Effect of Flexion Ratio on the Stable Formations and Propulsive Performance of Schooling Non-Uniformly Flexible Hydrofoils

Schooling fish swim with fins composed of stiff leading-edges and compliant trailing-edges, that is, non-uniformly flexible fins. We aim to better understand the influence of non-uniform flexibility on the flow interactions that occur while schooling. We present new experiments using a pair of hydrofoils, each composed of a rigid leading section and flexible trailing section where the ratio of the rigid section length compared to the foil chord length defines the flexion ratio. Prior research identified optimal flexion ratios that maximize propulsive efficiency for constrained pitching hydrofoils. Subsequent studies demonstrated that constrained flexible hydrofoils in an in-line formation receive efficiency benefits through collective interactions. However, the influence of the flexion ratio on the propulsive performance and hydrodynamic stability in self-organizing hydrofoil schools remains largely unexplored. We examine pairs of freely-swimming hydrofoils using air-bearing supported platforms. Detailed measurements of swimming speeds, cost of transport, and formation stability are acquired for multiple flexion ratios across different phase synchronizations and pitch amplitudes. Experimental results indicate that tailoring the flexion ratio notably reduces the cost of transport without adversely affecting the swimming speed of schools. These findings highlight the critical role of flexion ratio in facilitating beneficial fluid-mediated interactions among schooling foils.