Estimate of derivatives variance 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 determination of aerodynamic coefficients of high-speed re-entry vehicles (RVs) 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 $D\{m_x^\alpha \}$, $D\{m_x^\beta \}$ of derivatives of disturbing aerodynamic rolling moment coefficient $m_x$ with respect to attack and yaw angles versus governing parameters. An analytical integral solution of a set modeled 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 $m_x^\alpha$, $m_x^\beta$ at $3\sigma\{m_x^\alpha \}$ versus a degree of correlation dependence for the modeled autocorrelated function of irregular surface distortions of a sharp $\thicksim 10^o$-cone is provided.