Constructal design of glider wings: the intersection of aerodynamic and structural asymptotes

Abstract

When designing an aircraft, aerodynamic efficiency must be taken into account as well as structural integrity. While high-aspect-ratio wings minimize induced drag, they exponentially increase the bending moment and the required structural weight at the root of the wings. In this paper, “Constructal Theory” is applied to theoretically predict the optimal wing span for a glider. Instead of using complex and high-cost approaches such as “Fluid-Structure Interaction” to predict the optimal wing span, in this paper aerodynamic drag and structural weight are treated as two competing flow resistances that restrict the movement of the flying system. By formulating the total resistance function and applying the principle of the intersection of asymptotes, we analytically derive the geometric configuration that minimizes the global resistance. This mathematical optimization process shows that the geometry of an optimal wing is not a random occurrence, but it is a deterministic physical phenomenon driven by the equipartition of imperfection.