in each of the regression equations are soil and / or moisture content factors demonstrating that player-surface interaction quality could be manipulated through comprehensive soil management. The weak R2 values for sand were likely to be the result of limited variability within the sand data results. Grass cover was a predictor

An Investigation into the Link Between Soil Physical Conditions and the Playing Quality 319 variable but this may be a poor reflection of the below ground biomass present. Roots add strength to the soil matrix, but even after grass cover reduced, van Wijk (1980) recorded sustained soil strength because of roots retained in the soil. Furthermore, under conditions of drying, matric forces within the soil may add to strength but this would be less successful in coarse-grained material. The depth and spacing of the drains and time since rainfall or irrigation event may be more critical in coarse-grained (sand-based) rootzones when measuringstrength. The issue of top-dressing was also highlighted; the underlying soil type may be different to that recorded in the upper 50mm. Deeper sampling and particle size analysis using soil from a range of depths may have shown a different soil type. The result of this would be to include pitches that were not sand in the 'sand' category, limiting the production of reliable prediction equations. 3.3 Predicted v Actual Sand; wet conditnrs :so -r-t-

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Clayl.oam; ~t conditions -.."

::00

200,-------....,. 150

150

100 100

50

50

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..

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Fig. 2. Predicted v observed hardness (untransforrned data) for sand and clay loam pitches

under wet test conditions, using regression equations from Tabs. 1-2. Figure 2 demonstrates that for the sand based rootzones, predicted values were overestimated, limiting the reliability of the regression model. Although for a smaller data set, the proximity of the data points to the I:I line demonstrates that hardness values can be reliably predicted on clay loam soils. 4 Conclusions

A link between tests for player-surface interaction quality and components of the pitch that can be influenced by a Groundsman has emerged. Further research should undertake more frequent testing, on pitches of known soil type to verify the regression models discovered. Commercial applicability has been suggested. Bespoke software would enable a Groundsman to monitor player-surface interaction quality in real-time and periodic soil testing, would ensure model parameters are up to date.

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Poor regression results in some instances may have been the result of top-dressed pitches skewing particle size classification towards sand, or simply that sand-based pitches are less variable and regression equations could not be established. Finally, player-surface interaction tests are only one aspect of playing quality but are directly relevant to player safety . The facilitation of pitch management to maximize player-surface interaction quality should help minimize injury rates and associated costs .

5 Acknowledgements This research was sponsored by TurfTrax, Oakley, Bedfordshire, UK and the Engineering and Physical Sciences Research Council (EPSRC) under the Engineering Doctorate (EngD) program.

References Adams, W.A., Gibbs, RJ., Baker, S., & Lance, D. (1992) Making the most ofnatural turf pitches . A national survey a/winter gam es pitches with high quality drainage designs.

Natural Turf Pitch Prototypes Advisory Panel Report No. 10, Sports Council. Baker, S.W. & Gibbs, R) , (1989) Levelsof use and the playing quality of winter games pitches of different constructiontypes: case studies at Nottingham and Warrington. Jou rnal ofthe Sports Turf Research Institute . 65, 9-33. Bell, Mol. , Baker, S.W., & Canaway, P.M. (1985) Playing quality of sports surfaces: a review. Journal ofthe Sports Turf Research Institute, 61, 26-44. BSi (1990) Artificial Sports Surfaces. 7044-2.2:1990, London: British Standards Institute. Canaway, P.M. & Bell, Mol. (1986) Technical note: an apparatus for measuring traction and friction on natural and artificial playing surfaces. Journal ofthe Sports Turf Research Institute . 62, 211-214. Clegg, B. (1976) An impact testing device for in situ base course evaluation. Proceedings of the Australian Road Resea rch Bureau , 8, 1-6. DCMS/Strategy Unit (2002) Game plan: a strategy for deliveringGovernments sport and physical activity objectives. London: British Government. Hawkins, R.D. & Fuller, C.W. (1999) A prospectiveepidemiological study of injuries in four English professional football clubs. British Journal ofSport s Medicine. 33, 196-203. Holmes,G. & Bell, Mol. (1986) A pilot study of the playing quality offootball pitches. Journal a/the Sports TlII/ Research Institute, 62, 74-90. Holmes,G. & Bell, M.K. (1987) Standards ofplaying quality for natural turf Project Report, Sports Council/STR!. lOG (200I) Guidelines for performancequality standards part one; sports surfaces natural and non turf. Milton Keynes, UK: The Institute of Groundsmanship. Shildrick, J.P. & Dye, A.L. (1983) A review a/playing sur/aces research . London: National Turfgrass Council. van Wijk, A.L.M. (1980) Playing conditions 0/grass sportsfields . Wageningen: Centre for Agricultural Publishingand Documentation.

Measuring and Modelling the Goalkeeper's Diving Envelope in a Penalty Kick David G Kerwin I and Ken Bra; I

2

UWIC, Cardiff School of Sport, Wales, [email protected] University of Bath, Sport and Exercise Science, [email protected]

Abstract. The penalty kick is a key set play in competitive soccer which often determines the outcome of a match, and when used in its 'shoot-out' format, resolves tied games during the knock-out stages of international tournaments. 85% of penalty kicks in open play, and 75% in penalty 'shoot-outs', result in a goal being scored. The purpose of this study was to establish the area of a soccer goal - the diving envelope - which could not be defended by a goalkeeper when facing a penalty kick. Video analysis of the 2004 European championship penalties revealed that the time between ball strike and arrival at the goal line ranged from 500-700 ms. Officially the goalkeeper cannot move towards the penalty taker until the ball has been struck and the area that he has to defend is 7.32 m x 2.44 m (24 ft x 8 ft) with the ball having to travel from a fixed spot, 10.97 m (12 yd) from the centre of the goal line. An electrically driven ball launcher (BOLA, Bristol, UK) was used to deliver two sets of 20 ball launches at two experienced goalkeepers in a simulated penalty shoot-out. The goalkeepers took up position on a force plate located at the centre of a soccer goal. All trials were simultaneously recorded using three digital video cameras within an indoor sports facility which had previously been calibrated to facilitate 3D DLT reconstruction of the video data. The launch velocity remained constant at 21 m-s' (47 mph) whilst the direction and height of each trajectory was varied to include left and right shots directed to low, mid and high levels. A goalkeeper model was developed based on jumping ability, derived from ground reaction force data, and anthropometry. Based on the ball flight time and the goalkeeper model a region of the goal was identified comprising 28% of the area which cannot be protected by a goalkeeper, meaning that players could guarantee scoring if they shoot into this 'unsa veable zone' . Observations from the two penalty shoot-outs at the 2004 European Championships revealed that many players do not take advantage of this zone and continue to gamble on the goalkeeper guessing incorrectly when taking a penalty.

1 Introduction Penalty kicks in elite level soccer tournaments including World Cups from 19821998 and the European Nations Cup (Euro) 1996 included 81 penalties in open play of which 85% were successfully converted and 176 in penalty shoot-outs of which 75% were goals (McGarry and Franks 2000). The same authors reported that at least one of the finalists in each of these tournaments had won at least one match, including the 1994 World Cup Final, via a penalty shoot-out. Rule changes now allow a goalkeeper to move sideways prior to the ball being struck. As a result it is possible for a goalkeeper to move in anticipation of the kick being taken and in so doing, decrease the area of the goal to one side that he needs to defend. Obviously if he

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anticipates incorrectly, the unprotected area to the opposite side increases. The ball flight time for a typical penalty is around 600 ms (McMorris, Copeman, Corcoran, Saunders and Potter 1993) compared to the goalkeepers' diving motion which takes from 500-700 ms (McGarry and Franks 2003). In a previous study of goalkeepers' diving motion, two semi-professional and two college goalkeepers were required to dive towards a football suspended ±2.5 m from a centre line at varying heights (Suzuki, Togari, Isokawa, Ohashi and Ohgushi [988). The two semi-professionals recorded takeoff velocities close to 5 m-s", with the horizontal component being approximately four times that of the vertical component. These results do not reflect a normal penalty environment, where the goalkeeper is required to judge the flight of the ball and anticipate its arrival location and to adjust the width as well as the height of his dive. The purpose of this study was to measure maximumjumps and dives in a simulated penalty shoot-out to provide data to develop a model of a goalkeeper's maximum diving envelope.

2 Methods 2.1 Data Collection Two experienced goalkeepers (2[ yrs, 95 kg, 1.83m; 20 yrs, 76 kg, [.84 m) gave written informed consent. A soccer goal was located in a large indoor sports hall with an electrically driven ball launcher (BOLA, Bristol, UK) located 10.97 m (12 yards) from the goal line. Safety mattresses (crash mats) were placed around the goal mouth to protect the goalkeepers when landing. Three digital video cameras (OCRTRV-900E, Sony, Japan) were set at distances of II m to 25 m from the centre of the goal. One was located at the side to record the whole of the flight. A second was located at a height of 3.5m and angled to include the goal mouth and the majority of the ball flight. The third camera, directly behind and above the ball launcher, viewed the goal mouth (Fig. I). All cameras operated at 50 Hz with the shutter speed of 1/1000 s. A common trigger initiated three banks of 20 LEOs which illuminated in sequence at I ms intervals enabling the shutter opening times to be synchronized to I ms (see Kerwin and Bray 2004 for details). A 3D volume containing the goal mouth and the penalty spot was calibrated using a single pole with four 0.10 m spherical markers at I m vertical intervals. Video images were recorded whilst the pole was moved in sequence around 18 locations (Fig. I). A simulated penalty shoot-out was conducted with each goalkeeper. The launch speed was maintained at 21 m-s' (47 mph). Ten 'shots' were made to each goalkeeper's right with the launch angle being altered to produce a range of low, mid and high shots. The sequence was repeated to the goalkeepers' left. Video images from the camera behind the ball launcher were made of the goalkeepers performing a series of four maximal effort counter movement jumps (cmj) from a force plate (Kistler 9287BA, Switzerland) located at the centre of the goal. Force data (1000 Hz),

Measuring and Modeling the Goalkeeper's Diving Envelope in a Penalty Kick

323

'''''-

,

-

I',

Fig. 1. Equipment layout showing the calibration pole and camera locations, goal, crash mats and trigger unit linked to LEDs and force plate.

triggered with the same LED system, were numerically integrated to determine takeoff kinematics.

2.2 Data Analysis All digitizing was completed using the Target high resolution system (Kerwin 1995). Following six repeats of the calibration images, sequences of the ball flight were digitized from two views and reconstructed using 3D DLT techniques to determine the ball's trajectory. Images of each goalkeeper's dives were digitized from the instant that the ball left the launcher until his arm contacted the crash mat. The left and right toes and fingers, an estimated mass centre (-navel) and head centre were digitized. The planar motion of the goalkeepers was reconstructed using 2D DLT techniques (Kwon 1999). Images of the vertical jumps were used to determine maximum stretch (toes to fingers) and estimated arm span for each of the goalkeepers. Digitizing of the ball's trajectory commenced when the ball first appeared in both views. This instant varied from trial to trial depending on the launch angle. Extrapolated data for the unseen part of the ball flight were generated using a linear fit for the motion towards the goal (y). The missing lateral (x) and vertical (z) data were generated using Burg's prediction method (Mathcad 13™, Adeptscientific). Trials resulted in a 'goal', a 'save' or a 'miss' and therefore the ball did not always cross the goal line between the posts. To determine the theoretical flight time for each launch, the linear fit to the 'y' data from the ball's first appearance until it was 2.5 m from the goal line was used to generate the whole flight from y = 10.97 m (12 yards) to y = 0 m (goal line). The actual time at which the ball crossed the line (or until the minimum value ofy in a 'save' or a fingertip contact with the ball) provided an estimate of the time available to the goalkeeper to make a save. For each goalkeeper's dive, the nearest finger location to the ball at the time at which the ball crossed the goal line was determined . In addition, the closest a finger

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David Kerwin and Ken Bray

came at any time in the goalkeeper' s dive to the position where the ball crossed the line was determined . For those trials where the goalke eper made contact with the ball, the minimum value was at ball contact. Planar plots of the paths traced out by the goalkeeper's limbs (Fig. 2) during the dive represent the goal area which could be protected . A model of the goalkeeper' s maximum diving range was developed from the force plate and video images of the goalkeepers' jump s and the penalty dives. These values, together with the fingertip to ball distances, radii and angles, and mass centre position and takeoff velocity in all dives, provided data to inform the model used to the determine the goalkeeper' s maximum diving envelope.

3 Results and Discussion Of the 40 trials recorded , 32 were suitable for analysi s. One was off target, eight were saved by the goalkeeper, ·18 resulted in a goal. In the remaining trials, the ball struck either the bar or post. Thus a similar percentage of ' shots' in the trials, as have been reported in tournament soccer, resulted in a save (8/32). A plot of all 'shots' was expanded by assuming left/right symmetry so that 64 ball positions were generated (Fig. 3). The time for the ball to travel from the penalty spot to the goal line was 0.642 ± 0.014 s. This represents the time that the goalkeeper has to make a save for a penalty kick taken at 21 m-s" . When a 's ave' was made, contact with the ball occurred approximately 0.75 m in front of the goal line and ~600 ms from launch. The maximum vertical takeoff velocity achieved (cmj) was 2.9 m-s' and the maximum reach 2.84 m. The highest takeoff velocity (4. 13 m-s" ) was found in the penalty dives when there was a large horizontal velocity component. The images in Fig. 2 show four dives. When the ball was close to the goalkeeper (±2 m) from the centre of the goal (Fig. 2, upper images), the goalkeeper dived from his initial standing position with minimal prior foot movements. When the ball was aimed ju st inside the goal post or to a high central position, the goalkeeper stepped sideways by about 1.1 m before commencing his dive (Fig. 2, lower images). The time to make the side step constituted 66% of the total takeo ff time, and so whilst increasing his total diving range, his diving 're ach ' prior to the ball ' s arrival was restricted . By combining the data from all trials it was possible to map out the total area of the goal which the goalkeeper was able to defend. Based on the time of ball flight, the takeoff position and velocity, and the maximum reach of each goalkeeper, a model of the diving envelope which the goalkeeper could describe was developed . Initially the vertical takeoff velocity and reach (cmj) were used to predict the area that the goalkeeper could cover in a dive. The peak of this area was higher than the goal (2.44 m) in the centre, but narrower than the goal (7.32 m), and covered 65% of the goal area (Fig. 3 grey arch). If allowance was made for the goalkeeper stepping to the side before diving, and the time needed was ignored , he could cover almost all of the goal area (Fig. 3 dash and dot-dash arches). When the goalkeeper moved sideways before diving, his resultant velocity increased

Measuring and Modeling the Goalkeeper' s Diving Envelope in a Penalty Kick

325

"

., -)

Fig. 2. Images of the goa lkeeper 's movemen t in trials (BI ,4,5,8) . Black lines indicate the position of the goalkeeper as the ball crossed the goal line, grey lines track the complete dive with the locus of the closest finger tip traced throughout. The ball is plotted at the time when it crossed the goal line. Image dimensions = Yz the goalmout h (ie 3.66 m x 2.44 m).

but, in the time of ball flight to the goal line, the maximum area of the goal that he would be able to cover was 76% (Fig. 3 black arch). When the calculations were repeated with the goalkeeper reaching forwards by 0.75 m as seen in the 'saved' trials, the goal area and the reach radius were reduced, producing a revised area which could be covered of 72%.

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Fig. 3. Left image = zones of the goal which the mode l predict can be covered . Grey rectangle: goal area; dotted grey rectangle : 0.75 m goal area; black diamonds : limit of the goalkeeper 's dive; grey triangles : cmj reach; dash and dot-dash arches: cmj arch ±I m step prior to takeoff. Right image = the recorded ball locations in the pseudo penalty shoot-out (grey circles = actual shots and white circles = reflections about a central vertica l line, ie symmetry assumed) .

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David Kerwin and Ken Bray

4 Conclusions By modeling a goalkeeper's dive, it is possible to predict the area of the goal that he can defend in a penalty . There remains a region, around 28% of the goal, which cannot be covered. This zone comprises the comers of the goal. A tall goalkeeper may be able to move towards one post and save a wide-low shot aimed just inside the post. This was seen in the European Cup Final 2005 penalty shoot-out in Turkey. Even allowing for a goalkeeper's movements prior to ball strike, the two areas close to the top comers of the goal remain exposed. Data from a simulated penalty shoot-out resulted in a 'score to save ' ratio similar to that previously reported for international penalty shoot-outs. The data confirmed that there is an area of the goal that is unreachable in the time available. Based on the ball flight time and the goalkeeper model , a region of the goal was identified comprising approximately 28% of the area which could not be protected, meaning that players could guarantee scoring if they shoot into this 'unsaveable zone' .

Acknowledgements The authors gratefully acknowledge Torn Nakagami 's assistance in the field trails and in the data collection and data reduction phases of this study .

References Kerwin , D. G. (1995) Apex/Target high resolution video digiti sing system. In Proceedings of the Biomechanics Section ofthe British Association ofSport and Exercise Science (edited by 1. Watkins), pp. 1-4. Glasgow: BASES . Kerwin , D.G. and Bray, K. (2004) Quantifying the trajectory of the long soccer throw-in . Engineering in Sport 5. University of Davis California. (Eds. M. Hubbard , R.D.Metha and 1.M. Pallis) . International Sport Engineering Association publicat ion, 63-69 . ISBN 09547861-0-6. Kwon, Y.H. (1999) 2D Object plane deformation due to refract ion in two-dimensional underwater motion analysis. Journal of Applied Biomechanics. 15, 396-403 . McGarry , T. and Franks, I. M. (2000) On winning the penalty shoot-out in soccer. Journal of Sports Science, 18, 401-409 . McGarry , T and Franks , I. M. (2003) The science of match analysis . In Science and Soccer (edited by Reilly, T. and Williams , A. M.), pp. 265-275 . London : Routledge. McMorris, T , Copeman , R., Corcoran, D., Saunders, G. and Potter, S. (1993) Anticipation of soccer goalkeepers facing penalty kicks. In Science and Football II (edited by T. Reilly, J. Clarys and A. Stibbe) , pp. 250-253 . London: E & FN Spon . Suzuki , S., Togari , H., Isokawa, M., Ohashi, 1. and Ohgushi, T (1988) Analysi s of the goalkeeper's diving motion . In Science and Foothall (edited by T. Reilly, A. Lees, K. Davids and W.J. Murphy), pp. 468-475 . London : E & FN Spon.

Flow Visualization on a Real Flight Non-spinning and Spinning Soccer Ball Takeshi Asai I, Kazuya Se0 2, Osamu Kobayashi ' and Reiko Sakashita" Inst. of Health and Sports Science, Tsukuba Univ ., Tsukuba, Japan, [email protected] 2 Fac. ofEduc. Art and Science, Yamagata Univ ., Yamagata, Japan 3 Department of Aeronautics and Astronautics, Toka i Univ., Hiratsuka, Japan 4 Fac. of Educ ., Kumamoto Univ ., Kumamoto, Japan I

Abstract. Wind tunnel test with a full size non-spinning soccer ball was carried out to meas-

ure the aerodynamic forces (drag, lift and side force). The drag coefficient of a non-spinning soccer ball in the subcritical regime was nearly 0.43 and that of in the supercriticalregime was nearly 0.15. It is estimated that the critical Reynolds number of a soccer ball is about 2.2x105• In the visualization experiment using titanium tetrachloride, we compared the flow around the ball during a non-spinning, low-speed kick (5 m/s) and a high-speed kick (29 m/s). During the low-speed kick, the boundary layer separation point was about 90 degrees from the front stagnation point, while during the high-speed kick the separation point had receded to about 120degrees from the front stagnation point.

1 Introduction Many studies have been conducted on the aerodynamics of sports balls including golf (Bearman and Harvey, 1976; Smits and Ogg, 2004), cricket (Mehta, 1983), tennis (Haake et al. 2000; Mehta and Pallis, 2001), and baseball (Watts and Ferrer, 1987). Mehta (1985) carried out the first proper review of sports ball aerodynamics by covering in depth the sports of cricket, golf and baseball. Mehta (1985) discussed that the drag on a ball was dominated by the size and deflection of the wake . However, there have been few such studies on soccer balls (Carre and Asa i, 2004; Carre et al. 2004) . Contemporary soccer requires a player to be able to control the amount of spin on the ball when kicking it and to be able to intentionally generate a curve ball. It is thus extremely important to elucidate the aerodynamic properties involved in soccer. We therefore analyzed using a wind tunnel experiment the aerodynamic properties of a soccer ball during non-rotation. We also compared the flow properties surrounding spinning and non-spinning soccer balls in actual flight by a visualization experiment using titanium tetrachloride.

328

Takeshi Asai, Kazuya Sco, Osamu Kobayashi and Reiko Sakashita

2 Methods The wind tunnel used in the experiment was a low-speed circulating wind tunnel (with six-component wind-tunnel balance; maximum wind velocity: 40 m/s; measuring section: 1.5 x I m; turbulence level: ::;1 %) at the Department of Aeronautics and Astronautics, Tokai University. In the wind tunnel experiment we conducted measurements on a hand-stitched soccer ball (Size 5 Fevernova), and a thermally bonded type of soccer ball (Size 5 Roteiro), both of which were officially approved for international games. Each ball was supported at the rear, with the tip fitted to the sixcomponent wind-tunnel balance (Fig. I). The ball was stabilized to the shaft with an adhesive so it could not rotate.

Fig. 1. Photo of thewind tunnel experiment set-up Each of the following coefficients were calculated: wind velocity (V), force acting in the direction of the wind (drag (D), force acting perpendicular to the wind direction (lift (L)) , and force acting sideways based on a frontal view (S). The aerodynamic forces acquired in the experiment were converted to the drag coefficient (Cf), lift coefficient (Cd, and lateral force coefficient (C s ), as shown in equations 2-1 to 2-3: C = J)

c 5

=

D

(2-1)

L

(2-2)

S

(2-3)

!/2p V 2 A

!/2p V 2 A

where p is the density of air (p= 1.2 kg/rrr'), V is the flow velocity, and A is the projected area of the soccer ball (A = n x 0.11 2 = 0.038 rrr'). The wind velocity used in the tunnel experiment was set within a range of 7 m/s to 35 m/s. A visualisation experiment using titanium tetrachloride was also conducted in order to visualise the flow around the soccer ball during flight. A soccer ball was placed directly in front of a soccer goal 15 m away and we had a subject perform a straight kick that involved virtually no rotation and a side-spinning curve kick. Both kicks were placement kicks delivered at the same velocity, as would occur in a real

Flow Visualization ona Real Flight Non-Spinning and Spinning Soccer Ball

329

game. A high-speed VTR camera (Photron Ultima; Photron Limited) was set up at a midpoint between where the ball was placed and the soccer goal, and photographs were taken at 4,500 fps. The wake angle (W) was defined as a parameter expressing the size of the vortex area trailing the ball. W= 360 - 2 x SP (deg.)

(2-4)

Here, W is the wake angle, and SP is the angle made by the boundary layer separation point and front stagnation point.

3 Results and Discussion In the tunnel experiment, observation of the changes in drag in relation to wind velocity revealed that drag increased from 0.5 to 3.8 N as the wind velocity increased from 7 to 35 m/s, although the changes were not uniform. At a wind velocity of 12 to 15 mls a drag crisis was observed, whereby the drag coefficient temporarily decreased. Examination of the relationship between the Reynolds number and drag coefficient revealed that the drag coefficient was about 0.43 at a high range and about 0.15 at a low range. This meant that the critical Reynolds number for the nonspinning soccer ball in the present experiment was about 2.2 x 105 (Fig. 2). 0.5

__ Cd (Fevemova) --0-

0.4

Cd (Rotelrol

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o

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1000000

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There was little difference in the drag properties between the hand-stitched soccer ball and the thermally bonded one, although further research will be required to establish the details of variations between the two makes. Carre and Asai (2004) reported a wind tunnel experiment using a 1/4 miniature soccer ball whereby the critical Reynolds number for a non-spinningsoccer ball was about 1.3 x 105. The critical Reynolds number in the present study was found to be higher, however. This might be because the small size of a 1/4 miniature soccer ball compared with a full-sized ball means that the effect of stitching on the ball panelling would be comparatively large. In any case, the drag properties of this miniature ball were thought to be somewhere between those of a smooth ball and a golf ball. When a player performs a powerful shot or takes a free kick during an actual game of soccer, the initial velocity is commonly considered to be about 25 to 35 mls. In that case, the ball will reach the

330

Takeshi Asai, Kazuya Seo, Osamu Kobayashi and Reiko Sakashita

goal at the previous supercritical region related to the critical Reynolds velocity region. Images of the visualization experiment, which depicted the smoke trails produced by the titanium tetrachloride, were examined based on observations and the angle from the front stagnation point of the boundary layer separation point (tip of ball) . First, we compared the flow around the ball between a non-spinning low-velocity kick (5 m/s) and a high-velocity kick (29 m/s) . It can be seen during the low-velocity kick that the boundary layer separation point was about 90 degrees from the front stagnation point and the vortex region was comparatively large, while during a highvelocity kick the separation point had receded to about 120 degrees from the front stagnation point and the vortex region had also shrunk (Fig. 3).

(a)

(b)

Fig. 3. Flow visualization of a non-spinning soccer ball from above (ball velocity. (a) 5 mis, (b) 29 mls) (flow is from right to left)

Taneda (1978) reported that the critical Reynolds number during transition of a nonspinning smooth ball is about 3x 105 and that separation at no more than the critical Reynolds number occurs at a position of about 75 degrees from the front stagnation point , while separation above the critical Reynolds number occurs at about 135 degrees from the front stagnation point. In the case of a soccer ball, the difference between before and after transition was not as great as the smooth ball, but there was a difference up to about 30 degrees , which was also accompanied by a difference in the vortex region. In the present study , we compared the wake angle (W) between the subcritical time and supercritical time, and found a difference between the two at about 60 degrees, but there was no notable difference within each respective region (Fig. 4). 200 180

I• Soccer ball I

.,

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60

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o

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10

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* the separation angle from

Flow Visualization on a Real Flight Non-Spinning and Spinning Soccer Ball

331

Examination of lateral images during high-speed kicking of a spinning curve ball (26 m/s; 8 rps) showed that the separation point was positioned about 120 degrees from the front stagnation point , and the layer between the top and bottom surface of the ball became turbulent (Fig. Sa-c).

(a)

(b)

(c)

Fig. S. Flow visualization of a spinning soccer ball from side view (ball velocity : 26 mis, spin rate : 8 rps) (flow is from right to left and the ball is spinning from left to right)

Parietal images also showed that, as with the above, during high-speed kicking (29 m/s) of a non-spinning ball the separation point receded to about 120 degrees from the front stagnation point, and the vortex region also shrunk. On the other hand, during high-speed kicking (27 m/s; 7 rps) of the spinning curve ball the vortex was seen to deviate, due to the effects of a relative difference in fluid velocity caused by the rotation (Fig. 6a-c) . The curvature of the ball's trajectory was attributed to the generation of a lateral force caused by the vortex counteraction. However, although the separation point was not symmetrical on the left and right in relation to the direction of travel (top and bottom symmetry on the images) it was similar to about 124 degrees from the front stagnation point and the angle attained during high-speed kicking of a non-spinning ball. During a high-speed kick of a spinning ball also, the boundary layer became turbulent and the vortex region shrunk. The above findings suggest that, during high-speed kicking of a non-spinning ball, the boundary layer becomes turbulent. However, during high-speed kicking of a spinning curve ball it can also be assumed that the boundary layer is a turbulent layer, based on the position of the separation point and vortex region .

(a)

(b)

(c)

Fig. 6. Flow visualization of a spinning soccer ball from above (ball velocity : 27 mis, spin rate : 7 rps) (flow is from right to left and the ball is spinning in a counter-clockwise direction)

332

Takeshi Asai, Kazuya Seo, Osamu Kobayashi and Reiko Sakashita

4 Conclusion Examination of the relationship between the Reynolds number and drag coefficient for a non-spinning ball in the wind tunnel experiment revealed that the drag coefficient was about 0.43 at a subcritical region and about 0.15 at a supercritical region. This suggests that the critical Reynolds number was about 2.2 x 105• In the visualization experiment using titanium tetrachloride, we compared the flow around the ball during a non-spinning, low-speed kick (5 m/s) and a high-speed kick (29 m/s). During the low-speed kick, the boundary layer separation point was about 90 degrees from the front stagnation point, while during the high-speed kick the separation point had receded to about 120degrees from the front stagnation point.

References Bearman, P. W. and Harvey, 1. K. (1976) Golf ball aerodynamics. Aeronautical Quarterly, 27, 112-122. Carre M. 1. and Asai T. (2004) Biomechanicsand Aerodynamics in soccer, Biomedical Engineering Principles in Sports. G. K. Hung and J. M. Pallis Eds., Kluwer Academic plenum Publishers, pp 333-364. Carre M. J., Goodwill, S. R., Haake, S. 1., Hanna, R. K. and Wilms, J. (2004) Understanding the aerodynamics of a spinning soccer ball. The Engineer ing ofSport 5 (Eds. M. Hubbard, R.D. Mehta and 1.M. Pallis). Pub. The International Sports Engineering Association, Sheffield, UK, 70-76. Haake, S. 1., Chadwick, S. G., Dignall, R. 1., Goodwill, S. R, and Rose, P. (2000) Engineering tennis - slowing the game down. Sports Engineer ing, 3 (2), 131-143. Mehta, R.D., Bentley, K., Proudlove, M. and Varty, P. (1983) Factors affecting cricket ball swing. Nature, 303, 787-7R8. Mehta R. D. (1985) Aerodynamics of Sports Balls, Annual Review ofFluid Mechanics, 17, 151-189. Mehta, R. and Pallis, 1. (2001) The aerodynamics of a tennis ball, Sports Engineering 4(4), 177-IX9. Smits, AJ . and Ogg, S. (2004) Golfball aerodynamics. The Engineering ofSport 5 (Eds. M. Hubbard, R.D. Mehta and 1.M. Pallis). Pub. The International Sports Engineering Association, Sheffield, UK, 3-12. Taneda, S. (197X) Visual Observations of the Flow past a Sphere at Reynolds Numbers Between 10"-4 and 101\6. Jnl. Fillid Mech., 85, 187. Watts, R.G. and Ferrer, R. (1987) The Lateral Force on a Spinning Sphere: Aerodynamics of a Curvebal. Am. 1. Phys., 55,40-44.

Gaze Point Analysis in Movement Prediction of Soccer Players by Image Processing Yuusuke Hiramatsu', Shigemichi Ohshima' and Atsumi Ohtsuki' J

Department of Mechanical Engineering, Meijo University, Nagoya, Japan, [email protected]

Abstract. This paper describes the effect of positioningthe gaze point of a defensive player to predict the movement of an offensive player in a soccer game by using the recognition algorithm. In this research, positioningof the gaze point is systematically varied to predict the movement of the offensive player, target. Here, pattern images of the target moving to the right and left side (directional movement), and sweeping the left or right foot in front of the ball and moving to the right and left side (feint movements) are recorded by a digital camera. The stored feints movements are then matched with the directional movements to prediet the direction of movement of the target. The matching system is developed by mimicking brain function for image recognition. Therefore, in using the matching system, we can analyze the gaze point as a system that is similar to the visual information exchangeof the retina and brain. The optimum position of the gaze point is then evaluated based on the difference of the matchingdegree outcome in the oppositedirections.

1 Introduction In the soccer game, defenders basically try to predict/anticipate what offensive player is going to do with the ball, which direction offensive player is going to go. The offensive player uses "the feint" a part of a movement designed to trick/fake to distract the defenders. Defenders should not be cheated and react to the movement of the ball and the body language of the offensive player with the ball. According to the past research, in one-to-one in soccer game , the accuracy of prediction was influenced by the positioning of the gaze point of a defensive player. The effect of the gaze point positioning patterns was analyzed by dividing expert's group and beginner's group. The prediction ability of the expert's group was higher than that of the beginner's group. Therefore, we thought that the gaze point selection is crucial for the accuracy of prediction and that it is possible the effect of positioning the gaze point of a defensive player to predict the movement of an offensive player by using the matching system. The matching system is developed by mimicking brain function for image recognition . In using the matching system, we can analyze the gaze point as a system that is similar to the visual information exchange of the retina and brain . The optimum position of the gaze point is then evaluated based on the difference of the matching degree outcome in the opposite directions.

334

Yuusuke Hiramatsu, Shigemichi Ohshima and Atsumi Ohtsuki

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2 Experimental Conditions In one-to-one in soccer, as for relations between the offensive player and the defensive player, facing from the front, running in a row, and contact play are given. In this experiment, the situation of facing from the front is chosen from them. In this situation, the defensive player should predict whether the offensive player moves to the right or left. Figure I shows the schematic illustration of experiment. The feint is begun at a position away from the defensive player by two metres, and last touch is done at a position away from the defensive player by one metre in the front side of the defensive player. Sight of the defensive player is obtained from the camera put on a position away from the defensive player by four metres in the rear side of the defensive player. The feint images are obtained using a camera running at thirty frames per second, from the beginning of the feint to the last touch. Then these frames are converted into the one equal with sight of the defensive player. The set of the still pictures that consists of these converted frames is used for the numerical simulation to predict the movement of the offensive player.

3 Prediction System Developed by Mimicking Brain Function Figure 2 shows the variation matrix of the recorded images. Figure 2 (a) shows the four directional image patterns under consideration . Here, offensive player moves to the right or left by hooking the ball using the outside or inside of the foot without any feint. For example, d oL is the case in which the offensive player moves towards the left by hooking the ball using the outside of the left foot. And diR is the case in which the offensive player moves towards the right by hooking the ball using the inside of the left foot. Figure 2 (b) shows four feint image patterns under consideration the player's feint is done by sweeping the left or right foot in front of the ball and then as it lands on the ground use it to pivot and tum using the right or left foot to take the ball to the right or left. For example, F oL is the case in which offensive player moves towards the left after sweeping the right foot to take the ball to the left using the outside of the left foot. And, F iR is the case in which offensive player moves towards the right after sweeping the right foot to take the ball to the right using the inside of the left foot.

Gaze Point Analysis in Movement Prediction of Soccer Players by Image Processing

335

In this system, the first phase is image translation from the log-polar coordinate that is mimicking the translation from the retina to the brain (Jurie 1999). Here, the origin of the log-polarcoordinate is taken to be the gaze point under consideration. Figure 3 (a) shows the target image in the log-polar coordinate system. Gaze points on the target are selected to be on the waist, ancle and knee. Figure 3 (b) shows the image in the translated coordinate system. The images on the left and right are images produced when the origin is taken at gaze points I and 2, respectively. Figure 3 (c) shows the target in the translated coordinate system without the background. The dark portion is the target. It should be noted that the shape of the target in the coordinate system changes with the selected gaze point. The gaze points shown in the translated coordinate system include characteristic information that can be used to indicate the predicted movement. The amount of information varies with the position of the gaze point. Therefore, gaze point selection is crucial for the accuracy of prediction. Figure 4 shows matching of images produced by differential of Gaussian filter with four direction and five frequencies. These extracting features by DOG are mimicking the function of the visual processing at the primary visual cortex of the brain (Nakano, Morie and Iwata 20(3) . Figure 4 (a) shows the filtered directional images of one directional image depicted Fig.2 (a). Figure 4 (b) shows the filtered feint images of one feint image depicted Fig. 2 (b). One set of filtered feint image is matched against 40 directional images by the dynamic link matching method (DLMM) that is flexible template matching method.(Lades, Vorbruggen and Konen 1993). The right matching degree (ER; ) of one feint image (Fj ) is computed by summing the outcome of the matching to the 20 directional images towards the right (diR and doR ) by DLMM. The left matching degree (E l,) of one feint image (Fj) is computed the same as the right. The prediction parameter (E;) is defined the difference of the matching degree outcome in the opposite directions (E R; and ELJ. These parameters are defined as: I ' EN, =-

L(

I .,

L(

(I)

F, o d." ). E" =F, e a.; ). E , = EN, - E" n ,./ n ,.. , (0 : matching operation hy DLMM . * : o( outside) and i( inside ). j : Flame numbe r of Feint image )

Here, j (j=I ~ 31 frame) is frame number of feint image and n (=20 frame) is number of directional images each of left and right directions. If E;<-O. I then the defensive player predicts that the offensive player, target, moves to the left direction. If EpO.1 then the defensive player predicts that the offensive player moves to the right direction. If -0.1 < =E;<=O.I then the defensive player doesn't predicts whether the offence moves to the left or right. When the absolute value of E, is the larger, the confidenceof the defense for prediction is the larger.

4 Results Figure 5 (a) shows the nine gaze points based on the past research that the expert defensive player's gaze points are tend to be put on knee, waist and ankle in feint section.

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Gaze Point Analysis in Movement Prediction of Soccer Players by Image Processing

337

The simulation results are shown in Fig.5 (b), (c) those show the prediction parameter E, when the gaze point is put on each part of the knees of the offensive player who does Fu.. The vertical axis in graphs is the frame numberj and the second that is spent to last touch. The horizontal axis is the values of prediction parameter Ej • The predictions are done at the same time as behavior of the offensive player. The defensive player decides own behavior based on Ej since the 22nd frame to which the dot line is pulled. The defensive player reacts to the offensive player, when the seven frames with Ej of the same direction are accumulated between from the 22nd frame to the 31st frame. E, before the 21 st frame are used only for the gaze point movement of defensive player. The gaze point movements of two patterns are shown by arrows and double circles in FigA (b), (c). Gaze point movement has delay of about 133[ms] that is initiation of regular saccade (Dorris, Pare and Munoz 1997). When the movement of the gaze point happens since the 22nd frame, the prediction that begins to move is accumulated as the four frames with E of the same direction during the movement. Figure 5 (b) shows the gaze point patternI to Fil . that the gaze point is moved to the predicted direction. Figure 5 (c) shows the gaze point pattern2 to Fu. that the gaze point is moved to the opposite of the predicted direction. In Fig.S (b), the accumulation of E, become four frames on the left direction, and become six frames on the right direction. Because t j of the same direction more than seven frames are not accumulated, the defensive player cannot react to stop offensive player. In Fig.5 (c), the defensive player can react to stop offensive player by moving to the right, because the accumulation of the E, becomes seven frames on the right direction at the 28th frame. Figure 6 show the success rate of the defensive player to four subjects of the offensive player who does feint. The vertical axis in graphs is the kind of gaze point of seven patterns. The horizontal axis is the success rate that the defensive player stops the offensive player. There are the patterns of 100% in the fixed gaze point on the each part of knees and the moved gaze point respectively. The gaze patternI that the gaze point is moved to the predicted direction become 100% in Fig.6 (a), and it is corresponding to the past re search. When all gaze point pattern are evaluated at the same time, the gaze point pattern with 100% doesn't exist. Figure 6 (c) shows the average of Fig.o (a) and Fig.6 (b). The gaze point pattern2 is most high rate in Fig6 (c) among all gaze point pattern.

5 Conclusion The system to evaluate the relation between the feints and the gaze points patterns was proposed in the numerical simulation analysis. Then the effect of the gaze point patterns to predict the feints was researched and proposed by using the matching system. In the future, it will have to do that the result is fed back to the training site.

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Acknowledgment The authors would like to thank Mr. K. Inatorni at Meijo University for data processing.

References Jurie, F. (1999) A new log-polar mapping for space variant imaging. Application to face detection and tracking. Journal of the Pattern Recognition Society . 32, 865-875. Nakano, T ., Morie, T. and Iwata ,A. (2003) A Face/Object Recognition System Using FPGA Implementation of Coarse Region Segmentation. SIC E Annual Conf, Fukui , pp. 14181423. Dorris, C. Micheal., Pare , Martin., Munoz, P. Douglas. (1997) Neuronal Activity in Monkey Superior Colliculus Related to the Initiation of Saccadic Eye Movements. J Neurosci 17, 8566-8579. Lades, M., Vorbruggen, C. 1., Buhmann, 1., Lange , 1., Malsburg, v.d . c., Wurt z, P. R., and Konen , W. (1993) Distortion Invariant Object Recognition in the Dynam ic Link Architecture. IEEE Trans . Compt., vol. 42, no. 3, pp. 300-311.

Traction Testing of Soccer Boots Under Game Relevant Loading Conditions Thomas Grund ' and Veit Senner' , TU Miinchen, Faculty of Sports Science, Department of Sport Equipment and Material s, grund @sp.tum.de

Abstract. The final goal of this research is to determine anterior cruciate ligament (ACL) tensile forces under game relevant loading conditions with respect to different types of soccer boots and different stud design . To realize the given target a combination of experimental testing and computer simulation was chosen . Based on the findings of previous studies and the analysis of video-recorded injury situations in soccer, a new traction test device ("TrakTester") has been developed. The distinguishing feature of this device is to simulate and measure not only pure traction force between shoe and surface but also to simulate high risk loading situations such as the "plant-and-cut-maneuver". The resulting forces and torque transmitted to the tibia will be measured using a 6-component-Ioad-ccll. Comparative testing concerning the amount of traction and the extent of force and torque produced with different sole designs will follow. For calculation of ACL tensile forces the experimentall y determined loads transmitted to the lower leg will later be used as input data for a multi-body computer model of the human knee. The current paper will demonstrate the need for a new traction test device and illustrate the ongoing first steps of its development.

1 Introduction Knee injuries are one of the most frequent mjunes in soccer (Dvorak and Junge 2000) . Especially ruptures of the anterior cruciate ligament (ACL) are very severe , causing at least six months of rehabilitation and some cases the end of the active career of the injured player. Numerous studies showed a prevalence of non-contact ACL-injuries compared to contact ACL-injuries in team-sports (Myklebust, Engebretsen, Braekken, Skjolberg, Olsen and Bahr 2003) . The "plant-and-cut maneuver" (Besier, Lloyd , Cochrane and Ackland 2000) and the " one-leg jump-landing" (Olsen , Myklebust, Engebretsen and Bahr 2004) have been identified as the major non-contact injury mechanisms. Both mechanisms are characterized by a planted (fixed) foot, slight knee flexion , valgus-position of the tibia and internal rotation of the body . Investigators analyzed more in detail the kinematics of the plant-and-cut maneuver (McLean, Myers , Neal and Walters 1998; Sigward and Powers 2005). They all agree that the movements observed during a typical plant-and-cut seem not to be in a

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critical range for suffering an ACL-rupture. However the large variation between the subjects makes general statements impossible. Non-contact ACL-injuries were related to high traction forces between the sole and the playing surface (Heidt, Dormer, Cawley, Scranton, Losse and Howard 1996). They conclude that excessive traction increases the risk of foot fixation . A number of scienti sts (Heidt et al. 1996; Haake, Carre, Kirk and Senior 2004) then investigated the translational traction behavior of different boot types and different stud-design. Other authors concentrated on the rotational traction component (Valiant 1989; Heidt et al. 1996; Barry and Kummer 2000; Cawley et al. 2003) . However no information is available concerning the influence of the stud-design during combined loading situations such as cutting maneuvers. Therefore we attempt a new approach to obtain ACL tensile forces in situations which have the potential to cause injuries. The principle method is a combination of experimental traction measurements (using a mechanical test device) with a computer simulation. The focus of the presented paper is on the development of this traction test device .

2 Materials and Methods The determination of the unknown ACL-tensile force will be done by means of a computer simulation using a complex model of the human body and of the knee joint. For running this simulation realistic joint kinematics as input data are necessary. To achieve this data from TV recordings showing ACL-injuries in soccer we have chosen the computer based reconstruction method described by Krosshaug (Kro sshaug and Bahr 2005) . This data will then be used as kinematical target criterion in the optimization process of a forward dynamics problem using an existing computer model of the human body (Grund, Wallrapp and Senner 2004) . It will be combined with a detailed representation of the human knee joint (Lehner, Eichhorn and Senner 2005) allowing to determine the unknown ACL tensile force . A major difficulty in the development of this model is how to describe the contact between the playing surface and the studded sole of the soccer boot. To avoid the complex shoe-surface contact modeling we plan to use experimentally determined contact loads instead . These will be taken from simulations with a physical model , a traction test device, able to reconstruct ACL injury situations. As several assumptions and simplifications will have to be made in the development of this traction tester ("TrakTester") , it is clear that this physical model can only determine the resulting loads between boot and ground with limited accuracy. However we consider the measured contact load histories which will then be used as input for the computer model to be a good estimate of the situation to analyze.

2.1 Design Requirements Literature describes some state-of-the-art traction-test devices (Barry et al. 2000; Cawley et al. 2003). Both allow measurement of translational as well as rotational traction . The device of Cawley et al. furthermore allows the adjustment of plantar-

Traction Testing of Soccer BootsUnder Game Relevant Loading Conditions

34I

and dorsi-flexion and setting both, inversion and eversion up to 25 degrees. But there are some more demands on the test device that need to be fulfilled for a realistic simulation of an injury-situation and for the acquisition of the necessary data for the simulation: Replication of the full range of motion of the ankle joint in order to secure the realistic position of the tibia in reference to the boot and the playing surface, respectively (especially varus and valgus position of the tibia). Application of 3-component angular and 3-component linear momentum on the soccer boot. Appropriate dynamics of load application. Measurement of resultant forces and torques at the tibia (transmittable internal force) . Portable design of the test device in order to accomplish measurements on different playing surfaces and under various weather conditions. Comparable to the test devices mentioned above our TrakTester is controlled via software and a computer. In contrast to other devices we have chosen not to fix sample boxes of natural grass on a force plate . Instead we want to bring the device to the lawn (or other sport grounds) and measure the force and moment components with a built-in six-component load cell.

2.2 Some Design Details A stable frame supports an artificial lower leg and a simplified model of the foot. The anatomic shape of the foot is given through a silicone cast of a volume model of a 50th percentile male . Inside the silicone a metal structure simulates major behaviour of the foot's bones. The lower leg consists of a shaft of steel with an adapter for load transmission. The connection between lower leg and foot is a mechanical replication of the upper and lower ankle joint that assures the position of the joint axis and the range of motion based on the findings of Inman (Inman 1976). This artificial joint is shown in Fig. I and Fig. 2 shows the complete unit of the artificial leg (Ebert , Knauer and Senner 2005) .

Fig. I Ankle Joint Axis in the CAD-Model

Fig. 2 Artificial Lower Leg

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The load application will be challenging due to high dynamic movements to realize. To solve this problem we will either build a mechanism with a pre-stressed spring, a pneumatic solution or a combination of both. For recording the joint angles of the artificial ankle joint, two goniometers are implemented. The measurement of the transmittable internal force is accomplished by a 6-component load cell, located on the distal end of the surrogate tibia, just above the ankle jo int. Data acquisition will be conducted using a NI-DAQ-Card (National Instruments, Austin, Texas), a standard laptop with PCMCIA-Slot and the software NI LabVIEW (National Instrument s, Austin , Texas, USA). A modular construction will allow portability of the TrakTester by separating single components for purpo se of transportation.

3 Current Status The artificial foot, the lower leg and the artificial ankle joint are ready for use. Also the construction of the main frame has been completed. At the moment we are searching for the best techn ical solution for realizing the linear and rotational impact. The two models (three dimensional muscle-skeleton model of the player and the knee jo int model) have both been implemented in SIMPA CKTM (Intec GmbH, Wessling, German y), which is a commercially available multi-bod y-system software package. Fig. 3 and Fig 4 illustrate the two models.

Fig. 3 computer model of the human body

Fig. 4 Knee Joint Model (Lehner et al. 2005)

The human body is represented by 37 rigid segments. Additional masses are connected to 13 of them, representing wobblin g masses (Zauner 2002 ). The knee model by Lehner has been developed within the past 10 years (Lehner 1995; Lehner et al. 2005) and is now being validated by experiments with human cadaver knees. Representation of the major anatomic structures and the most important characteristics if the human knee jo int is realized.

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4 Discussion Nigg (1990) questioned the relevance of laboratory-based test devices in general because these tests only provide information on the surface-shoe-interaction. His conclusion was that the combination of laboratory material-tests and subject-tests would be the best to get meaningful information on what shoe-surface combination has the highest potential for reducingthe risk of injury. To our knowledge the presented study is one of the few studies which try to simulate a real injury-situation using a mechanical test device. Our aim is to increase our knowledge on what influence different stud-designs may have on the forces generated during a sport-specific movement. By comparative measurement of different soccer boots with the TrakTester it should be possible to obtain adequate input data for our models and to draw the correct conclusions from the simulations hereof. The main difference compared to known traction test devices (Heidt et al. 1996; Barry et al. 2000) is that we will test soccer boots under more realistic loading conditions. This means first testing under a combined situation instead of pure translational and/or pure rotational traction testing. Secondly this requires the application of the loads with respect to physiologic axis instead of a straight perpendicular force application. Although our TrakTester should be a step towards meaningful traction testing several limitations will have to be considered. The influence of the stud-design will only be investigated for one certain movement (the one for which we will determine the kinematic data from the TV recordings). Therefore generalisation of the results on any cutting manoeuvrewill be critical. Further it is almost impossible to adequately model the complex muscle interaction during a plant-and-cut manoeuvre. Therefore the simulation results will only be able to show tendencies, but nevertheless they will improve our understanding of what happens inside the knee in such situations.

5 Future Prospects Having once realized the entire procedure combining the TrakTester measurements with our computer model, the systematic development of an ACL-friendly stud design is the next logical step. Basing on extensive measurements with commercially available soccer boots we will focus on the question, if there are differences regarding the resulting ACL tension force for boots with cylindrical studs and those boots with studs formed in blade-style. Also prototype-boots with alternative sole layouts and a completely different alignment and shape of the studs will be analyzed.

6 Acknowledgement This study is supported by the "Verwaltungs-Berufsgenossenschaft" (VBG). We would also like to thank the "Deutsche Ful3ball Liga GmbH" for the free of charge access to TV recordings.

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References Barry , E.B., Kummer, R. and Milburn , P.D. (2000) The design ofa tract ion-measuring device for footware. In: Subic , A. and Haake , S. (Eds.) The Engineering of Sports - Research, Development and Inno vation . Blackwell Science , Oxford, pp. 103- 111. Besier, T.F., Lloyd, D.G., Cochrane, 1.L. and Ackla nd T.R. (2000) External loading of the knee joint during runni ng and cutt ing maneu vers . Med&Sci Sports&Exc. 33, 1168- 1175. Cawle y, P.W., Heidt, R.S., Scranton, P.E., Losse, G.M. and Howard M.E. (2003) Physiologic Axia l Load , Frictional Resistance, and the Football Shoe-Surface Interface. Foot&Ankle, Int 24, 551-556 . Dvorak, 1. and Junge, A. (2000) Football Injuries and Physical Symptoms - A Review of the Literature . Am J Sports Med 28, S3-S9. Ebert, C., Knaue r, C. and Senner V. (2005) Objectivat ing Safety Aspects of Ski and Snow board Boots by a New Testrigg and Optimized Prosthesis. Proceedings of 16th Internationa l Symposium on Ski Trauma and Skiing Safety. Niigata, Japan. 31. Grund, T., Wa llrapp, O. and Senner V. (2004) Simulations in Human Movement. Proceedings ofSIMPACK User-Meeting 2004, Wartburg, Eisenach, Germany. Haake, S.J., Carre , M.J., Kirk, R.F. and Senior T (2004) Traction of studded boots on turf. In: Hubbard, M., Metha, R.D. and Pallis, 1.M. (Eds .) The Engineering of Sports 5, Volume 2. International Sports Engineering Association. Pp.544-55 I . Heidt, R.S., Dormer, S.G., Cawle y, P.W., Scranton, P.E., Losse , G. and Howard, M. (1996) Differences in Friction and Torsional Resistance in Athl etic Shoe-Turf Surface Interfaces. Am J Sport s Med 24, 834-842 . Inman, T.V. (1976 ). The joints of the Ankle . 1-117, Baltimore: Willi ams and Wilkins. Krosshau g, T. and Bahr R. (2005) A Model -based image -matching technique for threedimens ional reconstruction of human motion from uncalibrated video sequences. J Biomech 38, 919 -929 . Lehner, S. (1995 ) 3D Simulation des men schlichen Kniegelenks. Diploma-the sis Munich University of applied scienc es, Department of Precis ion- and Micro -Engineering. Lehner, S., Eichhorn, S., Senner, V. (2005 ) Towards an asymmetric ski binding release : ACL versu s bindi ng forces with the rotated knee in deep flexion . In: Proceedings: 1st Wor ld Congress on Sports Injury Prevention, Oslo, Norway. McLean , S.G., Myers , P.T., Neal , R.I . and Walters, M.R. (1998) A Quantitative Ana lysis of Knee Joint Kinematics During the Sidestep Cutting Maneuver. Bulletin Hospital for Joint Diseases 57, 30-38. Myklebust, G., Engebretsen, L., Braekken, I.H., Skjo lberg, A., Olsen O.E. and Bahr, R. (2003) Prevention of Anterior Cruc iate Ligame nt Injuries in Fema le Tea m Handball Players: A Prospective Intervention Study Over Three Seasons. Clin J Sport Med . 13, 71-78 . Nigg , 8. M. (1990) Tge validity and relevance of tests used for the assessment of sports surfaces . Med&Sci Sport&Exc 22, 131-139. Olsen, O.E., Myk lebust, G., Engebretsen, L. and Rahr , R. (2004) Injury Mechanisms for Anterior Cruciate Ligament Injurie s in Team Handball - A Systematic Video Ana lysis. Am J Sports Med 32, 1002-10 12. Sigward, S.M. and Powers, C.M. (2006 ) The influence of gender on knee kinematics, kinetics and muscle activation patterns during side-step cutting . Clin Biomec h 21, 4 1-48. Valiant, G.A. ( 1989) A Method of Measuring Trans lational and Rotational Tract ion Characteristics of Footware. J biomech 22, 1091. Zauner , C. (2002 ) Integration of the man mode l Ramsis into MBS software Simpack - mode l comp arison and biomechanical simulation for verification. Master-the sis, Technische Universitat Miinchen .

Correlation Between Support Foot Placement and Goal Accuracy for Instep Kicks in the Soccer Field Giuseppe Marcolin, Nicola Petrone and Claudio Robazza University of Padova, Italy, [email protected]

Abstract. The aim of this work is to evaluate the correlation between the placement of the support foot on the ground and the precision of the shot: the placement of the support foot relative to the ball was supposed to have an effect on the shot precision for a given target. The goal was divided with a visual grid that enabled to identify six possible targets of the shot, high/low for vertical placement and left/center/right for horizontal placement. Skilled players were asked to perform repetitive penalty instep kicks in the soccer field with a defined target such as high/left or low/right. Ground reaction forces were recorded at the supporting leg by means of a force platform installed in a suitable board and the player's movement was video recorded. The position of COP at the kick instant with respect to the ball and the average trajectory of COP on the platform turned out to be correlated with successful targeting in such a way that training procedures can be defined to improve the player coordination for precision shooting. Finally, differences between free kicking and kicking with a goalkeeper were recorded, thus enabling us to analyze a realistic player behavior in the study.

1 Introduction Soccer is one of the most popular sports in Europe and in the world: the application of motion analysis techniques, EMG recording and force acquisition showed great advances in the last few years. The ball speed is correlated with the Ground Reaction Forces (GRFs) and the values that skilled players exhibit vertically, anteriorly-posteriorly and laterally are greater than among unskilled players (Barfield, ]998). The direction of approach to the ball has an influence on ground force components (Kellis, Katis and Gissis, 2004); lastly the ball speed in different ways of kicking (instep and side-foot) has also been investigated (Nunome, Asai, Ikegami and Sakurai, 2002). The aim of the present work is not only to study force magnitude in relation with ball speed, as known from previous works, but also to evaluate the correlation between the placement of the support foot on the ground and the precision of the shot in the soccer field in order to closely simulate what happens during a football match. The X-Y distance of the support foot from the ball and the foot orientation at the kick instant were supposed to have a correlation with the goal target sector. For this reason, the goal was divided with a visual grid enabling the subject to identify six possible targets of the shot, high/low for vertical placement and left/center/right for horizontal placement. Skilled players were asked to perform repetitive penalty instep kicks in the soccer field with a given target such as high/right or low/left: ground reaction forces were

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Nicola Petrone, Giuseppe Marcolin and Claudio Robazza

recorded by means of a force platform installed in a suitable board together with the kick instant.

2 Materials and Methods 2.1 Instrumentation The Ground Reaction Forces (GRF) at the support foot and the trajectory of the Centre of Pressure were measured by means of a Bertec force platform (600x400 mm, Model 4060, Bertec Corporation, U.S .A.). Signals were recorded on a National Instruments NI-PXI-I042 at 1000 Hz per channel. The force platform was fixed inside a wooden module (dimensions 1m x lrn , height 120mm) and placed on the football ground together with a set of 6 equal modules to create a suitable and safe runway for the player at a constant distance from the ground. The goal was divided into six equal rectangular sectors (2,44 m x 1,22 m) and a wooden rectangular panel was hanged in correspondence of the target sector. The instant of ball kicking and the average horizontal ball speed were detected by means of a suitable electric circuit including a support trigger under the ball, a trigger at the target panel , a LED at the force platform and a 3.6 Y battery. Two triggers, normally open , were connected in parallel to the NI-PXI-I042 and recorded synchronously with the force signals. The support trigger was applied on a hollow grid placed laterally to the force platform allowing the tester to adjust the position of the ball. The placement of the ball onto the support trigger closed the circuit closure and switched on the LED; at the kick instant, the circuit opened and the LED switched off until the ball hit the target , closing again the circuit and switching the LED on again . The trigger signal enabled to individuate the kick instant and to estimate the ball average speed on the basis of the ball flight time. Each test was filmed via two digital video cameras lYC GR-DYL357, one from the back and the other from the left side of the tester, both viewing the LED for image /force synchronization.

2.2 Test Protocol Tests were performed on a regular football field : the ball was placed centrally with respect to the goal, at a distance of 16m from the goal line. The balls were nr. 5 FIFA approved. Four non-professional players with experience in the secondary leagues were involved in the study: the data of the testers are summarized in Table 1.

Correlation Between Support Foot Placement and Goal Accuracy

(a)

347

(b)

Fig. 1. (a) Force Platform embedded in the wooden runway . (b) Detail of the ball trigger.

Fig. 2. Rear view of the experimental setup, for a right foot player.

TESTER

AGE

HEIGHT [em]

MASS IKe.1

FOOT

ROLE

I (M.C.) 2 (M.S.) 3 (E.Z.) 4 (G.M.)

29 29 32 27

183 186 168 184

84 80 67

RIGHT RIGHT RIGHT LEFT

Midfielder Midfielder Midfielder Forward

77

Table 1. Testers involved in the study.

Once in the football ground, the placement of the ball on the support grid and of the running pathway were chosen by each tester in order to follow his natural habit and to ensure the placement of the whole support foot on the force platform. All players were wearing standardized shoes for indoor soccer and were requested to read and sign an informed consensus about the tests.

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Nicola Petrone, Giuseppe Marcolin and Claudio Robazza

The test protocol was subdivided into several stages: Stage 1: warm-up . Before the kicking session, each tester performed a warm up concerning 5 minutes slow running, 6 series of 10m skip and rear kick running, 4 stretching exercises for the quadriceps, knee flexors, gastro and soleus. Stage 2: pilot shots for ball and runway placements. After 5 shots, the tester was requested to define the most suitable placement for the ball with respect to the platfonn and for the runway modules. This was done to reduce the influence that the use of a wooden surface, rather than a grass surface, might have on the kicking action. Stage 3. precision shots. Two series of 18 shots without goalkeeper were performed with a given target: for right-footed players, the first target was High-Left (HL); the second target was Low Right (LR) (the left footed targets were High Right and Low Left). Stage 4. power and precision shots with goalkeeper. A series of 16 shots with a goalkeeper, with the aim of scoring in the given target sector of the goal. Four possible targets, Low Right, Low Left, High Right, High Left were randomly mixed and communicated to the player immediately before each shot, with the request of shooting with the maximum power and aiming to the given target. The goalkeeper was asked to wait for the ball kicking before moving. Only successful shots (even if caught by the goalkeeper) aiming to the given target were analysed.

2.3 Data Analysis For each shot, the three components of Ground Reaction Forces Fx (anteriorposterior), Fy (medio-lateral) and Fz (vertical) were plotted synchronously with the trigger as in Figure 3. Peak values of Fz were normalized to the body weight and evaluated ; the average horizontal speed of the ball was also calculated as the ratio between the goal distance and the flight time. The COP of each shot was plotted in the platform system of reference within the interval between the instant of contact and 50 ms after the ball kick. The first part of the contact, from the Heel-Strike to the Foot Flat, corresponded to the raising of force Fz from zero to a peak and involved the settling of the ankle. The following part, from the Fz peak to the kick, corresponded to the swing phase before the ball kicking. For this reason, the COP trajectory occurring between the Fz peak and 50 ms after the kick was linearly approximated : the slope coefficient m was evaluated as shown in Figure 3, together with the coordinates of the Impact Point (IP), that is the position of the COP when the ball impacted. For each series with a given target, the different values of m and of IP coordinates were averaged : the IP scatter was expressed as an ellipse with semi axes equal to the x and y standard deviations. The slope m scatter was expressed as three lines pointing to the ellipse centre and defining the upper and lower standard deviation bands around the mean value of slope m, as reported in Figure 4. The coordinates of the impact point IP, measured in the platform reference system Oxyz as described in Fig. l .a, were transformed in the ball coordinate system OXY thanks to the knowledge of the placement of the ball trigger relative to the platform in the suitable grid shown in Fig. l .b.

Correlation Between Support Foot Placement and Goal Accuracy

-200

-100

100

200

349

300

(a)

(b)

f--

500

° 1

-1000

I

1

-=-.-'~=-

-5000.6

I-

Tlrro [soc)

]

Fig. 3. (a) COP trajectory for a right footed player (grey line) HL, linear approximation of the kick phase (black line) and COP at the impact (black points: smaller points for other successful shots) referred to the force platform system . (b) Corresponding GRF plots and trigger.

Low Right target

600

y

High Left target

( R)

( H I.)

550

I

2 - __ 3 -

-300

-

-r-

-,.-

350-+--

-.-

-200

Fig. 4. Comparative diagram between the different player s in the ball reference system .

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3 Results and Discussion The goal accuracies of the four testers were similar (1-27%,2-36%, 3-28%,4-25%), but lower than the values that may be expected with professional players. The values of normalized forces Fz were generally higher than values presented in the literature (Kellis et al. 2004): this can be due to the fact that in the present study the tests were performed in a football court and not indoor. The ball speed resulted lower than the values reported by Nunome et al. (2002): differently from that work, in this study the players had been asked to be precise, aiming to the given target. Speed was generally higher in the series of shots with goalkeeper. The final results of the four testers under investigation are compared in Figure 4, where left-footed player 4 has been reported by symmetry. Differences between HL and LR series can be appreciated. For each tester, paired t- test statistical analysis between the two series of free kicks with different targets (e.g. HL-LR) was carried out on the following parameters: the anterior-posterior coordinate of IP (xl?), the slope (m) of the COP trajectory trend line, the average ball speed (vm) and the normalized peak vertical force (Fz/BW). The anterior-posterior placement of the foot, coordinate xl?, proved to be significant for testers 3 and 4. The direction of the foot sole, slope m, was significant for testers I and 2. The ball speed vm was significant for tester 4 only; the normalized peak forces Fz/BW turned out to differ significantly (p<0.05) for testers 2, 3, 4, with a tendency for tester I (p=0.071). Further tests with professional players are supposed to confirm the method and hypothesisof the study.

4 Conclusions The anterior-posterior position of COP at the kick instant with respect to the ball and the direction of the support foot on the platform recorded in a soccer field turned out to be correlated for two testers out of four with different goal sector targets in such a way that training procedures ean be defined to improve the player's coordination for precision shooting.

References Barfield W.R. (1998) The biomechanics of kicking in soccer. Clin. Sports Med.; 17 (4): 71128. Kellis E., Katis A. and Gissis I. (2004) Knee biomechanics of the support leg in soccer kicks from three angles of approach. Med. Sci. Sports Exerc.; 36 (6): 1017-28. Nunome H., Asai T., Ikegami Y. and Sakurai S. (2002) Three dimensional kinetic analysis of side-foot and instep soccer kicks. Mcd. Sci. Sports Exerc.; 34 (12): 2028-36.

Analysis of the Influence of Rubber Infill on the Mechanical Performance of Artificial Turf Surfaces for Soccer Enrique Alcantara, David Rosa, Javier Gamez, Antonio Martinez, Mario Comin, Maria Jose Such, Pedro Vera and Jaime Prat Instituto de Biomecanica de Valencia (IBV), [email protected] Abstract. Artificial turf is increasingly being used in the construction of football pitches. Characteristic for this product is the infill, usually consisting of sand and rubber granulates. A significant role is attributed to it in the performance of the surface. At present, different materials and thicknesses, as well as grain sizes are used with little scientific support about their influence in mechanical and biomechanical properties. However, knowledge from materials science makes reasonable to think that grain morphology will also have a great influence in the field performance. This paper presents a research conducted to assess the influence of different parameters related to infill grain morphology on the mechanical properties of artificialturf, as well as on their wear with usc.

1 Introduction Installation of artificial turf for football pitches has experienced a huge increase in last years and a further increase is expected in next years after UEFA and FIFA arrived to an agreement for the rules to allow the use of artificial turf pitches in their competitions. Nowadays ' third generation' artificial turf field is used for soccer. Characteristic for this field is the infill consisting of sand and rubber granulate. A significant role is attributed to the infill in the performance of the surface at both mechanical and biomechanical level; mainly in relation to impact forces reduction, vertical deformation and ball bounce, which have been suggested as injury factors (Dura et al. 1999; Dura et al. 2002; Shorten and Himmelsbach 2002; Baroud, Nigg and Stefanyshyn 1999; Ekstrand and Nigg 1989). However, there are not scientific works published with this respect. Another point that needs clarification is about the influence in mechanical properties of infill compacting due to use of the field along time. Nowadays, the discussion is mainly on the type and thickness of rubber and sand to be used (Walker 1996) and the only parameter used to make a choice is the granulate size. Standards only consider the minimum size for the rubber, and the morphology of the grain (roundness) for the sand (FIFA 2005). However, from materials science knowledge, it is reasonable to think that grain morphology has a great influence in the mechanical performance of the field and thus, it could be used in the design of fields.

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The regulation bodies (FIFA, UEFA), in collaboration with several laboratories and research centers, have developed standard methods to measure the performance of football pitches (Socraturf 1999), which can be divided into technical and sports performance properties. This paper presents a research conducted to assess the influence of the type, grain morphology and size of rubber infill on artificial turf properties and their modification with use.

2 Material and Methods The work consisted in mechanical testing of a series of prototypes of artificial turf built using different infill in a same reference turf: FIELD TURF INC. FTOS IS (Field Turf Outdoor Series I for Soccer) and pile height 60 mm. Two different granulometries of cryogenic recycled rubber were used in the study; the particles of the first one are comprised between 1.4 mm and 2 mm of size (hereinafter "thick infill") and the second in the of 0.6 mm to 1.4 mm ("fine infill"). The following parameters were used to describe the grain morphology: -max: the larger particle diameter in the turf rubber filling. In this study, two rubbers were studied: fine rubber (1.4 mm) and thick rubber (2 mm). -leor: this is the index of coordination and corresponds to the value obtained from the division of the smallest diameter of the particles present in the infill by the largest diameter. <jlmin Icor=-(I) <jlmax -Mg: it corresponds to the granulometric mean of the infill rubber. It is obtained with the following equation: M = A% . (<\lmax+<\lmin) + B% . (<\lmax+<\lmin)+ ... (2) g

100

2

100

2

The equation has as many terms as different types of rubber of different granulometries are included in the turf infill. The value of the percentage in weight being added to the infill will be entered as A%, B%... -Dg: it is a measure of the degree of structural "disorder" measured in terms of information and corresponds to the number of parameters needed to characterise the granulometries and the ordering of the rubber infill. This parameter can take three values: Dg = I: infill is made of a single type of rubber. Dg = 2: infill is made of various types of rubber, all mixed in the same proportions in weight. Dg = 3: infill is made of various types of rubber and in different proportions in weight. -Ncycles: number of wear cycles by LISPORT.

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353

Ten prototypes were determined by statistical design of experiments using as variables the presence or not of sand, the thickness of rubber infill and the morphology parameters (Table I). Prototype

Sand (mm)

Rubberthickness

<1>max (mm)

Ieor

Mg

Dg

1

20

25 mm (thick)

2

0,7

1,7

1

2

20

25 mm (fine)

1,4

I

1

1

3

20

25 mm (50% thick50% fine)

2

1,35

1,35

2

4

20

25 mm (80% fine20% thick)

2

1,14

1,14

3

5

20

25 mm (40% fine60% thick)

2

1,42

1,42

3

9

NO

45 mm (thick)

2

1,7

1,7

I

10

NO

45 mm (fine)

1,4

I

1

1

Table 1. Prototypes description.

2.1 Mechanical Testing The mechanical properties of vertical ball bounce, force reduction and vertical deformation were tested according to FIFA standards (FIFA QUALITY CONCEPT). The tests were done on the prototypes with no wear (cero cycles) and after prototype wearing of 200 cycles and 2000 cycles using the LISPORT machine as described by FIFA. (FIFA 2005). Test were done at three points on each prototype. The parameters of study were Force reduction (FR), Standard vertical deformation (StY), Maximum deformation (Dmax) and Bounce height (H).

2.2 Data Analysis Data analysis consisted first in descriptive statistics of all parameters for comparison against FIFA requirements. Then an analysis of variance (p :s 0.05) was done to assess the influence of the type of infill and of the presence of sand. Finally, a linear regression analysis was done using Force reduction, standard vertical deformation. Maximum deformation and bounce height as dependent variables and all morphological parameters and number of cycles as independent variables. The regression equation was obtained for each dependent variable.

3 Results and Discussion The results of descriptive statistics showed that not all prototypes met FIFA requirements showing a clear influenceof the infill in field performance.

354

Enrique Alcantara et al.

The results of ANOYA presented statistically significant differences due to sand presence (Figure 1), in a way that FR (force reduction) and StY (standard deformation), are higher in the prototypes mounted without sand (prototypes 9 and 10) to the extent that both are outside FIFA specifications. There were no differences in bounce height and all prototypes met FIFA specifications. However, the variation of this property with use was higher without sand. 75

~

70

• .. •

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IlII

...........!!!~...

~

60 55

. ... ... .. .. . .... ..•... .. .•.. ... .•. .... ..

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0 .6

.

50

1llI 0 0200 ~ 2000

2 9 Prototype

2 9 Prototype

10

10

2

9

10

Prototype

Fig. I Comparison FR (%) , StY (mm) andball bounce (m)with (prototipes I an 2) and withoutsand (prototipes 9 and 10). FIFA requirementes (horizontal lines). Analysis of variance also reflected significant differences for morphology parameters (Figure 2). The compacting suffered by the prototypes with a mixture of granulometries in different percentages (prototypes 4 and 5) seems to be greater than for the other configuration showing a greater reduction if force reduction. and vertical deformation with wearing. In some cases, StY became lower than FIFA thresholds. Moreover, it should be mentioned that the most stable behavior in terms of force reduction and standard deformation parameters are achieved by prototypes 2 and 3, corresponding to the fine rubber granulate and to the 50% mixture of granulometries respectively. The bounce height did not show differences and for the five prototypes, remains stable with wear. 75

10

II

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65

~ ~ 60

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Analysis of the Influence of RubberInfill

355

The results of linear regression for each mechanical property are showed below in the form of mathematical equations : FORCE REDUCTION (FR) : The following equation predicts the value of the FR parameter from four input variables with an 84, 4% of the variance explained. A uniform size of rubber granules gives a high force reduction while a range of rubber granules sizes gives low force reduction. This is probably due to the compaction of the smaller granules between the larger granules giving a more resilient surface . This is confirmed by the fact that force reduction reduces with average granule size implyin that smaller ranules increase the hardness of the surface. FR = 72,950-(11,744· leor) -(6,258·Mg)-(5,702 ·<j>max)-(O,OOI · Neycle~ (3) STANDARD VERTICAL DEFORMATION (StV) : this equation predicts the value of the StY parameter from four input variables with an 88% of the variance explained. Increasing the disorder of the structure (Dg) will reduce StY without significant influence in Force Reduction . The effect in energy restitution should be studied as a greater disorder is ex ected to increase ener dissi ation b reor anisation. StY = 3,663-(6,323· Teor) -(0,000\2 · Ncyele~ -(1,625 · Dg)+(3,713· max) (4) MAXIMUM DEFORM AnON (Dmax): the following equation predicts the value of the Dmax parameter based on four input variables with an 86, 7 % of the variance explained. The influence of disorder is similar as for STv. Dmax = 3,233- (5,217· Teor) - (0,00013·Neyeles) + (3,414 · <1> max)- (1,397 ·Dg) (5)

I

I

BOUNCE HEIGHT (H) : The following equation predicts the value of the "H" parameter based on three input variables with a 71,4% of the variance explained. Increasing Disorder or the range of rubber granules sizes will increase ball bounce height. H = 1,0446+(2,48· leor)-(0,18 · <1> max)+ (0,059 · Dg)! (6) Values of force reduction and standard deformation parameters of the prototypes without sand under the rubber layer are outside the specifications determined by FIFA, whereby this composition of materials requires alternative constructions or materials if to be used to assemble artificial turf fields. With respect to the influence of parameters which define the granulometric composition of the infill on FTFA variables, Anova showed significant influence of granule size in all parameters but vertical bounce whereas linear regression analysis issued equation in which values of all mechanical properties can be predicted from those parameters. On the other hand, the mean granule size (Mg) showed a linear direct relationship with FR value in a way that as it increases the FR is reduced without altering another parameter. That means increasing either the size in general or the percentage of bigger grains .

I

356

Enrique Alcantara et al.

Parameters like StY and Dmax have an inverse relationship with Dg; thus as Disorder increases, they decrease. However, when Dg increases, vertical bounce ball increases too. Finally, this study has showed the effect of wear in surfaces. All properties decreased when the number of cycles increased.

4 Conclusions The results of this work provide a clear evidence that infill influences mechanical performance of artificial turf for soccer, in fact not all prototypes met FIFA requirements. Wear by use (number of cycles) appears to significantly reduce the value of all parameters that define deformation and force reduction, but not to vertical ball bounce. The value of variables such as FR, StY and Dmax showed an inverse linear relationship with leor, whereas it was direct with bounce height. The variation of the leor had more influence on the StY parameter. That means that as the ratio between the minimum and maximum diameter increases, bounce height increases and force reduction, StY and Dmax decrease. The maximum diameter of the infill particles (C1>max) influences the value of parameters studied, specially the value of Dmax and StY. Thus, if it increases, StY and Dmax increase, whereas the values of FR and bounce height reduce. Concluding, this work has showed that infill effectively influence performance of artificial turf pitches and this influence depends of granule size to a great extent. Results show that grain morphology can be used in the design of artificial turf infill and future studies about the role of infill "disorder" in artificial turf performance are deemed very interesting.

Acknowledgments The authors wish to thank the collaboration in this study of the cryogenic recycled rubber supplier Recipneu Lda.

References Dura, J. Y., Hoyos, J. Y. and Martinez, A. (1999) Theeffect of shock absorbing sports surfaces injumping. Sports Engineering, 2 (2),pp. 97-102. Dura, J. Y., Martinez, A. C. andSolaz, J. (2002) Testing absorbing materials: theapplication of viscoelastic linear model. Sports Engineering, 5, pp. 9-14. Shorten, M. R. and Himmelsbach, J. A. (2002) Shock attenuation of sports surfaces. The engin eering ofSports 4. S. Ujihashi andS. J. Haake (Eds.), pp. 152-159. Baroud, G., Nigg, B. M. andStefanyshyn, D. (1999) Energy storage andreturn in sport surfaces. Sports Engineering, 2, pp. 173-180. Ekstrand, J. andNigg, B. M. (1989) Surface-related injuries in soccer. Sports Medicine, 8 (I), pp.56-62. Walker, C. A. (1996) Experimental mechanics andartificial turf. The engineering ofSports . Haake (Eds.), pp. 239-242. FIFA quality concept. Handbook of test methods andrequirements forarti ficial turffootball soccer (2005). Socraturf (1999). Development of improved artificial turffields; CRAF-1999-70805.

Soccer Ball Modal Analysis Using a Scanning Laser Doppler Vibrometer (SLDV) Jouni Ronkainen and Andy Harland Loughborough University, j [email protected]

Abstract. Soccer manufacturers are investing significant amounts of time and money researching and developing soccer balls, using advanced materials and constructions in an attempt to create a ball that has better flight and impact characteristics. An important consideration in any structure subject to dynamic or impact loading is its mechanical response. The recent development of non-contact optical vibration measurement tools such as the SLDV have made the measurement of such responses a more realistic possibility. The technique of vibrometry utilises the Doppler principle to provide a measure of the surface velocity at the point at which a laser beam is incident. The SLDV benefits from its non-contact and nonmarking methodand the speed and ease with which measurements can be recorded. This paper reports the method and results from a study aimed at determining the dynamic responses of two different soccer balls. The balls are excited using either an acoustic source or mechanical shaker and the velocity of each ball's surface at a series of points is recorded. The natural frequencies and vibration mode shapes are identified and a comparison is made between the responses of each ball. Significant mode shapes were observed between 50 Hz and 1400 Hz. At the lower frequencies the mode shapes were observed to be independent of the outer panels, based more on the structure of the ball as a whole, at the higher frequencies the mode shapes were centred on individual panel oscillations. The soccer balls tested show some noticeabledifferences in mode shapes.

1 Introduction In 2006 the second largest sporting goods manufacturer, adidas, have predicted that they will sell 10 million replica world cup soccer balls worldwide (Reuters 2005). It is clear to see how important it is to manufacture and market balls effectively for the mass market as well as achieve acceptance at the professional level. Soccer is a global game and arguably the most popular sport on the planet. For the 2005/06 soccer season it is forecast that within the UK the English professional soccer clubs will have an income of approximately £ 1.935 billion (Mintel 2004), this figure is huge and illustrates the vast sums of money involved within the game. Due to the vast interest and money involved, manufacturers are spending significant amounts of time and money researching and developing soccer balls, using advanced materials and constructions in an attempt to create a ball that has better flight and

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JouniRonkainenand Andy Harland

impact characteristics. Therefore this paper explores an alternative method for soccer ball analysis through modal testing . An important consideration in any structure subject to dynamic or impact loading is its mechanical response . Traditionally these tests have been carried out by attaching accelerometers onto the target structure at locations that are predicted to yield results . However problems arise from this technique since attaching an accelerometer onto a structure will result in a mass loading effect, which results in the Frequency Response Functions (FRFs) being altered for the test structure. The actual attachment/detachment of the accelerometers can cause problems and the location at which they are attached onto the structure is crucial. The recent development of the optical vibration measurement tool, the laser Doppler vibrometer (LDV) allows the vibrational engineer to measure the mechani cal response of structures in a completely non-contact method unlike the accelerometer approach . This technique of vibrometry utilises the Doppler principle to provide a measure of the surface velocity at the point at which the laser beam is incident. Literature explains that LDV has seen great benefit in structures that are hot, light or rotating (Ewins 2000) . A FIFA 'inspected' soccer ball weighs between 410 to 450 grams, which undoubtedly would be affected by the mass loading effect of accelerometers. The SLDV allows a very high spatial density for the measured points on the target structure and therefore removes the need for predicting mode shapes for structures. The scanning capability for LDV is achieved by utilising two orthogonal mirrors to direct the measurement laser beam. Generally laser measurements have required the use of retroreflective marker tape attached onto the target structure in order for the laser interferometer to detect a signal back from the target structure. However preliminary testing using a Polytec PSV-300 SLDV on a plain white soccer ball, approximately 80% of the ball could be measured using the laser without retroreflectiv e marker tape, see "Fig, I" . Therefore for 80% of the ball a 'strong' signal to noise ratio (SNR) is achieved for data analysis .

Strong SNR

Poor SNR

Fig.I. Signal back from plainwhitesoccerball

This study compares the mechanical response functions of two different soccer balls in order to ascertain whether it is feasible to utilise a SLDV in order to assess the FRFs of soccer balls and to highlight if there are any differences

Soccer Ball Modal Analysis Using a Scanning Laser Doppler Vibrometer

359

2 Method Two soccer balls were tested; a plain white 32 panel '1lanually stitched puma ball and an adidas 32 panel thermally bonded ball. This choice allowed a typical match ball to be compared with a novel championship ball. The setup for the testing is pictured in "Fig.2" . The ball is suspended by fishing line attached at the valve, which allowed the known out of balance points, valve and counterbalance, to be removed from the measurem ent grid. A grid of orthogonal, equispaced points was projected onto the surface of the ball, which were used by the Polytec software to mark the grid points for measurement by the laser. This allowed any number of balls to be measured with exactly the same number and location of measurement points. B&K Conditioning Amplifier

I

Ball hanging by Fishing Wife

Spa

er

Power ~llfler

V obromel er Control r

SLDV ScennerHead

Fig.2. Modal analysis setup

The puma ball was initially excited acoustically and mechanicall y using a shaker via a stinger attachment. Both method s have their advantage s and disadvantages the main positive with the acoustic excitation source is that like the SLDV it is a noncontact method and therefore avoids mass loading the structure . The mechanical response of both the puma and adidas ball was then determined. In order to achieve this, the soccer ball was excited by white noise in a ' check out run' whereby the number of measurements at each point was kept to a minimum , with an average of three measurements taken at each grid point. Once the 'c heck out run' was completed the FRFs were analysed and the resonant frequencies of the soccer ball extracted . The next stage of the testing was to pinpoint the resonant frequencie s and in tum excite the soccer ball at a given resonant frequenc y. The excitation was inputted throu gh a continuous sinusoidal wave. The Polytee software was used to carry out a Fast Fourier Transform (FFT) working at a bandwidth of 20 kHz,

360

Jouni Ronkainen and Andy Harland

measuring 6400 FFT lines, taking 320 ms to record each individual measurement having a frequency resolution of 3.125 Hz. The measurement was carried out on a 5% rising trigger level in order to obtain useful phase information. Importantly for the measurements at resonant frequencies an average of ten measurements were taken at each grid point and the measurement consisted of 283 grid points. Since the known out of balance points on the ball were purposefully removed from the measurement grid it was interesting to see if they actually affect the measured values. Therefore a brief test was carried out whereby the valve was positioned at the centre of the measurement grid.

3 Results and Discussion The initial test where the puma ball was excited acoustically as well as mechanically showed very similar results are obtained through both excitation methods therefore to avoid duplicating work, the acoustic excitation method was used for further testing. The acoustic method was chosen because the setup time is quicker and less apparatus is required. To ascertain the resonant frequencies the FFT graph is analysed for white noise excitation, the graph is shown in "Fig.3." for the adidas ball. A comparison between the puma and adidas balls showed similar resonant excitation frequencies and are listed in Table.l .

Magnitude , prnrs

Freque ncy, Hz

500

1000

1500

Fig.3. Surface velocity FRF for white noise excitation of adidas ball

Soccer BallModal Analysis Using a Scanning LaserDoppler Vibrometer

361

, fior pumaand adid Table•• 1 Resonant requencies 1 as soccer ba11s PumaResonant Frequencies

adidas Resonant Frequencies

<100 Hz

<100Hz

150Hz

150Hz

284Hz, 334 Hz

278 Hz,309 Hz, 334 Hz, 362 Hz

950 Hz,981 Hz

950 Hz, 981 Hz

1000Hz, 1156Hz, 1175Hz

1000Hz, 1100Hz

1206Hz

1359Hz

As a general result for both soccer balls, at the lower frequencies of excitation the mode shapes were observed to be independent of the outer panels, based more on the structure of the ball as a whole as shown in "Fig.d ." At higher frequencies of excitation, above 500 Hz, the puma ball mode shapes were centred on individual panel oscillations shown in "Fig.5 ." whereas the adidas ball was not observed to exhibit this behaviour, presumably because of the difference in panel technology . It was observed that the stitched seams of the puma ball act as a skeleton, constraining the vibrations at high frequency. This is consistent with the findings of (Price 2005), who reported the structural rigidity given by the stiff seams of a manually stitched ball.

Fig.4. Puma ball excited at 334 Hz

Fig.S. Puma ball excited at 981 Hz

362

Jouni Ronkainen and Andy Harland

Both the puma and adidas ball exhibited the same behaviour when the valve was measured . The valve is much stiffer and therefore the maximum displacement observed at this panel is much less, shown in "Fig.6.", the central panel at maximum displaces 86 11m whereas the outer panels exhibit maximum displacement of 210 11m. This result is anticipated , but highlights the accuracy of the SLDV.

Fig.6. Puma ball excitation at 981 Hz, valve located on central panel

5 Concluding Remarks The approach utilised allowed mode shapes to be viewed graphically in threedimensional animations, showing interesting mode shapes for two different soccer balls. Different responses at high frequencies were observed which are attributed to the differences in manufacturing methods . Soccer balls are hit in transient dynamic fashion therefore it is assumed that the observed mode shapes would be excited. How these results correlate to match play performance would require further work. The approach utilised would be a valuable tool in acoustics research, validation of computer models, player safety research particularly focusing on head impacts and as shown to test differences in behaviour due to design modifications.

Acknowledgements The authors wish to thank the EPSRC for funding this work and the assistance of Mr. A. Hallam and Mr. S. Carr for their help with experimental instrumentation.

References Ewins, DJ. (2000) Modal testing: theory, practice and application, 2nd ed. research studies press , Baldock , England , pp.194-287 . Mintel (2004), Mintel international group ltd, "The football business, UK, December 2004" http ://reports.mintel.com/sinatra/reports/display /id=68234#about, ace. 6th January 2006 Price, D.S. (2005), PhD Thesis, Loughborough, "Advanced modelling of soccer balls." Reuters (2005), Posted io" Dec "World Cup ball back in traditional black and white" http://today.reuters.com/news/newsChannel.aspx?type=sportsNews, ace. 6th Jan 2006

9 Tennis

Synopsis of Current Developments: Tennis Stuart Miller ITF, London, UK, [email protected] There is a substantial body of scientific research in tennis, the major growth of which began in the late 1970s, around the same time as the introduction of the oversize racket and the subsequent change in playing style that it facilitated. As such, rackets constitute a significant part of the body of research. A second key element of tennis is the ball, which, although narrowly defined by the Rules of Tennis, is sufficiently important to warrant attention.

The Racket A seminal comparisons of the vibration and power characteristics of conventional and oversize racket was made by Elliott et al. (1980). This was followed by a complete descriptionof the ' sweet spot' of the racket by Brody (I 987a). The modem racket, being built out of aluminium, then graphite, has an inherently higher natural vibration frequency, and there was speculation that this was linked to upper limb injury. A series of research papers have subsequently been produced that examine the characteristics of racket vibration, includingthose of Tomosue et al. (1992) and Hennig et al. (1992). Recently, models of the tennis racket have been developed, such as those by Goodwill and Haake (2001), which have allowed the modification of its physical parameters and, thus, its performance, on a computer. The paper by Goodwill et al. will add to this body of knowledge by providingthe first known data of the spin-generating characteristics of a substantial numberof racket/string combinations. Surprisingly little is known about the orientation of rackets at impact, a gap in knowledge that will be addressed at ISEA by Choppin, using an advanced 3D analysis method. Rackets continue to become more sophisticated, and several contain methods by which the vibrationsdescribed above can be attenuated. One such method will be considered by Cottey and co-workers.

The Ball Ball-related research has often centred around an understanding of its impact with the racket (e.g., Grabiner et al., 1983), which is understandable, given the obvious importanceof this event. This line of research has been continued by authors such as Brody (1987) and further developedby Haake et al. (2003).

366 Stuart Miller The tennis ball has been further analysed from the perspectives of its impacts with the court surface (e.g., Brody, 1987), dynamic rebound properties (Miller and Messner, 2003) and its aerodynamics (e .g ., Goodwill et al., 2004) . The latter area is particularly relevant today given the increased speed with which elite players hit the ball and the considerable topspin applied in the majority of groundstrokes. The power that modem players generate means that the durability of tennis balls is a key issue, a detailed assessment of which will be given at ISEA 2006 by Steele, which includes the consideration of factors not previously reported in the literature. Meanwhile, Honda will provide an analysis of the force and displacement histories of dynamic impacts between a ball and a flat surface.

References Brody, H. (1984). That's how the ball bounces. The Physics Teacher, 494-497 , November. Brody, H. (1987a) . Tennis Sciencefor Tennis Players. Philadelphia : The University of Pennsylvania Press. Brody, H. (1987b). Models of tennis racket impacts. Internat ional Journal ofSports Biomechanics, 3, 293-296 . Elliott, B.C., Blanksby , B.A. & Ellis, R., (1980) . Vibration and rebound velocity characteristics of convention al and oversize tennis rackets. Research Quarterlyfor Exercise and Sport , 51, 608-615 . Goodwill, S.R. and Haake, S.J. (2001) Comparison of flexible and rigid body modelling of a tennis racket. In: Proceedings ofthe Materials and Science in Sports Symposium, San Diego, California, 223-236 . Goodwill , S.R., Chin, S.B. & Haake, SJ. (2004) Wind tunnel testing of spinning and nonspinning tennis balls . Journal o{ Wind Engineering & Industrial Aerodynamics, 92, 935958. Grabiner, M., Groppel , J.L. & Campbell , K.R. (1983). Resultant tennis ball velocity as a function of off-center impact and grip firmness . Medicine and Science in Sport and Exercise, 15,542-544. Haake, S.J., Carre, M.J. & Goodwill, S.R. (2003) The dynamic impact characteristics of tennis balls with tennis rackets, Journal ofSports Sciences, 21, 839-850 . Hennig, E.M., Rosenbaum, D. & Milani, T.L. (1992) . Transfer of tennis racket vibrations onto the human forearm . Medicine and Science in Sport and Exercise, 24, 1134-1140. Miller, S. and Messner, S. (2003) . On the dynamic coefficient of restitution of tennis balls. In Tennis Science and Technology 2 (edited by S. Miller), pp. 97-104 . Toronto : Webcom . Tomosuc, R., Mutoh, Y., Yoshinari , K. & Kawazoc, Y. (1992) . Vibrations ofa racket handle and the wrist joint in the tennis forehand drive. Journal of" Biomechanics, 25, 719.

Normal Impact of Hollow Balls on Flat Surfaces Yoshihisa Honda Kinki University, Japan, [email protected]

Abstract. Normal impact of hollow balls on flat surfaces is theoretically analyzed and the dynamic deformation of hollow balls is derived as an axisymmetric motion of an elastic spherical shell by using modal expansion method, where variation of contact area is taken into account. Numerical calculations were conducted and the dynamic characteristics are discussed. It is found that the center displacement of the ball possesses nearly a half-sine wave form while the reaction force has a triangular time history. It is also shown that the collision time decreases with increasing initial velocity of theball.

1 Introduction Many researchers have studied the impact phenomenon in ball games, such as golf, tennis, baseball and so on. Stronge (2000) has mentioned that collisions in a system of flexible structures will involve dynamic deformation of the structures. In most of the published analytical works, clubs, racquets and bats are treated as a continuous elastic bodies and their structural dynamics is discussed with emphasis on their vibratory modes. A hollow ball is also flexible and, therefore, collisions may generate vibratory motion in it. Hubbard and Stronge (200I) studied the bounce of a hollow ball on a hard flat surface by a quasi-static lumped model and a finite element model. The author examined the dynamic behavior of a hollow ball impacting at a point against a linear spring (Honda 2004). In this paper, the dynamic deformation of a hollow elastic ball on impact is theoretically studied as a continuous body. Axisymmetric motion of an elastic spherical shell with uniform thickness is adopted as a physical model, and is analyzed by using the modal expansion method, in which variation of contact area is taken into account. Numerical calculations were conducted and the dynamic characteristics of the impact phenomenon are discussed.

2 Theoretical Formulation 2.1 Analytical Model It is assumed that a non-spinning hollow ball impacts normally on a flat surface of an elastic body as shown in Fig. I. Therefore, the excited motion of the ball is axisymmetric about the diameter through the initial contact point. An elastic spherical shell

368

Yoshihisa Honda

, ,

. -,

Fig. I. Analytical model of a hollowelastic ball

with uniform thickness is adopted as a physical model of the ball. Both extensional and bending deformations are considered, but damping, nonlinearity and inner pressure are ignored. The density, Young's modulus, Poisson's ratio, the thickness, and the radius of the shell are denoted by p, E. v, h, and a, respectively. For convenience, the following expressions are written in a nondimensional form on the bases of length a. mass po'h, time a(p/E) "2. Therefore, the mass of the ball, which is 47Cpa2h in dimensional form, is 47C in nondimensional form. The dimensionless displacement components in the normal and meridian directions are denoted by w(¢J, 1) and u(¢J, 1), respectively, where r is the dimensionless time.

2.2 Equations of a Spherical Shell in Axisymmetric Motion Equations of axisymmetric motion of a spherical shell can be written as

' )- a (Qsm¢J af/J

(N 0+ N) ' ¢J + p.s .m ¢J = sm . ¢J -a w-" u sm

a (N cs mf/J . ) -

N

a¢J

1

ar-

ucos f/J +

Qsm¢J . + p"s .mf/J =sm¢J . aar1 U1'

( I)

2 ( )

where p ... and p., are the external distributed forces in the normal and meridian directions (Kraus, 1967; Soedel, 1993). Expressions for the internal forces denoted by N and Q can be found in the references. The displacement components can be expressed as

-

-

w(¢J,r)= L>J(r)Wj(¢J), u(¢J,r) = Lq ,(rp ,(f/J ),

(3)

, I

where ~{¢J) and V,(¢J) are the natural mode components. These mode components can be given by (4)

Nonnallmpact of Hollow Balls on Flat Surfaces

369

where the nonnegative integer n depends on modal numberi. and Pn( ) is the Legendre function of order n. The expressions for coefficients Cj and other parameters are given in the reference (Honda 2004). The modal participation factors q/1) satisfy the following differential equations. d2 M ~+Kq = F (r) (5) , dr' J J .I '

F,(r)= 2liJ(p"W, + p"UJsin¢drp,

(6)

where M, and K, are the equivalent mass and the equivalent stiffness ofthej-th mode, respectively, given by

(7) W J

= 2lif(W + U )sin¢drp =~[I + C n(n + I)} 2n + I 2

J

2

2

J

J

(8)

2.3 Impact on a Flat Surface The impact force is the interaction between the ball and the impacting or impacted body, and depends on their dynamic characteristics. In this analysis, simplified characteristics are assumed for the impacted body with a flat surface. The axis of symmetry of the ball is selected as the x-axis of a Cartesian coordinate system and that the flat surface is located at x= I. The x coordinate of the surface of the ball at ¢! can be expressed by x = (w+ I)cosrp-usinrp, (9) It is assumed that the restoring force applied by the impacted body on the ball is directed along the x-axis and that the magnitude of this force is proportional to the positive compression x-I . The following equations for the restoring force hold during the collision. p"=-k(x-I)cosrp, p,,=k(x-I)sinrp, (10) where k is constant, which represents the simplified elasticity of the impacted conservative body.

3 Numerical Results and Discussion Numerical calculation was carried out for a shell of h/a=0.02, v=0.3. The infinite series of Eq. (3) were truncated to include only the modes whose frequencies are lower than 50. A pair of modes with n=I have same equivalent mass 4lf and one of the pair which has zero frequency is the translational mode. Below 50 of frequencies, there are 89 bending modes and 48 stretching modes. The lowest nonzero frequency is 0.73508 (n=2 ; bending). The initial conditions are that the shell

370

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0 10

1

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1

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10

20

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30

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50

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c" G 0.08 ~ 0.06

~1.j

""

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~

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Initial Velocity

Fig. 3. Dependence on initial velocity (h/u=0.02, v=0.3, k=100)

contacts the flat surface at the point f/FO with a uniform velocity v() and that the shell and the surface are in a free state. The calculated coefficient of restitution (COR) is greater than 0.997 for vo
372

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2.0E-{)3 r- - -

-

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--,--

-

-

-

-r--

-

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---,--

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-

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, --

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u

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0.06 Center

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4 Conclusions In this paper, the dynamic behavior of a hollow ball during normal impact against a flat surface was analysed as an axisymmetric motion of an elastic spherical shell using a modal expansion method. It is found that the center displacement of the ball possesses nearly a half-sine form while the reaction force possesses triangular form in time histories. It is also shown that the collision time decreases with increasing initial velocity of the ball.

References Honda, Y. (2004) Impact Analysis of Hollow Elastic Balls. In: M. Hubbard, R. D. Mehta and 1. M. Pallis (Eds.), Engineering ofSports 5, 1. ISEA, Sheffield, UK, pp. 344-350. Hubbard, M. and Strange, W. 1. (2001) Bounce of Hollow Balls on Hit Surfaces. Sports Engineering, 4, 49-61. Kraus H. (1967) Thin Elastic Shells. Wiley, New York. Soedel W. (1993) Vibration ofShells and Plates (2nd ed.). Marcel Dekker, Inc., New York. Strange, W. 1. (2000) Impact Mechanics. Cambridge University Press, Cambridge.

Factors in Tennis Ball Wear Carolyn Steele, Roy Jones, and Paul Leaney Loughborough University, C.Steele@lboro .ae.uk

Abstract. Recent research has shown wear to affect ball performance during play, but contributing factors to wear differences have not been well identified. A framework has been developed to aide a systematic investigation into these factors. Several of these features are investigated in this paper, including repeated impacts , racket impact conditions, precipitation, and natural pressure loss. The results from these investigations are intended not only to give players a better understanding of what occurs during play, but also enable manufacturers and governing bodies to address specific areas of importance in ball wear and performance.

1 Introduction Ball wear is becoming an increasingly popular area of tennis research as the properties of new balls are well documented. Recent research has investigated the effects of ball surface condition on aerodynamics (Mehta and Pallis 2001), repeated impacts on ball mass loss (Capel-Davis and Miller 2003) , and the coefficient of restitution (Miller and Messner 2003) . While various stages of ball wear can be observed through play and simulated in laboratory experiments, these have yet to be incorporated into a structured study identifying the individual causes of differences in ball condition and performance. This paper presents a framework for identifying key areas contributing to wear differences with the intent to aide manufacturers and governing bodies in improving ball wear characteristics and monitoring the effect of wear on the game . Factors such as racket impact conditions, repeated impacts, precipitation, cloth construction, and natural pressure loss are discussed in this paper.

2 Framework Development A framework for investigating the causes of wear in tennis has been developed through extensive interviews with elite players . These interviews encompassed both the causes and effects of ball wear, as well as implications to ball performance, and were conducted at several professional tournaments where players were asked to consider not only their current training and playing environment, but also experiences throughout their career. These interviews were combined with a review of literature on ball characteristics and the game of tennis to provide a structure for the causes of ball wear (Steele 2005) . This framework is presented in Fig. 1.

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CarolynSteele, Roy Jones, and Paul Leaney

Natural andErr;ironmertal Factors

Fig. l. Framework used to assess factors in ball wear.

3 Play Wear through play is perhaps the most obvious cause to changes in ball properties. Two components of this factor are discussed in this paper: racket impacts and repeated impacts.

3.1 Racket Impacts Stringbed properties and impact speed were identified as important characteristics of racket impacts. For a given racket , string type and tension are variables players can modify to suit their preferences. Elite players are known to use high stringing tensions, favoring increased control over the power found with lower tensioned strings (Brody, Cross, and Lindsey 2002) . Players also emplo y a range of string types with differing properties, such as monofilament polyester and natural gut. Additionally, racket impacts have been influenced by recent improvements in racket technology and improved player fitness contributing to increased ball speed during play . These three factors were investigated using an air cannon to fire two premium grade, sateen weave balls (for each impact condition) at a rigidly clamped, oblique racket head . This method was used to isolate differences in racket properties as the air cannon itself causes no significant changes to ball mass during testing and the ball was not allowed to impact another oblique, abrasive surface that may have also affected mass loss characteristics. Figure 2 indicates the results of this work, with ball speed causing the most noticeable effect on mass loss. Stringing tensions did not produce mass loss differences , though natural gut caused higher mass losses than synthetic gut, while polyester caused less.

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3.2 Repeated Impacts Players often comment on the 'loosening up ' of the ball, or feeling of increased ball speed and lower stiffness, during the early stages of playas rubber is known to stiffen during extended rest. A wear rig was designed to cyclically wear the ball s at 30m/s with two oblique impacts (a racket and steel plate). To eliminate changes to

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Carolyn Steele, Roy Jones, and Paul Leaney

ball fuzziness and cloth stiffness during testing, ball cores were used to isolate changes in the rubber. The coefficient of restitution (COR) for the balls was evaluated for sixteen impacts at 30±Imls off a steel plate using a high speed camera running at 2,000 fps. Figure 3 shows the mean COR, plotted with one standard error. While there appears to be slight increase in ball COR through 40 impacts, the variation in standard error makes it difficult to form any definitive conclusions. The minimal differences also suggest that while the ball may not travel significantly faster, changes to ball stiffness may improve ball 'feel' for players.

4 Natural and Environmental Factors Additional components of ball degradation are those occurring due to innate differences in ball construction, such as core and cloth differences, and environmental conditions such as a temperature and precipitation. A cyclical wear machine with a rotating racket was used to project balls towards two oblique surfaces covered in ball felt. The system averaged 33.9 (0=1.76) ball impacts per minute with a racket head velocity of 14.63m1s (and approximate ball speed of 55m1s).

4.1 Precipitation Given no current methodology exists for evaluating wet tennis balls, a standardized process from a ball cloth manufacturer was used. Balls were submerged in water for five minutes, bounced ten times to release excess water, and then placed in the wear machine. Three balls were evaluated at each impact level. The first ball tested was a pressurized, sateen weave ball, while the second was the same ball produced with a water resistant dye. Figure 4 shows ball mass loss during testing, with the original weight being that of the ball immediately before it was placed in the machine. While both balls show similar rates of mass loss with repeated impacts, the untreated ball shows significantly higher initial losses due to the large amount of water absorbed by the ball while it was submerged. This figure also shows the success of the water resistant dye at minimizing ball weight increases due to moisture.

4.2 Cloth Construction A similar investigation was performed with a needle felt ball and a premium grade sateen weave ball. The needle felt ball showed significantly lower mass losses through extended testing, as shown in Fig. 5. These results differ from those presented by Capel-Davies and Miller (2003) that show greater losses from a needle felt ball and comment on the continued linear trend in mass loss through 1000 impacts, but the slowed rate of loss over extended impacts for a sateen weave ball. These differences could be due to the wearing mechanism, impact speed, or ball brand and highlight the need for standardized wearing proceduresand methods.

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4.3 Natural Pressure Loss Interviews and testing with elite players has highlighted their preference for pressurized balls, citing improved feel and performance (Davies 2005). Previous work has used punctured balls as an approximation of the changes to ball characteristics, but Fig. 6 indicates that through three months of natural ageing, internal pressures are still noticeably higher than standard atmospheric pressure . The high pressure gradient present when the balls are first opened is responsible for the high rate of initial pressure losses that slows with increased time. With regards to the dynamic COR for aged balls against a rigid surface, Fig. 7 indicates two groupings of aged balls - those under three months in age and those six months and older (including the punctured sample). These results also indicate that punctured balls approximate some aged balls in dynamic impact testing.

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Carolyn Steele , Roy Jones , and Paul Leaney

5 Conclusions The framework developed in this paper provides a structured method to examine and classify differing contributions to ball wear. Initial experimental work indicates that some factors play prominent roles in ball wear, with future work planned to investigate remaining areas of the framework such as court surface interactions. The following conclusions can be drawn from the completed studies : • Impact speed affects ball mass loss, making wear more noticeable to elite players using higher ball speeds . Mass loss is affected by string type but not string tension . • Core COR did not conclusively indicate repeated impacts may cause the ball to play faster . Future work is planned to investigate any changes to ball stiffness that may occur and the subsequent relationship to player feel. • Needle felt balls showed lower mass losses than sateen weave balls . • Water resistant ball felt can significantly reduce initial water absorption, though the rate of loss with impacts is consistent.

Acknowledgements The authors would like to thank Dunlop Slazenger for supporting this work and the Wolfson School of Mechanical and Manufacturing Engineering for providing laboratory facilities .

References Brody, H., Cross, R., and Lindsey, C. (2002) The Physics and Technology of Tennis . Racquet Teeh Publishing, Solana Beach . Capel-Davies, 1. and Miller, S. (2003) Durability of tennis balls worn in a test rig. In: S. Miller (Ed), Tennis Science & Technology 2. International Tennis Federation, Roehampton, pp. 113-122. Davies, G. (2005) Determination and analysis of dimensions of ' feel' in tennis ball impacts. PhD Thesis, Loughborough University. Mehta, R. and Pallis, 1. (2001) The aerodynamics of a tennis ball. Sports Eng., 4, 177-189 . Miller, S. and Messner, S. (2003) On the dynamic coefficient of restitution of tennis balls. In: S. Miller (Ed), Tennis Science & Technology 2. International Tennis Federation, Roehampton, pp. 97-104 . Steele , C. (2005) Tennis ball degradation. Internal Research Report, Loughborough University .

Measuring Ball Spin Off a Tennis Racket Simon Goodwill' , Jamie Douglas', Stuart Mille~, Stephen Haake' 1

2

Sports Engineering, CSES, SheffieldHallam University, [email protected] International Tennis Federation

Abstract. A series of experiments were carried out in which a spinning tennis ball was projected obliquely at a head clamped racket. In each experimenta different string was used in the racket frame. An automated image analysis algorithm was used to measure the velocity and spin of the ball. It has been found that, for the majority of impacts, the magnitude of the ball rebound spin was dependent on string stiffness. It has been concluded that the string stiffness influences the magnitude of stringbed lateral movement during impact. This differing magnitude oflateral string movement, in tum, influences the amount of ball reboundspin.

1 Introduction The research presented in this paper has been conducted in collaboration with the International Tennis Federation (ITF). The ITF are responsible for the rules of tennis, and there is currently no ruling which specifies the magnitude of spin which a tennis racket can impart on the ball. The absence of such a ruling could potentially lead to a situation similar to that in 1977 when a novel 'spaghetti' stringing system was introduced (Fischer 1977) . This racket had the inherent ability to apply considerably more spin onto the ball compared to a conventionally strung racket. The receiver could not predict the flight or bounce of the ball, and so gave the player who was hitting the ball an unfair advantage over the receiver. In 1978, the ITF banned this stringing system. In this paper, an experimental investigation of the oblique impact between a tennis ball and head clamped tennis racket is described. The aim of this study is to determine whether the string type (material and stiffness) affects how much spin is applied to the ball. Previous publ ished research (Goodwill and Haake 2004a) has suggested that the string type does not affect the rebound spin. However, it should be noted that Goodwill and Haake only tested a small sample of strings. In this current study a significantly larger sample size was used in an attempt to identify a relationship between string type and ball rebound spin .

2 Methodology Identical racket frames were strung at a tension of 270 N (60 lbs) for each of the thirty tennis strings that were tested . Each racket was strung 24 hours prior to being

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Simon Goodwill

tested . All the strings that were tested in this study were manufactured from either polyester or nylon (or some composite based on one of these materials).

2.1 Impact Test Experiment In this experiment, new pressurized tennis balls were projected at a nominal velocity of 25 m/s (56 mph) on to a head clamped tennis racket, as shown in Fig . I(a). Tests were conducted for a range of inbound ball spins between zero and 400 rad/s (3820 rpm) . The ball impacted with back spin and rebounded with top spin . This simulates the change in spin which occurs in a typical top spin ground stroke. The racket clamp was designed such that the racket could be rotated to give any relative impact angle The clamp pivots asymmetrically to ensure that the ball impact is always centered on the longitudinal axis of the tennis racket. In this experiment, the ball was projected at both 40 and 60 degrees to the normal, to simulate two different top spin shots. These angles were based on work by Choppin (2005) who measured maximum relative impact angles of 38° for good leisure standard players. A Phantom v4.0 high speed camera, operating at 1000 fps, was automatically triggered every time a ball was projected using the bowling machine. The camera was located 8 meters from the impact, and a typical image is shown in Fig. I(b) . The camera automaticall a sc lienee ofbitma file on to a la to P .

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2.2 Automated Image Processing Bespoke image analysis software has been written which automatically calculates the velocity and spin of the ball, before and after impact. For each impact, the camera captured a blank image before the tennis ball entered the frame . This was defined as the base image. Each subsequent image was then subtracted from the base image using a standard image subtraction algorithm in Matlab v7. This image matrix was then filtered to remove noise, and processed to detect the position of the tennis ball. Three mutuall y perpendicular lines were drawn on the ball, to allow the spin to be measured. The algorithm which was used to determine the ball spin is more complex and a full description of this method is beyond the scope of this paper. The algorithm was written in Matlab v7, and based on Hall (2002). It is assumed that the

Measuring Ball Spin Off a Tennis Racket

381

ball rotates purely around an axis that is perpendicular to the image plane. The basic function of the algorithm is to determine how much the ball rotates between a pair of consecutive images. Pattern matching is used to rotate the second ball image in the sequence so that it has the same orientation as the first image. The average rotation of each pair of images is used to determine the ball spin. The uncertainty in the measured velocity and spin values has been determined to be less than 2%.

2.3 String stiffness The main aim of this study is to determine whether string type affects how much spin is applied to the ball. However, defining a string solely by its material type does not differentiate between the wide range of, for example, polyester strings available. One parameter of a string that is commonly used to characterize its properties is the string stiffness (Lindsey 2002, 2004). The stiffness of the strings used in this study has already been obtained by Lindsey, and those values are used here. The string stiffness values quoted by Lindsey were measured on a single string, using the method described in Cross (2001).

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Tests were performed using inbound spins that ranged from zero to 400 rad/s. However, for simplicity, only the rebound spin results for inbound spins of 100 and 400 rad/s are presented here. These rebound spin values are plotted against the appropriate string stiffness values. Figure 2 (a)-(b) show the results for the ball impacting at 40° to the nonna!. It can be seen that all the polyester strings were stiffer than the nylon strings. In both Figs. 2 (a) and (b) it can be seen that the ball rebounds with highest spin from the rackets strung with polyester material (inbound angle 40°). However, in Fig. 2 (c) the rebound spin is essentially independent of the string stiffness (inbound angle 60°, inbound spin 100 rad/s). Furthermore, in Fig. 2 (d) it can be seen that the rackets strung with the polyester strings give the lowest rebound spins (inbound spin = 400 rad/s, inboundangle = 60°). 2.5

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It is difficult to identify the reason for the varying dependency between the string stiffness and the rebound spin using only the data in Fig. 2. However, the ball rebound velocity and rebound 'angle were also measured in this study. The actual values of the ball rebound velocity and angle are not presented here, but the results can still be used to further our understanding of the impact mechanism. This is done by considering the mode of the ball immediately prior to it leaving the surface. The ball can either be in sliding or rolling mode, and the spin ratio is used to define which mode the ball is in (Goodwill and Haake (2004a)). The spin ratio (SR) parameter is defined as,

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Measuring Ball Spin Off a Tennis Racket

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where OJ is the rebound spin, r is the ball radius (0.033 m) and V(x) is the horizontal component of the rebound velocity. Previous researchers have shown that SR can be, (I) Less than unity - the ball slides throughout impact. (2) Equal to unity - the ball rolls off the surface . (3) Greater than unity - the ball rolls during contact, and then leaves spinning faster than rolling. The spin ratio values for the impact tests in this study are shown in Fig. 3. The main point to note from this figure is that, for the majority of the impacts, the spin ratio is greater than unity . It can therefore be concluded that there is sufficient friction between the ball and stringbed to cause the ball to roll at some point during the impact which is consistent with the finding s of Goodwill and Haake (2004). The only exception to this finding is shown in Fig. 3 (d) . This figure shows that, for impacts at 60° and 400 rad/s, the spin ratio for the polyester strings is significantly lower than unity . This is interesting as it implies that the ball slides throughout impact on the stiffer strings .

3.2 Discussion There are two major findings in this work which are, I. For all impacts at 40°, the stiffer polyester strings impart more spin compared to the nylon strings. 2. For impacts at 60° and 400 rad/s, the polyester strings impart less spin . For all the impacts at 40°, Figs. 2 (a)-(b) clearly show that the balls rebounding from the polyester string s have a higher spin . Intuitively it might be concluded that the higher spin attained by the polyester strings might be due to a higher friction coefficient. However, the friction coefficient for virtually all the strings is high enough to induce rolling, and any value higher than this critical value does not increase the magnitude of the rebound spin (Daish 1972). The reason for the higher spins off the polyester strings is likely to be linked to the magnitude of the lateral stringbed deformation . This lateral deformation occurs becau se, during the compression phase of the impact , the ball grips the stringbed and causes the strings to deform laterally in the direction of the ball motion. The importance of this deformation in terms of the spin generation, is the recovery of the stringbed during the restitution phase . The stringbed will attempt to recover in some part to its original position. This causes the stringbed to move in an opposite direction to the motion of the ball. This stringbed motion acts to increase the relative ballsurface velocity. If the string is gripping the surface, then this motion will accelerate the ball rebound spin . The results in Figs. 2 (a)-(b) appear to suggest that the stiffer polyester strings are able to utilize this mechanism more effic iently . This may be because the strings are stiffer and therefore more able to recover. Alternatively, it may be because the stiffness of the strings will determine how fast the string can recover, and the stiffer strings recover in the most efficient time period . The second finding (based on the results in Fig. 2 (d) appears to contradict the conclusion discussed above . This is because the balls rebound off the polyester string with less spin . However, the results in Fig. 3 (d) highlight the point that the

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Simon Goodwill

ball is sliding off the polyester strings (SR < I) and therefore the impact mechanism is different for these impacts, compared with those described above . The lateral motion of the strings will now be reconsidered in an attempt to understand why the stiffer polyester strings now give less spin. In the impacts presented in Fig. 2 (d) the ball will have a tendency to want to travel a long lateral distance (due to the shallow impact angle) and want to slip (due to the high inbound spin) . In this extreme case the ball will attempt to deform the stringbed laterally, but the stiffer polyester strings will not be able to deform as much as the nylon strings. Therefore the impact on the stiffer strings will be more analogous to an impact on a rigid surface where the ball will be subjected to more sliding during the impact. So instead of the polyester strings gripping the ball and deforming laterally during impact, their high stiffness prevents this lateral deformation, and the ball has no option but to slide across the surface. The consequence of this is that, unlike in the other cases, any recovery of the lateral deformation during the restitution phase is less significant. The nylon strings have a greater ability to deform during the restitution phase, and therefore the ball is subject to less sliding on these strings.

4 Conclusions It has been found that, for balls inbound at 40 degrees to the normal of the string plane, the stiffer (polyester) strings give more spin . However, for balls inbound at 60 degrees, the stiffer strings generally give less spin . There is a considerable amount of anecdotal evidence that top professional players are using stiff polyester strings . In this study it has been shown that they will achieve more spin with polyester string , if the relative ball-racket impact angle is 40 degrees. This extra spin allows them to hit the ball harder, whilst keeping the ball in play, thus increasing their chance of winning the point.

References S., Goodwill, S.R. and Haake, S.J. (2005) 3D Player testing. In: Proceedings of the 6' International Conference on the Engineering of Sport (ed F. Moritz & S.J. Haake) . Cross, R. (200 I) Stretch tests on strings , Racquet Tech, September, 12-18. Daish, c.s. (1972) The Physics ofBall Games. English Universities Press, London. Fischer W. (1977) Tenni s Racket, US Patent 4273331 , 8'h December 1977. Goodwill, S.R. and Haake, S.J. (2004a) Ball spin generation for oblique impacts with a tennis racket , Experimental Mechanics, 44(2) , 195-206. Goodwill, S.R. and Haake, S.J., (2004b) Effect of string tension on the impact between a th tennis ball and racket. In: Proceedings of the 5 International Conference on the Engineering of Sport (ed M. Hubbard, R.D. Mehta & J.M . Pallis), 2,3-9. Hall, D. (2002) Three-dimensional reconstructionfrom planar slices, http://www .mathworks.com/matlabcentral/fileexchange/loadAuthor.do?objectType=autho r&objectld=982174 Lindsey, C. (2002) String Selector Map, Racquet Tech, February, 4-8 . Lindsey, C. (2004) String Selector Map 2004, Racquet Sports Industry,I(7), 24-29.

Chop~in,

3D Player Testing in Tennis Simon Choppin I, Simon Goodwill 2, Stephen Haake/ Sports Engineering Research Group, University of Sheffield, [email protected] 2 Sports Engineering, CSES, Sheffield Hallam University I

Abstract. Although qualitative shot analysis and rudimentary 2D player testing has been performed in the past, a comprehensive 3D study has yet to be done. This paper outlines a method that has been used to record player baseline shots and serves in 3D. The method allows accurate tracking of racket velocity (any point on racquet), ball velocity, impact instant, impact position, and all associated angular velocities. Details of the methodology used in obtaining recorded shots are described, as well as the planar/vector calculations used to obtain the required information from the recordings. The movement of racket and ball were considered just prior to, and post impact, but testing is not limited to this case. Two Phantom high speed cameras were used in the analysis at 1000 frames per second. To date, testing has been performed on recreational, to county level players with a mind to extend the testing in the future to world ranked professional players.

1 Introduction Player testing is an important tool, and has its place in sports science, engineering and biomechanics. To date, and with tennis analysis firmly in mind, photogrammetric player testing has generally been performed in 20 at low « 200fps) frame rates with a specific aim, whether this be some definition of player accuracy (Blievernicht, 1968), or more recently, studying advanced player kinematics (Knudson and Blackwell 2005). There has also been some notable 30 work performed using the OLT method on serve (Elliott, Marsh and Blanksby 1986) and backhand (Elliott, Marsh and Overhue 1989) strokes. This work is biomechanics based and is limited due to the technology and frame rate used at the time. The method proposed in this paper focuses primarily on the impact; the racket and ball movement just prior to, and post impact. Analysis is concentrated on the movements of the racket and ball only, biomechanical movements are not considered. This method varies from previous work, in that instead of obtaining quantitive measurement from the photos directly, specifically marked points on the racket are used to set-up a plane, and a point in space in the case of the ball. With this information it is possible to accurately track racquet velocity (any point on racquet), ball velocity, impact instant, impact position, and all associated angular velocities. The

386

Simon Choppin, Simon Goodwill, Stephen Haake

advantage of this method, is that unlike previous methods, velocities are not limited to a single tracked point, or singularly considered axis of rotation. It also allows further in-depth 3D analysis should the need arise (an example being the instantaneous rotation matrix and helical axis of rotation (Spoor and Veldpaus , 1980) of racket movement) the key being that this method does not limit the target objective of the testing, as long as it is grounded in racketlball dynamics . The testing performed to date has used recreational to county level players to refine and test the methodology, with a mind to move on to professional , ranked players in the future. The testing has been developed as a validation exercise to determine typical racket head speeds, impact angles and impact positions , for use in future testing .

2 Methodology All testing was performed using stereo videogrammetric methods and on a standard size, outdoor tennis court (although it should be noted that provisions for indoor testing have been made). Players were situated at the baseline in a calibrated 2x2x2m volume and recorded performing a variety of shots, the balls were fired from a repeatable air-cannon into the control volume, and all shots that landed within the court boundary were recorded. A checkerboard calibration technique was used to define 3D space (Choppin, Whyld, Goodwill and Haake 2005), with a set of global axes defined as in fig.1 Because this method used only two cameras, placement of the cameras, type of markers used (5 markers are needed on the racket), operating speed of the cameras, and the markers position on the racket are all vital aspects to this method, and a full methodology review was carried out to ensure the correct choices were made.

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2.1 Markers Set-up The purpose of the markers is not only to define the racket face as a plane , but also to define a set of local co-ordinate axes at each instant, for these reasons, it is vital that a minimum of three markers are visible to define the plane(two of which must be used for axes co-ordination) A reflective tape is used to create markers 20-25mm wide at five points on the racket face, markers 1-3 can be used to create the local axes set (figure 2.1.1), markers 4 or 5 are used if one of the markers 1-3 is not visible at anyone instant. A tape type marker is used so that it is visible from both sides of the racket. Ideally, spherical markers surrounding the frame of the racket would allow the markers to be seen from most orientations and also allow accurate tracking of the markers (a spherical object's centre can alway s be found in 20 image tracking). It was decided that tape markers - becau se of the minimum alterations to the appearance, and weight of the racket - would be the best in term s of gaining accurate results from player testing, and the one or two mm discrepancy in tracking accuracy was a worthy trade off. Plane and local axes generation Th e plane of the racket is defined algebraically as:

ax + by + cz + d

=0

(I)

Where (x,y,z) is any point on the surface of the plane, and the perpendicular vector to the plane is given as (a,b,c). Each vector is defined in terms of the global axes set set-up at cal ibration. The plane equation can be obtained from three points which exist in that plane . If three of the markers global co-ord inates can be given as:

(2) (3)

(4) The coefficients can be found quite simply from the knowledge of these three points(Anton) Local co-ordinates are set-up using by defining the axes as unit vectors from the position of two of the three mark ers (figure 2.) the z-axis is alway s normal to the face of the racket , hence :

z=

ai + bj + ck 2

?

?

a «b' +c -

(5)

Error in axes generation: Error testing on both the data collection and calculation stage s of anal ysis shows the plan ar/vector model for racket and ball anal ysis to be robu st and sufficiently accurate as to be insignificant in term s of error. For example, a point tracked on the racket

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directly from the images is typically around ±0.25mm from the same point tracked via the planar model using initial position and velocity vectors. The accuracy of the calibration method concurs with previous findings (Choppin, Whyld, Goodwill and Haake 2005).

r:113

'J)

2

5

Fig. 2 Local racket axes and their relation to the racket markers

2.2 Cameras The cameras were placed at either end of the net and focused on the centroid of a 2x2x2m volume situated at the baseline, from this orientation all the markers are visible at the point of impact and for 30 or so frames either side. A camera situated at the side of the player may have a clearer indication of the balls position in the global x-direction , but most of the markers are hidden around the time of impact, making it impossible to define the racket plane. The cameras were run at 1000 fps, at racket speeds of around 30 mis, the racket is moving around 30mm between frames and this was found to give an accurate analysis. Daylight provided sufficient light such that shutter speeds of 100~s produced no blurring or distortion of the images.

2.3 Analysis - Examples Using the method described in section 2.1, the plane and local co-ordinate set is defined for each instant as well as the point co-ordinates of the ball in each of these instants. Any point on the racket can be recreated at each instant (for example, the centre of mass, or the tip of the racket) assuming the racket travels linearly in the period of analysis the velocity vector of that point on the racket can be calculated. The balls velocity is assumed linear in x and z directions, but 2nd order polynomial in the vertical. Separate tests checking the validity of these assumptions , showed them to be valid. The impact point of the racket can be calculated by using a bisection method to calculate the time at which the perpendicular distance between the ball and plane is a minimum . If a set of points are carefully selected on the racket, it is also possible to ascertain the rotational speeds around certain axes with simple rigid body dynamics,

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for these to have any particular meaning, velocities must be transformed into the local co-ordinate set. If the ball is clearly marked, it is also possible to calculate 3D ball spins (Tamaki, Sugino Yamamoto 2004) , with translations and rotations for ball and racket, a full 6 degree of freedom model can be generated from which the possible racket/ball observations possible becomes vast.

3 Results Analysis shows that, a local axes set produced from markers 1 and 2 is typically less then 0.1° misaligned from a set produced from markers 2 and 3. Racket markers can be repeated to within 2mm , and the ball within lmm, meaning at 1000fps velocity uncertainties of ±2ms" and ± 1ms" respectively. Single Player Analysis: The results (shown in Table 1) for a single player are given below as an example of typical data collected. (Player plays once a week at recreational level) 6 Shots in total Playing Angle Average 26.6°

Max

Racket Speed (ms")

Impact accuracy(mm)

Average

Max

Average

StD

24.45

29.59

43.0

15.8

Table 1 Resultsof a single player analysis

Playing angle: The angle at which the racket impacts the ball, taking into account racket and ball velocities and the vertical angle of the racket at impact. Racket speed : The speed of the centre of mass of the racket immediately prior to impact. Impact accuracy: Distance in millimetres of the impact point from the stringbed centre.

4 Conclusions 4.1 Analysis and memodology Thorough testing of both the method and accompanying analysis method has proven them to be a reliable, accurate and versatile player testing procedure. The apparatus used in testing does not present any intrusions or distractions for the players, who are able to play on a standard tennis court indoors or outdoors. The testing can be per-

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formed in a controlled 'set-shot' way, or used to record particular shots during a game. The errors measured suggest that the model assumptions are fair for this application.

4.2 Player Testing To date, the player testing has adequately shown the effectiveness of the methodology, as well as helped refine certain aspects of its execution. The results obtained so far help to assess the characteristics of play for lower level players and perform separate analysis involving (for example) grip characteristics during impact, and validation of existing racket models.

4.3 Further Development The methodology and analysis method itself is at a usable stage of refinement and any further work would involve specialising the calculations for a specific purpose . In terms of player testing, to build a thorough cache of players' shots, up to high level professional players, will provide a large amount of highly relevant, useful data.

Acknowledgements I would like to thank the ITF for continued support throughout this project, and the players which have given their time and skill towards the continued understanding of the game of tennis.

References Anton. Lines and Planes in 3 space . Elementary Linear Algebra, (2000), Wiley. 8th Ed: 149-

15I. BlievernichU.G. (1968). "Accuracy in the Tennis Forehand Drive : Cinematographic Analysis." Res . Q. Ex. Sport 39(3): 776-779 . Choppin.S.B., Whyld.N.M., et aI. (2005). "3D Impact Analysis in Tennis." The Impact of Technology on Sport 1(1) : 373-378. ElIiott.B.C, Marsh .A.P, et aI. (1986). "A Three-Dimensional Cinematographic Analysis of the Tennis Serve ." International journal of Sport Biomechanics 2(4): 260-27 I. ElIiott.B .C, Marsh .A.P, et al. (1989). "The Topspin Backhand Drive in Tennis: A Biomechanical Analysis." The Journal of Human Movement Studies(l6): 1-16. Knudson.Duane.V. and Blackwell.John.R, (2005). "Variability of impact kinematics and margin for error in the tennis forehand of advanced players." Sports Engineering 8(2) : 7580. Spoor.C.W. and Veldpaus.F.E. (1980) . "Rigid Body Motion Calculated From Spatial CoOrdinates of Markers." Journal of Biomechanics 13: 391-393. Tamaki .T, Sugino.T, et al. (2004). "Measuring Ball Spin by Image Registration." The 10th Korea-Japan Joint Workshop on Frontiers of Computer Vision: 269-274.

An Extended Study Investigating the Effects of Tennis Rackets with Active Damping Technology on the Symptoms of Tennis Elbow Robert Cottey', Johan Kotze', Herfried Lamrner' and Werner Zimgibf HEAD Sport AG, Kennelbach, Austria, [email protected] Praxisklinik fur Orthopadie und Sportmedizin, Miinchen

Abstract. The aim of this research was to determine what effect an active damping tennis racket technology had on players suffering with symptoms of tennis elbow. The study was conducted to verify findings of previous research, which concluded that the symptoms of tennis elbow had been dramatically reduced by playing with a Head rackets containing the Head Chip system" (Kotze et al. 2003). A similar study over an extended period was completed to further substantiate these findings and to test the improved generation of 'Chip' rackets. This study used two versions of the Head Protector Oversize tennis rackets; both containing piezo ceramic fibres integrated with the electronic Chip systemt", but only half with the chip "active", thus providing a control. The subjects were male and female experienced tennis players diagnosed with either acute or chronic tennis elbow. They were given unspecified rackets to facilitate a blind study, and the subjects' elbow condition was medically assessed and recorded over an extended period of time. Results of the study indicated that for the players who were initially diagnosed with acute tennis elbow, a large improvement in their condition was recorded for those using the active rackets, whilst the players with the control rackets showed little improvement in their condition. Similar results were found for the players diagnosed with chronic tennis elbow although to a lesser extent; those using rackets with active chips showed an overall improvement, whilst the players with the control rackets again showed little sign of improvement. The results of the study have shown that an active damping technology, when applied to a tennis racket, can reduce the symptoms of both acute and chronic tennis elbow.

1 Introduction Tennis elbow (Lateral Epicondylitis) is the most common (Pluim and Safran 2004) and investigated injuries in tennis and although different forms of the injury also occur in other walks of life, it has predominantly been connected to tennis. Tennis elbow is defined as the occurrence of micro-fractures in the tendon attaching to the lateral epicondile of the forearm. The fractures cause swelling of the joint and intensive pain to the player, resulting in anything from slight discomfort to complete debilitation (Roetert et al 1995). In an extensive investigation, by Cooke et al (2002), into the current knowledge related to the injury, it was concluded that the nature of the injury is fairly well understood and thoug there were still many uncertainties regarding the exact cause the general consensus was that it is caused by repetitive

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impact loading. Hence manufacuturers have developed various technologies focused on reducing the effect of impact loading on the arm. These systems have traditionally all been passive damping systems, which means the mechanical vibration energy is dissipated via some damping material or mechanism in the form of material friction or heat and have never been proven to have any real effect on the actual injury. Head sport therefore went a step further in developing rackets with an active damping system in order to find a more affective damping solution. In an active damping system the mechanical deformation energy is converted into electrical energy, which is stored and released back into the material such that it actively damps the vibration, without using any external energy . The first series of rackets were tested during an independent study, during which carefully selected subjects, suffering from tennis elbow, were given the Intelligence i.X16 and i.S18 rackets (Fig. l a and Fig. lb) to play with as per usual, while being examined at the start and the end of a six week research period and their progress recorded (Kotze et al. 2003). Results from the tests were reassuringly positive. As a result, the design of the rackets was further improved in order to develop a racket specifically aimed at players with tennis elbow, which resulted in the new HEAD Protector series. From this new series the Protector OS (Fig. l c) was selected for another stringent set of medical testing. As before, the players diagnosed with either acute or chronic tennis elbow participated in the testing but this time in a more conclusive random, double blind, placebo controlled study to determine the effectiveness of the new rackets on their symptoms.

(a)

(b)

(c)

Fig. 1. Active damping piezo rackets from HEAD Sport: (a) i.S18, (b) i.X16, (b) Protector OS.

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2 Experimental Method Strict selection criteria were used to determine which of the possible candidates were used in the study; these comprised a preliminary medical examination, being within a certain age bracket, and play tennis at a predetermined ability level. The preliminary medical examination was conducted and candidates clinically diagnosed with epicondylitis humeri radialis and had the condition for at least 6 weeks were suitable for the study. It was also specified that the candidates had to have been free of any treatment for a minimum of 12 weeks prior to the start of the testing, and could not receive any subsequent treatment for their symptoms; this treatment included any injections or other therapeutic remedies. Candidates who were diagnosed with nerve compression syndrome, instabilities of the shoulder / elbow or if they suffered from arthrosis of the hurneroulnarjoint, were not allowed to participate in the study. Candidates had to be between the ages of 18 and 70 to prevent some degenerative factors influencing the results. The candidates also had to have at least 3 years tennis playing experience. Male and female players were randomly selected from those who met the prerequisite requirements. A total of 102 experienced tennis players from southern Germany, 58 men and 44 women were chosen to complete the study. The group had an average age of 51.2 years and the average playing experience was described as "Good". At the start of the investigation each participant was ' prescribed' a Head Protector Oversize tennis racket as the sole treatment for their condition. They were requested to reduce activities such as gardening, handiwork, or other manual and elbow-burdening activities. They were also asked to retain their usual tennis schedule using only the racket assigned to them at the start of the testing. Any other treatment of their conditions such as the use of injections or other therapeutic medicine was restricted. All activities that the participant completed were documented for the testing period. The selected participants were divided randomly into two groups, and a clinical investigation of these two groups was completed using an x-ray and an ultrasound test. The medical examinations were supervised by Dr. med, F.Soller, a scientific employee of the Orthopadie Klinikum Grol3hadern at the Ludwig-Maximilians Universitat Miinchen. The medical examination enabled further classification of the two groups into sub-groups determined by the diagnosed condition of the participants, either acute or chronic tennis elbow. Acute epicondylitis symptoms was the classification for those who had the painful symptoms for less than 3 months, and chronic epicondylitis defined as those who had suffered with the symptoms for more than 3 months. Two methods used to evaluate the severity of the pain are presented in this paper, one using the scoring method of Broberg and Morrey (1986) and the other using the classification of the Mayo Elbow Performance Index (in Morrey 1993). Both tests comprise of an objective and subjective part and have been used to compare the participants' symptoms before and after completion of the test period. The objective comprises of motion, stability and strength or ability to perform tasks, and the subjective part comprises of an evaluation based on an interview with the patient. For

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the purpo se of evaluating the participants elbow condition prior to and after the testing period these methods are suitable. A statistical anal ysis of the results was completed to determine if the difference betwe en evaluations made before and after the completion of study we re statistically significant. A two sample t-test was completed allowing the spread of data to be evaluated and to determine if there was a statistically significant improvement of the patients' cond ition. Doktoranden Herro F. Dorfle r defin ed the protocol for the participant evaluation, which consisted of an internal examination of the affected elbow using Sonography (with a 7.5MHz linear sound head) and radiography. The examinat ions were completed at the Orthopadischen Klinik und Poliklinik Grol3hadern which has a large orthopaedic department. Follow up examinations were at 6 and 12 weeks. The results taken were record ed and scored on a scale indicated by using the Borberg and Morrey and the Mayo Clinic Performance Index for the elbow . After each examination the tennis rackets were re-strung to the same tension , providing further control of the testing conditions. The Head Protector racket s were divided according to the original random grouping, both groups were given ident ical looking rackets, howe ver one set of rackets did not contain the active chip system, and so acted as a control group. The participants were not aware of the type of racket they were given for the testing. Only Dr Soller had prior knowledge of which type of racket each part icipant recei ved and had no personal contact with any of the partic ipants at any time during the testing. The careful organi sation of the groups and distr ibution of the racket s ensured that this was a double blind study and would show any effect that playing with a racket with the active ch ip system would have on the symptoms of tenni s elbo w.

3 Results and Discussion 3.1 Mayo Elbow Performance Index The group that was diagnosed with acute epicondyliti s showed an improvement in their condition for both the participants using the control racket s and the participants using the active racket s. Both distributions of the scores after 12 weeks showed a stati stically significant increa se, however the difference between the test results showed that for the participants using the racket s with the active chip system the increase was almost double, from an initial rating of 'poor' with an average score of 51. 7 to a final rating of 'excellent' average score of 97.7 comp ared with the control group rising from 'poor' with an average of 46.0 to a final rating of ' fair' and a score of 68.2 (Fig. 2a). The group diagnosed with Chronic epicondylit is increa sed from ' poor' 51.7 to 'good' 87.5 for the participants with the active chip sys tem compared with an initial rating of 'poor ' average of 47 .8 rising to a final rating of ' poor' average of 55.6 for the participants using the control rackets (Fig. 2b). For the chronic test results the rise in the sco re for the two groups were both statistically significant but the differ-

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ence between the rate of change was much greater for the participants that used the rJckcts with the active chi sy:.:;S. :. :tC;,;.·I1;,;.l.:...-_ -r ----, Boxplot of Init! I, nd score 11ft r 12 w ks u Ing the Broberg lind Morrey system I'arnapents doag.-ed with ~ EpoconcIy\ltrs

j

'~1

-

Boxplot of init! I, lind score lifter 12 weeks using ttl Broberg lind Morrey system P!lrtJoponts d

nosed WIth Chronoc Epocondy\ItJs

I j '~I~ I

12 weeks

Without Chip (/I)

(b)

Fig. 2. The scoringdistributions for the Mayo scoringfor the participants diagnosed with acute (a) and chronic (b) epicondylitis.

3.2 Broberg and Morrey Scoring System The examination of the participants and the scoring of their condition according to the Broberg and Morrey scale showed similar results . The participants diagnosed with acute epicondylitis using the rackets with the active chip system scores increased from an average rating of ' fair', score of 62.6 to a final rating at 12 weeks of 'good' 88.7, there was no change in category for the participants with the control rackets , starting at ' fair' with an average of 61.4 the final score after 12 weeks remained at ' fair' with an average of 69.0 (Fig. 3a). Statistically the results for the rackets with the active chip was significantly different and there was no difference in the condition for those patients with the control rackets. Similar results were observed for the participants diagnosed with chronic epicondylitis. The group using the rackets with the active chip scores rose, although the categories did not change , starting at ' fair' with an average of 60.4 remained so with an increased score of 72.6 after 12 weeks . The control racket participants also showed no change in the category ' fair' but a smaller increase in the average scores was recorded from 62.6 to a final score of 65.3 (Fig. 3b). A statistical analysis of these scores for the participants diagnosed with chronic epicondylitis showed that only the group that used the rackets with the active chip system had a statistically significant increase in their average scores even though the categorical ranking did not change.

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Boxplot of In tI I, nd score fter 12 weeks u ng the M yo Elbow Perform nee Index PllttJciPll"ts diognosed wtlh Chronic EpicDndyl.

-

1i

- - - -12weeb---'I1Itlo-1 - 12weebWith Chip

(a)

With out Chip

'~I,-

Initial 12 weeb With Chip

_

Initial 12 weeb Without Chip

(b)

Fig. 3. The scoring distributions for the Broberg and Morrey scoring for the participants diagnosed with acute (a) and chronic (b) epicondylitis.

4 Conclusion By using a random, placebo controlled, double blind study the true effects of using a HEAD tennis racket with an active damping EDS can be accurately assessed. These results confirm the previous study (Kotze et aI., 2003) that the symptoms of tennis elbow can be statistically and significantly reduced with the use of this specially designed tennis racket. Participants who used the HEAD Protector tennis rackets . equipped with the EDS showed a significant improvement in their diagnosed conditions for both the acute and chronic form of tennis elbow. The results for this extended study have yielded statistically significant results with a clear reduction of the complaint of tennis elbow for those participants using the rackets with the chip system compared to those using the control rackets.

References Broberg , M. A., Morrey , B. F. (1986) Results of delayed excision ofthe radial head after fracture . J Bone Joint Surg Am, 68 pp 669-74. Cooke A. (2000) . An overview of racket technology . In: Tennis Science & Technology (Ed. by S.1. Haake & A.O. Coe), pp. 43-48 . Blackwell Science Ltd, Oxford, UK. Kotze, J., Lammer, H., Cottey , R., Zimgibl, W. (2003) The Effects of active piezo fibre rackets on tennis elbow. Tennis Science and Technology 2. Edited by S. Miller . Published by the IIF. Morrey , B. F. (1993) The elbow and its disorders , 2nd edition, (edited by Morrey) Philadelphia: Saunders . Pluim, B., Safran, M. (2004) From Breakpoint to Advantage. A Practical Guide to Optimal Tennis Health and Performance. Racquet Tech Publishing, USA. Roetert E.P., Brody H., Dillman C.1., Groppel J.L., and Schultheis J.M. (1995). The biomechanics of tennis elbow : an integrated approach, Clinics in Sports Medicine, 14 (I), 47-57.

10 Watersports

Synopsis of Current Developments: Water Sports Jani Macari Pallis, Ph.D. Cislunar Aerospace, Inc., [email protected] Water sports continue to provide an arena of innovation for the sports engineer. The mixed fluid medium of air and water and the often harsh operating environment provide challenges in the design, instrumentation, technology implementation and material science for these sports.

Water Sports and the Sports Engineer Engineers in sports, recreation and fitness have the same goals as other sports professionals: enhance performance; prevent injury; assure safety; increase enjoyment and health benefits; support longevity, accessibility and diversity (to participate throughout the human life cycle regardless of physical challenge). Clearly, these papers presented on water sports exemplifyeach of these objectives. This series of work covers a wide range of water sports: water skiing, rowing, kayaking, surfing, swimming and white water rafting. Equally diverse is the athletic ability and situation of the sportsperson studied: world ranked and Olympic athletes (both male and female), individuals returning to or beginning a sport after a serious physical injury and those being rescued during water sport participation. The techniques utilized and the technical subject matter of each paper is likewise distinctive: full body scanning and computational fluid dynamics, testing of equipment for strength and durability, modeling of forces, instrumentation for performance monitoring, development of software analysis tools and use of optimization methods in design. In the following paragraphs the works of these authors (several just beginning their careers in the field) are summarized. The indoor paddling biomechanics of the 2004 Italian women's Olympic kayak team was analyzed by integrating data from both a motion capture system and instrumented footpads, seats and paddles. Paddle trajectory, trunk and limb motions (shoulder, pelvis, trochanters excursions, range of knee flexion) as well as force measurements from a dynamometric footpad were extracted. Motion symmetry and regularity were correlated to an athletic ranking system and demonstrated that the "best" athletes performed regular paddle trajectories and steady trunk motion - information which can be key criteria for an evaluation system for trainers. To provide an alternative to on-water performance analysis systems for rowing, an on-land feedback device using rowing ergometers was developed and tested by a

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Jani Macari Pallis, Ph.D.

member of the Austrian national rowing team. Portable units using load cells and strain gages were developed to measure reaction forces at the foot stretcher. On-land and on-water results were correlated to validate that similar reaction forces were indeed observed. Additionally, a monitor which displayed a history of key kinetic parameters provided feedback to the rower during on-land training . Computational Fluid Dynamic software was used to analyze the aerodynamics of a water ski jump for British Water Ski. Using the geometry of a ski jumper, water skis, fins, bindings, helmet and tow handle , seven key, characteristic positions were simulated to obtain changes in lift and drag throughout the jump on the components modeled . Mid-flight results demonstrated that the ski jumper's body accounts for about 33% of the total lift generated, stressing the important of proper position. Recent equipment failures during simulated white-water rescues have demonstrated the need for detailed measurement of loads created and which can be safely sustainable by equipment currently used for white water rescue . Areas explored included the potential forces involved in a white-water rescue , the forces a threeperson rescue team generates, an analysis of suitable ropes for white-water rescue and an analysis of the current mechanical advantage rescue techniques. Conclusions in each of these areas are drawn including information on the types of rope fiber materials that should be utilized. As part of a larger project directed at facilitating design of fins and surfboards for manufacture, a Computer Aided Design tool has been developed to facilitate 3dimensional design of surfboard fins. The tool also provides the basis for in-depth studies through the use of stress analysis and Computational Fluid Dynamics (CFD) software, to provide insight into potential design and material modifications. Drag and lift forces predicted by the CFD were fed into a Finite Element Analysis (FEA) to obtain displacements of the fin undergoing these hydrodynamic forces . A swimming aid for individuals with upper-arm amputation was developed using optimization methods . The effect on the front crawl was analyzed by simulation since the upper limb motion generates the most thrust. Researchers developed a swimming prosthetic to compensate for the body imbalance created by the missing limb. An optimization method was used in the design and an initial trial test was confirmed by an experiment.

The Future of Sports Engineering in Water Sports Water sports have the added complexity of a mixed fluid medium (air and water) which raises the bar in terms of engineering degree of problem difficulty. The environment of these sports can be quite harsh . However, water sports continue to attract both individuals and families and are enjoyed through the entire life cycle of a person even as their bodies age or physical ailments or disabilities develop . The sports engineer will continue to develop or utilize the newest innovations in computing technologies (both hardware and software), material science, emerging technologies (wirele ss and nanotechnology) and MEMS (Micro-Electro-Mechanical systems). As our population ages and to increase market share efforts will cont inue to attract broader populations to the sport through engineering innovation.

Computational Fluid Dynamic Analysis of a Water Ski Jumper John Hart, David Curtis, and Stephen Haake Sheffield Hallam University, Sports Engineering, CSES, John.Hart @shu .ac.uk

Abstract. Water ski jumping is one of the oldest disciplines in water skiing. The first jump was performed by Ralph Samuelson of Minnesota (US) in 1925, three years after he had invented waterskiing. Samuelson jumped 18 m off the end of a greased ramp. Today waterski jumping is an international sport with elite male athletes jumpingdistances in excess of 70 m. The Sports Engineering Research Group (SERG) at the University of Sheffield have conducted a Computational Fluid Dynamic (CFD) analysis of the aerodynamic system of a water ski jumper for British Water Ski (BWS) in support of their 2005 World Championship campaign in China. The geometries of the waterskijumperand associated equipment werecreated using SERG's in-house non-contact laser scanning facilities. Seven characteristic positional stages were analysed over the ski jump to obtain information on the fluctuations in lift and drag force acting upon the waterskijumper. The individual contribution of lift and drag, to the overall aerodynamic system of the waterski jumper, from each modeled component could be determined by the use of CFD. This indicated that the skis generate an average of 65 % of the entiresystem liftand drag, with the front thirdof the ski's creating up to 50 % of these forces.

1 Introduction SERG (Sports Engineering Research Group) were approached by British Water Ski in the Autumn of 2004 to investigate the aerodynamic system of a water ski jumper. This was to be conducted in advance of the water ski 2005 World Championships in Tianjin, China. The objective of the investigation was to identify areas of the current system where improvement was achievable , with the provision of possible solutions. Although the aerodynamics of Nordic ski jumping has been investigated, (Seo, Watanabe, and Murakami 2004; Virmavirta, Kivekas, and Komi 200 I), the aerodynamics of water ski jumping is an area devoid of research . This is despite the fact that water ski jumping was invented nearly 80 years ago when Ralph Samuelson of Minnesota (US) performed the first jump . Similarities however can be drawn between the two disciplines . Water ski jumpers try to manipulate their skis into a V flight style as used by their winter counterparts. However due to the dynamics experienced as a water ski jumper leaves the top of the jump ramp and climbs through the jump this is much harder to achieve . Water ski bindings are also rigidly fixed to the ski with no articulation, meaning that the jumper can not lean out as far over the skis as a Nordic ski jumper. Differences exist in the ski design between the two disciplines . Whereas Nordic jump skis have a fixed maximum width of 11 .5 cm, and a maximum length set as a function of jumper height, water skis have no maximum length, however width is

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limited to 30% of the ski length. Water jump skis commonly do not have a constant curvature (rocker) from the tip to the tail. The front third of the skis are angled upwards and turned out. This design feature of the ski is known as the Stokes tip. The ski also has a short fin attached to the underside at the tail. The aerodynamics of Nordic ski jumpers has also been investigated using CFD (Asai, Kaga, and Akatsuka 1997). However these studies have used simplified human geometry. In this current study SERG intended not only to investigate the aerodynamic performance of the ski, but provide as detailed a description as possible of the aerodynamic system around and over the ski jumper. SERG therefore used noncontact laser scanning techn iques to capture as realistic a human geometrical form as possible .

2 Geometric Model The basic modeled geometry, (Fig. 1), consists of ski jumper, "Connelly" water skis and appropriate fins, bindings , a "Jofa" sky diving helmet, and tow handle. The geometry was acquired using SERG's in-house non-contact laser scanning facilities. Scanning was performed using a ModelMaker X70 scanning system, to generate an initial point cloud representation of the geometric components. The point cloud data was then converted to a fully water tight NURBS (Non-Uniform Rational B-Splines) model, using Raindrop Geomagic Studio, that could be manipulated within a commercially available CAD (Computational Aided Design) package .

Fig. 1 Modeled skijumper geometry showing bothhandle grip styles

It was not possible to use an actual ski jumper to provide the human geometry used in this investigation due to time constraints . Instead an anatomically correct flexible mannequin was used which could be manipulated into a characteristic jump position. The mannequin upper torso was scanned twice, to obtain two different hand holds of the tow handle. During the jump flight the ski jumper alters the hand hold, from a double grip to single hand grip. The tow handle geometry was created using CAD . The individual scanned geometries were assembled in to a single model within the Fluent pre-processor Gambit. The identities of each component were preserved

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however to enable the individual contribution to drag and lift of each component to be determined.

3 Computational Model Computational mesh were constructed using Fluent's Gambit and TGrid mesh generators. Each mesh consisted of approximately seven million tetrahedral, prismatic, and hexahedral cells, concentrated in regions of detailed geometrical interest. The prismatic cells were constructed over the entire surface of the modeled geometry to ensure that surface boundary layers were adequatelycaptured. The CFD code Fluent 6.1 was used to perform the simulation. This solved the governing equations of fluid motion sequentially, with turbulence closure provided by the realisable k-e turbulence model used in conjunction with a non-equilibrium wall function model. All governing equations were discretised with 2nd order interpolation schemes. The modeled jump velocity and directional components were determined using the trajectory model, as detailed in the next section, and applied appropriately. Simulations were performed using 8 processors on a custom built Linux cluster, and converged results were obtained after a runtime of approximately 12 hrs. Postprocessing was performed using Fluent to obtain lift/drag forces, and all graphical output using CEI's Ensight8 software.

4 Modeled Jump The jump has been modeled in stages as a selection of snapshots in time as agreed with BWS. It is not yet possible to model a water ski jump from start to finish in a smooth transition using CFD, due to the geometrical changes that take place over the jump. BWS provided data of a jump performed by Jason Secls (2004 & 2005 European Jump Champion), detailing key geometrical angles of the ski jumper and skis over time, (Fig. 2).

Fig. 2 Modeled jump angles

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John Hart, David Curtis, and Stephen Haake

Using the BWS data , seven characteristic positions were chosen, including key reference positions; off the ramp, change of handle grip, and final position prior to landing. The ski jumper adjusts the tow handle grip from both hands to a single hand hold after approximately one second in the modeled jump. The scanned geometries were adjusted accordingly to the required angles using CAD, (Table I). Stage

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4.1 Trajectory Detailed data of a water ski jump flight trajectory does not currently exist. In particular there is no data concerning the velocity vector of the ski jumper at each stage of the flight. To obtain this information a standard projectile motion model has been used. A constant horizontal deceleration has been assumed over the jump based on existing jump data . This was determined from the known take off velocity, the length of the jump, and the final velocity required to cover the distance in the time jumped. During a jump a ski jumper not only travels forward but also to the side due to the approach path made towards the jump ramp . This side ways movement has been omitted. The water ski jumper hits the ramp with an initial velocity of 70 mph, and the distance jumped is 67 m over a time of 2.55 seconds. The ramp has a slope of 22° and a takeoff height of 1.8 m. The flight conditions, as shown in Table I . were applied to the simulation. Where Vx and Vy are respectively the horizontal and vertical velocity components, X and Y is the horizontal and vertical displacement of the ski jumper.

5 Results The predicted ratio of lift/drag force (LID) for the aerodynamic system of the water ski jumper is shown in Fig. 3. LID is seen to increase rapidly between stages 3 and 4 as the jumper maneuvers the skis into the characteristic V flight style . Maximum LID

Computational FluidDynamic Analysis ofa WaterSki Jumper

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is found to occur at stage 5 when the ski angle 8 is a maximum and the jumpers body is leaning out over the skis. This position can only be maintained for a short duration however as the jumper is already realigning their skis by stage 6 in preparation of landing. LID therefore decreases rapidly .

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406

John Hart, David Curtis, and Stephen Haake

obliquely. Consequently a significant region of low pressure was formed behind the Stokes tips, indicating the possibility of a large flow separation. Flow was indeed observed to separate behind the Stokes tip, Fig 5, with the formation of a large vortex core, from stage 4 of the flight. This vortex core separates cleanly away from the ski due to the upturned angle of the Stokes tips. Regions of separating flow were also observed from the ski jumpers rear , limbs, and helmet. Flow separation over the ski jumpers body can be seen in the oil flow plot in Fig.5. This shows how air flow moves over the body , with the spiral patterns indicating regions where vortex cores originate.

Fig. 5 Flow separation from skis & oil flow plot over ski jumpers body

6 Conclusions SERG has conducted a CFD analysis of the aerodynamic system of a water ski jumper for British Water Ski. Seven characteristic positions have been analysed over the jump, to obtain information in the fluctuations of lift and drag. It was found that the skis generate an average of 69 % of the entire system lift, with the Stokes tips creating up to 50 % of these forces . Large regions of flow separation are seen to form behind the Stokes tips. The ski jumper's body generates an average of 31 % of the total lift force , highlighting the importance of body posture.

References Asai, T., Kaga, M., and Akatsuka, T. (1997) Computer Simulation of the V-style Technique in Ski Jumping using CFD. Pro c. 6th Int. Symp. Computer Simulation in Biomechanics. Tokyo, Japan, pp. 48-49 Sea , K., Watanabe , I., and Murakami , M. (2004) Aerodynamic Force Data for a V-Style Ski Jumping Flight. Sports Engin eering. 7,31-39 Virmavirta, M., Kivekas, 1., and Komi, P.V. (2001) Take-off Aerodynamic s in Ski Jumping. In. Biomechanics. 34, 465-470

Feedback Systems in Rowing Arnold Baca, Philipp Kornfeind and Mario Heller University of Vienna, [email protected]

Abstract. On-land feedback devices using rowing ergometers provide an alternative for onwater systems. Inorder not to draw incorrect conclusions it is essential to compare the rowers' technique in the boat to that on the ergometer. Units for measuring reaction forces in the boat and at the ergometer have been constructed. Similarities in the reaction forces at the foot stretcher could be found for elite rowers.

1 Introduction Technique analysis in rowing involves the consideration of fine details of the movement of the rower with regard to the boat. In addition to kinematic analyses the study of the kinetics of the boat-rower system provides valuable insights into strengths and weaknesses (e.g. peculiarities in motion coupling) (Spinks and Smith 1994; Badouin and Hawkins 2004). Feedback systems incorporated directly in the boat are used in elite rowing (Smith and Loschner 2002). Data are processed on-board and may be transmitted to a PC located on the coach's launch using wireless communication technologies (Collins and Anderson 2004). Analyses of the rowing technique in the boat are difficult to realize and are very demanding in time and instrumentation. In many cases analyses are therefore based on rowing simulators (ergometers) on land (Page and Hawkins 2003; Loh, Bull, McGregor and Schroter 2004). In order not to draw incorrect conclusions from the training sessions on land it is essential to compare the rowers' technique in the boat to that on the ergometer (cf. Lamb 1989). A specific setup has been developed to compare the dynamics. Units have been constructed to measure reaction forces at the foot stretcher in two dimensions and may be used in the boat as well as at the ergometer (Concept 2 Indoor Rower Model D) with or without slides (a construction that is attached to the legs of the ergometer, allowing the ergometer to roll back and forth during the rowing stroke). Reaction forces at both feet are acquired separately. In addition to the forces at the foot stretcher the pulling forces also allow to draw conclusions on the rowing technique. In the case of ergometer measurements a force transducer is connected to the chain attached at the handle. In the boat, dynamomet-

408

Arnold Baca, Philipp Kornfeind and Mario Heller

ric oarlocks are used for this purpose. Data measured in the boat are recorded using a data logger or a Personal Digital Assistant (PDA). A comparison of reaction forces at the foot stretcher has been performed for elite rowers. The methods applied and selected results (case study) are presented in the sequel.

2 Methods Reaction forces at the foot stretcher are measured using two identical constructions (Fig. I) based on load cells (HBM, type HLC220) and strain gages (HBM, type XY91-6/120). The (portable) units may easily be attached to the foot stretcher of the boat or of the ergometer. Forces are induced into a cover plate made of aluminum. Components vertical (load cell) and parallel to the platform (strain gages) can be acquired. From the data recorded the resulting force vector (magnitude, orientation) is calculated. The load cell acts as double bending beam, the strain gages have been applied to acquire parallel forces. To obtain an optimal position to mount the strain gages, stress calculations have been performed utilizing the software Ansyst". A CAD model of the load cell has been constructed in order to simulate the load cases in longitudinal direction. The local maxima of the material tensions resulting from these simulationswere selected as positions for bonding the strain gages.

Fig. 1. Left: construction for measuringreaction forces at the foot stretcher, right: modified load cell with strain gages

The strain gages (2 measuring grids configured in a T-rosette arranged perpendicular to one another) have been configured as a full bridge. Because of their orientation in the circuit they compensate forces perpendicular to the load cell and simultaneously double the sensitivity in longitudinal direction. In order to condition and amplify the bridge signals a dual stage amplifier circuit was dimensioned, manufactured and integrated into the platform. In the boat the platforms are mounted directly to the foot stretcher by screwed connections, in the case of the ergometer quick clamps at the lower side as well as fastening angles at the upper side are used for fixation (Fig. 2).

Feedback Systems in Rowing

409

Fig. 2. Fixation of the platforms. Left: boat, right: ergometer The linear relationship between force and output voltage was investigated by performing a comprehensive calibration procedure with static loads in both force axes (normal and parallel) in positive as well as negative direction. The measuri ng points obtained by this procedure yield a nearly plane grid, showing a high linearity (Fig. 3).

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410

Arnold Baca, Philipp Kornfeind and Mario Heller

If horizontal force components are considered only, the following equation can be set up

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where Fs is the horizontal reaction force at the foot stretcher, Fp the pulling force and FGRF the horizontal ground reaction force in the direction of motion. A comparison of two different measuring systems is therefore possible . A typical example for one stroke is shown in Fig. 4. Measured (Fs*) and calculated horizontal reaction forces (Fs) at the foot stretcher are shown . Note that Fs* is the sum of components normal (load cell) and parallel (strain gages) to the foot stretcher considering its angle with respect to the boat/ergometer. A correlation of r=0.99 was calculated between the values (200 samples per second) of'F, and Fs* for this stroke.

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Feedback Systems in Rowing

4 11

3 Case Study Horizontal reaction force curves at the foot stretcher of an Austrian elite rower (national team) are presented in Fig. 5. All measurements have been performed on the same day. Remarkable asymmetries between left and right foot can be seen in all situations . In particular, the amplitudes of the right foot are higher during the pulling phase (negative forces). For the three ' successive strokes presented the quotients of the areas under the curves (negative parts only) of left and right foot are 0.68, 0.73 and 0.73 for the boat, 0.83, 0.82 and 0.80 for the ergometer with slides and 0.89, 0.91 and 0.90 for the ergometer without slides.

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Moreover, a specific irregularity marking the start of the pulling phase (denoted by little arrows in Fig. 5) can bee seen in both ergometer conditions as well as in the boat. One possible reason for the strong occurrence of this irregularity might be that the upper body of the rower under investigation straightens up too early at the start of the pulling phase. The rower may therefore benefit from feedback sessions on the ergometer. During these sessions knowledge-of-performance feedback is given. The time histories of the relevant kinetic parameters are displayed on a monitor in view of the rower during motion execution. The rower is thereby able to discover how changes in the movement pattern alter the shape of the curves.

412

Arnold Baca, Philipp Komfeind and Mario Heller

4 Conclusions and Perspectives Case studies indicate that peculiarities in the rowing pattern may also be observable when using rowing simulators. In these cases benefits are expected from the use of feedback systems based on ergometers. The results also indicate that the ergometer with slides compares better to onwater rowing . This is not surprising, since on the ergometer with slides the rower has to accelerate/decelerate the ergometer whereas on the ergometer without slides he/she has to accelerate/decelerate his/her body . It should, however, be considered that many (elite) rowers are not used to exercise on ergometers with slides . Upcoming experiments will also consider pulling forces for the comparisons. A variant of the on-land feedback system for use in the boat assisting both coaches and athletes and a cascaded double ergometer system are under development.

Acknowledgements We thank Armin Blaha and Emanuel Preuschl for their valuable contribution constructing the foot stretcher dynamometer.

In

References Baudouin, A. and Hawkins, D. (2004) Investigation ofbiomechanical factors affecting rowing performance. 1. Biomech. 37, 7, 969-976. Collins, D. 1. and Anderson, R. (2004) The use of a wireless network to provide real-time augmented feedback for on-water rowing. In: Proceedings of the American Society of Biomechanics 28th Annual Conference, Portland, USA, pp. 590-591 . Lamb , D. H. (1989) A kinematic comparison of ergometer and on-water rowing. Am . 1. Sports Med . 17,3,367-373. Loh, 1. M. H., Bull, A. M. 1., McGregor, A. H. and Schroter, R. C. (2004) Instrumentation ofa Concept II rowing ergometer for kinetic and kinematic data acqu isition, In: M. Hubbard, R. D. Mehta and 1. M. Pallis (Eds.), The Engineering o(Sport 5. Volume 2. isea, Sheffield, pp. 173-179 . Page , P. N. and Hawkins, D. A. (2003) A real-time biomechanical feedback system for training rowers. Sports Eng. 6,67-79. Smith, R. M. and Loschner, C. (2002) Biomechanics feedback for rowing. 1. Sport Sci . 20, 783-791. Spinks, W. L. and Smith , R. M. (1994) The effect s ofkinematic information feedback on maximal rowing performance. J. Hum. Mov . Stud . 27, 17-35.

Biomechanical Analysis of Olympic Kayak Athletes During Indoor Paddling Nicola PetroneI , Andrea Isotti' and Guglielmo Guerrini/ I

University of Padova, [email protected] Federation

2 Italian Kayak

Abstract. The aim of the work was the biomechanical analysis of elite female olympic kayak athletes during indoor paddling on ergometers. An integrated motion capture system was used for the acquisition of paddle trajectory, trunk and limbs motion and for the measure of forces developed by the athletes on a dynamometric footpad . Several quantitative biomechanical parameters were correspondently defined. Symmetry and regularity criteria were adopted to define a skill classification for each analysis parameter and a final correlation with sport results classification was investigated. This will help trainers to define suitable functional evaluation methods.

1 Introduction Olympic kayak is a spectacular discipline where technique, fitness and race strategy are essential factors for winning. Different athletes can develop different techniques and usually require specially designed equipment such as paddles and seats to give top performances: on the other side, new shapes or devices required adapted techniques. The work reports the experience developed with the Italian Female National team during the preparation of the past 2004 olympic games. By means of instrumented footpads, seats and paddles the motion patterns and the forces developed by the athletes during laboratory testing were recorded and compared with sport ranking.

2 Materials and Methods 2.1 Instrumentation and Testers The study focused on the measurement of kinematic and kinetic data during indoor paddling sessions performed on a rope paddling ergometer as shown in Fig. l.a . To measure kinematics, a motion analysis system Smart® (BTS - Italy) was used: 6 infrared coaxial cameras working at 50 Hz were placed around the ergometer and a volume of about 4x4x3 rrr' was calibrated. The testers were prepared with adhesive passive markers following the marker protocol presented in Fig. l.b and

414

Nicola Petrone,Andrea Isottiand Guglielmo Guerrini

I .e. In particular, 3 markers were placed on a special wireframe helmet, 3 markers were applied to the ergometer frame and 3 non-aligned markers were placed on the paddle as shown in the detail of Fig. l.b. Bone landmarks markers were symmetrically placed on the limbs with additional markers over C7, T12 vertebrae and the two PSIS (Posterior Superior Iliac Spine). Two rotational potentiometers were applied to the knees with straps, to measure the two flexion angles <j>L and <j>R as shown in Fig. l .b, zeroed with legs extended. The measure of forces applied by the feet was performed by means of a dynamometric footpad developed in a previous work (Petrone, Quaresimin and Spina, 1998) and fixed to the ergometer. Two force components, the forces normal to the footpad at the left (FNL) and right (FNR) foot were measured as shown in Fig. l.a by a synchronous data acquisition system at 200 Hz. Five elite female athletes volounteered for the study . All testers were taking part in the Italian National Team training and had obtained good results at the national level either in single (Kl) or double kayak (K2) . On the basis of recent performance results, the National Team Trainer ranked the testers in descending order. This ranking, antropometric data as well each athlete's best result are noted in Table 1. TESTER I IJ 2 SF 3 RA 4 FA 5 BT

PERSONAL BEST RESULT Olympic Gold Kl 500m National Champion KI 500m National Champion Kl 1000m National Champion K2 5000m National Champion K2 5000m

AGE 30 23 28 24 23

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m fke:]

178 174 172 170 175

74 73 86 65 73

Table. 1. Information about the five athletes involvedin the study.

2.2 Test Protocol Tests were performed on the same day after preparation in sequence of the 5 athletes. Each tester was asked to perform four runs of paced paddling on the ergometer set at constant resistance. The runs were conducted at 70 and 90 strokes per minute (spm) with two different types of seats : a normal fixed seat and a special rotating seat having a free rotational degree of freedom along the vertical axis. For each run at least 50 strokes were recorded. Each athlete was given a 5 minutes recovery period between each test.

2.3 Data Analysis Kinematic and kinetic data were analysed based on several criteria to determine possible correlations between different quantitative biomechanical parameters and the athlete's ranking. This can provide a useful tool to trainers in defining detailed protocols of functional evaluation and monitoring the training state of athletes during preparation. The first analysis criteria was based on the paddle motion.

Biomechanical Analysis of Olympic Kayak Athletes During Indoor Paddling

415

Fig. 1. (a) Experimental setup with indication of measured forces at feet, a detail of the paddle markers and a detail the dynamometric footpad. (b) Stick model of an athlete after a motion capture session, with indication of the global reference system XYZ, the knee flexion angles
416

Nicola Petrone, Andrea Isottiand Guglielmo Guerrini

occurred in the transverse plane Xl and in the frontal plane lY reported in Fig . 2, corresponding respectively to an upper and a posterior view. Ten cycles out of the 50 recorded were consistently extracted from each run and were projected on the cartesian planes. The stroke repeatability, defined as the scatter of the 10 cycles curves, the plot symmetry and the placement of curves centroid were considered as quantitative parameters. Trajectories for testers I and 5 are compared in Fig. 2. The second comparative parameter was the relative angle between shoulder and pelvis, named Ssp. It was defined through the introduction of two reference system s sharing a common vertical axis y' as the angle between the vector defined by the two PSIS at the pelvi s and the vector defined by' the two Acromiom markers at the shoulders. The two triads and the angle Ssp are sketched in Fig . 3.a at the end of a left stroke. This angle Ssp was suppo sed to be preferably low, indicating a more steady motion of the trunk with little rotation of the shoulders about the pelvis. In any case the angle should be symmetric in well balanced athletes with small deviations from an average value . Angles were calculated from the motion captures and positive and negative peaks of 10 significant cycles were compared, as reported in Fig . 3.b, where the four athletes are compared for the 90 spm run with rotat ing seat. Each line connects the two sides average values with Standard Deviation superimposed. The third data analy sis concentrated on the mot ion of the Great Trochanters (GT) in the sagittal plane XV. The motion ~GT of Left and Right GT were linearized between the two extreme points and plotted in the XY plane. The symmetry of the two slopes and the minor amount of elevation in the Y direction of the GT from the seat correlate to a good stroke technique. The fourth analysis focu sed on the range of flexion angles <j>L and <j>R at the two knees as indicated in Fig . I.b. The two paces and two type of seats runs were compared in diagrams such as Fig. 4.a and symmetry between the two legs were studied. Finally, the two normal forces applied to the footpad FNL and FNR were investigated, again plotted as in Fig. 4.b and evaluated in terms of symmetry between the two body sides.

3 Results and Discussion The different analysis criteria supported athlete comparison and the ability to define a relative classification of each tester for each criterion, as summarized in Table 2. The paddle motion analysis as in Fig. 2 showed how the best athletes were able to perform a symmetric, stead y and compact trajectory, whereas the worst tests showed asymmetric cycles with irregularities and open loops in the Xl plane. The analysis of angle Ssp as shown in Fig. 3 revealed how testers I and 4 were able to produce a compact symmetric trunk rotation, whereas testers 3 and 4 revealed a much higher range of rotation and tester's 5 results were strongly asymmetric. Motion analysis of the GT at the two sides exhibited the best result s for tester I, with the highe st symmetry and lowest delta Y, and the worst results for tester 3. On the contrary, tester 3 showed the best knee range of flexion where tester I demonstrated poor symmetry as can be seen in Fig. 4.a.

Biomechanical Analysis of Olympic Kayak Athletes During Indoor Paddling

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418

Nicola Petrone, Andrea lsotti and Guglielmo Guerrini

The footpad force analysis showed the best symmetry for tester 1 and the worst for tester 2. They were the only testers able to increase the forces at increased pace. Tester 2 showed the highest absolute normal forces, even if unbalanced. The presence of a rotating seat generally induced an increase in the knee range of motion and in the footpad forces, with the exception of tester 3 for which the seat resulted to be unsuitable. From the analysis of classification of different testers in Table 2, some biomechanical quantitative parameters like the shoulder-pelvis relative rotation Osp, the GT excursion and the footpad forces symmetry resulted in major interest in defining a functional evaluation protocol for trainers . A regular paddle trajectory should be considered a basic requirement. In general , all athletes, despite their national or international ranking, showed aspects of the paddling technique that may be improved and that were revealed by the present analysis . Further development of this study will focus on the measure of motion of these significant body angles during real sessions of paddling in the kayak. For this, suitable lightweight data acquisition systems and instrumented devices should be developed to better simulate the real boat dynamic behaviour and to give full freedom of motion to the athletes during the trial. TESTER I IJ 2 SF 3 RA 4 FA 5 BT

Paddle 2nd 4 1h 3rd 151 51h

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4 Conclusions The relative range of motion of the shoulder and pelvis of five elite female athletes was investigated, together with the trochanters excurions, the symmetry of the paddling action, the knee range of flexion and the footpad forces . The athletes were ranked based on recent event results . The different kinematic and kinetic parameters were correlated with skill levels and showed how the best athletes were able to perform regular paddle trajectories and steady trunk motion at the different trials .

References Petrone N., Quaresimin M. and Spina S. (1998) A load acquisition device for the paddling action on olympic kayak, II th International Conference on Experimental Mechanics, Oxford-UK, 24-28 August 1998, pp. 817-822.

So you think you know the ropes? White Water Rescue Ropes and Techniques Matt Barker Auckland University of Technology, New Zealand, [email protected] Abstract. Recent equipment failures during simulated white-water rescues have shown the need for detailed measurement of the loads created and the loads that can be safely sustained by the equipment currently in use for white water rescue. This research experimentally finds out; what are the potential forces involved in a white-water rescue? What forces can a threeperson rescue team generate? Which of theropes on themarket aresuitable for thedemands of white-water rescue? Which of the current mechanical advantage rescue techniques are best suited to the equipment available? Are there any experimental techniques that could improve the force generation and safety of the rescue system? Weak points in the complete rescue system are highlighted.

1 Introduction White-water rescue equipment can be made to fail using conventional rescue practices. If failures of this type were to occur in an actual rescue environment, catastrophic results would ensue for both rescuer and rescuee. The current investigation set out to try to answer these questions, 1. Which of the ropes on the market were suitable to the demands of whitewater rescue. 2. Which of the current mechanical advantage rescue techniques are best suited to the equipment available. 3. What force can a 3 man team generate 4. Are there any experimental techniques that could improve the force generation and safety of the rescue system?

2 Methods 2.1 Buoyancy Aid Testing On the Roberts Testing Equipment Serial number 97041 hydraulic test bed at Onehunga Chain and Rigging, the strength of the various components in the rescue harness and auxiliary clip in points of two manufacturers buoyancy aids were tested.

2.2 Rope Testing The following criteria was used to select ropes for the tests, they had to have a density of less than 1 so that they floated (Polypropylene, Polyethylene and Spectra

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fibres have a density of less than I), they had to be betwe en 6 and 8mm in diameter (below 6 mm they are hard to hold and over 8mm it is hard to coil them into useable throw bags ) and the materials used in construction had to be resistant to bacterial decay if left wet for extended per iods. Ropes obta ined were largely manufactured for use in yachting but two ropes are specially manufactured for use in aquatic rescue, PMI Water Rescue and Esprit Swiftwater Line. These ropes were tested on the Roberts Testing Equipment Serial number 97041 hydraul ic test bed at Onehunga Cha in and Rigging, when knotted and in the various 3: I mechani cal advantag e systems.

2.3 Haul System Testing A Tedea Huntleigh model no. 6 19 load cell was placed at the termin al end ofa haul system where the forces generated by a 3 man team with a combin ed mass of 230kg could be measured. The haulers wore normal training shoes and stood on a flat grass surface. The variables applied were, merely pulling the rope with hand s (Armstrong method), 3 to I pulley system , 6 to I pulley system , and 9 to I pulley system. To each of these variables were added, using or not using Petzl Ultralegere pulleys to reduc e frictional losses, and pulling with hands only or attaching slings to the haul line with a marlin spike hitch and wrapping these around the haulers back so they could all pull like a ' tug 0 war' anchorman. A vector pull was also tested where a 2man team tensioned a 3 to I pulley system while the third locked the system off. A sling was clipped to the middle of the system at 90 degre es to the rope line and then all three pulled with their hands on the sling.

3 Results Test

Force at failure

Type of failure

Hydrauli cs chest strap plastic buckle

4. 1kN

Macpac chest strap plastic buckle Hydraulic s chest strap plastic and metal buckle

1.6kN

Webb ing broke Webb ing pulled through buckle Pulled the centr al pin out of alloy buckl e

6.7kN

Macpac che st strap plastic and metal buckle 9.8kN

Stitch ing on buckl e broke

Hydraulic s 2004 cowst ail ring

2kN

Wcld broke

Hydraulics 2005 cowstail ring

II kN

Bent so as to trap webbin g

Macpac 2005 cowstail ring

2kN

Ring brok e

Hydraul ics 2004 cowstail

2.7kN

Webb ing broke

Macpac 2004 cows tail Hydraul ics 2005 Buoyancy aid shoulder strap

6.3kN

Stitchin g broke

4.3kN

Stitching brok e

Hydraulics 2005 Buoyancy aid waist strap

l .5kN

Fastcx buckle broke

Table.I, Buoyancy aid testi ng

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Table I shows the forces at failure for the components of the rescue harness incorporated into white water buoyancy aids as well as auxiliary attachment points that could be used to clip a person to a rope in a rescue. This testing highlighted some surprising mismatches in components and materials. Components of the same system varied in strength from 2kN to 9.8kN. The ring that attaches the cows tail to the chest strap was found to be a weak link in the both manufacturers system, failing at 2kN and the cows tail webbing and buckles used on the chest strap failed at as low as 2.7kN and 1.6kN respectively. Rope Spectralite 8mm Southern light Robline extreme Spectralite6mm Swiftwater line Econobraid 8mm PMI Water rescue 7mm Robline Albatross Econobraid 6mm

Construction Braided Polypropylene sheath, Spectra core Braided Spectra and Polypropylene blend Braided Polypropylene sheath, Spectra core Braided Polypropylene sheath, Spectra core Braided Polyester sheath, Polypropylene core Braided Polypropylene sheath and core Braided Nylon sheath, Polypropylene core Braided Polypropylene Braided Polypropylene sheath andcore

Fig 8 Overhand 15.4kN 11 .6kN 11 .3kN 11 .3kN 9.lkN 8.5kN 7.6kN 7.lkN 7.2kN 6.4kN 5.6kN 4.3kN 2.9kN

Table.2.Terminal knotstrength Table 2 shows the strength of the ropes using Overhand and Figure of Eight knots. The Figure of Eight knot with Donaghys' Spectralite rope and Southern Ocean's Southern light provided the strongest terminal knots failing at 15.4kN and Il.3kN respectively. The ropes specifically manufactured as water rescue ropes, PMI's Water rescue rope and Esprit's Swiftwater line, failed at 7.lkN and 5.6kN respectively. These ropes displayed separate sheath and core failure, probably due to the sheath and core materials not having similar stretch characteristics, therefore not loading across all fibres, leading to progressive failure at relatively low loads. Rope Inline 8 Spectralite8mm 15.3kN Southern light 9.8kN Robline extreme Spectralite 6mm 8.8kN Esprit Swiftwater line 7.lkN Econobraid 8mm 5.3kN 4.2kN PMl Water rescue Robline Albatross 4.3kN

Marlin- Clove spike hitch 13.4kN 13.9kN 1O.7kN 9.lkN 8.5kN 7.2kN 7.lkN 4.4kN 4.lkN

Truckers Tibloc hitch 1O.7kN IO.8kN 8.7kN

Table. 3. 3 to I pulley strength

6.6kN

Tape prussik prussik 9.4kN 2.3kN 5mm

6.3kN 6.8kN

3.5kN

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Table 3 shows the force at failure for the various 3 to 1 pulley systems. The best performing knot used to create the 3 to 1 mechanical advantage system was a Marlinspike hitch (Pawson 2001), although the Inline figure of Eight knot and Clove hitch sometimes were stronger than the Marlinspike hitch, they tightened up to such an extent during loading that they became impossible to untie thus leaving a knot, or knot and karabiner, in the rope rendering it useless as a clean throw or rescue rope later. Prussik knots although widely used and recommended by various authors (Ferrero 1998; Walbridge and Sundmacher 1995; Ray 1997), are in fact quite inadequate to handle the maximum forces able to be applied without slippage. 3 man Force Generation 12-

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Figure 1 shows the force able to be applied by a 3-man rescue team. With the inclusion of small karabiner pulleys, the force able to be applied was increased by 30%. The inclusion of slings in the haul system to allow the haulers to pull with the sling round their backs rather than holding the rope in their hands only, yielded a 12% increase in force. The haulers stated that the limiting factor when just hands were applied was their grip on the rope and that with the sling it was much easier to create a higher force but the limiting factor then became their traction . On the riverbank, there may well be boulders, tree roots or stumps that may allow greater forces to be applied with the sling system. The most significant increase in force was with a vector pull, using no additional equipment the force generated by our 3-man team was increased by 37%. Even more surprising is the fact that the original tensioning was achieved by a 2-man team, as one was locking the system off, so the actual increase from a 2-man 3:1 pulley to 3-man vector pull was 107%, making this a very efficient use of limited resources.

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4 Conclusions The force applied by moving water has an exponential relationship to the speed of flow . However the speed of water is not the only factor that rescuers have to overcome , as there is usually a large component of friction adding to the force required to free an object. Friction has a relationship to pressure and also rises exponentially, but is not calculated here, as friction is dependent on the way objects are trapped and the surface they are held against. The forces created by drag are 12kN for a swamped kayak and over 2kN for a body in water flowing at 5.3 metres per second (Bechdel and Ray 1985; Ray 1997). These figures will increase in faster flows and including variables based on friction, could lead to somewhat larger forces in actual rescues . Thoracic injury is avoided at loads of 4kN and 50% will receive injury of broken ribs on one side when well-distributed loads of 6.9kN are applied to the shoulders and chest, with a maximum survivable force of 8kN (Cavanaugh 2000) . Forces required to damage the vertebrae in adults is between 6 and 8kN (Cassillo 2005) . Given the above, rescue harnesses in buoyancy aids should be manufactured to withstand forces of between 6 and 8kN as a minimum as it is better to rescue someone injured than leave them to drown because the equipment failed at loads as low as 2kN as is presently the case . It is of little use to have some parts of the same rescue system built to take forces of 9.8kN when they are dependent on other components that fail at as low as 2kN. The separate components should be matched in their strength rating and an overall minimum rating should be formulated for these safety items. At present some buoyancy aid rescue harnesses could potentially fail under the forces generated by even simple rescues . Haul systems need to be able to produce loads of over 10kN in order to rescue swamped kayaks in swift water (Bechdel and Ray 1985; Ray 1997). Using prussik knots to form a 3 to 1 pulley system will give you a safety valve allowing slippage before the rope breaks but will ultimately limit the forces able to be applied to any system . It is therefore counter productive to apply a mechanical advantage system greater than 3 to I as the prussik will likely slip at greater loadings particularly when used on slippery (Moyer, Trusting, and Harmston 2000) Spectra sheathed or blended ropes . It is recommended to use a device such as the Petzl Tibloc to create a mechanical advantage haul system where it is necessary to have a traveling attachment point on the main haul line as this produces a stronger and more consistent traveling attachment point. The strongest haul systems were created using Spectra cored Polypropylene sheathed or Polyprop ylene and Spectra mixed braids of 8mm diameter using a Marlinspike hitch and karabiner pulleys wherever the rope ran round a karabiner. Indeed the reduction in friction with the addition of plastic karabiner pulleys added the equivalent of an extra person to a 3-man team making them well worth their 10 gram weight.

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Pulling using slings attached to the main haul line also creates a useful boost to peak force generation and may be even better in places where there is better traction . Ropes for aquatic rescue should be manufactured containing a significant proportion of floating fibres (Spectra, polypropylene and polyethylene). The ropes core and sheath should have similar elongation characteristics, so that the sheath and core share loads and are therefore stronger per cross sectional area than ropes where the core and sheath behave differently. These ropes should be manufactured with a target knotted tensile strength in excess of IOkN in 8mm diameter form, to be aligned with the strength of attachment points on kayaks, the maximal survivable loads through chest harnesses and the likely forces required in rescue of swamped kayaks .

Acknowledgments I would like to thank the following for their help in getting this research from the ideas stage to completion. Institute of Sport and Recreation Research New Zealand (Auckland University of Technology) for grant aid. Hydraulics (New Zealand) for supply of buoyancy aids and materials. Donaghys Ropes (Australia) for supply of ropes . Southern Ocean Ropes (New Zealand) for supply of ropes . Onehunga Chain and Rigging , Auckland, for use of their test bed.

References Bechdel , L. and Ray, S. (1985)Ri ver Rescue. Appalachian Mountain Club Boston Cassillo, F. (2005) Kinesiological and Anatomical approach to the Deadlift. Retrieved 14/1 0/2005 from http ://www.bodybuilding.com/fun/casi4.htm. Cavanaugh, J. (2000) The Biomechanics of thoracic trauma. BME 7160, Winter 2000. Retrieved 14/10/2005 from http ://ttb .eng .wayne.edul-cavanau/uc sdout.html Ferrero, F. (1998) White Water Safety and Rescue. Pesda Press, Wales Hopkins, R. (2003) Knots . Thunder bay Press, San Diego Moyer, T., Trusting,P. and Harmston.C, (2000) Comparative Testing ofHigh Strength Cord. Paper presented at 2000 International Technical Rescue Symposium Pawson, D. (200 I) Pocket guide to knots and splices . PRC publishing, London Ray , S. (1997) Swiftwater rescue. CFS Press , Ashville NC. Walbridge, C. and Sundmacher, W.A. (1995) Whitewater rescue manual . Ragged Mountain Press , Camden ME .

Computational Modelling of Surfboard Fins for Enhanced Performance Dave Carswell, Nicholas Lavery, and Steve Brown University of Wales Swansea, N.P.Lavery @swansea.ac.uk

Abstract. A Comput er Aided Design (CAD) tool called Fin Designer has been developed at the Universit y of Wales, Swansea for three-dimensional design of surfboard fins. This tool has been developed as part of a larger project aiming to facilitate design of fins and surfboards for manufacturers with user-friendly software and direct linking into manufacturing processes such as CNC machines and injection molding. This type of tool also provide s the basis for indepth scientific and engineering studies, using engineering software for stress analysis and Computational Fluid Dynamics (CFD) , giving deeper insights into potential impro vements from design and material modifications. Previous paper s (Lavery , Foster, Carswell and Brown 2005 ; Carswell and Lavery 2006) have dealt with the description of the geometrical models used in the software as well as preliminary computational results made possible by the software . In this paper the emph asis is on the correlation between drag and lift forces for surfboard fins as predicted and measured in a flow tank . Drag and lift forces predicted by the CFD were fed into a specially coded Finite Element Analysis (FEA) to obtain displacements of the fin undergoing these hydrodynamic forces. This paper presents preliminary validation of fluidsolid coupling on the standard benchmark of a cylinder, as well as some results for a single fin. While further verfication of the models are required , the current results appear to suggest that the displacements are of a couple of orders of magnitude smaller than those expected by current fin manufacturers, and hence that fin stiffness remains a strong candidate for fin design improvements.

1 Background A previous paper (Lavery, Foster et al. 2005) presented a detailed background to the current project, with a description of surfboard evolution over the past three decades, and the emphasis currently being placed on fin design as a means of increasing surfboard performance, largely brought about by relatively new attachment systems available which allow faster exchange of the fins to suit changing surfing conditions, but which are also lighter and less intrusive than previous systems . Wherea s higher profile water sports such as sailing, power boat racing and swimming enjoy a measure of engineering and scientific treatment in terms of technical understanding and product development, this is primar ily driven by economics, popularity and possibly their presence in Olympic and internat ional arenas . Over the

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DaveCarswell et al.

past decade , the number of surfers taking to the waters has seen a steady increase, fueled by a media portrayal of the sport as being cool and trendy , and possibly more importantly, its image has been replaced by professional surfers doing an exciting and sometimes dangerous job. The project currently underway at the Swansea University is applying rigorous engineering treatment to surfboard and fin design in the following areas/developments: Computer Aided Design (CAD) software, Computer Aided Engineering (CAE) and Experimental Validation of computational models . To date , and using the methodology described above, the project has addressed issues related to fin design, (Lavery, Foster et al. 2005 ; Carswell and Lavery 2006) , namely , as to whether glass-on fins induce less drag than fins fitted in boxes and whether the use of alternative NACA foils could provide lower drag , hence promoting a faster fin design . The answer to both these questions has been a cautious yes, but further work still needs to be done to assess the extent to which this is true.

2 Computational Modelling The progression to perform a CAE analysis , consisting of a CFD analysis followed by a Finite Element Analysis (FEA) stress analysis, is shown in Fig. I.

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2.1 Computer Aided Design for Surfboards and Fins Two specific CAD packages are being developed based on NURBS surfaces, one for fins (Fin Designer) and the other for surfboards (DAT Designer). Underlying geometrical algorithms are described in (Carswell and Lavery 2006). The data exchange format presently used is the 1GES (Nagel, Braithwaite and Kennicott 1980; Kennicott 1995).

2.2 Computational Fluid Dynamics Analysis CFD analysis is done using the commercial package Fluent, and fin data created in Fin Designer is imported into Gambit (Fluent mesh generator), using the 1GES format, as shown in Fig. 2.

New Computer Aided Design Software of Surfboard Fins for Enhanced Performance

427

Fig. 2. (a) CAD drawing to (b) CAE solid mesh for a typical fin

The fin is then enclosed within a fluid domain having inlet and outlet apertures through which flow is passed over the fin on a flat base to simulate boundary conditions on a surfboard. Four-noded tetrahedral elements are used for both solid and fluid domain. The analysis can be done for various velocities and angles of attack giving pressures on the fin surface and, hence, lift and drag forces. The Reynolds number, Re, is a classical non-dimensional engineering number. For cylinders it is determined, by the diameter, D, by Re = pUD/)1 (1) Where, p is the density, U is the velocity of flow at the inlet and )1 is the viscosity. The pressure coefficient, Cp, is defined by, Cp = (P-Po)! lhpU/ (2) Where, P is the pressure, Uo is the free stream velocity and Po is the static pressure. All these values are obtained from the CFD results.

2.3 Finite Element Analysis for Fin Deformation The deformation analysis uses the Finite Element Virtual Energy approach (Smith and Griffiths 1998) for elastic stress, with pressure derived from the CFD as a surface loading and performing a one-off stress analysis, i.e. assuming a steady state flow. Input options are the Young's Modulus, E, and Poisson's ratio, typical values being in the 10-20GPa and 0.29-0.32 ranges, respectively.

3 Verification of Deformation of a Solid Cylinder in Cross Flow As a benchmark to verify the fluid/structure coupling, models were run for a vertical solid cylinder positioned in a cross-flow and fixed at both ends. Reynolds numbers of 20 and 40 were examined, based on cylinder diameter, with a laminar model. The same mesh was used in both cases and was 150mm high and 4mm in diameter, consisting of 12,000 nodes and 60,000 elements. All measurements of pressure and

428

Dave Carswell et al.

displacement were taken from the middle of the cylinder. Although much greater Reynolds numbers occur to those given here, the test case is still valid as a check on the fluid-structure coupling. Fig. 3 (a) for Re=20 and Fig. 3 (b) for Re=40 show the calculated streamfunction patterns. Cp is plotted around the circumference of the cylinder and compared to previous numerical work by (Benson, Bellamy-Knights, Gerrard and Gladwell 1989) in Fig. 4, and it can be seen to compare relatively well. Benson et al. used a polar mesh for their computations and differs from the one used here as this used Cartesian coordinates. Discrepancies may be due to domain extent, mesh distributions and/or boundary conditions. The resulting deformed circumferences for various Young's moduli are shown in Fig. 5 and appear to be physically reasonable. At the time of writing, no previous experimental work was available to validate the deformation.

(a) Re=20

(b) Re=40 Fig. 3. Streamline patterns at Reynolds numbers of (a) 20 and (b) 40.

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Fig. 4. Pressure distribution Cp around the cylinder for Re=20 and 40.

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4 Validation of Drag, Lift and FEA of Fins An experimental rig has been constructed which used a flume with flow rates up to 1 ms together with load cells to measure drag and lift forces. Surfboard velocities measured by (Walker 1972) and (Paine 1974) are strongly dependent on wave height and can be in excess of 13 ms" . Thus, current full-scale fin experiments would only be valid for a small-wave surfing. 10

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Various fins provided by Daum Tooling Ltd. (RedX) have been tested against angle of attack. Results are presented for the middle Xl fin only. The experimental and numerical results for the drag to lift ratio are given in Fig. 6 (a). The numerical results obtained used a k-e turbulence model with standard wall functions and the Reynolds number based upon the inlet was about 50,000. The mesh contained 47,000 nodes and 220,000 tetrahedral elements with Young 's Modulus being lOGPa and Poisson 's ratio being 0.3. The drag and lift forces predicted by the CFD for fins at higher flow velocities leads to the prediction of very small tip displacements using the linear elastic FE Stress model developed for this work, Fig 6(b). These displacements are smaller than those given by manufacturers by a few orders of magnitude.

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Dave Carswell et al.

5 Conclusions The CAD software being developed at Swansea is providing clean CAD surfaces suitable for engineering analysis in a manner much easier to use than commercial CAD packages . The experimental data for the drag and lift for separate fins appear to follow expected trends . The current CFD results, by taking the average error , are within 10% for pressure and 30% of drag and lift forces of experimental tests and previous CFD work. Model accuracy needs to be improved . The fluid-structure coupling appears to be behaving as expected for low Reynolds numbers tested here but further work needs to be done to verify the correctness of the models and indeed the application to new designs with variable stiffness . This paper represents a first and thorough set of steps in the verification and validation of the models , and certainly preliminary results would suggest that there is a potential to modify stiffness proper ties of fins in ways which could have beneficial effects on drag/lift ratios for the fins.

Acknowledgments The authors would like to thank the other members of the team without whose help none of this would have been possible : Dr Ian Pearce, original developer of DAT98, Dr Adam Sere, for structural analysis and Mr. Graham Foster of JF Design Ltd., who designed the experimental rig. The authors would also like to thank Tom O'Keefe from Daum Tooling Ltd for his invaluable technical insights and sponsorship in the form of the numerous fin samples tested. Finally, the authors would also like to thank the School of Engineering at the University of Wales Swansea for the Research Incentive which has partly funded this work .

References Benson , M. G., P. G. Bellamy-Knights, 1. H. Gerrard and I. Gladwell (1989). "A Viscous Splitting Algorithm appl ied to Low Reynolds Number Flows round a Circular Cylinder." Journal of Fluids and Structures( 3): 439-479 . Carswell , D. and N. Lavery (2006) . 3D Solid Fin Model Construction from 20 Shapes Using Non-Uniform Rational B-Spline Surfaces. Advances in Engineering Software, (Accepted for publication) . Kennicott, P. R. (1995) . The Initial Graphics Exchange Specification (IGES) Version 5.3, IGES/PDES Organisation. Lavery, N., G. Foster, D. Carswell and S. Brown (2005) . "Optimization of Surfboard Fin Design for Minimum Drag by Computational Fluid Dynamics (Do Glass-on fins induce less drag than boxed fins?)." Natural and Artificial Surfing Reefs. Nagel, R., W. Braithwaite and P. Kennicott (1980) . Initial Graphi cs Exchange Specification IGES (Version 1.0). Washington, DC, National Bureau of Standards. Paine, M. (1974) . Hydrodynamics of Surfboards. Mechanical Engineering, University of Sydne y. Bachelor of Science. Smith, I. and D. Griffiths (1998) . Programming The Finite Element Method , Wiley . Walker ,1. (1972) . Recreational Surfing on Hawaiian Reefs. 13th Coastal Engineering Conference, Vancouver.

Development of Swimming Prosthetic for Physically Disabled (Optimal Design for One Side of Above-Elbow Amputation) Keiko Yoneyama and Motomu Nakashima Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, Japan

Abstract. Swimming is a suitable sport for the physically disabled, since the buoyancy provided by the water enables the whole body to be trained through it. However, physical disability may worsen theswimming form and affect body balance. Inthis paper, the effect of upperextremity amputation on the crawl swimming was firstly analyzed by simulation, since crawl is the most common stroke, and its thrust is mainly generated by the upper limb motion. Next, a swimming prosthetic which compensates for the amputated limb was designed using an optimization method. Finally, a swimming prosthetic was manufactured based on theresults of theoptimization, andtheprosthetic' validity was confirmed by a preliminary evaluation.

1 Introduction Swimming is a suitable sport for the physically disabled since the buoyancy provided by the water enables the whole body to be trained through it. However, the physically disabled may not be able to swim using a suitable swimming form, and their body balance may worsen compared to the able-bodied. Especially for people who have recently have been disabled, they may lose their interest in swimming since they may not be able to swim as they used to do. Therefore, a swimming prosthetic is needed which can decrease the influence of the physical disability, but only few prosthetics have developed before (Sawamura 1999, http://www.oandp.com/products/trs/sports-recreation/swimming.asp, and http://www.hanger.com). However, these studies have not clarified the influence of amputation theoretically, and not designed optimally in order to decrease the influence of amputation. The aim of this study is to develop a swimming prosthetic for the physically disabled. In this paper, the case of a one-side, upper-extremity amputation, and front crawl stroke is investigated, since the front crawl stroke is the most common in swimming, and its thrust is mainly generated by the upper extremity motion. In this paper, the influence of upper-extremity amputation on the front crawl swimming stroke is analyzed first. Second, a prosthetic which decreases the influ-

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ence of the amputation is designed by an optimizing calculation. In addition, a prosthetic is manufactured based on the results of the optimization, and the validity is examinedby conducting a preliminaryevaluation.

2 Simulation Analysis of the Influence of Upper-Extremity Amputation on the Front Crawl For the analysis in this chapter, the swimming human simulation model SWUM developed by the authors (Nakashima, Miura, and Sato 2004) is used. In SWUM, the human body is expressed as a rigid body which consists of 21 elliptic cylinders, and the fluid force is calculated by modeling without solving the flow field. Inputting relative motion as the joint angles into SWUM, absolute motion and the fluid force acting on the human body are obtained as outputs. Details of SWUM are available at the web site (http://www.swum.org/). By changing the length of the upper arm, lower arm and hand, three kinds of upper-extremity amputation (Sawamura 1999) are expressed. That is, (I) : hand amputation (hand length 10%), (2): below-elbow amputation (lower arm length 50%), and (3): above-elbow amputation (upper arm length 90%). In each case, only the leftside was changed. These amputationsare shown in Fig. I. Each case is analyzed for 20 cycles in the same swimming form as for ablebodied swimmer. The simulation result of the locus of the human body for 20 cycles is shown in Fig. 2. The X-Y plane expresses water surface, and the Y-axis is the heading of the able-bodied swimmer. In addition, X and Yare normalized by body height. Stroke length L, which means the advanced length in one cycle, and (), which means the angle between the propulsive direction at the present and the previous cycles, are shown in Table 1. Note that the value for the able-bodied swimmer in Table I is a single value, whereas the values for amputations are in ranges. That is, while absolute movement of the able-bodied swimmer converged after 3 cycles, the result for amputations did not converge because of the unbalance caused by the amputation. The results in Fig. 2 and Table I indicate that upper-extremity amputation has a negative effect of swimming speed and direction. Also, the shorter the upperextremity is, the larger the negative effect. Therefore, above-elbow amputation, whose influence on swimming motion is the largest, was decided as the target of the following part of this paper. Shoulder load, for the case of the above-elbow amputation (3), was examined next. The force F acting in the human body's longitudinal axis as a reaction to thrust, and the torque T about the frontal-horizontal axis caused by this force, are considered to be the main components of the load, and are calculated by the simulation. Fig. 3 shows the result of time history for F and T for the 20th cycle. The values in Fig. 3 are normalized by body height, cycle, and water density. The right (non-amputated) side is displayed with a delay of a half-cycle to be in phase with the left. The peak visible in the figure (at 1== 19.4) is a result of the motion used to push the water. It can be seen that this type of amputation worsens the body balance, since the load on the amputated shoulder is extremely lower than normal, whereas the load on the nonamputated shoulder is larger than normal.

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Fig. 3 Time history of the force in the longitudinal axis F and the torque about the frontal-horizontal axis T on shoulder

3 Optimal Design of Swimming Prosthetic 3.1 Optimization Procedure A prosthetic for above-elbow amputation, whose influence on swimming stroke is the largest as calculated in the previous analysis, was designed. A prosthetic which has no moving parts was selected because of ease of water-proofing, cost and ease of use in swimming. In addition, a cylinder-shaped prosthetic was chosen, since it is bilaterally-symmetric around the longitudinal axis of the upper arm. The prosthetic consists of 2 cylindrical units (Unit I: Root, Unit 2: Tip) to give the degrees of freedom to the optimization, and 6 design variables were selected (radius, length and relative density of each unit). Fig. 4 shows how the prosthetic fits an amputee. In this paper, the ' optimal' prosthetic was defined as one which allows the amputee to swim with the swimming form closest to the able-bodied swimmer. In order to realize this, load difference on the shoulders between the amputated and nonamputated sides should be minimized. Based on this definition, the objective function was defined as a next formula:

434

Keiko Yoneyama and Motomu Nakashima

/=(F -F )2 / F 2 + (T -T / T2 r Z r r Z)2 r Where : F : Force in human body's longitudinal axis on shoulder T : Torque about frontal-horizontal axis in steady state on shoulder r : Right (non-amputated) side Z : Left (amputated) side ( )

2

=

(I)

Mean square for one cycle

That is, the objective function/represents the mean square load difference for one cycle between right and left shoulders, divided by the mean square load on the nonamputated shoulder. The optimum prosthetic is one which minimizes this function. The SUBPLEX module of the OPT package in NETLIB (http://www.netlib.org/), which is the non-linear optimization routine, was used for optimization.

3.2 Optimization Results The optimized values of the design variables are shown in Table 2. The optimized profiles of the prosthetic are shown in Fig.5 . After optimization, unit 1 became thicker and shorter, and its relative density became greater than unit 2. I

Fig. 4 Fitting image of prosthetic

Fig. 5 Optimized profile of prosthetic

Table 2 Optimized values of design variables

Radius [mm]

Length [mm]

Relative density

Unit 1

54.2

68.8

1.87

Unit 2

29.5

373

0.099

The history of force in the human body's longitudinal axis F and torque about the frontal-horizontal axis T on the shoulder in steady state after optimization are shown in Fig.6 . Comparing Fig.6 with Fig.3, it can be seen that the load on the shoulder of the amputated side became much greater, and that on the non-amputated side became smaller. That is, the load on the shoulder of both the amputated and non-amputated side became as great as that of the able-bodied model by optimization. Also, the swimming speed improved to 91% of that for the able-bodied model, and the direction stabilized to a level of 3.5 deg curving in 1 cycle . From these re-

Development of Swimming Prosthetic for Physically Disabled

435

suits, it was found that swimming speed and direction were also improved in aiming to match the load on the right and left shoulders.

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(a) F (b) T Fig. 6 Time history of F and T after optimization

4 Manufacture of Swimming Prosthetic Based on Optimal Design and Preliminary Evaluation 4.1 Manufactured Swimming Prosthetic and Experimental Method A prosthetic was manufactured based on the optimal design found in the previous chapter, and the validity of the optimization was examined by conducting a preliminary evaluation, in which several subjects, fitting on the prosthetic, evaluate the effectiveness of the design. In this experiment, since it was difficult to secure enough amputated subjects, a prosthetic for the able-bodied, imitating the above-elbow amputation by flexing the elbow joint, was manufactured . Size and relative density of this prosthetic are shown in Table 3, and a fitting image of the prosthetic is shown in Fig.7. The prosthetic consists of a semi-cylindrical socket, cushion, fixing belt, Unit I, and Unit 2. The size of the socket was chosen to match the diameters of the subjects' upper arm. In addition, a cushion is used to fill an individual difference in diameter of the upper arm. Material of unit I is acrylic, and that of unit 2 is polyethylene resin foam. These materials were selected based on their optimized relative density, and all are rustproof and waterproof. The subjects were five able-bodied healthy males. All of the subjects can swim easily, despite no experience of serious training. There were 4 trials for each subject, that is; trial 0: able-bodied, trial I : imitating an amputee without prosthetic, trial 2: imitating an amputee with an optimized prosthetic, and trial 3: imitating an amputee with an unoptimized prosthetic. The optimized prosthetic used in trial 2 was manufactured based on the results of the optimization. Trial I did not involve any units of prosthetic , and the unoptimized prosthetic of trial 3 consisted only unit 2. In each trial, subjects swam at a self-determined appropriate speed. The evaluation method was questionnaire, evaluated directly after each trial. The evaluation questioned ease of swimming and load on the shoulders, as well as other areas which do not relate to the optimization, for example, the validity of the structure of the socket.

436

Keiko Yoneyama and Motomu Nakashima

4.2 Experimental Results The results of the evaluation for ease of swimming are shown in Fig.8. Scores are normalized so that 100 corresponds to the level trial 0 (able-bodied), and 0 corresponds to the level of trial I (without prosthetic) . Since all evaluations of trial 2 (optimized prosthetic) are higher than those of trial I, the effectiveness of the prosthetic is confirmed. In addition, since four subjects answered that trial 2 was better than trial 3 (unoptimized prosthetic), the validity of the optimization can be also confirmed. Table 3 Size and relative density of prosthetic Length[mm] Diameter[mm] Relative density Unit 1 60.0 50.0 1.23 Unit 2 345 37.5 0.082 10'-.

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Fig. 7 Fitting image of prosthetic

Fig. 8 Evaluation about ease of swimming

5 Conclusions In this paper, the influence of an above-elbow amputation was analyzed using simulation, and a swimming prosthetic which is able to decrease this influence was designed by an optimization. A prosthetic was manufactured based on the optimization, and a preliminary evaluation was performed. Following an analysis of3 kinds of upper-extremity amputation, the influence of above-elbow amputation was found to be the greatest. Then, in the result for the optimal design of a swimming prosthetic (consisting of 2 cylinder units without moving parts), an optimized prosthetic can greatly improve the balance of load on both right and left shoulders. Finally, the effectiveness of a prosthetic and the validity of the optimization were confirmed by a preliminary evaluation . In this study, the prosthetic for the able-bodied was manufactured, because of the difficulty to secure enough amputated subjects . Therefore, in the future, modification based on the result of evaluation by amputee will be expected.

References Nakashima M., Miura Y., and Sato K. (2004) Swimming Human Model "S WUM " to Analyze Dynamical Swimming Problems . The Engineering of Sport 5, vol. I. 594-600 Sawamura S., (1999) Amputation and prosthetic 4th edition. Ishiyaku Publishers, Inc. Tokyo (In Japanese)

Author Index

Ae M., 137 A1am F., 127 Alcantara E., 351 Anderson B.C , 167 Anderson R., 155 Andreopou1os Y., 28 1 Asa i T ., 327 Ashley A., 305 Auer M., 287 Baca A., 407 Barker M., 419 Baurle L., 25 1 Bissuel M., 69 Blackburn K., 2 17 Bourban, P-E ., 263 Brabant, J-D ., 69 Bramley A.N., 63 Bray K., 32 1 Brown S., 425 Carre MJ ., 115, 203, 235 , 313 Carswell D., 425 Caton c., 79 Chong L., 23 Choppin S., 385 Combaz E., 263 Comin M., 351 Cottey R., 391 Cox A., 205 Curtis D., 401 Custer D., 45 Dixon N., 241 Douglas J., 379 Drane PJ., 5 Fauve M., 25 1, 263 , 287 , 299 FederolfP., 287 , 299 Fischer C , 263

Fitzpatrick K., 155 Fleming P., 24 1 Fliege I., 97 Fuss F.K ., 43, 5 1,57 GamezJ., 35 1 Geraldy A., 97 Goodwill S.R., 379 , 385 Gotzhein R., 97 Grund T., 339 Guerrini G., 413 Haake SJ., 115,235,379, 385,401 Harland A., 205, 211 , 357 Hart 1., 401 Heller M., 407 Hintzy F., 85 Hirai N., 275 Hiramatsu V., 333 Holmes C , 211 Honda V., 367 Hopkins 1., 23 Horvais N., 85 Hoshino Y ., 161 HubbardM ., 177, 183 Hytjan A., 305 Igci Y., 281 Iida H., 137 Irwin G., 189, 195 Ison A., 29 Isotti A., 413 Jaitner T., 97 , 103 James D.A., 235 James I., 217 , 229 , 315 Jenk ins M., 79 Jennings-Temple M., 315 Jones R., 2 11, 373 Justham L., 205

438

AuthorIndex

Kaczmarski H., 23 Kagawa H., 35, 293 Kaps P., 269 Kerwin D.G., 175, 189, 195,321 Kimmel W., 183 Kobayashi 0 ., 223, 327 Kobayashi Y., 161 Koch r., 103 Koike S., 137 Komfeind P., 407 Kotze J., 391 Kuhn T., 97 Lammer H., 391 Lavery N., 425 Leaney P., 373 Leeds-Harrison P., 315 Lukes R., 115 Luthi A., 287, 299 Manin L., 69 Manson lA.E., 263 Marcolin G., 345 Martinez A., 351 Mather S., 135 McLeod A., 217 Michaud V., 263 Miller P., 305 Miller S., 365, 379 Mizota T., 149 Mossner M., 269 Mueller M., 121 Murakami M., 223, 275 Nachbauer W., 257, 269 Nakashima M., 431 Naruo T., 149 Nathan A., 3, 23 Niebhur D., 103 Niegl G., 51, 57 Ohgi Y., 275 Ohtsuki A, 333 Oshima S., 333 Pagliarella R.M., 91

Pallis lM., 399 Petrone N., 345,413 Petzing i ., 211 Phillips A., 63 Plummer CJ.G., 263 Prat r., 351 Redfield R., 109 Rhyner H., 251, 263, 287, 299 Richard M., 69 Robazza c., 345 Ronkainen r, 357 Rosa D., 351 Russell D., 11 Sajima T., 143 Sakashita R., 327 Samozino P, 85 Sch iestl M., 269 Schindelwig K., 257 Scott N., 293 Senner V., 121,249,339 Seo K., 223, 275,327 Shaw R.H., 5, 17 Sheets A.L., 177 Sherwood J.A., 5, 17 Shipton P., 229 Shiraki H., 137 Smith L., 29 Strangwood M., 77, 79 Steele c., 373 Stefanyshyn OJ., 167 Subic A., 91,127 Such MJ., 351 Sutela c.. 109 Suzuki S., 161 Takahashi M., 35 Tempia A., 91 Trapp M., 103 Tsunoda M., 143 Vera P., 351 Vickers A., 229 Vogwell J., 63

Author Index Walshe A., 305 Watkins S., 127 Webele.,97 WeberM., 305 Weinbaum S., 281 West A., 205 WheelerM., 305 Wimmer M., 121 Wood G., 217 Wright i.c, 167 WuQ .,281

Yabu M., 143 Yamaguchi T., 143 Yoneyama T., 35, 293,431 Young c, 241 Zable J., 305 Zimgibl W., 391

439

Subject Index accelerometer, 155 aerodynamics atmospheric boundary layer, 149 baseball, 23 cycling, 115 helmets , 127 golf ball, 149 dimple design , 143 magnus force, 223 rugby ball, 223 ski, 269 soccer, 327 spinning ball, 23 water ski jumping, 401 wind tunnel, 127, 149,327 air cannon, 17 ball spin baseball, 23 tennis, 379 baseball, 23 bat, 5, 11,35 durability, 5 holding methods, 35 properties, II , 17 sensation of sting , II softball, 29 biomechanics baseball, 35 cycling, 85, 103 total knee arthoplasty, 121 disability,431 golf, 155 swing, 161, 167 wrist release, 161 gymnastics musculoskeletal work, 195 shoulder compliance, 177 kayak, 413 motion analysis, 413 orthosis development, 431 ski, 257, 293 swimming, 431

tennis elbow, 391 climbing dynamics of speed, 51 equipment anchor, 45 belay, 69 experimentation, 69 fall arrest, 45 holds, 57 instrumentation, 69 modelling, 69 rock, 69 rope forces in a fall, 63 safety, 45, 63 sport climbing, 57 coefficient of restitution, 29 computational fluid dynamic s (CFD) surfboard fins, 425 water ski jumping, 40 I cricket bowling delivery, 205 oblique ball impact on pitch, 235 pitch rolling , 229 safety ,229 cycling aerodynamics, 115, 127 ambient intelligence system , 97 biomechanics, 121 helmets, 127 indoor simulation, 103 mountain bikes rear linkage dynamics, 91 rear shock modelling, 109 non-circular chain rings, 85 physio logical data , 103 racing wheels, 79 rolling resistance , 115 team training , 97, 103 total knee arthoplasty, 121 track cycling , 115 disability, 431

442

Subject Index

drag cycling helmets, 127 soccer ball, 327 water ski jumping, 401 dynamics climbing climbing speed , 51 sport climbing, 57 cycling, 91 gymnastics, 189 mountain bikes, 91 ski, 263 ergometer kayak, 413 rowing, 407 experimentation baseball, 5, 17 climbing, 69 golf, 149 traction testing, 339 field hockey, 241 finite element analysis (FEA) ski, 263 surfboard fins, 425 flow visualisation titanium tetrachloride, 327 football (see also soccer) goal keepers diving envelope, 32 i modelling, 321 penalty kick, 321 pitch playing quality, 315 soil physical conditions, 315 turf, 315 friction, 251, 269, 305

moment, 137 kinetic energy, 167 real-time kinematic data , 155 robot , 161 swing , 161, 167 wrist release , 161 gymnastics balance strategies, 183 dynamics, 189 high bar, 177, 189, 195 musculoskeletal work, 195 shoulder compliance, 177 swing giant, 177 longswing, 189, 195 surface compliance, 183 gyroscope, 155 hydrodynamics, 425 ice friction , 251 ski,251 impact oblique cricket ball on pitch, 235 racket , 373 tennis balls, 367 injuries tennis elbow , 391 instrumentation accelerometer, 155 climbing, 51, 57 golf, 137 gyroscope, 155 kayak, 413 rowing , 407 ski, 257, 293 kayak,413

golf ball aerodynamics, 143 dimple design , 143 trajectory analys is, 149 clubs instrumented grip handle , 137

lawn sport cricket , 205, 229, 235 field hockey, 241 rugby, 211 lift baseball , 23

Subject Index

rugby ball, 223 soccer ball, 327 water ski jumping, 40 I lift mechanics snowboarding, 281 magnus force, 223 materials bicycle wheels structural foams, 79 ski, 251, 263 measurement football, 321 golf,137 mechanical performance artificial turffor soccer, 351 mechanical properties bindings, 287 ski,287 modelling climbing, 69 football, 321 mountain bike rear shock, 109 track cycling, 115 moment of inertia, 17 motion analysis, 23 kayak,413 ski,275 mountain bikes rear linkage dynamics, 91 rear shock modelling, 109 orthosis , 431 rescue ropes, 419 robot, 161 rolling resistance, 115 rowing ergometers, 407 rowing instrumentation, 407 rugby ball launch characteristics, 211 kick,211 kick multi-optimisation, 223 magnus force, 223 safety buoyancy aids, 419

443

climbing, 45, 63 cricket, 229 white water rescue, 419 scanning laser doppler vibrometer (SLDV),357 simulation computational fluid dynamics (CFD), 40 I , 425 cycling, 103 finite element analysis (FEA), 263,425 ski alpine skis, 263, 287 base materials, 251 binding, 287 carving , 299 downhill , 269, 281 friction , 251,269, 305 ice, 251 jumping, 257, 275 leg joint motion , 293 mechanical properties, 287, 299 motion analysis, 275 snow, 269, 305 snowboarding, 281 snow friction, 269, 305 ski, 269, 305 soccer (see also football) artificial turf, 351 ball flow visualisation, 327 modal analysis, 357 non-spinning, 327 spinning, 327 boots, 339 gaze point analysis, 333 instep kick, 345 movement prediction, 333 scanning laser doppler vibrometer (SLDV),357 traction testing, 339 vibration, 357 softball , 29 sport climbing, 57

444

Subject Index

swimming, 431 tennis 3d player testing, 385 active damping technology, 391 ball hollow, 367 spin, 379 wear, 373 racket, 373, 379 tennis elbow, 391 thermal efficiency, 127 trajectory baseball , 23 golf ball, 149 kayak paddle, 413 rugby ball, 211 turf artificial, 351 ground reaction loads, 345 mechanical behaviour of soil, 229 rootzones, 3 15 rubber infill morphology, 351

soil physical conditions, 315 surface traction, 315 synthetic ball interaction, 241 evaluation, 2 I7, 241 wear , 217 vibration scanning laser doppler vibrometer (SLDV),357 soccer, 357 water kayak,413 rowing, 407 ski jumping, 40 I surfing, 425 swimming, 431 white water rescue, 419 water ski jumping, 40 I wear synthetic turf, 217 tennis ball, 373