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Geek Culture / Plane on conveyor belt problem

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dark coder
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Posted: 13th Dec 2007 22:18 Edited at: 14th Dec 2007 16:45
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So here's the problem; you have a runway sized conveyor belt and a plane at one end(a 747 for argument's sake). The conveyor belt will move at the exact inverse of the plane's speed, so if the plane is moving across the runway/belt at 10M/s the conveyor belt's surface moves at 10M/s in the opposite direction(like a normal treadmill would). The question is, can the plane take off?

[EDIT]

Clarification on page 2:

To clarify this. I put a pole in the ground, which does not move at all. My runway conveyor belt is static too. If the plane moved at 10M/s down the runway relative to this static pole, i.e. our air speed is 10M/s. The conveyor belt's surface will move at 10M/s relative to the pole in the exact opposite direction. There is no wind at all, and if people still have issues understanding the scenario then the conveyor belt could move at a minimum speed of 10M/s in the opposite direction to where the plane will go as well as move at the inverse of the plane's air speed. The actual speed of the conveyor belt isn't so important.

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AaronG
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Posted: 13th Dec 2007 22:24
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I think not, because the two will move against eachother at an even pace.

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Van B
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Posted: 13th Dec 2007 22:25
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I'd say no, the plane needs to move forwards in order to build lift in the wings, no way for that to happen if the plane is in a fixed position, really all it's doing is turning it's wheels.


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Xenocythe
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Posted: 13th Dec 2007 22:25
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It will take off, but when first going up in the air the plane will hesitate because the wheels against the conveyor belt while in air.


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Grandma
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Posted: 13th Dec 2007 22:27 Edited at: 13th Dec 2007 22:28
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Quote: "The question is, can the plane take off?"


Not unless the belt stopped. If the belt would suddenly stop though, the passangers might experience some slight uncomfortable forces.

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dark donkey
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Posted: 13th Dec 2007 22:27
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Well i think not. But thats me. I think the plane has to be actually moving to create the lift to take off. In this case the engines will be on and it will be trying to move but it wont be because of the conveyor belt. But interesting question non the less. Also it might if you have some really powerfully fans in front of it but they would have to be really really powerful to thrust the air against the wings.
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Cash Curtis II
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Posted: 13th Dec 2007 22:28
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I'd say no as well, because the plane uses lift to take off which is generated as it speeds up in relation to the atmosphere. That is, air moving under the wings. On the treadmill it's speeding up relative to the treadmill but not the atmosphere, so no lift is created.


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Benjamin
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Posted: 13th Dec 2007 22:30 Edited at: 13th Dec 2007 22:30
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I think the one thing people forget is that the wheels don't provide traction on a plane, rather they serve to eliminate friction between the ground and the plane. The wheels can turn freely without the plane moving, and if the engines provide sufficient force (very little is necessary), the plane won't actually move backwards. The same can be said without engines, if the friction is 0%.

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dark donkey
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Posted: 13th Dec 2007 22:32
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@Benjamin: Yes.... but the question was if the plane was moving as fast as the tread mill. And there is always friction unless your in a hover car . Just that circels moving generate less.
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The Nerd
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Posted: 13th Dec 2007 22:33
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Quote: "but the question was if the plane was moving as fast as the tread mill."


---
Taken from original post:
Quote: "The question is, can the plane take off?
"


Hehe

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Benjamin
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Posted: 13th Dec 2007 22:34 Edited at: 13th Dec 2007 22:35
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Quote: "Yes.... but the question was if the plane was moving as fast as the tread mill."

Yes, in the opposite direction. If the plane is going at 600km/h, and the treadmill was going in the opposite direction at the same speed, all that would happen is that the wheels would turn at twice the speed - there's little friction between the wheels and the plane so it would have little effect on its motion. The wheels would have to be locked in order to deliver full motion from the treadmill to the plane.

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dark donkey
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Posted: 13th Dec 2007 22:35
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I didn't mean like that . I mean the question was if it was
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The Nerd
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Posted: 13th Dec 2007 22:36
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Quote: "I didn't mean like that . I mean the question was if it was "


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dark donkey
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Posted: 13th Dec 2007 22:39
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Quote: "little effect on its motion."


Now i get what ya mean. But still its going as fast as the treadmill. So it would need to generate some lift so a pair of its wheels could get of the ground so it could take off.

Excellent theory non the less but this wont be solved until we have a big conveyor belt and a plane.
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Benjamin
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Posted: 13th Dec 2007 22:40 Edited at: 13th Dec 2007 22:41
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Quote: "But still its going as fast as the treadmill. So it would need to generate some lift so a pair of its wheels could get of the ground so it could take off."

In the opposite direction! It would generate lift, the plane would move forwards with little resistance.

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Robin
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Posted: 13th Dec 2007 22:41
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Don't planes take off when their speed relative to the air reaches a certain value? hence its good to take off into a headwind, then you don't need to go as fast because your speed relative to the air will be greater anyway.
but yeah, if it's an idealised frictionless case you're saying, the plane will just stay still and the treadmill will run through under the wheels, no? therefore it won't take off.

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Benjamin
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Posted: 13th Dec 2007 22:42 Edited at: 13th Dec 2007 22:44
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Quote: "therefore it won't take off"

Yes it will, because:

Quote: "The conveyor belt will move at the exact inverse of the plane's speed"


In other words the plane is moving, just like conveyor is. Just in the opposite direction.

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Robin
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Posted: 13th Dec 2007 22:44
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yeah, but relative to the *air*, the plane is stationary...

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Benjamin
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Posted: 13th Dec 2007 22:45 Edited at: 13th Dec 2007 22:46
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I already explained why it isn't stationary.

It would only be stationary if it was moving at enough speed to counteract the little effect the conveyor would have on it, but the plane is moving at a much higher speed than this.

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Cash Curtis II
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Posted: 13th Dec 2007 22:48
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When you're looking at the plane, it is stationary. There is no airflow over the wings, therefore no lift.


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dark donkey
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Posted: 13th Dec 2007 22:49
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Quote: "In the opposite direction! It would generate lift, the plane would move forwards with little resistance."


Yea i mean in the opposite direction. Look at the pic it how i mean but first it would have to create the lift wich is cant. So it cant take of no matter what

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Benjamin
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Posted: 13th Dec 2007 22:50 Edited at: 13th Dec 2007 22:52
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Compare it to roller skating down a conveyor belt. Would you slow down? No, but the wheels would turn faster. This is because there is friction between the conveyor and the wheels, but no friction between the wheels and the person. Thus, the movement of the conveyor wouldn't have any effect on your movement, as the wheels turn freely under you.

It's important to remember the distinction between wheel speed dictating the vehicle speed, and vehicle speed dictating the wheel speed.

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IanM
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Posted: 13th Dec 2007 22:52
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I can't believe that everyone except Ben said it wouldn't take off

If the wheels were moving the plane forward and the treadmill was moving backwards at the same speed then the actual speed of the plane would be zero ... except that's not the case.

The engines are pushing backwards against the air, not the treadmill. With the engines producing forward thrust, the speed of the treadmill has no effect on the speed of the plane (beyond a little friction, easily overcome by the engines).

You guys have really surprised me this time, and that's not in a good way

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dark donkey
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Posted: 13th Dec 2007 22:55
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Quote: "Compare it to roller skating down a conveyor belt. Would you slow down? No, but the wheels would turn faster. This is because there is friction between the conveyor and the wheels, but no friction between the wheels and the person. Thus, the movement of the conveyor wouldn't have any effect on your movement."


Nice theory again but this would mean the plane would have to move on ground then go onto the conveyor belt?. I don't exactly understand the phsics you explain but i think i know what you mean.

Also another thing has crossed my mind. the airplane motor like blows air behind it sort of if you get what i mean. This might be why an airplane might be diffrent from a car at moving.
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Xenocythe
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Posted: 13th Dec 2007 22:56
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What you talkin' bout willis?

My previous post:
Quote: "It will take off"



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David R
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Posted: 13th Dec 2007 22:57 Edited at: 13th Dec 2007 23:00
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It will take off, provided the treadmill doesn't turn against the wheels to the point that it stops them from turning or something.

EDIT:

Can aeroplane wheels 'lock'? I know they just turn and all, but surely they must have some degree of lock when coming into contact with a surface? (In terms of locking against their pivot/hinge/axle)


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Benjamin
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Posted: 13th Dec 2007 22:57 Edited at: 13th Dec 2007 23:02
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Quote: "the airplane motor like blows air behind it sort of if you get what i mean. This might be why an airplane might be diffrent from a car at moving."

Exactly, a car depends on its wheels to move. If the wheels of a car are moving at 100km/h, the car will move at that speed. However, with a plane the wheels don't provide the traction (they are simply there to roll), thus the wheels can be moving at 200km/h while the plane is only moving at 100km/h.

I should point out that when DC said the plane is moving at the inverse speed, he was referring to the plane itself and not the wheels. The wheels will move at the combined speed of the plane and the conveyor belt.

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dark donkey
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Posted: 13th Dec 2007 23:00
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Yeah so the plane would move forwould and create lift. So Benjamin and IanM are right. But of course it appears that it will not move but when you think about it it creates momentum. So yeah the plane would move.
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dark coder
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Posted: 13th Dec 2007 23:03
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Well at least it didn't take too long for people to agree here! Almost up to reply #400 on Facepunch Studios .

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TDK
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Posted: 13th Dec 2007 23:05 Edited at: 13th Dec 2007 23:10
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Quote: "I can't believe that everyone except Ben said it wouldn't take off "


I can't believe the opposite!

For lift to effect the wings of a plane, a higher pressure has to exist below the wing than above it. This can only happen when the plane¡s wings are cutting through the air at a considerable speed.

In the conveyor belt situation, the plane isn't moving - only the wheels (and of course the conveyor belt) are so lift cannot be generated.

If it worked like that, why the hell do airports have two mile runways instead a set of rollers for each wheel of the aircraft.

[Edit] Having read a few posts which appeared while writing mine, I thought I should quantify that I assumed the OP comment:

Quote: "The conveyor belt will move at the exact inverse of the plane's speed"


would remain true as the plane accellerated. Looks like some of your comments assumed this wasn't true...



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Benjamin
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Posted: 13th Dec 2007 23:07 Edited at: 13th Dec 2007 23:12
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Quote: "In the conveyor belt situation, the plane isn't moving"

Why do people keep saying this? DC already said the plane is moving - at the inverse speed to the conveyor belt. It's not a car, it's a plane. A car in this situation would be stationary because the conveyor belt would carry it backwards (you can't turn the wheels of a car without moving the car).

Quote: "If it worked like that, why the hell do airports have two mile runways instead a set of rollers for each wheel of the aircraft."

The plane will still have to use the entire stretch of the conveyor belt to take off.

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Robin
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Posted: 13th Dec 2007 23:12
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yes...it's moving at the inverse speed to the converyor belt, which means the net speed is zero. if it was stationary, locked on the treadmill, then the plane would move backwards at whatever speed the treadmillwas going.

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Benjamin
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Posted: 13th Dec 2007 23:13 Edited at: 13th Dec 2007 23:14
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Quote: "yes...it's moving at the inverse speed to the converyor belt"

The plane, not the wheels. The wheels would be moving at twice the speed.

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David R
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Posted: 13th Dec 2007 23:14
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Quote: "inverse of the plane's speed,"


This is just being pedantic, but I'd like to add: You can't have inverse speed. Speed has only magnitude, not direction. You could have an inverse velocity, and that'd make sense.


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IanM
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Posted: 13th Dec 2007 23:14
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@Veintitres, sorry - missed your post mate.

@TDK,
The fact that the plane is on a treadmill doesn't stop the engines from producing thrust and pushing the plane forwards. The thrust is generated by pushing the air backwards which is independent of the treadmill.

How about this one - if I put a rollerskate on a running treadmill, attach a piece of elastic to the skate, stretch the elastic to double its size, then release the skate, do you think the skate will stay stationary, move backwards or move forwards?

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Robin
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Posted: 13th Dec 2007 23:16
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the wheels will just be moving at whatever speed necessary to maintain the plane at a constant 'inverse speed' to the treadmill (ie. when the plane is stationary)

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Mnemonix
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If it was a helicopter and not a plane it would be able to take off I think. The moral of the story is, always buy from Mnemonix Helicopters inc. © and you will be able to fly regardless of the current large treadmill conditions.

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dark donkey
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Posted: 13th Dec 2007 23:18
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Quote: "How about this one - if I put a rollerskate on a running treadmill, attach a piece of elastic to the skate, stretch the elastic to double its size, then release the skate, do you think the skate will stay stationary, move backwards or move forwards?"


Its fun solving thease.

But i think this would depend if teh skate got a bit of a run up before hitting the belt.

Actually scrap that its about momentum. The wheels are free moving so it depends on how much momentum it has.
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TDK
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Posted: 13th Dec 2007 23:24 Edited at: 13th Dec 2007 23:28
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Just edited my previous post while you were typing.

I also just had a rethink about it too. The plane's forward thrust isn't through the wheels is it? Therefore forward movement isn't affected by the speed of the wheels.

I therefore officially change my mind and now agree with those who say it will still go down the conveyor belt and eventually take off!

One to make you think though...

[Edit] Posts are appearing quicker than I can type replies, so everything is a bit disjointed...

Anyway, the point is that the jet engine of a plane gives movement to a plane in relation to the surrounding air - not the conveyor belt so it would move regardless of the conveyor belt - which is what some of you were trying to explain earlier...

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Robin
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Posted: 13th Dec 2007 23:30
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hmm yeah but surely if it's moving down the conveyor belt, then it's defeating the actual question, which just says the plane is moving at an inverse speed. If it's moving down the treadmill, it has a different/larger opposite speed to the treadmill.

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Jeff032
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Posted: 13th Dec 2007 23:42
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I believe that we can simplify this to...
Does the plane move in relation to the air?

If the plane does move, then it could take off if it can get moving fast enough.

If the plane does not move, then no air moving over wings, no lift, no take off.

(I think it can take off though)

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Posted: 14th Dec 2007 00:11
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Quote: "hmm yeah but surely if it's moving down the conveyor belt, then it's defeating the actual question, which just says the plane is moving at an inverse speed. If it's moving down the treadmill, it has a different/larger opposite speed to the treadmill."

err.... no.

the plane takes off just fine... almost all of you phail.

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Inspire
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Posted: 14th Dec 2007 00:45
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I agree with Benjamin and everyone who said it will take off.

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code master
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Guys, It's rather simple.

If you put a block on a conveyor belt, it's going to move in the same direction and with the same speed as the belt is, ignoring any small amount of air resistance. Now imagine that the block is now an airplane. Pretending there is no friction on the wheels, the plane will remain in place, even though the belt is moving. So we can safely say the plane is in static position. Apply the thrust of the engines to that, and it will move forward and take off.



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Van B
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Posted: 14th Dec 2007 13:03
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I don't see how it could possibly take off.

The very principles of flight rely on the vehicle creating lift by air passing under it's wings - so for it to take off it would need a lot of force to push it up. If the plane is on a conveyor belt that is keeping the plane in the same position, then the only force applied to the actual plane is the ambient wind speed hitting it.

If there was a lot of wind hitting the front of the plane, then it could take off, but that would not need a conveyor belt or even wheels, just a massive amount of wind force.

Don't you guys think that if this was possible they'd be doing it already - like airports could be put in parking lots and rooftops.


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Jeff032
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Posted: 14th Dec 2007 13:16
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Ok...

A plane's wheels don't make it move, which is why they have to toe it to the runway. It moves because of the thrust from the jet engines. The wheels simply serve to eliminate most of the friction between the plane and the ground. Therefore, it will still move forward if placed on a conveyor belt. You can use the conveyor belt to spin the wheels much faster than the plane is moving, and it will have only a very little effect, because the wheels are not entirely frictionless.

It obviously can't take off if the conveyor keeps it in place, but thats the thing, the conveyor doesn't keep it in place. It still moves.

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Peter H
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Posted: 14th Dec 2007 13:36 Edited at: 14th Dec 2007 13:37
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Quote: "The very principles of flight rely on the vehicle creating lift by air passing under it's wings - so for it to take off it would need a lot of force to push it up. If the plane is on a conveyor belt that is keeping the plane in the same position, then the only force applied to the actual plane is the ambient wind speed hitting it.
"

Quote: "
Don't you guys think that if this was possible they'd be doing it already - like airports could be put in parking lots and rooftops."

the key here is that the question is a trick. It makes you think that the plane won't be moving, but it will.

airports don't use it because there is no reason to waste money on huge conveyor belts that only make your wheels spin faster (and thus wear out faster).

airplanes either have thrust from a propeller (rare these days) or a jet engine. either one would push the airplane through the air, and the wheels just spin on whatever surface you are on... if there is a conveyor belt underneath going the opposite direction, the wheels just spin faster.

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Van B
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Posted: 14th Dec 2007 13:44
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Quote: "The conveyor belt will move at the exact inverse of the plane's speed, so if the plane is moving across the runway/belt at 10M/s the conveyor belt's surface moves at 10M/s in the opposite direction(like a normal treadmill would)."


The conveyor belt is moving at the exact opposite speed of the plane, not the wheels - so the plane is always in the same place, not moving forward at all. The thrust from the plane is immaterial because it's being countered by the 'treadmill'.

You seem to be backing up the 'take off' by saying the plane will be moving forward because of it's thrust, which is not what the original post states. Airports don't use conveyor belts because they would have no affect at all!.


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Peter H
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Posted: 14th Dec 2007 13:50 Edited at: 14th Dec 2007 13:51
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the treadmill has no way to counter the thrust of the plane.

the wheels on the plane have very little friction, and are not linked to any sort of driving system (during takeoff).

Quote: "The conveyor belt is moving at the exact opposite speed of the plane, not the wheels - so the plane is always in the same place, not moving forward at all."

so... if the plane is not moving forward.... and the conveyor belt is moving at the "inverse" speed... then the conveyor belt isn't moving.

Quote: "Airports don't use conveyor belts because they would have no affect at all!."

exactly! the airplane would take off just fine.

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BiggAdd
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Posted: 14th Dec 2007 14:01 Edited at: 14th Dec 2007 14:03
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The plane will take off. As the driving force for a plane has nothing to do with the runway itself, the plane will be traveling at 10m/s relative to the air and 20m/s relative to the runway.

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