Mesa Mike's Midden of Musings

As predicted, of course. The Mythbusters proved it in last night's show.

There has been lots of discussion on the internet about whether an airplane on a conveyor belt could take off, if the conveyor belt moved in the opposite direction at the same speed as the airplane. The problem is usually stated something like this:

"A plane is standing 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 plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the plane take off?"

The people who say no, typically reason that for an airplane to take off, it needs airflow over the wings (more than just the amount the propeller blows), but since the airplane can't move forward, there is no airflow over the wings, therefore the airplane can't take off.

But this begs the question. Of course the airplane needs to move forward at a speed great enough to supply the lift in order to take off. That's kind of integral to the idea of "taking off." Whether the airplane can do so is exactly the question we are being asked, I think.

The faulty assumption is that the contraption is designed to prevent the airplane from gaining forward speed. That, however, is not stated in the problem. People make this assumption, I guess, by analogy to walking on a tread mill where one does not go forward, but stays in one spot as the treadmill goes backward at the same speed one is walking forward.

But airplanes don't propel themselves forward by pushing against the ground (or the treadmill in this case) like walking people or cars do. Airplanes' forward thrust comes from the "equal and opposite reaction" of the action of throwing stuff backwards (air, in the case of a propeller plane, or the hot expanding gases of spent fuel in the case of a rocket).

It amazes me that so many people just don't get it, even after having it explained and demonstrated. Many of them claim that the Mythbusters experiment was flawed, because "the plane actually did move forward!" For some reason, they thought that the "wheel speed" of the plane was to match the conveyor belt speed. But the original question only says that the speed of the conveyor belt matches the speed of the plane.

The assumption that the "speed of the plane" means it's wheel speed relative to the belt is an unwarranted assumption, in my opinion. Unwarranted, because it makes the original question illogical. The only way for the wheel speed to match the belt speed is for neither the plane nor the belt to be moving at all; or for the plane's engines to be providing just enough thrust to match the very minimal force of the wheel friction in order to keep it from being dragged backwards. But the question is, "can the plane take off?" This implies that the plane should be trying to take off, which means full thrust, not just minimal or no thrust. So it must be that the "speed of the plane" must be relative to the ground.


For your amusement, see the comments on The Mythbusters forum.
Other comments are at Kottke's nice discussion of the puzzle.

Oh, and I just discovered this definitive analysis of the question.