Efficiency characteristics of crescent-shaped wings and caudal fins

Caudal (tail) fins of fish and aquatic mammals that cruise long distances, and wings of certain birds, often have the shape of a crescent moon. This study investigates how the crescent shape contributes to the traveling performance of these animals. A steady-flow theory (Maskew, 1982) that correctly models the trailing wake was used to analyze lifting surface efficiency, which is dependent on the level of induced (or vortex) drag for a given lift and span of the lifting surface. This analysis shows that backward curvature of a wing improves induced efficiency to a value greater than that of the flat untwisted wing of elliptical shape considered optimal in classical wing theory (Prandt, 1921 and Munk, 1921). This increase of induced efficiency results from the nonplanar trailing vortex sheet produced by the crescent-shaped wing at a given angle of attack.