To the beachgoer, sand is simply one of the pleasures of summer. To the scientist, it's a bit of a mystery - sometimes acting like a liquid (when poured) and other times like a solid, or even a gas.

Or, in one case, like none of the above. When a projectile hits a pile of sand - say, a golf ball landing in a bunker - the faster it is traveling, the sooner it comes to a stop. (Ordinarily, faster things take longer to stop, such as with a block sliding down a ramp.)

Two University of Pennsylvania physicists now say they can explain this intuition-defying puzzle.

Hiroaki Katsuragi and Douglas J. Durian developed a formula for the forces in "granular impact cratering," published last month in the online edition of Nature Physics. The forces include drag, which depends on the square of the object's velocity, and friction, which depends on the type of material and how deep the object penetrates.

"Anybody can drop a ball in the sand," Durian says. "Nobody could predict how far it would go in."

So first, Katsuragi repeatedly dropped a 1-inch steel ball into a container of tiny, sand-like glass beads. He experimented with a variety of heights, and took photographs of the falling ball every 20 microseconds. That helped the pair develop the formula.

The duo pursued the puzzle out of academic curiosity. But Durian predicts it might help in commercial applications, too, such as the design of bunker-busting missiles or of mixing blades used to combine pharmaceutical powders.

"There'll be no practical use to Tiger Woods," he quips.

Actually, there might. University of Western Ontario physicist John de Bruyn, an expert on granular materials, says the formula may help an engineering colleague of his - a golfer who studies which kind of sand works best in a sand trap. Fore!

- Tom Avril