Passive mechanical models of fish caudal fins: effects of shape and stiffness on self-propulsion

Fishes are found in a great variety of body forms with tail shapes that vary from forked tuna-like tails to the square-shaped tails found in some deep-bodied species. Hydrodynamic theory suggests that a fish's body and tail shape affects undulatory swimming performance. For example, a narrow caudal peduncle is believed to reduce drag, and a tuna-like tail to increase thrust. Despite the prevalence of these assertions, there is no experimental verification of the hydrodynamic mechanisms that may confer advantages on specific forms. Here, we use a mechanically-actuated flapping foil model to study how two aspects of shape, caudal peduncle depth and presence or absence of a forked caudal fin, may affect different aspects of swimming performance. Four different foil shapes were each made of plastics of three different flexural stiffnesses, permitting us to study how shape might interact with stiffness to produce swimming performance. For each foil, we measured the self-propelling swimming speed. In addition, we measured the forces, torques, cost of transport and power coefficient of each foil swimming at its self-propelling speed. There was no single 'optimal' foil exhibiting the highest performance in all metrics, and for almost all measures of swimming performance, foil shape and flexural stiffness interacted in complicated ways. Particle image velocimetry of several foils suggested that stiffness might affect the relative phasing of the body trailing edge and the caudal fin leading edge, changing the flow incident to the tail, and affecting hydrodynamics of the entire foil. The results of this study of a simplified model of fish body and tail morphology suggest that considerable caution should be used when inferring a swimming performance advantage from body and tail shape alone.