# Stone Skipping Gets Scientific

John Roach
for National Geographic News
January 8, 2004

With a sidearm toss and flick of the wrist, people young and old have been skipping stones across bodies of water for thousands of years. The object is simple: get as many bounces as possible.

Jerdone Coleman McGhee of Wimberley, Texas, holds the current Guinness Book of World Records title for a 1992 toss that yielded an impressive 38 bounces across the Blanco River in central Texas.

Want a shot at beating McGhee? Toss your stone so it hits the water at the "magic angle" of 20 degrees.

The hint comes from a team of French scientists who constructed a stone-skipping machine to find out the optimal speed, spin, and angle for the maximum number of bounces.

"If one changes slightly the initial conditions—different velocity, etc.—at this angle of 20 degrees, the stone still has more chances to rebounce than for any other angle," said Lydéric Bocquet, a physics professor at the University of Lyon.

Bocquet and his colleagues published their findings in last week's issue of the science journal Nature, concluding that "modern scientific insight" may benefit the ancient art of stone skipping.

Jerry Gollub, a physics professor at Haverford College in Pennsylvania, said the paper is indeed a nice example of bringing scientific thought to an old problem. "The emergence of a simple rule for optimizing the number of bounces when skipping stones is certainly a nice result," he said.

Anatomy of a Skip

According to Bocquet, a stone skips on the water for much the same reason a water skier is able to skim across the surface. The stone and water skier receive a force from the water related to the speed with which they travel across it. (For physics buffs: The force is proportional to the squared speed of the stone.)

Just like a water skier, "as the velocity of the skier increases, he can feel the upward force," said Bocquet.

Spin, which helps stabilize the stone as if flies through the air and bounces off the water, is another important factor in successful stone skipping.

"The basics are more or less simple," said Bocquet.

What surprised Bocquet and his colleagues, however, was that no matter how they changed speed and spin, stones always had the best chance at bouncing when they hit the water at an angle of 20 degrees.

Stones that enter the water at angles less than 20 degrees bounce but lose much of their energy dragging through the water, while stones that enter at angles greater than 45 degrees don't bounce at all—they sink.

Stone-Skipping Machine

Bocquet first got interested in the physics behind stone skipping after his eight-year-old son asked him about it while they, as millions of fathers and sons have done before, were skipping stones together at a river.

"I first thought about it as a funny hobby, a kind of wink where physics can help understand everyday life," he said. The hobby resulted in a set of equations published in the American Journal of Physics in 2002 describing the optimal speed and spin for a toss.

According to his equations, to match McGhee's Guinness Book of World Records pinnacle of 38 skips requires a stone tossed at 25 miles per hour (40 kilometers per hour) with a spin of 14 rotations per second.

The paper caught the attention of Christophe Clanet, a physics professor at the Institut de Recherche sur les Phènoménes Hors Equilibre in Marseille. As a way to get his students at Ecole Polytechnique in Paris interested in the scientific process, he had them construct the stone-skipping machine.

"The project went on really nicely," said Bocquet. "A real scientific apparatus was constructed controlling all the parameters of the throw and recording it using a high-speed camera, which is a really difficult and tricky task."

Using the machine, which launches aluminum discs across a pool of water, the researchers arrived at the "magic angle" of 20 degrees.

In the near future, Bocquet said he and his colleagues hope to attempt the world record with their machine, testing the equations and theory of what's required to achieve the maximum number of bounces.