Optimization of the clubface shape of a golf driver to minimize dispersion of off-center shots
The objective was tu optimize the post-impact conditions of a golf driver and golf ball in order to minimize dispersion of a drive for off-center hits. When a golf ball is struct by a clubhead at a point away from the "sweetspot" on the clubface, spin is induced on the ball which makes it curve during flight. Over the years, clubmakers have made the clubface slightly convex in shape in order make off-center hits land as close to the fairway as possible. A general, three-dimensional impact model using principles of momentum conservation on rigid bodies was used to extract the spin and velocity vectors of the ball after impact. An aerodynamic-model including drag, lift and skin friction was then used to obtain the landing position of the ball. An optimization routine was used to calculate the optimum clubface shape to minimize golf ball dispersion from the middle of the fairway, for off-center hits. In order to have an accurate simulation of impact on a computer, the mass and inertia tensor of the clubhead was experimentally measured. The clubface shape relative to the center of gravity of the clubhead was also measured. The impact computer program and golf ball trajectory computer programs were verified by using the golfing robot "Iron Byron" to hit various shots on the clubface of a particular driver. The computer simulation yielded results of ball landing positions from the middle of the fairway that fell within the standard deviations of those experimentally measured. The optimization routine was used to find the optimum clubface shape to minimize golf ball dispersion for off-center hits, for a particular driver swung at a certain initial velocity in a certain direction. The clubface shape was modeled in the impact program as an ellipsoid. After running the optimization program, the average dispersion from the middle of the fairway for the worst possible off-center hit locations was reduced on the average from 8.075 to 2.198 yards. The optimization program demonstrated its effectiveness in determining the optimum clubface to minimize dispersion of off-center hits.
Computers and Structures
Winfield, D., & Tan, T. (1996). Optimization of the clubface shape of a golf driver to minimize dispersion of off-center shots. Computers and Structures, 58 (6), 1217-1224. https://doi.org/10.1016/0045-7949(95)00220-0