Rational New Approach to the Response of an Aircraft Encountering Atmospheric Turbulence

Abstract

Based on the technique of expanding a random function in terms of statistically orthogonal random functionals, a method is developed for analyzing the response of an aircraft to a stationary, weakly non-Gaussian atmospheric turbulence. The atmospheric turbulence is characterized through the correlation functions, and no other ad hoc assumptions are necessary. The expansion kernels enable us to construct various probability density functions of interest—e.g. , the joint probability density function of the response velocity and acceleration. To illustrate the method and demonstrate some of the effects due to the non-Gaussian nature of atmospheric turbulence, the simple case of the plunging motion of a rigid aircraft in a turbulent gust is presented in detail. It is found that even when the aircraft responds as a linear system, a nearly Gaussian turbulent gust can render an aircraft response highly non-Gaussian.