A continuous analytical shaft model for fast dynamic simulation of the golf swing

Abstract

The intricate physical interaction between the golfer and golf club has driven the development of numerous dynamic golf swing models over the past few decades. Within these golf swing models, the shaft is represented analytically, and simplifications are often made to strike a balance between the demanding computation required for simulating full swings and running optimizations. Despite recent progress in modeling golfer biomechanics, there has been a marked lack of experimental validation surrounding the dynamic behaviour of the analytical shaft models used in golf swing simulations. The purpose of this study was to evaluate the simulated behaviour of an advanced, continuously-parameterized analytical golf shaft model using experimental data collected in constrained mechanical property experiments as well as golf swing motion capture experiments. In the constrained experiments, the model predicted the experimental shaft’s static deflection and bending frequency within a relative error of 1%. In simulations of full swings, the model authentically replicated the unique bending patterns for each of the 20 golfers in the motion capture experiment. The root mean square errors for the shaft droop, lag, and twist angles for all swings ($N=200$) were $1.14^{\circ }$, $0.83^{\circ }$, and $0.85^{\circ }$, respectively, and the clubhead speed at the time of impact was predicted to within $-\,2.9$ to 0.6%. Empowered by symbolic computation, the model is computationally efficient enough for fast simulations of full swings ($<1$ s CPU time) on a desktop computer, thereby enabling golf shaft design optimization.