A Two-Armed Forward Dynamic Model of a Golf Drive: A Simulation and Optimization Tool for Golf Equipment and Biomechanics
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Date
2023-04-27
Authors
Ferguson, Spencer
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Golf club manufacturers and golf’s governing bodies both have clear interests in understanding
how equipment design changes affect the performance of a golfer. Traditionally,
to capture this interaction it was necessary to engage in time-consuming and expensive
experimental testing. With the comprehensive modeling and computing tools available
today, an opportunity exists to develop a forward dynamic model of a golf drive that can
perform much of this testing in a virtual environment using predictive dynamic simulations.
The experimentally-validated novel forward dynamic model developed in this thesis is a
synthesis of four sub-models: a two-armed model of the golfer with 13 individual biomechanical
joints, a continuous analytical flexible shaft model based on a Rayleigh beam
formulation, an adjusted impulse-momentum clubhead-ball impact model, and a golf ball
aerodynamic model. In concert, these sub-models combine to fully simulate a golf drive
from biomechanics to ball flight.
Experimental validation of the model was aided by the completion of a motion capture
experiment in which the biomechanics, club kinematics, and ball launch conditions of ten
elite golfers were quantified using three unique drivers. To validate the shaft model, the
grip kinematics of a training dataset of experimental swings were used to drive an isolated
model of the club while stiffness properties were tuned to minimimize the difference between
simulated and experimental clubhead deflection. The golf ball aerodynamic model was
validated using a set-aside training dataset of launch conditions and ball flights, showing
excellent agreement and marked improvement over previous spin-rate dependent models.
The biomechanical timings of the full model were optimized subject to a cost function
maximizing carry distance while penalizing shots hit sufficiently far offline. Comparing the
optimized swing to the biomechanics of the motion capture study participants showed that
the model successfully reproduces swing traits of elite golfers. Additionally, the resultant
ball speeds of the model closely matched the median of the experimental participants.
Using the validated model, a series of “what-if?” predictive dynamic simulation experiments
were performed. Pertinent findings related to golf’s distance debate included the
positive correlation between both club and tee length and driving distance. The effects of
wind on optimal golf drives were studied showing that golfers can benefit from a different
combination of ideal launch conditions and ball position depending on the presence of a
headwind or tailwind. Finally, with two unique drivers it was shown how club design can
have an effect on the dispersion of mis-hits caused by noise in the biomechanical timings
of the swing.
Description
Keywords
golf, sports engineering, predictive dynamic simulation, forward dynamic model, dynamic modeling, golf swing, golf equipment, golf biomechanics, multi-domain modeling