Angrier said:
Relative to you, the plane"s speed is zero. Relative to you, the air around the tip of the wing is zero. Wasn"t that the whole point of the question? That next to a bystander, the plane is not moving forward. So where"s that draft...?
That"s what I got from both the question and the first posted explanation.
The fact that the same folks who posted all that say that it moves (which makes perfect sense the way that they say it) is why I"ll be looking at the math.
The problem with the idea that the plane does move forward is that any translational motion of the aircraft is immediately transfered to rotational motion in the tires of the landing gear.
The conveyor belt, as per the original question and first answer, is designed to respond to the rotation of the wheels by matching the tangent acceleration.
If that is the case, then the plane does not move forward. Period.
If the plane is to become airborn, it then has to happen with no horizontal velocity. Thus my previous mental model of the problem in which the plane is subjected to vertical force, but not horizontal. There is no horizontal momentum on the body of the aircraft, relative to the ground.
A few folks imply that horizontal translations relative to the belt are the same as translations relative to the ground. As per the universal laws of gravitation, this is not the case.
Folks who know a bit about aircraft here say that there is no vertical lift without horizontal translation because the engines do not cause compression of the air above the wings, thus the plane does not become airborn.
Nonetheless, the engines do provide a force against the air, and by Newton"s Third Law, the air returns this force. Since the conveyor belt takes time to react, and the force is ever present and increasing, then the plane is lurching forward at small increments, while the belt adjusts to meet the tangent acceleration.
Eventually, these lurches will be powerful enough to provide enough forward momentum that the plane will lift off. The air velocity will be much, much higher than that for a normal take off.
Thus, the plane both lifts off and does not lift off, going by the consensus of those who know more about aircraft, the laws of physics, and those who have had more time with the problem, but ignoring peoples" specific answers as to whether the plane lifts off.
Therefore, we have a paradox that can only be resolved through math or experimentation, even if all components are ideal with the exception that the plane and belt both have a mass (they would have to for this to make any sense).
Could it be that something in the original question was misquoted?