Unified physics theory explains animals' running, flying and swimming

e. "It doesn't matter whether the animal has eight legs, four legs, two, even if it swims with no legs."

First conceived by Bejan and published in 1996, the constructal law arises from the basic principle that flow systems evolve so as to minimize imperfections -- energy wasted to friction or other forms of resistance -- such that the least amount of useful energy is lost.

The theory applies to virtually everything that moves, Bejan said. For example, his earlier work has examined how the law explains traffic flows, the cooling of small-scale electronics and river currents.

The researchers, funded by the National Science Foundation, report that the constructal law predicts universal relationships between animals' body mass and speed, as well as the frequency and force of the strides, beats or undulations that propel their bodies forward.

"Running, swimming and flying occur in vastly different physical environments and, likewise, involve quite different body mechanics," Bejan said of the new application of constructal law. "Nonetheless, there are strong convergences in certain functional characteristics of runners, swimmers and fliers."

For example, the stride frequency of running vertebrates bears the same relationship to the animals' mass as does the rate at which fish swim. Similarly, the velocity of runners conforms to the same principles as the speed of birds in flight.

The force generated by the muscular "motors" of runners, swimmers and fliers also conforms with surprisingly little variation to a universal value dependent only on muscle mass, Marden said. Why this relationship should be so had remained mysterious, he said.

In the absence of a unifying theory for such design features, biologists had looked to mechanical constraints for an answer, the researchers said. Many authors have suggested that effects of scale in locomotion stem from biomechanical safety factors: the need to avoid premature failu

Contact: Kendall Morgan
Duke University

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