# THEOREI'ICAL MODEL AND EXPERIMENTAL TESTS FOR TENNIS IMPACT DYNAMICS

• F. Casolo

## Abstract

Only the very short phase of the ball-net Impact, lasting few hundreds of seconds, is here analyzed. This critical phase is influenced by the dynamic characteristics of ball and racket and obviously by the initial conditions, such as position and velocity, of racket and ball right before their contact. Aim of this research is that of verifying a rather simple mathematical model recently developed, in order to highlight the influence of each single racket parameter on the impact and to set up correct procedures for experimental tests of rhckets and balls. BACKGROUND The forces transmitted from the ball to the hand. then to the arm and to the shoulder, cause a displacement of the involved body segment which is proportional to their Impulse; they result to be at least one order of magnitude as high as any other force acting during the impact. Therefore, in the mathematical model. any muscular action is neglected and the racket is considered as freely hinged to the forearm. Writing the equation of dynamic equilibrium it is possible to calculate the equivalent mass. that can be substituted to the athlete's body during the Impact phase. This mass depends on the subject's anthropometry and approximates to 1 kg. This means that the racket which is free in the space with 1 kg fixed to the handle responds exactly like the one which is handled by the tennis player. if their position and speed before the impact are equal. I In order to formulate the equation of the bail's motion during its sinking in the net. it is required to know the racket's Inertial parameters, as well as other parameters quite simply obtainable, e.g. from the diagram force deflection. for both racket and ball. This system of equations can be useful for example to determine, in relation to the racket's features, the rebound speed of the ball or the force transmitted to the athlete. 5 An experimental device has been built to validate the theoretical results and to test different rackets in various play conditions. This apparatus consists of: a special "tennis bail gun", a frame allowing the automatic release of the racket during the impact and a system oflaser barriers to measure ball's and racket's speed before and after the impact. Other simple mechanical systems have been used for static measures of racket strings and ball properties. Different handle constraints have been tested with and without the equivalent mass and held by the player as well. Various rackets and string tension have been tested. The preliminary results are in good agreement with the mathematical approach. Some interesting deductions can be easily Inferred from a combined theoretical and experimental approach. The rebound coefficient of the racket, for instance, is mainly affected by the ball characteristics and by the inertia of the racket; a higher string tension does not increase the rebound speed; or else, the player's wrist stiffness has no influence on the impact; and so forth.