Drag Characteristics for Optimally Span-Loaded Planar, Wingletted, and C Wings

Abstract

This paper focuses on the drag characteristics of optimally span-loaded planar, wingletted, and C wings. The span load is optimized resulting in minimum induced or total drag. The wing-root bending moment is kept constant for all analyzed wings to ascertain that different wings have comparable weight. The optimum span loadings for the different types of wing are calculated using a fast and simple numerical method. The wings are analyzed in the Trefftz plane, infinitely far behind the wing. Lagrange multipliers are used to calculate the optimum span loading resulting in minimum induced or total drag, with the wing-root bending moment and/or the lift coefficient as constraint. The induced drag can be calculated using the optimum span loading. The profile drag is assumed to be a function of the local lift coefficient. The results indicate that the C wing does not have real aerodynamic performance advantages compared to a wingletted wing. For wings with span and/or aspect ratio constraints, a winglet offers a drag reduction relative to a planar wing.