Aerodynamic stability modes of low aspect ratio wings

Abstract

An incomplete understanding of the unique aerodynamic flight regime of low aspect ratio (LAR) wings has slowed the development of Micro Aerial Vehicles (MAVs) as the stability characteristics are not well predicted. In this research, a complete dynamic model for canonical flat plate (0% camber) wings is developed based on experimental data for static and damping stability derivatives at a Reynolds number of 7.5×10; the latter results represent the first study aimed at estimating the rate derivatives for LAR wings at low Reynolds numbers. Using this model, the nonlinear equations of motion are numerically integrated and compared with the initial condition response of a linear model. These results show good agreement and indicate that the nature of the loading created by roll stall results in purely aerodynamic lateral modes which, unlike conventional aircraft, are not attributed to geometric features such as the vertical tail. When the angle of attack is held constant, a divergent Dutch roll-type mode is observed which is manifested by divergent, high amplitude perturbations in sideslip, bank angle, roll rate and yaw rate; in the presence of prescribed angle of attack oscillations at similar frequencies to the natural frequencies of the pure lateral response, the nature of the mode fundamentally changes. The interactions between the time histories of angles of attack and sideslip skews the evolution of the roll moment and causes the bank angle φ to drift away from its equilibrium value. This represents a stability mode which is specific to LAR wings, and is referred to as the roll resonance mode; the initial condition response of the linear system does not represent this behavior although a linear time variant (LTV) model in which the Lβ is updated at every time step is seen to capture the main features of the motion. The significance of these purely aerodynamic stability modes for LAR wings suggests a cause for the instabilities experienced by flying MAVs, as these modes must be accounted for when sizing passive or active stabilization features.