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The importance of the leading-edge sweep angle of propulsive surfaces used by unsteady swimming and flying animals has been an issue of debate for many years, spurring studies in biology, engineering, and robotics with mixed conclusions. In this work, we provide results from three-dimensional simulations on single-planform finite foils undergoing tail-like (pitch-heave) and flipper-like (twist-roll) kinematics for a range of sweep angles covering a substantial portion of animals while carefully controlling all other parameters. Our primary finding is the negligible 0.043 maximum correlation between the sweep angle and the propulsive force and power for both tail-like and flipper-like motions. This indicates that fish tails and mammal flukes with similar range and size can have a large range of potential sweep angles without significant negative propulsive impact. Although there is a slight benefit to avoiding large sweep angles, this is easily compensated by adjusting the fin’s motion parameters such as flapping frequency, amplitude and maximum angle of attack to gain higher thrust and efficiency.

Flapping flight and swimming are increasingly studied both due to their intrinsic scientific richness and their applicability to novel robotic systems. Strip theory is often applied to flapping wings, but such modeling is only rigorously applicable in the limit of infinite aspect ratio (A) where the geometry and kinematics are effectively uniform. This work compares the flow features and forces of strip theory and three dimensional flapping foils, maintaining similitude in the rolling and twisting kinematics while varying the foil A. We find the key influence of finite A and spanwise varying kinematics is the generation of a time-periodic spanwise flow which stabilizes the vortex structures and enhances the dynamics at the foil root. An aspect-ratio correction for flapping foils is developed analogous to Prandtl finite wing theory, enabling future use of strip theory in analysis and design of finite aspect ratio flapping foils.

The importance of the leading-edge sweep angle of propulsive surfaces used by unsteady swimming and flying animals has been an issue of debate for many years, spurring studies in biology, engineering, and robotics with mixed conclusions. In this work we provide results from an extensive set of three-dimensional simulations of finite foils undergoing tail-like (pitch-heave) and flipper-like (twist-roll) kinematics for a range of sweep angles while carefully controlling all other parameters. No significant change in force and power is observed for tail-like motions as the sweep angle increases, with a corresponding efficiency drop of only ≈ 2%. Similar findings are seen in flipper-like motion and the overall correlation coefficient between sweep angle and propulsive performance is 0.1-6.7%. This leads to a conclusion that fish tails or mammal flukes can have a large range of potential sweep angles without significant negative propulsive impact. A similar conclusion applies to flippers; although there is a slight benefit to avoid large sweep angles for flippers, this could be easily compensated by adjusting other hydrodynamics parameters such as flapping frequency, amplitude and maximum angle of attack to gain higher thrust and efficiency.

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