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Old May 18th 15, 09:34 PM posted to rec.aviation.soaring
J. Nieuwenhuize
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Default Bent up wings on Schempp-Hirth and Jonkers glider

If we go back to theory, the perfect wing is a double super-ellipse (Lamé curve):
http://en.wikipedia.org/wiki/Superellipse

Both the top view and the dihedral of the wing should have the shape of a super-ellipse for lowest induced drag for a given bending moment (structural weight) and wetted area (profile drag at high speeds). Both the A350 and the Dreamliner are very close to this ideal:
wallpaperswide.com/download/boeing_787_dreamliner-wallpaper-1920x1200.jpg

Another plus compared to a wing without dihedral and winglets is that the interference drag between the winglet and the wing is much reduced.

Such a gradually curved wing is impossible to build because all the control surfaces would have a bend in them. The wing with sections progressively canted more and more (polyhedral) is a good compromise.

It also helps with flutter apparantly. The Vortex shedding frequency of the various sections make the critical flutter speed for such a wing higher, allowing either a higher VNE, or a less stiff and thus lighter wing structure.