Optimum Muscle Design for Oscillatory Movements

A simple model represents oscillatory movements such as many animals use for running, swimming or flight. A plate is oscillated in a fluid by a pair of muscles that exert the forces needed to overcome its inertia and hydrodynamic drag. The muscles have spring-like tendons. Empirically-based equations that take account of the force exerted by a muscle and the rate at which it is shortening are used to estimate the metabolic energy cost of the oscillation. The maximum shortening speed (νmax) of the muscles and the elastic compliance of their tendons are varied to find the optimum combination that minimizes metabolic cost. If hydrodynamic forces predominate (as in swimming), the cost is highly sensitive to muscle speed (which should be relatively high) but less sensitive to compliance. If inertial forces predominate (as in running) the cost is highly sensitive to tendon compliance, and less sensitive to muscle speed (which should preferably be low). The muscles that power the locomotion of various animals are discussed in the light of these conclusions.