Estimating variance of second-order derivatives of an aerodynamic rolling moment coefficient with respect to attack and yaw angles of a rotary body with small irregular surface distortions at supersonic flow

The paper is devoted to one of acute issues of determining aerodynamic properties of high-speed reentry vehicles (HSRV) of the rotary-body shape with small irregular surface distortions of a composite thermal protection coating, i. e. an issue of assessment of a scale of variance D{ mxαα },D{ mxββ },D{ mxαβ } of second-order derivatives of aerodynamic disturbance rolling moment coefficient mx with respect to attack and yaw angles α and β, respectively, at a zero spatial angle of attack. An approximate analytical integral solution of the posed problem for a rotary body with a given autocorrelated function of irregular distortions of its surface is obtained on the basis of Fourier expansion of the surface distortion and a method of differential locality hypothesis used to evaluate pressure variations. The obtained solution is qualitatively analyzed. A curve of practically ultimate values of mxαα,mxαβ,mxββ at 3σ{ mxαα } versus a degree of correlation dependence for the modeled autocorrelated function of irregular surface distortions of a sharp 10°-cone is provided.