Parametric Representation and Shape Optimization of Flapping Micro Air Vehicle Wings

Abstract

The effects of wing planform on the aerodynamic performance of a rigid wing in forward flapping flight and hovering configurations were investigated in this paper. The planform design space was parameterized using a new, modified Zimmerman method based on low aspect ratio Zimmerman planform designs. The aerodynamic forces on the wing were calculated using Peters' aerodynamics with an assumed inflow coupled with blade element theory. A multiobjective optimization approach was taken to find the best planform designs for three objectives: wing area, peak power input, and an aerodynamic force based on the kinematic configuration – lift for hovering and thrust for forward flight. A gradient-based optimizer and the ε-constraint method were used to find the Pareto front of optimal designs with the aerodynamic force as the primary objective function. The choice of primary and secondary objective functions is important in determining the optimal planform. The Pareto optimal planforms for the case when only area is considered as a secondary objective function drastically differ from the optimal planforms when only power is taken as a secondary objective function. As the secondary objective ε values change over the design space, so do the optimal planform shapes.