This paper focuses on aerostructural optimization of wings with winglets. A NewtonKrylov flow solver for the Euler equations is interfaced with a finite-element structures solver for the aerostructural solution. A gradient-based optimizer is used for optimization, where gradients are calculated by the coupled discrete-adjoint method. Pareto fronts of optimal solutions are constructed for weight and drag, which are competing objectives in the context of wing design. Three winglet configurations are considered: winglet-up, winglet-down, and raked wingtips. These are compared to optimized planar wings of the same span. The aerostructural optimization cases reveal that the winglet-down configuration provides the largest benefit in comparison to the optimized planar wings by increasing the span of the wing at the deflected state.

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Through aerostructural optimization, this paper presents progress towards characterizing the potential e ciency gains of drooped wings for commercial aircraft in transonic flight. The drooped wing is a nonplanar configuration with downward spanwise camber from the wing root to the tip. The aerostructural optimization cases include two load conditions: cruise and 2.5g. The single 2.5g maneuver load condition is used for structural sizing of the wing. In all cases, the projected span of the wing remains unchanged. The results show that such a wing has the potential to improve aircraft range by 2.6% relative to an optimized planar wing of the same projected span. The reason is that the drooped wing pushes the tip vortex further away than the planar wing and increases the projected span at the deflected state. Furthermore, if the drooped wing is permitted to have curved leading and trailing edges, a 4.9% range improvement in comparison to an optimized planar wing with straight leading and trailing edges is possible by further reducing wing weight and wave drag.

This paper presents an aerostructural perspective on the potential benefits of wingletted wings in comparison to planar wings of the same projected span. There is no consensus in the current literature on the e ciency gains possible from winglets. Conclusions made in the past vary significantly depending on the design problem considered and the fidelity of the tools used. The present paper takes a step further towards understanding the tradeo↵s in the design of wingletted wings using high-fidelity numerical optimization based on both purely aerodynamic and fully-coupled aerostructural analysis. The high-fidelity analysis in both cases uses the Euler equations to model the flow along with a friction drag estimate based on the wetted surface area. Three configurations are considered: winglet-up, wingletdown, and planar. The results show that winglets oriented downward produce a greater drag reduction than winglets oriented upward for two reasons. First, the winglet-down configuration moves the tip vortex further away from the wing from a purely aerodynamic standpoint. Second, the winglet-down configuration has a higher projected span at the deflected state due to the structural deflections. This indicates that fully-coupled highfidelity aerostructural optimization is required to quantify the benefits of winglets properly. We present results for two variants of the Boeing 737NG aircraft: B737-600 and B737-900. The winglet-down configuration can reduce the total drag by up to 2% at the same total weight as the optimal planar counterpart. These conclusions are applicable to new wing designs, as opposed to retrofits; the potential e ciency improvements o↵ered by retrofitted winglets may be di↵erent.

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