A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?

Comments from another forum

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@A1200



Errr, NO! But the tyres will ge hot


Wol.

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@A1200

No, since no pressure will be generated under the wings to give the aircraft sufficient lift.

Last edited by amipal on 24-Feb-2006 at 05:01 PM.

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@amipal

This is not a simple answer. People at work have been arguing all week about if it will or not. DaveP and my finance manager spent 20 mins chatting online about the issue, at one point I saw algebra on the screen so god knows who won that discussion!

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@A1200

Seccond thoughts, YES; but the wheels will be rotating twice as fast,
the tyres will probably explode..

The plane is Jet powered, so it will still move forward throgh the air
regardless of what the ground is doing.


Wol.

Last edited by Wol on 24-Feb-2006 at 06:26 PM.

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@A1200

A car would slip, a plane won't but the use of the word speed in the question is suspect. What speed is it tracking, the speed on the ground or the speed on the conveyer belt? Trick question IMO.

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@A1200

If the speed of the conveyorbelt runway matches the "speed" of the wheels/plane then I'd reckon it would stand still as the air needed to generate the lift would appear to be moving as normal as if the plane was indeed stationary.

So no, in my mind it wouldn't take off.

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@Wol

Ah! You are probably right, as the wheels are not generating the movement but the jets/propellors themselves which act on the air around them.

Good thinking!

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@L8-X

Yes it can, but the wheels will go backwards twice as fast as normal.
AFAIK Planes are not wheel driven, its the thrust behind (or infront) that moves the plane to take off speed but the plane might take a bit longer to take off because of the added drag on the undercarrage.

well, thats my theroy anyway...

wizz.

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@All

http://www.straightdope.com/columns/060203.html


And from http://www.pprune.org/forums/showthread.php?t=209859&highlight=conveyer (need to register I believe)

Quote:

Well, yes. That was my original thought when I posted this thread. However, in reading some of the arguments on the original site, I am now convinced that the aircraft will fly. The basic argument says that since the wheels of the aircraft are free to rotate (i.e. not powered like a car) the movement of the conveyor belt will do nothing except cause the wheels to rotate. Assuming no friction, the aircraft will remain stationary. Now... start its engine, and it will pull itself forward through the air until it gains sufficient speed to take off. The difference between this and a similar question involving a car is that a car powers itself by pushing against the ground, while an aeroplane powers itself by pushing against the air.

Some other nice things from that forum / thread;

Quote:

Quote: If an aircraft is in flight and inside it, a bird is also in flight, does the aircraft feel the weight of the bird? No

Quote:

Quote: And If the aircraft is flying at, say, 500 kts and the bird has a max speed of 100 kts - will the bird manage to fly from the back to the front of the aircraft? Yes

Haven't read all of it yet tho


Not the best proof but ok

Last edited by Seer on 24-Feb-2006 at 07:58 PM.

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@Seer

Quote:

If an aircraft is in flight and inside it, a bird is also in flight, does the aircraft feel the weight of the bird?

Quote:

No

I`m not sure about this one. A bird can`t fly in a vacuum so we can assume it`s creating downwards momentum in the air in order imbue itself with upward momentum to overcome gravity. As the atmosphere in the `plane is sealed this momentum must ultimately be transferred to the `plane, so it DOES feel the weight of the bird I reckon.
Anyone else got any thoughts?

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@L8-X

Quote:

Ah! You are probably right, as the wheels are not generating the movement but the jets/propellors themselves which act on the air around them.

The result of the pushing against the air is movement relative to the ground, however if the ground is moving the opposite way there will be no movement.

So, it doesn't matter what the engines push against. The result will be a pane moving relative to the conveyer but not relative to the air, it will never get the speed necessary to generate lift and thus not take off.


Look at it another way though:
Imagine the plane puts it's brakes on and only the conveyer moved the plane forwards, if the conveyer could move the plane at sufficient speed it would take off without using engines at all - because it would then be moving relative to the air fast enough to generate lift.

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Whyzzat?

@minator

No! Pushing against the air results in movement relative to the air, all that changes with the conveyor present is the friction at the wheel bearings.

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Fraggle

- insert profound text here -

@Frags

From the same site a reply to that;

Quote:

Two scenarios. First, imagine a totally enclosed cabin. The cabin contains the pilot, the bird, many billions of air molecules, amongst other things. The aircraft's wings have to carry the weight of everything in the cabin. Makes no difference whether the bird is on the floor of the cabin or not, it is still in the cabin, and so still needs to be carried. Scenario number two: an open ####pit aeroplane, with the bird flying six inches above the top of the ####pit, at the same speed as the aeroplane. The bird is clearly carrying its own weight, and does not require the aeroplane to carry its weight. The reason for the difference, I think, is that in the first case, the downwash from the bird's wings strikes the floor of the cabin and exerts a force on the floor of the cabin which is equivalent to the weight of the bird. Whereas in the second case, most of the downwash from the bird's wings escapes from the aeroplane. I've never actually seen proof of this explaination, though. The interesting things is the in-between situation. For example, the open-cockpit aeroplane with a bird sitting on the seat. During the flight, the bird decides to take off and leave the aeroplane. At what point does the aeroplane stop carrying the bird's weight? You can apply a very similar argument to the bird moving at 100kt and the aircraft moving at 500kt.

Anyway, how are you going to proof any of that ? Bolt a balance under it ?

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@Seer
Good thread this, I like mechanical puzzles.

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Fraggle

- insert profound text here -

Quote:

J.A.F.O., The conveyor belt does not oppose the forward motion, apart from the negligible effect of friction within the wheel bearings easily overcome by the power of the engines, as seen every day when aircraft taxi on stable ground! Hold a toy car in the air then press it onto a moving treadmill such that the wheels spin up, but the car does not move relative to the air or the fixed ground outwith the treadmill. You are holding the toy car in a fixed place, with the only effect being that the treadmill causes the wheels to spin. Now use your hands to move the toy car "up" the treadmill, in the opposite direction to that at which the belt is moving. What are your hands doing? They are applying an external force to the car, NOT RELATED to the moving belt system, in order to move it relative to the air. In this case, the reaction is between your hands and the surfaces of the toy car. This is the EXACT SAME FORCE the engines on an aircraft would provide, with the reaction in that case being between the air (every bit as "external" to the system as your hands), the engines and their exhaust. Does anyone HONESTLY believe that they will not be able to push a simple toy car up a moving supermarket checkout belt, or exercise machine? The principle is almost exactly the same as that of the aircraft on the conveyor belt runway as far as I can see, and it works fine! The aircraft would fly.

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@Frags

Quote:

No! Pushing against the air results in movement relative to the air, all that changes with the conveyor present is the friction at the wheel bearings.

Pushing against the air pushes the plane forwards, the conveyer will be generating the exact same force in the opposite direction so the planes stands still, it's wheels will however be turning furiously.

Just to complicate things the front wheels will be pushing downwards and the back wheels pushing upwards since there will also be a rotational force involved.

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Whyzzat?

@minator

Quote:

minator wrote: @Frags Quote: No! Pushing against the air results in movement relative to the air, all that changes with the conveyor present is the friction at the wheel bearings. Pushing against the air pushes the plane forwards, the conveyer will be generating the exact same force in the opposite direction so the planes stands still, it's wheels will however be turning furiously. Just to complicate things the front wheels will be pushing downwards and the back wheels pushing upwards since there will also be a rotational force involved.

That`s just it, the conveyor generates an opposing force but it only acts to turn the wheels, not push the plane.

edit: to clarify, the conveyor DOES push the plane but only in that it increases the rpm of the wheels hence the friction at the bearings therefore (phew) it`s a relatively small increase which the engines would easily overcome.

If the conveyor was fast enough to generate a frictional force in the wheel bearings that was large enough to balance the force from the engine then I suspect the tyres would slip against the tarnac or the wheels would come off altogether :o)

Last edited by Frags on 24-Feb-2006 at 09:09 PM.
Last edited by Frags on 24-Feb-2006 at 09:08 PM.
Last edited by Frags on 24-Feb-2006 at 09:07 PM.
Last edited by Frags on 24-Feb-2006 at 09:07 PM.

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Fraggle

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@Seer

Quote:

Does anyone HONESTLY believe that they will not be able to push a simple toy car up a moving supermarket checkout belt, or exercise machine? The principle is almost exactly the same as that of the aircraft on the conveyor belt runway as far as I can see, and it works fine! The aircraft would fly.

Except this is a bad analogy because the exercise machine is not going to react to movement and a toy car is very low mass.

Imagine your toy car was a real car and the exercise machine could react instantly and move at any speed. You first have to overcome the inertia of moving the car which is going to be difficult, after that it's a straight fight between you and friction, but the friction will rise with speed. It has unlimited energy, you don't.

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Whyzzat?

@Frags

You posted this just as I posted mine...

Quote:

If the conveyor was fast enough to generate a frictional force in the wheel bearings that was large enough to balance the force from the engine then I suspect the tyres would slip against the tarnac or the wheels would come off altogether :o)

Yes, it all comes down to how much force the conveyer can generate, if it's unlimited it'll win on friction.

What I think would happen is the front tyre would eventually burst, then the bearings would fuse and the plane would just disintegrate due to stresses.

Last edited by minator on 24-Feb-2006 at 09:16 PM.

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Whyzzat?