The dynamics of tennis ball impacts on tennis rackets.

A model of a tennis ball impact on a tennis racket has been developed in this study. An \nexperimental investigation was conducted to detennine the dynamic properties of several different \ntennis balls. The balls were propelled at a piezoelectric force platform and the force acting on the \nball was sampled, along with the ball rebound velocity. A visco-elastic model of this impact was \ndeveloped and a set of model parameters were determined empirically for each ball type. The \nvalues of these parameters were independent of the ball impact velocity. \nThe next stage of the study involved an experimental investigation of a ball impact on a head \nclamped tennis racket. In this experiment, tennis balls were propelled at the geometric string centre \nof a tennis racket. High speed cinematography was used to determine the ball and stringbed \ndeformation during impact, and speed gates were used to measure the ball rebound velocity. A \nvisco-elastic model of this impact was developed. The ball component of this model was identical \nto that for a model of a ball impact on a rigid force platform. The model parameter for the \nstringbed component was obtained from a simple quasi-static compression of the stringbed in \nwhich the applied force and resulting deformation were measured. \nThe final stage of this study involved an investigation of the impact between a tennis ball and a \nfreely supported tennis racket (this support method has been shown to be equivalent to a player \ngripping the tennis racket). In these experiments, the ball, stringbed and racket deformation were \nmeasured during impact, along with the velocity of the ball and racket after impact. A model was \ndeveloped to simulate this impact in which it was assumed that the racket acted as a onedimensional \nflexible beam. \nThe models which have been developed in this study are advancements of those which have been \nused in previously published literature. Experimental data was used to assess the accuracy of the \nresults which were calculated by the models. An excellent correlation was found between the data \ncalculated by the model and that measured experimentally.