Optimum Induced Drag of Wingtip Devices: The Concept of Best Winglet Design

Abstract

Sustainable air transportation requires aerodynamically efficient airplanes. Thus, reduction of drag is of paramount importance. From a pure induced drag perspective, this goal can be achieved by the adoption of nonplanar configurations such as C-Wings, Joined Wings or with other design options such as wingtip devices (winglets). Under the assumption of inviscid flow with wake aligned with the freestream velocity, several winglet designs are investigated and general properties are demonstrated. In particular, under optimal conditions, given a closed simply connected wingtip region bounded by a curve, any winglet design geometrically included in that region will be less efficient than the winglet whose lifting line is represented by the bounding curve. Moreover, closed winglets are characterized by undetermined optimal aerodynamic load but unique and global minimum for the induced drag. Finally the Box Winglet and several variations of it are proposed as effective forms to reduce induced drag.