Professor Alain Goriely might not be Calamity Jane riding the Deadwood Stage but he could just be one of the first people to truly understand what makes a "whip crack-away".
As a staple element of physicists’ stores of trivia, the explanation for what makes a whip crack has been believed for nearly 100 years. However, Professor Goriely has thrown the standard ideas for a loop – in fact, it is the loop in a cracked whip that is responsible for all the noise.
"The crack of a whip comes from a loop traveling along the whip, gaining speed until it reaches the speed of sound and creates a sonic boom," Professor Goriely of the University of Arizona Department of Mathematics said.
As early as 1905, physicists understood that a whip crack is a sonic boom produced when some part of the whip reached a supersonic speed. High-speed shadow photography experiments in 1927 clearly showed the sonic boom being created.
More recently, accelerations of the tip were recorded at 50,000g (where 1g is the acceleration of a falling object). However, those observations created a puzzle - the tip was moving at twice the speed of sound (Mach 2) when the crack was created. Why wasn’t the crack heard when the tip hit the speed of sound?
Professor Goriely’s collaboration with his graduate student Tyler McMillen of the University of Arizona Program in Applied Mathematics has answered this and other questions.
"Although the loop travels at one speed, some parts of the whip, including the tip in the final stages of motion, travel twice as fast. Even though those parts are moving twice as fast, it is the loop itself that generates the sonic boom," Professor Goriely said.
The idea that the tip travels twice as fast as the loop is like how the uppermost point on a car tire is traveling at twice the speed of the car for just an instant.
"A whip is specially crafted to accelerate a loop in its body to high speeds. The tapering of a whip makes a loop traveling along it speed up by a factor of ten. The lightweight free end allows an extra factor of two to three in speed. For realistic whips, the tip can reach speeds more than 30 times the initial speed," he said.
Although the cracking of a whip may seem like an unusual motion, it appears in other circumstances. One is the roll-cast in fly-fishing. It is also the motion of a sperm’s tail, used to propel it forward.
Professor Goriely is not a professional whip cracker himself. He can perform most simple cracks but is still working on the most difficult ones.
"Whipping is not as dangerous as it seems unless you so something stupid or you practice inside – I have been banned from doing it inside!"
His interest in the problem originated at a scientific meeting in Hungary where he saw a type of traditional Hungarian dancing that involves whip cracking.
"I realized that it was a very unusual problem in terms of filament dynamics. When I got back home, I did a complete bibliographic search and found that nothing substantial had been done at the theoretical level. We decided with Tyler to work on it. The first step was to buy a whip – everybody should try."
The research will appear in an upcoming issue of Physical Review Letters published by the American Physical Society.
Journal
Physical Review Letters