To many sports fans, the month of June is synonymous with the Wimbledon tennis tournament. Thousands of people will flock to the All England Lawn Tennis Club to watch the players battle it out on the grass courts, and millions more will watch the tournament on television. But many tennis officials, players and spectators complain that the speed of the players’ serve on “fast” courts, like those at Wimbledon, has simply become too quick. Indeed, most games at Wimbledon are won on the strength of a player’s serve alone rather than following a long rally. And for some players over 30% of their sets end in tie-breaks.
Possible solutions to this situation include changing the surface or the dimensions of the tennis court, limiting the power of the racket or changing the tennis balls. Getting rid of the grass and replacing it with a slower surface would clearly solve the problem. However, the grass courts at Wimbledon are the heart and soul of lawn tennis and this will never be a viable option. A more popular suggestion is either for the players to use wooden rackets or to limit the power of the racket in some other way. The International Tennis Federation (ITF) is currently investigating whether there is indeed a practical way to limit the power of the racket.
One of the most popular suggestions for slowing down the game is to change the balls. One approach would be to make the balls bigger. This would influence the interaction between ball and the racket, the ball’s flight through the air, and its bounce on the ground. The ITF, the world ruling body of the game, has thus embarked on a challenging series of projects to study the physics of tennis.
Currently the rules of the game state that a tennis ball should have a mass between 56.7 g and 58.5 g, and a diameter between 65.41 mm and 68.58 mm. The ITF proposes that larger tennis balls (up to 71 mm) could be used on fast courts such as those at Wimbledon. But before such a rule change is made it is important to study its effect on the game.
To simplify the problem, the first stage of the investigation has concentrated on non-spinning tennis balls. Simon Goodwill at the ITF fired both standard-sized balls (65 mm in diameter) and balls that were 8% larger (69 mm in diameter) at velocities of up to 60 m s-1 (135 mph) from a compressed-air gun at a tennis racket. Using light guides he measured the impact and rebound velocities for both freely suspended and rigidly clamped rackets.
Only small differences were found in the velocities with which the different-sized balls rebounded from the racket and these were attributed to slight variations in the stiffness and mass of the balls. Balls that have either a higher mass or stiffness were found to rebound faster from the racket. This is because the racket strings deform more than they would with a lighter or less stiff ball. More energy will therefore be returned to the heavier or stiffer ball, causing it to rebound at a higher speed.
At the University of Sheffield, we carried out an aerodynamic study on the standard and larger-sized balls by mounting non-spinning balls on a force platform in a closed-circuit wind tunnel. We found that the drag coefficients, which relate the drag force on the ball to its velocity, diameter and density, remained constant over a large range of velocities for each size of tennis ball. Rod Cross of the University of Sydney carried out a similar study confirming that the airflow around tennis balls is unlike the airflow around other types of ball.
When the airflow around a smooth sphere is even and laminar, the drag coefficient is high. But at high velocities, the airflow undergoes a transition from laminar to turbulent flow and the drag coefficient drops by more that a factor of two. Indeed, over the years golf balls have acquired dimples to induce this transition and consequently lower the drag at much lower velocities. This is why dimpled golf balls travel greater distances than smooth ones. Tennis balls, on the other hand, do not seem to experience this transition and the drag coefficient remains constant regardless of velocity. We found that the dominant factor affecting the drag coefficient was the height of the nap above the surface of the tennis ball – in other words, “fluffier” balls have a higher drag coefficient. This might explain why tennis players comment that a ball travels faster as the nap is worn off during a game.
Another major factor governing the ball’s flight through the air is its diameter. A larger ball experiences a higher drag force due to its increased cross-sectional area, which causes it to slow down more than a standard-sized ball. The knock-on effect is that the larger ball lands at a steeper angle, causing it to rebound off the court at a steeper angle.
This brings us to the impact of the balls with the court. Standard and larger-sized balls were projected at both clay and acrylic courts using a bowling machine that can fire the balls at speeds of up to 50 m s-1. The impact and rebound of each ball were recorded using a high-speed video camera that recorded 9000 frames per second. We found that both balls rebounded with a slightly higher velocity from an acrylic court that they did from a clay court. The larger ball, however, rebounded at a slightly steeper angle than the standard-sized ball, especially on the clay surface. Although this angle amounted to less than 2°, when added to the fact that the larger ball also hits the court at a steeper angle, a player will notice a significant difference in the way the larger ball “plays”.
We also analysed the complete trajectories of balls that were served with a velocity of 50 m s-1 and bounced just inside the service line. The larger balls travel 15 cm less than the standard balls before landing on the court, and arrive at the baseline approximately 30 ms later on both acrylic and clay surfaces.
This may not sound significant but the difference between the standard and larger balls may be as large as the difference between clay and acrylic courts. Players know that clay is a much slower surface than acrylic and therefore the effect of a larger ball will be significant.
This year the ITF will propose a rule change that will allow larger tennis balls to be used to assess players’ reactions in tournaments. Meanwhile, the next stage for the physics investigation is to include the effects of spin and racket design on the ball’s impact and trajectory.
