APPARENT COEFFICIENT OF RESTITUTION SURFACE OF A PADDLE RACKET

  • Aldo J. Viollaz
  • Aluísio O.V. Avila
  • José C. Pio da Fanseca
  • Aldo J. Viollaz
Keywords: paddle racket, restitution paraboloid, dynamics

Abstract

The aim of this study is to determine the theoretical apparent coefficient of restitution (ACOR) for impacts on a paddle racket free and at rest under shooting normal to its surface. The surface representing the ACOR is determined from the laws of the mechanics. Assuming that the (absolute) coefficient of restitution (COR) is constant, this surface is a ratio of two quadratic functions, which in turn can be approximated quite well by a quadric (elliptic paraboloid). Excepted the intercept all the coefficients of this elliptic paraboloid are only function of the physical parameters of the rackets and the ball mass. This relations allows us to calculate the restitution surface without need of costly experimentation, it is only needed to know the masses of the racket and the ball, the two principals inertia moments of the racket and the restitution coefficient at some point. Laboratory experiments were carry out using several paddle rackets by mean of a set up to measure the speed of the ball, with Peak Performance motion analysis system, based on 180 Hz video cameras and a software for automatic tracking. The ball trajectory was reconstructed in 3-D using two synchronized cameras, calculating this way the average velocity of the ball before and after the contact with the racket, and the ACOR as the quotient of this two velocities. A third camera was used to locate the impact point. The measurements were taken using two preimpact ball velocity (17 and 30 m/s) and two type of grip support: free and held by a player arm. The experimental data where adjusted by the mean square method, and show a very good fit to the theoretic surface, and also to the approximating elliptic paraboloid, been the average error of the fit equal to 0,01.