A theory for the lateral response of airplanes to random atmospheric turbulence

John M. Eggleston
May 1957

The lateral motions of an airplane flying through continuous random isotropic turbulence have been derived in terms of (1) the transfer functions relating the motion in the various degrees of freedom to the yawing moment, rolling moment, and side force, (2) the statistical forces and moments at the center of gravity due to gust velocities acting on the lifting surfaces of the airplane, and (3) the power spectra of the three orthogonal components of gust velocity acting on the airplane along the flight path. The method takes into account the random variations of gust velocity across the span and along the fuselage. Solutions are given in the form of equations relating the power spectra of the angular motions of the airplane to the power spectra of the gust velocities. Three airplanes of different size are used to demonstrate the method, illustrate characteristic trends, and exhibit some simplifications possible in the calculations. For these airplanes the effects of horizontal gusts (that is, gusts parallel to the flight path) and side forces due to gusts on the airplanes were found to be negligible. By using one of the example airplanes, a comparison is drawn between the present theory and several less comprehensive theories for calculating the effect of gusts on wings of finite span and the effect of gusts on the motions of the complete airplane.

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