Plane on a treadmill...

[JPreston]

....The rubber in the tyres would have overheated and melted earlier than this....

It all depends on the assumptions and operating parameters, which are not clearly defined in the original statement and so no definate answer can be proposed.

Well I didn't write the original website, but a few posts in I said we should assume all the normal things like no friction, zero windspeed, constant mass, no external actions etc etc.

It's still not very well worded but I think everyone gets the right idea.

[badass]

This is my reasoning:



the force diagram shows the 4 forces acting on the plane: the forward arrow is the thrust of the plane, which is exactly equal to the resistance displayed by the treadmill (normally this reistance is relatively low, however the movement of the treadmill acts as resistance to the motion of the wheel). The weight of the plane is balanced by the reactionary force of the treadmill.

In this situtation the plane is stationary. Speed does not "cause" forward movement, acceleration does: this is a change in (relative) velocity. As the treadmill changes speed to match that of the plane's wheels, the plane never overcomes the resistance offered by the treadmill and so never moves forward, relative to the ground.

In reality, the tires would slip etc etc and there would be wind moving across the wings which might cause the plane to lift off the ground slightly. If this happened the resistance offered by the treadmill on the wheels would be overcome and the plane would accelerate forward and probably take off. The rubber in the tyres would have overheated and melted earlier than this....

It all depends on the assumptions and operating parameters, which are not clearly defined in the original statement and so no definate answer can be proposed.

You're analysing it too much. The treadmill does the same speed as the plane backwards.
The plane will take off, its just that the wheels will be spinning twice as fast as they normally would at any point.
I will ask you this question aswell.
How is the treadmill moving if the plane isn't?

[Steve B]

the plane isn't moving as the plane does not displace linearly. the wheels just spin round on their axis, but no forward acceleration is produced because the treadmill speed is always equal to the speed of the air moving across the wings, i.e. no net displacement

[redsky009]

You're analysing it too much. The treadmill does the same speed as the plane backwards.
The plane will take off, its just that the wheels will be spinning twice as fast as they normally would at any point.
I will ask you this question aswell.
How is the treadmill moving if the plane isn't?

the belt of the treadmill moves, the device itself doesnt (relative to the ground) the wheels move, the plane doesn't (relative to the ground)

Think of it as you pushing against a wall - the harder you push, the more the wall pushes back (neither of you move relative to the ground). Only when you overcome the maximum force the wall can offer, does the wall fall over and you accelerate forward.... as the treadmill is constantly increasing with the speed of the planes wheels, that force is never overcome.

[redsky009]

Well I didn't write the original website, but a few posts in I said we should assume all the normal things like no friction, zero windspeed, constant mass, no external actions etc etc.

It's still not very well worded but I think everyone gets the right idea.

I don't think we can assume no friction - this would make the entire idea preposterous, friction is what makes the wheels spin and what causes the thrust from the engines

If we ignore friction between the wheels and belt, but keep the friction between the engines and the air, then the plane would move forwards, but you cant just pick which forces you ignore in a closed system....

air movement etc etc I agree with...

[MSIC]

I don't think we can assume no friction - this would make the entire idea preposterous,

Because otherwise this discussion is entirely practical?

[redsky009]

Wow, i can't believe how much i am sucked into this.
Surely the issue of tyres and treadmills is (in a way) irrelevant?

If we assume, as the proposition suggests, that the treadmill succesfully manages to move in an equal and opposite movement to the tyres. So this takes the tyres/treadmill out of the equation, and we are left in effect with a tube with wings, hanging in mid air that gravity does not cause to fall to the floor.
It has no physical connection to the ground, in other words.

The question then, surely, becomes
"If the jet engines spin up, can it propel a device forward through air?"

Is my argument valid, or flawed, before I make any further steps?

But it is connected to the ground, thats the point. The speed of the treadmill isn't constant, it changes to match the thrust of the plane (and hence the speed of the wheels) and so can't be ignored. The wheels spinning and the thrust of the engines are not separate - where do the wheels get the force to spin? The engines. Think about it, if the treadmill was spinning faster than the thrust of the engines, the plane would move backwards. If the thrust of the engines was faster than the speed of the treadmill, the plane would move forwards.

The problems states than the treadmill matches the speed of the wheels. The wheels aren't powered by anything other than the thrust of the engines and so the force produced by the engines is matched by the force produced by the treadmill....

[redsky009]

Because otherwise this discussion is entirely practical?

Yes

[badass]

I will say this again:
How can the conveyor be moving is the plane isn't
If instead of jet engines, you had a giant hand pushing the plane, would it take off in this situation, or would the fact the treadmill is going backwards at whatever speed suddenly mean that it matches whatever force you apply to the back of the plane.

[JPreston]

I don't think we can assume no friction - this would make the entire idea preposterous, friction is what makes the wheels spin and what causes the thrust from the engines

If we ignore friction between the wheels and belt, but keep the friction between the engines and the air, then the plane would move forwards, but you cant just pick which forces you ignore in a closed system....

air movement etc etc I agree with...

Oi! No more nit-picking from you please. I mean zero friction on the wheel bearings but perfectly grippy tyres. The normal simplifying assumptions you make in the bizarre world of inextensible strings, point masses and so on apply here. Otherwise you will be asking for the bhp of the engines, coefficient of friction of the belt and tyres and the wattage of the treadmill next

[redsky009]

I will say this again:
How can the conveyor be moving is the plane isn't
If instead of jet engines, you had a giant hand pushing the plane, would it take off in this situation, or would the fact the treadmill is going backwards at whatever speed suddenly mean that it matches whatever force you apply to the back of the plane.

Its quite easy, the plane isn't moving and neither is the treadmill... the belt of the treadmill is moving and so are the wheeels of the plane.

Giant hand situation, nope still wouldn't take off, sorry bud. to take your analogy a step futher, if you imagine a giant hand on the back of the plane as the engines, imagine an equally giant hand on the front of the plane pushing back (this is the treadmill) with exactly the same force - the plane doesn't move.

Its all a matter of forces.

[redsky009]

Oi! No more nit-picking from you please. I mean zero friction on the wheel bearings but perfectly grippy tyres. The normal simplifying assumptions you make in the bizarre world of inextensible strings, point masses and so on apply here. Otherwise you will be asking for the bhp of the engines, coefficient of friction of the belt and tyres and the wattage of the treadmill next

I loike to pick nits I do

[Skyrail]

It won't take off, yeah nothing new but lol just throwing in my opinion. Too lazy to read anymore then the first page at the moment.

I would explain why I think so but I feel ill and very lazy.

So for now it just won't, accept it.

[JPreston]

...
Giant hand situation, nope still wouldn't take off, sorry bud. to take your analogy a step futher, if you imagine a giant hand on the back of the plane as the engines, imagine an equally giant hand on the front of the plane pushing back (this is the treadmill) with exactly the same force - the plane doesn't move.

Its all a matter of forces.

Why is there a hand pushing the plane back? The treadmill exerts zero force on the plane because the (frictionless) wheels freely rotate. All that happens is the wheels spin faster.

[Skyrail]

Oh just reading the second to last post before me what I think is exactly what Redsky is saying.

[autopilot]

This is brilliant. I have not laughed so much in ages, especially at all the people getting really wound up over lol

The clever thing about this riddle is the simplicity of it. People seem to think the treadmill has some kind of invisible grip on the plane.

Read the whole thread to see nichomach's excellent turn around

Don't fret redsky009, the penny will drop soon