Plane on a conveyor belt

ICBM

Sambostar said:

I see what you're getting at, but the way I understand the question is that the conveyor increase exactly the same amount as the ground speed increases.

Yes. In exactly the same way as the speed of the undriven wheels rises to match that of the pane on a normal runway.

Maynehead said:

Whether the wheels are driven or not is irrelevant. For the plane to move in relation to the ground there must be a speed differential between the rotational speed of the wheels and the rotational speed of the conveyor belt in the opposite direction. This is ruled out by the definition of the question.

No. In the thought experiment, the conveyor is moving forward relative to the ground at the same speed as the plane, in order to keep the wheels stationary.

The plane is propelled forward by the engine thrust alone, how it is supported is completely irrelevant.

Chalky

I see your point @Maynehead - if the word 'exactly' is taken at its logical absolute, then the boundary condition is max thrust = infinity then conveyor belt speed = infinity, and the wheel speeds cannot exceed infinity and so the aircraft sits still.

Like a bent version of Zeno's paradox, it leaves reality way behind by making the word 'exactly' a logical constraint.

CabbageCat

Sambostar said:

They couldn't build a conveyor that big anyway that is capable for doing 570mph..

The conveyor need only be as long as the contact point with the wheels. The plane would never move.

Fatfingers

I really don't understand the argument about this. I can't see that the plane's wheels or the conveyor belt have any bearing on it at all. Surely all that matters is the airspeed over the wing. The engines fire, the plane moves forward, airspeed gets high enough to lift the plane, it takes off. It's that straightforward as far as I can see. 

CabbageCat

Depending on how much this question is practical vs theoretical the answer is different. Would a plane take off if it had solid lumps of immobile rubber in place of wheels? I suspect it would drag along for a bit, chuck up some smoke, distintegrate, then nose-plant the plane before it got to take-off speed.

CabbageCat

Fatfingers said:

I really don't understand the argument about this. I can't see that the plane's wheels or the conveyor belt have any bearing on it at all. Surely all that matters is the airspeed over the wing. The engines fire, the plane moves forward, airspeed gets high enough to lift the plane, it takes off. It's that straightforward as far as I can see. 

Think about what the wheels are doing, powered or unpowered. If the conveyer is going 1000mph then, for the plane to move forward at 1mph, the wheels MUST be going at 1001mph (or the rpm equivalent). The question states that the two must be equal. The plane cannot move forwards. It is tethered to the conveyor.

stickyfiddle

As stated, it depends on what's happening to the air and the ground beneath the conveyor. 

Regardless of the wheel/conveyor situation, the plane's engines will pull it through the air. Assuming the plane is not tethered to anything, this means it would move forwards.

when that happens, either it falls off the front of the conveyor, or the conveyor is conceived in such a way that it can move parallel to the ground, or the conveyor is so long that the plane would travel along it. 

The fact of whether or not the wheels rotate is entirely independent from the speed of the air passing over the wings, and the speed of the engines. This is the in the example and also in real life - they rotate on a real plane during takeoff because the plane is moving along the runway, not that other way around.

Chalky

Chalky said:

I see your point @Maynehead - if the word 'exactly' is taken at its logical absolute, then the boundary condition is max thrust = infinity then conveyor belt speed = infinity, and the wheel speeds cannot exceed infinity and so the aircraft sits still.

Like a bent version of Zeno's paradox, it leaves reality way behind by making the word 'exactly' a logical constraint.

Plus the statement that it is a 747 or indeed that it is an airplane is utterly irrelevant. That is just the logician's distraction to the sleight-of-hand of the word 'exactly'.

Thanks for the education @Maynehead !

CabbageCat

Another theoretical factor is that the wheels would not turn at all without any forward movement provided by the jet and forward movement had already been shown to be "impossible" since the wheels cannot turn relative to the ground.

The jets would fire, the wheels would not move, the conveyor wouldn't move. Or, the wheels would instantly turn at infinite rpm and so would the conveyor. It is, indeed, a paradox.

stratman3142

Taking a free body diagram view:

For a body to lift away from the earth's surface there needs to be a component of force in the upwards direction that exceeds the downwards force (i.e. exceeds the mass of the body multiplied by the earth's gravity).

If there's no lift from the wings (because there's no forward motion and no wind) then the jet engine would at least have to be angled with respect to the horizonal and a produce a sufficiently large component of force in the upwards direction to overcome the mass times gravity (as would be the case for a rocket).

menamestom

Being that thrust is a much higher force than drag, it should be able to take off, but to get forward motion the wheels still need to be going faster than the conveyor in the opposite direction.  Since the question states they always go at the same speed the plane can not achieve forward motion under this condition. 

I think it's a bit of a trick question, the conveyor would have to be going extremely fast to increase drag enough to match the thrust of the plane.  In a real world scenario (not that a plane on a conveyor belt is very real whatever way you look at it) thrust would overcome the drag of the wheels on the belt, unless the belt went at an implausibly fast speed.

Winny_Pooh

Assuming the wheels are regular and finite they would burn out during intial acceleration as the weight of the plane places force on the wheels in addition to the wear of speed. The conveyer would essentially tether it.
If the wheels were tougher or not finite the movement of air from the engines (the air in the experiment is stationary) would push the plane off the belt and away.

Think of the air as being like water and a wheeled boat being half submerged with its prop pushing it forward against the conveyer.

Ravenous

Ahem...

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

Maynehead

Chalky said:

Chalky said:

I see your point @Maynehead - if the word 'exactly' is taken at its logical absolute, then the boundary condition is max thrust = infinity then conveyor belt speed = infinity, and the wheel speeds cannot exceed infinity and so the aircraft sits still.

Like a bent version of Zeno's paradox, it leaves reality way behind by making the word 'exactly' a logical constraint.

Plus the statement that it is a 747 or indeed that it is an airplane is utterly irrelevant. That is just the logician's distraction to the sleight-of-hand of the word 'exactly'.

Thanks for the education @Maynehead !

Phew, I welcome the support. I was loosing hope that someone on here would actually understand the point that I was making!

paul_c2

1) No such conveyor exists, or can exist - a conveyor belt cannot "measure the speed of the wheels" of a plane, yet alone match them - I dare say while a 747 takes off at 180mph, the wheels have a design safety factor so they could cope with 300+ mph without serious issues etc.

2) Even if a system were to exist which DID generate drag, that drag would and could be overcome by extra thrust. Look at a seaplane taking off, there's tons of drag yet it is able to overcome this and take off (and land successfully) on water in not-ideally-smooth conditions.

ICBM

I didn't know it was an already-familiar internet discussion...

Which is because there is no discussion if you understand how planes work.

I'm almost sure it's been practically demonstrated with a light plane and a flatbed lorry simulating the 'conveyor', anyway. The plane takes off.

Maynehead

menamestom said:

Being that thrust is a much higher force than drag, it should be able to take off, but to get forward motion the wheels still need to be going faster than the conveyor in the opposite direction.  Since the question states they always go at the same speed the plane can not achieve forward motion under this condition. 

I think it's a bit of a trick question, the conveyor would have to be going extremely fast to increase drag enough to match the thrust of the plane.  In a real world scenario (not that a plane on a conveyor belt is very real whatever way you look at it) thrust would overcome the drag of the wheels on the belt, unless the belt went at an implausibly fast speed.

Yep, we're both on the same page.

CabbageCat

Ravenous said:

Ahem...

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

Funny how accurate it is:

"So, people who go with interpretation #3 notice immediately that the plane cannot move and keep trying to condescendingly explain to the #2 crowd that nothing they say changes the basic facts of the problem. The #2 crowd is busy explaining to the #3 crowd that planes aren’t driven by their wheels."

Maynehead said:

Phew, I welcome the support. I was loosing hope that someone on here would actually understand the point that I was making!

Dude, I've been with you from the start. We are #3 crowd.

Maynehead

ICBM said:

I didn't know it was an already-familiar internet discussion...

Which is because there is no discussion if you understand how planes work.

I'm almost sure it's been practically demonstrated with a light plane and a flatbed lorry simulating the 'conveyor', anyway. The plane takes off.

In practice the plane would take off, due to the physical limitations of designing a conveyor belt that precisely satisfied the requirements.

However, as I mentioned, this is more of a thought experiment than a practical one, and assuming the wording in the question is taken at face value, the plane cannot take off, as a speed differential between that of the wheels and the inverse of the belt cannot be achieved.

By the way, I haven't read any of the internet blurb, but as soon as I thought it through thoroughly this was the only logical conclusion.

viz

It's as though the aircraft were on incredibly slippery ice - no matter how hard the engines burn the wheels just spin, the aircraft is not propelled forwards, and never gains lift.