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Moving Forward

Steven Vogel

Principles of Animal Locomotion. R. McNeill Alexander. xii + 371 pp. Princeton University Press, 2003. $49.50.

For a long time, the study of animal locomotion was a stepchild, a subject that got trapped in an interdisciplinary crevice as science became more fragmented and specialized. Serious work was scarce during the 250 years that followed the appearance of Giovanni Alfonso Borelli's De Motu Animalium in 1680. That's no longer the case. About 1930, at the University of Cambridge, zoologist James Gray initiated a renaissance that has in the years since become ever broader conceptually, phylogenetically and geographically.

Progress in the modern era has resulted from integration—of muscle physiology, kinematic analysis, solid and fluid mechanics, and functional morphology; of the efforts of biologists and physical scientists to work together; of new laboratory techniques and powerful computers. Little has turned out to be simple: The structural materials of animals are complexly flexible and anisotropic; muscles have proved to be most peculiar and diverse engines; tasks are awkwardly difficult to define and describe. And, of course, the overall anatomical arrangement of most creatures is rather complicated, given that they lack wheels and axles (or propellers and drive shafts), at least on the macroscopic scale, and must therefore move their legs (or wings or fins) back and forth rather than rotating them. Animals commonly minimize the attendant inertial work by storing energy for the short term, most often with elastic materials but occasionally in the form of gravitational potential energy, as when we walk.

Remarkably, rules continue to emerge—maybe not as laws of the kind on which physics is built, but as quantitatively predictive understandings that go far beyond mere statistical summaries and extrapolations. The central figure of the era has been R. McNeill Alexander of the University of Leeds, recently retired after a career that can only be described as astonishing, given his output of books, papers, students and catalytic influence. We now have his most general look at the subject in Principles of Animal Locomotion, a remarkable volume that simply must be read by anyone contemplating any kind of work on, or in imitation of, muscle-driven motion. This is no ordinary summing up but rather a synthesis, an explication of principles—the title needs no disclaimer.

Locomotion takes a host of forms—flying, swimming, burrowing, and terrestrial gaits both familiar and obscure. Muscle-powered animals come in a wide range of sizes and move through a variety of media, so they face opposition from a diverse mix of physical agencies. And we can judge their outputs by no simple or even single measure—an animal's fitness may depend on maximal or sustainable speed, acceleration, cost of transport relative to either distance or time, or some combination of these. Design criteria (if one can use the word design in this context without raising hackles) are more diverse and less self-evident than in vehicles of human devising.

Alexander doesn't hide the multidimensional complexity of the subject, but he doesn't hide behind it either. The strongest features of this book are the insights into underlying principles that come from his consideration of just this diversity of devices. In addition, he gives perceptive suggestions for future investigations and guidance as to the degree of confidence one should place in past work. His approach combines recognition of the range of relevant physical phenomena with sensitivity to the peculiar nature of success in this context.

Biology makes ever-increasing use of scaling arguments, essentially the notion that the size range of animals that do the same thing can be pressed into service as an analytic tool. This book provides as strong a case for the power of this approach as one will find. Size versus cost of different modes of transport, the relationships between gait transition speeds and animal size, the relative importance of force and work in determining the cost of locomotion for animals differing in size—scaling pervades every page.

Related to scaling are dimensionless numbers, devices less familiar to biologists. Reynolds number, the ratio of inertial to viscous forces, takes its proper place for swimming and flying. We see how the Strouhal number, a dimensionless frequency, helps us understand the ubiquitous reciprocation of diverse appendages. Even people used to these handy formulations will be surprised at the variety of applications for which the Froude number, the ratio of inertial to gravitational force, provides insight. Beyond giving the practical speed limit for surface ships, it defines the transition point between walking and trotting and between trotting and galloping—its application to animal locomotion being one of Alexander's many specific contributions. It even applies to the crawling of caterpillars and maggots.

Useful work on animal movement ranges from theoretical advances of daunting mathematical complexity to descriptions of morphology that are almost devoid of quantification. Principles of Animal Locomotion lies in the middle of that range, but with a peculiarity that needs a note. The mathematical level here couldn't be simpler—an occasional derivative and nothing that might challenge a typical science major. But the level of the quantitative reasoning would be daunting to the same undergraduate. And the presentation is severely distilled, covering a lot of ground at no trivial level of sophistication. And, like many books about organisms, this one presupposes a range of prior knowledge of biology. Alexander makes relatively few formal demands, but the reader has to call up a lot of casually acquired observations. In short, one should read it in short bouts separated by intervals of contemplation. The reader should be a participant—and can indeed be a participant where the basic subject lies so close to personal experience.

This book bears comparison with James Gray's summing up, Animal Locomotion, published in 1968—especially because Alexander, educated at Cambridge when Gray was still active, stands as his most direct successor. Gray recounts, in still-useful form, the varieties of ways animals get around, and although he outlines the physical mechanisms that seem to be involved, he strays only minimally from biology. Alexander, by contrast, achieves a vastly richer integration with physics and engineering. In addition, he brings to bear decades of recent progress in muscle physiology. The older book describes, the newer one synthesizes.—Steven Vogel, Biology, Duke University

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