Effects of friction between the ball and strings in tennis
R. Cross
Physics Department, University of Sydney, Sydney, Australia
Abstract When a tennis ball is incident at an oblique angle on a tennis racket, the ball slides or rolls along the strings before it rebounds. The dynamics of this interaction in a direction perpendicular to the string plane are determined by the coefcient of restitution (COR). In a direction parallel to the string plane, the dynamics depend on the coefcients of sliding (lS) and rolling (lR) friction, and also depend on the COR. For example, if lS 0, and if the ball impacts in the middle of the strings, then the ball will rebound with no change in its spin or parallel speed. Spaghetti strings, with a high value of lS, are banned from competitive tennis since they can be used to impart excessive spin to the ball. It is shown that the most useful strings are those with lS > 0.3 and that the performance of the strings deteriorates sharply if lS drops below about 0.3.
Keywords: tennis, strings, coefcient of friction
Nomenclature
D e eA F I m M N R v1 v2 vin vout V2 VR b h1 h2 Distance to line of action of N (Fig. 2) Coefcient of restitution Apparent coefcient of restitution Friction force Moment of inertia of ball about its CM (2mR2/3) Mass of ball (57 g) Mass of racket Normal reaction force Radius of ball (32.5 mm) Incident velocity of ball in racket frame (Fig. 1) Rebound velocity of ball in racket frame (Fig. 1) Incident velocity of ball in court frame (Fig. 1) Rebound velocity of ball in court frame (Fig. 1) Rebound velocity of racket head Incident velocity of racket head (see Fig. 1) Head tilt (see Fig. 1) Angle between incident ball and string plane (Fig. 1) Angle between rebounding ball and string plane (Fig. 1)
Correspondence address: Rod Cross, Physics Department, University of Sydney, Sydney NSW 2006, Australia. Fax: +61 2 9351 7727. E-mail: cross@physics.usyd.edu.au
2000 Blackwell Science Ltd Sports Engineering (2000) 3, 85±97

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