Will a plane take off on a conveyor belt?

Because Billy is generating wheel speeds that the treadmill can't match. He's running away from the treadmill. Even when stationary (to the ground) he's already doing the treadmill speed forwards relative to the belt, any increase in his speed is a plus (causing the forward motion).
And any increase in the belt speed automatically increases Billy's relative to the belt.
And any increase in treadmill speed is cancelled because Billy is "attached" to the ground (and not the belt).
It is impossible for the treadmill belt to catch up since Billy has the treadmill's own speed relative to the belt to start with, in the opposite direction.
Different situation.
The aircraft is not "attached" to the ground, it starts on the belt and is not connected to the ground at all.

 

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You still dont understand that the conveyor is NOT moving relative to the ground in my scenario, it stationary!
big edit:
Once again, think of your car:

basicaly, (minus the difference in propultion systems, but this would stil work for a jet car!)
you speedometer is the perihperal speed. The road is the treadmill speed, and the car is plane speed.
If your in the car, the speedometer and road always match speeds, and you are always stationary relative to the car (if your not, your either adjusting the seat or have seriouse rust problems!)

Now, We can see too, that the ground off the road moves too at the same rate, thus had you airfoils you would lift. See, road doesnt move relative to ground, but it still satisfies out treadmills equation.

-Andrew

 

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Belt or conveyor system (the structure)?
The belt has to move relative to the ground, surely? Otherwise it might as well be the ground...

 

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oli,
you an aerospace engineer?
comment on this post:
http://sciforums.com/showpost.php?p=1440075&postcount=68
describe how it differs from the OP.

 

Then your scenario is totally inconsistent with the original question. In it, the conveyor is moving backwards compared to the forward motion of the plane, so it most certainly IS moving relative to the ground! Otherwise, why even bother HAVING a conveyor????????????????????????????

 

No but thats my point, it doesnt have to move relative to the ground, and it could be ignored from this observer.
Once again, its not moving backwards compared to the planes forward motion but compared to the wheels peripheral motion, huge difference.

 

The thrust is due to Billy not being on the same frame of reference as the skateboard (he is on the ground, not the treadmill).
Doesn't that apply to the air as well - which would be applying the thrust to the plane?
Let's say there was a Chanook helicopter pulling the plane forward...
The plane is on the conveyor belt, but the Chanook is on a different frame, so the Chanook is essentially the same as Billy.

So far, so good, right?

Now, how does the thrust being developed by the planes jet engines any different than the plane being towed by the Chanook (or Billy pulling it)?

 

Not as such. I'm an engineer with aerospace predilections and a couple of credentials in that area

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Because it's the Billy thing again, the wind in this case is Billy and it's decoupled from the conveyor, which the aircraft in the OP isn't.
The wind is relative to the ground, not the belt. And the kite is in the wind.

Damn' it's 05:36 - time for bed I think.
Catch you later guys.

 

But if the conveyor speed matches the wheels' motion exactly then the wheels aren't moving. If they aren't moving then the plane isn't.
It does have to move relative to the ground, that's what generates lift.

Chinook

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Yup, that would work.
In this case the plane is already coupled to the conveyor and has to move "forwards" to stay in the same place relative to the ground (by engine thrust). But since it's relative to the ground then there's no lift.

 

Wrong, just as the speed of the road going by your window matches the wheels speed, yet im sure you can agree your car does move relative to the air and ground.
The conveyers speed is relative to the plane in my example, keep that in mind.
Edit: you are right about it having to move relative to the ground of course

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-Andrew

 

But the air is not coupled to the the conveyor belt, so how is it different than the Chinook?

 

OK, 'simple' math, the purest of logic.

All vectors are from the plane's perspective, that is the pilot is the observer

given:
groundspeed=airspeed
wheelspeed=planespeed+beltspeed
wheelspeed=beltspeed

let groundspeed=100mph (I'm trying to prove it's taking off so, it had better have some ground speed, and if it works, then it works)
let beltspeed=groundspeed (relative to the pilot the belt and ground are moving together. For more understanding relative to a ground based observer, the belt is motionless... however we are working from the planes observer)
then
axelspeed=beltspeed
axelspeed=100mph
beltspeed=100mph

planespee=0mph (relative to ITSELF remember, not to the ground)

wheelspeed=planespeed+beltspeed
100mph=0mph+100mph
100mph=100mph

All equations work... thus it seems the plane can take off, given the scenario is viewed from the pilot's perspective.

Edit: I think I will furthur point out why, in a perfect system, the observer cannot be the ground. (so everything from heron is relative to the ground)
If there is 0 friction on the axel on the wheel, and infinite of the wheel to the belt, then wheelspeed=conveyer+plane as I said above
If conveyer speed=wheelspeed
then: sub the other equation in and we have:
conveyerspeed=convayerspeed+plane
Now at first this makes the plane look like it does infact stay still, but lets furthur examine it and say that
planespeed=a*t (acceleration*time)
Now if the plane has a mass of 100KG and applies a force from the engine of 100N (both of which are completely unaffected by anything the wheels or conveyer can do)
then a=1m/s
and subbing that in:

conveyerspeed=convayerspeed+1m/s*t
uh oh!
the only possible conclusion for this equation is that time=0. But time wont stop because of a conveyer, nor will the planes engine fail...
There is thus a flaw in my maths, or the conditions...
If you can find the flaw in my maths fine... if not...

Now, if the it is an imperfect system, we are gonna need some coefficients of friction or something., otherwise i could say that the friction of the wheel to the belt is 0.. and thus no matter how much it scrapes against the belt, it wont move, and this thus the belt wont move even if the plane is moving forward.
Allowing the plane to take off like it were on ice.

-Andrew

 

Very sorry but that's completely false logic.

It's simple algebraic addition, just as I said earlier. If the belt's speed is 100mph toward the rear of the plane and the plane is matiching that with a forward speed of 100mph then the two speeds totally cancel out (+100-100 =0) which would be BOTH the groundspeed and airspeed - zero. The plane will be stationary realitive to the ground - NOT realitive to the belt passing backward beneath it. Exactly like the runner on a treadmill.

 

You dont seem to understand, in this perfect system, the spining wheel has no effect on the axels movement forward, however the movement forward can have an effect on the wheel!
To clarify: the planes forward motion would make th wheel spin, as well a conveyors backwards motion would make the wheel spin, however te backwards motion of the convayor would not caus the plane to move backwards (even if the plane was not using its engine) nor would the plane moving forwards cause the conveyor to move backwards (other than what our wierd computer would do when int detected the wheel in motion)

EDIT: furthurmore the original condition was
wheelspeed=planespeed+conveyorspeed
and conveyorspeed=wheelspeed
so if the convayor is moving one way 100mph and the plane moving forward 100mph the wheel would be moving 200mph, and thus the conveyor would have to move 200mph... but then the wheel would be turning at 300mph so the conveyor would have to move 300mph... ad infinitum
-Andrew

 

Not in the least! You are adding speeds when you should be subtracting - thus the major flaw in your vision of the problem.

<----------- attempted motion of plane

------------> countering motion of conveyor

Each are equal in value.

When they are added algebraically, the net result is zero.

 

Oli, you are usually right-on with your physics, but you are mistaken here. The conveyor belt does not cancel forward motion. The wheel/conveyor belt speed has nothing to do with the plane/air speed. The plane does not depend on friction between wheels/conveyor belt to move forward through the air. A propeller or jet engine derives its thrust by pushing against the air/atmosphere, the wheel speed is immaterial. If the conveyor belt is powered to move rearward by its own electrical motor or otherwise, it has no effect on the thrust produced by the aircraft engines. The wheels will simply spin at a greater speed than if the conveyor belt were not in motion toward the rear of the plane.
A plane that derives its thrust from either a propeller or jet engine will be able to take off from the conveyor belt, unless the tires blow out due to their increased rotational speeds.

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oli,
assuming frictionless bearings how fast must the conveyor belt move to pull the plane backwards?

now, while you are chewing on that question lets apply engine thrust.

can you explain this oli?

 

If you "put teh brakes on" and the wheels are locked, it seems to me that the engines will still propel the plane forward, given they have enough thrust.

I'm swicthing camps.

 

And when you’re moving in your car do the wheels (centres) move relative to the ground? Yes, by definition. Put the car on a rolling road so that the rollers match the wheel speed and how far does it go?

If the conveyor is going backwards and the plane isn’t moving relative to the belt (engines off) which way does the plane go?
Backwards.
So the plane needs forward motion relative to the belt to remain in the same place relative to the ground.
As the plane speed increases the conveyor speed increases (as stated in the OP).
The relative motion through the air will be zero.
Point of pedantry:

.
Yeah?
No. It’s the air being thrown backwards by the power plant (action-reaction) that provides thrust.

Frictionless bearings? Doesn’t come into it. The wheels roll because of friction between the belt and the wheel periphery.
It doesn’t matter how fast the plane, therefore, wheels move: the OP stated that the conveyor belt always matches the wheel speed.

Only if the engines provide enough power to overcome the friction between ground and wheels, in which case they scrub the tyres.
Turncoat.

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Well, that's really what this comes down to, isn't it?

If the Chinook can drag the plane fast enough to generate lift, the tires will rub on the surface of the conveyor belt (just as the tires of little Billy's skateboard will rub on the treadmill).
If the jet engines are powerful enough, we will have the same exact effect as being dragged by the Chinook.