Here's an interesting logic problem

I subscribe to Jason Kottke's blog, at Kottke.org. He often has interesting things to report, so I tune in via NewGator. This way I get notified everytime there's a new post. Actually, I subscribe to bunches of websites and blogs (news, humor, etc.). It's better than the 6 o'clock news and the newspaper, for keeping abreast of things (heheh, he said "things").

Jason proposes the following problem:

"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?"

Here was my answer (that I posted to his comments block):

Assuming the plane could take off and fly if there were no conveyor belt, the conveyor belt makes no difference at all. Really.

There is no power to the plane's wheels, so contact with the ground is just to hold the thing up. A plane has wheels because skids (unless on water or snow) don't work very well. Of course, other things work less well.

There is another aspect to the problem, as stated. If the conveyor belt is "smart" and always moves the same speed and opposite direction to the plane ... if the plane is standing still relative to the ground, is the conveyor belt moving, at all? Of course, the forces that move the plane forward don't depend on the ground (or the speed relative to the ground, for that matter). The relative ground speed of a plane taking off into a strong wind is measurably slower than the plane's airspeed. That's why they call it "airspeed", because that's what matters.

I thought it was a trick question, but it's really just so simple that it fools you into thinking it must be somehow "harder". Unless the plane's wheels can propel it forward (like the jet in The Jewel of the Nile--you can see the drive mechanism plainly as it taxies around), the conveyor belt will make no difference. It's the air and the air's speed relative to the plane that matters. In a fast-enough wind (at least hypothetically), the plane wouldn't even need a runway. Actually, though, before the plane's thrust could become strong enough to counter a 100+ MPH wind, the plane would be blown backwards rather catastrophically.

In physics we learn that planes move because their propellers or jet engines throw large masses of air backwards at high speeds, and the plane is simply obeying Newton's Third Law. Rockets work the same way, except that they bring their propellent mass with them (since there ain't no air in space, y'know).