1. ANALYSIS OF NONCONFORMING COEFFICIENTS OF RESTITUTION IN GOLF DRIVERS USING A FINITE ELEMENT APPROACH Engineering Project Proposal By: Brian Hill Advisor: Ernesto Gutierrez-Miravete Fall 2010

2. What is Coefficient of Restitution? COR is a number between 0 and 1 that represents a percentage of energy transferred during an impact event. Usually expressed a ratio to pre and post impact velocities. COR = V out /V in. COR = 0 is a perfectly inelastic collision. All energy is absorbed at impact. COR = 1 is a perfectly elastic collision. All energy is retained and transferred at impact.

3. COR and Golf In 1998 the United States Golf Association (USGA) limited COR in drivers to 0.830. In 2002, rumors that the USGA would increase the COR limit from 0.830 to 0.860 put the golf world on edge. Club manufacturers began producing thinner faced titanium alloy drivers that would get the club’s COR to 0.860. This was due to the “Trampoline” effect. The face of the driver would deform during impact and return to it’s original geometry after impact. Leaving more energy absorbed and returned to the ball instead of lost (as heat, friction, sound, etc.). USGA later ruled the COR limit to remain at 0.830, and all drivers above that limit were considered nonconforming and illegal in play. Large debate about the use of the nonconforming clubs in both the recreational and professional world.

4. COR and Golf Theoretical limit of COR in golf drivers is about 0.910 – 0.930. Difference in performance for a rigid clubface (.768 COR) vs. one at the COR limit of 0.830 is about 10- 15 yards less at a swing speed of 110 mph. Difference of a clubface at a COR of 0.830 vs. 0.860 is about 5.6 yards less at a swing speed of 100 mph. For slower swing speeds the difference is less. Largely only effects professionals or players with higher swing speeds.

5. The Project Analyze the “trampoline” effect using finite element software packages ANSYS and LS-DYNA. Test various contact simulations with different clubface thicknesses and swing speeds. Use stationary clubface and control velocity of the ball. Used idealize boundary conditions for the clubface and a ball calibrated to a COR of 0.830. Plot comparative charts that show the relationship of face thicknesses on COR at different speeds.

6. References: K. Tanaka et al., Construction of the finite-element models of golf balls and simulations of their collisions, Proc. of the Institution of Mechanical Engineers, Part L: J of Materials: Design and Applications 220 (1) (2006), pp. 13–22. A.W. Pugh et al., Characterization of the materials in golf ball construction for use in finite element analysis, Procedia Engineering, Volume 2, Issue 2, The Engineering of Sport 8 - Engineering Emotion, June 2010, Pages 3231-3236 K. Tanaka et al., Experimental and finite element analyses of a golf ball colliding with a simplified club during a two-dimensional swing, Procedia Engineering, Volume 2, Issue 2, The Engineering of Sport 8 - Engineering Emotion, June 2010, Pages 3249- 3254 www.fanklygolf.com, September 21, 2010. GOLF CHANNEL Newsroom. “USGA, R&A Rule on 'Spring-Like' Effect.” thegolfchannel. August 6, 2002. September 21, 2010 “What is C.O.R.? What is CT?” wishongolf. September 21, 2010 “Conflicts surrounding the Callaway ERC driver.” golftoday. September 21, 2010 “Coefficient of restitution.” wikipedia. September 21, 2010 Kelley, Brent. “Clubhead Speed.” about. September 26, 2010