Envelopes for Flight Through Stochastic Gusts

Abstract

This paper presents a technique to guarantee, with specified probability, that a steady flight state can be maintained when stochastic wind gusts act upon an airplane. The technique allows quantification of the probability that the plane leaves its flight envelope because of gusts, risking damage or loss of control. The paper presents linearized, time-invariant dynamic equations for the airplane with gust velocity as the input. It treats the gust velocity as a stationary random process and appends a coloring filter to the linearized airplane equations so that the input is Gaussian white noise. The paper analyzes the effect of this noise on the airplane’s dynamics, introducing the notion of stationary flight and a stationary flight envelope to guarantee, with specified probability, steady flight under such conditions. It presents a numerical example of a general aviation aircraft performing various steady flight maneuvers in moderate turbulence, showing substantial reductions in the steady flight envelope for some combinations of maneuvers, turbulence, and safety margins. It also shows how feedback control can enlarge the stationary flight envelope by alleviating gust loads but concludes that, for the aircraft and controller examined, actuator limitations hinder gust alleviation.