I think we are confusing several different things. Elliptical wing has nothing to do with the wing thickness.
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You can have thick and thin elliptical wings. Early He 111s had elliptical wings.
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Later ones got tapered leading edges, semi-elliptical?
As Drgondog has already stated "
threoretical elliptical wing (which did not exist in purest form) was to develop an optimized lift loading and maximum reduction to induced drag."
Basic wing design for the P-47 goes back to the P-35, or earlier?
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Seversky and crew were using straighter leading edges than Heinkel and Supermarine.
The wing design did give them room for things like guns and landing gear (Seversky sort of missed that one but wanted to save the plane on a wheels up landing)
The elliptical planform was supposed to give less drag than wing of the same area and thickness that used straight or parallel edges. Turned out that by carefully selecting the taper of the wing you could get close to the elliptical benefit and since nobody was actually using a pure elliptical wing anyway the benefit turned out to be very small.
P-47s problem was that it weighed over twice what the Spitfire did for only about a 33% increase in wing area which requires Divine intervention for short take-off and landing, not fancy wing tips