Analysis of Wing Rock Due to Rolling Moment Hysteresis

Abstract

This paper examines the single-degree-of-freedom wing-rock dynamic characteristics due to the presence of hysteresis in the static rolling-moment coefficient with respect to the sideslip angle. Two simplified hysteresis cases are considered: one represents full hysteresis and the other represents partial hysteresis. The approach used for analyzing the problem is analytical, using the multiple-time-scales method. Using such an approach, approximate solutions for the wing-rock amplitudes and frequencies as functions of the hysteresis parameters are obtained. These analytical solutions, which lead to considerable insight into the aerodynamic hysteresis effect on wing rock, are demonstrated to be in good agreement with the numerical results. It is also shown that, unlike the case involving the nonhysteretic type of nonlinearity, in the presence of the hysteresis, wing rock can occur before the loss of the dynamic roll-damping derivative.