Optimal hyperelliptic cambered span configurations for minimum drag

The current study considers an analysis of hyperelliptic cambered span wing configurations, optimized for minimum drag. This study encompasses a multidimensional design optimization approach wherein the wing geometries are optimized with respect to both span load and spanwise camber to achieve minimum aerodynamic drag. A discrete vortex element method was coupled with a constrained gradient-based optimization routine to achieve these drag-optimal design configurations. Optimum drag configurations were obtained at a fixed design lift coefficient as well as a fixed bending moment constraint. Navier-Stokes simulations were also performed, which revealed an L∕D gain of 29.01 and 25.35% at design conditions, relative to an elliptically loaded planar wing for the upward and downward cant configurations, respectively. Different wake trace characteristics for the two hyperelliptic cambered span configurations were observed along with surface flow features indicating different wake vortex and boundary-layer transition behaviors for the two hyperelliptic cambered span configurations.