## Loud Loop: New explanation of whip-snapping unfurls

Peter Weiss

The explosive crack of a bullwhip can frighten cattle into a pen and even keep lions and tigers at bay. From scientific investigations dating back nearly a century, researchers had concluded that whips make loud sounds when their tips attain supersonic speeds and send shock waves—little sonic booms—through the air.

WHIP IT. A loop accelerating along a whip's length may break the sound barrier with a bang.

That long-standing explanation may not withstand a new analysis, however. Calculations by applied mathematicians Alain Goriely and Tyler McMillen of the University of Arizona in Tucson indicate that another part of the whip—a loop rolling down the whip's length—also goes supersonic when it's near the tip and begins to uncoil. This creates the whip's signature cracking sounds, they say.

The Arizona findings may also solve a puzzle that emerged from earlier observations. Several years ago, Peter Krehl of the Ernst Mach Institute in Freiburg, Germany, and his colleagues examined a cracking whip with a photographic method that shows shock waves. Oddly, they didn't record any shock waves until the tip velocity reached 744 meters per second, or more than twice the speed of sound in air.

Look to the loop for the reason, Goriely says. When flicked by a skilled whip-cracker, a whip curls into an outward-moving loop that accelerates because of the whip's taper. Goriely and McMillen developed equations that account for a loop's curvature, tension, and speed as it zips along an extended, elastic rod. They describe their whip model in an upcoming Physical Review Letters.

By feeding their equations into a computer, Goriely and McMillen determined that the leading edge of the loop would break the sound barrier while still partially curled. Even though the tip's speed is also supersonic, the tip at that moment remains in the leading edge's wake and can't create shock waves, Goriely explains.

Still, says Krehl, a tuft—called the cracker or popper—at the very tip of a whip must play a role since a whip won't crack without one. Nathan P. Myhrvold of Intellectual Ventures, a technology and investment company in Bellevue, Wash., agrees that the new analysis is inconclusive because it neglects the cracker. Computer simulations by Myhrvold indicate that some big dinosaurs could have created sonic booms with their whip-like tails, possibly for communication.

Goriely says he plans soon to build a laboratory whip, with a smoothly diminishing cross-section, to put his theories to the test.

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## References:

Goriely, A., and T. McMillen. In press. The shape of a cracking whip. Physical Review Letters.

Peterson, I. 2000. Whips and dinosaur tails. Science News Online (March 18).

## Sources:

Alain Goriely
Department of Mathematics
University of Arizona
617 North Santa Rita
Post Office Box 210089
Tucson, AZ 85721

Peter Krehl
Ernst-Mach-Institut
Institut für Kurzzeitdynamik der Fraunhofer-Gesellschaft
D-79104 Freiburg
Germany

Tyler McMillen
Department of Mathematics
University of Arizona
617 North Santa Rita
Post Office Box 210089
Tucson, AZ 85721

Nathan P. Myhrvold
Intellectual Ventures
14150 NE 20th Street
Bellevue, WA 98007

From Science News, Volume 161, No. 22, June 1, 2002, p. 341.