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> I suspect if you made a wing out of a flat piece of material, tilted at the appropriate angle of attack, it would be sufficient to fly a plane.

You don't have to suspect. Many aerobatic aircraft (not to mention many high performance military aircraft) have wings that are symmetrical top to bottom (they aren't exactly flat but the top-bottom symmetry is enough to prove the point). They still fly. (The article mentions this.)



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