Running, hopping and trotting: tuning step frequency to the resonant frequency of the bouncing system favors larger more compliant animals

A long-lasting challenge in comparative physiology is to understand why the efficiency of the mechanical work done to maintain locomotion increases with body mass. It has been suggested that this is due to a more elastic step in larger animals. Here, we show in running, hopping and trotting animals, and in human running during growth, that the resonant frequency of the bouncing system decreases with increasing body mass and is, surprisingly, independent of species or gait. Step frequency roughly equals the resonant frequency in trotting and running, whereas it is about half the resonant frequency in hopping. The energy loss by elastic hysteresis during loading and unloading the bouncing system from its equilibrium position decreases with increasing body mass. Similarity to a symmetrical bounce increases with increasing body mass and, for a given body mass, seems to be maximal in hopping, intermediate in trotting and minimal in running. We conclude that: (1) tuning step frequency to the resonant frequency of the bouncing system coincides with a lower hysteresis loss in larger, more-compliant animals; (2) the mechanism of gait per se affects similarity with a symmetrical bounce, independent of hysteresis; and (3) the greater efficiency in larger animals may be due, at least in part, to a lower hysteresis loss.