The Response of an Airplane to Random Atmospheric Disturbances

The statistical approach to the gust-load problem which consists in considering flight through turbulent air to be a stationary random process is extended by including the effect of lateral variation of the instantaneous gust intensity on the aerodynamic forces. The forces obtained in this manner are used in dynamic analyses of rigid and flexible airplanes free to move vertically, in pitch, and in roll. The effect of the interaction of longitudinal, normal, and lateral gusts on the wing stresses is also considered. The method of analyzing the rigid-body motions is similar to that used for analyses of the dynamic stability of airplanes, in that the equations of motion are referred to stability axes and expressed in terms of conventional stability derivatives. The method of analyzing the dynamic effects of structural flexibility consists in an extension of a numerical-integration approach to the static aeroelastic problem and is in a form which offers the possibility of calculating divergence and flutter speeds with relatively little additional effort. The mean-square values, correlation functions, and power spectra of some of the aerodynamic forces required in this type of analysis are calculated for one special correlation function of the atmospheric turbulence. It is shown, for instance, that if the span is relatively large compared with the integral scale of turbulence, the mean- square lift and root bending moment directly due to the gust are substantially reduced when the differences in instantaneous intensity of the turbulence along the span are taken into account. However, if the motions of the airplane are taken into account the mean-square root bending moment may be increased as a result of these differences. Also, the mean-square pitching moment is shown to be substantially increased if the tail length is relatively large compared with the scale of turbulence. Finally, the wing stresses due to longitudinal, normal, and lateral gusts are shown to be statistically independent under certain conditions