Hard to stop. A mathematician has explained why volleyballs are prone to erratic movements at certain speeds.

Serving Up an Aerodynamic Crisis

Staff Writer

DAVIS, CALIFORNIA--Sometimes a softer touch pays off. Volleyball players often bash the ball to obtain the fastest possible serve. But slower serves can swerve unpredictably--by as much as a meter--and now a mathematician has explained why. The large, light volleyball routinely enters a curious aerodynamic state rarely seen with other balls.

The key factor is drag, and its effects depend on speed. When a ball moves through the air, a long tangle of swirling air trails behind it. At low speeds, this "turbulent wake" is large and drags on the ball. But if a ball moves faster than a certain speed, the size of the wake suddenly decreases and the drag plummets. The speed range in which this happens is known as the drag crisis, and balls moving in it can behave unpredictably. But in most sports the balls hurtle so fast that the drag crisis never comes into play.

Not so for volleyball, reports Thomas Cairns, a mathematician at the University of Tulsa in Oklahoma who coached the women's volleyball team there for 17 years. Cairns and his students videotaped volleyballs launched from a serving machine and then analyzed their trajectories using a computer. In some serves the balls moved with top spin, in which the top of the ball rotates toward the oncoming air and the bottom rotates away from it. In those cases, the top of the ball effectively moved faster through the oncoming air than the bottom half did. In fact, sometimes the top of the ball moved fast enough relative to the air to avoid the drag crisis, while the bottom half moved so slow it dipped into it, he reported here 13 September at the 5th International Conference on the Engineering of Sports.

The unusual half-and-half state can reverse another key effect of spin--the aerodynamic lift force--which can make a ball swerve up or down, or side to side. In spite of its name, the lift ordinarily pushes a ball with top spin down, so that it sinks faster than a similar serve with no spin. But Cairns observed a serve with top spin that floated farther than a matching spinless serve. He also saw spinning serves that swerved to the "wrong" side and even a few serves that swerved first one way and then the other.

Certain players already take advantage of strange aerodynamic effects, too, says Rabindra Mehta, an aerodynamicist at NASA's Ames Research Center in Moffett Field, California. "The men get up there and try to hit the ball as hard as they can," he says. "But if you watch the women, they hit it at about 15 meters per second, which is where this effect comes in."

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The 5th International Conference on the Engineering of Sport

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