# So, you have a plane on a conveyor belt...

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4 hours ago, Blasty McBlastblast said:

I guess whether or not the aeroplane will fly depends almost entirely* on the amount of air passing by the wing, resulting (or not) in lift either via the Bernoulli effect (pressure differential) or Newtonian deflection (conservation of momentum)

To achieve the outcome of air moving past the wing you could either:

• move the wing through the stationary air
• move the air around the stationary wing

The first option is precluded by the conditions of the experiment (i.e. a fictional magically-powered conveyor that can instantaneously reach any speed such that friction is provided to prevent the craft from moving forward.)

If you hadn't noticed, there is an unending dispute over whether these are, in fact, the actual conditions of the experiment. As @K^2 has helpfully derived, it is not enough for the belt to reach a high speed; the belt must continually accelerate in order to exert constant force on the plane. Since all known formulations of the problem talk about the speed of the belt, not some constant acceleration, this interpretation is...unlikely.

3 hours ago, DAL59 said:

The treadmill isn't an ideal treadmill, nor does it match the speed of the wheels.

"match the speed of the wheels" is an idea you still have yet to define.

2 hours ago, Gargamel said:

While in contact with the treadmill, the wheels will by default be matching the speed of the treadmill.

Depends on how you define it.

2 hours ago, K^2 said:
17 hours ago, sevenperforce said:

You're conflating static friction and kinetic friction. A wheel which is slipping while rolling has less purchase than a wheel which is not slipping while rolling.

Landing gear is going to remain firmly in the static friction regime. It's what it's designed to do. A slipping wheel cannot provide lateral forces allowing any sort of control. And while rudder does assist at all in early stages of landing or late stages of takeoff, you rely on wheels for much of steering during runup. If wheels began to even just noticeably slip during takeoff before you are ready to rotate, you would not be able to keep the plane on the runway. This I can tell you from first-hand experience.

Well, yes, a slipping wheel is useless for steering, but what does that have to do with this experiment?

The sorts of friction that increase as a function of RPMs will reduce traction as the wheel-belt interface skips between static friction and kinetic friction. This means the belt must work harder and harder to add momentum to the wheel.

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We have race cars that operate at higher speeds than landing gear failure point. Other than additional reinforcement, their physical properties are not that different. If what you were suggesting was remotely true, these cars would not be able to keep themselves on the race track.

All I'm suggesting is that a continuously-accelerating belt arrangement will rapidly reach RPMs at which slippage will become non-negligible. I didn't say this was necessarily below the failure point for real airplane wheels. You're the one who posited the continuously-accelerating belt that was never part of the original formulation of the problem.

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Real landing gear will fail way earlier, and one that's specifically designed to last as long as possible, made from same materials, merely slightly earlier. In both cases, in matter of seconds or less, I might add.

Yes, if the failure speed of the belt is greater than the failure speed of the wheels, for any reason, then trivially the wheels will fail first.

Edited by sevenperforce

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6 minutes ago, p1t1o said:

What on Earth does one use a 200kt belt for?!

These would be belts used for power transmission/timing/sync applications - similar to the belts you find in a car engine.

Fastest conveyer belt is apparently 'only' 15m/s (30 knots) at a german mine

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11 minutes ago, mrfox said:

These would be belts used for power transmission/timing/sync applications - similar to the belts you find in a car engine.

Fastest conveyer belt is apparently 'only' 15m/s (30 knots) at a german mine

lol well that certainly makes more sense!

***

This question about conveyors is exactly analogous to taking off with a tailwind - which is done, in practice, every. single. day. Can a plane take off in a tailwind of any speed? Of course not, that would be insane, there's obviously a limit. But can it be done? Yes its a normal everyday thing.

***

The video below is NOT that, but I think it will catalyse some extra talk on the subject:

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5 hours ago, sevenperforce said:

"match the speed of the wheels" is an idea you still have yet to define.

The tangential velocity always matches the tangential velocity of the wheels.

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1 hour ago, DAL59 said:

The tangential velocity always matches the tangential velocity of the wheels.

"The tangential velocity" relative to what? The ground? The plane? The wheel hub? The wheel surface?

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1 hour ago, sevenperforce said:

"The tangential velocity" relative to what? The ground? The plane? The wheel hub? The wheel surface?

I assume there's a device on the aircraft to measure the rpm of the wheel. That gives you a velocity for a given wheel diameter and that velocity gets matched by the belt relative to the stationary ground which results in the accelerating belt.

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14 hours ago, Reactordrone said:

I assume there's a device on the aircraft to measure the rpm of the wheel. That gives you a velocity for a given wheel diameter and that velocity gets matched by the belt relative to the stationary ground which results in the accelerating belt.

Wait, so now the aircraft is controlling the belt?

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Turns out the plane does take off, but there are....consequences:

(ignore the windows joke for now, thats for that other thread)

Edited by p1t1o

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And here I am thinking K^2's explanation being reasonable enough.

This truly is more decisive than projecting the Earth. (or am I wrong again ?)

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31 minutes ago, YNM said:

This truly is more decisive than projecting the Earth. (or am I wrong again ?)

Are you bringing the curved-vs-flat-runway topic to the discussion?

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6 hours ago, sevenperforce said:

Wait, so now the aircraft is controlling the belt?

Even if it isn't, an ideal treadmill would have the same effect.

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41 minutes ago, DAL59 said:

Even if it isn't, an ideal treadmill would have the same effect.

But what is the treadmill actually designed to do?

You said, "The tangential velocity always matches the tangential velocity of﻿ the wheels﻿."

That doesn't answer the question of what the treadmill is designed to do. It makes a (rather undefined) claim about what happens when the whole system is turned on and running.

What is the treadmill instructed to do?

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41 minutes ago, sevenperforce said:

What﻿ is the treadmill﻿ instructed to do?

Doing extensive philosophical justification.

Edited by YNM

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4 hours ago, sevenperforce said:

What is the treadmill instructed to do?

Be a fulcrum of pointless argument.

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I throw one in here for a laugh.

I believe the the purpose of the belt is to moved opposite to the acceleration of the vehicle on it. It has to, or the vehicle would easily leave the belt.

As a non-science major, I would say a plane takes off, unless a conveyer belt can accelerate to cancel out the plane's acceleration. So far, the last part appears to be purely hypothetical.

But that's not fun. So I'll ask instead, if a plane accelerates to 50 kph and the belt matches that speed, is the plane moving forward, or is it stationary?

Edit: I don't factor the landing gear wheels into the matter because I don't know how they know the difference between runway tarmac and a conveyer belt.

Edited by 55delta

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1 hour ago, 55delta said:

So I'll ask instead, if a plane accelerates to 50 kph and the belt matches that speed, is the plane moving forward, or is it stationary?

That's kinda the point of the entire thread.....

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2 hours ago, 55delta said:

So﻿ I'll ask instead, if a plane accelerates to 50 kph and the belt matches that speed, is the plane moving forward, or is it stationary?

The rational consensus so far is depends.

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7 hours ago, 55delta said:

I throw one in here for a laugh.

I believe the the purpose of the belt is to moved opposite to the acceleration of the vehicle on it. It has to, or the vehicle would easily leave the belt.

As a non-science major, I would say a plane takes off, unless a conveyer belt can accelerate to cancel out the plane's acceleration. So far, the last part appears to be purely hypothetical.

But that's not fun. So I'll ask instead, if a plane accelerates to 50 kph and the belt matches that speed, is the plane moving forward, or is it stationary?

Edit: I don't factor the landing gear wheels into the matter because I don't know how they know the difference between runway tarmac and a conveyer belt.

If you have the plane with it's propeller set to give it 50 kph forward motion, while the belt is set at 50 kph backwards, the plane will go forwards at 50 kph. (Well, could be slightly  below 50kph forward because of the tiny amount of friction you could experience in the wheel's bearing)

the wheels would simply free spin at two times the speed they would if there was only the plane rolling at 50 kph on runway

Do the same with a classic car on a conveyor belt however, and it would appear stationary

all because of the different mean of propulsion :

a classic car uses the wheels to 'push' against the road to provide forward motion.

A plane pushes against the air to provide forward motion,which is not affected by whatever would happen on the ground

Now, if you mount an aircraft engine and propeller on your car instead of it's classic engine, and put the wheels in free spin, it would behave like the plane described before on a conveyor belt

After that, most of the remaining arguing in this thread could be resumed around the scenario that the belt no longer tries to match the vehicle speed, but the wheel's rotation speed instead, which results in some kind of edge case which quickly get to either infinite speeds or mechanical failure ^^

Edited by sgt_flyer

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On 5/26/2018 at 5:54 AM, sgt_flyer said:

Now, if you mount an aircraft engine and propeller on your car instead of it's classic engine, and put the wheels in free spin, it would behave like the plane described before on a conveyor belt

Friction

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There is a plane parked on a conveyor belt. The plane fires up it's engine and attempts to take off. The belt runs in the opposite direction. Does the plane take off?

Given that the OP doesn't specify a speed or method of conveyor belt control I'll go with the belt running at about the plane's normal takeoff speed or less and the plane taking off since there is an insignificant increase in drag.

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Does this thread solely exist to troll everyone? To tell who has a rudimentary grasp of aerodynamics and who does not?

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the question is less a physics problem, rather its a great lesson in how vaguely/poorly defined scenerios can cause angst and confusion - because everyone assumes their own 'obvious' assumptions to the question are... obvious.

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1 hour ago, Gordon Fecyk said:

Does this thread solely exist to troll everyone? To tell who has a rudimentary grasp of aerodynamics and who does not?

This thread? No. But whoever first coined the question probably didnt understand it themselves or made it vague on purpose. Its almost deliberately designed to cause the maximum contention.

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Just now, p1t1o said:

Its almost deliberately designed to cause the maximum contention.

No, it's not.

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7 minutes ago, Gargamel said:

No, it's not.

I said "almost"

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