Here is the puzzle, as stated on kottke.org.
“A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?”
I’m going to re-define the problem a bit, as the way it is currently written, it is a bit vague. There are various versions of this floating around the web, like the one over at kottke.org, a second variant over at kottke.org, and Tempus Fugit.
Scenario 1: A jet plane is sitting on a conveyer belt. The conveyer belt is designed so that the movement of the belt will offset any movement of the plane that might be caused by the thrust from the jet engines—the plane will not be able to move forward because of this. The plane has unlimited fuel, and the runway is infinite in length. Will this plane be able to take off?
If you change the assumptions slightly, then the picture changes completely.
Scenario 2: A jet plane is sitting on a conveyer belt. The conveyor belt will move at a speed equal to the speed of the plane, as measured the second earlier, but in the opposite direction. The plane will be able to make forward progress, albeit slowly due to the offset movement of the conveyer belt. The plane has unlimited fuel, and the runway is infinite in length. Will this plane be able to take off?
My take on it is that if the plane is unable to make forward progress, the plane will be unable to take off. The plane in Scenario 1 can make no forward progress—no forward motion means that there is no air moving over the wings—so the amount of lift generated is not great enough to lift the plane from the conveyor belt. Given unlimited time and fuel, the plane in Scenario 2 will eventually be moving forward fast enough to take off. The movement of the air over the wing surfaces is what generates lift for an airplane. The amount of time it takes to reach to reach takeoff speed is irrelevant.
Please comment on the two scenarios.