Optimal Flying Wings: A Numerical Optimization Study

The optimal shape of flying wings for subsonic and transonic speeds is examined using high-fidelity numerical optimization tools. The first result in the study is a lift-constrained drag minimization, performed on an un-swept, rectangular wing. By varying the spanwise twist distribution of the wing we are able to reproduce the elliptic optimum predicted by low speed inviscid theory. Using this result as a reference, we explore four different optimization formulations, considering the addition of bending moment constraints, static stability constraints and dynamic stability constraints. In each case, we explore the design space of the problem using both planform and surface shape variables to determine the optimal shape. Using these techniques, we show that the addition of stability constraints has a significant impact on the optimal surface shape of the wing. In particular, we show that at lower speeds, airfoil shape is sufficient to satisfy static stability constraints, while dynamic stability constraints require the addition of sweep. We also show that at higher speeds, shape is insufficient to satisfy either stability constraint, static or dynamic, and that the addition of sweep is necessary.

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