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