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Unread 20 Dec 2006, 15:42   #1
Ste
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A Plane Problem

Some of you have probably seen this before.

"A plane equipped with fixed horizontal engines and wheel landing gear is placed on a huge treadmill runway. The treadmill has a clever design and always matches the speed of the plane, but runs in the opposite direction. Will the plane take off and fly or not?"

A crappy diagram



It's confused me for a while but I think I have my answer...
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Unread 20 Dec 2006, 15:50   #2
Knight Theamion
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Re: A Plane Problem

first response: it won't take off, because he has no speed, there is no lift


which is wrong, it will take off, which is explained later.
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Unread 20 Dec 2006, 16:01   #3
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Re: A Plane Problem

Of course it will. It'd take off in exactly the same way, assuming that the wheels are ideal (ie have zero friction).

The only reason it wouldn't take off (as theamion claims) was if the impetus to get moving was provided by the wheels, which is not the case.
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Unread 20 Dec 2006, 16:02   #4
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Re: A Plane Problem

There's no forces from the air running against the plane. The plane needs the oppostie resistance from the air to be able to take off.

My understanding of the technical words to describe how it works isn't that great, but I know roughly how planes take off. There's no air circulation over the wings (as it's exactly stationary, due to the treadmill moving at EXACTLY the same speed as the wheels), so it would just keep rolling on and on and on and on.
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Unread 20 Dec 2006, 16:04   #5
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
There's no forces from the air running against the plane. The plane needs the oppostie resistance from the air to be able to take off.
Why would it be stationary relative to the air?
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Unread 20 Dec 2006, 16:05   #6
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Re: A Plane Problem

I was hoping Jakiri would take longer to post

I agree with him btw...
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Unread 20 Dec 2006, 16:05   #7
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
Why would it be stationary relative to the air?
Because Ste said the treadmill works in a way where the plane never moves forward - whatever speed it goes out, it is counteracted by the treadmill's speed.
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Unread 20 Dec 2006, 16:06   #8
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Re: A Plane Problem

Quote:
Originally Posted by Ste
I was hoping Jakiri would take longer to post

I agree with him btw...
I can delete my posts if you prefer!
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Unread 20 Dec 2006, 16:07   #9
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
Because Ste said the treadmill works in a way where the plane never moves forward - whatever speed it goes out, it is counteracted by the treadmill's speed.
Why would it be counteracted by the treadmill's speed? What you said would be true for a car, not for a plane.
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Unread 20 Dec 2006, 16:09   #10
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
Why would it be counteracted by the treadmill's speed? What you said would be true for a car, not for a plane.
How can the plane push air downwards beneath its wings if it's standing still?
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Unread 20 Dec 2006, 16:15   #11
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
I can delete my posts if you prefer!
Nah it's ok - So long as people have a go at the problem before reading the posts below I'm sure it'll be ok

(Or just don't trust that we're correct)
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Unread 20 Dec 2006, 16:15   #12
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
How can the plane push air downwards beneath its wings if it's standing still?
Who said the plane was standing still?
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Unread 20 Dec 2006, 16:16   #13
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Re: A Plane Problem

I get the feeling it would take off but not very safely as there will be force against the plane to generate lift.
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Unread 20 Dec 2006, 16:19   #14
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Re: A Plane Problem

Quote:
Originally Posted by Ste
Who said the plane was standing still?
It's the wording of your original post. This hypothetical treadmill is apparently matching the plane's speed EXACTLY. Therefore the plane moves nowhere. It can thrust and thrust and thrust from its engines, but no air is moving (except maybe a small amount around the engine area, but that's not enough to lift it into the air).
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Unread 20 Dec 2006, 16:22   #15
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
It's the wording of your original post. This hypothetical treadmill is apparently matching the plane's speed EXACTLY. Therefore the plane moves nowhere. It can thrust and thrust and thrust from its engines, but no air is moving (except maybe a small amount around the engine area, but that's not enough to lift it into the air).
Wheels TK, the plane has wheels...

The engines don't power the wheels and the treadmill doesn't affect the engines.
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Unread 20 Dec 2006, 16:27   #16
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Re: A Plane Problem

Quote:
Originally Posted by Ste
Wheels TK, the plane has wheels...

The engines don't power the wheels and the treadmill doesn't affect the engines.

The wheels have next to no power in them. They exist purely so the plane doesn't skid along the ground. The plane's thrust is primarily (if not entirely) from its engines.

This "magical" treadmill (which couldn't exist in reality) is the key of the question. It prevents the plane from moving as whatever speed the plane moves at due to the thrust of its engines, it will be counteracted. It'll never accelerate or move off the treadmill as the force pushing AGAINST the plane is exacty equal to the force pushing forward.

The engines don't make it take off. The engines give it enough thrust to push through the air, then direct the air underneath the wings. Without movement from the plane through the air, no air will be directed underneath the wings.
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Unread 20 Dec 2006, 16:31   #17
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Re: A Plane Problem

tomkat is right.
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Unread 20 Dec 2006, 16:34   #18
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Re: A Plane Problem

Strictly speaking, the problem is meaningless if you don't assume it can take off - because if you believe it makes it so the plane can't take off because the air is stationary around it, the speed of the plane is zero and thus the ground isn't moving. Of course, instantaneously, the plane has a speed relative to the air again, and so you get an infinitely fast progression.

The only sensible way of looking at it, if you want to consider what people think it means, is that if the ground has the same speed as the speed of the outer surface of the wheels. Assuming that...

Quote:
Originally Posted by Tomkat
Hmmm there isn't actually an answer to it apparently (I looked it up out of curiosity).

The argument given is the same as mine - that in theory the plane is completely stationary (due to the treadmill exerting the exact same force against the wheels). In practice, I expect it would as it'd be impossible to regulate the treadmill's speed to match the plane's speed exactly.
Under a frictionless environment, then nothing changes. Because friction is zero (either between the wheel and its axel, or between the wheel and the road) there is no way in which the track can interact with the plane. You get a reaction force and nothing else.

I was going to do an analysis of different frictional environments, but then I realised that it was trivially obvious that the amount of friction would not be sufficient because airplanes need brakes and whatnot to stop them when landing on a runway. The necessity of the use of these things to stop a plane when the engine isn't running shows that the force is significantly less than half that of the maximum output of the engines when going at a speed sufficient to take off, and thus the friction between the wheels and the track alone in the above example would be not be able to stop the plane moving.
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Unread 20 Dec 2006, 16:34   #19
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Re: A Plane Problem

Someone explain this please. I can't see how tomkat could possibly be wrong, but i have a sneaky feeling he is. Im confused.
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Unread 20 Dec 2006, 16:36   #20
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Re: A Plane Problem

Oh its ok I get you both now.
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Unread 20 Dec 2006, 16:39   #21
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
Under a frictionless environment, then nothing changes. Because friction is zero (either between the wheel and its axel, or between the wheel and the road) there is no way in which the track can interact with the plane. You get a reaction force and nothing else.
The entire theory is completely hypothetical and wouldn't ever work in reality. The treadmill would need to be able to attain an infinite speed, as would the engines. We'd be more likely to see the wheels on the plane pop before anything.

But in answer to the question "would it take off" (ignoring friction issues and speed issues), the answer is simply "no", because there is no air flow over the wings.

PS I deleted that post you quoted because it kind of ruins the thread
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Unread 20 Dec 2006, 16:40   #22
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Re: A Plane Problem

The wheels are simply moving twice as fast.

The plane itself isn't affected if you assume the friction between the wheels and the plane is zero.

The plane will move forward and will take off when it reaches the required air speed.
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Unread 20 Dec 2006, 16:41   #23
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Re: A Plane Problem

Quote:
Originally Posted by idimmu
The engine creates a force forwards and the wheels turn due to friction between the wheels and the floor

consider a scenario where the floor is really smooth, no friction on the wheels, the plane will still move forwards even though the wheels arent moving
This isn't the same, as the plane is moving around here so therefore has airflow.


Quote:
Originally Posted by idimmu
or a scenario where the plane has no wheels and just has bricks, given a powerful enough engine, the plane could overcome the friction between the 'bricks' and the ground and still move forwards

in this scenario the plane would take off. what id imagine would happen is the wheels wouldnt roll nicely over the ground, but be dragged along by the body of the plane whilst rotating at the same speed as the ground is moving
This is similar. The plane wouldn't take off. If it could, then why do we have runways at airports? Surely we could just mount all the aircraft on bricks and have them take off from stationary positions? The plane needs the air to move under its wings.
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Unread 20 Dec 2006, 16:42   #24
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
The entire theory is completely hypothetical and wouldn't ever work in reality. The treadmill would need to be able to attain an infinite speed, as would the engines. We'd be more likely to see the wheels on the plane pop before anything.

But in answer to the question "would it take off" (ignoring friction issues and speed issues), the answer is simply "no", because there is no air flow over the wings.

PS I deleted that post you quoted because it kind of ruins the thread
For starters, it's not a theory. If I would call it anything, I'd call it a thought experiment. Secondly, I don't like being told how modelling in physics works by someone who hasn't studied either the philosophy of physics or physics itself. Thirdly, you will notice that I commented upon more than the frictionless case. Fourthly, you haven't explained why it wouldn't have moving air beyond simply stating it over and over again.

I don't think you've understood the problem
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Unread 20 Dec 2006, 16:43   #25
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Re: A Plane Problem

Quote:
Originally Posted by Ste
The wheels are simply moving twice as fast.

The plane itself isn't affected if you assume the friction between the wheels and the plane is zero.

The plane will move forward and will take off when it reaches the required air speed.
Why would you assume the friction between the wheels and the plane is zero?

There would be no air speed. The treadmill stops the plane from moving forward.

You have to read the initial question again. This isn't a regular treadmill, that the plane can eventually accelerate against and take off. It is being held stationary by the magical super forces of exact speed.
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Unread 20 Dec 2006, 16:44   #26
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
The entire theory is completely hypothetical and wouldn't ever work in reality. The treadmill would need to be able to attain an infinite speed, as would the engines. We'd be more likely to see the wheels on the plane pop before anything.

But in answer to the question "would it take off" (ignoring friction issues and speed issues), the answer is simply "no", because there is no air flow over the wings.

PS I deleted that post you quoted because it kind of ruins the thread
Imagine you have a toy plane that you are holding onto a conveyor. The wheels are moving but the plane is not. If you push the plane forwards it will move. In this case your hands are forward force that in reality would be the engines.

It doesn't matter how fast the conveyor is going - it doesn't affect the plane. Just the wheels.

If the plane is moving forward there is air moving over the wings. Hence it is possible to fly.
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Unread 20 Dec 2006, 16:44   #27
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
Why would you assume the friction between the wheels and the plane is zero?
Because it's the simplest way to model it. You don't have to, which is why I demonstrated that under any consideration of real materials, ie not a frictionless world, it can still take off.

Quote:
Originally Posted by Tomkat
There would be no air speed. The treadmill stops the plane from moving forward.
Stop saying this. Please.

How are you modelling friction?

Quote:
Originally Posted by Tomkat
You have to read the initial question again. This isn't a regular treadmill, that the plane can eventually accelerate against and take off. It is being held stationary by the magical super forces of exact speed.
Oh gods.
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Unread 20 Dec 2006, 16:46   #28
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
This isn't the same, as the plane is moving around here so therefore has airflow.
No - it IS the same.


Quote:
This is similar. The plane wouldn't take off. If it could, then why do we have runways at airports? Surely we could just mount all the aircraft on bricks and have them take off from stationary positions? The plane needs the air to move under its wings.
Because in Idimmu's analogy the plane is still moving as well - it's just taking more energy to move it.
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Unread 20 Dec 2006, 16:47   #29
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
For starters, it's not a theory. If I would call it anything, I'd call it a thought experiment. Secondly, I don't like being told how modelling in physics works by someone who hasn't studied either the philosophy of physics or physics itself. Thirdly, you will notice that I commented up on more than the frictionless case. Fourthly, you haven't explained why it wouldn't have moving air beyond simply stating it over and over again.

I don't think you've understood the problem

Let's assume that (as in idi's example) the plane is being held up by an invisible force, but stationary (on bricks is a fine example).

The engines can thrust and thrust and thrust and thrust, but they aren't pushing against anything. They're just blowing hot air out.

To generate enough air underneath the wings, the plane needs to be moving through the air at a high speed. We know it isn't moving, as the treadmill is stationary (I assume) and the plane isn't moving off the treadmill. So no air flow exists (and any that does would just be generate by the engines and is insignificant).
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Unread 20 Dec 2006, 16:47   #30
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
Let's assume that (as in idi's example) the plane is being held up by an invisible force, but stationary (on bricks is a fine example).
NO NO NO.

THE PLANE IS NOT STATIONARY.

For the plane to be stationary, the amount of friction from the ground would have to be enormous, which is not the case.
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Unread 20 Dec 2006, 16:48   #31
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
Let's assume that (as in idi's example) the plane is being held up by an invisible force, but stationary (on bricks is a fine example).

The engines can thrust and thrust and thrust and thrust, but they aren't pushing against anything. They're just blowing hot air out.

To generate enough air underneath the wings, the plane needs to be moving through the air at a high speed. We know it isn't moving, as the treadmill is stationary (I assume) and the plane isn't moving off the treadmill. So no air flow exists (and any that does would just be generate by the engines and is insignificant).
You really are misunderstanding the whole thing.

Try my toy plane experiment.
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Unread 20 Dec 2006, 16:54   #32
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
NO NO NO.

THE PLANE IS NOT STATIONARY.

For the plane to be stationary, the amount of friction from the ground would have to be enormous, which is not the case.
Yes, it would have to be enormous.

If you want to assume there's no friction then you should assume there's no airflow either, so I'm still right

In reality the treadmill couldn't exist. I have said this a few times already

In relation to the AIR, the plane is stationary. How is it supposed to move forward?
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Unread 20 Dec 2006, 16:55   #33
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Re: A Plane Problem

Quote:
Originally Posted by idimmu
They're pushing against air.
Yeah but not enough air to lift the plane up. The engines exist to move the plane forward. If the plane is being held back (by a big rope, or by some bricks, or by superglue) then it won't go anywhere.
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Unread 20 Dec 2006, 17:03   #34
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Re: A Plane Problem

Lets go over this in detail.

Let us first assume that there is a first order relationship between friction and velocity (that's y=mx + c, where y is friction, x is velocity and m and c are the coefficients of kinetic and static friction respectively, for all you GCSE maths types out there)..

This is a pretty safe assumption, because it's true.

Next: if you have a static force on an object, then it will take the same amount of time and distance to accelerate to a velocity as the object would to come to a stop from that velocity when the force opposes the movement.

For the next bit, I'll explain it as if the forces were constant (which is fine, the net impulses aren't changed by assuming this, and we're only effectively dealing with the plane at two points, when it's stopped and when it's taking off, so we're not losing any particularly useful information).

Lets call the force from the engines E.

Let us call the (constant in this example) friction force F.

The net force when taking off is E - F.

The net force when landing, from the wheels alone (no breaks, or flaps or whatnot) is F.

Now, let us assume that the plane doesn't need breaks or flaps when landing. It just stops of its own accord.

In this case E - F = F

E = 2F.

Would it take off on a rolling runway made of the same materials? Lets investigate!

The friction between the wheels and the track works as if the velocity was twice what it usually is, so y(2) = 2mx + c, not just mx + c. However, if c is greater than 0, which it is, y(2) is less than y, because 2mx + c is less than 2mx + c + c, obviously.

So, the friction in that case would be less than 2F, so there would still be some resultant force on the plane, so it would still accelerate. It would still take off, albeit over a very long time if c is small.

Remember that this is assuming that a plane will just roll to a halt once you've got it down on the ground.

Do I really have to go into the real world, where you have to use breaks and whatnot, in which case E - F = F + K, where K is the retardation force provided by the breaks (etc), and is in all likelihood larger than F?

Please say I don't.

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Unread 20 Dec 2006, 17:04   #35
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Re: A Plane Problem

I just thought of an example that might help people see how I'm thinking (I admit I might be wrong, but then the entire thing is hypothetical anyway).

If you're running on a road, then you feel the air blow against your face. Because you're pushing through it.

If you're running on a treadmill, you feel no air blow against your face. Because you aren't pushing against it (ignoring the air being moved round by your arms and legs moving).

With no significant air movement, the plane wouldn't be able to take off.


I dunno if that helps you see how I'm seeing the problem, but hopefully it might.
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Unread 20 Dec 2006, 17:04   #36
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
In relation to the AIR, the plane is stationary. How is it supposed to move forward?
You do know how plane engines... work... don't you?
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Unread 20 Dec 2006, 17:05   #37
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
I just thought of an example that might help people see how I'm thinking (I admit I might be wrong, but then the entire thing is hypothetical anyway).

If you're running on a road, then you feel the air blow against your face. Because you're pushing through it.

If you're running on a treadmill, you feel no air blow against your face. Because you aren't pushing against it (ignoring the air being moved round by your arms and legs moving).

With no significant air movement, the plane wouldn't be able to take off.


I dunno if that helps you see how I'm seeing the problem, but hopefully it might.
Whether or not there is resultant airflow is the answer of the question, not what you have to base your argument upon.
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Unread 20 Dec 2006, 17:07   #38
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Re: A Plane Problem

Quote:
Originally Posted by horn
how many posts should it take a good teacher to get this across to the children tomkat? you're rubbish!
I hope this is just a teaching exercise to make me think about the problem in more detail!
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Unread 20 Dec 2006, 17:07   #39
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
Whether or not there is resultant airflow is the answer of the question, not what you have to base your argument upon.

No. How easy was that!
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Unread 20 Dec 2006, 17:08   #40
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
Lets call the force from the engines E.

Let us call the (constant in this example) friction force F.

The net force when taking off is E - F.

The net force when landing, from the wheels alone (no breaks, or flaps or whatnot) is F.

Now, let us assume that the plane doesn't need breaks or flaps when landing. It just stops of its own accord.

In this case E - F = F

E = 2F.

As the treadmill is moving at the exact speed, then it is exerting exactly the same force as the engines are thrusting, so surely E = F.
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Unread 20 Dec 2006, 17:11   #41
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Re: A Plane Problem

must admit i agree with tomkat here. the treadmill is controlling the speed of the ground the plane traveling on is moving at, it is not controlling the air around it.

as tomkat says the airplane takes off by manipulating the air around it to create lift. the air around the plane whilst on the treadmill is essentially stationary...right?
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Unread 20 Dec 2006, 17:13   #42
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
As the treadmill is moving at the exact speed, then it is exerting exactly the same force as the engines are thrusting, so surely E = F.
You clearly haven't understood what I posted, as the F is the friction between the plane and a stationary runway.
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Unread 20 Dec 2006, 17:13   #43
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Re: A Plane Problem

im in agreement with tomkat, there would be no forward velocity relative to the air around the plane, and thus no lift.
Think of it this way. If you are running on a treadmill which matches your speed, do you still feel the same air resistance against your face as you would if you were running on ground?
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Unread 20 Dec 2006, 17:14   #44
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Re: A Plane Problem

I give up. I prove it with actual proper maths and you still don't believe me.

Did you know that 0.9 recurring is equivilent to 1?
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Unread 20 Dec 2006, 17:17   #45
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Re: A Plane Problem

I think the main problem we have here is that Mark is thinking about this in a realistic sense, in which case the treadmill could never possibly exert the exact same force back. In that case, yeah, the plane would probably eventually build up enough speed and power to pull off the treadmill, and have accumulated enough to be able to take off.

But in this hypothetical situation, the treadmill can move at an infinite speed, thus preventing the plane from moving anywhere, no matter how much force it exerts from its engines.
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Unread 20 Dec 2006, 17:18   #46
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Re: A Plane Problem

Quote:
Originally Posted by MrL_JaKiri
You clearly haven't understood what I posted, as the F is the friction between the plane and a stationary runway.
Ok, so then E = F + T

Where T is the force exerted by the treadmill on top of friction (F) to counteract whatever forces the engines can exert (E).
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Unread 20 Dec 2006, 17:18   #47
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
I think the main problem we have here is that Mark is thinking about this in a realistic sense, in which case the treadmill could never possibly exert the exact same force back.
No.

Quote:
Originally Posted by MEEEEE
Strictly speaking, the problem is meaningless if you don't assume it can take off - because if you believe it makes it so the plane can't take off because the air is stationary around it, the speed of the plane is zero and thus the ground isn't moving. Of course, instantaneously, the plane has a speed relative to the air again, and so you get an infinitely fast progression.

The only sensible way of looking at it, if you want to consider what people think it means, is that if the ground has the same speed as the speed of the outer surface of the wheels.
Quote:
Originally Posted by Tomkat
But in this hypothetical situation, the treadmill can move at an infinite speed, thus preventing the plane from moving anywhere, no matter how much force it exerts from its engines.
You still don't appear to know how planes work, or how friction works, or both.
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Unread 20 Dec 2006, 17:19   #48
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Re: A Plane Problem

Actually, my analogy has given me food for thought.
In the running on treadmill example, the force is applied against the ground ( running ) , with a plane that force is applied to the air.

Im back to the "hmm, not sure" stage. It would need to be shown through experiment for me

perhaps the root of the confusion is in the wheels, so lets remove those from the equation.
Assume the plane's wheels and the threadmill surface are replaced with magnets of equal charge ( therefore the plane hovers ).
Would it take off now? I suspect it would
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Unread 20 Dec 2006, 17:19   #49
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Re: A Plane Problem

Quote:
Originally Posted by Tomkat
Ok, so then E = F + T

Where T is the force exerted by the treadmill on top of friction (F) to counteract whatever forces the engines can exert (E).
Quote:
Originally Posted by MEEE AGAIN
The friction between the wheels and the track works as if the velocity was twice what it usually is, so y(2) = 2mx + c, not just mx + c. However, if c is greater than 0, which it is, y(2) is less than y, because 2mx + c is less than 2mx + c + c, obviously.

So, the friction in that case would be less than 2F, so there would still be some resultant force on the plane, so it would still accelerate. It would still take off, albeit over a very long time if c is small.
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Unread 20 Dec 2006, 17:25   #50
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Re: A Plane Problem

I can't really emphasise my argument without repeating myself again and again so :shrug: .

I found this though:

Quote:
Originally Posted by http://www.meignorant.com


The aircraft will not fly. Wheels don't make an aircraft fly, nor does thrust (look at a glider). The force that makes an aircraft fly is the air that passes over the wings creating lift (air moves at more velocity over the top of the wing than the lower surface, creating a low pressure area - therefore, lift).

The treadmill always moves at the same speed as the aircraft - so the aircraft can never gain forward momentum in relation to the static (unmoving) neighboring air, therefore the wings can not create lift. In effect, the treadmill, the wheels and the engines don't even matter in the 'problem' - if the aircraft can not move in relation to the air (and create lift) they might not as well even be moving. Even an aircraft using very heavily 'blown' wings and flaps (using engine bleed air) require at least a small amount of forward motion to create the extra lift which is used for very low speed takeoffs. (Search the NASA site for more details...)

Simply put it's not an aircraft's engines that make it fly, it's the result of the movement of the air over the wings (the engines simply move the aircraft forward, creating that movement.) No movement no lift. No lift, no fly.

Mike Kopack
FAA Airframe and Powerplant Technician
EX USAF F-16A/B/C/D Crew Chief
http://www.lucky-devils.net
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