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 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 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

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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

~

•

•

•

•

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•

~ 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 .

7.3 kN 23 62 1m 15 m 6 43 m 1 5m 07 m 0.12

H,

80

Fig. 1. Fall configuration parameters, fall towerand virtual hand

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 :

PI

Ii

(1)

Fmax_hand

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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The brake coefficient is related to the magnitude of the impact force at the last runner, they increase together. On the contrary, a high brake coefficient corresponds

RockClimbing Belaying Device Analysis, Experiments and Modeling

73

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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Fig. 3. Braking coefficients evolution during a fall arrest

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.

a

g - ,. ---APM~:;;:::;;;:::::::----I

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Fig. 4. Simulation results compared to measurements for Figure 8 and Reverso Brakes

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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--•

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-

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·"3

'.

··_------ 1

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(a)

Fig. 1. Thermal profiles for (a) single-sided and (b) dual-sided heating. Table 1. Mean sample and pore dimensions for modified PMI 51IG (1465 Pa). Temperature Time (min) I 185 (I) 185 (I) 2 190 (I) I 230 (I) 2 240 (I) 2 200 (sm) I 240 (sm) I

Height (mm) 8.4 8.2 7.5 7.2 7.1 7.1 8.1

Width Length No. (mm) (mm) pores 130.6 278.5 130.5 275.0 136.0 285.6 127.6 269.5 111.5 240.0 40.1 39.8 41.08 41.01

of Mean

area

(mrrr')

10 5 7 16

5

80.2 70.6 34.4 3.6 1.7

Fig. 2. Central pores after dual-sided heating of PMI 51IG foam (185 °C / I min. / 1465 Pa).

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 .

(a)

(b)

Fig. 5. SEM imaging of shear failure surface of (a) a pore; and (b) an untreated core.

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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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

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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

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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

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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

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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.

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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

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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.

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

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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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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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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-

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Simula tor

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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Thomas Jaitner, Marcus Trapp, Dirk Niebuhr, Jan Koch

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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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

Mountain BikeRearShock Modeling, Testing, and Evaluation

III

maximum pressure that can be generated in chamber 2 during the compression stroke. Sea l head

Piston

Dam per body

Air

Shock body

During compression, PA increases as VA is reduced, oil flows into the piston through the cc valve (Qee flows right to left). Qre also flows left as oil moves out of the piston through the parallel flow paths of the low speed compression port and the high speed relief valve (if the maximum pressure is reached in the piston chamber) . VI increases as V2 and VN2 decrease. The pressurized nitrogen chamber is designed to prevent a vacuum from developing in Chamber 2 (and I), but the model does allow a vacuum to develop in chamber I under high compression speeds. During the rebound stroke, the motion of the damper body over the piston is reversed, and the speed is controlled by the oil flow rate through the rebound port (Qre now flows to the right which is defined as positive). The rebound force is proportional to the square of Qre' Fig. 2a shows the calculated rebound, and low and high speed compression flow rates (Qre) through the piston resulting from various values of PI - Pp• Rebound flows are positive, while low & high speed compression flows are negative. Fig 2b shows the calculated value of Qee for various pressure differences . This is flow through the compression initiation control valve. In this case a Pp - P z of -4 atm. is required before the cc valves opens, allowing significant relative motion between the damper body and the piston. The important dynamic effects of the shock are captured by a bond graph model (Kamopp et. al., 2006), depicted in Fig. 3. The primary model input (flow source) is the relative velocity of the ends of the shock. C elements represent energy storage due to fluid compression, and R elements describe dissipation losses due to fluid flow through the various orifices. The energetic elements of the model are described clockwise from the flow source (Sf) . Energy is: stored in the air chamber, stored as pressurized oil in chamber I, dissipated due to compression and rebound oil flow, dissipated through the cc valve, and stored in the nitrogen chamber. cc spring represents the stiffness (kee) of the cc valve spring. A "top-out" spring cushions full rebound but is not engaged in the testing protocol of this paper. The rest of the structure of this bond graph captures the kinetics, and kinematics of the shock.

112

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100

'"'e

100

l/)

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0

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u - 50 , -100 ~ -150 a - 200

I

- 10 -5 0 PI -P ,

5

m

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U -100 u 0 -15 0

o

-6

a m

2

Fig. 2. Qrc and Qcc versus pressure drop

,------, ' R ' l .(lmp reb 1-------: \ :: flowd C ::

'1

I.

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:

c mpliance i

. :1

: \ \1', :

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:

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"

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,

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1- - - - - - 1 '("'"

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Fig. 3. Rear shock bond graph

A coupled set of nonlinear differential equations was derived from the bond graph in accordance with Kamopp et al. (2006) . These were simultaneously solved using the commercial computational package Mathematica to calculate the force experienced at the ends of the shock as a result of a prescribed input velocity profile .

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

Mountain Bike Rear Shock Modeling, Testing, and Evaluation

113

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.

- 4 00

f.=C==:::r--=

-600 Z Q)

o

- 8 00

~--,...-=j-~~J--j-

- 10 00

1-1 - 1 2 0 0

o

~ -1400

- 1 6 00 rr=--~~~~~L~-=~J - 75 - 50 - 2 5 0 25 50 75

Velocity, mm /s Fig. 4. Applied shockforce versus relative velocity The shape of the output curve can be manipulated by changing model parameters which relate to physical design parameters within the shock: The peak to peak range of forces at zero velocity was adjusted by modifying the initial pressure and volume in the N2 chamber; the aspect and skew of the graph were adjusted by changing the product of damping orifice discharge coefficient and area (i.e. CDA for the orifices in the piston rc valve), and the curve offset near zero velocity was adjusted by modifying the initiation pressure for cc valve actuation . In Fig. 4 the test data is the dotted line and the tuned model prediction is the lighter of the thick curves. TDC and BDC are the top and bottom of the compression stroke. The compression portion of the prediction curve fits the data better than rebound . Tested rebound magnitudes are lower than predicted during the first half of the rebound stroke. The thin, solid curve demonstrates halving the compression initiation pressure. A lower initiation pressure allows compression flow sooner and thus the compression side of the curve is offset upward and less than the tuned curve. Rebound is not affected by this change. The thick and darkest curve is for a 20% decrease in rebound orifice CdA value. Rebound forces are higher for all rebound but more so as velocity increases . After tuning the model at 1Hz, it was applied to the 5Hz case as shown in Fig. 5. The dotted curve is still the test data. There is good agreement between the test data

114

Robin Redfieldand Cory Sutela

and the model in this case with the most notable discrepancy occurring at the compression initiation transitions near zero shock velocity.

z

2000

..-----.---~---,--~.-.--~

1 000

I----+----+----f--,y~

O t--- - -+- - - t-----79-+----;

Q)

o

g - 1 0 0 0 1----b_=--+--:7"!:...--t---~ ~

...... - 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.

116

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

118

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.

120

Richard Lukes, Matt Carre and Stephen Haake

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)

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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 .

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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.

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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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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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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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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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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

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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

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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-

190

David Kewin and Gareth Irwin

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.

Predicting High Bar Forces intheLongswing

191

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.

90 StAill Ofl.ugt . • ,. hmrse Dytwcics

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Ftg.I Force profiles (N) for one longswing (gymnast C) with personal ized inertia data .

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

Predicting High Bar Forces in the Longswing

193

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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David Kewin and Gareth Irwin

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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Gareth Irwin and David G Kewin

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

Musculoskeletal Workin the Longswing on HighBar

197

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

2

E

2

2

(1)

2

bar

IFy_ + __ IFz_2 = __ 2 Ky

2

x,

3

Egymnast =

L fMP i =!

i .

dt

(2) (3)

198

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 .,

lh

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90

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270

360

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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

199

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21 19 z- 17

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o

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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

206

Laura Justhamet.a!'

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-

Quantification of the Cricket Bowling Delivery

207

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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For all treatments, PR reduced significantly after 7 days of wear, compared to the control (p

c + otan¢>

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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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Cohesio n (c). kNm" 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) / =

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(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:

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(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.

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(13)

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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) (

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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: (/)( =

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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

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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

242

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.

244

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

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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

246

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

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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.

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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.

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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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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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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-

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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.,--

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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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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 (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

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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 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', 0 = 0.6, d = 0.42 g mm) and fresh snow (Ko = 1.7xlO- m2, 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

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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

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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

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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

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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.

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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

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296

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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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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

384

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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:

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388

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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).

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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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Robert Couey et al

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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Robert Cottey et al

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-

An Extended Study Investigating the Effects of TennisRackets with Active Damping

395

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.

396

Robert Cottey et al

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

400

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

402

John Hart, DavidCurtis, and Stephen Haake

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

Computational Fluid Dynamic Analysis ofa Water Ski Jumper

403

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

s

Vx

V\ ·

X

Y

(m/s)

(m/s)

(m)

(m)

54.10

15.50

29.0\

11.72

0.00

1.80

79.70

38.50

35.65

28.22

7.3\

\2 .87

6.08

28.40

79.70

30 .80

55.80

27.24

1.9\

28 .11

8.62

22.90

74.60

23.40

55.80

26.67

-1.28

36.86

8.72

19.20

64 .20

19.10

55.80

25.87

-5.69

48 .67

7.15

1.98

13.20

62.00

10.30

24.00

25.52

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5.82

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25 .80

95 .00

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Time (s)

a

p

r

1

0.00

29.40

85.10

2 3

0.45

37.80

1.00

4

1.33

5

1.78

6 7

Table. 1 Modeledjump conditions

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

405

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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Fig. 4 % Contribution to lift and drag at eachjump stage Fig. 4. shows the contribution to lift and drag of the skis and jumper at each jump stage . It was found that over the entire jump the skis account for 68 % of the lift generated, with the Stokes tips accounting for 50 % of this force. The body of the ski jumper generates an average of 31 % of total lift, clearly demonstrating the importance of the ski jumpers posture . As would be expected regions of high pressure were observed to form on all leading surfaces of the ski jumper. Regions of high pressure were also observed to form on the inside edge of the ski, and the underside of the Stokes tips. This was due to the inclined attack angle of the ski, causing the tips to strike the atmosphere

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-

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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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