So I recently got into this huge debate. The question? Will a plane that's moving forward on a treadmill, only to have the treadmill match its speed, take off and fly?

Here's the original question that was posed to me:

http://www.boingboing.net/2006/12/11/airplanetreadmill-pr.html

I say the plane will NOT fly. Planes fly because of lift. The plane has to be moving through the air in order to create lift. If the plane is being held stationary in relation to the air because of the treadmill's motion, then lift is impossible, and thus, so is flight. I posted this in defense:

http://www.nasa.gov/audience/forkids/home/F_How_Do_Planes_Fly_Text.html

The other fellow believed that the plane would fly. He posted these in defense of his position:

http://www.straightdope.com/columns/060203.html
http://youtube.com/watch?v=-EopVDgSPAk

First of all, I had to criticize his choice of sources. His defenses were an internet blogger and a youtube user. My defense was freakin' NASA. Yet no matter what I said, he would not be convinced. And no matter what he said, I was not convinced. So what do you guys think?

No, there would be no air current flowing over the wings since the plane ultimaetly would be staying in the same place so it would not lift off.

It all depends on how you look at the problem, but Cecil Adams is correct in saying that the plane will take off if the friction between the plane and the wheel bearings is zero. A plane generates its forward acceleration not by friction between its wheels and the runway, but by pressure exerted on the air. A plane on a treadmill with its engines off with wheel bearings of zero friction will not move, no matter what speed the treadmill attains.

In real life, however, there is a very small component of friction exerted between the plane and its wheels through the wheel bearings, so that the acceleration of the treadmill will have a very small effect on the acceleration of the plane. Therefore, if you could have a treadmill that could reach theoretically infinite velocity, you could force the plane to remain stationary and grounded. The coefficient of kinetic friction between the ball bearings in an airplane wheel is liable to be extremely small, however, which would mean that the treadmill would need to accelerate drastically faster than the plane was attempting to accelerate.

Furthermore, as long as the plane's engines are on, the plane is applying a constant forward force which must be countered by a directly proportional acceleration of the treadmill (F_plane/m_plane = a_treadmillµ, where µ is the (extremely small) coefficient of friction of the ball bearings)). As the velocity of the treadmill, as increased by its constant acceleration, approaches the speed of light, the amount of power required to continue its acceleration will go to infinity (by the principles of Einsteinian relativity), and the plane will eventually take off as the acceleration of the treadmill goes to zero.

In the entirely theoretical case (zero friction), the plane takes off.
In the somewhat more real-world case (friction, but infinite power capacity and zero heat), the plane takes off.
In the actual real-world situation (it is not possible to generate enough power to maintain the constant acceleration), the plane takes off.

The plane will take off.

Note that none of this disputes that a plane remaining stationary to the air won't take off (it won't), but rather that it is impossible to use a treadmill to hold a plane in place.

Yes it will take off and fly, it is generating thrust by accelerating air, it does not care how fast the treadmill is going, and will still accelerate.

It occurs to me - the only way to stop the plane from taking off would be for the coefficient of friction to be great enough such that the ball bearings generate enough heat so as to sever the wheel struts of the plane and land its belly on the treadmill.

So is the original problem impossible? Since it is impossible to actually have a treadmill that can stay on top of the plane's acceleration, is the whole point in trying to argue that it would take off while being stuck on a treadmill a pointless assertion?

Right. If you could magically conjure a force that could counteract the force exerted by the plane's engines (such as placing the nose of the plane against a wall and assuming that neither the wall nor the plane will collapse from the force exerted by jet engines), then it would not take off, but a treadmill can't stop a plane.

It isn't only that, if you get a wheel going fast enough(far beyond the speed at which it would disintegrate) it will act like a foil bearing, which is to say the plane would fly on the ground effect generated by the wheel.

Ha, I thought so! I told the guy I had the original debate with that his youtube video actually hurt his argument. I said that if the plane is allowed to outrun the treadmill, then the treadmill might as well not exist in the equation, thus making the scenario pointless. I said that his video never did produce the situation in which the speed of the plane was matched by the treadmill's motion, since the only time the plane was "still" was while its motor was off and the string was holding it in place. He argued that the string holding the plane was the same thing as the plane being relatively stationary due to its acceleration being matched by the treadmill, and I STRONGLY disagreed.

Plus, I wanted proof that an experiment with a plane on a treadmill could actually produce flight, and he never showed me anything conclusive. But it was a frustrating argument because I felt like the guy just didn't get it, and I could tell he felt exactly the same about me. It was nice to have a good argument that didn't break down into flaming, though. ;p

Muthafuckin planes on muthafuckin treadmills? I remember last SEN Doodan you got mad at me because I said some kid's sunken colony map was stupid. Now I get punched with this in the face. Okay.

Ya... the treadmill is nothing to support what is going on here... Simply what that is doing is pushing the air though the plane to make it go up the treadmill, but it doesn't matter weather the treadmill is moving or not... it is still going to go. So really, the whole moving thing under the plane isn't going to help the kid out... Let your 'opponent' if you will Doodan to stick with this day time job and try to get some sleep at night without using drugs to do so,

It will be able to achieve flight, but not movement.

Funny, Syphon .
The only way this would be possible if the room was shaped and the treadmill had grooves to create VERY strong air currents. In that case, yes, it would basically be flying but not moving. It's probably possible to create a treadmill, a lightweight plane, and a room to do this. Not round wheels, but maybe something like 10 X's, each rotated an additional 36 degrees from base position to make up for uneven treadmill (might require much more, maybe just 90/90/90/90 X wheels). A properly shaped room could manipulate air currents to make a loop-di-loop and hit the wings. This would, however, require insane speeds or larger grooves in the treadmill, and the wheels have to scale with that... might even force the treadmill to break the speed of light barrier, making it impossible.

I don't know. Might be possible, might not be. But NEVER could the standard plane on a gigantic treadmill do this.

And The Point To Have No Movement But Flight Is What?

if the plane was on a tread mill and it wans't moving would be impossible as people said due to the wheels not being the way it goes forward. But just for science sake if the plane had it's prop/jet on full blast and wasn't moving it would not lift off due to the need for air moving over it's wings for lift.

If you would like I could get into the whole how lift works definition.

Of course it can take off, because the conveyer belt isn't moving.