A flight mechanics-based justification of the unique range of Strouhal numbers for avian cruising flight

Abstract

In this paper, analytical expressions for cycle-averaged aerodynamic forces generated by flapping wings are derived using a force model and flapping kinematics suitable for the forward flight of avian creatures. A strip theory-based formulation is proposed and the analytical expressions are found as functions of the amplitude of twist profile, mean twist angle, the flow separation point on the upper surfaces of the wings, and Strouhal number. Numerical results are obtained for a rectangular planform as well as for a representative avian wing planform. Utilizing these results, it is shown that there exists a narrow Strouhal number range where cycle-averaged net thrust, lift, and lift to drag ratio are optimal for a given flow pattern over the upper surfaces of the wings. This narrow Strouhal number range, found to be between 0.1 and 0.3, corresponds to the cruising range for a large number of avian creatures, as documented in current literature. An explanation, based on force constraints and local optimization in aerodynamic force generation, is provided for the unique range of Strouhal numbers utilized in avian cruising flight. The results and the approach outlined in the paper can be utilized to design efficient bio-inspired flapping vehicles.