The flawed assumption here is that the wheels have anything to do with the equation.

Look at a real-world analogy to this problem: a seaplane taking off upstream on a moving river. This is quite obviously possible, as it’s done all the time in places like Alaska. The river serves as the treadmill.

The ability of the aircraft to be driven forward has essentially nothing to do with the wheels/floats/skids/etc., and everything to do with overcoming whatever friction exists between the landing gear and the surface (or, in the case of wheels, internal friction in the bearings). Relative to the thrust of the engine(s), this friction approaches zero, or a plane would never be able to take off from a *stationary* surface!

Since the wheels of the airplane are serving solely as a support, not as a driving force (unlike in a car, which is propelled forward by a force transmitted through its wheels), the plane will take off just fine. The only possible hang-up would be that the wheels will be turning twice as fast as normal, which has the possibility of overstressing the tires and/or wheel bearings. (In a typical piston single, like a Cessna 172, this wouldn’t be an issue, but in something like a 747, which has a rotation speed approaching 200 MPH, you might encounter tire failure before you gained enough airspeed to lift off.)

cl

No, not impossible — it would take off. Modern planes take off because the jet engines push the plane forward, and the wheels aren’t hooked to an engine like in a car. So with a treadmill moving backwards, the only difference when the plane takes off is that the wheels would move much faster, but the plane would still move forward.

I assume that the treadmill is going to keep the plane from making any forward motion, in which case there would be no air passing over the wings which means there would be no lift.

If the plane is able to move forward on the treadmill, then obviously the plane would be able to take off. The issue is whether air moves over the wings, right? A stationary plane can’t take off because no air is passing over the wing.

I assume that the treadmill is going to keep the plane from making any forward motion

That’s a flawed assumption. Try it with a model airplane and a real treadmill if my seaplane analogy isn’t working for you.

The treadmill can only prevent a vehicle from moving if that vehicle’s sole source of forward movement derives from friction between its wheels and the surface (i.e., a car or motorcycle). If you put an airboat on wheels and stuck it on a treadmill, it would move forward, regardless of how fast the treadmill was going. If you put a jet engine on the roof of a car and fired it up, the car would move forward on the treadmill too, again regardless of how fast the treadmill was going.

The frame of reference most people have for vehicles in motion is a car (or motorcycle or bicycle), and in order for a car to move forward, its wheels have to push backwards against the ground. An airplane, be it propeller- or jet-driven, derives forward motion from pushing against the *air*, not the ground. The wheels simply serve as a convenient means to reduce friction with the runway.

Another thought experiment that might convince you: consider a car and an airplane at rest on an icy road/runway. When you stomp on the gas pedal in the car, what happens? When you push the throttle forward in the airplane, what happens?

cl

Ok, let me try again.

I acknowledge that outside of the treadmill scenario, the plane is moving forward because the engines are pushing it through the air. However, until it has enough speed to take off the ground (either thanks to the wings creating lift or the engine being strong enough to lift the plane off the ground without wings) its motion is still going to be based on the frame of reference of the ground on which it’s sitting.

If the plane were ‘off’ on a treadmill, it would move backwards along with the treadmill. If you turn on the engine and gain enough thrust to bring the plane up to the same speed as the moving ground, it would remain stationary.

Am I right so far?

Assume that the treadmill always adjusts speed to remain at the same speed as the airplane, how does the plane ever create enough lift with its wings to become airborne? The air around the plane is stationary. The only air moving is the air moving through the jet engines which, as far as I know, just creates forward motion and not the lift that’s created by the air moving over the wings and that lift would be what is required to become airborne.

Is that right?

With the air being stationary around the plane, I don’t see how it’s possible for the plane to create life and become airborne. What’s important is the speed of the wings relative to the speed of the air. As long as the air is stationary in relation to the wings, it should never be able to take off.

Well, it’s quite obvious that the plane wouldn’t take off without the snakes, seeing how it needs more than just engine speed to take off.

However, if there were snakes on the plane, or even chasing the plane, the plan would take off out of fear. It’s pure science.

-Cheezer-

Actually, assuming frictionless or nearly frictionless wheel bearings (close to reality), if the plane was off on a moving treadmill, the plane would remain stationary, or nearly stationary. As Chris said, unlike cars, planes’ movements are not coupled with their wheels. The wheels merely serve as a way of reducing friction with the ground; technically, a plane could take off with a set of blocks of butter well-attached to the body.

BoingBoing posted a comment which I think sums up the issue (as I see it) fairly well:

The hold still people are allowing the flaw of the thought experiment (the bad idea of trying to use a treadmill to hold a plane still to persist) to go unnoticed and are accepting as an assumption you could hold a plane still while it’s engines are on full. A better way to do this would be to just chain the damn airplane to the ground.

The take off people are obsessing on the flaw of the experiment, and the necessity of higher rolling friction for a treadmill to have an effect on the airplane. A pilot could actually do this by applying break pressure to the wheels to increase the friction effects.

Depending on which assumptions you accept or reject, a physical impossibility occurs. If you accept you could generate enough backward momentum to hold the plane still relative to the ground’s reference frame (which I think was a precondition of the problem as I saw it stated) then the hold-still people are right. If you reject the treadmill as a mechanism of holding a plane still, then the take off people are right.

I don’t think that summation captures how most “hold still” people think about the problem, but only a small fringe group. I think when people first think about the problem, they think about a plane similar to a car, which leads them to the “hold still” conclusion. I doubt they’re usually thinking about wheel friction.

Also, the precondition he refers to is not in the problem as originally stated. Sorry, the plane takes off.