Plane on a conveyor belt

stratman3142

Well I've come to the conclusion that I don't know the answer and can't rationalise the question. And I thought physics was my best subject.

RocknRollDave

I'm from an Arts background so....lovely, well-worded responses, guys,   and a lovely drawing in the OP.


......no fucking clue what you're talking about, mind....  

Sporky

Physics doesn't much help. Pilots and people too beloved of physics tend to ignore the critical part of the question because it doesn't fit neatly into a physics approach.

It's a bit like if you asked "A mouse, who can speak only Esperanto, wishes to book a hotel room in Moscow - how does he go about it?", and all the biologists go off about how mice don't have vocal cords (which descends into a side argument about how they shouldn't really be called cords, they're really flaps) and the neurologists start on how mice lack the brain power to comprehend the concept of booking a hotel, let alone speaking Esperanto.

The question is clear, and arguing with the question means missing an opportunity to revel in the ridiculous.

A5D5E5

You might as well all be arguing about which way is up in a painting by Escher.  

In the real world the plane takes off.  In the alternate reality of the question (and note it has to be a pretty odd reality) it doesn't.  There isn't anything else to say.

The xkcd link earlier answered the question completely.

Sporky

A5D5E5 said:

 
In the real world the plane takes off.  In the alternate reality of the question (and note it has to be a pretty odd reality) it doesn't.  There isn't anything else to say.

I wish I was smart enough to have come up with such an excellent answer. Spot on.

Maynehead

Ok, maybe some examples will help.

Assume you are looking side on at the plane, as in the diagram in the first post.

First suppose that the belt is stationary, and the wheels are turning at 1mph. The result is that the plane moves to the left at 1mph.

Now suppose that the belt is moving to the right at 10mph and the wheels are turning at 11mph. The net velocity of the plane is still 1mph to th left.

Likewise if the belt is moving to the right at 10mph and the wheels are turning at 9mph, the net velocity will be 1mph to the right.

However, NONE of the above scenarios satisfy the constraint set out in the question, which is that the belt and the wheels are moving at the exact SAME speed (in opposite directions).

When the belt and wheels DO move at the same speed, the plane's net velocity is 0, i.e. not moving left or right, stationary.

Regardless of whether the belt moves at 10mph, and the wheels turn at 10mph, or the belt moves at 700mph and the wheels turn at 700mph, the resultant velocity of the plane will be zero.

Now the critical part: it is not possible at any point during the (thought) experiment for the plane to move left or right without breaking this rule. For the plane to move, the wheels MUST be moving at a different speed to the belt (see above examples), and as the question implies, this is not possible as the belt always EXACTLY matches the speed of the wheels.

(Just to cover all bases, this assumes perfect adhesion between the wheels and the belt, i.e. no skidding.)

Sporky

Which means that if you're going to apply classical reductionist physics to it, either the plane's engines don't work, or after a very, very short period of time the conveyor belt and wheels hit relativistic speeds, turn into plasma and you're into classic XKCD What-If territory again.

stratman3142

All this theory is making my brain hurt. I vote for an empirical approach. Let's construct an experiment. Then we can come up with a theory that fits what's observed in practice.

Maynehead

Sporky said:

Which means that if you're going to apply classical reductionist physics to it, either the plane's engines don't work, or after a very, very short period of time the conveyor belt and wheels hit relativistic speeds, turn into plasma and you're into classic XLCD What-If territory again.

Which is why I attempted to introduce the real world concept of resistance, with which it will be possible to establish a stable equilibrium without things spinning off into infinity in the first fraction of a millisecond...

In retrospect this probably only served to muddy the waters and create even more tangents for people to wander off into.

Sporky

stratman3142 said:

All this theory is making my brain hurt. I vote for an empirical approach. Let's construct an experiment. Then we can come up with a theory that fits what's observed in practice.

I don't think you could build the conveyor.

It's a bit like trying to solve the "irresistible force meets immovable object" paradox - no universe can support both.

sinbaadi

I thought this was stupid until I read the OP properly.

Can the aircraft take off whilst in a stationary position (assuming no headwind)?  No.

The question is whether you would be able to move the aircraft at all given the rules imposed by the treadmill.

Of course nothing happening at the wheels is stopping a Eurofighter at full thrust, so a rolling wheel isn't go to either, and that thing just grabs a massive wodge of air and pulls itself through it.  The aircraft is going to build airspeed and accelerate.

But if a wheel rolls at 1 mph over a surface that rolls in the opposite direction at 1mph, that wheel is not going anywhere.  End of.  Add as many zeroes as you like.

I don't think the aircraft can take off without breaking the rules of the thought experiment.  The wheel has to turn at a speed greater than that of the conveyor for the aircraft to have the first iota of its forward momentum, but both have infinitely high possible speeds.

OK, time to hit youtube.

Sporky

sinbaadi said:

I don't think the aircraft can take off without breaking the rules of the thought experiment.

Exactly.

Everyone who says it can take off is applying real-world physics to a scenario which inherently and explicitly precludes real-world physics.

Maynehead

sinbaadi said:

I thought this was stupid until I read the OP properly.

Can the aircraft take off whilst in a stationary position (assuming no headwind)?  No.

The question is whether you would be able to move the aircraft at all given the rules imposed by the treadmill.

Of course nothing happening at the wheels is stopping a Eurofighter at full thrust, so a rolling wheel isn't go to either, and that thing just grabs a massive wodge of air and pulls itself through it.  The aircraft is going to build airspeed and accelerate.

But if a wheel rolls at 1 mph over a surface that rolls in the opposite direction at 1mph, that wheel is not going anywhere.  End of.  Add as many zeroes as you like.

I don't think the aircraft can take off without breaking the rules of the thought experiment.  The wheel has to turn at a speed greater than that of the conveyor for the aircraft to have the first iota of its forward momentum, but both have infinitely high possible speeds.

OK, time to hit youtube.

And we have another winner!

Btw the only value the YouTube "proof" videos offer is entertainment.

CabbageCat

Sporky said:

stratman3142 said:

All this theory is making my brain hurt. I vote for an empirical approach. Let's construct an experiment. Then we can come up with a theory that fits what's observed in practice.

I don't think you could build the conveyor.

It's a bit like trying to solve the "irresistible force meets immovable object" paradox - no universe can support both.

I think it can be built without breaching the original parameters by using my locked wheels scenario. It might be ignoring some implied parameters and introducing one whose absence is implied but it is achievable in real life.

monquixote

Maynehead said:

sinbaadi said:

I thought this was stupid until I read the OP properly.

Can the aircraft take off whilst in a stationary position (assuming no headwind)?  No.

The question is whether you would be able to move the aircraft at all given the rules imposed by the treadmill.

Of course nothing happening at the wheels is stopping a Eurofighter at full thrust, so a rolling wheel isn't go to either, and that thing just grabs a massive wodge of air and pulls itself through it.  The aircraft is going to build airspeed and accelerate.

But if a wheel rolls at 1 mph over a surface that rolls in the opposite direction at 1mph, that wheel is not going anywhere.  End of.  Add as many zeroes as you like.

I don't think the aircraft can take off without breaking the rules of the thought experiment.  The wheel has to turn at a speed greater than that of the conveyor for the aircraft to have the first iota of its forward momentum, but both have infinitely high possible speeds.

OK, time to hit youtube.

And we have another winner!

Btw the only value the YouTube "proof" videos offer is entertainment.

So do we have to assume that the wheel is infinitely tractable? 

Myranda

Sporky said:

stratman3142 said:

All this theory is making my brain hurt. I vote for an empirical approach. Let's construct an experiment. Then we can come up with a theory that fits what's observed in practice.

I don't think you could build the conveyor.

It's a bit like trying to solve the "irresistible force meets immovable object" paradox - no universe can support both.

We could create a scale model using a running machine and a remote control plane... a handful of sensors... 

rig up an arduino to control speeds exactly ... could even add weights etc to ensure a proper scale experiment

monquixote

Myranda said:

Sporky said:

stratman3142 said:

All this theory is making my brain hurt. I vote for an empirical approach. Let's construct an experiment. Then we can come up with a theory that fits what's observed in practice.

I don't think you could build the conveyor.

It's a bit like trying to solve the "irresistible force meets immovable object" paradox - no universe can support both.

We could create a scale model using a running machine and a remote control plane... a handful of sensors... 

rig up an arduino to control speeds exactly ... could even add weights etc to ensure a proper scale experiment

At any scale the conveyor needs to instantaneously spin up to infinite speed.

Maynehead

If by that you mean it always maintains traction with the belt surface then yes, that is one of the many assumptions.

Ofcourse you can circumvent the problem completely by appying the brakes and powering through the locked up wheels with the sheer force of the engines and take off that way, with the wheels, and therefore the belt, never turning; but that would not be in the spirit of the question

Myranda

monquixote said:

Myranda said:

Sporky said:

stratman3142 said:

All this theory is making my brain hurt. I vote for an empirical approach. Let's construct an experiment. Then we can come up with a theory that fits what's observed in practice.

I don't think you could build the conveyor.

It's a bit like trying to solve the "irresistible force meets immovable object" paradox - no universe can support both.

We could create a scale model using a running machine and a remote control plane... a handful of sensors... 

rig up an arduino to control speeds exactly ... could even add weights etc to ensure a proper scale experiment

At any scale the conveyor needs to instantaneously spin up to infinite speed.

Pretty sure a 747 doesn't achieve FTL speeds... I think we could use much lower speeds ... how about 5 times the take off speed for the model plane? that would be a much greater difference than between 747 take off speed and maximum speed (160-180 take off and 675 maximum) ... you'd need a VERY well made conveyor but it should still be possible

Myranda

What if we simplify the model?

Totally remove the wheels and bolt the plane to the ground - with bolts capable of resisting the force of the engines.

Then put a forcemeter on the tips of the wings tethered to the ground.

If the engines move enough air past the wings to produce any lift it will be recorded on the forcemeters - we know how much lift is required to lift the plane (more than the force its mass exerts downwards).