Plane on a Treadmill

[Warder60]

As we're all internet forum addicts... I'm sure we've heard of the "Plane on a Treadmill" puzzle.
And just to summarize - the question is, if a plane is on an infinitely long treadmill that is capable of accelerating to match the speed of the plane, will the plane take off?

There's no official answer, and you can find die hard supporters of both answers.

Well, Mythbusters is taking it on. They actually originally planned to air it a month or so ago, but delayed it. If I'm correct, it's airing this upcoming Wednesday - the 30th.

Perhaps everyone would be interested in placing bets for takes off vs. doesn't take off. Moderators would have to be in control of what wins, theoretically the Mythbuster result. But they've had controversial results in the past, and could end up with a "possible" or "unknown" result, etc. So we'd have to let our moderators choose winner or tie/no result.

Anyone remember if this (plane on a treadmill) has been discussed here before?

 

[Warder60]

Re: CyBookie - Plane on a Treadmill

as a quick addition -- part of the debate is what exactly does the puzzle mean. Mostly on what is implied by the treadmill's ability. Generally I think it's accepted that the treadmill will match the plane's wheel's acceleration and velocity. So as the wheels start to go, the treadmill begins to go the other direction.
(hopefully this helps clarify for those new to the question)

 

[aeroclone08]

Re: CyBookie - Plane on a Treadmill

It will still take off.

 

[ISUboi12]

Re: CyBookie - Plane on a Treadmill

im not an engineer or a physicist. the classes i took in either discipline are not enough to even merit an educated guess.... in fact i studied social science so excuse any of my ignorance.

however i was under the impression that air pressure above and below the wings is what caused lift. if the propulsion is negated by the treadmill and the wings are unable to actually cut through the air and create an air pressure differential how can lift be created?

 

[Aaron Jacobs]

Re: CyBookie - Plane on a Treadmill

Its a dumb question because the thrust is generated by the turbines not by an axle spinning the wheels, and with the turbines spinning it will create the pressure change and thus you have lift

PS I'm a Fine Arts major, it doesn't take a genius to figure this out.

 

[ISUCyclones]

Re: CyBookie - Plane on a Treadmill

are you serious? Im an ME and this is a dumb question.

 

[ISUKyro]

Re: CyBookie - Plane on a Treadmill

I'm staying out of this, all I'll say is the wheel speed does not mean a thing. How fast the wings are splitting the air is what counts. In other words how fast the plane is moving relative to the ground (not the treadmill). As the air splits the wing the particle on top moves faster (greater distance to travel) than the particles on the bottom thus creating lift.

 

[redrocker]

Re: CyBookie - Plane on a Treadmill

So MythBusters got a Big Treadmill, huh?

I agree, it will not take off, but what do I know.

 

[cyfan964]

Re: CyBookie - Plane on a Treadmill

Where are the aeronautic engineers? I know there are a couple on this board and I am sure this question got brought up in school.... and i'm sure they know the answer.

 

[cyfan964]

Re: CyBookie - Plane on a Treadmill

And for the record I would put a LARGE sum of money on the plane taking off.

 

[JRCampy]

Re: CyBookie - Plane on a Treadmill

Lift is created by the air on the top of the wing moving faster than air going below the wing (low pressure on top of the wing vs. high pressure below it). If you were to place the plane on a treadmill you're not moving any air over the wings. Just think of yourself running on one, do you feel a breeze the faster you run?? No, so the plane would definitely NOT take off...

 

[isuno1fan]

Re: CyBookie - Plane on a Treadmill

It will not take off....case closed. ME grad with Thermodynamics classes taken.

 

[cyfan964]

Re: CyBookie - Plane on a Treadmill

Exactly how does the conveyor belt keep the plane's speed in check? The wheels are free to move - the conveyor belt can speed up as much as it wants, but the plane still has forward thrust from the prop/turbine.

 

[cmoneyr]

Re: CyBookie - Plane on a Treadmill

The speed of the "runway", or treadmill in this case, is irrelavent. The plane is pushed forward by the thrust from the engines, not the wheels, the wheels basically spin freely. I don't know if Mythbusters will be able to prove this or not with their tests, but I would bet money that the plane will take off under the right conditions of a test.

If a plane was landing on a treadmill that was matching it's speed exactly would it just come to a hault as soon as it hit the ground? No.

 

[IsUaClone2]

Re: CyBookie - Plane on a Treadmill

Lift is created by the air on the top of the wing moving faster than air going below the wing (low pressure on top of the wing vs. high pressure below it). If you were to place the plane on a treadmill you're not moving any air over the wings. Just think of yourself running on one, do you feel a breeze the faster you run?? No, so the plane would definitely NOT take off...

This summarizes best without using engineering language. Lift is created as the difference in speed relative to the air and the wing. If the air doesn't move, the plane doesn't move. The difficulty in this excercise is keeping the treadmill pace equal to the plane's attempt at acceleration.

Another way to look at it is that it is easier to take-off against the wind rather than with the wind. Accordingly, if the turbines are not allowed to propel the edges of the wing because the turbine force is negated by the rotation of the wheels against the treadmill, it is a no go. Again the trick will be to match the treadmill and plane acceleration.

 

[tim_redd]

Re: CyBookie - Plane on a Treadmill

At first I thought it wouldn't take off, but now I think it would. Think of a person on roller skates, er roller blades on a treadmill. Think of two cases, the treadmill not running, and when the person on the treadmill is stationary, ie wheels and treadmill at the same speed. Now think of an outside force such as another person pushing the guy on the treadmill. This would be the thrust of the jets. It would take the same force to push the person forward the same relative amount whether or not the treadmill is on or off, assuming frictionless bearings.

I think the key part of the whole question is the speed of the wheels. If I understood this question, the speed of the wheels means absolutely nothing in the whole scheme of things.

 

[ISUKyro]

Re: CyBookie - Plane on a Treadmill

If it helps some to think of it. Imagine a building just to the side of the belt. As the planes wheels are going 300mph against the belt, if the plane is standing still relative to the building then it is not going to take off. Even though the engines would be producing a great deal of thrust, there would be no lift. No lift, no flight.

 

[jumbopackage]

Re: CyBookie - Plane on a Treadmill

If the forward motion was being generated by the wheels of the plane, the plane obviously isn't going to go anywhere. The difference here, being that the forward thrust of the aircraft is generated by either a prop or a jet (or potentially a rocket), so it doesn't matter how fast the wheels are traveling, merely how fast air is traveling over the wing. That's the difference between indicated airspeed, and true groundspeed.

The problem we have here though, is that to move the plane forward through the air, the wheels have to spin relative to the air moving over the wing while the plane is on the ground, not just relative to the treadmill. The whole earth isn't moving any faster, just the treadmill, so the air won't be moving any faster as the wheels accelerate. Of course the whole system depends greatly on the treadmill being able to determine the amount of thrust, and hence how fast to turn. That's going to be the key part of the whole thing.

My vote is that the plane will not take off, but the treadmill will make the difference. The treadmill is going to have to go VERY VERY fast in order to keep up, and the wheels will probably seize and snap off at some point, since the entire thrust of the aircraft will be just trying to overcome the friction caused by the spinning wheels, which for most aircraft is pretty small, as opposed to pulling the whole plane through the air.

The more thrust you have, and the faster it's applied, the harder it will be for the treadmill to keep up. If you slap a rocket plane on there, I don't' think it's probably feasible for the treadmill to keep up, though theoretically possible (probably). Put a Piper cub on there and slowly throttle the engine up, and I bet it stays on the ground given a fast enough treadmill. The treadmill is going to have to spin WAY faster than the plane is capable of normally going though.

 

[JRCampy]

Re: CyBookie - Plane on a Treadmill

This summarizes best without using engineering language. Lift is created as the difference in speed relative to the air and the wing. If the air doesn't move, the plane doesn't move. The difficulty in this excercise is keeping the treadmill pace equal to the plane's attempt at acceleration.

Another way to look at it is that it is easier to take-off against the wind rather than with the wind. Accordingly, if the turbines are not allowed to propel the edges of the wing because the turbine force is negated by the rotation of the wheels against the treadmill, it is a no go. Again the trick will be to match the treadmill and plane acceleration.

Guess that's why I only made it through two years of Aerospace Engineering, couldn't talk the talk... :wink:

 

[jumbopackage]

Re: CyBookie - Plane on a Treadmill

If a plane was landing on a treadmill that was matching it's speed exactly would it just come to a hault as soon as it hit the ground? No.

The difference being that the aircraft has already acheived a positive forward velocity, enough to keep it airborne. Upon landing, if the treadmill was spinning fast enough that the resistive force generated by the wheels spinning is enough to match the forward energy stored in the aircraft, yes the plane would come to an immediate stop.

The treadmill will not be matching the relative velocity of the world around the aircraft, but the forward force applied to the aircraft by it's engines and it's relation to the mass of the aircraft.