747 on a treadmill conundrum..

[Anomalocaris]

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If however the treadmill starts at a backwards speed of Vrotate (the speed the a/c lifts off) and maintains this, the aircraft will probably take off fine as long as the tyres can handle it. In this case the maximum tyre speed is 2*Vrotate.

When considering whether an aircraft's tires can handle the stress of rolling at twice the normal rate of rotation at take off, keep in mind that take off run is not the most stressful part of the an airplane tire's designed duty cycle.

By far the most wearing part of the an airplane tire's duty cycle is at the moment of landing, when a non-rotating tire hits the ground carrying the entire aircraft's downward momentum upon it, and has to be spun up to its rolling speed in a short distance by the drag of the runway contact. This is when you typically see a big puff of smoke coming off of the tires of a 747.

As a result, The lifespan of an large airplane's tires are not rated in terms of how many miles it had rolled on the ground, or how many take off runs the tires had made. Instead it is rated based on how many full load landings the tire can sustain. During early jet age, a main landing gear tires have life span as short as 12-15 landings. Then the tire would be worn out and has to be replaced. Modern civil airliner tire lives are much longer, but the limiting factors remains how many landings, not how many takeoffs.

It could well be that the stress on the tire of rolling at twice its normal designed rate is nothing compare to the stress of the initial ground contact when the plane makes a hard landing. In that case, running the plane on a treadmill during takeoff would be nothing to the tires.