Mechanical control of swimming speed: stiffness and axial wave form in undulating fish models

Abstract

The purpose of this study was to investigate the mechanical control of speed in steady undulatory swimming. The roles of body flexural stiffness, driving frequency and driving amplitude were examined; these variables were chosen because of their importance in vibration theory and their hypothesized functions in undulatory swimming. Using a mold of a pumpkinseed sunfish Lepomis gibbosus, we cast three-dimensional vinyl models of four different flexural stiffnesses. We swam the models in a flow tank and powered them via the input of an oscillating sinusoidal bending couple in the horizontal plane at the posterior margin of the neurocranium. To simulate the hydrodynamic conditions of steady swimming, drag and thrust acting on the model were balanced by adjusting flow speed. Under these conditions, the actuated models generated traveling waves of bending. At steady speeds, the motions of the ventral and lateral surfaces of the model were video-taped and analyzed to yield the following response variables: tail-beat amplitude, propulsive wavelength, wave speed and depth of the trailing edge of the caudal fin. Experimental results showed that changes in body flexural stiffness can control propulsive wavelength, wave speed, Froude efficiency and, in consequence, swimming speed. Driving frequency can control tail-beat amplitude, propulsive wavelength, Froude efficiency, relative rate of working and, in consequence, swimming speed. Although there is no significant correlation between rostral amplitude and swimming speed, rostral amplitude can control swimming speed indirectly by controlling tail-beat amplitude and relative power. Compared with live sunfish using undulatory waves at the same speed, models have a lower Froude efficiency. On the basis of the mechanical control of swimming speed in model sunfish, we predict that, in order to swim at fast speeds, live sunfish increase the flexural stiffness of their bodies by a factor of two relative to their passive body stiffness.