A Treatise on Tumbling

Thursday, October 01, 1998
While some physicists strive to understand the subatomic building blocks of matter, Elisha Moses occasionally pursues less grandiose mysteries. A student recently asked Moses, who teaches at the Weizmann Institute in Rehovot, Israel, the following question: What makes a sheet of paper flutter back and forth as it falls, while a business card tumbles end over end?

To tackle the problem, Moses and Andrew Belmonte of Penn State built a quarter-inch-wide aquarium and dropped thin strips of plastic of various weights and lengths into the water to see how they fell. The unusual thinness of the tank reduced the falling to essentially two dimensions, making the subtle motions of the tumbling plastic strips much easier to study.

Using small aluminum particles in the water to illuminate the water currents, Moses and Belmonte were able to observe tiny vortices that curled around the edges of the strips as they fell. These vortices provide lift to the falling sheets, much the way air passing over an airplane wing creates lift. The vortices do this by slightly decreasing the water pressure above the sheet. The higher pressure below supports the sheet.

The effect is small, but it's enough to lightly support a broad, flat sheet of paper or a large dried leaf. As one side of the sheet rises above the other, a vortex begins to form at the rising edge. This vortex soon breaks away; another vortex then forms on the opposite end of the sheet. This shifting of vortices may contribute to the characteristic seesaw motion of fluttering.

With increasingly dense or shorter strips, the rising end tips up farther and farther. Eventually the strips begin to fall end over end. This sort of sharp transition exists in all sorts of periodic motion, even walking. There's a maximum speed a person can walk. To go any faster, you need to start running. Walking is like fluttering, Moses notes, and running is like tumbling. "Think of a pendulum that swings higher and higher," he says. "If you have enough momentum, it will go over the top and down the other side."
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