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Friction between ball and strings R. Cross
hin hout hR lR lS x1 x2
Angle between incident ball and horizontal (Fig. 1) Angle between rebounding ball and horizontal (Fig. 1) Approach angle of racket head (see Fig. 1) Coefcient of rolling friction Coefcient of sliding friction Angular velocity of incident ball Angular velocity of rebounding ball lifeless or lacking the power of new strings. These observations are not consistent with laboratory measurements of the rebound of a ball at normal incidence. If one drops a steel ball vertically onto the strings of a horizontal, head-clamped racket, there is almost no measurable difference in bounce height between new and old strings, at a 1% level, even if the racket contains strings that are 10 years old. Similarly, there is no obvious difference in bounce height between different types of string or different string tensions (Cross 2000a). These results show that the energy lost in the strings during an impact is negligible. In the case of an impact with a tennis ball, racket power can be increased by decreasing the string tension so that the ball is not as severely deformed, in which case the energy loss in the ball is reduced. The question is, by how much Detailed calculations for normal incidence show that the rebound speed of the ball increases by a negligible amount for the range of string tensions commonly used in tennis rackets. For a tennis ball incident on a head-clamped racket, the normal component of the rebound speed of the ball can be increased by about 7% when the string tension is halved (Bower & Sinclair 1999; Cross 2000b). However, the speed of a ball struck by a moving racket depends mainly on the speed of the racket head, and depends only weakly on string tension. For example, if the string tension is reduced from 60 lb (27.2 kg) to 50 lb (22.7 kg), the serve speed increases typically by only 0.7% and the rebound speed for a groundstroke increases typically by only 1.1% (Cross 2000b). Consequently, any differences between strings are more likely to be associated with differences in the transverse motion of the ball, as determined by the coefcient of friction between the ball and the strings.

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