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Originally Posted by MrL_JaKiri
It will increase the friction between the wheels and the axel, however.
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By the time the speed of the threadmill is of such height as to make the friction between the wheel and axel large enough to overcome the plane's thrust, the airplane has already taken off, given the fact that the threadmill moves at the same speed as the aircraft does.
Additionally, the wheelcasing would likely be torn apart before said friction gets that high.
Edit: Whee, multiple edits.