Investigation on conditions of minimum induced drag of closed wing systems and C-wings

TLDR: In this paper, a theoretical method for predicting minimum induced-drag conditions in a nonplanar lifting system is presented based on lifting line theory and the small perturbation acceleration potential.

Abstract: A theoretical method for predicting minimum induced-drag conditions in a nonplanar lifting systems is presented in this paper. The procedure is based on lifting line theory and the small perturbation acceleration potential. Under the hypotheses of linearity and rigid wake aligned with the freestream, optimality conditions are formulated using the Euler-Lagrange integral equation with constraints on fixed total lifting force and wing span. Particular attention is paid to analysis and numerical treatment of the Hadamard finite-part integrals involved in the solution process. The minimum induced-drag problem is then formulated and solved numerically and analytically. In the case of annular wings, closed-form expressions for the optimal circulation distribution, the normalwash, the induced-drag coefficient, and the efficiency are presented. Optimal annular wings and C-wings are extensively analyzed