# Measurements of the horizontal and vertical speeds of tennis courts

## Abstract

Tennis courts are normally classified as fast or slow depending on whether the coefficient of sliding friction (COF) between the ball and the surface is respectively small or large. This classification is based on the fact that the change in horizontal ball speed is directly proportional to the COF if the ball is incident at a small angle to the horizontal. At angles of incidence greater than about 16° it is commonly assumed that the ball will roll during the bounce, in which case one can show that the ratio of the horizontal speed after the bounce to that before the bounce will be 0.645 regardless of the angle of incidence or the speed of the court. Measurements are presented showing that (a) at high angles of incidence, tennis balls grip or ‘bite’ the court but they do not roll during the bounce, (b) the bounce:speed ratio can be as low as 0.4 on some courts and (c) the normal reaction force acts through a point ahead of the centre of mass. An interesting consequence is that, if court A is faster than court B at low angles of incidence, then A is not necessarily faster than B at high angles of incidence. An exception is a clay court which remains slow at all angles of incidence. The measurements also show that the coefficient of restitution for a tennis ball can be as high as 0.9 for an oblique bounce on a slow court, meaning that the ball bounces like a superball in the vertical direction and that slow courts are fast in the vertical direction.

This is a preview of subscription content, access via your institution.

## References

• Brody, H. (1979) Physics of the tennis racket,American Journal of Physics,47, 482–487.

• Brody, H. (1984) That’s how the ball bounces.The Physics Teacher,22, 494–497.

• Casolo, F., Vallatta, A. & Caffi, M. (1994) Measurement of the dynamic properties of tennis balls. ITF Technical Centre Library Report ITF-L-130

• Cross, R. (1999) Dynamic properties of tennis balls,Sports Engineering,2, 23–33.

• Cross, R. (2000) Effects of friction between the ball and strings in tennis,Sports Engineering,3, 85–97.

• Cross, R. (2002a) Measurements of the horizontal coefficient of restitution for a superball and a tennis ball,American Journal of Physics,70, 482–489.

• Cross, R. (2002b) Grip-slip behavior of a bouncing ball,American Journal of Physics,70, 1093–1102.

• Gobush, W. (1994) Spin and the inner workings of a golf ball, inGolf the Scientific Way, (Ed. Cochran, A.J.) Aston Publishing Group. pp. 141–145.

• Haake, S.J., Rose, P. & Kotze, J. (2000) Reaction time testing and grand slam tie-break data, inTennis Science and Technology (Eds. Haake, S.J. and Coe, A.O.), Blackwell Science, Oxford. pp. 269–275.

• Hierrezuelo, J., Catolicos R. and Carnero C. (1995) Sliding and rolling: the physics of a rolling ball.Physics Education,30, 177–182. ITF (1997) An initial study on performance standards for tennis court surfaces, ITF Roehampton. ITF (2002)

• ITF Approved tennis balls and classified court surfaces, Roehampton, pp. 27–32.

• Maw, N., Barber, J.R. and Fawcett, J.N. (1976) The oblique impact of elastic spheres.Wear,38, 101–114.

• Maw, N., Barber, J.R. and Fawcett, J.N. (1981) The role of elastic tangential compliance in oblique impact.Journal of Lubrication Technology,103, 74–80.

• Pallis, J.M. and Mehta, R.D. (2000) Tennis science collaboration between NASA and Cislunar Aerospace, inTennis Science and Technology (Eds. Haake, S.J. and Coe, A.O.), Blackwell Science, Oxford. pp. 135–144.

• Tabor, D. (1994) The rolling and skidding of automobile tyres.Physics Education,29, 301–306.

• Thorpe, J.D. & Canaway, P.M. (1986) Performance of tennis court surfaces II. Photometric methods for measuring pace and bounce under playing conditions.Journal of Sports Turf Research Institute,62, 101–117.

## Author information

Authors

### Corresponding author

Correspondence to Rod Cross.

## Rights and permissions

Reprints and Permissions

Cross, R. Measurements of the horizontal and vertical speeds of tennis courts. Sports Eng 6, 95–111 (2003). https://doi.org/10.1007/BF02903531