The Chaos of the Fall

For centuries, physicists have had no trouble predicting the paths of cannonballs, but figuring out how a feather falls had them stumped. Now, a team of researchers has figured out why flat objects are so tricky to predict. After recording how thin metal disks sink through a syrupy fluid, they report in today's issue of Nature that the tilting and tumbling bear the signature of chaos--a behavior in which tiny changes in starting conditions can have unpredictably large effects. What's more, the sinking disks yielded the first instance ever of chaotic behavior switching on, off, and back again.

Researchers have long sought to predict how flat objects fall through air or water. After World War II, for example, the Navy and Air Force wanted to understand how depth charges and other objects sink so they could place them more accurately. But by the 1960s, researchers were getting frustrated, because their experiments didn't point to any general rules.

Physicists Stuart Field of Colorado State University in Fort Collins, Franco Nori of the University of Michigan in Ann Arbor, and colleagues revisited those early experiments by placing very thin disks, less than a centimeter wide, into beakers of glycerol solution. They video-taped the slowly falling disks, then digitized the images and had a computer measure the angle of the disk at intervals of 1/60 of a second. As they changed factors like disk size and density or fluid viscosity and density, they found several basic types of falling. Small disks in viscous fluids plummeted steadily. Slightly larger disks in runnier fluids wafted back and forth like a falling leaf. Both paths could be predicted.

But even denser disks in even runnier fluid--analogous to a feather in air--behaved very differently. They oscillated for a while with increasing amplitude, then suddenly flipped over and tumbled. The angles were entirely unpredictable. Field and Nori also discovered an unusual pattern: The disks' motion did not irrevocably pass from periodic to chaotic, but skipped back and forth. "We have never seen this in a real, physical system," says Nori.

Discovering chaos in the motion of falling bodies gives a new twist to this old problem. "It's very interesting to see [the problem] reanalyzed from a modern perspective," says Hassan Aref, a physicist at the University of Illinois, Urbana-Champaign. He wonders what properties of the fluid might be causing the intermittent transition to chaos. "It's the same physics that goes into designing airplanes or submarines," he says. "I think you might see a lot of people becoming interested."

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