Asymptotic Aerodynamic Theory of Oscillating Rotary Wings in Axial Flight

An asymptotic aerodynamic theory of oscillating rotary wings in axial flight is developed. The theory is based on the following small parameters: (i) the ratio of the average velocity across the rotor's disk to the velocity of the rotor's edge; (ii) the ratio of the velocity of a blade's oscillatory motion to the average velocity across the rotor disk; (iii) the ratio of a blade's chord to the rotor radius; and (iv) the ratio of the frequency of the rotor rotation to the characteristic frequency of a blade's oscillations. In the first significant approximation, the problem of computing unsteady aerodynamic loads on the blades is reduced to solving a set of linear integral equations which resemble those of the classical lifting-line theory of Prandtl [NACA Report 116, 1921]. It is shown that under certain restricting conditions which are formulated in the text, the solution of this set of equations recovers the well-known results of Theodorsen [NACA Report 496, 1935] and of Loewy [J. Aero. Sci., 24 (1957), pp. 81-92].