Tennis Industry magazine

 

Spin Off the Court and Strings

By Rod Cross

I noticed something interesting at the Australian Open in January. That is, I could sometimes read the label on the ball as the ball travelled over the net, even though the players were hitting topspin groundstrokes. The ball was hardly spinning at all even though the players were trying to make it spin. The problem was, the players weren’t hitting the ball hard enough to make it spin. The ball bounced off the court spinning rapidly but it stopped spinning as soon as it came off the strings. Instead of reversing the direction of spin, as the players were trying to do, all they were doing by hitting the ball was bringing the spin to a stop.

An interesting question is how the spin off the court affects the spin that players get off the strings. Men tend to hit the ball harder and can therefore generate more topspin than women. But if they hit the ball with more topspin then the ball will come off the court spinning even faster. That means that men have to work harder to reverse the direction of spin in order to return the ball with topspin.

Suppose that two players get into a long topspin baseline rally where both players are hitting the ball at the same speed straight up and down the middle of the court. A typical rally is shown in Fig. 1 where the ball travels over the net with spin S1, bounces off the court with spin S2, and comes off the strings with spin S1. Provided both players keep hitting the ball at the same speed and at the same height over the net, the ball will get stuck in a groove where it spins clockwise at S1 or S2 while it travels left to right and then spins counter-clockwise at S1 or S2 as it travels back from right to left. The spin changes from S1 to S2 every time the ball hits the court and it changes from S2 back to S1 every time the player hits the ball. In reality the speeds and spins will change during the rally but it is easier to figure out what is happening if we assume that the speeds and spins remain constant for at least two consecutive hits.

Spin, figure 1

Spin Off the Court

When a ball hits the court in a rally situation, the change in spin depends on the amount of friction between the ball and the court and on the vertical speed of the ball. The spin will change typically by about 1,500 rpm on a fast court and by about 2,000 rpm on a slow court. A ball hit higher over the net will tend to hit the court at a higher vertical speed, in which case the change in spin will be proportionally higher, but 1,500 or 2,000 rpm is typical. A ball hit with say 1,000 rpm of topspin will therefore bounce off the court with about 2,500 rpm on a fast court or 3,000 rpm of topspin on a slow court. If the ball is hit with 1,000 rpm of backspin then it will bounce off the court with 500 rpm of topspin on a fast court or 1,000 rpm of topspin on a slow court. Regardless of the spin of the ball before it bounces, a fast court changes that spin by around 1,500 rpm and a slow court changes it by around 2,000 rpm, assuming that the ball is hit from behind the baseline and lands about 6 feet short of the other baseline. In other words, S2 = S1 + 1,500 on a fast court and S2 = S1 + 2,000 on a slow court.

Spin Off the Strings

When a player hits the ball, the direction of spin off the court needs to be reversed in order to return the ball with topspin. Depending on how hard the player hits the ball and how steeply the racquet rises up the back of the ball, a player can change the spin by anything between about 1,000 rpm and 6,000 rpm. Suppose that the change in spin is X. Then the spin off the strings is S1 = X - S2. For example, if the spin off the court is S2 = 3,000 rpm and the change X = 4,000 rpm then the spin off the strings is S1 = 4,000 – 3,000 = 1,000 rpm. However, if S2 and X are both equal to to 3,000 rpm then S1 = 0 and the ball will come off the strings without any spin at all. That’s what I was seeing in some of the women’s matches in January.

Rearranging the above terms with a little math shows the following handy relationships: S1 = (X – 1,500) ÷ 2 and S2 = (X + 1,500) ÷ 2 for a fast court rally, while S1 = (X – 2,000) ÷ 2 and S2 = (X + 2,000) ÷ 2 in a slow court rally. If we substitute X = 1,500 rpm for a fast court and X = 2,000 rpm for a slow court then S1 = 0 in each case. The player therefore needs to change the spin by at least 1,500 rpm on a fast court and 2,000 rpm on a slow court to return the ball with topspin. Otherwise the ball will be returned without spin or with backspin. Fig. 2a shows a slow court rally when X = 2,000 rpm, S1 = 0, and S2 = 2,000 rpm. Fig. 2b shows a slow court rally when X = 3,000 rpm, S1 = 500 rpm, and S2 = 2,500 rpm. Figures 3a and 3b show the corresponding situations on a fast court: Fig. 3a when X = 2,000 rpm, S1 = 250 rpm, and S2 = 1,750 rpm; Fig. 3b when X = 3,000 rpm, S1 = 750 rpm, and S2 = 2,250 rpm.

Spin, figure 2

Note that the spin off a slow court is faster, but that makes it harder, not easier, for the player to return the ball with topspin.

See all articles by

About the Author

Rod Cross retired in 2003 as an honorary member of the Sydney University staff and continues to work on the physics of sport and forensic physics. He is a physicist and co-author of The Physics and Technology of Tennis available from the USRSA.

 

Frasure-Footer-Ad-336x280-FINAL

TI magazine search

TI magazine categories


TI magazine archives


 
 

Movable Type Development by PRO IT Service