A Theory of the Response of Airplanes to Random Atmospheric Turbulence

Abstract

A theory is given for the aerodynamic forces and moments which act on an airplane as a result of flight through turbulent air, and for the associated dynamic response of the airplane. I t starts with Ribner's spectral theory of the phenomenon, and extends it to a specific formulation of the forces and moments. This is achieved by expanding the downwash field of a single spectral component in a power series in the neighborhood of the airplane. Spanwise variations of the gust intensity are included, and the wing can be treated by any applicable lifting line or surface theory. The final expressions give the forces and moments in terms of a set of aerodynamic derivatives like those used in stability and flutter analysis. Consideration of the equations of motion, and the airplane transfer functions, shows that the final response quantities of interest can be obtained in the form of one-dimensional power spectra. Tables and graphs of the relevant input spectra are given.