Ok. There are threads on this all over the internet. There are several here at SciForums:
http://www.sciforums.com/search.php?searchid=1914126

Lucky for you guys, the kind folks at MythBusters (http://dsc.discovery.com/fansites/mythbusters/mythbusters.html) are poised to take this one on. Here's a preview:

http://www.youtube.com/watch?v=KSBFQOfas60&feature=related

Now, I've been researching this a bit online, and the answer to me seems obvious. I have been wrong before, though. Either way, make your case. After the MythBusters airs on January 30th, someone can report the results, possibly post a YouTube video of the clip, and tell us how right they were.

After that, this thread will be locked, and all future threads about airplanes and conveyor belts will be deleted. So if you're tired of seeing this, you only have to see it for two more weeks.

Enjoy.

The answer is, depending on how they word the precise question, one of the following is true:

(1) The plane moves forward relative to the ground (on which the coveyor belt mechanism sits) and the air, and takes off.

(2) the plane remains stationary relative to the ground/air (and conveyor belt mechanism as a whole) and does not take off; or

(3) most commonly, the question is so hypothetical and ambiguously worded that you cannot tell whether the plane moves forward relative to the ground/air/coveyor belt mechanism as a whole, and different people makes arguments about their preferred interpretation of the question (interpreting it as either (1) or (2) above) and fail to notice that those who disagree with them have simply interpreted it in another way.

Honestly, I usually saw (3), where the "rotation of the plane's wheels exactly cancels out the motion of the conveyor belt" (which suggests that plane was stationary relative to the ground), but where other people noted that the plane's engines would have pushed it forward. (It's true that the engines would push the plane forward in the real world...but it is also true that *if* that happens then "rotation of the plane's wheels exactly cancels out the motion of the conveyor belt" is probably untrue under the most common reading of that phrase, assuming the wheels are on the belt and freely rotating.)

Why? What is the reason for this nonsense for in reality it will never happen.

geeeeeeeeeeeese not agaaaaaain

geeeeeeeeeeeese not agaaaaaain

Reality is a bitch ain't it! :p

I would say it depends on how exactly one sets up the conditions, as has been noted. Obviously lift depends only on the plane's motion through the air, and not all on its motion relative to the ground. First case:

belt moving, plane wheels locked engines off. Obviously the plane moves backwards. The air flow over the wing is from back to front - equivalent to taking off in a following wind (more thrust required)

Second case: engines have unlimited thrust, belt has limited speed, then some arbitrary thrust is sufficient to allow the plane to become airborne (since lift depends only on motion relative to air, not ground)

Third case: engines have limited thrust, belt has unlimited speed. Then at best the plane remains stationary relative to the air, at worst moves backwards relative to the air.

Fourth case: belt has unlimited speed, engines have unlimited thrust. Um - take your pick, I suppose......?

I would say it depends on how exactly one sets up the conditions, as has been noted.

I think this is exactly right.

The argument about the answer is probably exactly because the question IS so ambiguously worded. The way I understand it is that the plane is fixed so that it's wheels can spin but it is held fixed relative to the ground (either by being chained or by having enough thrust to keep it in the same place). But it is fixed in position relative to the ground. Because it is held fixed, it cannot take off, because there is no air moving over the wings to create lift.

Conversely, suppose you took an airplane and set it on the deck of an aircraft carrier. The plane is fixed (again by chains or thrust) to the deck of the aircraft carrier, so it is motionless according to an observer on the deck. Then speed the boat up, perhaps into an oncoming wind. If the boat gets going fast enough, then the plane can take off without moving relative to the deck.

Again, sorry to all for digging up internet bones. BUT I am interested to see how they do it on TV.

Of course the plane takes off. The wheels have nothing to do with the plane's acceleration.

This thread has happened so many times...

If the boat gets going fast enough, then the plane can take off without moving relative to the deck.

Eek.
No. That's not how it works. I suppose the ship's movement has some effect, but what really happens is the jet builds up thrust by pushing against the plate behind it rather than just air.

The way I understand it is that the plane is fixed so that it's wheels can spin but it is held fixed relative to the ground (either by being chained or by having enough thrust to keep it in the same place). But it is fixed in position relative to the ground. Because it is held fixed, it cannot take off, because there is no air moving over the wings to create lift.

No. The plane's not fixed relative to the ground, it's just on a conveyor belt. It's a ruse. The ground has nothing to do with its acceleration as the wheels don't accelerate the plane. The engines do.

That's how riddles work. They divert your attention.

No. That's not how it works. I suppose the ship's movement has some effect, but what really happens is the jet builds up thrust by pushing against the plate behind it rather than just air.

The thrust isn't what's important... It's the lift. As long as the plane is, say, chained to the deck of the aircraft carrier, it will be moving into the wind, which will create lift.

Consider planes taking off and landing at an airport. The always take off and land into the wind, because is it easier to get off of the ground. Now let the wind speed increase and the ground speed decrease. The plane can still get off of the ground in, say, a very large head wind.


That's how riddles work. They divert your attention.

Perhaps we should dedicate some time to understanding the statement of the question.

The body in question is the plane. The following forces are acting on it:

-gravity (Fg)
-the normal force (Fn)
-lift from the wings (Fl)
-thrust from the engines (Ft)
-aero drag (Fd)
-rolling resistance (Frr)

Let's say the plane is pointing to the right in the diagram. Go ahead and draw that plane on a sheet of paper. The engine thrust will be represented by an arrow to the right. The aero drag will be represented by an arrow pointing left, as will the rolling resistance. Of course, gravity will be an arrow pointing down, the normal force will be an arrow pointing up, and lift will be an arrow pointing up. These are all the forces acting on the plane that are relavent to the problem. Go ahead and draw those on there now, and label them as I did in the above list.

Ok, first pretend the conveyor belt isn't moving, i.e. it is a normal runway. You'd agree that the plane can take off right? That's because the thrust vector (Ft) is much larger than the sum of the much smaller drag vector (Fd) and rolling resistance vector (Frr). Ft > Fd + Frr.

Now, change the scenario so it matches the problem at hand. The conveyor belt is now moving in a direction opposite that of the plane, at the same speed as the plane. Since speed requires a frame of reference, lets use the ground as the common reference point for the plane and the belt...its just the easiest way. So the plane moves to the right in our diagram, and the belt surface the plane is on moves left. The speed of the belt exactly matches the speed of the plane, so the wheels end up rotating at twice the speed they normally would at any time the plane is moving relative to the ground. All this does is make the rolling resistance vector a little bigger. The extra rolling resistance comes from bearing friction and the actual rolling resistance of the tires on the runway.

But, this extra rolling resistance is not enough to keep any real, flyable plane from accelerating in the forward direction. Ft > Fd + Frr. The drag force isn't changing due to the belt moving, so the rolling resistance force would have to get much bigger in order to stop the plane from moving. This isn't happening with free rolling wheels that are rotating at double their normal speed. So the plane will accelerate, and the wings will create lift. I don't think its necessary to get into what happens with the force of gravity, the normal force, and the lift force at this point. I think we'd all agree that with enough lift the plane can take off. And it will, because the small increase in rolling resistance will not be enough to prevent the plane from reaching the airspeed required for take off.

If this scenario was set up as a real experiment, the only way the plane would not take off is if the extra rotation rate of the wheels caused them to fail in some way before the plane could take off, or there were some crazy tailwinds present. Alas, at this point the problem is being over analyzed. The point of the problem is to understand that the plane moves by acting on the air, not by driving the wheels....

Hmm. The way that this answer reads, the plane is allowed to move relative to the ground. Ok. Then I agree, it WILL take off.

However, the way I understand the question is that the plane is not allowed to move relative to the ground.

What if there was a big fan in front of it blowing air at it.

Should work the same. The fan should provide lift to get it off the ground, provided the plane was constrained so that the drag doesn't push the plane backwards.

Isn't this how a wind tunnel works?

Ahh sweet memories.

The thrust isn't what's important... It's the lift.

The thrust is what moves the plane forward which causes air to flow over the wings which provides lift.

As long as the plane is, say, chained to the deck of the aircraft carrier, it will be moving into the wind, which will create lift.

Consider planes taking off and landing at an airport. The always take off and land into the wind, because is it easier to get off of the ground. Now let the wind speed increase and the ground speed decrease. The plane can still get off of the ground in, say, a very large head wind.

Yes. But, I don't think that aircraft carriers are going to be moving fast enough to really provide that much lift. The plate that the jet engine pushes onto provides more thrust more quickly which provides the lift.

I could be wrong here, but I really don't think the motion of the ship has much of a role. It can't help but have some but not a significant amount.

The plane can still get off of the ground in, say, a very large head wind.

Hell, with a strong enough wind, the plane will lift off the ground without moving at all.
But, this has nothing to do with the conveyor belt scenario.

Hmm. The way that this answer reads, the plane is allowed to move relative to the ground. Ok. Then I agree, it WILL take off.

However, the way I understand the question is that the plane is not allowed to move relative to the ground.

Yes, Ben, there's always a certain ambiguity in the way the question is worded.

IF the conditions are such that the conveyer speed perfectly matches the forward motion of the plane to the point that the plane is stationary in relation to the ground AND the air around it, it cannot take off.

That's because without some forward motion there is NO air flowing across the airfoil (wings) to create any lift. Just as a runner on treadmill feels no breeze because he is stationary in relation to the surrounding air.

Bottom line? No air motion, no lift - plane remains in place.

Edit: You could also compare it to a car on a dyno.

IF the conditions are such that the conveyer speed perfectly matches the forward motion of the plane to the point that the plane is stationary in relation to the ground AND the air around it, it cannot take off.

The problem is that the wheels have little to no effect on the forward motion of the plane. The wheels don't provide thrust, the engines do. The wheels just spin.

If the wheels were braked, then it would slow the plane down some, sure. But that's stupid. The scenario is meant to be set up like an ordinary plane taking off, with the sole exception being that the ground is a conveyor belt rather than fixed.

The thrust is what moves the plane forward which causes air to flow over the wings which provides lift.



Yes. But, I don't think that aircraft carriers are going to be moving fast enough to really provide that much lift. The plate that the jet engine pushes onto provides more thrust more quickly which provides the lift.

I could be wrong here, but I really don't think the motion of the ship has much of a role. It can't help but have some but not a significant amount.



Hell, with a strong enough wind, the plane will lift off the ground without moving at all.
But, this has nothing to do with the conveyor belt scenario.


Just for the case in point, an aircraft carrier will ALWAYS head into the wind during takeoffs. Every bit of lift generated is taken advantage of.

Every bit of lift generated is taken advantage of.

Yes. But it's not significant is the point.

The problem is that the wheels have little to no effect on the forward motion of the plane. The wheels don't provide thrust, the engines do. The wheels just spin.

If the wheels were braked, then it would slow the plane down some, sure. But that's stupid. The scenario is meant to be set up like an ordinary plane taking off, with the sole exception being that the ground is a conveyor belt rather than fixed.

No one said anything about the wheels providing thrust!! If they are allowed to freely rotate AND the forward motion provided by the thrust of the engine is cancelled by the speed of the conveyer - the thing just sits there like a rock on concrete.

Try throwing a ball off the real of a train at a speed matching the train's speed - it goes nowhere but straight down. In other words, the rock is stationary with respect to the ground (and the air) - and so is the plane. There can be NO forward motion if the "ground" is moving backwards beneath it at the same speed it's trying to move forward. It's called 'speed cancellation.'

Yes. But it's not significant is the point.

If it's not significant at all, then why delay takeoffs a couple of minutes while the ship comes about?

If they are allowed to freely rotate AND the forward motion provided by the thrust of the engine is cancelled by the speed of the conveyer

How would that happen? The wheels have nothing to do with thrust. The only way the conveyor belt would have significant effect would be if the wheels provide thrust. Sure, there's some friction, but that much? Don't think so.

Try throwing a ball off the real of a train at a speed matching the train's speed - it goes nowhere but straight down.

That's because the thrust provided to the rock is coming from the ground. That is, you're standing on the ground (the train) and you're transferring... hmm... nomenclature nomenclature.... You're using the ground (train) as a platform to project the rock from.

The plane is just resting on the ground, it's not being pushed or pulled by anything having to do with the ground.
The engines push (or pull) the air not the ground.

Man.
I don't understand why people have such a hard time with this.
This is so simple...

How would that happen? The wheels have nothing to do with thrust. The only way the conveyor belt would have significant effect would be if the wheels provide thrust. Sure, there's some friction, but that much? Don't think so.



That's because the thrust provided to the rock is coming from the ground. That is, you're standing on the ground (the train) and you're transferring... hmm... nomenclature nomenclature.... You're using the ground (train) as a platform to project the rock from.

The plane is just resting on the ground, it's not being pushed or pulled by anything having to do with the ground.
The engines push (or pull) the air not the ground.

Man.
I don't understand why people have such a hard time with this.
This is so simple...
No, the plane is NOT on the ground - it's on the belt that is moving in the opposite direction of where the plane wants to go. Just like the guy running on the treadmill - he's getting nowhere and neither is the plane.

You are right about two things, though: it IS very simple and I don't understand why you cannot see it.

OK - consider it this way. The guy on the treadmill is holding a model glider in his hand. If he were running on the ground (providing thrust with his legs), the plane would develop enough lift to rise if he released it (and enough forward motion to go a little way).

Now he's on the treadmill - running just as fast as he was on the ground a minute ago. He's still providing forward thrust - same amount - with his legs. He releases the plane and what does it do? Falls like a rock!

Let's start with an automobile on a conveyor belt. If you put an automobile on a physically-realizable conveyor belt that operates as specified the automobile will indeed have zero velocity with respect to the ground. The conveyor belt is physically realizable because there is a direct relationship between the wheels' rotation rate and the automobile's speed with respect to the surface.

The problem is that the situation with a plane on a conveyor belt is not analogous to an automobile. There is no such relationship between the rotation rate of an airplane's wheels and the plane's velocity. An airplane does not have driven wheels.

Let's start with an automobile on a conveyor belt. If you put an automobile on a physically-realizable conveyor belt that operates as specified the automobile will indeed have zero velocity with respect to the ground. The conveyor belt is physically realizable because there is a direct relationship between the wheels' rotation rate and the automobile's speed with respect to the surface.

The problem is that the situation with a plane on a conveyor belt is not analogous to an automobile. There is no such relationship between the rotation rate of an airplane's wheels and the plane's velocity. An airplane does not have driven wheels.

Incorrect statement, the airplane's wheels ARE indeed driven, indirectly - by the thrust supplied by the plane's engine. And that's precisely why a plane "rolls" along the runway prior to liftoff.

But if that forward rolling motion is canceled out by the belt, the wheels STILL roll but the plane goes nowhere. Just like your car on the belt, there's no forward motion. And for a plane, no forward motion means no air moving across the wings - and that equals NO lift being generated.

Back up and read my previous post about a runner carrying a model plane and then doing so while on a treadmill. That comparison IS valid and correctly shows the relationship between thrust and stationary vs moving surface.

The term "driven wheel" has a very specific meaning. It means that the wheel receives power from the powertrain of the vehicle. An airplane has no powertrain. Instead, the wheels on an airplane rotate freely.

Ahh good. Tempers are flaring :)

It's comforting to me, at least, that there are intelligent people on both sides of this conversation.

Either way, let's all pause for a second and get a complete statement of what is exactly going on.

1.) Is the plane moving relative to the ground or not?

Just like the guy running on the treadmill - he's getting nowhere and neither is the plane.

That's because the guy is pushing off the ground in order to propel himself forward. A plane does not do this.

OK - consider it this way. The guy on the treadmill is holding a model glider in his hand. If he were running on the ground (providing thrust with his legs), the plane would develop enough lift to rise if he released it (and enough forward motion to go a little way).

Now he's on the treadmill - running just as fast as he was on the ground a minute ago. He's still providing forward thrust - same amount - with his legs. He releases the plane and what does it do? Falls like a rock!

Again. The thrust is being provided by pushing against the ground. This does not occur in planes.

There is no such relationship between the rotation rate of an airplane's wheels and the plane's velocity.

Exactly.

I mean, I'm sure there is some drag from the wheels. But I seriously doubt that there is enough drag to prevent the plane from achieving flight speed.

Incorrect statement, the airplane's wheels ARE indeed driven, indirectly - by the thrust supplied by the plane's engine. And that's precisely why a plane "rolls" along the runway prior to liftoff.

But if that forward rolling motion is canceled out by the belt, the wheels STILL roll but the plane goes nowhere.

There's the problem.
If.
Your hypothetical fails. The forward motion is not cancelled out by the conveyor belt.
Why should it?

1.) Is the plane moving relative to the ground or not?

Absolutely.

1.) Is the plane moving relative to the ground or not?
Of course it is. The plane has a very real forward thrust equal and opposite to the rearward acceleration of the air by the plane's propellers. How can a physically-realizable conveyor belt exert a rearward directed force on the plane solely through wheels that rotate nearly freely?

Is this conveyor belt moving the plane forwards?

The conveyor belt is moving to the rear. Here is one statement of the problem:
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?
The basic premise is that the motion of the conveyor belt will make the plane's airspeed be identically zero. The basic flaw in this premise is that the conveyor belt cannot exert a force on the plane through the plane's wheels to make this so. In other words, the premise involves some kind of magic.

Unless there are no engines in this scenario?

How can a physically-realizable conveyor belt exert a rearward directed force on the plane solely through wheels that rotate nearly freely?OK, forget the "physically-realizable" bit, and assume the abstract scenario.

By a law of Newton, any body, wheeled or not, will remain stationary wrt to the surface with which it is in contact, unless acted upon by a force. Suppose this surface to be moving in such a way that the flow of surrounding air over this body, stationary wrt to the surface, say a wing, is from back to front.

Then in order for the air flow to remain zero over the body (wing), this body must exert some force (engine thrust) on the surrounding air to exactly balance the motion of the surface wrt surrounding air. Then, as a result of the application of thrust, this air flow is no longer aft to front, but stationary; this exactly equivalent to a body at rest wrt to a surface which is itself at rest wrt surrounding air, except some forward force (thrust) is already being applied


But in order to get lift, our wing needs a significant forward speed. Then the thrust (force) required to generate such forward speed must not only overcome (neutralize) the "rearward" motion of the surface, but also generate additional force sufficient to provide enough forward speed in order to generate lift.

As I said before, we don't know how to do these otherwise simple sums unless we know the available forward force on the wing via thrust, or at what speed the surface is moving; that is, what force our our wing needs, first to come to rest wrt surrounding air, and then gain additional forward speed wrt surrounding air to create lift.

See, I told you I am a physicist!

See, I told you I am a physicist!
Ummm, right.

The conveyor belt exerts a tiny, tiny force on the plane. Think of a matchbox car. Suppose you put a matchbox car on a section of track and the pull the track out from underneath the car. The car doesn't move much because there is little friction between the wheel axles and the wheels. This is why those matchbox cars zoom so nicely.

Now mount a propeller on the matchbox car and put the contraption on its track. The propeller acts to move the car forward. To make the car stand still you will have to pull the track backwards very quickly. You will have to pull the track backwards much faster than the car would normally go forwards.

A matchbox car just has a very smooth shaft. The airplane wheels are on ball bearings. The matchbox car has a lot more wheel friction than does an airplane. Short of magic, the conveyor belt cannot stop the plane from taking off.

Ummm, right.

The conveyor belt exerts a tiny, tiny force on the plane. Think of a matchbox car. Suppose you put a matchbox car on a section of track and the pull the track out from underneath the car. The car doesn't move much because there is little friction between the wheel axles and the wheels. This is why those matchbox cars zoom so nicely.

Now mount a propeller on the matchbox car and put the contraption on its track. The propeller acts to move the car forward. To make the car stand still you will have to pull the track backwards very quickly. You will have to pull the track backwards much faster than the car would normally go forwards.


Precisely! And nowhere is it stated that the speed of the conveyor is limited!! It's allowed to move backward at the exact same speed as the plane is moving forward - relative to the conveyor.

Therefore, it acts JUST like the example you provided and the plane sits still relative to the air. No takeoff. Simple cancellation of the two movements acting in opposite directions (as far as the plane OR matchbox car is concerned.)

t's allowed to move backward at the exact same speed as the plane is moving forward - relative to the conveyor.
There is no physical mechanism that enables this statement to make any sense. You might as well put the conveyor belt hundreds of miles from the plane and ask the same silly non-physical question. In either case, the conveyor belt does not exert a force on the plane. End of story.

The problem with what the MythBusters are doing (and the plane will take off) is that they are governed by the laws of physics. On the other hand, this "plane on a conveyor belt" problem is not governed by the laws of physics. In short, its a bunch of claptrap.

There is no physical mechanism that enables this statement to make any sense. You might as well put the conveyor belt hundreds of miles from the plane and ask the same silly non-physical question. In either case, the conveyor belt does not exert a force on the plane. End of story.

The problem with what the MythBusters are doing (and the plane will take off) is that they are governed by the laws of physics. On the other hand, this "plane on a conveyor belt" problem is not governed by the laws of physics. In short, its a bunch of claptrap.

Ohhhh - nor you are getting rather obstinate! There's nothing that violates any physical laws in the least. No more so than someone on a treadmill or a car on a dynomometer.

And the only reason the MythBuster's plane might take of is because they may not be able to precisely match the speeds. It would require a VERY fast conveyor AND a ginger touch on the conveyer speed controller.

If the wheels rotate freely then they cannot have any effect on the plane's speed, it will take off.

The reason the MythBuster's plane will take off is because it will achieve the requisite speed with respect to the air needed for takeoff. A real conveyor belt will not be able to stop that from happening. Of course a mythical conveyor belt possessed with some magical force can stop the plane from taking off. So why not put the conveyor belt on the Moon? It will still possess the requisite mythical force needed to prevent takeoff, won't it? Sans such a mythical force, a real plane on a real conveyor will take off.

The wheels are only there to minimize drag. Even if the conveyor belt was moving at ten times the maximum speed of the plane it would still take off. Provided the wheels can take such massive centrifugal force lol

hmmmm...

I think I'm beginning to change my mind....

hmmmm...

I think I'm beginning to change my mind....

What is it that still creates some doubt ?

You see, the wheels just hold the plane up.
The wheels rotate freely, like the wheels of a model car:

if you put a model car on a sheet of paper and then quickly pull the paper from under it,
the model car will not stick to the paper.. it will stay pretty much in it's place.
But the wheels move. The wheels have very little impact on the speed of the model car,
because the wheels rotate near freely.

This very little impact on speed (because of the little drag between the wheels and their axis)
of the much heavier plane is insignificant.
The plane takes off.

:)

Precisely! And nowhere is it stated that the speed of the conveyor is limited!! It's allowed to move backward at the exact same speed as the plane is moving forward - relative to the conveyor.

Therefore, it acts JUST like the example you provided and the plane sits still relative to the air. No takeoff. Simple cancellation of the two movements acting in opposite directions (as far as the plane OR matchbox car is concerned.)
The speed of the plane is always exactly relative to the speed of the conveyor, but that has no physical significance as to whether the plane can take off or not. For example, the wheels can be moving 200 mph relative to the surface of the conveyor belt. The surface of the conveyor belt would see the wheels moving 200 mph relative to it. That, however, has no physical meaning as to whether the plane has forward motion due to the thrust of its engines relative to the windless air. It also has no physical meaning as to what the speed of the conveyor belt is relative to the ground, or air (the ground and air are in the same frame of reference). The planes engines could, for example, push the plane to a speed of 100 mph relative to the ground/air frame of reference. The conveyor belt could move rearward at 100 mph relative to the ground/air. The wheels, and the plane itself, would be moving at 200 mph relative to the belt surface, and vice versa, but a light plane could take off because it was moving at 100 mph relative the air, its airspeed.

What is it that still creates some doubt ?

The fact that my initial assessment was the other way. When in doubt, always trust your first instinct :)

The fact that my initial assessment was the other way. When in doubt, always trust your first instinct :)

Ah ;)
Maybe what I said in post 43 will help you visualize it ?

The wheels are only there to minimize drag.
Exactly. The proponents of the "plane won't take off theory" use some unexplainable, nonexistent, and nonphysical mechanism to justify their argument. Rather than wheels, why not a plane on skis? Perfect, friction-free skis that is. The only force between the conveyor belt and the plane is the normal force. With this, there truly is no difference between this discussion and that of an irresistible force encountering an unmovable object.

Note well: This "plane on a conveyor" discussion is not tantamount to a discussion of the number of angels that can dance on a point of a pin. That problem, at least, has been solved: 8.6766*1049 is an upper bounds for the density of angels dancing on the point of a pin (http://headofapin.net/).

The speed of the plane is always exactly relative to the speed of the conveyor, but that has no physical significance as to whether the plane can take off or not. For example, the wheels can be moving 200 mph relative to the surface of the conveyor belt. The surface of the conveyor belt would see the wheels moving 200 mph relative to it. That, however, has no physical meaning as to whether the plane has forward motion due to the thrust of its engines relative to the windless air. It also has no physical meaning as to what the speed of the conveyor belt is relative to the ground, or air (the ground and air are in the same frame of reference). The planes engines could, for example, push the plane to a speed of 100 mph relative to the ground/air frame of reference. The conveyor belt could move rearward at 100 mph relative to the ground/air. The wheels, and the plane itself, would be moving at 200 mph relative to the belt surface, and vice versa, but a light plane could take off because it was moving at 100 mph relative the air, its airspeed.

Sorry, but you math does not add up. There's no forward motion left to produce the 100 mph you state in your final sentence.

All forward motion has been canceled in your example by the rearward motion of the conveyor and the rotation of the wheels. There is no ground/airspeed left over.

Sorry, but you math does not add up. There's no forward motion left to produce the 100 mph you state in your final sentence.

All forward motion has been canceled in your example by the rearward motion of the conveyor and the rotation of the wheels. There is no ground/airspeed left over.
Read again Read-Only. The wheel/plane speed was 200 mph relative to the surface of the conveyor belt. The conveyor belt moved rearward at 100 mph relative to the ground and the wheel/plane moved forward at 100 mph relative to the ground. The plane engine is thrusting against the air, not the conveyor belt, so the wheels are just free-wheeling as no thrust is transmitted through them.

When i was first told this puzzle it only took me two seconds to get the wrong answer. It seemed so easy using vectors...

But my error was pointed out to me - and how i laughed, and laughed.

According to Newtons laws, in order for one object to act upon another, a force must be presant.

The forces between the plane and the belt are all done through the wheel.
The purpose of the wheel of a taking off plane is: to provide a means of resting the plane on a surface, while allowing it to move about the surface with as little friction as possible.
Thus, there are 2 forces acting between the belt and the plane: the normal force, and various forces of friction.

The normal force is of course govourned by gravity, the speed of the belt has nothing to do with it, it can only decrease as the lift of the plane increases. As planes have been taking off for a hundred years, this isnt a problem.

The force of friction however is. It is proportional to the normal force, and the coefficiant of friction.

In the abstract scenario (to coin a previous posts' phrase.)
the wheel is of course perfect, with no force of friction whatsoever. This leaves no forces for the surface (the conveyer belt) to act upon the plane, and thus even a belt travelling at the speed of light could not make the plane budge, wheras even the tiniest force from the engine would make it accelerate indefinatly. Plane takes off.

In a more realistic scenario, there are of course forces of friction.
Two scenarios here:

1. Wheels locked.
With the wheels locked, the primary force is the force of static friction between the belt and the wheels. in this case, the speed of the belt is also irrelevent, the same scenario would occur if you applied the brakes on a normal runway: The wheels stay at the same relative position to the surface untill the force of friction is overcome. Now, this static friction has a maximum attainable force (as the plane increases thrust, the force of friction increases, keeping the plan at rest, untill this maximum is reached), after which the force dercreases. and the plane will move (and take off.)
The question then becomes simpler: which is more powerfull, the engine or the brakes?(the brakes have a higher force of static friction than the wheels on the road, you can verify this by slamming your brakes on the highway and admiring the skidmarks, if it were not the case, the wheels would keep rolling.)
I wager the engine is more powerfull.

2nd Scenario, free-rotating wheels.
In this case, its a different type of friction, the force of roling friction.
Now, this too has a maximum achievable force, and while speeding the belt will increase the force, it only can untill this maximum has been reached. After which, the force will decrease, then remain constant.
Proof? If you floor the accelerator of your car, your wheels will spin-out, and you will leave more trackmarks. If the force continued to increase with the speed, you would not leave the marks.
Once again; which is stronger, that force or the engine? In a car, it's the engine. Id wager a plane yields similar resaults.

Conclusion:
In no scenario is there a force which is proportional to the speed of the belt and can increases indefinatly. The plane will take off.

If you believe other wise: show me the force.

NOTE: I realised I used car examples in my post; it very easy in this case to commit a false analogy in this case, while the relationship between the car and ground is similar to that of the plane and ground (and such for determining forces on the wheel, it was a good example) the propulsion methodes are different, and as such, one cannot say that because a car/human on a treadmill won't take off, a plane on a treadmill won't. The car/human relies entirely on their being a force of friction kept between the ground and wheels (the conveyor belt removes this force by moving backwards) the plane attempts to keep this force to a minimum, and relies on the force of its exhaust/air to propel it.
To furthur denote the difference; cars cannot move at all with the perfect wheel described in the abstract scenario.

-Andrew

I would say it depends on how exactly one sets up the conditions, as has been noted. Obviously lift depends only on the plane's motion through the air, and not all on its motion relative to the ground. First case:

belt moving, plane wheels locked engines off. Obviously the plane moves backwards. The air flow over the wing is from back to front - equivalent to taking off in a following wind (more thrust required)

Second case: engines have unlimited thrust, belt has limited speed, then some arbitrary thrust is sufficient to allow the plane to become airborne (since lift depends only on motion relative to air, not ground)

Third case: engines have limited thrust, belt has unlimited speed. Then at best the plane remains stationary relative to the air, at worst moves backwards relative to the air.

Fourth case: belt has unlimited speed, engines have unlimited thrust. Um - take your pick, I suppose......?
People seem to forget that the wheels on a plane have nothing whatsoever to do with it's propulsion. The propeller is what propels the plane. Once the engine starts, all the conveyer belt will do is cause the wheels to turn faster as the plane moves forward. It will have no effect whatsoever on the velocity of plane except for energy lost due to friction, which should be minimal.

Both of the planes on the Mythbusters episode are going to take off with no problem whatsoever.

A plane taking off directly to the west is taking off on a runway that is being conveyed to the rear of the plane at several thousand hundred miles per hour, at my latitude. But no doubt I am misinterpreting things.

The various statements of the problem confuse. If the conveyor is supposed to exactly match the axle center speed relative to the belt as "0", then the slightest accelleration of the plane forward relative to the belt increases the belt speed, which increases the relative wheel speed, which increases the belt speed, and so forth until the ratio of the two speeds asymptotically approaches 1 too closely to differentiate under physical measurement. I do not know what the effects of transonic belt speeds would have on the aerodynamics of a wing a few feet above it, but the sonic booms should be entertaining to suitably distant spectators.

If the conveyor is supposed to exactly match the rotation speed at the point of contact, then simply locking the brakes and greasing the belt should keep it from entering the feedback loop to infinity while the plane takes off.

But the whole matter seems vaguely defined.

But one thing is sure: Once we have persuaded airplanes that air speed and ground speed are interchangeable by fiat, a conveyor capable of this kind of behavior would make an excellent short landing strip, maybe a hundred feet long. Simply run it up to the planes flying speed, have the plane set down on it, instantly relabel the plane's flying speed its "belt speed" (making its air speed 0) and bring the belt to a stop. The air force should look into this for carrier landings - it would be a lot safer.

A plane taking off directly to the west is taking off on a runway that is being conveyed to the rear of the plane at several thousand miles per hour, at my latitude. But no doubt I am misinterpreting things.



No doubt about it - you are. When walking westward, have you ever noticed that slightly over a thousand mph wind (at the equator, it becomes less as the lattitude increases) striking you in the face???? :D

- When walking westward, have you ever noticed that slightly over a thousand mph wind (at the equator, it becomes less as the lattitude increases) striking you in the face???? How is that relevant ?

Aside from correcting my "thousands", a mental glitch ( Meant "hundreds") I mean ?

Wind speed was not part of the problem's statement.

Cool ride at the State Fair: a vertical motorized pulley setup that moves cable through a free wheeled runner - like a light rail car tracker, only the wire moves and it's vertical, about four feet of cable between the pulleys. The wheeled runner has a hand grip, like a little T handle. The whole thing is about a hundred feet up. The fairgoer holds a handle connected to the wheeled runner, and steps out into space next to the pulley cable. As soon as he starts to fall, the pulley starts running cable through the runner as fast as he is "falling" - cancelling out his vertical motion, the same way the conveyor cancels the horizontal motion of the plane. So he can just stand there in space, effortlessly looking around like a scuba diver hanging in the water.

Neat, huh ?

How is that relevant ?

Aside from correcting my "thousands", a mental glitch ( Meant "hundreds") I mean ?

Wind speed was not part of the problem's statement.

Not talking about the problems statements - just pointing out the fact that your "conveyor" (the Earth) is taking the air with it as it rotates. That's why it's possible to have things on the face of it without them being immediately blown away.

Not talking about the problems statements - just pointing out the fact that your "conveyor" (the Earth) is taking the air with it as it rotates. And the relevnace of that to the problem is - - - ?

The plane will not take off. The plane needs to be in actual motion in order for the wings to create lift. There is no way the plane will lift off of the ground.

The plane needs to be in actual motion in order for the wings to create lift.
Nothing's preventing the plane from being in actual motion.

The plane will take off, because the rotation of the wheels in whatever direction and at whatever rotational speed have no influence whatsoever on the plane.
The wheels have no way of transferring any force to the plane.

The plane will take off, because the rotation of the wheels in whatever direction and at whatever rotational speed have no influence whatsoever on the plane.
The wheels have no way of transferring any force to the plane.
Actually, they do. At low airspeeds the weight of the plane is carried by the undercarriage instead of the wings, and hence the wheels. That's why airplanes also (in addition to the airbrake and reverse thrust) brake on landing with using ordinary brakes on the wheels.

However, since a plane is not a car, it will, of course, take off.

The plane will not take off. The plane needs to be in actual motion in order for the wings to create lift. There is no way the plane will lift off of the ground.

By "actual motion" do you mean the it must move relative to the ground? If so, then why can model airplanes fly in wind tunnels?

The vertical cancellation of speed seems to have wide applicability (imagine the airplane on a vertical conveyor belt).

For example, such a conveyor belt could be made very lightweight, and lifted by a relatively small balloon. It could then maintain in suspension beside it, by vertical cancellation of the falling speed and horizontal cancellation of any movement in that dimension, an object of almost any weight - the only expense and trouble would be getting it into position, and joining it to a wheel running on the track, after which the power necessary in maintaining the belt speed would be much less than that requried to lift and carry the object itself.

There is a very simple analogy:

Put grandpa in his wheelchair on a treadmill. Start the treadmill and start to push him. NO MATTER how fast the treadmill is going, you will be able to advance the chair, compared to the ground.

Exact same problem with the plane.

Actually, they do. At low airspeeds the weight of the plane is carried by the undercarriage instead of the wings, and hence the wheels. That's why airplanes also (in addition to the airbrake and reverse thrust) brake on landing with using ordinary brakes on the wheels.

However, since a plane is not a car, it will, of course, take off.

By "actual motion" do you mean the it must move relative to the ground? If so, then why can model airplanes fly in wind tunnels?

Not if the wheels can rotate freely.

There is a very simple analogy:

Put grandpa in his wheelchair on a treadmill. Start the treadmill and start to push him. NO MATTER how fast the treadmill is going, you will be able to advance the chair, compared to the ground.

Exact same problem with the plane.

That's a good analogy, however sometimes the question is worded with term like complete "grip", geared wheels and garbage like that.

There is a very simple analogy:

Put grandpa in his wheelchair on a treadmill. Start the treadmill and start to push him. NO MATTER how fast the treadmill is going, you will be able to advance the chair, compared to the ground.

Exact same problem with the plane.

Provided you push the chair from beside the conveyor belt.

Of course... :) Or pulling it with a rope from the front standing on the floor...

I wish to restate my earlier post somewhat differently. if the plane is allowed to move forward, relative to the ground, then of course it will take off. Put a plane on a real conveyor belt, and this is definitely what will happen.

Most of the times I have seen the question posed, however, there is a weird condition that requires that the rotation of the planes wheels exactly counter the motion of the conveyor belt. That condition is a little vague and it can be interpreted in more than one way, but the intent seems to me to be that the rotational speed of the wheels (at the point where they contact the conveyor belt) is the same as that of the conveyor belt itself at that same point, save that the two are rotating in different directions.

If that condition is true, then either (i) the plane is not moving forward or (ii) the plane's wheels are partially "skidding" as the plane moves forward. If the plane were moving forward *and* the wheels were freely turning, then the "speed of the wheels" > the "speed of the conveyor belt."

Now, WHY would this condition be true? In the real world, it never would, assuming the planes engines were functioning normally and at full blast. One possible answer is that the planes engines are being gunned just enough to keep the plane steady on the conveyor belt, and not enough to accelerate (in which case, the plane does not take off).

In short, I think the answer is: (i) if you ignore the condition, the plane takes off easily/* or (ii) if you take the condition seriously, and interpret it the way I do, the problem looks to be simply silly and turns into a semantic problem more than a physical one.

--------------
/* I'd suggest that anyone who thinks the plane definitely takes off every time is likely ignoring the condition, as inconveniently implausible.

The plane won't take off, it doesn't have a pilot.

Seriously you just have to think:
( The plane direction in this instance is just the direction it would normally face to fly)

<-- Plane
-----> Belt Direct

This would cause the plane to fly backwards off the belt. You've probably seen films where people running on treadmills fly backwards. Not proper flight.


<-- Plane
<---- Belt Direction


At one point the planes wheels wouldn't be able to spin as fast as the belt, causing the plane to start moving in the direction of the belt which would cause air to move around the wings generating lift.

In essence it's dependant on the direction of the belt.

I would put the mathematics up, unfortunately I can't do it to the level I'd like so I won't.

lets break this down.

1) Plane on a conveyor belt does not move, whereas conveyer belt moves

2) Plane on a conveyer belt moves opposite of the direction of a conveyer belt

3) Plane on a conveyer belt moves in the same direction as a conveyer belt...thus speed relative to the ground is higher

At my local airport luggage goes on the conveyor and
planes go on the runway.
None of the luggage takes off, even the bags with wheels.

At my local airport luggage goes on the conveyor and
planes go on the runway.
None of the luggage takes off, even the bags with wheels.

helloooo...aerodynamics of a shape of an object is what makes planes fly...their wings' shape.

lets break this down.

1) Plane on a conveyor belt does not move, whereas conveyer belt moves

2) Plane on a conveyer belt moves opposite of the direction of a conveyer belt

3) Plane on a conveyer belt moves in the same direction as a conveyer belt...thus speed relative to the ground is higher

No absolute friction or B.S physics conditions? Real world?

Plane takes off on all 3 - provided there is enough runway(belt?).

No absolute friction or B.S physics conditions? Real world?

Plane takes off on all 3 - provided there is enough runway(belt?).

well in:

1) condition I would say that the plane moves back relative to the conveyer belt since it first tilts its nose up and than since nothing acts on it to move it further it rolls back on a conveyer belt as a result...in fact it might even tilt back.

2) condition, the plane moves 0 m/s relative to the ground...and so there is no wind being swept under the wing...so it does not lift off or anything...however...if the plane moves at much faster velocity in opposite direction to the conveyer belt direction velocity than it has a chance at lifting off since it is providing lift by itself

3) the plane will lift off faster this way than if it was going from a runway

K I misunderstood 1.

However I just had an idea...what if the conveyer belt was extremely hot and the plane surface was extremely cold...wouldn't that create difference in pressures? And such could be used to the advantage of the lifting force. Would it not?

Analogy of a ground effect experienced by Ekranoplan

http://upload.wikimedia.org/wikipedia/en/2/27/Pic_4459.jpg

helloooo...aerodynamics of a shape of an object is what makes planes fly...their wings' shape.

Yes, because air is passing the wing, the uneven pressure produced above and below the wing results in lift.
If the plane is not moving relative to the air it will not take off.
Even out on a runway, if the plane is travelling at 100 mph and the wind is travelling at 100 mph, if they are going in the same direction, it will not lift at all.


I'm not too sure about this thread. Is it a joke?
Are people just pretending to think a plane will take off because its wheels are spinning round,
or do they really think it?

Yes, because air is passing the wing, the uneven pressure produced above and below the wing results in lift.
If the plane is not moving relative to the air it will not take off.


I'm not too sure about this thread. Is it a joke?
Are people just pretending to think an unmoving plane will take off,
or do they really think it?

have you seen my scenarios?

The notion here is to use a conveyer belt to an advantage of the aircraft, perhaps giving it an impulse would help, so that the engines kick in to create a lift and keep the aircraft afloat once the aircraft is in the air.

Basically An engine of the aircraft will have to turn on extremely fast to provide the lift needed to keep the aircraft afloat once it is accelerated to the needed speed by the belt. Also if such is impossible...than there must be air space between the ground and the airplane once its engines turn on...that means the belt must be at angle to the ground

I now realize that all is this is extremely dangerous as...the engines will need to start in extremely short period of time while the aircraft is basically going on momentum from the impulse created by the belt and whilst falling...so no, only military jets might benefit from this system, but even so, its too dangerous.

It doesn't matter what speed the conveyor belt is doing
nor what speed the plane is doing.
The only thing that mattters is the speed of the air over the wings.

The shape of the wings means that air passing over the wings results in a variance in pressure above and below the wing, resulting in lift.

That is why a plane will fly in an air tunnel.

Well Captain Kremmen, the belt will generate a lift of the upper portion of the plane for sure, the plane will tilt nose up at an angle to a conveyer belt...since movement of conveyer belt relative to the ground created wind under the wing of the airplane...However in order for the plane to lift of trully it will need to turn its engines on to generate its own lift since the belt will no longer create wind pressure change under the plane's wings...ALSO the plane will be moving in a momentum from the speed gained by the accelerated belt.

In conclusion...in order for the plane to lift of from the moving belt, the plane must be first attached firmly to the moving belt. At a particular speed of the moving belt, the hatches of the planes which are attached to the belt will experience a force up created by the lift from the wings of the plane...as the speed of the moving belt will increase further on...that force will create more tension between the hatches and the plane. At one point the hatches must release the plane so that it will lift off from the high velocity momentum created by the high speed of the belt.

During this stage the plane will lift off and move up from the momentum of its mass created by inertia of the moving belt...however that inertia will decrease as the gravity force will overcome the up acceleration...so the plane will have to have its engines turn on to create the lift needed to keep it aloft.

Understood?

What I have described above is what happens with paper airplanes...First we create an aerodynamic shape for a plane.

Than we run with the plane and hold it firmly in our hands so that it gains momentum relative to the ground creating wind under its wings...than we release the plane, so that it moves on momentum relative to the ground...

however the paper plane momentum will soon be exhausted because of friction from air and gravity acting downwards...whereas a normal plane will have its engines turn on allowing it to go on flying

I'm not too sure about this thread. Is it a joke?
Are people just pretending to think a plane will take off because its wheels are spinning round,
or do they really think it?


What they are really thnking is that the plane would accelerate forward on a conveyor belt just as easily as it would on a runway. Since the acceleration of the plane is no different than it would be on a runway, the plane should take off as it would on a runway.

The notion that the plane is held almost motionless—with the only significant motion being that its wheels are rotating—is an interpretation of the way the question is usually framed, but really makes no physical sense when you consider how an airplane (and its wheels) work. In reality, the force from the engines should accelerate the plane forward, which would, in turn, make it possible for the plane to take off.

The question is a semantic one, not a physics question, because it turns on whether you interpret the question itself as having a motionless plane with spinning wheels or one which accelerates normally. It seems to me that the former cannot take off (assuming the air is otherwise calm), and the latter can.

Had a thought: In the interpretation where the wheel assembly is frictionless, and the conveyor accellerates in response to sensed forward motion of the wheel in an attempt to "catch up" (thereby joining a positive feedback loop that ends in near-light speeds of the conveyor)

if we suppose any vertical irregularity whatsoever on the belt, the "sonic boom" pressure waves will be created continuously beneath the plane's wings, very soon after this feedback loop gets started.

Would they lift the plane ? Let's suppose mach 10 or thereabouts in a few seconds, achieved as the plane rolls forward at 1 mph.

Had a thought: In the interpretation where the wheel assembly is frictionless, and the conveyor accellerates in response to sensed forward motion of the wheel in an attempt to "catch up" (thereby joining a positive feedback loop that ends in near-light speeds of the conveyor)

if we suppose any vertical irregularity whatsoever on the belt, the "sonic boom" pressure waves will be created continuously beneath the plane's wings, very soon after this feedback loop gets started.

Would they lift the plane ? Let's suppose mach 10 or thereabouts in a few seconds, achieved as the plane rolls forward at 1 mph.

mach 10 near ground? what sort of metal and how meters thick is the hull of this airvehicle to witstand such force? :eek:

No one said anything about the wheels providing thrust!! If they are allowed to freely rotate AND the forward motion provided by the thrust of the engine is cancelled by the speed of the conveyer - the thing just sits there like a rock on concrete.

Try throwing a ball off the real of a train at a speed matching the train's speed - it goes nowhere but straight down. In other words, the rock is stationary with respect to the ground (and the air) - and so is the plane. There can be NO forward motion if the "ground" is moving backwards beneath it at the same speed it's trying to move forward. It's called 'speed cancellation.'

Exactly......this was my initial thought when I put the scenario through my mind.

Thrust creates lift ONLY when the object can be propelled through space causing air to push upwards on the wings.

If a fan was infront of the plane while on the conveyor belt, the fan would have to produce the same amount of air speed/lift that the plane needs to get off the ground in a normal scenario.......when the plane passes the fan it will immediately stall and crash into the ground.

Understood?

It's a good problem.
I was pretty certain it wouldn't take off, but I'm not so sure now.

I've seen an argument, much in line with Pandaemoni's, that says that the conveyor belt will have no effect on the speed the plane moves forward at, just the speed that the plane's wheels spin at. The plane thrusts forward against the air, not the ground. That sounds right. In which case the plane will move forward at near normal speed and take off.

Can I change my vote please?


All will be solved.
Mythbusters, Jan 30th.

Why? What is the reason for this nonsense for in reality it will never happen.

There's no reason. They are confusing aircraft with luggage. There is some similarity in that some suitcases have wheels. But ,after much careful observation , I am convinced that suitcases on a conveyor belt move relative to the ground.

It's a good problem.
I beg to differ. This question is ill-posed and invokes magic. The problem will not be resolved on January 30th because those who espouse the view that the plane will not take off will simply claim that the boys at MythBusters didn't set things up correctly. The problem is that there is no physically-realizable setup that will do what the "plane won't take off" proponents claim.

The wheels are free-spinning. When thrust is applied, plane moves forward. Plane flys. Its only confusing because the way the problem is worded throws you for a loop if do not think of the free-spinning wheels. It will be nice to bury this hatchet once and for all on Jan. 30.

mach 10 near ground? what sort of metal and how meters thick is the hull of this airvehicle to witstand such force? That interpretation of the statement of the problem requires the conveyor to acheive very high speeds, so I think we are supposed to simply assume it can.

As I said on an earlier page, it ought to be pretty interesting for suitably distant observers.

The plane thrusts forward against the air, not the ground.
Strictly speaking, the plane is unaffected because the forces that limit its speed (air resistance and the small friction forces in the wheels) are mostly independent of how fast the conveyor belt is running (at least up to the point where the tyres overheat and burst). How a conveyor belt affects the top speed of other objects/vehicles can get quite complicated. For a person running on a treadmill it's simple: a person can only accelerate their legs back and forth at a limited rate, so their top speed is limited with respect to the surface they're running on.

For a car it's not so simple: a car's top speed is the speed at which the thrust generated by the engine matches the air resistance, leaving no net force to accelerate the car. The air resistance is independent of the conveyor belt, but the thrust is limited by the engine's efficiency, which drops if the engine starts running too fast. So if you drive a car (say) North on a conveyor belt running South at (say) 30 km/h, your top speed will be reduced, but only by some fraction of the conveyor belt's 30 km/h.

I beg to differ. This question is ill-posed and invokes magic. The problem will not be resolved on January 30th because those who espouse the view that the plane will not take off will simply claim that the boys at MythBusters didn't set things up correctly. The problem is that there is no physically-realizable setup that will do what the "plane won't take off" proponents claim.
Yea, I see where this is going:

Commentator: In [some year], two physicists at [Whatever] University were preparing a presentation on the plane-on-a-conveyor-belt problem for their students. But then they stumbled upon a problem that they did not expect. The conclusion this would lead them to now threatens to undermine our very understanding of the forces of nature.

Physicist dude: Well basically, in the plane-on-a-conveyor-belt problem a plane is set on a conveyor belt, with the, uh, belt running backwards just fast enough to cancel out the plane's forward motion. The question is then whether the plane will take off or not. The correct answer is, of course, that it won't, since with zero airspeed the wings won't generate any lift.

To begin with, we just wanted to challenge our students to see if they'd be able to deduce this answer by themselves. It was only when we were planning to explain by exactly what mechanism the conveyor belt was stopping the plane that we realized things weren't so simple. It obviously wasn't the air resistance, and every highschool physics student has heard that kinetic friction coefficients are independent of velocity so it couldn't be friction in the wheels either. We knew at once that we were dealing with a new phenomenon physics couldn't currently explain.

Commentator: Two months later both physicists published a paper in Nature where they argued that the plane must be being held back by a new, previously unknown fundamental force of nature. But to be able to hold a plane in place it would have to be stronger than any previously encountered force, a force so devastating that it threatens to unravel the very fabric of our universe...

The wheels are free-spinning. When thrust is applied, plane moves forward. Plane flys. Its only confusing because the way the problem is worded throws you for a loop if do not think of the free-spinning wheels. It will be nice to bury this hatchet once and for all on Jan. 30.

I agree with others: there will be no hatchet burying. Free-spinning wheels exist in the real world, but in the hypothetical problem, they do not. The wheels in the hypothetical revolve at a particular speed, keyed off of the speed of the belt itself. You can ignore that condition, but then you are answeriung a different question than the one actually posed.

It's rather like the old gem of "Suppose you are stranded on a desert island with a sealed can of beans and nothings else, how do you stave off starvation?" If you answer: "I use a rock (or can opener) to open the can of beans," you have found a way to stave off the hunger, but only by ignoring the hypothetical condition that makes the problem difficult in the first place.

This question might as well be "Suppose 1 = 7, what does 1 + 2 equal?" Some people will answer "3", and "3" is certainly correct in almost every other context, but given the loopy supposition the question imposes, things get ... not real "complicated," just "arbitrary." The big difference is that 1 = 7 is obviously absurd, whereas the notion of the wheels moving at the same rotational speed as the conveyor belt is superficially plausible until you think about it.

Mythbusters can no more put this question to bed than they could the 1 + 2 question.

Like I said, there is no difference between this question and that of an irresistible force versus unmovable object. The resolution of both is that they are stupid questions.

I agree with others: there will be no hatchet burying.
Only for those who persist in trying to find a "correct" answer to a meaningless question. The "problem" is only interesting because it aims to distract readers/listeners from a false law they're taking for granted (that conveyor belts can "cancel out" a plane's motion) with an apparently legitimate problem that they can pat themselves on the back for answering "correctly".
"Suppose 1 = 7, what does 1 + 2 equal?"
In modular arithmetic (http://en.wikipedia.org/wiki/Modular_arithmetic), we'd say that 1 + 2 is congruent to 3 + (any multiple of 6), modulo 6. Congruence has all the properties of an equivalence relation. If you want to stick with regular integer equality, then 1 + 2 = 3 regardless of what erroneous assumptions anyone makes.

Like I said, there is no difference between this question and that of an irresistible force versus unmovable object. The resolution of both is that they are stupid questions.

Of course not and your analogy is false. It is kind of funny how people can not see the solution to a rather SIMPLE question....

Omg...
Can anyone of the people thinking the plane will not get airborne, please show me the force that prevents it to ? And how that force is transferred to the plane ? Thank you.

Gravity. Were not quite certain exactly how it couples to the plane. The best guess involves gravitons. ;)

Seriously, it depends on the reading of the problem. The no fly point of veiw goes something like this:

1. The air surrounding the wings is considered to be at rest with the ground. Prop wash and entrainment of the air by the conveor are disregarded.

2. The top surface of the conveor belt is moving 100mph front to back of the plane.

3. The wheels are in no skid contact with belt, and a speedometer that is geared to the rotation of the wheels reads 100mph forward.

Under these constrains, the plane is stationary to the ground, the engine idling just enough to overcome the rolling friction of the tires.

I suspect this is the original way the problem was intended, as it is a simple lesson in Gallilean addition of velocities. As the problem got spread around it became garbled, resulting in 5 page message board silliness, among other things.

Gravity. Were not quite certain exactly how it couples to the plane. The best guess involves gravitons. ;)

Seriously, it depends on the reading of the problem. The no fly point of veiw goes something like this:

1. The air surrounding the wings is considered to be at rest with the ground. Prop wash and entrainment of the air by the conveor are disregarded.

2. The top surface of the conveor belt is moving 100mph front to back of the plane.

3. The wheels are in no skid contact with belt, and a speedometer that is geared to the rotation of the wheels reads 100mph forward.

Under these constrains, the plane is stationary to the ground, the engine idling just enough to overcome the rolling friction of the tires.

I suspect this is the original way the problem was intended, as it is a simple lesson in Gallilean addition of velocities. As the problem got spread around it became garbled, resulting in 5 page message board silliness, among other things.

And what happens when someone full throttle's the plane ? It takes of..
"...the engine idling just enough to overcome the rolling friction of the tires."

The rolling friction being of course insignificant in comparison with the thrust of the airplanes engines.

I suspect this is the original way the problem was intended, as it is a simple lesson in Gallilean addition of velocities.
I doubt it, since there are many better lessons in Galilean velocity addition (person walking on a boat/train, etc.) and many people when they first encounter this problem assume that the conveyor belt can "cancel out" the plane's speed the same way a treadmill can hold the person running on it in place. So it's a trick question, and the best answer is to state that if you put a real plane on a real conveyor belt, the plane won't be held in place like the problem assumes.

What the plane-won't-take-off proponents are doing is getting caught up in a silly semantics exercise yielding an unhelpful answer. If someone comes up and asks you what happens if you fly a plane over the edge of the world, do you start talking about planes in outer space because you're compelled to answer a question about a plane leaving the Earth? Or do you tell them that the world is, in fact, roughly spherical, has no edge, and that if you fly a plane in a "straight" line in any given direction, you'll end up back where you started?

And what happens when someone full throttle's the plane ? It takes of..
"...the engine idling just enough to overcome the rolling friction of the tires."

The rolling friction being of course insignificant in comparison with the thrust of the airplanes engines.


If the pilot full throttles the engines, you no longer have that the wheel rpm indicated speed is equal to the conveor belt speed, of course. But that is not the problem at hand.

If the pilot full throttles the engines, you no longer have that the wheel rpm indicated speed is equal to the conveor belt speed, of course. But that is not the problem at hand.

Of course you still have equal speed. The conveyor belt adapts to the speed of the wheels, no ?

I doubt it, since there are many better lessons in Galilean velocity addition (person walking on a boat/train, etc.) and many people when they first encounter this problem assume that the conveyor belt can "cancel out" the plane's speed the same way a treadmill can hold the person running on it in place. So it's a trick question, and the best answer is to state that if you put a real plane on a real conveyor belt, the plane won't be held in place like the problem assumes.

What the plane-won't-take-off proponents are doing is getting caught up in a silly semantics exercise yielding an unhelpful answer. If someone comes up and asks you what happens if you fly a plane over the edge of the world, do you start talking about planes in outer space because you're compelled to answer a question about a plane leaving the Earth? Or do you tell them that the world is, in fact, roughly spherical, has no edge, and that if you fly a plane in a "straight" line in any given direction, you'll end up back where you started?

You do understand that the rolling resistance of the wheels transfer a net drag on the body of the plane, don't you?

As I stated the problem, it's not a trick question.

Of course you still have equal speed. The conveyor belt adapts to the speed of the wheels, no ?

No. The conveyor belt maintains a constant 100mph wrt the ground. If you accelerate the plane in the opposite direction, the wheel rpm must either increase, or the wheels must skid.

You do understand that the rolling resistance of the wheels transfer a net drag on the body of the plane, don't you?
You do understand that this drag is a) negligible and b) roughly the same as it would be if the plane were on a regular runway, don't you?
As I stated the problem, it's not a trick question.
Good for you. But I was referring to the problem stated on the Mythbuster video and at least two threads here at sciforums:
62061
53562

Regardless of how you look at it, the presence of the conveyor belt hardly changes anything. Why do you think it's in the problem in the first place?

No. The conveyor belt maintains a constant 100mph wrt the ground. If you accelerate the plane in the opposite direction, the wheel rpm must either increase, or the wheels must skid.

Then the rpm increases..
It doesn't really matter, the plane gets off in any situation except when the wheels are locked or are spinning in the opposite direction (motorized), and even then..

Ok. There are threads on this all over the internet. There are several here at SciForums:
http://www.sciforums.com/search.php?searchid=1914126

Shame on you :mad:

LOCKED!


;)

While we are at it, we should start a poll about 0.999... = 1 (no people, this isn't an invitation to derail this thread).



Anyway, the plane takes off. Why? The AIR SPEED along the wings is not zero...

0.999 does not equal 1

and yes the plane does take off

The question is a typical bar room bet.
It is posed in a way that makes the "mug" make a false assumption.

In this case the false assumption is that because it takes you great effort to stay where you are on a moving treadle, that a plane will use its power just staying where it is.

You forget that the plane has a free running wheel, and only needs a small amount of its power to overcome the friction on that wheel, which is all that is holding it back. The rest of its power will move it forward as usual, and the plane will take off.

Like any good bar room bet, when you know the trick, you wonder how you were taken in.
I would certainly have bet a pint of beer on it.

This is just too funny. I saw the commercial for the mythbuster's episode and had to laugh and I cannot wait to watch it and see what kind of terrible hypotheses they can come up with. The answer to this problem is clearly laid out on the first page of this post and I cannot understand why this concept is so difficult to grasp for so many people in here. The plane will fly and like many have already stated there is no magical force that is going to hold the plane back when that propeller starts moving at full thrust.

Also...when you start getting into the realm of infinite series and sequences you will soon understand that 0.999...(and the '...' is extremely important as it means repeating infinitely) does so equal 1. Quick easy example: you all agree that 0.333...(repeating) = 1/3, 0.333...(repeating) x 3 = 0.999...(repeating) and 1/3 x 3 = 1, therefore 0.999...(repeating) = 1.

Only one day to go now till the mythbuster boys
finally and incontrovertably give the answer.

I hope it takes off now, since I've changed my mind.

I think a lot of people here are being clever in hindsight.
I've asked a few smart people who have never heard of the problem,
whether they think the plane will take off,
and most of them thought the plane would stay in the same spot, same as I did.
When I explained why it wouldn't, they agreed at once.

After the MythBusters airs on January 30th, someone can report the results, possibly post a YouTube video of the clip, and tell us how right they were.
The plane took off. End of story.

Except of course that the naysayers will claim that the MythBusters didn't set things up correctly. Since the correct setup is not physically achievable, this argument will never end -- that is, unless somebody live up to his promises ...

After that, this thread will be locked, and all future threads about airplanes and conveyor belts will be deleted. So if you're tired of seeing this, you only have to see it for two more weeks..

Give a bit of time for Monday morning quarterback discussions, and then lock this stupid thread. I for one say good riddance.

While we are at it, we should start a poll about 0.999... = 1 (no people, this isn't an invitation to derail this thread).
0.999 does not equal 1
Also...when you start getting into the realm of infinite series and sequences you will soon understand that 0.999...(and the '...' is extremely important as it means repeating infinitely) does so equal 1. Quick easy example: you all agree that 0.333...(repeating) = 1/3, 0.333...(repeating) x 3 = 0.999...(repeating) and 1/3 x 3 = 1, therefore 0.999...(repeating) = 1.

Come on guys, seriously.

The plane took off. End of story.

Ha ha.

You know. Normally, it feels good to be right, but this was so obvious that I just feel bad for the people who were wrong.
Not bad enough not to mock them though.

Ha ha!

The plane took off. End of story.

Ahh damn. I missed it. I'll have to catch it on YouTube.

I am on the record with a `No' vote.

Except of course that the naysayers will claim that the MythBusters didn't set things up correctly. Since the correct setup is not physically achievable, this argument will never end -- that is, unless somebody live up to his promises ... Give a bit of time for Monday morning quarterback discussions, and then lock this stupid thread. I for one say good riddance.

Talking of me, I presume?

After that, this thread will be locked, and all future threads about airplanes and conveyor belts will be deleted.

So let it be said, so let it be done.

We shall discuss this for one or two more days, then the thread will be locked.

All future threads asking this question will be locked and linked here.

Apparently, it doesn't matter how fast the wheels of a plane spin before it takes off. Myth busted.


Next up --- how fast can Discovery cancel this stupid stupid "smash lab" show.

Talking of me, I presume?
Nah. I was not referring to you. You also said
hmmmm... I think I'm beginning to change my mind....

To recap, the plane took off for the simple reason that there is no direct coupling between the rate at which the plane's wheels are rotating and the plane's air speed. Planes don't have driven wheels. All that the conveyor belt does is make the plane's wheels rotate faster. It does not change the plane's speed.

For those that insist on endowing the conveyor with a magical ability to affect the plane's motion through its freely-rotating wheels, I insist on endowing the plane with magical wheels that have no friction. With this, the problem reverts to an irresistible force versus an unmovable object. Such discussions might be fine fodder for the philosophy forum, but not this one.

I'm still curious about the "sonic boom" pressure waves that would be created by the belt under the "catching up with the tire rim speed" infinite feedback interpretation of the problem.

Could they knock the plane into the air, potentially ?

Dang. Where are all you naysayers? It seems you had the rug pulled right out from underneath you and you just took off.

Oh, there you are. You all flew on over to the forums at the MythBusters web site, 40 pages and counting, mostly from people who are saying "They didn't set things up right", "That wasn't a real conveyor belt", "That wasn't a real airplane", or just "That video doesn't prove anything."

Dang. Where are all you naysayers? It seems you had the rug pulled right out from underneath you and you just took off.

Oh, there you are. You all flew on over to the forums at the MythBusters web site, 40 pages and counting, mostly from people who are saying "They didn't set things up right", "That wasn't a real conveyor belt", "That wasn't a real airplane", or just "That video doesn't prove anything."

LOL.. sad actually.. ;)

Dang. Where are all you naysayers? It seems you had the rug pulled right out from underneath you and you just took off.

Oh a pun. How cute.

( :) )

Oh a pun. How cute.

( :) )

It's late and I'm outta here,..but what do you call half a dozen Greek guys perving on a Mormon chick sunbaking in the Midwest?

Con voyeur belt.

Back to the physics.

Plane taking off.

http://www.youtube.com/watch?v=IbRcg3ji_Pc

The pilot. Where did they get such a deadbeat.
The commentary says he looks surprised when the plane takes off.
:rolleyes:

Ok.

MOD NOTE:

All threads about planes and conveyor belts will be locked from now until infinity.

Also DH was right and I was wrong.