Models and the scaling of energy costs for locomotion.

To achieve the required generality, models designed to predict scaling relationships for diverse groups of animals generally need to be simple. An argument based on considerations of dynamic similarity predicts correctly that the mechanical cost of transport for running [power/(body mass x speed)] will be independent of body mass; but measurements of oxygen consumption for running birds and mammals show that the metabolic cost of transport is proportional to (body mass)-0.32. Thus the leg muscles seem to work more efficiently in larger animals. A model that treats birds as fixed wing aircraft predicts that the mechanical power required for flight at the maximum range speed will be proportional to (body mass)1.02, but the metabolic power is found to be proportional to (body mass)0.83; again, larger animals seem to have more efficient muscles. A model that treats hovering hummingbirds and insects as helicopters predicts mechanical power to be approximately proportional to body mass, but measurements of oxygen consumption once again show efficiency increasing with body mass. A model of swimming fish as rigid submarines predicts power to be proportional to (body mass)0.5 x (speed)2.5 or to (body mass)0.6 x (speed)2.8, depending on whether flow in the boundary layer is laminar or turbulent. Unfortunately, this prediction cannot easily be compared with available compilations of metabolic data. The finding that efficiency seems to increase with body mass, at least in running and flight, is discussed in relation to the metabolic energy costs of muscular work and force.