Liu Y K
Med Sci Sports Exerc. 1983;15(5):388-92.
Several investigators have demonstrated experimentally that ball-rebound velocity after an eccentric impact against a tennis racket remains unchanged for two extreme conditions of grip firmness, i.e., when the grip is firmly clamped and when it is allowed to stand freely on its butt. The present study utilized a simple mathematical model from classical impact theory to provide analytical support for their experimental findings. It was shown that the functional relationship between the approach and rebound velocity of the ball is dependent on five dimensionless numbers: 1) the ratio of the ball to racket mass; 2) the ratio of the radius of gyration about the racket pivot to the distance of the geometric center of the racket head to the pivot; 3) the coefficient of restitution between the ball and the racket string ensemble; 4) the ratio of the distances of the center of mass and the center of the strings to the pivot; and 5) the ratio of the grip length to the distance from the pivot to the center of the strings. Because the mass and length ratios are very small numbers for tennis, the rebound-to-approach velocity of the ball is principally a function of the coefficient of restitution, which is practically independent of the conditions of grip firmness. Using published data generated from other experiments, analytical estimates were obtained for the values of the coefficient of restitution between a tennis ball and a racket strung to typical tensions for various rebound-to-approach velocity ratios. These estimates were validated directly by an independent experiment.
几位研究者通过实验证明，在两种极端握拍牢固程度的情况下，即握拍被紧紧夹住以及握拍底部自由放置时，网球在偏心撞击网球拍后的反弹速度保持不变。本研究利用经典碰撞理论中的一个简单数学模型，为他们的实验结果提供分析支持。结果表明，球的趋近速度与反弹速度之间的函数关系取决于五个无量纲数：1）球与球拍质量之比；2）球拍绕轴的回转半径与拍头几何中心到轴的距离之比；3）球与球拍弦线组合体之间的恢复系数；4）质心与弦线中心到轴的距离之比；5）握把长度与轴到弦线中心距离之比。由于对于网球来说，质量比和长度比是非常小的数，球的反弹速度与趋近速度主要是恢复系数的函数，而恢复系数实际上与握拍牢固程度无关。利用其他实验得出的已发表数据，针对各种反弹速度与趋近速度之比，获得了网球与以典型张力穿弦的球拍之间恢复系数值的分析估计。这些估计通过一项独立实验得到了直接验证。
