Description
Induced drag represents one of the major airplane drag components especially in some phases of the flight such as take-off and landing, where it represents 80% of the total drag. At cruise conditions the induced drag can even be 50% of the total drag. This is the reason why its minimization is fundamental to reduce consumption of fuel and have a more sustainable transportation system. Under the assumption of rigid wake aligned with the freestream velocity, an induced drag minimization variational procedure previously introduced at San Diego State University is extended to address wings which present intersections, corners, and are highly nonplanar. The geometrical corners are addressed with a regularization procedure, based on splines and preserving the continuity of the function and its first and second derivatives. The intersections are analyzed as a limit case of several wings brought close to each other. The investigations reproduced known results available in the literature but also explained relevant properties of nonplanar systems, such as the non-uniqueness of the optimal circulation distribution for the cases in which there are closed paths; however, the optimal value for the induced drag is numerically shown to be unique, representing, then, a global optimal condition. Several general properties have also been determined. In particular, it is shown that the best possible winglet minimizing the induced drag is the Box Winglet (i.e., a closed box at the tip of the wings). Moreover, it is demonstrated that Strut-Braced Wing and the corresponding Truss-Braced Wing, with an arbitrary number of juries, have the same optimal induced drag. Finally, it is discovered that under optimal conditions the juries of a Truss-Braced Wing should be unloaded or at most loaded with constant aerodynamic load, to avoid penalty on the induced drag. The developed numerical procedure is extremely fast and takes a few seconds on a common laptop, representing an effective preliminary design tool tailored for the early conceptual design phases.
