Scaling of Airplane Dynamic Response to Stochastic Gusts

This paper studies the scaling of airplane dynamic response to stochastic wind gusts, with focus on the relationship between airplane size and airspeed variations. The results have applications in the design and control of small-scale aircraft for robustness with respect to turbulence. Using linearized equations of motion and the Dryden model of gusts, the paper presents analytical and numerical scaling laws for the phugoid natural frequency and damping ratio, and the variances of the airspeed and flight-path angle. The results show that small aircraft are more susceptible to high frequency gusts, that the phugoid damping ratio does not depend directly on airplane size, that the airspeed and flight-path angle variances can be parameterized by the ratio of the phugoid natural frequency to a characteristic turbulence frequency, and that the coefficient of variation of the airspeed decreases with increasing airplane size. Numerical examples validate the results using models of 11 different airplanes, particularly the NASA Generic Transport Model, a hypothetical transport aircraft similar to a Boeing 757, and the NASA T2 subscale jet transport, an operational 5.5% scale model of the Generic Transport Model.