Propulsive efficiency of spatiotemporally asymmetric oscillating appendages at intermediate Reynolds numbers.

Many organisms use flexible appendages for locomotion, feeding, and other functional behaviors. The efficacy of these behaviors is determined in large part by the fluid dynamics of the appendage interacting with its environment. For oscillating appendages at low Reynolds numbers, viscosity dominates over inertia, and appendage motion must be spatially asymmetric to generate net flow. At high Reynolds numbers, viscous forces are negligible and appendage motion is often also temporally asymmetric, with a fast power stroke and a slow recovery stroke; such temporal asymmetry does not affect the produced flow at low Reynolds numbers. At intermediate Reynolds numbers, both viscous and inertial forces play non-trivial roles---correspondingly, both spatial and temporal asymmetry can strongly affect overall propulsion. Here we perform experiments on three robotic paddles with different material flexibilities and geometries, allowing us to explore the effects of motion asymmetry (both spatial and temporal) on force production. We show how a flexible paddle's time-varying shape throughout the beat cycle can reorient the direction of the produced force, generating both thrust and lift. We also evaluate the propulsive performance of the paddle by introducing a new quantity, which we term "integrated efficiency". This new definition of propulsive efficiency can be used to directly evaluate an appendage's performance independently from full-body swimming dynamics. Use of the integrated efficiency allows for accurate performance assessment, generalization, and comparison of oscillating appendages in both robotic devices and behaving organisms. Finally, we show that a curved flexible paddle generates thrust more efficiently than a straight paddle, and produces spatially asymmetric motion---thereby improving performance---without the need for complex actuation and controls, opening new avenues for bioinspired technology development.