Bifurcation analysis of a flapping wing MAV in longitudinal flight

The subject of flapping wing Micro Air Vehicles (MAVs) has been an area of increasing interest, posing challenges in the fields of aerodynamics and vehicle dynamics and control. Recent innovations in both computational models and unsteady aerodynamics have led to predictions in the performance of aerodynamic models that are close to the observed flight of natural flyers. This has allowed for the development of flight dynamics models of these proposed MAVs. However, the low Reynolds number region in which they operate, coupled with the periodic nature of the inputs to the control surface and the flexibility of the primary force-generating surfaces, has led to body models that are far from conventional, well established models used in the aerospace industry. It is therefore diffcult to evaluate stability and sensitivity to design and operational parameters. This paper examines the feasibility of using continuation methods on a fully developed rigid flapping wing model to produce a deeper understanding of the inherent nonlinear be- haviour in longitudinal flight. The model is coupled to a continuation algorithm, AUTO07, to determine the stability deviation with varied design and operating parameters. From this, areas of interest can be then analysed in detail using time simulations. The continu- ation analysis is additionally carried out with constraints on the translational velocities to produce solutions of the vehicle in hover. The results shown demonstrate the existence of multiple steady-state solution branches within flapping wing flight and provide insight into the variations in behaviour of the nonlinear periodic system as input parameters vary. They also demonstrate the ability of the vehicle to achieve stable hovering flight.