Comparing Models of Lateral Station-Keeping for Pitching Hydrofoils

Fish must maneuver laterally to maintain their position in schools or near solid boundaries. Unsteady hydrodynamic models, such as the Theodorsen and Garrick models, predict forces on tethered oscillating hydrofoils aligned with the incoming flow. How well these models predict forces when bio-inspired hydrofoils are free to move laterally or when angled relative to the incoming flow is unclear. We tested the ability of five linear models to predict a small lateral adjustment made by a hydrofoil undergoing biased pitch oscillations. We compared the models to water channel tests in which air bushings gave a rigid pitching hydrofoil lateral freedom. What we found is that even with no fitted coefficients, linear models predict some features of the lateral response, particularly high frequency features like the amplitude and phase of passive heave oscillations. To predict low frequency features of the response, such as overshoot and settling time, we needed a semiempirical model based on tethered force measurements. Our results suggest that fish and fish-inspired vehicles could use linear models for some aspects of lateral station-keeping, but would need nonlinear or semiempirical wake models for more advanced maneuvers.