Envelopes for Flight Through Stochastic Gusts

Abstract

probability, that a steady ight state can be maintained when stochastic wind gusts act upon an airplane. First we linearize the airplane dynamic equations and present them as a linear time invariant system with the airplane’s velocity and angular velocity as the state and gust velocity as the input. We then treat the gust velocity as a stationary random process and append the dynamics of a coloring lter to the linearized airplane equations so that the input is Gaussian white noise. We analyze the eect of the noise on the airplane’s dynamics, using the resulting equations to quantify the eects of stochastic wind gusts on an airplane’s steady ight envelope. During the analysis we introduce the notion of stationary ight and a stationary ight envelope to guarantee, within a specied probability, steady ight under such conditions. We also present a numerical example of a general aviation aircraft in steady level ight through moderate turbulence. In the example, the airplane’s cruise speed uctuates with a variance of 1.2 m 2 /s 2 and we show examples of stationary ight envelopes for this case.