Stability derivatives for a flapping wing MAV in a hover condition using local averaging

Abstract-We present an analytically tractable method of obtaining the stability derivatives for a flapping wing MAV, in the vicinity of a hover condition, using local averaging techniques. The analytical stability derivatives are obtained for the longitudinal equations of motion, under the constraint of symmetrical flapping with respect to the longitudinal axis of the central body. The analysis results in an eigenvalue structure consisting of two stable subsidence modes and one unstable oscillatory mode. Analysis shows a modal structure consistent with the standard VTOL structure. The unstable oscillatory mode is close to the imaginary axis, consistent with the modal structure of hovering helicopters. Scaling properties are consistent with previous numerical results. The method does not require numerically intensive calculations or frequency response analysis to gain an approximation of the stability of a potential flapping wing MAV in the vicinity of a hover condition.