A computer simulation model of tennis racket/ball impacts

• DOI: 10.1007/s12283-010-0056-x
• Publication Date: 2010-12-15T15:12:15Z
• Authors: Jonathan A. Glynn; Mark A. King; Sean R. Mitchell
• Keywords: Racket; Ball (mathematics); Tennis ball; Coefficient of restitution

A forward dynamics computer simulation for replicating tennis racket/ball impacts is described consisting of two rigid segments coupled with two degrees of rotational freedom for the racket frame, nine equally spaced point masses connected by 24 visco-elastic springs for the string-bed and a point mass visco-elastic ball model. The first and second modal responses both in and perpendicular to the racket string-bed plane have been reproduced for two contrasting racket frames, each strung at a high and a low tension. Ball/string-bed normal impact simulations of real impacts at nine locations on each string-bed and six different initial ball velocities resulted in <3% RMS error in rebound velocity (over the 16–27 m/s range observed). The RMS difference between simulated and measured oblique impact rebound angles across nine impact locations was 1°. Thus, careful measurement of ball and racket characteristics to configure the model parameters enables researchers to accurately introduce ball impact at different locations and subsequent modal response of the tennis racket to rigid body simulations of tennis strokes without punitive computational cost.