Plane on a Treadmill

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jbhtexas

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Oct 20, 2006
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If the plane's speed increases, then the belt will also increase, which will keep the plane in a stationary position to a reference point.

Only if the increasing speed of the wheels turning on the treadmill will develop enough friction forces to oppose the thrust of the engines...which won't happen in any practical application.

Look at this equation carefully:

F = (m) (a).

If there is a net force acting on the mass of the airplane, it accelerates and moves.
 

CloneFan65

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Ft = Force from thrust
FD = Force of drag
Ff = Force of friction

For a plane to takeoff from a runway or treadmill
Ft > FD + FfFf = μFn. μ is the coefficient of friction and Fn is the normal force of the runway/treadmill on the planes landing gear.

Please explain how increasing the speed of the treadmill will increase the force of friction, thus preventing the plane from moving forward in relation to the ground.

Whoa. Dude broke out the subscripts and greek letters. Hardcore. :notworthy:
 

CyPlainsDrifter

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THERE IS FRICTION!!!! HOW ARE WE SAYING THAT THERE ISN'T FRICTION!?!?!?!?!? WHERE DID IT GO????


OK, we'll leave it in. What percentage of the plane's thrust is used to overcome the friction in the wheels/bearings, in your estimation? 1%, 2%, 0.1%......?? (It's a really small number by any means..... and that's why people are leaving it out.)

Now double that and you have the amount of thrust needed (approximately) to overcome the increased friction because the wheels would be spinning at double the speed. All the remaining thrust is driving the plane forward, up to it's lift off speed.
 

mjlane

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THERE IS FRICTION!!!! HOW ARE WE SAYING THAT THERE ISN'T FRICTION!?!?!?!?!? WHERE DID IT GO????

Also, we're ignoring friction because in this scenario, it is fairly meaningless. The fact that you don't understand that speaks volumes.
 

cmoneyr

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Cool, lets all just go copy and paste formulas from wikipedia that we don't understand.

Please explain to me how the plane can move faster than the belt if they are moving at the same speed.
You honestly can't be a teacher, serously? SERIOUSLY?? This is either the best trolling of all time or you are the worst teacher of all time.
 

twittkop

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Only if the increasing speed of the wheels turning on the treadmill will develop enough friction forces to oppose the thrust of the engines...which won't happen in any practical application.

Look at this equation carefully:

F = (m) (a).

If there is a net force acting on the mass of the airplane, it accelerates and moves.

I'm in agreement with you that the plane will takeoff. Does the coefficient of friction increase with speed? If not, even if you increase the speed of the treadmill to infinity, the plane is still going to takeoff.
 

CyPlainsDrifter

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Cool, lets all just go copy and paste formulas from wikipedia that we don't understand.

Please explain to me how the plane can move faster than the belt if they are moving at the same speed.

It's because the belt is NOT ACTING ON THE PLANE proper..... and thus not affecting its speed. It is merely ACTING ON THE WHEELS and doubling their speed. The wheels are FREE-WHEELING and don't affect the speed of the plane.

Oh, and the plane is NOT moving faster than the belt.... it doesn't need to. It only needs to move fast enough to create lift. Assume that take-off speed is 100mph and the treadmill is moving 100mph and the wheels are moving 200mph.

I still don't think you are listening or thinking this through. If you really are a science teacher, you can easily grasp this if you just try, instead of trying to fight it. At least I hope that is the case.
 

cmoneyr

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Sorry Daddymac, back to the action.

I'm going to repost this again because I think it's a good example that is easy to follow:

Take a shopping cart, a treadmill and a length of rope. Tie the rope to one end of the shopping cart, like you were pulling it behind you. Put the cart on the treadmill and turn it on with the rope slacked. The cart would be stationary, the wheels of a shopping cart do not produce and power and are there only to spin as the pusher provides thrust. Assume for this example that the wheels of a shopping cart are designed as well as wheels on a plane to provide as little friction as possible.

So we have a cart on a moving treadmill, just sitting there. Now take the rope and begin to pull on the cart, does the cart remain stationary? No, the wheels spin at an increased rate based on the speed you pull and the speed of the treadmill. Since the wheels do not factor into how fast a shopping cart moves, the cart moves forward with an increased wheel speed.

Now, double/triple/quadruple the speed of the shopping cart as you are still pulling on the rope. Does the increased speed stop you from being able to pull the shopping cart forward? No, once again, the wheels spin faster and faster, (I'm assuming for this that the wheels won't fall apart), but no matter how fast they spin the cart will only move forward equal to the amount of force you are pulling the rope.

Now, if we replace the shopping cart with a plane, the plane only needs to be able to move forward to make air pass over the wings and therefore create lift. Since the plane/shopping cart will move forward how ever fast you pull it/however fast the jets propel it, the plane will take off as normal.

Pulling on the rope is analogous to the thrust of a jet engine in this situation.

htown can you tell me how you think this is wrong?
 

cmoneyr

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Please explain to me how the plane can move faster than the belt if they are moving at the same speed.
The plane is not moving faster than the belt, that's the biggest component of this problem. They are always moving at the same speed. BUT, as we have tried to tell you, that doesn't mean that the plane isn't moving, it simply means the wheels are spinning twice as fast as the plane is moving.
 

CycloneWanderer

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Let me join in and try and get some things straight. Is the treadmill moving forward or backwards? if it is moving backwards, and if it always moves at the same rate that the wheels are then the plane will not actually move and create no lift from the wings and not take off. if it is backwards but can't completely compensate the plane's thrust then the plane will move forward and eventually be able to take off if it has enough air over the wings creating enough lift. if it is going forward I don't really know what would happen but if the plane is able to fly then it should take off. As long as the plane is providing enough thrust to be able to fly without the treadmill because if not it seems it might slow down as soon as it lifted off the treadmill, since it no longer has that thrust being provided, but it would seem easily possible for it to lift off if it were able to give itself enough thrust once lifting off the treadmill.

My first post on this and I really don't know anything about physics but this would seem to make sense - but could be completely wrong since a lot of things may make sense but don't work like it "logically" should.
 

jdoggivjc

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Think of it this way:

If the plane was sitting on the treadmill with the engines completely off and the treadmill running at 30 mph, what is the plane doing? Assuming no friction, the plane is stationary since the wheels are free to turn. The wheels of the plane are travelling at 30 mph, but the plane is going 0 mph in relation to a fixed reference point.

Now, let's just say that you gave the plane a push with a very large hand (jet engine). What would happen to the plane? Would it continue to sit still or would it move forward? Of course, it would move forward at a speed equal to the amount of force. Increase the force/thrust, and you will increase the speed.

The speed of the plane and the speed of the plane's wheels are most definitely NOT equal. This seems to be the point at which you are stymied.

Your theory isn't quite correct, simply because if there was no friction the tread on the treadmill would slide underneath the wheels without moving them. The wheels move BECAUSE of friction, not in spite of it :wink: However, your theory is a good explanation in the spirit of the argument.

Also, those that argue that you would need an infinitely long treadmill for this to work just aren't getting the spirit of the argument. The maximum length the treadmill would need to be in order for the plane to take off would be the length of a standard runway, and I'm guessing probably 1/2 to 2/3 of that length simply because I don't think most planes actually need the entire runway to take off.
 

cmoneyr

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if it is moving backwards, and if it always moves at the same rate that the wheels are then the plane will not actually move and create no lift from the wings and not take off.
Where do I begin. First, that's wrong. I'm guessing you haven't read the thread, but we've already said that the treadmill, for all intents and purposes, cannot possibly be going to speed of the wheels. If the plane was moving forward at 50mph, the wheels also rotate at 50mph. Now put a treadmill underneath the plane moving backwards at 50mph, the wheels would then have to compensate by rotating at 100mph, so then the treadmill moves at 100mph, so then the wheels rotate at 150mph, and so on and so forth.

The second part of what you said is basically right. As long as the plane is producing enough thrust to take off of a normal runway, then it will take off of a treadmill moving at the same speed.
 

cmoneyr

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Also, those that argue that you would need an infinitely long treadmill for this to work just aren't getting the spirit of the argument. The maximum length the treadmill would need to be in order for the plane to take off would be the length of a standard runway, and I'm guessing probably 1/2 to 2/3 of that length simply because I don't think most planes actually need the entire runway to take off.
Exactly, since the treadmill in this problem is basically filler, the plane would realistically need the same amount of runway, give or take a little.
 

htownclone

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So numerous people have stated that the treadmill and plane are moving at the same speed, and the wheels are moving faster....sooooooo....the plane is not moving down the treadmill it is essentially staying in place. Am I right?
 

jdoggivjc

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So numerous people have stated that the treadmill and plane are moving at the same speed, and the wheels are moving faster....sooooooo....the plane is not moving down the treadmill it is essentially staying in place. Am I right?

Only if there is no thrust being applied to the plane. Once thrust is applied to the plane then it the plane will be moving just as fast as if there were no treadmill.
 

htownclone

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Only if there is no thrust being applied to the plane. Once thrust is applied to the plane then it the plane will be moving just as fast as if there were no treadmill.

but the whole myth is that the plane, not the wheels is moving as fast as the treadmill.
 

CycloneWanderer

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can a plane producing enough thrust to go fifty miles per hour literally stay in the same place if placed on a treadmill which is rotating at the rate of 50 miles per hour in the opposite direction if no other forces are applied?
 

CloneFan65

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can a plane producing enough thrust to go fifty miles per hour literally stay in the same place if placed on a treadmill which is rotating at the rate of 50 miles per hour in the opposite direction if no other forces are applied?

No. For a car, yes, because the wheels are what's driving the car. But a plane is propelled by the jets friction with the air. At my first reading I thought the plane would stand still until someone reminded of how a plane is propelled.
 
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