Hydrodynamic advantages of a low aspect-ratio flapping foil

A high aspect-ratio foil is known to be advantageous in terms of both thrust and efficiency in flapping propulsion. However, many species of fish have evolved a low aspect-ratio hydrofoil, which naturally leads one to search for its physical advantages in locomotion. Here we study the flow physics of a hydrofoil in angular reciprocating motion with negligible free-stream velocity to reveal the effects of an aspect ratio on hydrodynamic performance. By establishing a scaling law for the thrust of a foil of general shapes and corroborating it experimentally, we find that the thrust of an angularly reciprocating foil is maximized at a low aspect ratio of 0.7 while hydromechanical efficiency continuously increases with an aspect ratio. This result suggests that a low aspect-ratio foil can improve thrust produced by the foil when they start from rest, but at the expense of efficiency.