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# The Science of Spin

### This is an excerpt from Tennisology by Thomas Rowland.

Everywhere, things spin - heavenly bodies, subatomic particles, children's toys, gyroscopes. Spinning is a fundamental action of the natural world. Our planet revolves as well, at a speed of about 1,000 miles (1,609.3 km) per hour at the equator. It's a good thing that the atmosphere, glued to the surface by the force of gravity, rotates with it at the same speed. If it didn't, a ball tossed to serve at Flushing Meadows would be somewhere just outside Trenton by the time a player reached to hit it. Fortunately, the ball moves at the same speed as the rest of the planet and stays in the same position relative to the player. Tennis players can use an understanding of the physics of spin to modify to their advantage the effects of gravity on their strokes.9

When applied to a tennis ball, spin creates uneven forces that alter the course of the ball through the air. A spinning ball can skid at midcourt or cause a lob headed for the players' box to suddenly drop like a stone on the service line. It is almost impossible to strike a ball without applying any spin whatsoever, but manipulating strokes by purposefully applying spin can make one a master of the game.

Our understanding of spin comes from Daniel Bernoulli, an 18th century mathematician working at the University of Basel. Bernoulli's principle states that the faster a gas or fluid is flowing, the lower its pressure. This principle is best explained in terms of how airplanes fly. The wing of a 747 is cambered so that the curvature is greater on the top than on the bottom. Because the same amount of air flows over both the top and bottom of the wing as the plane flies, the air on top must flow faster. (It has farther to go due to the curvature, yet in the same time duration as the air beneath the wing.) According to the principle, the slower-moving air on the bottom has greater pressure than the air on the top, and the wing is pushed up.

### Topspin

The same thing happens when a tennis ball is made to spin as it sails across the court. Imagine you're looking at the ball from the side and it's moving from left to right. If the ball is not spinning, the air pressure above and below the ball will be equal and the only action in the vertical direction will be gravity, which causes the ball to fall as it passes over the net. But if a player hits a forehand so that the ball is spinning counterclockwise from your viewpoint, the air just at the surface of the ball will be spinning as well. The air at the top of the ball directly meets the surrounding air as the ball travels, sort of like a headwind. Conversely, the air attached to the bottom of the ball moves in the same direction as the air it meets, like a tailwind. As a result, the air at the bottom of the ball travels faster than that at the top. According to Bernoulli, the pressure on the top of the ball will be greater than that underneath as it flies over the net. This will make the ball dive, or curve downward, rather than follow a straight path (figure 6.1).

http://www.humankinetics.com/AcuCustom/Sitename/DAM/117/E6177_480251_ebook_Main.png

The Bernoulli effect when a ball is hit with topspin.

Reprinted from J. Groppel, 1992, High tech tennis, 2nd ed. (Champaign, IL: Human Kinetics), 111, by permission of the author.

That's topspin. Applying this type of rotation to the ball causes it to land short of where it would by gravity alone. Then, when the ball does strike the court, another altered action takes place: It bounces higher. As discussed previously, the angle at which a ball rebounds is normally about the same as the angle at which it hits the court. If it arrives at 60 degrees relative to the near court, it departs at 60degrees relative to the far court. However, a ball hit with topspin comes down more vertically than a ball that's not spinning does. Consequently, it rises more abruptly. When the ball is struck briskly, it bounces up with greater speed.

Topspin is created when a player sweeps the racket face up and over the top of the ball. A ball hit is this fashion dips up (because the racket face moves up to strike the ball), falls shorter, and rebounds higher and with greater velocity. The ball can be struck safely by the player with greater velocity.

Among the most common mistakes that a tennis player commits are vertical errors, or errors of depth. The ball must be struck within the angular window of acceptance, defined as the range of angle of the ball leaving the racquet that will allow it to both cross safely over the net yet still land in the opponent's court. This window is affected by several factors, including the height of the contact point, where on the court the ball is struck, and - most important - how hard the ball is hit. Physicist Harold Brody discovered that the window of acceptance shrinks by about half when a ball is struck at a speed of 70 mph compared to that leaving the racquet at 50 mph.1,2 This means that slowing the velocity of the ball improves the chances for a good shot. However, no player wants to help his opponent by slowing the ball. This is where topspin helps. Using topspin, the player can hit the ball harder but the window of acceptance will not decrease as much as it would with a flat stroke because the ball will be less likely to go long. Topspin makes the ball drop earlier and keeps hard-hit strokes in the court.

Björn Borg was the first real master of topspin, and with his enormous success the shot quickly caught on. Borg had his rackets strung extremely tightly - a tension of about 80 pounds per square inch. His powerful shots would rise to pass about 6 feet (1.8 m) above the net but then rapidly plummet to drop well within the baseline. His opponents said it was impossible to get any rhythm going against him while defending shots like that. Today's game, with its emphasis on power shots delivered from the baseline that Borg pioneered, would be quite impossible without reliable topspin to keep the ball in the court.