Big and slow: large-amplitude motions for highly efficient swimming*

When a swimmer flaps its appendages, it adds momentum to the surrounding fluid, which, by action/reaction, propels the swimmer. When the propelling thrust balances the swimmer’s drag, the swimmer cruises at a constant speed. A swimmer can add a fixed amount of momentum to the fluid in two ways: by accelerating a small mass of fluid to a high speed, or by accelerating a large mass of fluid to a low speed. In other words, a swimmer can maintain a given speed using small and fast motions, or big and slow motions. A recent scaling theory suggests that big and slow motions are preferred for high propulsive efficiency. Here, we report experiments on large-amplitude heaving and pitching foils of high propulsive efficiency. Direct force and power measurements are understood in the context of the scaling theory, and we use flow visualization to further understand our findings.