Of course it will fly. The plane is producing thrust at the body, not the wheels. It doesnt matter whats going on at the wheels. If it was a car with wings, NO it wouldnt take off.

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or better yet...

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02 Ford F-250 4X4 PSD...zero body damage
67 Weimann 18' Jet boat...zero body damage except for the trailer drags on the ground from time to time