Conceptual Puzzle: Runway Belt

[John Galt]

Originally Posted by st.cronin

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?

Yes, or they will eventually fall off. But the plane will move forward either way. Little itty bitty wheels will never stop a jet engine from pushing the plane forward.

I'll try one more example (even though I'm running out of ideas). Imagine a plane made out of balsa wood with a jet engine attached. If you put it on the treadmill, the engine would tip through the plane before the treadmill would exert any force to stop the plane from moving. Since planes aren't made of balsa wood, the engine carries the rest of the plane with it whether the wheels want to go forward or not.

[st.cronin]

Originally Posted by John Galt

Yes, or they will eventually fall off. But the plane will move forward either way. Little itty bitty wheels will never stop a jet engine from pushing the plane forward.

I'll try one more example (even though I'm running out of ideas). Imagine a plane made out of balsa wood with a jet engine attached. If you put it on the treadmill, the engine would tip through the plane before the treadmill would exert any force to stop the plane from moving. Since planes aren't made of balsa wood, the engine carries the rest of the plane with it whether the wheels want to go forward or not.

I'm afraid I don't understand that example at all.

[John Galt]

Originally Posted by st.cronin

I'm afraid I don't understand that example at all.

Well, I tried. The example was just meant to show that a jet engine is going forward whether the wheels want to go to or not. The wheels just aren't relevant to the equation. They will break long before they force a jet engine just to stay floating in space.

[Arctus]

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.

I agree with all of this.

However, this plane has wheels which spin freely. Because of this, the jet engine (or whatever else propels the plane forward) will cause the wheels to roll forward. They have to, they have virtually no resistance to the lateral force being created by the jet engine.

The lateral force will continue to make the wheels roll forward until which point in time there is sufficient lift to allow the plane to become airborn.

In this case, this lift is never realized, because the treadmill prevents the necessary airflow under the wings.

[st.cronin]

Originally Posted by John Galt

Well, I tried. The example was just meant to show that a jet engine is going forward whether the wheels want to go to or not. The wheels just aren't relevant to the equation. They will break long before they force a jet engine just to stay floating in space.

But the wheels are not forcing the jet engine to do anything. The jet engine's force gets transferred to the wheels, since there exists that friction between the wheels and the surface, unless there is some limit placed on their ability to spin (as on an actual runway).

[John Galt]

Originally Posted by Arctus

I agree with all of this.

However, this plane has wheels which spin freely. Because of this, the jet engine (or whatever else propels the plane forward) will cause the wheels to roll forward. They have to, they have virtually no resistance to the lateral force being created by the jet engine.

The lateral force will continue to make the wheels roll forward until which point in time there is sufficient lift to allow the plane to become airborn.

In this case, this lift is never realized, because the treadmill prevents the necessary airflow under the wings.

OK. One more idea. Put the plane on the treadmill with no wheels. Turn the jet engine. Make the treadmill go at a speed and acceleration the opposite of the plane. Then, you might be able to keep the plane in place. The belly of the plane will get really freakin' hot and the treadmill would probably burn a hole in it, but let's ignore that. Let's just assume you keep the plane in place that way.

What wheels do is take away the friction on the belly. Instead of having a treadmill which drags the plane in the opposite direction, they remove all the friction on the belly of the plane and spin freely.

[John Galt]

Originally Posted by st.cronin

The jet engine's force gets transferred to the wheels

The force also continues to exist wholly independent of the wheels by the pressure put on air.

OK, one last idea (for real this time). You know where this treadmill would almost work - outer space (although with gravity to prevent the plane from just floating away). The reason that it doesn't work on Earth is because the jet engine is putting out a signficant force on the air.

[Buccaneer]

I am agreeing with JG.

[st.cronin]

Originally Posted by John Galt

The force also continues to exist wholly independent of the wheels by the pressure put on air.

OK, one last idea (for real this time). You know where this treadmill would almost work - outer space (although with gravity to prevent the plane from just floating away). The reason that it doesn't work on Earth is because the jet engine is putting out a signficant force on the air.

I apologize for being a dunce but

The force cannot exist indepently of the wheels, how can it. On an actual runway, the wheels are absorbing some of the force of the jet engine - otherwise, they wouldn't move, because there is nothing to make them move. So the treadmill is set up in such a way that the wheels can absorb ALL of the force of the jet engine.

I may not have that right, but that's what it seems like to me.

And then the other way to look at is, for the plane to move forward, the wheels HAVE TO SKID. And there is no provision in the problem for the wheels to skid. So, maybe they skid, and maybe they don't, but if the plane moves forward, then the whole operation looks a lot different than the way the problem describes it.

[finketr]

paging PilotMan and TerpKristin

[John Galt]

Originally Posted by st.cronin

I apologize for being a dunce but

The force cannot exist indepently of the wheels, how can it. On an actual runway, the wheels are absorbing some of the force of the jet engine - otherwise, they wouldn't move, because there is nothing to make them move. So the treadmill is set up in such a way that the wheels can absorb ALL of the force of the jet engine.

I may not have that right, but that's what it seems like to me.

And then the other way to look at is, for the plane to move forward, the wheels HAVE TO SKID. And there is no provision in the problem for the wheels to skid. So, maybe they skid, and maybe they don't, but if the plane moves forward, then the whole operation looks a lot different than the way the problem describes it.

Instead of "skid," just insert the words "spin freely." The plane is essentially on ice - the wheels are like pinwheels - how fast they spin is barely relevant or irrelevant to the force the engine is putting on the surrounding air.

[st.cronin]

Originally Posted by John Galt

Instead of "skid," just insert the words "spin freely." The plane is essentially on ice - the wheels are like pinwheels - how fast they spin is barely relevant or irrelevant to the force the engine is putting on the surrounding air.

No, in fact it is the OPPOSITE problem of it being on ice. On ice, there would be no way for the wheels to spin, since there would be no traction. Thus the force of the jet would not be absorbed, and the plane would move forward.

On the treadmill, instead of there being no outlet for the wheels to spin, there is no limit to how fast the wheels spin, and thus no limit to how much of the jets energy they can absorb.

[John Galt]

Originally Posted by st.cronin

No, in fact it is the OPPOSITE problem of it being on ice. On ice, there would be no way for the wheels to spin, since there would be no traction. Thus the force of the jet would not be absorbed, and the plane would move forward.

On the treadmill, instead of there being no outlet for the wheels to spin, there is no limit to how fast the wheels spin, and thus no limit to how much of the jets energy they can absorb.

Ice is actually the same problem - imagine a plane on ice with wheels and without wheels. The result is the same - the plane moves forward. That's because the spinning of the wheels just doesn't matter.

[Arctus]

Originally Posted by John Galt

Instead of "skid," just insert the words "spin freely." The plane is essentially on ice - the wheels are like pinwheels - how fast they spin is barely relevant or irrelevant to the force the engine is putting on the surrounding air.

I believe there is disagreement on what "spin freely" means.

I presumed that "spin freely" means that the wheel is unconstrained. The force of the jet translates to the wheels rolling freely. The conveyor belt does not inhibit the wheels, it rolls freely in the opposite direction.

Based on your quoted post, I think that you interpret "spin freely" as that there is a negligible frictional force between the wheel and the conveyor belt, to the point that the wheel can easily slide across they conveyor belt.

I don't know what the correct interpretation is, but I believe it is the cause of our differences.

[st.cronin]

Originally Posted by John Galt

Ice is actually the same problem - imagine a plane on ice with wheels and without wheels. The result is the same - the plane moves forward. That's because the spinning of the wheels just doesn't matter.

I take it you think the spinning of the wheels does not represent a loss in force?

[Mr. Wednesday]

I think it's a question of whether there is any friction in the wheel bearings. In the ideal limit, the frictional force exerted by the ground (opposing the plane's motion) creates a torque on the wheels, but there's no opposing force on the plane itself because the wheels spin freely.

However, I believe any imperfections in the bearings will result in opposing force being transmitted to the plane.

Theoretically, then, this conveyor belt can prevent the jet from taking off.

[Mr. Wednesday]

Dola, but, that's assuming that it goes really fast, much faster than the wheels are spinning, because most of the frictional force will go into accelerating the wheels, not retarding the plane. Now, I realize that our conveyor is sufficiently unusual that this is not a "reasonable" problem, but I think for any "reasonable" wheel bearings, within the limits of the problem the plane will not be prevented from taking off. I am not a mechanical engineer, though, so I don't have an intimate knowledge of the characteristics of wheel bearings.

[Buccaneer]

Originally Posted by st.cronin

I take it you think the spinning of the wheels does not represent a loss in force?

It does not represent a total loss in force, therefore positive acceleration (and ultimately, lift) can be acheived.

[Mr. Wednesday]

Upon further reflection, I think my conceptualization is right (partial transmission of frictional force to the plane), but I may have been sloppy with my terminology and exact formulation of the behavior of the forces/torques/etc. in the system.

[Toddzilla]

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.

Correct!

However, for the purposes of this puzzle, the fact that there is a treadmill underneath the wheels of the plane, that acts as if there is *infinite* friction between the wheels and the ground. Meaning, the wheels can never move forward.

[Toddzilla]

John,

Your concept about a plane sitting on ice being able to take off is a correct one, but it is irrelevant compared to the original problem.

Given the way the problem was originally stated, the only way the plane can propagate down the runway/conveyor belt is for the wheels to skid across the conveyor, since any actual turning of the wheels would produce an equal movement by the conveyor.

In *reality* this would likely happen - if any of this is indeed likely - but for the purposes of the original question, I think we are to assume the wheels do not skid, rather they maintain contact with the conveyor.

Quiksand was right (surprise) in that this puzzle has turned into an arguement over semantics.

[Rich1033]

Nothing to add really. Just that I want to see this on Mythbusters.

[ANut]

Todd: I'm here to tell you that the airplane *would* move forward and take off regardless of the fact that the belt is moving underneath it. The wheels don't have to skid in order for this to happen. It is not likely that in reality the wheels would skid. This is not an argument over semantics, it is a misunderstanding of the physical principles involved.

Understand one thing: it's easy to get caught up in the idea that any vehicle that rolls along the ground behaves like a car. Aircraft do not behave like cars. This is primarily because they propel themselves differently. Cars push on the ground to move forward, but planes push on the air.

In the case of a car on a conveyor belt, the propulsive force is lost when the belt moves exactly at the same speed as the part of the tire that is touching it "wants to spin", because the car gets its force from friction between the tire and the ground. But with an airplane, the force comes from the engine accelerating the air going through it, and the wheels and tires are only there to reduce the effect of friction with the ground.

Why do wheels reduce the effect of friction with the ground? They roll instead of skidding. This should be so easy to recognize that even a caveman could see it, OMG GEICO'D.

So if we set up this problem and we throttled up the engine, as it started to roll forward the belt would move backwards causing the wheels to spin twice as fast as they normally would, but because friction in the wheel bearings is very small, this would not significantly slow down the plane. It would accelerate normally and take off.

There is another potential rabbit hole you could go down, and Mr. Wednesday has already danced around it once: if you assume that the "speed of the wheel" is the tangential speed of the wheel surface, then you'd quickly get to the infinitely fast belt problem, but if you assume that the speed of the wheel is the lateral speed of the wheel hub (axle), you do not have this problem. The reason the question doesn't specify is to preserve some of its trickiness. If it *did* clearly say the belt moves at the speed of the hub of the wheel, or the speed of the structure of the aircraft (same thing), then someone who initially thought the belt could prevent the plane from moving forward would come to the paradox that if the plane didn't move forward, the belt would be stopped also. Since this is obviously troublesome, they'd either insist that the question is a poor one or they'd realize their logical flaw and the reality: the belt has *no way* of stopping the plane because the wheels will just spin freely. Anyway the correct interpretation of the problem is the only logical one: the belt moves backwards as fast as the airplane moves forward, but the plane takes off anyway.

[gstelmack]

Originally Posted by ANut

Anyway the correct interpretation of the problem is the only logical one: the belt moves backwards as fast as the airplane moves forward, but the plane takes off anyway.

I'm always amused by answers like this: the question starts off with an unreality (assuming the conveyor precisely matches the wheels), but we are still supposed to reach a logical conclusion.

However, I'd point out that the question specifies that the speed of the conveyor matches the "rotation" of the tires, hence the belief by many that you either end up with an infinitely fast conveyor, or the wheels have to skid along the conveyor (since if the airplane is moving, the lateral speed must be greater than the rotational speed that is moving the conveyor).

[Toddzilla]

ANut,

So I understand this clearly...

Say on a normal runway, with the airplane engines set to 10%, the airplane would move forward at 5 MPH while rotating at 2000 RPM (all numbers used for illustrative purposes).

On a conveyor belt, you say with the engines set to 10%, the airplane would still move forward at 5MPH, but the wheels would have to spin at 4000 RPM (or faster) to counteract the speed of the conveyor belt.

Right?

Given that explanation, I think gstelmack makes the counterpoint, that we are not talking about a standard conveyor belt, rather one that (1) will always maintain contact with the wheels and not lose traction and (2) will always move exactly the same speed as the wheels so that the wheels cannot move the plane forward.

So long as the wheels maintain contact with the ground, the plane will never move forward. And so long as the plane never moves forward, there will never be lift, and the wheels will never lose contact with the ground.

Hrumph.

[John Galt]

Originally Posted by Toddzilla

so that the wheels cannot move the plane forward.

That is the key problem, IMO. Unlike with a car, wheels do not move a plane forward. They are just there to stop the belly of the plane from hitting the ground.

[Toddzilla]

Originally Posted by John Galt

That is the key problem, IMO. Unlike with a car, wheels do not move a plane forward. They are just there to stop the belly of the plane from hitting the ground.

Correct - however in this case, the wheels are preventing the plane from moving forward since they cannot roll forward and cannot slide. How is the plane going to move one foot forward? Based on the parameters of the problem, it is impossible. The wheels will not skid, they will not break apart, they can't roll faster than the conveyor belt, and they can't levitate off of the conveyor.

So how does the plane move forward? No one has been able to explain that without violating the parameters of the original problem.

[gstelmack]

Originally Posted by John Galt

That is the key problem, IMO. Unlike with a car, wheels do not move a plane forward. They are just there to stop the belly of the plane from hitting the ground.

But if the plane is moving forward, then the wheels are also moving forward. If the wheels are moving forward, then they are either:

1) Not in contact with the conveyor.

2) Skidding along the conveyor.

3) Have special gearing that allows them to spin at a slower rate than they are moving forward laterally.

4) Have zero friction with the conveyor and aren't spinning at all.

5) Some other not-well-explained phenomena that explains how the wheels rotate much slower than their forward speed.

This is all because their lateral movement must be faster than the rotational movement, or else we violate the conditions specified in the test that the belt is keeping up with the wheels, because if the belt were keeping up with the wheels, and the wheels were spinning as the plane moves, then the plane would be in the same location laterally as the conveyor and wheels rotate at same speeds.

Or in other words, stop focusing on the jet and the conveyor and start explaining the behavior of the wheels during the alleged takeoff.

[Toddzilla]

Well, I *finally* got an explanation that made sens to me as to why the plane indeed WOULD take off. I won't try to explain it, I'll quote the email as was quoted to me:

Originally Posted by tempus fugit

The difference between a car and a grounded airplane is that a car uses its wheels to propel itself forward, and an airplane moves itself forward by moving air. They assume that the runway moving backwards would move the plane backwards. This is what would happen with a car (that is in gear), so why not for an airplane? Well, because an airplane’s wheels are free rolling. There is obviously some friction, so there would be some small backwards force, but it would be infinitely small as compared to the forward thrust of the airplane.

You can test this with a piece of paper and a matchbox car (which has free rolling wheels like an airplane… or like a car in neutral.) Place the paper on a table, and place the matchbox car on the paper. Take your hand, and hold the car still with a lightly placed finger on top of the car. At this point you are providing no forward thrust, and the “conveyor belt” is not moving. The car remains stationary. Now, continuing to hold the airplane with a lightly placed finger, and start to pull the paper out from under the car, in the backwards direction. According to Neal’s logic, the car should push back on your finger with the same force that you are exerting on the paper… but this is not what will happen. You will find that your lightly placed finger is not stressed to any noticeable extent. The paper will slide out, and the wheels will spin, but the car will not be propelled backwards. The reason for this is is that the rotation of the wheels is not related to the movement of the matchbox car except by the very small friction component of the axle, which your lightly placed finger can easily control.

So now we have established that movement of the surface beneath a free wheeling object does not exert a noticeable force on the object. Next, we’ll see what happens when the object is trying to move forward. Attach a string to the matchbox car. Place the car at one end of the paper, and use the string to start pulling the car forward with a steady force. As the car moves forward, start pulling the paper out from under the car, backwards. Do you feel increased resistance as you pull the string? Of course not. The wheels are free rolling! Spinning the wheels does not make the object move!

When an airplane takes off, there is one major forward force… the forward thrust. The main rearward force is air resistance. The turning of the wheels provides a small frictional force, but because the wheels are free-rolling, this friction is very small. Unless the wheels are locked, the friction is always going to be less than the thrust, which means that the overall force is still forward, and the plane will still move.

[gstelmack]

So my #3 is basically what is happening, where the "special gearing" is basically what they call "free rolling wheels".

Or in other words, there is a host of information not obvious to most in the word "airplane" in the original question.

[Toddzilla]

Originally Posted by gstelmack

So my #3 is basically what is happening, where the "special gearing" is basically what they call "free rolling wheels".

Or in other words, there is a host of information not obvious to most in the word "airplane" in the original question.

Well, yeah. The wheels don't move the plane forward, they just roll. I suppose thery could be some kind of engine on the plane that powers the wheels for taxi-ing and such, but by and large, the wheels on a plane are free rolling.

[Toddzilla]

Dola - a better example, maybe...

Take a toy car to the supermarket and hold it in place on the moving conveyor in the checkout line. It is very easy to do, since there is negligible friction in the wheels/axle/whatever. In fact, even with the conveyor on, you can move the car forward and backwards with relative ease. It doesn't really matter how fast the conveyor is moving, or it what direction, you can move the car forwards and backwards on the conveyor without much more effort than if the conveyor was still. The jet engines on the plane will move the plane down the runway the same way your finger moves the car.

[cartman]

Another assumption then would be the length of the treadmill. If simply the thrust of the engines is enough to overcome the inertia of the wheels on the opposite moving treadmill, would the treadmill be long enough to allow the plane to reach Vr (sorry, can't do a subscript of the r) and get off the ground? Or will it simply move slowly forward until it falls off the end of the treadmill?

[cartman]

Dola,

everybody send this one in to the Mythbusters immediately so they can settle it once and for all. I'd love to see them strap a jet engine on top of a car on a dynometer.

[QuikSand]

Originally Posted by Toddzilla

Well, I *finally* got an explanation that made sens to me as to why the plane indeed WOULD take off. I won't try to explain it, I'll quote the email as was quoted to me:

Thanks for quoting that - a very good contribution to the discussion.

[BrianD]

I'm still not sure I buy Toddzilla's forwarded post.

If the plane's engines are off but the runway starts running, the plane's wheelse aren't going to start spinning, the whole plane will just move backwards. Even if the runway is started very quickly at the beginning so that the wheels do spin, I would expect them to only spin for a short while before they stop and the plane just moves backwards. Why would this be different with the jets running?

[Toddzilla]

Originally Posted by BrianD

I'm still not sure I buy Toddzilla's forwarded post.

If the plane's engines are off but the runway starts running, the plane's wheelse aren't going to start spinning, the whole plane will just move backwards. Even if the runway is started very quickly at the beginning so that the wheels do spin, I would expect them to only spin for a short while before they stop and the plane just moves backwards. Why would this be different with the jets running?

Because the jet engines are appling thrust directly to the airplane, while the runway is applying thrust to the wheels of the plane which transfers that thrust to the axle and then to the plane, and it is here where 99.999999999% of that thrust is lost due to the relative lack of friction between the wheels and the axle.

Again, think of the matchbox car on the conveyor belt at Safeway - it doesn't really matter how fast the conveyor is moving if you have your finger on the car, you'll be able to hold the car still - none of the thrust from the conveyor is transfered to the car itself because there is very little friction betweens the wheels and the car's axle. Now try and hold the conveyor belt still without the car in between - you can't, because there is a lot of friction between your finger and the conveyor.

[Pumpy Tudors]

Originally Posted by BrianD

I'm still not sure I buy Toddzilla's forwarded post.

If the plane's engines are off but the runway starts running, the plane's wheelse aren't going to start spinning, the whole plane will just move backwards. Even if the runway is started very quickly at the beginning so that the wheels do spin, I would expect them to only spin for a short while before they stop and the plane just moves backwards. Why would this be different with the jets running?

The runway isn't going to move if the wheels aren't spinning.

[ANut]

Originally Posted by gstelmack

So my #3 is basically what is happening, where the "special gearing" is basically what they call "free rolling wheels".

Or in other words, there is a host of information not obvious to most in the word "airplane" in the original question.

No and no. There is no special gearing, and the term "free rolling wheels" just means that the wheels are normal wheels without any artificial or abnormal restrictions on them. The wheels will have some small amount of friction in the bearings, but on the whole they will freely turn when a torque is applied.

Also, the plane is a normal airplane. It could be a 747 or a small Cessna, it doesn't really matter.

However, I'd point out that the question specifies that the speed of the conveyor matches the "rotation" of the tires, hence the belief by many that you either end up with an infinitely fast conveyor, or the wheels have to skid along the conveyor (since if the airplane is moving, the lateral speed must be greater than the rotational speed that is moving the conveyor).

The question says that the conveyor matches the speed of the wheel, opposite the direction of rotation. Note that the wheel moves forward at the same speed as the fuselage and the rest of the aircraft, it just happens to also rotate. You can take "opposite the direction of rotation" to mean "opposite the direction of aircraft motion." I grant you that when any human being reads any text he is bound to make his own interpretation, however my interpretation is extremely simple, and it follows all the laws of classical physics and logic: there's no infinitely fast conveyor, wheels skidding, or anything else.

[JHandley]

Ok, then there must be some skidding.

Just using arbitrary numbers to keep the math simple, let's say that the wheel is exactly 1 foot in diameter. If there are no outside forces applied to the wheel, it will travel 100 feet of trademill in 100 rotations. You're saying that if there is forward thrust applied to the plane, attached to the wheel, it will travel more than 100 feet of treadmill in 100 rotations. The only way that's possible is if the wheel has travelled without rotation (skidded), or has lost contact with the treadmill(taken flight).

Is this what you are refering to when you say a "minimal amount of friction"? Because there must be friction to overcome to make the wheel travel without rotating.

[Mr. Wednesday]

There's a minimal amount of friction where the rotating part of the wheel assembly meets the fixed part of the wheel assembly -- not where the wheel meets the conveyor.

[Bad-example]

An example that might help. Imagine the plane is a VW bug. Place 2 matching conveyor belts under the wheels on each side, so you can stand behind and push from solid ground. If you push the car and the belts start turning, you would still be able to move the vehicle forward. Unless someone put on the brakes, the car would move forward no matter how fast the belts turned.

[CU Tiger]

THe wheels on the plane spinning are a result of propulsion not a source.

The speed of the wheels has no correlation to the speed of the engine.

The whels simply reduce friction by moving easier than the plane underbelly.

The wheels could be locked still, unable to spin and the jet engines would drag them downy the runway and lift.

The plane is moving the EXACT same speed either way. The tires would be tunring at infinitly more RPMs however

[BrianD]

Originally Posted by Pumpy Tudors

The runway isn't going to move if the wheels aren't spinning.

No it isn't, but I think it helps conceptually to think of that situation. If the plane was sitting idle and the runway was moving, what would happen? Most likely, the wheels would never turn and the plane would move backwards (relative to the ground). The runway doesn't roll the wheels, it just pulls them along.

Why, when the plane is in motion, would the runway not pull the wheels along instead of just causing them to spin faster?

[JHandley]

Originally Posted by Mr. Wednesday

There's a minimal amount of friction where the rotating part of the wheel assembly meets the fixed part of the wheel assembly -- not where the wheel meets the conveyor.

Then I'm still lost, because in my head, I can't make a wheel that is 1 foot in diameter travel more than 100 feet in 100 revolutions unless it skids or moves without rotation in someway.

[MJ4H]

Think of it this way. If you were sitting on your living room floor holding only a landing gear in front of you over such a strip of conveyor belt, do you think it would be impossible to take your arm and move the landing gear forward on the conveyor belt?

I'm sure (I hope) you would not think that, as this should demonstrate that the conveyor belt will not be exerting a force against your arm.

If you followed this far, you should now understand what is meant by the wheels are "free-rolling" and see why the plane will move forward when it has a means of propulsion unconnected to the belt or the wheels (the jet engine, or your arm in the example above).

[JHandley]

I apologize, I was using the wrong term. The only excuse was it was late last night when I posted and I posted this morning before heading to work. I'll try this again:

Just using arbitrary numbers to keep the math simple, let's say that the wheel is exactly 1 foot in circumference. If there are no outside forces applied to the wheel, it will travel 100 feet of trademill in 100 rotations. You're saying that if there is forward thrust applied to the plane, attached to the wheel, it will travel more than 100 feet of treadmill in 100 rotations. The only way that's possible is if the wheel has travelled without rotation (skidded), or has lost contact with the treadmill(taken flight).

I understand the idea of a free rolling wheel, and I can understand that the plane can move forward on a treadmill moving backwards, but only if the wheel skids. If the wheel maintains contact with the treadmill the entire time, and does not ever skid, there is simply no way that a circumference of 1 foot can travel more than 100 feet in 100 revolutions regardless of how fast or slow the revolutions are.

[Arctus]

I was trying to not get completely sucked into this, but I have an hour to kill, so here goes nothing.

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?

I've read some compelling arguements as to why the plane will still be able to take off, and came very close to changing my beliefs. However I still believe that the plane will not be able take off. I'll walk you all through my rationale.

The plane as a dynamic system

The plane needs to be treated as a dynamic system, not a static one. The forces acting on the plane are not balanced, and this results in the movement of the plane itself. This is very straightforward. The means of propulsion (it does not matter if its propeller or jet or something else) creates a force which will push the plane forward unless there is an opposing force exterted on the plane. In the example given, there clearly is no other force exerting itself on the plane. Since the wheels offer no lateral resistance, they roll forward across the surface of the massive conveyor belt.

Relative to the surface of the conveyor belt, the plane behaves as one is accustomed to seeing at an airport. Regardless of the behavior of the conveyor belt itself, an individual (lets call him Adam) standing in front of the plane on they conveyor belt would watch the plane approach and eventually pass them, and the plane's wheels would roll across the surface of the conveyor belt.

The conveyor belt

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

I interpret this as the velocity of the conveyor belt surface relative to the earth is opposite as the velocity of the plane relative to the conveyor belt. The conveyor belt would have zero velocity relative to Adam, who is standing on the belt itself.

Bob, who is standing alongside the conveyor belt, would observe Adam travelling at the identical speed that Adam observes the plane travelling.

The conveyor belt does not exert a force on the plane, nor does it cause the wheels to rotate. The discussions regarding the wheels rotating infinitely fast are not correct. The only way for this to happen is if the plane was "pinned" in a fixed position relative to the conveyor belt. This is not the case. Adam, whose point of reference is relative to the conveyor belt, witnesses a plane taxi-ing normally. Bob witnesses a stationary plane, just as I witness a stationary person on a treadmill at my gym. It is only by definition of the puzzle itself that the plane is "pinned" in place from Bob's perspective.

Flight?

I don't think so. The plane needs velocity from Bob's perspective to get enough lift under its wings. The conveyor belt prevents this.

I don't suspect that this concept is much different than that of an aircraft carrier.

Aircraft take off to the front, into the wind, and land from the rear. Carriers steam at speed, for example up to 35 knots (65 km/h), into the wind during take-off in order to increase the apparent wind speed, thereby reducing the speed of the aircraft relative to the ship.

http://en.wikipedia.org/wiki/Aircraft_carrier

I'm not a huge fan of citing wiki, but in this case I think its valid.

[st.cronin]

Originally Posted by JHandley

I apologize, I was using the wrong term. The only excuse was it was late last night when I posted and I posted this morning before heading to work. I'll try this again:

Just using arbitrary numbers to keep the math simple, let's say that the wheel is exactly 1 foot in circumference. If there are no outside forces applied to the wheel, it will travel 100 feet of trademill in 100 rotations. You're saying that if there is forward thrust applied to the plane, attached to the wheel, it will travel more than 100 feet of treadmill in 100 rotations. The only way that's possible is if the wheel has travelled without rotation (skidded), or has lost contact with the treadmill(taken flight).

I understand the idea of a free rolling wheel, and I can understand that the plane can move forward on a treadmill moving backwards, but only if the wheel skids. If the wheel maintains contact with the treadmill the entire time, and does not ever skid, there is simply no way that a circumference of 1 foot can travel more than 100 feet in 100 revolutions regardless of how fast or slow the revolutions are.

Yes, exactly. If you are going to say that the plane will achieve flight, I think you have to say how this is possible. I have not seen anybody do this without violating the parameters of the problem.

[Toddzilla]

Originally Posted by st.cronin

Yes, exactly. If you are going to say that the plane will achieve flight, I think you have to say how this is possible. I have not seen anybody do this without violating the parameters of the problem.

The correlation of holding a toy car on the conveyor belt at the store is the perfect analogy.

* The tires of the car always maintain contact with the conveyor
* The tires never skid or slip
* The tires are always moving

You can move car the backwards and forwards on the belt with very little force applied to the car, and the above three conditions will always hold.

The concept that was hard for *me* to get my head around, and I suspect it may be vexing you as well, is the fact that the rotation of the wheels and the movement of the car body is for all practical purposes independent of one another.

How fast the conveyor moves is irrelevant, and what direction the conveyor moves is irrelevant. You will always be able to hold the car still, and you will always be able to move the car forward and backwards with relative ease. And that is because the wheels on the car do nothing to the car other than provide a frictionless connection between the car and the conveyor (it is frictionless at the axle). The wheels don't propel the car forward, and they don't slow the car down. They so nothing. And therefore the conveyor does nothing. And so you can move the car with your finger independent of whatever the conveyor does. The car is the plane and your finger is the jet engine.