Aerodynamics of spinning and non-spinning tennis balls

Abstract

The aerodynamic properties of a tennis ball are obtained using wind tunnel measurements. In the first phase of this study, the drag coefficient of a variety of new and used non-spinning tennis balls was measured. The measurements were conducted in the Reynolds number range of 85×10 3< Re<250×10 3, which corresponds to a velocity range of 20< U<60 ms −1 (45< U<135 mph). The data for the new tennis balls revealed that all balls have similar drag coefficients, within the repeatability of the experiment. However, it was shown that a heavily worn ball exhibits a significant decrease in drag coefficient. A simple trajectory plot was used to illustrate the significance of this drop in C D, on a typical tennis stroke. It was shown that if the drag coefficient of the worn ball was reduced even further, then the ball would travel faster through the air, and give the receiver a significantly shorter time to react to the shot. In the second phase of this study, the drag and lift coefficients of new and used spinning tennis balls was measured. This testing was conducted by placing the ball inside the working section of the wind tunnel, held between two horizontal shafts. The ball was spun at rates up to 2750 rpm, which is representative of a typical top spin shot hit by a professional player. The data showed that the lift coefficient for all the new balls was identical. However, the lift coefficient was generally lower for the heavily worn ball compared with the new ball. A trajectory plot was calculated to illustrate the effect of the lower drag and lift coefficients of the worn ball, compared to the new ball. It was shown that the lift coefficient value has little effect on the reaction time of the receiver. It was also shown that a lower lift coefficient reduces the window of opportunity for the server because the player is less able to utilise the spin to control the shot to ensure that the ball both clears the net and also lands in the service box. This highlights the fact that it may not be in the manufacturers interest to produce a ‘faster’ tennis ball with a lower drag coefficient, because the ball may also have a lower lift coefficient, thus reducing the players ability to play certain strokes.