A theoretical study of helicopter rotor noise

Abstract

A comprehensive theoretical study of the problem of helicopter rotor noise radiation is presented. The theory includes blade slap, rotation noise and vortex noise effects. Peak spectral levels over the “vortex noise” region are shown to be due to the higher harmonics of the rotational noise. An exact theoretical expression for the noise radiation has been used as the basis for the development of a comphrehensive computer program to calculate helicopter noise at any field point, including all effects of fluctuating airloads and all possible rigid and flexible blade motions. Under very reasonable approximations an analytic expression has been found for the sound field far from the helicopter. Computations based on this expression have also been made. The results show that it is the very high harmonics of the loading which contribute to the important harmonics of the sound field. For instance, calculation of the tenth harmonic of a four-bladed rotor requries a knowledge of loading harmonics up to the sixtieth. Details of such loadings are not available from theory or experiment. Rotor aerodynamic loadings have therefore been reviewed in detail and empirical harmonic decay laws derived. Loading phases appear to be best described as random, and this introduces simplification in the theory, together with the necessity for definition of a correlation length. Results of a parameter study show trends in agreement with experiment, both for overall levels and for spectrum shape. Sound at the higher harmonics is basically proportional to thrust times disc loading times tip velocity squared. For the lower harmonics the dependence on tip velocity is to the 2B power where B is the number of blades. The effect of forward speed is to increase the sound radiated forward and decrease that radiated aft, causing a difference of as much as 20 dB for the second and third harmonics at a forward Mach number of 0·25. The overall sound directionality pattern is found to have a minimum slightly above the plane of the disc and a broad maximum about 20° below. The effects of both the near field and blade motion effects are found to be small. The theory generally shows fair agreement with experiment for overall levels and good agreement for trends, and should therefore be of direct use for design trade-off studies to minimize noise in future helicopters.