Minimizing Induced Drag with Lift Distribution and Wingspan

摘要

Minimum induced drag for fixed gross weight and wingspan is obtained from the elliptic lift distribution. However, minimum induced drag for steady level flight is not obtained by imposing the constraints of fixed gross weight and wingspan. Because required wing-structure weight is a function of wingspan and lift distribution, there exist an optimum lift distribution and wingspan for a given weight and weight distribution that minimizes the induced drag in steady level flight. This optimum lift distribution can vary significantly from the elliptic lift distribution, depending on the design constraints. Analytic solutions for three such optimum lift distributions are presented for rectangular wings with varying sets of design constraints. These design constraints are 1) weight, maximum stress, and chord length fixed; 2) weight, maximum stress, and wing loading fixed; and 3) weight, maximum deflection, and wing loading fixed. It is shown that each of these optimum lift distributions results in lower induced drag than a fixed elliptic lift distribution for the same design constraints.