The location of the aerodynamic center, with respect to the center of gravity, determines the longitudinal static stability of an aerial vehicle. While most studies in the past focused on high Reynolds number (Re) flows, we consider flows at low Re (100 <Re< 6000) past an end-to- end wing and a finite wing of various semi-aspect ratio (0.25 <sAR <5). It is shown that two-dimensional computations, even for an end- to-end wing, are inadequate for accurate prediction of aerodynamic coefficients. The chordwise pressure distribution, as well as the variation of aerodynamic coefficients with angle of attack (a) at low Re, are significantly different from that at high Re. Beyond a certain a, the flow is associated with a large recirculation zone, resulting in a non-linear variation of the aerodynamic coefficients with a. The conventional defini- tion of the aerodynamic center is too restrictive at low Re. Owing to the non-linear variation of the pitching moment with change in a, it is not possible to determine one single location where it is invariant over a large range of a. The aerodynamic center is, therefore, determined over various sub-regimes of a. It varies significantly over the sub-regimes. The wing-tip vortex significantly affects the vortex shedding, flow structures, and pressure distribution on a finite wing. The locations of the aerodynamic center and center of pressure move fore, toward the leading edge, with a decrease in aspect ratio compared to that for an end-to-end wing

Starting with an initial guess and an objective such as minimizing drag or maximizing lift, optimal shapes can be generated that meets the specific objective.  Micro aerial vehicles (MAV) and unmanned aerial vehicles (UAV) operate in low. Reynolds number regime. It is well known that airfoils designed for operation at high Reynolds number do not perform well in low Re. We solve PDE constrained optimization problem to design airfoils that has good performance at low Re. We perform multi-objective optimization to obtain an airfoil with desired pitching moment  coefficient and drag coefficient.