The Relationship between the Coefficient of Restitution and Energy Losses in Tennis Rackets

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Abstract
The relationship is investigated between the apparent coefficient of restitution and the losses in preimpact kinetic energy of the ball for tennis rackets whose handles are constrained by various clamping modes. The complete energy balance equation of the racket-ball system is derived, and experimental results involving four test rackets are then used to evaluate the various components of the total energy loss for the standardized hand-held mode and the vice-clamping mode. Results demonstrate that the apparent coefficient of restitution is not, as previously thought, independent of the clamping mode but varies significantly with the constraining condition applied to the handle, and with the preimpact velocity of the ball. The relative energy losses in the strings are comparatively small, whereas the losses in the ball increase exponentially with the magnitude of the impulse. The major part of the total loss in kinetic energy of the impacting ball is due to the spatial postimpact recoil motion and internal vibrations of the racket frame.

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