Eifect of Steady Rolling on Longitudinal and Directional Stability

The effects of steady rolling on the longitudinal and directional stability of aircraft have been studied theoretically. Simplifying assumptions have been made with regard to the longitudinal and lateral motions of the airplane in order to obtain a solution which shows the principal effects of the rolling motion. Rolling has been found, to cause instability if the directional and longitudinal stabilities are different when the rolling frequency exceeds the lower of the pitching and yawing natural frequencies of the nonrolling airplane. This instability lasts only during the time the airplane is rolling and would not, therefore, affect the normal flight of an airplane. In the case of airplanes of short span and high density, carrying most of their weight in their fuselages, and flying at hlgh altitudes, this instability might cause dangerous attitude changes during rapid rolls. If the directional and longitudinal stabilities are about equal, the instability due to rolling will not occur. If the rate of roll exceeds both the pitching and yawing natural frequencies of the nonrolllng aircraft, the aircraft will be stable. A continuously rolling aircraft will be stable in this case even when the no__rolllng aircraft has a certain amount of instability about one axis. Applications of these conclusions to rolling airplanes and missiles are discussed