So long as the wheels are part of the body themselves, there is a treadmill that could stop the plane from taking off. A theoretical one at the very least. Since it is part of the body, a portion of the force used to push the wheels back will transfer to the plane as a whole. This makes sense since the plane cannot move forward and just leave a solid part of it behind. The problem would be one of getting a treadmill that could exert enough force on the wheels to completely counter the forward thrust of the engine without just breaking the wheels.

It would work similar to this. If I tied a rope around your arm and pulled back on it, could I keep you from running forwards? The power is all in your legs, but the effect on the body from an external source is still a factor. I think everyone here is assuming the treadmill will be using only the wheels of the plane for its speed, but I can't imagine why anyone would make that assumption. All modern treadmills I have seen can move on their own opening up the possibility to increase the force on the wheels independant of their actual motion.

I think I'm going to weigh in and agree with omg, Origin and the rest who say the plane will take off. The essential point to remember when talking about a plane is we're talking only about the motion of air around the wings, not the motion of the plane relative to the ground. The propellars or jets from a plane only serve to cause air flow, they don't do anything to make the plane move. In fact, the only reason a plane moves forward at all is because its continually falling towards the ground and being lifted back up by the wings. Just as an aside, a rocket engine is different because it causes thrust directly with thermal energy, instead of moving the air around.

Look at it a different way. If you have a plane tied with a rope to a stationary object, and then you use big fans in front of the plane to cause air movement, the plane will eventually take off. This is how wind tunnels work. In this situation, the plane itself is stationary while the wind around it is moving fast enough to cause lift under the wings.

Now, think of the fact that both a propellar and a jet engine are designed to move air from the front of the plane towards the back. The only difference being that a propellar blows the air directly over the wings and the jet engine just blows it out behind the plane. In both cases, pressure differentials in the air will cause it to flow back behind the plane, just like a floor fan causes air flow in your house even though the fan itself doesn't move. Even if the plane could be held stationary relative to the ground, using a conveyor belt, the engines themselves will create airflow and once sufficient lift is generated, the plane will take off.

Here's a good link explaining relative velocity.

Ok...so as obvious as it is to me and most others here...I don't think I'd mind watching this on Mythbusters...as some people here clearly need to watch it and get their facts straight.

Yes, there is friction. But the rolling friction from the wheels is negligible - at take off speads, the air friction alone is already a much bigger factor.

A plane that can propell itself forward from a stationary position (beating inertia, rolling, driveline and air frictions), and accelerate itself to take off speeds just by moving air, cannot and will not be stopped by a threadmill.

QFT

that's right... I quoted myself. 

Because I know I'm right and anyone who read what I wrote should obviously not be arguing about this anymore. 

No, It won't. It will stay in the same place. The plane will need to do the take-off speed plus the speed of the belt if they want to fly.

The answers are pretty obvious here. It's kind of a trick question.

Speed is relative for all objects. Whatever speed the airplane is traveling at relative to the ground is irrelevant; whatever speed the airplane is traveling at relative to the surrounding atmosphere is absolutely and entirely what matters. 

Thus, if the airplane is moving at a speed relative to surrounding air that is suitable for take off, it will take off. Otherwise, it will not take off.

 I don't think anyone is arguing if the plane's own motive thrust can overcome the treadmill.  What we are saying is that the myth seems to prescribe a plane that cannot move.  By the rules of the myth it's only ever allowed to provide itself enough thrust to overcome the backwards thrust produced by it's wheels friction with the treadmill.  And thus no airspeed is obtained and thus no lift. 

If you put a plane on an infinite treadmill going to the left at 200mph and let the plane get up to 200mph due to the friction on it's wheels, theorotically it would still be able to overcome this with its own motive thrust because its motive thrust is based on relative windspeed and is limited by such.  Therefor it would be able to slowly speed up and overcome the leftward 200mph thrust until it reached a speed vector of 0.  At that point the wheels would be rolling along the belt at 200 mph, but the plane relative to the earth would still be moving a 0mph and the same would be true of the airspeed over the wings. Thus no lift here.

Now since the plane's motive thrust is limited by the relative airspeed , which is currently at 0, it is capable of continuing to speed up and taking off on the treadmill if it should choose to do so.  

But as I said before the myth is poorly worded and I don't think anyone here can really claim to have the absolutely correct interpretation of the myth.  I really hope they do a better job of explaining the myth on the show, but in the meantime I have double checked my season pass and am looking forward to it =)

@Bod, thats pretty much what I said in my first post also =) 

 I can assure you that there is some speed at which a spinning treadmill can offset a *small* amount of thrust from the plane due to friction.  They are saying takeoff speed which is about 60-65 mph for a smallish craft.  A treadmill running at that speed against the landing gear will most certainly produce enough rolling resistance to require some thrust from the engine to counter the rearward "pull" from friction.  I certainly won't be much thrust, however, and again, regardless, there is no lift from airflow.

An interesting thing to note with coefficient of drag as it pertains to rolling resistance is that the softer the two surfaces, the more rolling resistance there is.  Steel on steel would, of course, be very little.  Rubber on Concrete a bit more.  Rubber wheels on a treadmill which will also be a "softish' surface or at least deform to some degree, will provide a bit more resistance.

However...

I think as one poster has said above -- we are misunderstanding the intent of the "myth" becase this one is so obviously impossible.