Cats' Paws and Catapults: Mechanical Worlds of Nature and People by Steven Vogel

Author:Steven Vogel [Vogel, Steven]
Language: eng
Format: epub
Publisher: W. W. Norton & Company
Published: 2000-01-17T05:00:00+00:00

FIGURE 9.13. The essential difference between walking and running. In the former what matters is the weight of the appendage since storage between strides is gravitational. In the latter the elasticity of tendons provides the equivalent reservoir for absorbing and releasing energy.

R. McNeill Alexander, of Leeds University, who has done the best work ever on the mechanics of walking and running, found the rule that sets the switch point. Except for the value of a constant, the formula for the gait transition point is the same one that gives the period of a pendulum. Whether you’re a crow or kangaroo shifting from walking to hopping, or a human or dog (or even an insect) switching from walking to trotting, you follow Alexander’s rule. Switching happens when the square of your speed is around half of gravitational acceleration times the distance between your hip and the ground. For a middle-size human, again, that’s about a twelve-minute mile or five miles per hour. For a smaller animal, the transition speed is lower; you walk while a small child, dog, or cat must trot to keep pace.21

While gravitational storage isn’t of much value above the transition speed, energy storage is still very much in the picture. When jogging or running, you use elastic rather than gravitational energy storage, stretching tendons rather than swinging legs up and down. The storage mode differs, and the two gaits are unmistakably distinct. In a way, gravitational storage is the special case, used only as legs rise and fall in walking. All the other common gaits—trotting, galloping, hopping, and so forth— depend on elastic storage. A hopping kangaroo, for instance, regains about 40 percent of the energy absorbed in landing when it bounces up again. In storing the energy by stretching tendon, it’s using the protein collagen as its battery—the same stuff the ancients took from cows for their ballistae and the main material of our own tendons. Collagen has a resilience of about 93 percent—that is, 7 percent of the energy put in when it’s stretched fails to reappear in mechanical form when it springs back. That’s not bad, better than the ordinary rubber we make from the sap of rubber trees. But where collagen brings home the bacon is in the amount of energy it can store relative to its weight—nearly twenty times that of spring steel.

The problem of appendages that repeatedly change directions isn’t limited to terrestrial locomotion with legs. Insects beat their wings up and down at frequencies up to almost (in the smallest ones) a thousand times a second. We’ve known about (and wondered at) these remarkable rates for a long time. During the 1940s an unusually gifted Finnish investigator, Olavi Sotavalta, compiled a compendium of wingbeat frequencies simply by listening to them. Or perhaps not so simply: Sotavalta not only had perfect pitch but had trained himself to distinguish fundamental notes from overtones, avoiding, as he put it, the “soprano-tenor error.” Tone-deaf people like me resort to microphones, recorders, and other bits of electronic assistance.

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