Plane on a conveyor belt

HAL9000

ICBM said:

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. 

Hmmm, not sure that's true. It will certainly be the case that an inch of movement at the circumference of the wheel will equate to contact point moving an inch forward on the belt, but I don't think that necessarily means that both the wheel and belt are moving at the same speed. Imagine the aircraft on a normal runway - one rotation of the wheel means the contact point has moved along the runway a distance equal to the circumference; it doesn't mean the wheels are moving at the same speed as the runway.

Sambostar

So it's all down to whether you measure speed by revolutions per second or mph and whether the diameter of the rollers on the conveyor are larger or smaller than the planes wheels?......

hywelg

menamestom said:

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 diameter of the tyre is 1m, it is revolving at 1 revolution per second.

And there ladies and gentlemen we have the crux of @menamestom problem. Fundamental lack of understanding of both mathematics and physics.

The rotational speed, i.e the linear velocity of the periphery of the tyre would be twice the ground speed of the aircraft or the conveyor speed,relative to the ground.

And no, the revolutions per second of the wheels is dependant on the diameter. If the conveyor always matches the forward motion of the aircraft (in the OP 'the speed of the wheels', it cannot mean anything else or the premise fails as the conveyor speed very rapidly tends to infinity) then the revolutions per second of the wheel = πr/Vp where r is the radius of the wheel and Vp is the forward velocity of the plane.

DiscoStu

The wheels are entirely relevant to the question. They are attached to the plane and are what allows the plane to move forward (by way of the thrust created by the engines) but by sitting on a surface moving in the opposite direction at an equal speed the wheels cannot move forward ergo the plane cannot move forward.
The question posed is not 'can the plane move forward?' it is 'can the plane take off?' and the answer is no as you need airflow OVER the wings to create lift.

HAL9000

The only way to deal with a paradox is to accept it and move on ;-)

Garthy

Sambostar said:

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?

Have you not noticed that Jet Cars do not do burnouts? It'll move on the conveyer.

To take this to the Nth level- how do you think the shuttle maneuvers in space with nothing but itself to push against? It's in a frictionless environment yet can move as it pleases.

Same with letting balloons go etc.

Sporky

Garthy said:

Have you not noticed that Jet Cars do not do burnouts? It'll move on the conveyer.

Which means that you're rejecting part of the premise, same as everyone else who thinks the plane can move and/or take off.

Forget what the vehicle is for the moment.

The question states that the conveyor moves at the same speed as the wheels, but in the opposite direction. Therefore the wheels don't move relative to the conveyor.

You can argue all you like that it's impossible (because it is), but that part of the question fixes the wheels' position, and as the plane is attached to the wheels the plane also cannot move. If it can't move, it can't generate airflow over the wings, which means it can't generate lift, which means it can't fly.

Nomad

I can scarcely believe some of the ill-informed and plain wrong shite that is being babbled in this thread.

Axe_meister

You could do this experiment at home.
get a little rubber band propeller model aircraft and place it on a sheet.
First let the aircraft move along the sheet.
Next pull the sheet towards you (Equivalent to the opposite direction of the wheels rotation). In relation to the ground and air it will move at twice the speed.
Now pull the sheet backwards the aircraft will remain stationary in relation to ground/air. But will move forward in relation to the sheet.

Emp_Fab

FORGET THE DAMN WHEELS !!!  They, and the conveyor belt are mental distractions !

The ONLY thing that causes movement - of anything - ever - is the application of force.  The physics of this conundrum, as with everything else on this planet, must obey Newton's Laws of Motion (https://en.wikipedia.org/wiki/Newton's_laws_of_motion).

Look at the problem entirely in terms of the forces being applied - because they are the only things that matter.  The conveyor does not impart any* force upon the plane, so the movement of it is of no consequence.  The wheels impart no force upon the plane, so they are irrelevant too.  The ONLY forces acting upon the plane are the thrust from the engines and the drag from the wind resistance.  That's it.  When you can see it like that, it's obvious that the plane will move forward.

For the plane to remain stationary, there MUST be an equal and opposite force applied to counter the engines' thrust (Newton's third law).  No if's or but's....  it MUST.

WHERE IS THAT FORCE COMING FROM THEN ?  The no-flyers believe that it comes from the conveyor.  Think about that for a moment - with wheels that rotate and have zero (or near as makes no odds) friction, just how is that rearward force going to be transferred to the plane ?  The answer is; it can't be.  The conveyor moves backwards and all it does, all it can do is make the wheels rotate.  It cannot impart any force upon the plane, because the wheels just go around and around.  It can do this no more than you can run up a hill wearing roller skates !  All the conveyor is doing is making the wheels spin.  It is not imparting any force upon the plane, therefore the only forces being applied to the plane, as stated earlier, are the thrust from the engines and the drag from the wind.  Therefore, the plane will move.

If you still have doubts, picture this;  You have a Boeing 747 sitting on a conveyor belt.  The force of four Rolls-Royce RB211's is just shy of a quarter of a million pounds of thrust at full throttle.  If the plane is to remain stationary, then you have to apply a quarter of a million pounds of thrust to counter the engines.  You think that backwards thrust is going to come from a conveyor belt that's pulling on greased wheels that just spin around ?  Really ?  Then for that to be true, the following must also be true;  You are standing on a motorised treadmill wearing roller skates.  The treadmill starts moving.  I can stop you from sliding off the end with one hand.  A child could stop you falling off the end with one hand, even if the treadmill was powered by a V12 truck engine.  There is no means for any force that could counter the plane engines' thrust to be transmitted to the plane.  Therefore the plane engines win and the plane moves forward through the air, and..... takes off.


(* as previously mentioned, in a perfect model with frictionless bearings, this is true, however there is inevitably going to be a miniscule degree of friction in reality, so yes, if you did this for real, the conveyor would impart a very very small force on the plane in the same direction of travel, but the force from the engines would render that irrelevant).

Sambostar

menamestom

hywelg said:

menamestom said:

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 diameter of the tyre is 1m, it is revolving at 1 revolution per second.

And there ladies and gentlemen we have the crux of @menamestom problem. Fundamental lack of understanding of both mathematics and physics.

The rotational speed, i.e the linear velocity of the periphery of the tyre would be twice the ground speed of the aircraft or the conveyor speed,relative to the ground.

And no, the revolutions per second of the wheels is dependant on the diameter. If the conveyor always matches the forward motion of the aircraft (in the OP 'the speed of the wheels', it cannot mean anything else or the premise fails as the conveyor speed very rapidly tends to infinity) then the revolutions per second of the wheel = πr/Vp where r is the radius of the wheel and Vp is the forward velocity of the plane.

Sorry, typo there, I meant the circumference, not diameter.  But yeah, you're right I have got that wrong anyway.  Been a while since I did physics!   But the fact remains it's not a physics problem, it's a logical paradox.  So the plane wont take off what ever I said

Sporky

Emp_Fab said:

FORGET THE DAMN WHEELS !!!  They, and the conveyor belt are mental distractions !

So you're rejecting the question that's actually posed, and instead substituting your own. Which is why you and ICBM keep getting the answer wrong - you reject a constraint that fundamentally changes the puzzle.

Gassage

Has anyone given any due consideration to how to land it back onto the belt yet?

Nomad

Would someone please post a picture of a 747 drive shaft, showing how it connects to the wheel?

JohnnyPlectrum

It'll fly if the pilot applies power, it has no choice, but it does alter the interpretation of the question.
However, as I would measure treadmill speed in m/s and wheel speed in rpm I think that's allowed.
I'm sure this is a simple GCSE question gone bad. 
Accepting that it won't fly because the engines aren't running is far easier to grasp.

Sporky

Nomad said:

Would someone please post a picture of a 747 drive shaft, showing how it connects to the wheel?

Planes don't have driven wheels, but it doesn't make any difference.

In order for the plane to take off it has to move. The constraints in the original question preclude the plane moving. It's pretty simple, and all the people getting angry about it and going on about how planes work simply haven't read (or haven't understood) (or have rejected) the question that was originally asked.

If you think it has anything to do with wheels being driven or not then you've either not read, not understood, or rejected the original question.

Paul_C

So . . . if it was a small, four wheeled trolley with a bar sticking out either side and two people standing on the floor started to push it, as the wheels rolled forwards, the conveyor belt would move in the opposite direction, which would turn the wheels but not stop the trolley moving forwards. If the conveyor belt had a fixed length they should be able to push it off the end. . . but would the rotation of the wheels accelerate almost instantly to infinity and explode or remain at a constant speed if the pushing was at a steady pace?

Sporky

Paul_C said:

So . . . if it was a small, four wheeled trolley with a bar sticking out either side and two people standing on the floor started to push it, as the wheels rolled forwards, the conveyor belt would move in the opposite direction, which would turn the wheels but not stop the trolley moving forwards. If the conveyor belt had a fixed length they should be able to push it off the end, but would the rotation of the wheels accelerate or remain constant if the pushing was at a steady pace?

If you have the same constraint that the conveyor belt exactly matches the speed of the wheels then you can't push the trolley - basically you're performing the same function as the engines on the jet.

It's an impossible conveyor belt. Or, rather, it can only work at all if the thing on it has driven wheels. If the thing on it is propelled any other way then the conveyor belt is impossible, and the thing cannot move.

This is why (as others have also said) it's a paradox and a thought experiment, not a solvable question about physics.

Rocker

Impossible for the plane to take off and fly.  It is the air movement over and under the wing that provides the lift  and the engine that provides the forward movement to cause the air movement over and under the wing.

In my naivety I thought everyone knew why aeroplanes fly.  Seems I was wrong.