Shape, flapping and flexion: wing and fin design for forward flight

Both kinematics and morphology are critical determinants of performance in flapping flight. However, the functional consequences of changes in these traits are not yet well understood. Traditional aerodynamic studies of planform wing shape have suggested that high-aspect-ratio wings generate more force per area and perform more efficiently than low-aspect-ratio wings, but these analyses may neglect critical components of flapping flight such as unsteady fluid dynamics and wing or fin flexion. In this paper, we use an unsteady potential flow analysis that incorporates wing flexion to test predictions of optimal wing shape under varying degrees of unsteady motion and wing flexion. We focus on forward flapping flight and examine the effects of wing/fin morphology and movements on thrust generation and efficiency. We test the model by comparing our predictions with kinematic data derived from the aquatic flight of the ratfish Hydrolagus colliei. Our analyses show that aspect ratio and the proportion of area in the outer one-fifth of the wing can characterize wing shape in terms of aero- or hydrodynamic performance. By comparing the performance of wings that vary in these two parameters, we find that traditional predictions of optimal wing shape are valid only under limited circumstances (when flapping frequency is low, wings are stiff or wings are tapered at the tips). This indicates a complex relationship between locomotor traits and performance and helps explain the diversity of wing kinematics and morphologies observed in nature.