I first saw this question posed in the Math discussion folder at work (back before the Classifieds where restricted). Then today a story from The Straight Dope (original here) showed up on Digg where there was a pretty spirited discussion about it. Simply put:

A plane is standing on a runway that can move (think of 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 wheel’s speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?

The answer seems obvious: the conveyor will keep the plane stationary, no air will move past the wings, thus no lift will be generated, and the plane will stay on the ground. The plane can’t just jump into the air. It sounds simple enough, and this was my take on it for the first few minutes I pondered the question. But the first assumption this argument is based on is wrong. All I needed was for some to frame the situation a certain way and I saw my mistake. The plane will not stand still relative to the ground.

What people fail to realize is that half of the situation is irrelevant. It doesn’t matter that the plane sits on a conveyor that is moving backwards. Why? Because a plane needs airspeed to take off; ground speed is irrelevant. A plane uses a jet/propellor to push/pull it through the air. The wheels don’t drive the plane, they just allow it to move over the ground with very little friction (as opposed to the belly of the plane sliding over the ground). Therefore, the engine acts on the air, moving the plane forward despite the conveyor. At the point of takeoff, the wheels will be spinning twice as fast.

People in the “no” camp usually bring up friction and force and physics equations, but once they’ve gotten that far they are thinking too much. For the record, the conveyor would indeed exert a backward force – on the wheels – but the majority of this force is not transferred to the plane because the wheels spin (almost) freely. The slight force transferred to the plane by the wheels due to friction would still be overcome by the force the engine generates on the air. As you can see from the Digg page above, the two camps typically continue to talk right past one another with very few people swapping sides; it all boils down to the initial assumption of whether or not the plane will stand still.

Another mistake people make is assuming that the question is posed as a real world situation having an advantage over a typical runway. In fact, the plane would need at least the same distance to become airborne and most likely more than a conventional runway because of the slightly increased friction from the wheels spinning faster. The conveyor is only there to confuse you.

I find the whole thing incredibly fascinating no matter which side you’re on. Such a simple question can raise incredibly strong and opposite opinions in even the most learned individuals and both sides will swear they are 100% right and the other side is crazy. I believe the plane will take off – the wheels will be spinning twice as fast when it leaves the ground. Now where are the MythBusters when we need them?