|Ivars Peterson's MathTrek|
March 20, 2000
Swinging a leather bullwhip's thick, rigid handle in an arc gives the whip angular momentum. Sharply reversing the motion's direction sends a wave down the whip. As the wave travels toward the tip along a tapering path, it moves more and more rapidly--a consequence of the conservation of angular momentum. In the end, the narrow tips supersonic motion through the air produces a shock wave.
The same conservation principle is at work in the flicking of a locker-room towel or, at subsonic velocities, during a golf swing, karate chop, or javelin throw.
Noise-making whips can be made from various materials, including paper, fiber, and leather. Though the designs may differ in many respects, such whips typically have a tapering cross section. Many feature a thin cord or string, called a popper (or cracker), at the tip.
Sauropod dinosaurs of the family Diplodocidae have enormous tails that gradually narrow to thin, delicate tips. Since the late 19th century, when the fossil remains of the Apatosaurus (formerly known as Brontosaurus) and other family members were first uncovered, observers have often likened the tails to whips and have speculated about what purpose those tails might have served. Some paleontologists suggested that diplodocid tails could have been used as defensive weapons, for example. More recently, several have speculated that, like bullwhips, such tails were meant to be noisemakers.
Nathan P. Myhrvold of Microsoft Research in Redmond, Wash., worked with paleontologist Philip J. Currie of the Royal Tyrrell Museum of Paleontology in Drumheller, Alberta, to develop computer models of diplodocid tails to show that tail tips could have reached supersonic velocities. Myhrvold updated this research last month at the Gathering for Gardner IV, held in Atlanta in honor of writer, magician, and puzzlist Martin Gardner (see Martin Gardner's Lucky Number, Sept. 8, 1997).
The Apatosaurus was about 90 to 100 feet long, with its tail accounting for nearly half of that length. At a hefty 35 tons or more, a single specimen weighed as much as half a dozen African elephants.
Weighing more than 3,000 pounds by itself, an Apatosaurus tail is roughly 3 feet wide at its base and gradually tapers to the width of a human thumb. The last few yards of tail are made up of rather small, fragile bones and weigh less than a pound.
Myhrvold's simulations show that a wave traveling from one vertebra to the next down such a tail could ultimately reach a speed of 1,300 miles per hour--fast enough to generate an enormous sonic boom. At an estimated 200 decibels, its loudness would rival that of a massive naval gun. And the sauropod could generate such a crack in less than a fifth of the energy that it required to take one step.
"We cannot prove that supersonic tail cracking occurred, but it is physically feasible," Myhrvold contends.
Because the plant-eating sauropods must have had enormous appetites and probably maintained vast grazing territories, its possible to imagine such loud booms as signals among these widely dispersed, solitary creatures.
A heavily used bullwhip is most likely to fail near the junction between its thick handle and the flexible leather extension. Interestingly, paleontologists have found that vertebrae in the transition zone between a tail's stiff muscular base and the flexible whiplash section are sometimes fused together--suggesting the repeated application of a large stress to this region.
Curiously, however, only about half of the diplodocid specimens examined to date shows such bone fusion. Myhrvold suggests that only the males made extensive use of this noise-making capability, perhaps to attract mates or establish dominance. Maybe it was big guys making loud noises for love, he remarks.
The recent discovery and ongoing excavation of a pair of sauropods in Wyoming, one identifiable as a male and the other as a female, has now lent credence to Myhrvold's idea. Only the male specimen has fused vertebrae.
"I am now more convinced than ever," Myhrvold insists.
It's also possible that an Apatosaurus tail had a highly flexible extension, equivalent to a bullwhips popper. Creating shock waves stresses a bullwhip's popper and causes it to fray and wear out, so it has to be replaced after 1,000 or so cracks. Finding fossil evidence of a similar, expendable (but potentially renewable) structure at the tip of a sauropod tail would provide additional evidence of its noise-making function.
Meanwhile, other ventures in the new realm of cyberpaleontology beckon investigators.
Copyright 2000 by Ivars Peterson
Barsbold, R., P.J. Currie, N.P. Myhrvold, et al. 2000. A pygostyle from a non-avian theropod. Nature 403(Jan. 13):155.
Myhrvold, N.P., and P.J. Currie. 1997. Supersonic sauropods? Tail dynamics in the diplodocids. Paleobiology 23(No. 4):393.
Zimmer, C. 1997. Dinosaurs in motion. Discover (November):97.
Basic information about the Apatosaurus is available at http://en.wikipedia.org/wiki/Apatosaurus.
The Royal Tyrrell Museum has a Web site at http://www.tyrrellmuseum.com/.
The Gathering for Gardner IV celebration has a Web site at http://www.G4G4.com/.
Comments are welcome. Please send messages to Ivars Peterson at email@example.com.