OK, I know that the impetus behind my plane and conveyor post was the similar post made on Jason's site, and that the bulk of the unusually large traffic to my site that day was from his link to my post. However, in case any of you who read this aren't also reading Jason's website, I thought I'd repost some information that he put up today:

Mythbusters is taking this one on. They built a quarter-mile conveyor, and will attempt to launch an ultralight off of it. The episode will air next month. Anyone in the Los Alamos area who has the Discovery channel, PLEASE invite me over to watch it as I have no means at my house.

An interesting note is that they have a slightly different wording to the problem than was used in Kottke's post (and mine). Here is the original wording:

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?

And here is the Mythbusters wording:

If a plane is traveling at takeoff speed on a conveyor belt, and that conveyor belt is matching the speed in reverse, can the plane take off?

This is a much simpler wording, but I think it actually exacerbates the ambiguities that arose in discussion of the initial wording. Both statements fall prey to an ambiguity in frame of reference. Clearly, in both cases, the plane moves relative to the conveyor belt... but in what frames are the speeds measured? Is the plane travelling at takeoff speed relative to the conveyor? Or relative to the Earth (and its atmosphere).

You'll recall from the previous discussions on this question that if the plane is moving at "takeoff speed" relative to the atmosphere then it takes off and it doesn't really matter what the conveyor is doing. If the plane is moving at "takeoff speed" relative to the conveyor and the conveyor is moving at "-takeoff speed" relative to the Earth, then the plane isn't moving relative to the atmosphere and it just sits there. For an even weirder interpretation, consider the plane moving at "takeoff speed" relative to the conveyor, and the conveyor moving at "-takeoff speed" relative to the plane! In this case, the plane and conveyor are moving in opposite directions and at the same speed relative to each other... but what the plane-conveyor system is doing relative to the Earth is undefined, thus the plane could be stationary relative to the atmosphere, or could be traveling at nearly the speed of light. This interpretation obviously sheds little light on the problem.

Personally, I find it very odd that you might measure the speed of the plane in one frame of reference and the speed of the conveyor in another. It is a very unnatural way to conduct one's affairs and leads to oddities like the last case stated above. Also, no rigid body moves with a non-zero speed in its own frame of reference. Thus, if we're saying that both the conveyor and the plane are moving at some speed > zero, then we are presumably talking about measuring these speeds in the Earth frame. While this is not the only way to interpret the wording, it is the only way that makes any real sense. And in this interpretation of the wording, the plane takes off.

I hope that the Mythbusters guys don't try to inflict some bizarre frame combination on us.

But, of course, in a real-world scenario, the stationary plane sitting on a moving conveyor would be rather difficult to pull off, since the plane doesn't have very fine control over its thrust at very low power and the conveyor has almost no influence on the plane's velocity since those pesky free-rotating wheels separate them. I think it will actually be rather difficult to keep the plane from accelerating.

However, I think the Mythbusters crew is reasonably scrupulous and won't go out of their way to demonstrate a conclusion that is only valid in the most contrived of interpretations.

500 years of modern physics predicts that the plane will take off, and so do I. I look forward to see the experimental results.

SCIENCE!