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Why is a simple rectangular wing with winglets not better than an elliptical wing in terms of induced drag and produced lift?

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  • $\begingroup$ It’s an interesting information. I am curious to read the reference behind the description. $\endgroup$
    – Mad Max
    May 1, 2019 at 21:39

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If using Prandtl's lifting line theory, then mathematically/analytically, ignoring issues of wing weight that lead to bell shaped lift distributions and other sorts of intrusions of reality (e.g., stall behavior) the elliptical wing with the elliptical lift distribution is optimal for minimizing induced drag given a fixed wing area.

You can get an elliptical distribution of lift from a rectangular wing via twist, winglets, or other mechanisms, but it will only be elliptical at one cL value. At other values, it will not be elliptical, and thus suboptimal.

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  • $\begingroup$ I'm not sure what you mean by "optimal" and "can't be improved on" because a planar elliptical wing does not produce an elliptical lift distribution. $\endgroup$
    – Lysistrata
    May 2, 2019 at 3:36
  • $\begingroup$ A wing with an elliptical chord distribution (and minimal sweep, minimal dihedral, and moderate aspect ratio) produces an elliptical lift distribution. $\endgroup$
    – MikeY
    May 2, 2019 at 10:58
  • $\begingroup$ No, a planar elliptical planform wing definitely does not produce an elliptical lift distribution. (Twisted wings are a different matter.) This was known to Prandtl and his students as far back as 1937. See, for example, among many dozens of other papers: Peter F. Jordan, "Exact Solutions for Lifting Surfaces", AIAA Journal, Vol. 11, No. 8, 1973., pp. 1123-1129. Peter F. Jordan, "On Lifting Wings with Parabolic Tips", ZAMM 54, pp. 463-477, 1974. $\endgroup$
    – Lysistrata
    May 2, 2019 at 14:06
  • $\begingroup$ OK, I'll caveat my answer to what Prandtl's LLT infers. $\endgroup$
    – MikeY
    May 2, 2019 at 15:51
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    $\begingroup$ @Lysistrata So what planform of a wing without twist, sweep, dihedral, winglets ... produces an elliptical lift distribution? Can you post an image that contrasts it with an elliptical wing? $\endgroup$
    – xnor
    May 2, 2019 at 19:39

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