Analytical study of the subsonic wing-rock phenomenon for slender delta wings

Abstract

An analytic expression describing the aerodynamic roll moment has been obtained from the numerical simulation of wing rock. This expression is used in the equation governing the rolling motion of a delta wing around its midspan axis. The result is used to construct phase planes, which reveal the general global nature of wing rock—stable limit cycles, unstable foci, saddle points, and domains of initial conditions leading to oscillatory motion and divergence. An asymptotic approximation to the solution of the governing equation is obtained; this result provides expressions for the amplitudes and frequencies of limit cycles. The present analysis provides a penetrating global view of the wing-rock phenomenon.