A leetle riddle

by plekter • 27 Sep 2008, 10:50 • Journals
Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?
image: treadmill_diagram
Discuss.

Yes it will
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Arachon 27 Sep 2008, 11:51
No.
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plekter 27 Sep 2008, 11:52
Why not?
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Arachon 27 Sep 2008, 11:54
As I get it, the plane is not moving an inch.

In order for a plane to take of, it needs to move at a certain speed, so that the wings can create the low and high pressure around the wing... which in turn creates the lifting ability of the wing.
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plekter 27 Sep 2008, 11:55
But it ain't the wheels that moves the plane, it's the engines!
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Arachon 27 Sep 2008, 11:57
If the conveyor belt matches the speed generated by the engines, transfered to the wheels; the plane will not move. Agree?
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plekter 27 Sep 2008, 11:58
Yes, but since the wheels don't excersice any substantial force to the plane and the engines do, the plane will move, agree?
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Arachon 27 Sep 2008, 12:01
No.
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plekter 27 Sep 2008, 12:02
Then where does the entire anti-engine force go, since for the plane not to accelerate the sum of forces has to be zero?
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Arachon 27 Sep 2008, 12:10
The force/accelration generated by the wheel is a function of the force generated from the engine, atleast that is how I picture it.

So if this combined force is eliminated by the conveyor belt, then the sum will be equal to 0; pf course this is set in a system which cannot be made in real life.
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plekter 27 Sep 2008, 12:12
Of course.. It's just that since the wheels exersice a minimum of friction and thus a minimum of force to the plane, the belt has to move awfully fast...
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GoodGuyGary 27 Sep 2008, 11:52
no i don't think he can cos even if it gains the speed needed, it won't take off upright?
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Panda 27 Sep 2008, 11:52
Yes it can
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k1pa 27 Sep 2008, 11:53
dont understand
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jetro 27 Sep 2008, 11:53
"the speed of the weels?"... i suppose the speed increases as the 747 takes off... does the speed of the conveyor stays the same or does it increase simultaneously?

I'd say no.
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plekter 27 Sep 2008, 11:53
It increases to always match the speed of the wheels
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jetro 27 Sep 2008, 11:55
Then no since the airplane has to gain speed in order to get into the air, the engines won't do. => NO

Still something tells me the correct answer is yes, knowing how tricky/fucked up physics sometimes really are.

You study ...?
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plekter 27 Sep 2008, 12:00
I study computer engineering..

Well we have the paradox of the wheels and a belt moving at a speed that makes the plane stands still, but the wheels don't exersice any force to the plane, but the engine does.
Practically the speed of the belt and wheels will quickly rise to infinity i guess..
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Panda 27 Sep 2008, 12:09
The planes speed is determined by the propeller/engines not the wheels :)
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jetro 27 Sep 2008, 12:13
Thats what I said..The weels just make sure the plain actually moves, the engines etc provide the power to do so.
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drv4c 27 Sep 2008, 11:55
old stuff, has been done on couple of shows(with smaller planes though), can't remember if it worked
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OfficerCohen 27 Sep 2008, 11:57
depends where the flaps are :p
the hmmm altitude nevigation

edit: the more i read, the more i understand i didnt understood a thing :D
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yellowpowerranger 27 Sep 2008, 11:57
it will take off because the wheels can freely turn. Its just that the wheels will turn twice as fast as usual but the plane can take off, np

+ jets are generating air displacement and thrust, so why shouldnt it take off?
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plekter 27 Sep 2008, 12:04
But if the wheels turn twice as fast as usual, won't that just make the belt go twice as fast?
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yellowpowerranger 27 Sep 2008, 12:07
you cant compare this to the conveyor belt in a fitness studio because jets - as i mentionned above - are creating air displacement + thrust. No matter how fast the conveyor belt is turning the plane will take off due to the jets
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plekter 27 Sep 2008, 12:09
Yes, but that contradicts to the belt again.
Anyways, it's practically impossible for the belt to keep the plane still. Only if we assume that the belt can run at infinity nP, and that there's no such thing as friction or that the wheels never slips.
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fredd 27 Sep 2008, 12:00
it took off on mythbusters
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skooli 27 Sep 2008, 12:04
of course it can, the thrust is not created by fast moving wheels but by the engines
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yellowpowerranger 27 Sep 2008, 12:08
exactly what i think
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ng 27 Sep 2008, 12:13
so a jumbojet could start on a flight carrier from a conveyor belt? :O nice
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skooli 27 Sep 2008, 12:15
a flight carrier is too short for a jumbo to gain enough speed.
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plekter 27 Sep 2008, 12:17
Quoteas wide and long as a runway.
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skooli 27 Sep 2008, 12:19
a jet which is normally capable of taking off from a carrier could also take off from a carrier with a conveyor belt running in the oppisite direction at the speed of light (given the tires dont break)
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plekter 27 Sep 2008, 12:21
and also given that there's no friction in the wheel-mechanics of the plane
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sol 27 Sep 2008, 12:17
No, forward momentum is required for it to take off.
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skooli 27 Sep 2008, 12:25
i hereby declare you dumb
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EYJohn 27 Sep 2008, 12:22
http://en.wikipedia.org/wiki/Lift_(force)

If its not actually moving, hence no air resistance, therefore no drag/lift . so it cant fly.

(this principle applies to specific planes, This is the primary force for planes such as gliders however the 747 also relies on the engine to produce the lift it requires to take off)

I'm gonna go with No.
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plekter 27 Sep 2008, 12:23
But will it stand still?
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EYJohn 27 Sep 2008, 12:29
Pah you got me on that one ^^. the conveyor belt running in the opposite direction matching the speed of the wheels suggests that it will not move, but if it does start moving and reaches the speed it requires then it will take off
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skooli 27 Sep 2008, 12:26
http://mythbustersresults.com/episode97
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sol 27 Sep 2008, 12:34
That plane is clearly moving. Did you read the journal?
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plekter 27 Sep 2008, 12:36
Do the problem ever state that the plane has to be stationary? That's rather the question, not a prerequisite.
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sol 27 Sep 2008, 12:38
'The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.'

If it were to exactly match the speed of the wheels then the plane shouldn't be moving forward, it should just be rolling along the conveyor-belt.

Regardless, forward momentum is required for lift.
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plekter 27 Sep 2008, 12:40
So the force generated by the engines get promptly deleted by crossfire admins? :D
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sol 27 Sep 2008, 12:45
What?
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plekter 27 Sep 2008, 12:46
To rephrase my question, since the engines generate a wast amount of force, where does this force go if the plane remains stationary?
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loctarar 27 Sep 2008, 12:59
The "force" doesn't go anywhere -_-. Plz... the system in composed mainly from: airplane body, wheels, ground and the belt. The airplane body accelerates relatively to the GROUND by pushing some gas behind and generating some difference of momentum (thats the definition of force F=dp/dt. Just like breaking a balloon and letting the air going out it will accelerate). The interaction between the belt and the wheels is irrelevant.
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plekter 27 Sep 2008, 13:00
That's what I'm trying to make him realize ;)
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loctarar 27 Sep 2008, 13:03
You should try it by explaing to him why this won't work for a car :P. A car uses the friction between the wheels and the ground to gain speed (it spins the wheels behind and the friction force pushes the vechile in front). So if you place a car in the mud it will just spind the wheels for nothing. If you place the plane in the mud it will obviously move because it is accelerated by other types of force.
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plekter 27 Sep 2008, 13:04
But it's much more fun to watch him struggle!
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sol 27 Sep 2008, 14:08
See gaso's reply, I misinterpreted the question.
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skooli 27 Sep 2008, 12:37
no matter how fast the conveyor belt moves, the plane will still go forward because the airplane engines force doesnt act on the wheels but on the air. as long as the tires dont break due to the stress it doesnt matter how fast they are going, the plane can still gain speed
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sol 27 Sep 2008, 12:45
I interpreted the question as though the plane could theoretically stay stationary, my bad.
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Gaso 27 Sep 2008, 13:14
Hmm. I've seen the same question phrased a bit differently, where the conveyor belt matches the speed of the plane, not the wheels. Then it will most definately take off, as the wheels only rotate at 2x speed when compared to a normal runway (assuming the wheels are frictionless).

(All speeds towards the plane's cockpit)
speed of the plane = Vp
speed of the conveyor belt = Vc
speed of the wheels = Vw

Speed of the wheels equals speed of the plane minus speed of the conveyor belt:
Vw = Vp - Vc

As is stated, the speed of the conveyor belt opposite to the speed of the plane:
Vc = -Vp

Therefore speed of the wheels:
Vw
= Vp - (-Vc)
= Vp + Vp
= 2 Vp
= - 2 Vc

But when the speed of the conveyor belt matches the speed of the wheels, hmm...

Edit: Here's The Straight Dope's take on the wording of this question:
QuoteHowever, some versions put matters this way: "The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation." This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. Nonsense. The question thus stated asks the impossible -- simply put, that A = A + 5 -- and so cannot be framed in this way. Everything clear now? Maybe not. But believe this: The plane takes off.

- Cecil Adams
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qpr 27 Sep 2008, 14:05
649. Kent - [Isola #11] 747 7:47
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xeoxis 27 Sep 2008, 14:27
This isn't a riddle, it's just math.
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raptus 27 Sep 2008, 14:57
in theory, the plane will NOT lift, and as soon as I find my textbooks I'll show you why, we asked a professor of physics on our university years ago and he explained it

just a note; believing that wheels are irrelevant because they are not the means of propulsion is wrong
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Gaso 27 Sep 2008, 15:09
Mythbusters tested this in real life, and the plane did indeed take off.

Time to doubt the credentials of your physics professor.
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raptus 27 Sep 2008, 15:17
don't know if you watched that episode but they did it in a different way
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loctarar 29 Sep 2008, 18:54
So you say that a plane with the wheels in mud will not take off? (the mud particles under the wheel move with same speed as the wheel in the opposite direction so it's kinda the same phenomen).
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raptus 1 Oct 2008, 14:36
it's not the same thing, the plane will eventually move out of the mud because the mud does not move in the opposite direction with the matching speed and the contact between the mud and the wheels is different than the contact between the belt and the wheels, this is not a car you're talking about, however eventhough the wheels on the plane are not the means of propulsion they still represent the contact between the land that the plane is moving on and the plane itself and whilst wheels themselves aren't the propulsion they do make a big difference in lifting the plane

I read you stating up that a car uses the friction between the wheels and the ground to gain speed, if you believe that a plane doesn't use the same friction then you are mistaken otherwise you could have the runway made out of ice and wheels be substituted by iceskates, every plane uses friction between it's contact with the ground/water and the ground/water itself to lift off

if you want a full explanation on why it wouldn't lift in theory(which can't be checked) I can pull out the drawings we made(I don't have the formulas anymore)
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quad 1 Oct 2008, 19:13
Since the plane's propulsion is relative to the air and not to your conveyor belt, it WILL accelerate, regardless of what happens to the wheels. Unless you bolt your plane to the ground, anything between it's wheels and the ground is just a friction, and moreover, it's a rolling friction, that for a given plane is constant regardless of it's any speed involved. From the plane's reference system, the ground speed makes absolutely no difference. If the wind was blowing from it's tail forward with 200kph, then you might have a problem :)

I believe your professor was talking about something else!
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