Physics of the groundstroke in tennis

Understanding the physics of the groundstroke in tennis is important for the International Tennis Federation, tennis brands and players. As a research centre we recently published a paper in the journal of Sports Sciences on this subject. Following publication the paper was featured in a short article in Men’s Health magazine.
Cover of Men’s Health Magazine May 2011

The text from the article is shown below;
"An effective groundstroke in tennis requires topspin – a ball that dive-bombs as it crosses the net, then skips forward low and fast. British researchers writing in the Journal of Sports Sciences tested several racket designs and found that a heavier racket with a higher center of mass increase ball speed and topspin. "You can hit it harder, and it will still land in bounds," says Tom Allen, Ph.D., a sports engineer and the study’s lead author. The downside: A heavier racket can slow your stroke. Allen suggests adding lead tape to the outside of the rim, applied at the 12 o’clock spot. Start with a 5-gram strip (about 6 inches long). Test it during practice, and if your swing feels normal, add another layer of lead, but remove it if you notice a difference."

The aim of this blog is expand on the article and explain the science.

What we did

We created a finite element (computer) model and simulated a groundstroke. The latest version of this model is shown in the figure below. We tested a number of racket designs with the aim of finding the key performance parameters. The design features we changed were 1) stiffness, 2) mass and 3) balance point. We used data collected from a large number of rackets to ensure we had the correct range of values for these three features.

Finite element model of a tennis ball and racket developed in collaboration with Prince Sports

What we found  

Stiffness: Racket stiffness had a small effect. The exit speed of the ball was only 9% higher for a stiff racket.

Mass: Racket mass had a large effect. The exit speed and topspin of the ball were 37% and 23% higher for a heavy racket.

Balance point: Racket balance point also had a large effect. The exit speed and topspin of the ball were 32% and 21% higher for a head-heavy racket.

What it means

Increasing the stiffness of the racket reduces the energy lost in the collision. As stiffness had only a small effect energy losses are similar for all rackets. Increasing the mass of the racket or moving the balance point towards the tip increases the momentum transferred to the ball in the form of exit speed and topspin. Therefore, variations in mass or balance point between rackets will have a large effect on the transfer of momentum to the ball.

The main assumption of our study was that the speed of the shot remained constant. In reality a player’s swing speed is likely to decrease if you add mass to their racket. A reduction in impact speed will have the negative effect of decreasing the transfer of momentum to the ball. Therefore, the player should use a racket with the correct "swing weight" for their strength and playing style. As highlighted in the Men’s Health article, a player can customize the mass and balance point of their racket using lead tape.