Performance variation due to stiffness in a tuna-inspired flexible foil model

Tuna are fast, economical swimmers in part due to their stiff, high aspect ratio caudal fins and streamlined bodies. Previous studies using passive caudal fin models have suggested that while high aspect ratio tail shapes such as a tuna's generally perform well, tail performance cannot be determined from shape alone. In this study, we analyzed the swimming performance of tuna-tail-shaped hydrofoils of a wide range of stiffnesses, heave amplitudes, and frequencies to determine how stiffness and kinematics affect multiple swimming performance parameters for a single foil shape. We then compared the foil models' kinematics with published data from a live swimming tuna to determine how well the hydrofoil models could mimic fish kinematics. Foil kinematics over a wide range of motion programs generally showed a minimum lateral displacement at the narrowest part of the foil, and, immediately anterior to that, a local area of large lateral body displacement. These two kinematic patterns may enhance thrust in foils of intermediate stiffness. Stiffness and kinematics exhibited subtle interacting effects on hydrodynamic efficiency, with no one stiffness maximizing both thrust and efficiency. Foils of intermediate stiffnesses typically had the greatest coefficients of thrust at the highest heave amplitudes and frequencies. The comparison of foil kinematics with tuna kinematics showed that tuna motion is better approximated by a zero angle of attack foil motion program than by programs that do not incorporate pitch. These results indicate that open questions in biomechanics may be well served by foil models, given appropriate choice of model characteristics and control programs. Accurate replication of biological movements will require refinement of motion control programs and physical models, including the creation of models of variable stiffness.