Wing planform dependency on optimum supersonic airfoil

When a wing of airplane is designed, it is necessary to have knowledge regarding planforms considered their optimum airfoils in order to design efficiently, because each wing planform has both of advantage and disadvantage. In this study, the wing design problem for supersonic transport is carried out for different planforms for two different planforms. Multi-objective problem, which is minimization drags for two supersonic cruise conditions (transonic and supersonic flight) is solved to obtain knowledge of the supersonic airfoil from the viewpoint of the multi-point design. Two types of planforms are considered—a cranked arrow wing with a high sweep-back angle and a single tapered wing with a low sweep-back angle. Optimization problems are carried out by efficient global optimization, which is evolutionary algorithm based on the Kriging surrogate model. To acquire design knowledge, a parallel coordinate plot and functional analysis of variance (functional ANOVA) are applied. The design results showed the difference airfoil between two planforms. The optimum airfoil for the single tapered wing has a small or negative camber at the leading edge to minimize the supersonic cruising. On the other hand, the optimum airfoil for the cranked arrow wing has an airfoil with a lower thickness and larger camber at the leading edge.