Comparison of Induced and Parasitic Drag on Wings with Minimum Induced Drag

Abstract

Minimizing the induced drag for steady level flight is a variational problem that requires solving for the optimum lift distribution given a set of design constraints. From lifting-line theory, minimizing the induced drag is, in part, achieved by varying the Fourier coefficients used to describe the section lift. The elliptic lift distribution minimizes the induced drag for a wing with fixed weight and wingspan by setting all but the first coefficient to zero. If wingspan is allowed to vary, a negative third Fourier coefficient is utilized to reach an optimum lift distribution that further reduces the induced drag for stress-limited designs. However, to produce an optimal section-lift distribution for minimum induced drag, the wing is required to vary twist along the span, which contributes to the parasitic drag component and may compromise the benefits gained from minimizing the induced drag. Here, the effect of these lift distributions on the parasitic drag is investigated. It is shown that twisting the wing to produce optimal lift distribution that minimizes induced drag can increase the parasitic drag values enough to nearly cancel or surpass the benefits gained by the reduction of the induced drag depending on the aircraft and flight conditions. One aircraft example is studied. Other aircraft might have different results.

Aerostructural performance improvement in an unmanned long endurance aircraft using adaptive wing concept

“…This sort of tradeoff between C Di and C Dp is natural and has been reported elsewhere, for example, Ref. 20.…”

“…This result is related to the Bell Shaped Lift Distribution (BSLD) with connections to optimal design, tailless aircraft, proverse yaw, and avian formation flight. [18][19][20][21] Control surface trim optimizations were carried out with various objective functions in Ref. 22 to generate optimal flap deflections for the Goland wing and for a blended wing-body.…”