Loads and propulsive efficiency of a flexible airfoil performing sinusoidal deformations

This paper presents the application of state-space airloads theory to a flexible airfoil performing sinusoidal deformations at high Reynolds numbers. Given the two-dimensional motion of a flexible airfoil, we derived the closed forms for the propulsive force, lift force, generalized forces of pitching and bending as functions of reduced frequency k, dimensionless wavelength z  , and dimensionless amplitude A/(2b)A/(2b). We also calculate the power required to perform this sinusoidal deformation and the propulsive efficiency. Our results show a positive, time-averaged propulsive force for all k>k0=π/zk>k0=π/z, which is when the wave speed is greater than the moving speed. At k=k0k=k0, which is when the moving speed reaches the wave speed, the motion reaches a steady-state with all forces being zero. When k