Static Thrust Analysis for Helicopter Rotors and Airplane Propellers

Abstract

This paper presents a solution for the relation between the blade angle, thrust, and torque coefficients of a helicopter rotor in hovering flight. This analysis presents the case wherein the induced velocity at a given radius, rt is set up as a function of the thrust at that radius and a semiempirical constant, k\, is introduced to account for the viscous shearing forces in the flow. Equations have been derived which yield, upon graphical integration, the thrust and torque for the general case of blades with any solidity, twist, or taper. The solutions for the integrals of the equations for the special case of a constant chord, untwisted blade are also presented. The results apply to a helicopter operating in or out of ground effect, and values of the semiempirical constant, ki, which have been calculated from experimental data, are presented for the entire range. This method gives values of the thrust and torque coefficients which are in good agreement with the available experimental data. Since the static thrust case of an airplane propeller is identical to that of a helicopter rotor in hovering flight, this method can be used for the calculation of the static thrust and torque of modern variable pitch propellers.