The stability of rotor blade flapping motion at high tip speed ratios

Abstract

Summary. In this Report a method of obtaining the transient solution of the helicopter rotor blade flapping motion is developed and the effective damping of the motion determined for tip speed ratios up to unity and above. When reverse flow over the retreating blade is ignored, it is found that the motion becomes unstable in the region of tip speed ratios of [the square root of] 2 for values of inertia number up to 2. However when the equation of motion is modified to take into account the reverse flow over the retreating blade, the flapping motion becomes unstable at tip speed ratios between 2.2 and 2.8. Use is made of a digital computer in performing the numerical processes necessary to the method, which could be applied to solving other linear differential equations with periodic coefficients.