Minimum Induced Drag Conditions for Truss-Braced Wings

Abstract

Traditional monoplane aircraft have been used for many decades. A promising improvement is represented by truss-braced wing configurations because studies have shown potential advantages in terms of fuel savings and overall efficiency. These investigations have been carried out in relatively complex multidisciplinary design and optimization computational frameworks, and thus some theoretical questions regarding the optimal conditions under which the induced drag is minimized need to be specifically addressed. This is achieved in this paper by extending the variationally derived theoretical model that the authors developed for nonplanar wings, closed systems, and multiwings to handle multiple closed paths (typical situation in the case of truss-braced wings) within the wing system. A regularization procedure, based on splines and preserving the continuity of the function and its first and second derivative, is introduced to address the geometrical corners. It is verified that, under optimal conditions, the actual value of the induced drag is a global minimum and that there is an infinite number of possible aerodynamic loads achieving the optimum. In some of them, the central part of the upper wing is more loaded, whereas in other cases, the lower wing and outer portions of the upper wing carry more aerodynamic forces. Finally, it is shown that a jury should be unloaded or at most have constant circulation to avoid penalty on the induced drag.