Biomechanical and modelling analysis of shaft length effects on golf driving performance Ian C. Kenny B.Sc. (Hons) Faculty of Life and Health Sciences of the University of Ulster Thesis Submitted for the Degree of Doctor of Philosophy September 2006 ii Table of Contents ii Table of Contents vii Acknowledgements viii Abstract ix Nomenclature x Declaration xi Research Communications xii List of tables xvi List of figures xxi List of appendices 1 Chapter 1: Introduction 2 1.0 Introduction 2 1.1 Research background 7 1.2 Contribution to research and thesis outline 9 1.3 Aims of the research 10 Chapter 2: Review of literature 11 2.0 Introduction 12 2.1 Effect of equipment on drive performance 13 2.1.1 Shaft 15 2.1.2 Shaft length 21 2.1.3 Swingweight 23 2.1.4 Effect of materials on dynamic performance 25 2.2 Performance measures in golf 26 2.2.1 Handicap 29 2.2.2 Carry & dispersion 30 2.2.3 Clubhead & launch characteristics 31 2.3 Limitations to previous club effect studies 32 2.4 Co-ordination in swing patterns 33 2.4.1 Kinetic chain 37 2.4.2 X-factor 42 2.4.3 Neuromuscular input to consistency 45 2.5 Anthropometrics iii 2.6 Muscle function during the golf swing (Electromyography) 47 2.7 Variations in swing mechanics 50 2.8 Biomechanical modelling & computer simulation 53 2.9 Simulation studies - advantages and limitations 56 2.9.1 Redundancy 58 2.10 Segmental human modelling & application to golf 59 2.10.1 Muscle 64 2.10.2 Bone 65 2.10.3 Anthropometrics and scaling 66 2.11 Optimisation of human movement 68 2.12 Validation of simulated results 72 2.13 Justification of the present study 75 2.14 Summary 77 Chapter 3: Methodological issues 78 3.0 Introduction 79 3.1 Test club features and criteria 79 3.1.1 Physical properties 80 3.1.2 Static testing 81 3.1.3 Club assembly 84 3.1.4 Conclusions 84 3.2 Appropriate selection of launch monitors 85 3.2.1 Data collection 87 3.2.2 Data analysis 88 3.2.3 Correlational analysis 88 3.2.4 Conclusions 89 3.3 Inter-subject variability 89 3.3.1 Methods 91 3.3.2 Data analysis 94 3.3.3 Results 94 3.3.4 Discussion 100 3.3.5 Conclusions 102 3.4 Effect of skin markers on golf driving performance 102 3.4.1 Methods 103 3.4.2 Results 106 iv 3.4.2.1 Launch characteristics 106 3.4.2.2 Temporal data 107 3.4.4 Discussion 107 3.4.5 Conclusions 109 3.5 Summary 109 Chapter 4: Kinematic analysis of the golf swing for low-medium handicapped golfers using drivers of different shaft length 110 4.0 Introduction 111 4.1 Methods 111 4.1.1 Equipment 111 4.1.2 Subjects and test protocols 120 4.1.3 Data collection and processing 120 4.1.4 Variable selection and calculations 122 4.1.5 Data analysis 125 4.2 Results 125 4.2.1 Posture and angular motion 125 4.2.2 Temporal factors 134 4.3 Discussion 136 4.3.1 Effect of club length on positional variation 137 4.3.2 Effect of club length on angular velocity 139 4.3.3 Effect of club length on timing 141 4.4 Summary 143 Chapter 5: Analysis of driving performance and accuracy for shots on performed the range and in the laboratory using clubs of different shaft length 144 5.0 Introduction 145 5.1 Methods 146 5.1.1 Equipment 146 5.1.2 Subjects and test protocols 147 5.1.3 Data collection and processing 149 5.1.4 Variable selection 151 5.1.5 Data analysis 152 5.2 Results 152 5.2.1 Test environment 152 v 5.2.2 Carry and dispersion 155 5.3 Discussion 159 5.3.1 Effect of testing environment on shot performance 159 5.3.2 Effect of shaft length on carry and dispersion 163 5.4 Summary 166 Chapter 6: Analysis of driving performance for elite golfers using drivers of different shaft length 168 6.0 Introduction 169 6.1 Methods 170 6.1.1 Equipment 170 6.1.2 Subjects and test protocols 172 6.1.3 Data collection 172 6.1.4 Variable selection 174 6.1.5 Data analysis 175 6.2 Results 177 6.2.1 Shot performance 177 6.2.2 Launch conditions 182 6.2.3 Shot performance and launch conditions relationship 184 6.3 Discussion 192 6.3.1 Effect of shaft length on shot performance and ball launch characteristics 192 6.4 Summary 198 Chapter 7: Prediction of the effect of shaft length through development and validation of a full-body computer simulation of the golf swing 200 7.0 Introduction 201 7.1 Methods 202 7.1.1 Subjects and experimental tests 203 7.1.2 Experimental data processing 204 7.1.3 Model construction 206 7.1.4 Application of experimental data for inverse and forward 219 dynamics 7.1.5 Variable selection 222 7.1.6 Data analysis 224 7.2 Validation 225 vi 7.2.1 Clubhead velocity 225 7.2.2 Marker kinematics 229 7.2.3 Force output 230 7.3 Results 231 7.3.1 Angular velocity 231 7.3.2 X-factor 235 7.3.3 Timing 235 7.3.4 Muscular force output 237 7.4 Discussion 241 7.4.1 Model validation 242 7.4.2 Effect of driver shaft length on swing kinematics 244 7.4.3 Effect of driver shaft length on swing kinetics 248 7.5 Summary 250 Chapter 8: Summary, conclusions and recommendations for future research 252 8.0 Summary 253 8.1 Conclusions 256 8.2 Recommendations for future work 257 Appendices 260 References 290 vii Acknowledgements I would like to thank my supervisors Dr. Eric Wallace and Dr. Desmond Brown for their support and guidance. My thanks also go out to those who tirelessly helped during testing: Dr. John Brown for his technical assistance, Alex McCloy, and to all the other golfers that gave of their time. Thanks also go to Jim Hubbell and Mary-Jane Rodgers at the USGA Test Centre. For their help during experimentation, testing the clubs and answering numerous questions, thanks go to Dr. Stuart Monk, Dr. Andrew Johnson (and his father), and to Matt and Simon at Birmingham University. Finally, special thanks go to the R&A Rules Ltd. in St. Andrews for funding my research and to Dr. Steve Otto for his continued support and drive for the project. viii Abstract The purpose of this thesis was to determine how shaft length affects golf driving performance. Shaft length effects on the golf swing have been of interest to several researchers (including Egret et al. , 2003; Reyes and Mittendorf, 1999 and Mitzoguchi and Hashiba, 2002). A range of drivers with lengths between 46" and 52", representing lengths close to the 48" limit imposed by the R&A Rules Limited (2004), were assembled and evaluated. A 5-camera three dimensional motion analysis system tracked skin markers attached to 9 low-medium handicapped (5.4 ± 2.8) golfers. Clubhead and ball launch conditions and drive distance and accuracy were determined for 5 low- medium handicapped golfers (5.1 ± 2.0) and 7 elite golfers (0.21 ± 2.41) who performed shots on a purpose-built practice hole. Finally, motion analysis was conducted for an elite golfer (+1 handicap) and experimentally obtained marker data was used to drive a large-scale musculoskeletal model. Low-medium handicapped golfers demonstrated more significant variation in performance due to shaft length than elite golfers. Postural kinematics remained largely unaffected, as were ball spin, launch angle and swing tempo. As shaft length increased from 46" to 52", initial ball velocity (+ 1.90 ms -1, p < 0.05) and ball carry (+ 14 yds, p < 0.001) increased significantly for low-medium handicapped golfers. As shaft length increased from 46" to 50" initial ball velocity (+ 1.79 ms -1, p < 0.01) increased significantly for elite golfers. Ball carry (+ 4.73 yds, p = 0.152) also showed NS increases for elite golfers. Furthermore, as shaft length increased, for all club comparisons there were NS decreases (p = 0.063) in shot accuracy for low-medium handicapped golfers, but no decrease in accuracy for elite golfers. Model simulated results, including posture, timing and predicted muscle force compared well with experimental results (r > 0.98, p < 0.05). Simulations showed that for the range of clubs modelled (46" to 50") hip/shoulder differential angle at the top of the backswing increased significantly (+ 6.13º, p < 0.001) as shaft length increased, and each 2" increase in shaft length required a NS additional 4.5 N force (p = 0.117) to maintain normal swing kinematics. The results from this thesis indicate that modest improvements in shot performance brought about by increasing driver length are the result of increased hip/shoulder differential angle at the top of the backswing and increased predicted muscle force. ix Nomenclature ADD Address CFD Computational fluid dynamics CNS Central nervous system COG Centre of gravity COM Centre of mass COR Coefficient of restitution DOF Degree of freedom GRF Ground reaction force IMP Impact MOCAP Motion capture (data) MRI Magnetic resonance imaging NS Non-significant PGA Professional golfer’s association SSC Stretch shortening cycle TOB Top of backswing USGA United States Golf Association x Declaration “I hereby declare that with effect from the date on which the thesis is deposited in the Library of the University of Ulster, I permit the Librarian of the University to allow the thesis to be copied in whole or in part without reference to me on the understanding that such authority applies to the provision of single copies made for study purposes or for inclusion within the stock of another library.