Modelling of tennis ball impacts on a rigid surface

Abstract

A viscoelastic model of a tennis ball impact at normal incidence on a rigid surface is presented in this study. The ball model has three discrete elements that account for the structural stiffness, material damping and momentum flux loading. Experiments using a force platform are performed to determine the force that acts on the ball during impact, for a range of ball inbound velocities. The inbound and rebound velocities of the ball are measured using speed gates. The contact time and coefficient of restitution for the impact are also determined in these experiments. The model parameters are determined such that the values of the coefficient of restitution and contact time that are calculated by the model are consistent with those values determined experimentally. The model can be used to calculate the force that acts on the ball during impact. Generally, the force-time plots calculated by the model were consistent with those determined experimentally. Furthermore, the model can be used to calculate the three components of the force that acts on the ball during impact. It is shown that the main component of the force during the first 0.6 ms of impact is that due to momentum flux loading. This is approximately equal in magnitude for each ball type and explains why the total force acting on each ball is very similar during this period.