ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

The limitations placed on the size of flapping wing micro-air vehicles (MAV’s) means that they operate in a region of highly unsteady aerodynamics, dominated by 3D effects. Thus, a comprehensive flight dynamics model would be nonlinear, with associated problems in evaluating stability and control. Nonlinear dynamical systems theory – specifically bifurcation methods – is therefore seen to be useful for analysing the flight dynamics system of equations.

An aerodynamic model has been created to capture the flow regime, using a modified blade element theory. The model is initially limited to rigid body modes, with only the effects of inertial accelerations of the flapping wing being coupled to the modified quasi-steady aerodynamic analysis. The system is periodically forced and an appropriate form of numerical bifurcation analysis is then applied to this system. From this, tools for looking at the oscillatory steady states can be developed, especially in response to perturbations in wing beat parameter changes; the flap, lag and feather frequencies and amplitudes. The stability analysis and steady state variation will then be used to define preliminary simplified vehicle control system boundaries, and also create a base of knowledge for introducing other effects such as structural dynamics, wind gusts/perturbations and ultimately time-dependent aerodynamics.