Conceptual Puzzle: Runway Belt

[MJ4H]

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. There is no wind. Can the plane take off?

[Toddzilla]

um, no...and the answer is so blindingly obvious, I weep for your offspring.

EDIT: I asked my father-in-law this question, he's the top Aeroacoustical Engineer at NASA (seriously), to get a response. His contemplative silence and "Let me think about this" led me to reconsider how trivial the question is - or isn't in this case. My apologies.

[MJ4H]

You should probably know 2 things:

1) I did not create this puzzle/question
2) I know an actual rocket scientist (personally) that got this wrong at first.

[Raiders Army]

If I'm imagining this, then of course the plane can take off; all I have to do is imagine it.

[Airhog]

Plane will take off. Use newtons third law, the thrust of the jets. The wheels do not provide power to the ground. The jets provide thrust.

[KWhit]

Uh, no.

Lift is created by the air moving across the wings. No wind = no air moving across the wings. No lift.

[Brillig]

Use a Harrier.

[MJ4H]

Harriers are excluded from this problem

[st.cronin]

It seems the question hinges on whether the plane's wheels can gain any traction on the conveyor. My guess is they can't, and therefore the plane will never gain any forward momentum. BUT I'm not a physicist, or even really all that bright.

[albionmoonlight]

The plane will still go forward.

The thrust is provided by the jets, not through the wheels.

Leaving aside the minimal friction involved (and, there is very little friction involved because it is, you know, a wheel): If the plane is pushed forward at 100 MPH, and the runway is going backwards at 100 MPH, then the wheels will spin at 200 MPH.

Think of it this way. If the plane is just floating in space, and the jets start, won't they push the plane forward? The presence or absence of the ground (or how fast the ground is moving) just isn't relevant to the problem.

[Airhog]

Originally Posted by albionmoonlight

The plane will still go forward.

The thrust is provided by the jets, not through the wheels.

Leaving aside the minimal friction involved (and, there is very little friction involved because it is, you know, a wheel): If the plane is pushed forward at 100 MPH, and the runway is going backwards at 100 MPH, then the wheels will spin at 200 MPH.

Think of it this way. If the plane is just floating in space, and the jets start, won't they push the plane forward? The presence or absence of the ground (or how fast the ground is moving) just isn't relevant to the problem.

Exactly. another analagy is pretend you are rollerskating on a treadmill. And someone gives you a rope. If you are pulled foward, the speed of your wheels would increase, but you would still move foward

[cartman]

But isn't the thrust of the jets that causes the wheels to move in the first place? If that is canceled out by the treadmill, then there is no lift on the wings. If there were no wheels, and the treadmill was set to counteract the thrust of the engines, the plane isn't going anywhere.

[WVUFAN]

Originally Posted by cartman

But isn't the thrust of the jets that causes the wheels to move in the first place? If that is canceled out by the treadmill, then there is no lift on the wings. If there were no wheels, and the treadmill was set to counteract the thrust of the engines, the plane isn't going anywhere.

I think you've got it right.

Using Albionmoonlight's analogy of the rollerskater on a treadmill, only without a rope. The speed of the conveyor belt would increase to counter the thrust of the engine, so it still would remain stationary, so no lift.

[spleen1015]

I think the plane would take off twice as fast.

The jets and the conveyor will make the wheels spin the same direction.

[Airhog]

Originally Posted by WVUFAN

I think you've got it right.

Using Albionmoonlight's analogy of the rollerskater on a treadmill, only without a rope. The speed of the conveyor belt would increase to counter the thrust of the engine, so it still would remain stationary, so no lift.

nope, because the wheels are not driven by the conveyor, the air is. The rope on the treadmill is the thrust of the engine.

[cartman]

To me, a similar example is a car on a dynometer or a bicycle on a trainer. In both of those examples, the car is driving the wheels or the bicyclist is pedaling, but they don't move from their position. How is that different than a plane on a treadmill?

[Airhog]

because the only method of propulsion is the direct application of the force to the ground through the engine and transmission.

The engines have no connection to the wheels.

Imagine being in the air with the landing gear down. If you were able to turn the wheels as fast as the plane was moving in the opposite direction, would the plane stop moving?

[cuervo72]

Heh...this went on for 447 pages here:

http://forum.physorg.com/index.php?showtopic=2417&st=0

[Glengoyne]

Originally Posted by cuervo72

Heh...this went on for 447 pages here:

http://forum.physorg.com/index.php?showtopic=2417&st=0

I've been sucked into this before. I chuckled when I saw the thread title. I'm not sure that anyone can really produce an answer that won't be disputed.

My take.

The jet and the long ass treadmill are at rest.

The Jet fires up its engines, and would move forward. BUT the runway kicks in and magically counteracts the forward movement that should be created by the engines.

That is easy to grasp when the engine is barely idling. I think it should even be reproducable. The runway can negate the forward progress of the jeg because it can exert a force on the plane in the direction opposite of its propulsion.

The problem comes when you throttle up.

On one hand you say that the runway will only be able to exert a limited amount of negating force on the plane, as the only way it can impact the plane is through the wheels contacting the ground. The force the runway can exert in linear fashion parallel to the engine's thrust is limited by the plane's weight and the coefficient(sp?) of friction. So at some point the engines will be able to overpower the ability of the treadmill to exert a force on the plane.

On the other hand the problem seems to brush this aside by simply saying that the runway can match the speed of the wheels...without exception. Embracing this, you can easilly see the plane at a permanent stand still. Exactly the same as if it were bolted to the ground or some massive structure.

So, as far as I can tell, there is no satisfactory answer to the question at hand.

EDIT: fwiw I'm in the camp that the treadmill can't exert a force on the plane in order to counteract the thrust of the engines.

[MJ4H]

Originally Posted by Glengoyne

BUT the runway kicks in and magically counteracts the forward movement that should be created by the engines.

bzzt

[st.cronin]

Originally Posted by MattJones4Heisman

bzzt

Why? It sounds right to me.

[cartman]

I see the flaw in my thinking/the wording of the problem. The treadmill part is what throws you off. If the wheels are going forward at 5 MPH, then the treadmill is moving backwards at 5 MPH, which means that the wheels are now going forward at 10MPH, etc. You get into an infinite loop problem real quickly here.

[MJ4H]

The motion of the belt does not affect the motion of the plane. The wheels spin freely.

[KWhit]

Doh! I was wrong before. The only real question that matters in this is "Will the plane move forward?" I overlooked the jets or propeller - those are what gives the plane thrust. That thrust wouldn't be counteracted by the wheels, so the plane would move forward normally and would take off.

[gstelmack]

Originally Posted by MattJones4Heisman

moving in the opposite direction of rotation.

I believe this is the imprecise part of the question. Are we saying the conveyor belt rotates in opposition to the rotation of the tires, meaning that the conveyor belt moves front to back, or that the conveyor belt moves in the opposite direction of the wheel at contact, meaning it moves back to front? Mixing movement and rotation in this phrase makes the question imprecise.

However, sounds like a great idea for Mythbusters to test...

[gstelmack]

Originally Posted by MattJones4Heisman

The motion of the belt does not affect the motion of the plane. The wheels spin freely.

Depends on the answer to my question. If it acts like a typical treadmill, this is patently false. You don't move anywhere or get a breeze no matter how fast you run on a treadmill. Same with placing a bicycle or any other item on the treadmill, you'll just spin the treadmill faster.

Unless it moves opposite to a treadmill, in which case the conveyor moves faster as the plane revs up, and makes it take off quicker.

[KWhit]

Originally Posted by gstelmack

You don't move anywhere or get a breeze no matter how fast you run on a treadmill. Same with placing a bicycle or any other item on the treadmill, you'll just spin the treadmill faster.

But you would if you had a jet strapped to your back.

[QuikSand]

Originally Posted by MattJones4Heisman

The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

It seems to me that this phrase is at the center of the apparent paradox. I'm not really sure how to properly interpret this, but I suspect that if you grant this condition as it is intended, you get the intended whimsical answer to the puzzle.

But there's enough am,biguity in this phrase, to me, to leave this as much a puzzle of semantics as it is physics.

[John Galt]

Originally Posted by MattJones4Heisman

The motion of the belt does not affect the motion of the plane. The wheels spin freely.

It's funny. I thought this one was easy. It seems like this Monty Hall-ish potential.

For those having trouble understanding why this above conclusion is right, imagine a plane flying in the air with its landing gear down. Even if the wheels are spinning super-mega-ultra fast in the opposite direction, the plane will continue forward. Now put a surface at the base of those wheels. No matter how fast the surface/treadmill moves in the other direction, the plane will continue to move forward as the wheels spin freely.

This is totally different than a person on a treadmill because we move forward by virtue of our friction with the ground. We (at least most of us) do not have an engine sticking out of our rear ends.

[Toddzilla]

Look at it this way:

Assume for a second there is no conveyor and no wheels - the plane is just sitting on the ground with the landing gear up on it's "belly". If you fire the engines up, there is going to be some thrust that wants to propel the plane forward. If there is sufficient lack of friction between the plane and the ground, the plane will move forward. If the engines are strong enough, the plane will move fast enough to create lift on the wings and the plane will take off.

If the plane - again on its belly with landing gear up - is resting on a conveyor belt that is perfectly neutral, the engines will propel the plane forward and it will take off. If the conveyor is moving *backwards*, then the engines will have to work harder in order to get the plane to move forward fast enough to take off. If the conveyor is so programmed to always *exactly* counteract the thrust from the engines, then the plane won't move and it will sit still.

The last example is our original example - except in the original the plane is on wheels - the conveyor is still counteracting the thrust of the jets by moving backwards. However, there is a giant ambiguity as to whether the conveyor - acting to exactly counter the movement of the wheels - is sufficient to exactly counteract the thrust of the jets.

That is the crux of the problem, and in my original (snarky) response, I assumed that *all* of the thrust provided by the engines would translate to the movement of the wheels, which in turn would be counteracted by the conveyor, and so the plane would never move forward.

I envision a place where they test jet engines - like that recent commercial for the Air Force - and hypothetically they put a wing on the engine and all of a sudden at a certain force, the wing and the engine suddenly take off into the air. Lawl.

[albionmoonlight]

It sounds like (though you can never be too careful) that no one is arguing that a motionless plane will suddenly take off based on nothing but a huge amount of counteracted forward thrust by the engines.

So, this question really boils down to: given the conditions above, will the plane move forward or stay still?

For the reasons given above, I think that it will move forward.

[MJ4H]

Originally Posted by Toddzilla

counteract the thrust from the engines

Here is the misconception

[gstelmack]

Originally Posted by MattJones4Heisman

Here is the misconception

That's easy to say. Where is the proof?

In some of the examples above, what happens if there are chocks in front of the wheels? This whole debate centers on whether or not the conveyor belt acts like chocks in front of the wheels or like slick ice. And the question as worded does not give sufficient information. As Quik said, it's worded to give a specific answer someone wants, but not sufficient for everyone who reads it to understand that point.

[st.cronin]

Originally Posted by albionmoonlight

It sounds like (though you can never be too careful) that no one is arguing that a motionless plane will suddenly take off based on nothing but a huge amount of counteracted forward thrust by the engines.

So, this question really boils down to: given the conditions above, will the plane move forward or stay still?

For the reasons given above, I think that it will move forward.

I'm not sure I understand everything that's been said, but let me ask this: Is it possible for the treadmill to work in such a way that the plane does NOT move forward, regardless of what its engines do? Note, I am not asking is it possible to interpret the question that way - I am asking if it is possible to design a treadmill that way.

[albionmoonlight]

Originally Posted by st.cronin

I'm not sure I understand everything that's been said, but let me ask this: Is it possible for the treadmill to work in such a way that the plane does NOT move forward, regardless of what its engines do? Note, I am not asking is it possible to interpret the question that way - I am asking if it is possible to design a treadmill that way.

I don't think so. Now, I am pretty out of my league talking about mechanical physics, but it seems to me that the wheels of the plane are designed to provide as little friction as possible between the axle and the wheels themselves.

I don't think that you can impart any amount of force to the wheels (which is what the runway would be doing) that could flow through the low-friction wheel mechanism and counteract the forward thrust of the engines.

[st.cronin]

Originally Posted by albionmoonlight

I don't think so. Now, I am pretty out of my league talking about mechanical physics, but it seems to me that the wheels of the plane are designed to provide as little friction as possible between the axle and the wheels themselves.

I don't think that you can impart any amount of force to the wheels (which is what the runway would be doing) that could flow through the low-friction wheel mechanism and counteract the forward thrust of the engines.

I guess then my next question is what does the friction between the wheels and the axle have to do with anything. I mean, I understand that in designing a wheel, you might want some principle expressed in the axle, but it seems irrelevant to the puzzle. In terms of the puzzle, the wheels turn, and the airplane moves forward. If the wheels don't turn, the airplane will either skid, or not move forward. The setup implies that the wheels will be turning, but that this action won't result in any forward motion. Unless, of course, as some have suggested, the puzzle is worded in such a way as to be tricky, and the treadmill's motion is compounded with the wheel's motion.

[BrianD]

How can the plane move forward in this example? Since a plane doesn't slide but only rolls along the ground, having the runway roll at the same speed in the opposite direction should completely counter the thrust from the engines.

It would seem like the same thing as holding a toy car on a running treadmill. The wheels spin to match the ground, but it still doesn't go anywhere.

[MJ4H]

Originally Posted by gstelmack

That's easy to say. Where is the proof?

The proof is that the conveyor belt does not affect the thrust of the airplane in any way. They literally have nothing to do with each other.

[st.cronin]

Originally Posted by MattJones4Heisman

The proof is that the conveyor belt does not affect the thrust of the airplane in any way. They literally have nothing to do with each other.

Yes, but the way the problem is set up, wouldn't the thrust of the engines result only in really, really fast spinning wheels?

[Mr. Wednesday]

Originally Posted by MattJones4Heisman

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation. There is no wind. Can the plane take off?

By the "speed of the wheels", do you mean the tangential velocity at the point in contact with the belt?

[JPhillips]

How many five year olds does it take to turn the conveyor belt?

[cuervo72]

Originally Posted by Mr. Wednesday

By the "speed of the wheels", do you mean the tangential velocity at the point in contact with the belt?

And by "conveyor belt", what do you mean? An African or European conveyor belt?

[Toddzilla]

So you put an automobile on one of those contraptions to measure speed (or whatever) and the car remains in one place while the engine revs and the tires spin madly. That's pretty obvious.

Put the same automobile on the same contraption, but instead of using the automobile engine, you strap a jet engine to it. Does it move or not?

[st.cronin]

Originally Posted by Toddzilla

So you put an automobile on one of those contraptions to measure speed (or whatever) and the car remains in one place while the engine revs and the tires spin madly. That's pretty obvious.

Put the same automobile on the same contraption, but instead of using the automobile engine, you strap a jet engine to it. Does it move or not?

Well, I give up.

[John Galt]

Originally Posted by Toddzilla

So you put an automobile on one of those contraptions to measure speed (or whatever) and the car remains in one place while the engine revs and the tires spin madly. That's pretty obvious.

Put the same automobile on the same contraption, but instead of using the automobile engine, you strap a jet engine to it. Does it move or not?

Any object/person on a treadmill that moves forward by virtue of friction on the ground will not move on such a treadmill. Any object that has a jet engine on it does not move based on the friction with the ground and so it will move forward.

Think of them not as wheels, but as pinwheels spinning endlessly in the wind.

[Toddzilla]

I think the key is this - clearly the jet engine is NOT going to make the wheels turn, so the force of the jet engine is going to (In my mind) force the car off of the contraption.

I admit this isn't a real good example, since the contraption used for cars isn't a flat treadmill as in our airplane example, rather it is designed specifically to not let the car move forward or backwards.

So if you use the car-jet engine example, and put the car on a treadmill, and we agree that the jet engine isn't powering the wheels, what happens?

Well, the jet engine will propel the car forward, and that will cause the wheels to roll. As the wheels roll, as per the original question regarding the airplane, the treadmill counteracts the wheel's motion and so the car should remain in place.

[John Galt]

BTW, there is a reason they test planes in wind tunnels and not on treadmills.

[st.cronin]

Originally Posted by Toddzilla

I think the key is this - clearly the jet engine is NOT going to make the wheels turn, so the force of the jet engine is going to (In my mind) force the car off of the contraption.

I admit this isn't a real good example, since the contraption used for cars isn't a flat treadmill as in our airplane example, rather it is designed specifically to not let the car move forward or backwards.

So if you use the car-jet engine example, and put the car on a treadmill, and we agree that the jet engine isn't powering the wheels, what happens?

Well, the jet engine will propel the car forward, and that will cause the wheels to roll. As the wheels roll, as per the original question regarding the airplane, the treadmill counteracts the wheel's motion and so the car should remain in place.

This is pretty much my thinking - that the result of the jet will just be really fast wheels spinning in place. In order for the plane to move forward at all, the wheels HAVE to skid, don't they?

[John Galt]

Originally Posted by Toddzilla

I think the key is this - CLEARLY the jet engine is NOT going to make the wheels turn, so the force of the jet engine is going to (In my mind) force the car off of the contraption.

I admit this isn't a real good example, since the contraption used for cars isn't a flat treadmill as in our airplane example, rather it is designed specifically to not let the car move forward or backwards.

So if you use the car-jet engine example, and put the car on a treadmill, and we agree that the jet engine isn't powering the wheels, what happens?

Well, the jet engine will propel the car forward, and that will cause the wheels to roll. As the wheels roll, as per the original question regarding the airplane, the treadmill counteracts the wheel's motion and so the car should remain in place.

No it won't. A jet engine propels something forward by expulsion of flaming fuel. It displaces air and moves forward whether it has wheels attached or not.

If a plane is on ice with no wheels (ie no friction), it will still move forward very fast with its jet engine.

[st.cronin]

Originally Posted by John Galt

No it won't. A jet engine propels something forward by expulsion of flaming fuel. It displaces air and moves forward whether it has wheels attached or not.

If a plane is on ice with no wheels (ie no friction), it will still move forward very fast with its jet engine.

But the plane in the problem is NOT on ice. I agree that on ice, it could achieve lift, but that would be a different problem.