Plane on a conveyor belt

ICBM

thumpingrug said:

I cant believe this has run to 9 pages.   

Especially as HAL9000 gave the correct answer in the second post.

monquixote

ICBM said:

thumpingrug said:

I cant believe this has run to 9 pages.   

Especially as HAL9000 gave the correct answer in the second post.

It comes down to that people interpret what is being asked differently and make different assumptions

https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/

You and I assume option 2 whereas some people assume option 3 which comes to a different conclusion.

Sambostar

No, it comes down to people misunderstanding the question.

Forget that the thing has wings, if a jet propelled car tried to accelerate on a treadmill that matched it's velocity and acceleration in the opposite direction exactly, then it would effectively remain in static position relative to the air around it. 

It would appear to not move.  No air speed, no take off.

You can add as many jet engines as you want, the conveyor would still match their thrust and acceleration in the opposite direction.

HAL9000

ICBM said:

thumpingrug said:

I cant believe this has run to 9 pages.   

Especially as HAL9000 gave the correct answer in the second post.

Kind of you to say so @ICBM but reading through the thread I'm guessing that this is more an 'irresistible force meets unmovable object' paradox. That is the aircraft MUST move because (assuming frictionless wheel bearings) there is no force preventing it from doing so. However, the aircraft CAN'T move due to the constraint that the wheels must rotate at the same speed as the conveyor.

Paradox lost (and paradox regained) ;-)

ICBM

HAL9000 said:

ICBM said:

thumpingrug said:

I cant believe this has run to 9 pages.   

Especially as HAL9000 gave the correct answer in the second post.

Kind of you to say so @ICBM but reading through the thread I'm guessing that this is more an 'irresistible force meets unmovable object' paradox. That is the aircraft MUST move because (assuming frictionless wheel bearings) there is no force preventing it from doing so. However, the aircraft CAN'T move due to the constraint that the wheels must rotate at the same speed as the conveyor.

Paradox lost (and paradox regained) ;-)

No, it doesn't say the plane can't move, only that the conveyor moves at the same speed as the wheels. That will always be true as long as the tyres aren't skidding on the surface. Yes, it does mean that the speed of both will rise to infinity - but that's allowed, this is a thought experiment.

There is another famous thought experiment which starts something like "Imagine a passenger on a tram which is travelling at the speed of light…" Impossible! At the speed of light the tram would have infinite mass and so need an infinite amount of energy to reach it. Does that invalidate the rest of the thought experiment? No.

The plane/conveyor thought experiment is actually useful because it shows that the wheels and the conveyor are a red herring, and can be simply ignored. The only thing that matters is the airspeed, which is independent of what the plane is resting on. That's exactly why a seaplane can take off from a trailer when it isn't moving relative to it.

Sambostar

I think in this question lie the secrets to the Universe. 

Those who think the plane will take off would vote for Hilary, voted to stay in the EU and don't like Marmite.

If I had a Facebook account I'd unfriend everyone who thought the plane could take off.

Seriously though I asked two people in the pub and got two different answers.

The argument gets far more heated on PistonHeads.

Sporky

ICBM said:

No, it doesn't say the plane can't move, only that the conveyor moves at the same speed as the wheels. That will always be true as long as the tyres aren't skidding on the surface. Yes, it does mean that the speed of both will rise to infinity - but that's allowed, this is a thought experiment.

But when as they approach infinity they'll turn to plasma and the plane will be destroyed, without having moved. Either nothing moves at all at any point, or the wheels and conveyor hit relativistic speeds instantly. Otherwise the constraints in the question haven't been met.

As you say, it is a thought experiment, and the experiment - by stating that the conveyor matches the speed of the wheels - locks the plane in position. In the real world that couldn't happen, which is why HAL is correct that it's a paradox. Every time you say the wheels are irrelevant you're saying that you're not going to answer the question that was posed, and you're going to answer a different one instead.

ICBM

Sporky said:

As you say, it is a thought experiment, and the experiment - by stating that the conveyor matches the speed of the wheels - locks the plane in position.

No, read the question. It does not say that the plane is locked into position, only that the conveyor matches the speed of the wheels. That is true at *any* speed if the tyres aren't skidding, including an infinite speed.

Sporky said:

In the real world that couldn't happen

Obviously, but this is a thought experiment and not the real world...

It's not a paradox, it's a good way of showing exactly what makes a plane fly - airspeed, not ground speed.

HAL900 answered the question exactly, and correctly, the first time. He was even right that it's not the engines "pushing against the air" that moves the plane - it's the reaction thrust, although that's another non-intuitive question which is possibly best avoided .

Sambostar

The defining answer for me on PistonHeads was that if it worked, then the conveyor would be deployed at every airport around the world.

So a jetcar will also accelerate then @IBCM, because it's engine too is acting on the air, not the wheels?

Even though it's ground speed which is also it's airspeed (If there is no wind) and forwards acceleration is matched exactly by a conveyor moving and accelerating in reverse to the direction of travel?  Because that is what the question states.  The speed of the wheels are matched by the speed of the conveyor. 

So to be clear, by your rationale, the jetcar would accelerate on the conveyor?

Sambostar

https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/comment-page-16/

ICBM

Sambostar said:

So to be clear, by your rationale, the jetcar would accelerate on the conveyor?

Yes. As long as the accelerating force is not transferred via the wheels.

That's the difference - if it is transferred via the wheels then you simply have a rolling road situation. This is presumably why it confuses people.

Emp_Fab

Yes, it would move.  Because of the basic Newtonian force equations.  The conveyor is imparting zero force on the car.  The problem is that, mentally, it's difficult to get your head around the concept of frictionless wheels, that a mass sitting on a movable platform with zero friction between them, would remain still if the platform moved beneath it.  It would.  However, in the real world, there is friction and yes, in the plane conundrum the conveyor would impart a force on the plane and therefore make the plane move backwards a bit - but the value of that force compared to the forward thrust of the engines is inconsequential. 

Sambostar

But how can it accelerate relative to it's ground or air position when it's mass is sitting on wheels whose acceleration in revolutions is matched by the conveyor travelling in the opposite direction?

ICBM

Because Newtonian mechanics is correct, as Emp said. It is true that for the system to work the conveyor speed has to rise to infinite, so it has to remain only a thought experiment.

If you think this is hard to get your head around, just imagine what it must have been like for people to understand Newton's ideas when the closest to frictionless movement and balanced forces anyone could have experienced was ice skating.

Let alone Einstein.

Axe_meister

Think about the rotation of the wheels.
The force of the engine will try and create forward motion.
This means the wheels will rotate anti clockwise so left to right.
If the belt is moving in the opposite direction I.e. Right to left it is moving in the same direction the aircraft want to go anyway therefore adding to the speed of the plane. So the plane will take off in half the distance.
However if the belt ran in the same direction I.e left to right the aircraft would remain stationary with the wheels turning at twice the rate

menamestom

@icbm correct the plane is not locked into position, not physically anyway. But for the plane to move forward and gain airspeed it has to go faster than the conveyor. The tyres to revolve faster than the conveyor does in the other direction otherwise relative to the air the plane will not be moving. So lets say the conveyor is moving at 1m/s. To remain stationary the plane wheels would need to move at 1m/s. To gain any forward motion, the wheels need to go over 1m/s. So if the circumference of the tyre is 1m, it is revolving at 1 revolution per second. To gain any forward motion, it would need to be revolving > 1m/s, but if it did a condition of the question would be broken. To gain any forward motion, the conveyor and the wheels would have to be moving at different speeds.

EDIT.  Typo, diameter changed to circumference 

monquixote

Two other solutions: 

Once the wheels and conveyor had spun up the energy being dissipated into heat by the wheels would be equal to the output of the planes engines so the plane would be lifted off the ground by the forces generated by the superheated air expanding under the wings.

Once the conveyor had spun up it would pull air towards the plane causing it to lift off the ground.

hywelg

Jesus, is this still going on??????

Sambostar

It goes on for 39 pages on PistonHeads

Sporky

ICBM said:

Sporky said:

As you say, it is a thought experiment, and the experiment - by stating that the conveyor matches the speed of the wheels - locks the plane in position.

No, read the question. It does not say that the plane is locked into position, only that the conveyor matches the speed of the wheels. That is true at *any* speed if the tyres aren't skidding, including an infinite speed.

I did not say that the question says the plane is locked into position. You've misread that just as you still misread the original problem.

I said - right there in the bit you quoted - that the experiment locks the plane into position by stating that the conveyor matches the speed of the wheels.