Minimum Induced Drag for Tapered Wings Including Structural Constraints

Numerical Method for Rapid Aerostructural Design and Optimization

“…However, it has been shown that the elliptic lift distribution is not the only solution for minimizing drag under all conditions [20][21][22][23][24][25][26][27][28][29]. In particular, when structural effects are considered, it has been shown that drag is typically minimized using a non-elliptic lift distribution that depends on the design constraints [12,13,[16][17][18][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Lowfidelity and analytic aerostructural methods are valuable for identifying these non-elliptic lift distributions and for understanding how structural considerations affect the minimum-drag solution.…”

“…Many of these methods require time-consuming and computationally expensive coupling between high-fidelity aerodynamic and structural solvers. However, there are relatively few studies that approach this multidisciplinary problem from an analytic or low-fidelity point of view W [39][40][41][42][43][44][45][46][47][48][49]. Prandtl seems to be the first do so, and in 1933, he identified a bell-shaped lift distribution that minimizes induced drag on a rectangular wing with fixed gross weight and moment of inertia of gross weight [39].…”

“…More recently, Phillips et al [47,48] and Taylor and Hunsaker [49] relaxed many of Prandtl's assumptions and extended his approach to account for the effects of the planform shape on the wing-structure weight and the effects of the wing weight distribution on the bending moments. They identified lift distributions that minimize induced drag under constraints of fixed gross weight [47], fixed net weight [48], fixed wing loading [47,48], and fixed stall speed [48].…”

“…They identified lift distributions that minimize induced drag under constraints of fixed gross weight [47], fixed net weight [48], fixed wing loading [47,48], and fixed stall speed [48]. However, in order to obtain analytic solutions, Phillips et al [47,48] limited their results to rectangular wings with a single ideal weight distribution, and Taylor and Hunsaker [49] limited their results to linearly and elliptically tapered wings with the same ideal weight distribution. In fact, all of the analytic studies discussed here are limited in application to wings with specific planforms and/or weight distributions.…”

“…The purpose of this paper is to present a low-fidelity numerical method that extends the work of Phillips et al [47,48] and Taylor and Hunsaker [49] to more practical aircraft configurations with arbitrary planforms and weight distributions. We will apply the method to a high-endurance unmanned aircraft configuration to demonstrate how it can be used for rapid conceptual design and for gaining intuition about the aerostructural design space.…”