A closer look at the induced drag of crescent-shaped wings

Abstract

Recent interest in the induced drag characteristics of crescent-shaped wings has led to a closer look at the methods used for determination of induced drag from computational aerodynamic methods. Induced drag may be computed by integration of surface pressure, or by evaluation of a contour integral in the Trefftz plane. A high-order panel method was used to study the induced drag of crescent and elliptical wings using both techniques. Induced drag computations using surface-pressure integration were strongly affected by panel density and angle of attack. Accurate drag computations for the crescent wing were obtained only when the spanwise as well as chordwise panel density was extremely high. Trefftz-plane results for the two wing planforms do not show this sensitivity to panel density or angle of attack. Span efficiencies of 0.994 for the crescent wing and 0.987 for the elliptical wing were computed by the Trefftz-plane technique. Substitution of a force-free, rolled-up wake geometry on the crescent wing did not change the pressure-integrated drag significantly. The slightly higher span efficiency of the crescent wing is attributed to a more nearly elliptical spanwise lift distribution. The chord distribution of the elliptical wing was modified to produce an elliptical span-loading on a wing with an unswept quarter-chord line. This wing demonstrated a span efficiency equal to that of the crescent wing.