«A Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Approved June 2014 by the Graduate ...»
The Relationship of Club Handle Twist Velocity
to Selected Biomechanical Characteristics of the Golf Drive
A Dissertation Presented in Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
Approved June 2014 by the
Graduate Supervisory Committee:
Richard Hinrichs, Chair
ARIZONA STATE UNIVERSITY
I would like to thank Dr. Rick Hinrichs for his guidance and many years of patience through this lengthy process, helping me bring it to its final culmination. Thanks to my committee members Dr. Shannon Ringenbach, Dr. Debbie Crews and Dr. Natalia Dounskaia for their help in clarifying my direction and providing their time while working with me to get it right. Thanks to Penny Pandelisev for helping me navigate the administrative procedures along the way and for making sure I had the right forms filled out in a timely fashion. I express my gratitude to Kelly Skinner and Finbarr Kirwan of the United States Olympic Committee for their support and for allowing me to set my PhD as a professional goal and allot time towards its completion. Thanks to Dr. Greg Rose and Dave Phillips for their knowledge in co-developing the TPI 3D biomechanical analysis with me, plus their support in allowing me to include data from swings that were captured at the Titleist Performance Institute. Also my appreciation to Dr. Paul Wood and Dr. Erik Henrikson for stepping in at the last minute with helpful data on club and shaft dynamics.
My thanks to my brother, Steve Cheetham for his stewardship of AMM, keeping it on track these many years and helping me develop the AMM3D system from the beginning, with his always constructive comments. Thanks to Dr. Mary Thomas, notice I wrote “Doctor”, you may have gotten there first but I am not far behind, so thanks for the enthusiasm and encouragement from you and Dan in these last few months.
Finally, a special dedication to my wife Bridget and my daughters Mandy, Katie and Jenny for your love, support and patience over all these years and for being the reason that I strive to achieve my goals. Mandy, I started this PhD before you were born and now you are a senior at college yourself. I love you girls. This is for you. It took a long time but I finally did it!
LIST OF TABLES
LIST OF FIGURES
LIST OF SYMBOLS / NOMENCLATURE
CHAPTER1 GENERAL INTRODUCTION
2 GENERAL METHODS..............
3 STUDY 1 - CLUBHEAD SPEED AND DRIVING ACCURACY
4 STUDY 2 - WRIST AND FOREARM ANGULAR VELOCITIES
5 STUDY 3 - PELVIS AND THORAX ANGLES
6 GENERAL CONCLUSION...........
APPENDIXA A DETERMINISTIC MODEL OF THE FULL SWING IN GOLF
B LITERATURE REVIEW
Table 1 Categorization Method for Strength of Correlation Levels.………................…….…… 15 Table 2 Descriptive Statistics for Handle Twist Velocities...………………………..............…… 20 Table 3 Means and Standard Deviations for Clubhead Speed and Driving Accuracy.............. 21 Table 4 Correlation Statistics for HTV with Clubhead Speed and Driving Accuracy.……........ 21 Table 5 Single Factor ANOVA Results for Clubhead Speed and Driving Accuracy.………….. 23 Table 6 Correlation Statistics for HTV with Lead Forearm Supination Velocity at Impact....... 37 Table 7 Single Factor ANOVA Results for Forearm, Wrist and Elbow Angular Velocities….. 38 Table 8 Correlation Statistics for Pelvis and Thorax Angles………...…………………………… 44 Table 9 Single Factor ANOVA Results for Pelvis and Thorax Angles at Impact………………. 47 Table 10 Pelvis and Thorax Rotation Values at Impact from Several Studies……………….…..50 Table 11 Arm Rolling and Shaft Twisting Terminologies of Different Investigators………..…… 75
Figure 1. Deterministic Model from Ball Displacement at Landing to Club Handle.
...………..… 1 Figure 2. The AMM3D Golf Full Body Motion Analysis System...………………………………… 8 Figure 3. Digitizing the Body Segments to Create Anatomical Reference Frames……......…... 9 Figure 4. The TPI 3D Full Body Avatar of a Golfer.……....………………………………………… 9 Figure 5. Immediately after Impact a Rapid Drop in Clubhead Speed is Evident….……………. 10 Figure 6. Deterministic Model of Clubhead Closing Velocity and its Sub-Factors..…………..… 11 Figure 7. Handle Twist Velocity against Clubhead Closing Velocity………....………………..…. 12 Figure 8. Relationship between Swing Plane, Handle Twist and Clubhead Closing Velocities.. 13 Figure 9. Rigid Body Clubhead Speed against Actual Clubhead Speed
Figure 10. Scatter Plot of Clubhead Speed and HTV (n=94)
Figure 11. Scatter Plot of Driving Accuracy and HTV (n=70)
Figure 12. Definition of Lead Wrist Set Angle
Figure 13. Lead Wrist Set Angle and the Golfer’s Position at Release
Figure 14. Lead Forearm and Wrist Angle Components and the Golfer’s Position at Release.
.. 31 Figure 15. Lead Wrist Release Velocity in the Downswing
Figure 16. Lead Forearm and Wrist Release Angular Velocity Components in the Downswing.
. 32 Figure 17. Club Handle Twist Velocity during the Downswing and the Twist Release Point....... 33 Figure 18. Scatter Plot of Lead Forearm Supination Velocity against Handle Twist Velocity...... 37 Figure 19. Scatter Plot of Thorax Rotation against Handle Twist Velocity at Impact
Figure 20. Scatter Plot of Thorax Side Bend against Handle Twist Velocity at Impact.
............... 45 Figure 21. Scatter Plot of Pelvis Rotation against Handle Twist Velocity at Impact
Figure 22. Scatter Plot of Pelvis Rotation against Handle Twist Velocity at Impact
Figure 23. Low and High Handle Twist Velocity Golfers shown at Impact
Figure 24. Deterministic Model of the Golf Swing with a Driver
Figure 25. Relationship between Swing Plane, Handle Twist and Clubhead Closing Velocities.
To get a complete picture of the theoretical relationships between the various mechanical factors in the golf swing that contribute to the required result, it is helpful to use a process called deterministic modeling. This process was developed by Dr. James Hay (Hay & Reid, 1988).
Deterministic modeling uses a top-down, block-style, flow chart to completely map out the mechanical parameters that determine the result of the performance of a motor skill. The mechanical parameters are shown as factors and sub-factors in the diagram. Figure 1 shows a section of a model for the golf swing, from ball displacement at landing, down to the club shaft and handle contributions. The complete model is presented in Appendix A.
Figure 1. Deterministic Model from Ball Displacement at Landing to Club Handle The goal of the drive is to propel the ball as far as possible in the required direction.
An important result is the ball displacement at landing. This becomes the top level of this section of the model. Note though that here we are only looking at carry and are ignoring bounce and run, however Appendix A shows the complete model. Having defined the key factor we now break it down into the sub-factors by which it is directly determined. Acceleration due to gravity will directly affect the flight, as will air resistance. Air resistance has two major portions drag and lift.
The displacement at landing will also be affected by the relative height of the ball at launch, that is, how high the tee-off point was relative to the landing point. Ball velocity at launch will also directly affect the carry because it includes the initial speed of the ball and its initial direction of flight. The ball velocity will interact with air resistance to affect drag and lift, as will the ball characteristics such as size and shape. At this level we also see ball spin which affects the lift of the ball. Launch is defined as the moment the ball leaves the club face. At the next level down, both ball velocity and spin are affected by the clubhead velocity and position at impact, plus the ball and clubhead characteristics such as coefficient of restitution, friction and mass. It is also important to include that the ball is initially stationary. Clubhead velocity at impact includes its speed and direction. Direction is the direction the club is traveling at impact, which can be partitioned into path, its horizontal direction at launch and attack angle, its vertical direction at launch. Clubhead position at impact includes the relative position of the clubhead and the ball.
The parameters making up position at impact are dynamic loft, which is the number of degrees that the face is pointing up or down, face angle, which is the number of degrees that the face is pointing left or right, and contact point, which is where the ball contacts the club on the face and how far that is from the center of percussion. Continuing to the next sub-factors, the velocity and position of the clubhead at impact are determined by its linear and angular components. The linear velocity of a point in the middle of the clubface has x, y, and z component velocities, but of more interest to our discussion is the angular velocity of the club face which is composed of its velocity in the swing plane, that is, its angular velocity around a normal to the swing plane, and the velocity with which it is closing with respect to the ball, this is its angular velocity around a line vertical to the club face but local to the clubhead and moving with it during the swing. There may also be angular motion in and out of the plane of the swing, but near the impact area this is very small because here the motion is primarily planar (Kwon, Como, Singhal, Lee, & Han, 2012).
Now we step to the bottom level of the model. We will concentrate on the angular components because they are of importance to this research. Both clubhead swing plane velocity and closing velocity are affected by club handle twist velocity, club handle swing plane velocity, the inertial characteristics of the clubhead and shaft (moment of inertia, mass, etc.), and the shaft flexibility.
With this outline as a basis, Study 1 focused on clubhead speed, driving accuracy, and handle twist velocity. More detail in wrist/forearm actions and body posture were investigated in Studies 2 and 3.
If we look at what physically happens during the downswing of a high speed swing, we find that the body undergoes strenuous motion that includes both rotation and translation. The pelvis moves toward the target during the downswing, while the thorax initially moves toward the target but then, just before impact, moves away from the target (Rose & Cheetham, 2006). Also during the downswing the pelvis and thorax rotate rapidly, first accelerating early in the downswing, then decelerating just before impact, in a sequential manner (Cheetham et al., 2008).