Lunate-tail swimming propulsion as a problem of curved lifting line in unsteady flow. Part 1. Asymptotic theory

Abstract

The asymptotic theory of a high-aspect-ratio wing in an incompressible flow is generalized to an oscillating lifting surface with a curved centreline in the domain where the reduced frequency based on the half-span is of order unity. The formulation allows applications to lightly loaded models of lunate-tail swimming and ornithopter flight, provided that the heaving displacement does not far exceed the mean wing chord. The analysis include the quasi-steady limit, in which the crescent-moon wing problem considered earlier by Thurber (1965) is solved and several aerodynamic properties of swept wings are explained. Among the important three-dimensional and unsteady effects are corrections for the centreline curvature and for the spanwise components of the locally shed vortices. Comparison of the lift distributions obtained for model lunate tails with data computed from the doublet-lattice method (Albano & Rodden 1969) lends support to the asymptotic theory.