Interpolation of aerodynamic damping of lifting rotors in forward flight from measured response variance

With the necessity of experimentally measuring the aerodynamic derivatives of lifting rotors in forward flight, it becomes desirable for reasons of parametric resonance to measure the variance data of the response to white noise inputs, and then to interpolate with the numerically computed variance values for different assumed values of the damping parameter or the inertia number. Accordingly, methods are developed to compute directly the blade response variance matrix up to high rotor advance ratios for a series of inertia numbers. Numerical results refer to a rigid blade flapping model with an elastically restrained flapping hinge at the rotor centre. Different combinations of the advance ratio, tip-loss factor, flapping restraint parameter and inertia number are included. The white noise excitation is treated without and with input modulation, the latter case including azimuthwise blade input variation. The mean square response study of the model shows that up to an advance ratio of the order of 0·3 and at conventional values of the inertia number the perturbation approach is satisfactory. The numerical scheme, in addition to solving directly the response variance equations which are similar in structure to the original blade dynamic equations, makes use of the fact that the variable part of system parameter functions are independent of the inertia number. Compared to earlier studies the methods therefore offer significant saving in machine time. Numerical results pertaining to previously proposed experimental and analytical models show excellent agreement.