Would the plane take off?

[Hilltop Customs]

This debate seems to be making it's way on every message boards so I tought I'd try it here.
So here it goes.

A plane (747 passenger jet) is sitting on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the planes speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction).

The question is:

Will the plane (747 passenger jet) take off or not?

Wow this question changes everytime I see it. But its all relative to where you measure the motion of the jet from. There are 3 distinct objects to measure the speed from: the conveyor, the air, and the ground off of the conveyor(basically the same as air assuming theres no wind).

If its airspeed the jet will easily take off, the speed measured at the wheels will be 2x the actual speed.

If the groundspeed is considered to be a stable object(the ground) off of the conveyor then the plane will always take off. Once again with the wheels spinning at 2x the rate of a normal takeoff, just like with airspeed.

Now if its groundspeed(assuming that the conveyor is considered the ground) the jet will never take off becasue it is motionless compared to the surrounding air and there will be no lift generated by the wings. The groundspeed in this case would quickly accelerate to infinity and the landing gear would disintegrate. This is because the aircraft is still applying force to the air and trying to accelerate....which is constrained, by the question, not to(because speed of jet - conveyor = 0). The only way to apply a force to negate the forward thrust is friction created by the landing gear, thus the extreme acceleration of the conveyor to the point of failure.



Its a horribly ambiguous question....no wonder everyone doesnt agree on an answer. Good questions have single correct solutions....this on the other hand is a perfect example of a badly worded question that has amazingly wasted a lot of peoples time