DETERMINATION OF THE COEFFICIENT OF DRAG OF THREE DIFFERENT TENNIS BALLS USING A WIND TUNNEL

Abstract

INTRODUCTION: The constant improvement of tennis rackets and coaching has changed the current game to such an extent that critics complain it is dominated by the serve. Tennis balls are being served at higher velocities with each improvement. There may soon be a point at which the receiver may not be able to react quickly enough. Before any changes can be suggested, it is necessary to have a complete understanding of the game of tennis in terms of the ball mechanics and flight. This paper documents preliminary study of the aerodynamics of tennis balls. METHODS: The investigation considered three different tennis balls, differing both in construction and quality of nap. The three ball types used are as follows: an unspoiled pressurized ball fresh from its container; an unspoiled ‘permanent’ pressure ball fresh from its container; and a well worn pressurized ball showing significant visual reduction in quality and overall bulk of nap. By using the above set of tennis balls, the effects of both construction and surface quality on a balls flight through the air were analyzed. Initial testing involved an investigation of the velocity profile of the wind tunnel. It was found that the velocity was constant across the working section up to the maximum velocity of 26ms-1. This result meant that the complete viewing area of 230mm could be used for collection of data. Three different tennis balls were dropped through the working section of the wind tunnel using an electronically activated ball drop apparatus. The wind velocity was increased in equal increments of 3ms-1, from zero to 26.3ms-1, dropping all three balls at each setting. The motion of the ball during flight was captured digitally using a KODAK Motioncorder at a frame rate of 100fs-1 and a shutter speed of 1/1000 second. The frames containing the flight of the ball were transferred from the Motioncorder and captured digitally on a computer, creating a store of several images over the duration of the flight. Data was collected from individual images using OPTIMAS 6 which exported the data to Microsoft Excel 5. The analysis used three points on the circumference of the ball, producing chords to find the its center. The resulting trajectory of the ball was viewed in the form of a graph of displacement versus time. A second order polynomial which explained the data set was fitted to the chart. The differentiation of this gave the acceleration of the ball during flight. RESULTS: The results obtained from the tests were plotted on a graph of coefficient of drag (CD) versus the Reynolds number. This chart showed that the ball with the significant removal of nap had a lower CD when compared to the balls with a brand new nap. A computational model was developed to predict the trajectory of a tennis ball. Using the results from these tests on a ball hit horizontally with an initial velocity of 26.3ms-1 and zero spin, it was estimated that the ball with the significant removal of nap would travel 1m further than the balls with unspoiled nap.