On The Coefficient Of Restitution Of Tennis Rackets

Abstract

The evolution of research on tennis equipment has recently introduced some parameters for the evaluation of the racket's efficiency. Among them, the most used in current practice is the coefficient of restitution of the racket (COR), that is simply defined as "the ratio of the rebound speed to the incident speed of the ball for orthogonal impact". Remarkable differences between values of COR reported in the tennis literature are mainly due to the various test conditions adopted. In order to compare different results, some important test parameters must be imposed for a better COR definition. Our recent laboratory tests show that the COR of the same racket is mainly affected by: - kind and conditions of balls kind and tension of strings impact velocity. Moreover, they show that the largest portion of energy is lost because of ball's deformation. Figure 1 shows the coefficient of restitution of a ball, at different impact velocities and on a rigid wall. Furthermore, in a tennis shot, ball deformation for a given velocity is affected by the other test parameters listed above. The augments of string's tension, for instance, increases the ball deformation and consequently decreases COR. This highlights that the traditional coefficient of restitution is not a direct measure of the racket frame efficiency, but it involves the behaviour of ball, strings, frame and grip restraint together. Therefore, in order to be compared by means of COR, rackets must be tested with the same kind of balls and the same kind of strings at equivalent string tension (i.e. tension that gives the same stiffness to the string plane). We suggest to test the racket at four different ball velocities in order to analyse different play conditions; thus we propose a new COR which should contain four values. Moreover, the knowledge of the influence of balls and strings allows to evaluate the portion of COR that is related only to the racket's frame characteristics.