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Generally, I have seen that the planform of an elliptical wing consists of two different types of elliptical curves

The elliptical curve towards the leading edge has a lower value for semi-minor axis and the curve towards the trailing edge has a higher value of semi-minor axis

What is the reason for such a geometry?

(Image is attached for reference)

Typical elliptical planform

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It's because the center axis for the ellipses has to be along the thickest section of the wing, because there is also a taper in thickness that must be accommodated as the ribs get smaller and smaller toward the tip. In your sketch, the thickest section is at 40% of chord and the taper in both planform and thickness must be oriented to that 40% chord line, hence the asymmetrical curves.

The placement of the axis of maximum thickness is a function of the particular airfoil selected, that is, the point of maximum thickness of the airfoil section itself. For structural efficiency, this is normally also the location for the main spar. In the sketch, which resembles a Spitfire wing planform, the broken line will be more or less the main spar location, with the nose ribs on the left and the main ribs on the right, with the ellipse curves placed to maintain the 40% forward/60% aft ratio out to the tip.

If the thickest section of the wing was at 50% of chord, then the ellipses would be symmetrical.

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  • $\begingroup$ You might also note that it is easier to construct a wing with a straight main spar than one which is curved. $\endgroup$
    – Eric S
    Nov 17, 2020 at 18:06
  • $\begingroup$ I assume you mean curved as in the upper and lower caps having a curvature toward the tip to be in conformance with the ellipse of the planform.But the caps on a Spitfire spar are straight, not bowed and it lives with that imperfection for ease of manufacture.The difficult part manufacturing wise is the ribs with each having a custom profile with complex flanges to mate to the skins properly, and the need to form compound shapes in the leading edge skins, requiring them to made on a stretch press, or stamped in parts and welded together, then heat treated, instead of a simple single wrap bend. $\endgroup$
    – John K
    Nov 17, 2020 at 18:47
  • $\begingroup$ What I mean is if the wing were a perfect ellipse then the main spare would have to curve backwards which is harder to make compared to a spar that is straight. I'm the upvoter so I like your answer, but I thought that the manufacturing difficultly of a compound curved spar is part of the reason for keeping the thickest part of the airfoil in a single line. $\endgroup$
    – Eric S
    Nov 17, 2020 at 20:51
  • $\begingroup$ Oh I see what you mean. It would be more correct to call it a 'double semi-ellipical" wing I suppose. $\endgroup$
    – John K
    Nov 18, 2020 at 1:06
  • $\begingroup$ Makes complete sense. So, the center axis should change according to the maximum thickness of the airfoil and the ellipse should be designed accordingly. Understood. $\endgroup$
    – Tanay
    Dec 8, 2020 at 9:58

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