Why does a tennis ball spin? (Physics, Cambridge)

For a tennis fan, there are few sights more mesmerising than a perfect shot from Rafa Nadal on a clay court. The ball loops high and far over the net. As it comes down, it looks as if it’s too long. The crowd sigh. Then, as if Nadal’s got the ball on a string, or a magic force-field at his disposal, the ball suddenly drops, just on the baseline. It’s in! What’s more, as the ball spins off the clay in a brief puff of dust, it suddenly accelerates, so that Nadal’s opponent mistimes his shot and shanks it way into the air. He’s been the victim of Nadal’s celebrated topspin. Nobody does it like Nadal on clay!

Roger Federer, one of the world’s great players, puts an astonishing 2,700 revolutions per minute of spin on a ball on some of his forehand ground strokes. But that’s nothing compared to Nadal, who can set the ball spinning at over 5,000 revolutions per minute.

Of course, a tennis ball doesn’t spin all the time. Sometimes it can bounce flat off a player’s racquet and fly straight and true over the net and perform exactly as Newton’s laws of gravity say it should. It will loop down to the ground as soon as the acceleration due to gravity exceeds the acceleration imparted by the tennis ace’s mighty thwack. And when it hits the court on the far side, it will bounce on towards the far end of the court, leaving the ground at pretty much the same (but opposite) angle that it landed.

So that’s what happens on the actually quite rare occasions when the player hits the ball squarely. That is, the racquet is swung towards the ball in exactly the opposite direction that it arrives with the racquet face at right angles. If the player slices the racquet at an angle to the ball’s flight, the racquet and ball will meet at an angle and then something different happens.

Effectively, the racquet is dragged over the ball when it impacts, and the friction between racquet and ball makes the ball roll briefly over the face of the racquet as it arrives. As it bounces back, it continues to roll or spin. The flatter and faster the racquet slices across the ball, the more the ball will spin – provided the main force of the racquet on the ball is still forward. To maximise the spin, the striker needs to whip the racquet over the ball at top speed at the same time as driving forward to send the ball over the net.

If the racquet is sliced over the top of the ball, the top of the ball spins forward and the bottom spins backwards. So the ball spins towards the opponent as it leaves the racquet. This is topspin. It requires a lot of energy because the top of the ball is typically already spinning towards the striker after bouncing off the court, so he is having to reverse its spin.

If the racquet is sliced under the ball, the top of the ball spins backwards and the top spins forwards. So the ball spins back towards the striker as it leaves the racquet. This is backspin, and requires less energy because the striker is spinning it in the same direction it’s already spinning.

As the spinning ball travels through the air, it interacts with it. Because the fluffy surface of a tennis ball is quite rough, the friction drags a thin layer of air around with the ball as it spins. So with a topspinning ball, the ball drags the air over and down at the front and under and the opposite way at the back, and creates a turbulent wake behind the top of the ball. As the ball’s forward momentum drops and the ball begins to loop down, the drag and turbulence have more and more effect, making the ball drop suddenly, much earlier than gravity alone would make it.

Isaac Newton noticed this phenomenon as long ago as 1672, when watching his fellow students play tennis in Cambridge, but it is called the Magnus effect after the German physicist Gustav Magnus who studied it in the 1850s. The Magnus effect comes into play in many ball sports. Spinners in cricket use it to fool batsmen, as the ball suddenly drops earlier than they expect. Baseball pitchers use it to throw curveballs. It’s surprisingly sensitive to air conditions and becomes much more pronounced when the air is humid. If the wind is blowing towards the striker, the effect will be even more exaggerated.

For the player trying to return a spinning ball, the problems don’t end with its tricky deviation in the air. As soon as it hits the ground, the spin makes it bounce in surprising ways. With topspin, the spin adds to the natural roll of the ball as soon as it bites the ground, and so it shoots off faster than it actually landed. With backspin, the effect is the reverse, and the ball can almost stop dead in the air as it bounces. The extra friction on clay courts magnifies this effect; the slickness of grass, especially when damp, minimises it.

Federer on form is one of the best strikers of the ball tennis has ever seen, hitting it incredibly fast and true. But no wonder he prefers playing Nadal, the king of spin, on grass. On clay, Nadal is very, very difficult to beat. A spinning tennis ball has made Rafa the ‘King of Clay’, winner of the French Open an amazing eight times already at the time of writing.