A blade-element analysis for lifting rotors that is applicable for large inflow and blade angles and any reasonable blade geometry

Abstract : Simple approximate s9lutions are derived for the relationships between the rotor thrust and flight-path velocity components and the rotor blade angle, torque, and in-plane forces. These approximate solutions, based upon the assumption of a triangular distribution of blade circulation and a parabolic variation of blade-element profile drag with lift, are sufficiently accurate for preliminary calculations and the determination of the equilibrium angle of attack and lateral tilt of the tip-path plane. A set of more exact blade-element equations is then derived giving the relations between the thrust and flight path velocity components and the equilibrium blade angles, torque, and in-plane forces and moments. Neither the blade-element nor the approximate solutions are dependent upon the usual approximations that the inflow angle and blade angle of the blade elements are small angles. Thus the present equations should be useful for convertaplane as well as helicopter calculations. It appears that nonlinear blade twist may be desirable for a convertaplane rotor in order to obtain useful propeller efficiencies. Therefore, the blade-element equations have been arranged so that any reasonable distribution of blade twist may be used. Also, the equations were set up in terms of an arbitrary blade-chord distribution since it was found that the use of the actual blade-chord distribution and the elimination of the usual assumption that the blade airfoil extended inboard to the axis of rotation largely eliminated the necessity for the usual reverse-flow corrections.