Plane on a conveyor belt

viz

Chris, in the pure mathematical model it is a paradox, because it involves infinity. That's just the case, whether I believe it or not. On the other end of the spectrum, in the engineering model, you have things like time lag between wheel and belt, friction, heated bearings, implausible conveyor systems, finding an airline willing to try it, the universal constant of the speed of light, etc etc. In the engineering model, there is no paradox, just an outcome depending on the parameters. But the question is a logic question and it results in a paradox. 

I think that's all I can really say about it - I've reached the end of my reasoning! Cheers

Handsome_Chris

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

viz

Well, the thing is, in order to take off, planes need to move at 360mph relative to the still air around them, not relative to moving conveyor belts beneath them, so the relative difference in speeds between wheel and belt won't cause the lift. 

Handsome_Chris

viz said:

Well, the thing is, in order to take off, planes need to move at 360mph relative to the still air around them, not relative to moving conveyor belts beneath them, so the relative difference in speeds between wheel and belt won't cause the lift. 

Please pardon me for not quoting my sources reference the aforementioned 747.

http://www.aerospaceweb.org/question/performance/q0088.shtml

Saying that I believe @Gassage may have mentioned the take off speed issue before.

Maynehead

Handsome_Chris said:

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

This has been covered many posts ago but I will reiterate.

If the plane's body is moving forwards relative to a "stationary" observer, let's say, at 1mph, and the belt is moving backwards at 1mph, the WHEEL SPEED, which is the value we're actually interested in, is 2mph.

But that means the wheel speed (2mph), is different compared to the belt speed (1mph). How can this be possible, given that the belt speed always EXACTLY MATCHES the wheel speed?

You are proposing a situation that is explicitly precluded by the conditions set out in the question. In the context of the question, this situation is completely out of scope and to base your argument around it is trying to answer the wrong question.

You are effectively answering the question: "If the speed of the wheels can be different to the speed of the conveyor, can the plane take off?" To which the answer would be, of course it can.

Axe_meister

You are all forgetting the speed of the belt is moving in the opposite direction to the rotation of the wheel. The force of the wheel to overcome friction is left to right, ergo the same force will be applied by the belt in the oppose direction, effectively doubling the traction. 
Experiment. Place a rubber (no not that kind) on a table. 
Take another one and drag it across the first. Now move both in opposite direction to each other.
note the above has nothing to do with the thrust, purely the friction of wheel against belt

viz

Handsome_Chris said:

viz said:

Well, the thing is, in order to take off, planes need to move at 360mph relative to the still air around them, not relative to moving conveyor belts beneath them, so the relative difference in speeds between wheel and belt won't cause the lift. 

Please pardon me for not quoting my sources reference the aforementioned 747.

http://www.aerospaceweb.org/question/performance/q0088.shtml

Saying that I believe @Gassage may have mentioned the take off speed issue before.

180 then. I was just trying to use your example. I misunderstood what you meant - when you said 360 I assumed you were doing so in relation to take-off speed. Anyway the important thing is air speed, and if there isn't any, the plane doesn't lift off the ground. That's the thing I'm trying to say. Not very well obviously. 

A5D5E5

viz said:

Well, the thing is, in order to take off, planes need to move at 360mph relative to the still air around them, not relative to moving conveyor belts beneath them, so the relative difference in speeds between wheel and belt won't cause the lift. 

I'm not sure if you are doubting that the plane would take off in the real world (as distinct from the world the question inhabits) or not, but just in case you are...

A 747-400 can produce about 1,000,000 N of thrust.   At those levels you can disregard friction in the bearings (if not, buy some better bearings) and rolling resistance and any other factors.  1 million newtons of thrust won't be stopped from going about its business.

The same plane weighs about 350,000 kg on take off so it would accelerate at about 3m per sec per sec (assuming full thrust from the start which is obviously a simplification).

In the real world it would do this on a runway, a conveyor, a sheet of ice, or if it was suspended in mid air by an alien anti gravity divice as there is no material force opposing that million newtons of thrust.

Take off speed is 290 km/h which is about 80m/s so our plane takes off about 25 to 30 seconds after the pilot presses the loud pedal - which feels consistent with planes I've flown in.

CabbageCat

A5D5E5 said:

viz said:

Well, the thing is, in order to take off, planes need to move at 360mph relative to the still air around them, not relative to moving conveyor belts beneath them, so the relative difference in speeds between wheel and belt won't cause the lift. 

I'm not sure if you are doubting that the plane would take off in the real world (as distinct from the world the question inhabits) or not, but just in case you are...

A 747-400 can produce about 1,000,000 N of thrust.   At those levels you can disregard friction in the bearings (if not, buy some better bearings) and rolling resistance and any other factors.  1 million newtons of thrust won't be stopped from going about its business.

The same plane weighs about 350,000 kg on take off so it would accelerate at about 3m per sec per sec (assuming full thrust from the start which is obviously a simplification).

In the real world it would do this on a runway, a conveyor, a sheet of ice, or if it was suspended in mid air by an alien anti gravity divice as there is no material force opposing that million newtons of thrust.

Take off speed is 290 km/h which is about 80m/s so our plane takes off about 25 to 30 seconds after the pilot presses the loud pedal - which feels consistent with planes I've flown in.

...and what speed would the wheels be going?

...and what speed would the conveyor be going?

(Edit...and apparently the brakes on a 747 would stop it from taking off if it was laden)

Handsome_Chris

Maynehead said:

Handsome_Chris said:

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

This has been covered many posts ago but I will reiterate.

If the plane's body is moving forwards relative to a "stationary" observer, let's say, at 1mph, and the belt is moving backwards at 1mph, the WHEEL SPEED, which is the value we're actually interested in, is 2mph.

No we are not interested in the 2 mph at all.  You may not only be interested in it, but find it fascinating, but I do not care that you are interested in that as it has nothing to do with resolving the question.

Also the plane is moving forward relative to a stationary object, the thing the conveyor belt is attached to.

Maynehead said:

You are proposing a situation that is explicitly precluded by the conditions set out in the question. In the context of the question, this situation is completely out of scope and to base your argument around it is trying to answer the wrong question.

No I am not.


If the plane moves forward at 1 mph taking the wheels with it, the conveyor belt's aircraft facing surface moves at 1 mph in the other direction. At no point in the question above does it mention the rotation of anything, let alone the wheels.  @Maynehead, that is just something some people have decided to assume, for some reason.  If it must mean that then surely it would have been stated in the original question?

Handsome_Chris

CabbageCat said:

A5D5E5 said:

viz said:

Well, the thing is, in order to take off, planes need to move at 360mph relative to the still air around them, not relative to moving conveyor belts beneath them, so the relative difference in speeds between wheel and belt won't cause the lift. 

I'm not sure if you are doubting that the plane would take off in the real world (as distinct from the world the question inhabits) or not, but just in case you are...

A 747-400 can produce about 1,000,000 N of thrust.   At those levels you can disregard friction in the bearings (if not, buy some better bearings) and rolling resistance and any other factors.  1 million newtons of thrust won't be stopped from going about its business.

The same plane weighs about 350,000 kg on take off so it would accelerate at about 3m per sec per sec (assuming full thrust from the start which is obviously a simplification).

In the real world it would do this on a runway, a conveyor, a sheet of ice, or if it was suspended in mid air by an alien anti gravity divice as there is no material force opposing that million newtons of thrust.

Take off speed is 290 km/h which is about 80m/s so our plane takes off about 25 to 30 seconds after the pilot presses the loud pedal - which feels consistent with planes I've flown in.

...and what speed would the wheels be going?

...and what speed would the conveyor be going?

(Edit...and apparently the brakes on a 747 would stop it from taking off if it was laden)

The speed of the wheels would be the same as the rest of the aircraft it is attached to, assuming structural integrity.

The conveyor belt would be travelling at the same speed as the aircraft (it's attached to the wheels) but in the opposite direction.  RTFQ

A5D5E5

CabbageCat said:

A5D5E5 said:

viz said:

Well, the thing is, in order to take off, planes need to move at 360mph relative to the still air around them, not relative to moving conveyor belts beneath them, so the relative difference in speeds between wheel and belt won't cause the lift. 

I'm not sure if you are doubting that the plane would take off in the real world (as distinct from the world the question inhabits) or not, but just in case you are...

A 747-400 can produce about 1,000,000 N of thrust.   At those levels you can disregard friction in the bearings (if not, buy some better bearings) and rolling resistance and any other factors.  1 million newtons of thrust won't be stopped from going about its business.

The same plane weighs about 350,000 kg on take off so it would accelerate at about 3m per sec per sec (assuming full thrust from the start which is obviously a simplification).

In the real world it would do this on a runway, a conveyor, a sheet of ice, or if it was suspended in mid air by an alien anti gravity divice as there is no material force opposing that million newtons of thrust.

Take off speed is 290 km/h which is about 80m/s so our plane takes off about 25 to 30 seconds after the pilot presses the loud pedal - which feels consistent with planes I've flown in.

...and what speed would the wheels be going?

...and what speed would the conveyor be going?

(Edit...and apparently the brakes on a 747 would stop it from taking off if it was laden)

I'm not answering the question, I'm simply stating what would happen if you put a plane on a conveyor belt in the real world, but...

...At take off the axle would be going 290km/h, the conveyor would (under one interpretation of the question) be going 290km/h in the opposite direction and the wheels would be rotating so that the circumference was travelling at 580km/h.  And I'd be on my way to New York unaware that my plane was causing an argument in an obscure corner of the Internet :-)

sinbaadi

Handsome_Chris said:

Maynehead said:

Handsome_Chris said:

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

This has been covered many posts ago but I will reiterate.

If the plane's body is moving forwards relative to a "stationary" observer, let's say, at 1mph, and the belt is moving backwards at 1mph, the WHEEL SPEED, which is the value we're actually interested in, is 2mph.

No we are not interested in the 2 mph at all.  You may not only be interested in it, but find it fascinating, but I do not care that you are interested in that as it has nothing to do with resolving the question.

Also the plane is moving forward relative to a stationary object, the thing the conveyor belt is attached to.

Maynehead said:

You are proposing a situation that is explicitly precluded by the conditions set out in the question. In the context of the question, this situation is completely out of scope and to base your argument around it is trying to answer the wrong question.

No I am not.


If the plane moves forward at 1 mph taking the wheels with it, the conveyor belt's aircraft facing surface moves at 1 mph in the other direction. At no point in the question above does it mention the rotation of anything, let alone the wheels.  @Maynehead, that is just something some people have decided to assume, for some reason.  If it must mean that then surely it would have been stated in the original question?

If the plane moves forward then you aren't following the rule imposed by the experiment.  For the 1:1 ratio to remain for the entire experiment, the wheel cannot move at all.

Maynehead

Handsome_Chris said:

Maynehead said:

Handsome_Chris said:

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

This has been covered many posts ago but I will reiterate.

If the plane's body is moving forwards relative to a "stationary" observer, let's say, at 1mph, and the belt is moving backwards at 1mph, the WHEEL SPEED, which is the value we're actually interested in, is 2mph.

No we are not interested in the 2 mph at all.  You may not only be interested in it, but find it fascinating, but I do not care that you are interested in that as it has nothing to do with resolving the question.

Also the plane is moving forward relative to a stationary object, the thing the conveyor belt is attached to.

Maynehead said:

You are proposing a situation that is explicitly precluded by the conditions set out in the question. In the context of the question, this situation is completely out of scope and to base your argument around it is trying to answer the wrong question.

No I am not.


If the plane moves forward at 1 mph taking the wheels with it, the conveyor belt's aircraft facing surface moves at 1 mph in the other direction. At no point in the question above does it mention the rotation of anything, let alone the wheels.  @Maynehead, that is just something some people have decided to assume, for some reason.  If it must mean that then surely it would have been stated in the original question?

So it comes down to our different interpretations of the term "speed of the wheels".

Again I have already addressed this precise issue a few pages back, stating the precise reasons behind my choice of interpretation.

Ref. http://www.thefretboard.co.uk/discussion/comment/1248147/#Comment_1248147

P.S. I'm beginning to believe that almost any further questions posed can be addressed by one of my previous posts in this thread, which is great as it will save me a lot of typing

Handsome_Chris

sinbaadi said:

Handsome_Chris said:

Maynehead said:

Handsome_Chris said:

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

This has been covered many posts ago but I will reiterate.

If the plane's body is moving forwards relative to a "stationary" observer, let's say, at 1mph, and the belt is moving backwards at 1mph, the WHEEL SPEED, which is the value we're actually interested in, is 2mph.

No we are not interested in the 2 mph at all.  You may not only be interested in it, but find it fascinating, but I do not care that you are interested in that as it has nothing to do with resolving the question.

Also the plane is moving forward relative to a stationary object, the thing the conveyor belt is attached to.

Maynehead said:

You are proposing a situation that is explicitly precluded by the conditions set out in the question. In the context of the question, this situation is completely out of scope and to base your argument around it is trying to answer the wrong question.

No I am not.


If the plane moves forward at 1 mph taking the wheels with it, the conveyor belt's aircraft facing surface moves at 1 mph in the other direction. At no point in the question above does it mention the rotation of anything, let alone the wheels.  @Maynehead, that is just something some people have decided to assume, for some reason.  If it must mean that then surely it would have been stated in the original question?

If the plane moves forward then you aren't following the rule imposed by the experiment.  For the 1:1 ratio to remain for the entire experiment, the wheel cannot move at all.

@sinbaadi, how am I not following the rule of the entire experiment?  For every 1 mph the aircraft is moving forward the wheel is moving 1 mph forward, the top surface of the conveyor belt is moving 1 mph in the other direction.

viz

Handsome_Chris said:

sinbaadi said:

Handsome_Chris said:

Maynehead said:

Handsome_Chris said:

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

This has been covered many posts ago but I will reiterate.

If the plane's body is moving forwards relative to a "stationary" observer, let's say, at 1mph, and the belt is moving backwards at 1mph, the WHEEL SPEED, which is the value we're actually interested in, is 2mph.

No we are not interested in the 2 mph at all.  You may not only be interested in it, but find it fascinating, but I do not care that you are interested in that as it has nothing to do with resolving the question.

Also the plane is moving forward relative to a stationary object, the thing the conveyor belt is attached to.

Maynehead said:

You are proposing a situation that is explicitly precluded by the conditions set out in the question. In the context of the question, this situation is completely out of scope and to base your argument around it is trying to answer the wrong question.

No I am not.


If the plane moves forward at 1 mph taking the wheels with it, the conveyor belt's aircraft facing surface moves at 1 mph in the other direction. At no point in the question above does it mention the rotation of anything, let alone the wheels.  @Maynehead, that is just something some people have decided to assume, for some reason.  If it must mean that then surely it would have been stated in the original question?

If the plane moves forward then you aren't following the rule imposed by the experiment.  For the 1:1 ratio to remain for the entire experiment, the wheel cannot move at all.

@sinbaadi, how am I not following the rule of the entire experiment?  For every 1 mph the aircraft is moving forward the wheel is moving 1 mph forward, the top surface of the conveyor belt is moving 1 mph in the other direction.

^ I think maybe you haven't understood that the aircraft isn't moving. 

Handsome_Chris

viz said:

Handsome_Chris said:

sinbaadi said:

Handsome_Chris said:

Maynehead said:

Handsome_Chris said:

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

This has been covered many posts ago but I will reiterate.

If the plane's body is moving forwards relative to a "stationary" observer, let's say, at 1mph, and the belt is moving backwards at 1mph, the WHEEL SPEED, which is the value we're actually interested in, is 2mph.

No we are not interested in the 2 mph at all.  You may not only be interested in it, but find it fascinating, but I do not care that you are interested in that as it has nothing to do with resolving the question.

Also the plane is moving forward relative to a stationary object, the thing the conveyor belt is attached to.

Maynehead said:

You are proposing a situation that is explicitly precluded by the conditions set out in the question. In the context of the question, this situation is completely out of scope and to base your argument around it is trying to answer the wrong question.

No I am not.


If the plane moves forward at 1 mph taking the wheels with it, the conveyor belt's aircraft facing surface moves at 1 mph in the other direction. At no point in the question above does it mention the rotation of anything, let alone the wheels.  @Maynehead, that is just something some people have decided to assume, for some reason.  If it must mean that then surely it would have been stated in the original question?

If the plane moves forward then you aren't following the rule imposed by the experiment.  For the 1:1 ratio to remain for the entire experiment, the wheel cannot move at all.

@sinbaadi, how am I not following the rule of the entire experiment?  For every 1 mph the aircraft is moving forward the wheel is moving 1 mph forward, the top surface of the conveyor belt is moving 1 mph in the other direction.

^ I think maybe you haven't understood that the aircraft isn't moving. 

@viz , why would the aircraft not be moving?  Once thrust is applied the aircraft would start moving.

I think maybe you haven't understood that the aircraft is not a car.

Gassage

As I have mentioned the hard bit is landing it back onto the coveryor belt....

viz

Handsome_Chris said:

viz said:

Handsome_Chris said:

sinbaadi said:

Handsome_Chris said:

Maynehead said:

Handsome_Chris said:

Well, @viz, you say that, but for every 1mph the plane and wheel moves forward the conveyor belt's aircraft facing surface move 1mph in the other direction.  This means that when the 747 reaches 180 mph that the belt's surface is doing 180 mph in the other direction. Even though the aircraft is moving at 360 mph relative to the surface of the belt, it still takes off.

Seeeeemples. 

This has been covered many posts ago but I will reiterate.

If the plane's body is moving forwards relative to a "stationary" observer, let's say, at 1mph, and the belt is moving backwards at 1mph, the WHEEL SPEED, which is the value we're actually interested in, is 2mph.

No we are not interested in the 2 mph at all.  You may not only be interested in it, but find it fascinating, but I do not care that you are interested in that as it has nothing to do with resolving the question.

Also the plane is moving forward relative to a stationary object, the thing the conveyor belt is attached to.

Maynehead said:

You are proposing a situation that is explicitly precluded by the conditions set out in the question. In the context of the question, this situation is completely out of scope and to base your argument around it is trying to answer the wrong question.

No I am not.


If the plane moves forward at 1 mph taking the wheels with it, the conveyor belt's aircraft facing surface moves at 1 mph in the other direction. At no point in the question above does it mention the rotation of anything, let alone the wheels.  @Maynehead, that is just something some people have decided to assume, for some reason.  If it must mean that then surely it would have been stated in the original question?

If the plane moves forward then you aren't following the rule imposed by the experiment.  For the 1:1 ratio to remain for the entire experiment, the wheel cannot move at all.

@sinbaadi, how am I not following the rule of the entire experiment?  For every 1 mph the aircraft is moving forward the wheel is moving 1 mph forward, the top surface of the conveyor belt is moving 1 mph in the other direction.

^ I think maybe you haven't understood that the aircraft isn't moving. 

@viz , why would the aircraft not be moving?  Once thrust is applied the aircraft would start moving.

I think maybe you haven't understood that the aircraft is not a car.

I wasn't wishing to be rude. 

To answer you, the question of whether the aircraft moves is the exact crux of the question, and is what I've been talking about throughout the thread. The puzzle states that the conveyor matches the wheels. We have discussed that this means the backwards velocity of the belt matches the tangential velocity of the wheels. That implies that the plane is not moving. But as I have explained in the trolley and rope analogies, even the conveyor won't provide any counter force even at an infinite spinning speed, so that's why it's a paradox. The question implies the plane doesn't move, but it also implies that it will. 

Maynehead

@Handsome_Chris sorry, I posted the wrong link in my previous post (there are so many that they're getting a bit out hand!) I have now edited the post to correct the link.