# Plane on Conveyor Belt

The original article can be found here:

The idea is that the plane takes off on a conveyor belt going in the opposite direction at the same speed and the plane achieves flight… right? But that’s impossible.

The flight of an airplane is based on lift and I don’t think I have to explain that in detail.

Here’s a question… when you run on a treadmill does wind suddenly accelerate past you? No… it doesn’t. The air current stays relatively stable. If you were to run outside though you would notice as you run you feel wind resistance against you. Stick your hands out a car window on the highway and you can experience lift for yourself. I guarantee though that if you put your arms out the wind while you are car was accelerating on a moving platform going in the opposite direction at equal speed… you would be disappointed.

The only thing really being worked on a plane in that scenario is the wheels of the plane. You still don’t have enough fluid force going around the air foils to create any upward lift even though you have acceleration.

To further my point… imagine a plane in a vacuum with this same set up. Obviously there is no lift because there is no air flow. The plane can’t take off. But it’s not just the lack of air, but also the lack of acceleration AGAINST the air.

You are accelerating the plane in this scenario, but you’re not accelerating it against the air current. Ever notice that a in a wind tunnel a model plane can be in a still state and attain lift once the wind is turned on? The acceleration isn’t what is important. It’s the air going around the foils at increased speed.

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It’s noted by Cecil in the article that the forward thrust overcomes the moving platform… if the moving platform always moves the same speed then that’s not true at all unless we assume it doesn’t.

Even if there is some lag between how quickly the moving platform can adjust, it still isn’t enough to compensate for the lack of air flow around the air foils.

Even if it is the case that the plane travels faster than the treadmill that means it just has to accelerate X times faster in order to achieve lift.

Example a light craft achieves lift at 70Mph… and the platform moving against moves at 60 then the light craft has to achieve 130Mph roughly to achieve lift.

If the moving platform was always the same speed as the craft, the plane could NEVER achieve lift.

The difference between me on the treadmill and a plane on a treadmill is that the part of me that’s contacting the treadmill is also involved in the generation of power to produce forward movement on my part. That’s not true of the plane. The production of forward movement in the airplane is independent of what’s happening at the wheel-treadmill interface. So it doesn’t matter how fast the treadmill is going–as fast as the plane, or even faster than the airlplane–the airplane moves forward and takes off.

ETA: Note that if the plane is standing still on a non-moving treadmill, and the treadmill begins moving backwards, and the plane’s wheels have a low enough friction coefficient, then the plane will not move backwards but will stay still while the wheels roll under it. (The plane will move a little because there’s always friction–but the point is the plane doesn’t have to move nearly as fast as the treadmill. The treadmill’s motion does not impart the same velocity to the airplane.)

Take a propeller plane.

The propellers are really doing all the work, but the wheels are still an important part of the mechanism obviously.

If this propeller plane starts at rest along with the moving platform, and accelerates with the platform accelerating at the same rate, but in an opposite direction the plane will appear stationary.

I think the argument here is that the planes propulsion is from the propeller and not the wheels that in those cases the wheels would just magically ignore the moving platform beneath it. But it’s not the case. Even though the propeller is causing the forward acceleration, it’s still the wheels which are in contact with the ground who are responsible for the acceleration.

Even in the case with a jet turbine it would be the same thing.

If there were a craft that didn’t require wheels and started in a hovering mode, that would be a different situation as the platform below would have no impact on it.

Define what you mean by “important.” They’re rather essential in holding the plane off the ground–but from the point of view of forward acceleration, add nothing to it, and in fact subtract quite a bit (due to friction).

You’re just plain wrong that an airplane’s acceleration has anything to do with its wheels. For one thing, how do you contend that those wheels are responsible for the acceleration? If you look at most airplanes (easiest to see on simple piston engine planes, e.g Piper J-3 Cub - Wikipedia), they’re not powered–in fact, there’s no machinery at all going to the wheels–how are they responsible for the acceleration?

Or, even better, look at a seaplane. No wheels at all! And yet, it manages to accelerate on its pontoons, and even take off.

Actually, that is probably a useful alternative formulation of this problem–one that shows that the fact that the airplane has wheels is irrelevant. (I’m sure someone has suggested it before). Replace “airplane” with “seaplane” and “treadmill” with “river with current exactly equal to speed of treadmill.” Same problem, but no wheels (more of a risk of breaking the pontoons, but the point is that the force back is relative to the drag on the pontoons, and the force forward is proportional to the power of the motor)–the pontoons themselves don’t add to the forward force. They’re just floats.

Try this: Think of an airplane one second before takeoff. Accelerating, sure. Wheels on ground, sure.

Now think of that airplane one second after takeoff. Accelerating, sure. Wheels on ground, nope.

If the wheels on the ground were responsible for the airplane’s acceleration, you’d expect a dramatic change between the acceleration before and after takeoff.

Now I’ve flown in airplanes quite frequently, and have never felt such a change at the moment of takeoff. Have you?

What distinction are you trying to make between causing and responsible for?

Okay try doing it with just the fuselage dragging on the ground. I’d say it lowers friction quite a bit wouldn’t you?

Again take away the wheels.

Water isn’t the same surface as say concrete or rubber. So moot point. Not a good example at all. You could theoretically have a take off without pontoons as well.

Exactly… they are just floats. They don’t serve the same purpose as wheels on the ground.

I’m not surprised by that at all. I just mentioned that a hovering craft would not have to deal with the forces at work on the ground and could still freely accelerate.

No… not really.

Okay… here is a better idea.

Lets remove the wheels and still keep the plane on the ground.

Lets add a lubricant to the moving platform that makes the friction almost 0.

Now accelerate the plane and the platform at the same rate, but in opposite directions.

The plane will stand still.

Point is: Velocity of treadmill does not have a direct correlation with the velocity of the airplane. The plane can move forward even as the treadmill moves backward with equal velocity–because the wheels roll freely.

I can wear roller skates on a treadmill, and pull myself along the rails at 5mph, while at the same time the treadmill is moving backwards at 5mph. Any backwards force imparted to me from the treadmill by friction in the wheel mechanism is trivially overcome by the power of my arms pulling on the rails. I move forward.

Same with the plane, but replace “arms and rails” with “propellers” or “jet engines” or whatever you’d like.

Not true. See the analogouse skater on a treadmill situation I mentioned before.

The velocity of the treadmill does not impart an equal* velocity to the body on the treadmill, as long as the friction between them is low.

*(or even clearly correlated, once an additional forward force is added to the mix)

It kind of makes sense and it kind of doesn’t.

Someone needs to test it out with a real jet. Not a remote control plane, but a real airliner.

Sorry for the triple post, but another related illustration occurs to me. Take that wheelless, lubricated plane you mentioned. Attach bars to it, and attach trucks to those bars on either side, where the trucks aren’t on the treadmill but on the ground. Start the treadmill. Now have the trucks accelerate the other way. Their movement pushes the plane forward–and because of the lubrication, they are hardly pushed backward at all. They can accelerate the plane to an arbitrary speed, treadmill notwithstanding. The speed of the treadmill is for all intents and purposes irrelevant.

Or think of it as a toy plane, and there’s a kid sliding it across the treadmill. The kid can slide it at whatever speed it wants, the speed of the treadmill only making it possibly a tiny bit more difficult to do so–but only a tiny bit, and certainly not enough to make it possible for the plane to reach a speed corresponding (“corresponding” because in this case it’s just a toy plane) to takeoff speed.

I know Mythbusters did it, but to my recollection not everyone was happy with the way they interpreted the situation. I haven’t seen the episode myself.

Well, let me ask again: How are the wheels “important” in the plane’s acceleration? I’m just asking you to explain your contention.

And what, as you understand it, is the purpose of those wheels? Please, be specific.

You miss the point: what changes between the moment before and after takeoff? It’s the same question I’ve been asking all along: What, in your understanding, are the wheels doing?

What you’re confused by here are two separate cases:

(1) the thing moving backwards is the thing the airplane is pushing against to go forward. E.g. moving north at 100 kts airspeed in a 100 knot wind from the north. Result: Indicated airspeed, 100 knots, ground speed zero.

(2) The airplane on, or on a frictionless surface on, or for that matter, immediately over the treadmill. The thing the propeller or jet is pushing against is air. The thing moving is the treadmill. Result, airplane moves forward independent of the treadmill.

Heh. Let’s see if Cecil’s right when he says, "message-board discussions of this question tend to feature a lot of posters who haven’t yet arrived at BR #1 talking right past those who have, insisting more and more loudly that the plane won’t take off. "

I just watched the ep and didn’t think it was done very well.

I was probably wrong in the case of the frictionless surface.

But I still say that there is enough friction between a commercial jet and the ground to keep it on the ground due to gravity or what not against the surface of a moving platform.

Okay new question.

If say the plane was on something like a chassis dynamometer… could it still take off? Would it jump off the dynamometer or would it stay stationary.

Actually… that would have been a better way to test than a tarp connected to a truck.

The prop pulls the plane through the air. The wheels just keep it off the ground. They have nothing to do with acceleration.

A plane can take off from water with floats or soft ground, snow or ice, with skids.

It would hop over the wheel on the dyno and then take off.

This guy explained it better than cecil

Are we really doing this again? Are we? Really?