[Severed Hand of Skywalker]

Originally Posted by centerchannel68 

Ugh. Some of you people are so dense. Here's an idea. Buy a foam airplane. Put some little wheels on it, maybe a plastic hotwheels car. See if it flys. Now tie a string to it, and put it on a treadmill. I promise you IT WILL NOT FLY, because it needs AIRFLOW OVER THE WINGS in order to fly, period.

Anybody who says otherwise just does not understand the very basics of why an airplane flies.

Ya that is what I was going to say.

Picture a human hang glider. He runs down a hill to get airflow over the wings and fly. If you put the same guy on a treadmill with the hang glider he will get zero airflow unless he is facing a hurricane.

[centerchannel68]

Originally Posted by Zeeb 

I have never been good at "story problems" and I have no idea, but this sounds like a good problem for the Mythbusters. Someone write them.

There really isn't anything whatsoever to bust. No moving air= no flying plane. Comprehende? It's really that simple.

[Gossamer]

Originally Posted by centerchannel68 

There really isn't anything whatsoever to bust. No moving air= no flying plane. Comprehende? It's really that simple.

But...but...but...what about some ridiculous nuance that I don't understand???

[BRussell]

I personally don't see how it could take off, but all the "smart" answers on the internet seem to suggest that it does take off. Here's an example.

First the obvious-but-wrong answer. The unwary tend to reason by analogy to a car on a conveyor belt--if the conveyor moves backward at the same rate that the car's wheels rotate forward, the net result is that the car remains stationary. An aircraft in the same situation, they figure, would stay planted on the ground, since there'd be no air rushing over the wings to give it lift. But of course cars and planes don't work the same way. A car's wheels are its means of propulsion--they push the road backwards (relatively speaking), and the car moves forward. In contrast, a plane's wheels aren't motorized; their purpose is to reduce friction during takeoff (and add it, by braking, when landing). What gets a plane moving are its propellers or jet turbines, which shove the air backward and thereby impel the plane forward. What the wheels, conveyor belt, etc, are up to is largely irrelevant. Let me repeat: Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward. This generates lift on the wings, and the plane takes off. All the conveyor belt does is, as you correctly conclude, make the plane's wheels spin madly.

That doesn't make any sense to me, but there it is.

This seems to be the key sentence: "Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward."

But I thought it was specified that the plane can't move forward relative the ground. I thought that was the assumption behind the thought experiment. :???:

[f1000]

To add to what TETENAL and Calimus have said, if a treadmill-runway's linear speed was set to be inversely proportional to a plane's axles' linear speed, then the plane's wheels should be spinning at twice the normal rate by the time the plane reaches takeoff speed. If the wheels and axles can handle such rotational velocities, and the engines' thrust can overcome the additional friction, then the plane should still be able to take off.

[f1000]

Everyone concerned with the plane's relative speed to the ground needs to study up on reactionary forces. A jet/rocket engine doesn't require something to push off against; that's why they work in air/space without any ground (or in the latter's case, even air) to push off against.

While it's true that a moving treadmill would impart negative force against the plane, this is mitigated by the fact that there's a poor transferral of this force via the relatively frictionless wheels connected to the plane.

I don't know what the upper limit for wheel rotational speed is, but rocket cars travel a whole lot faster along the ground than planes do. This doesn't necessarily mean, though, that a Boeing 747's wheels are engineered to handle double rotational speeds. Where's our German Aerobus engineer when you need him?

[centerchannel68]

But the original poster said that the plane couldn't move. Right? IF there's airflow, it can take off. Heck, a plane can take off while sitting on the ground during a thunderstorm, which is why small planes are tied down after they're done using them.

[::maroma::]

Here's a real brain tickler:

How many internet forum monkeys does it take to answer a simple aeronautical question?


My brain hurts already.

[BRussell]

Originally Posted by centerchannel68 

But the original poster said that the plane couldn't move. Right?

That's what I thought too. That's why I don't understand f1000's statement about being too concerned with speed relative to ground. How can you not be concerned with it when it's the very premise of the thought experiment?

[Calimus]

Might as well make this thread more confusing.

If you have a can filled with air in a vacuum and poke a hole in one side, we all know that the can would move in the opposite direction due to the escaping air pushing out the side of the can.

If you had a can filled with a vacuum surrounded by normal air, and poked a hole in one side, what would happen? Assuming zero G for both cases.

[Gossamer]

Originally Posted by BRussell 

I personally don't see how it could take off, but all the "smart" answers on the internet seem to suggest that it does take off. Here's an example.
That doesn't make any sense to me, but there it is.

This seems to be the key sentence: "Once the pilot fires up the engines, the plane moves forward at pretty much the usual speed relative to the ground--and more importantly the air--regardless of how fast the conveyor belt is moving backward."

But I thought it was specified that the plane can't move forward relative the ground. I thought that was the assumption behind the thought experiment. :???:

Your quote makes more sense than what i was saying. There's no way wheel speed, spinning or not, can affect the speed of the plane.

[Calimus]

After some thought, I realized a flaw in my hypothesis. Friction would actually decrease as the treadmill went faster, so you could spin the treadmill as fast as you want, but it would never be able to transfer enough energy to the plane in order to have any meaningful effect in slowing the forward motion. Therefore, even in a theoretical sense, the plan will take off.

If the problem states that the plan doesn't move, then it has nothing to do with the treadmill, there has to be some other force holding it in place.

[d4nth3m4n]

Originally Posted by centerchannel68 

But the original poster said that the plane couldn't move. Right?

actually, he didn't. therein lies the confusion.

Originally Posted by kc311v2 

I read this off another forum and I can't find the link, but the question went like this:

Imagine an airplane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the airplane take off?

notice that it doesn't seem to say anything about holding the plane at 0 ground speed. it's a common false assumption that the negative speed of the belt will hold the plane in place.

[Zeeb]

Originally Posted by centerchannel68 

There really isn't anything whatsoever to bust. No moving air= no flying plane. Comprehende? It's really that simple.

Apparently its not, considering how many posts we have here.

[voodoo]

Originally Posted by centerchannel68 

Dude, you don't know what your talking about. Groundspeed doesn't matter in an airplane..it's all about airspeed. So hypothetiically, if you put a huge FAN in front of an airplane that blew a lot of air at 300mph, the plane could take off standing 'still'. I've seen an ultralight actually take off backwards into a stiff headwind.... ie, it was facing into the wind, and the little engine it had could not move the plane forward, but the airspeed was such that the plane went into the air, and when the pilot pulled back the throttle, he was actually traveling backwards, very slowly, but still climging and flying.

You didn't understand what I wrote, I notice. I do know quite a lot about airspeed, groundspeed, planes, v1, v2, et al.

I agree with everything you wrote above, but it has nothing to do with what *I* wrote. As Dan said, imagine a rollerskate on a treadmill with the aforementioned properties.

Can you push it forward? Of course. Thus the plane will fly.

V

[voodoo]

Originally Posted by d4nth3m4n 

see, but it's not keeping the plane from moving, it's just matching the [accelerating] speed of the planes wheels. it REACTS. the plane will gain speed no matter how [amazingly] fast the wheels are spining.

da?

Precisely. /thread



V

[voodoo]

Originally Posted by centerchannel68 

Ugh. Some of you people are so dense. Here's an idea. Buy a foam airplane. Put some little wheels on it, maybe a plastic hotwheels car. See if it flys. Now tie a string to it, and put it on a treadmill. I promise you IT WILL NOT FLY, because it needs AIRFLOW OVER THE WINGS in order to fly, period.

Anybody who says otherwise just does not understand the very basics of why an airplane flies.

Pull the string babe. The thrust of the engines is utterly independant of what is happening on the ground. The only reson for carriage on a plane is to minimise friction. (helps landing as well)

As was said of the F4, with enough horsepower anything flies. (although jet engines don't create any horsepower as such )

V

[d4nth3m4n]

Originally Posted by Gossamer 

Lighten up

gotta say, it's more frustration with the </thread> crap rather than you.

[ort888]

Ok dudes, what about this. The same problem, only you have a helicopter sitting on a giant rotating platform that is spinning in the opposite direction of the blades.

Dude...

[Gossamer]

Originally Posted by Calimus 

After some thought, I realized a flaw in my hypothesis. Friction would actually decrease as the treadmill went faster

There is static friction between the wheels and the treadmill making the wheels turn, and there is kinetic friction in the wheel bearings. As you speed up, the kinetic friction in the wheel bearings would increase. That is why when you're doing a bearing selection, the projected RPM must be taken into account.

Originally Posted by ort888 

Ok dudes, what about this. The same problem, only you have a helicopter sitting on a giant rotating platform that is spinning in the opposite direction of the blades.

Dude...

If the blades are spinning at 0 RPM with respect to the air around them, there's no lift. That's why at a certain speed helicopters tend to get a bit weird. If you're traveling at 200mph and the tip of the blade is also traveling at 200mph, then on one side of the copter the blade will be doing 400mph with respect to the ground, and the other will be doing 0mph.

[analogika]

The original question is completely irrelevant.

The jets/propellers move the plane forward and make it lift off.

Whether the wheels are spinning forward, backward, or at all, is only of interest inasmuch as the wheel bearings would minutely brake the plane - or not.

It's like those shaggy-dog jokes that make you count the number of passengers on a bus over twenty stops, and the final question is what color the bus was.

[BRussell]

Originally Posted by analogika 

The original question is completely irrelevant.

The jets/propellers move the plane forward and make it lift off.

Whether the wheels are spinning forward, backward, or at all, is only of interest inasmuch as the wheel bearings would minutely brake the plane - or not.

But the plane can't move forward, because the treadmill will just speed up along with it. I don't think the question is what powers the plane to move forward - it doesn't matter that the wheels aren't themselves powering the movement. It just matters that as the plane wants to go forward, the treadmill slips beneath it, preventing it from going anywhere.

I'm completely willing to believe that it can take off, I just haven't heard any convincing reason why it should. The only thing that makes sense to me is Rob's explanation that no moving air = no flying plane.

[d4nth3m4n]

the plane's not the only thing spinning its wheels.

i'm out.

[Gossamer]

Originally Posted by BRussell 

But the plane can't move forward, because the treadmill will just speed up along with it. I don't think the question is what powers the plane to move forward - it doesn't matter that the wheels aren't themselves powering the movement. It just matters that as the plane wants to go forward, the treadmill slips beneath it, preventing it from going anywhere.

I'm completely willing to believe that it can take off, I just haven't heard any convincing reason why it should. The only thing that makes sense to me is Rob's explanation that no moving air = no flying plane.

Imagine a skate on a treadmill. You're holding a string attached to the skate. Start the treadmill, and pull on the skate. Does it move? Of course. The wheels do practically nothing to affect the velocity or acceleration of the plane.

[centerchannel68]

Originally Posted by voodoo 

You didn't understand what I wrote, I notice. I do know quite a lot about airspeed, groundspeed, planes, v1, v2, et al.

I agree with everything you wrote above, but it has nothing to do with what *I* wrote. As Dan said, imagine a rollerskate on a treadmill with the aforementioned properties.

Can you push it forward? Of course. Thus the plane will fly.

V

Ah. I didn't read it clearly. Yeah, if it can move forward.... the wheels spinning their guts out would be irrelevant, providing they don't explode due to heat buildup or centrifugal (sp?) forces.

[centerchannel68]

Originally Posted by BRussell 

But the plane can't move forward, because the treadmill will just speed up along with it. I don't think the question is what powers the plane to move forward - it doesn't matter that the wheels aren't themselves powering the movement. It just matters that as the plane wants to go forward, the treadmill slips beneath it, preventing it from going anywhere.

I'm completely willing to believe that it can take off, I just haven't heard any convincing reason why it should. The only thing that makes sense to me is Rob's explanation that no moving air = no flying plane.

Yeah but I read the question wrong. It wouldn't matter if the belt was spinning, not spinning, bla bla bla. The only reason airplanes have wheels is to reduce friction so they can attain the speed necessary for flight. I suppose, technically, there would be a speed at which point the friction of the wheels is greater than the thrust, but that speed would be way WAY higher than is necessary for the plane to lift off the belt in the first place.

Assuming the wheels and tires are super-indestructo wheels, the spinning belt would not matter. In the real world, I'm guessing the tires would overheat and explode before the thing could take off.... because basically, the belt is going to DOUBLE the rotational speed of whatever speed the plane is moving forward... thus... if liftoff is only capable above 300mph, the wheels are going to need to survive 600mph speeds in order for the plane to actually take off.

So... yeah. Wheels= just to spin, support the weight, and reduce friction. The thrust of the engines would still drive the plane forward, provided it has enough. In an ultralight with only 5hp, it might be different.

[Mithras]

Originally Posted by Gossamer 

Imagine a skate on a treadmill. You're holding a string attached to the skate. Start the treadmill, and pull on the skate. Does it move? Of course. The wheels do practically nothing to affect the velocity or acceleration of the plane.

Very very helpful example, thanks.

[BRussell]

Yes that analogy makes sense. It still doesn't make sense to me with the airplane, but I guess I'll accept it.

[JohnM15141]

No, it will not fly.

Airplanes fly due to air flowing across the lifting surfaces(airfoil). The airfoil creates lift to overcome gravity. Thrust produced by the propellor(or jet) overcomes the drag that holds the airplane stationary, the airplane will move through an airmass and air flows(wind) over the wing, this is the relative wind, which creates lift. More thrust, begets more wind over the wing, begets more lift, when lift overcomes the weight of the aircraft, it flies!

Now, in our case the conveyor belt moves the opposite direction that the airplanes thrust is pushing. For example, if our airplanes produces enough thrust to move forward 60 MPH the conveyor will move the opposite direction 60 MPH.

The aircraft is moving 60 MPH over the conveyor belt but, to us standing next to it, the airplane is not moving. Just like the fat dude on the treadmill running for all he's worth, he's not moving relative to us standing beside him amazed at how fast he is running and going nowhere. It is the same for the airmass too! There is no movement, thus no relative wind, and no lift being created. The Airplane does not fly.

However, there is the rare exception: VToL aircraft use thrust directed over lifting surfaces to create enough lift to get the airplane to fly with little or no forward movement. It will fly off our conveyor then accelerate to 60 MPH in the airmass of our example...Cool, huh? I love airplanes!

Originally Posted by kc311v2 

I read this off another forum and I can't find the link, but the question went like this:

Imagine an airplane is sitting on a massive conveyor belt, as wide and as long as a runway. The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the airplane take off?

[asd]

I am suprised the number of people who say the plane will not take off. I am a physicist and this is a pretty simple problem. It definitely WILL take off, the (linear) speed of the tires being twice that of the plane at take off.

The best analogy is the skate board on a treadmill post from earlier. The key is to imagine pulling the skate board via a string attached to it. This is equivalent to the force of the engine on the plane. As u pull the skate board up the treadmil, the wheels will spin faster than they would otherwise (by an amount equal to the speed of the treadmill). If u think about it its pretty simple, i think.


Alan

[centerchannel68]

Originally Posted by JohnM15141 

No, it will not fly.

Airplanes fly due to air flowing across the lifting surfaces(airfoil). The airfoil creates lift to overcome gravity. Thrust produced by the propellor(or jet) overcomes the drag that holds the airplane stationary, the airplane will move through an airmass and air flows(wind) over the wing, this is the relative wind, which creates lift. More thrust, begets more wind over the wing, begets more lift, when lift overcomes the weight of the aircraft, it flies!

Now, in our case the conveyor belt moves the opposite direction that the airplanes thrust is pushing. For example, if our airplanes produces enough thrust to move forward 60 MPH the conveyor will move the opposite direction 60 MPH.

The aircraft is moving 60 MPH over the conveyor belt but, to us standing next to it, the airplane is not moving. Just like the fat dude on the treadmill running for all he's worth, he's not moving relative to us standing beside him amazed at how fast he is running and going nowhere. It is the same for the airmass too! There is no movement, thus no relative wind, and no lift being created. The Airplane does not fly.

However, there is the rare exception: VToL aircraft use thrust directed over lifting surfaces to create enough lift to get the airplane to fly with little or no forward movement. It will fly off our conveyor then accelerate to 60 MPH in the airmass of our example...Cool, huh? I love airplanes!

Yeah it will, because hte friction of the wheels isn't keeping it in place. I read it like you did, where the plane had to stay stationary, but upon closer inspection, it doesn't say that. The thrust of the engines would still push the airplane forward, provided the thrust is enough to overcome the friction and drag created by spinning wheels (which is minimal). The airplane won't stand still dude. Sorry.

[JohnM15141]

Only thrust is overcoming the friction of the conveyor belt. But, thrust does not create lift, never has never will. Airflow over the airfoil creates lift. In the example no airflow is present. Also, airplanes do not care about tirespeed, never have never will. And it does not matter if the conveyor belt matches the linear speed of the tire or the rotational speed of the tires, it still results in the airplane being stationary relative to an object next to the conveyor belt. As long as there is no movement through an airmass there is no relative wind over the airfoil, no lift is generated. If the aircraft tries to accelerate to gain forward momentum the conveyor belt accelerates to match it, and the airplane still does not move relative to a stationary object. In aviation the only time tirespeed is a factor is when you exceed the designed tirespeed, the tires will fail. Thats the only number that factors in for tires on an airplane.

Originally Posted by asd 

I am suprised the number of people who say the plane will not take off. I am a physicist and this is a pretty simple problem. It definitely WILL take off, the (linear) speed of the tires being twice that of the plane at take off.

The best analogy is the skate board on a treadmill post from earlier. The key is to imagine pulling the skate board via a string attached to it. This is equivalent to the force of the engine on the plane. As u pull the skate board up the treadmil, the wheels will spin faster than they would otherwise (by an amount equal to the speed of the treadmill). If u think about it its pretty simple, i think.


Alan

[JohnM15141]

It does not say that...there is no forward motion in the example. If the conveyor belt matches the linear speed of the tire then the the conveyer belt moves backwards 1 mile as the Tire translates forward 1 mile, thus no motion relative to a stationary object. If you want it in terms of rotational speed, then the conveyer belt moves 12 inches for every 12 inches of tread that rolls over it, thus no motion relative to stationary object. No movement relative to a stationary object(say..the airmass) means no relative wind, no relative wind means no lift generated, which equals no flight.

As far as you saying "The airplane won't stand still dude." You are just adding more to the question that is not there...

Originally Posted by centerchannel68 

Yeah it will, because hte friction of the wheels isn't keeping it in place. I read it like you did, where the plane had to stay stationary, but upon closer inspection, it doesn't say that. The thrust of the engines would still push the airplane forward, provided the thrust is enough to overcome the friction and drag created by spinning wheels (which is minimal). The airplane won't stand still dude. Sorry.

[slpdLoad]

Of course it doesn't take off. No pilot is going to try to take off of a giant moving conveyor.

[JohnM15141]

ha ha! In the Navy they call it the "Cat"

A catapult launch is kinda like our conveyor belt except it hurls the airplane through the airmass and generates lift much faster then if the aircraft where to accelerate on thrust alone...

Originally Posted by slpdLoad 

Of course it doesn't take off. No pilot is going to try to take off of a giant moving conveyor.

[macgeek2005]

If the airplane on the conveyor belt did manage to take off... then the minute the back wheels lifted off the ground, the airplane would ZOOM forward, as it was technically not moving before.....

[f1000]

Originally Posted by JohnM15141 

Now, in our case the conveyor belt moves the opposite direction that the airplanes thrust is pushing. For example, if our airplanes produces enough thrust to move forward 60 MPH the conveyor will move the opposite direction 60 MPH.

Do the following thought-experiment for me. Let's assume that the plane's wheels don't in fact touch the ground. When the plane's engines begin to thrust, the plane will experience a net forward motion per Newton's laws. Now, let's envision that a conveyor belt underneath the plane, but not touching it, starts to move in an equal and opposite direction to the net forward motion of the plane. Obviously, unless it was in contact with the plane, the conveyor belt would do nothing to affect the net forward momentum of the aircraft.

Now let's add the wheels back into the mix. As long as the wheels imparted negligible friction, the conveyor belt would do little to affect the plane's forward speed. The conveyor belt might as well be made of teflon or ice.

[JohnM15141]

But that is not what is going on in the question, unless..ha ha!..you are eliminating gravity from the picture... However gravity is assumed since it as well as friction, are not specifically eliminated. i.e. all airplanes sitting on a runway are held in place by gravity, friction and inertia...the "givens" in our equation, regardless of whether its an asphalt runway or a giant imaginary conveyor belt. So thrust is required to overcome the inertia and friction of the wheels on the runway, the thrust of the aircraft engine will overcome the inertia of the airplane, friction of the wheels will be eliminated once lift is created and the wheels leave the runway, but lift will not be created until the aircrat begins moving through the airmass, the aircraft will not move through the airmass because the conveyer belt is increasing with the tire speed to keep the aircraft stationary relative to a stationary object next to the runway.

Originally Posted by f1000 

Do the following thought-experiment for me. Let's assume that the plane's wheels don't in fact touch the ground. When the plane's engines begin to thrust, the plane will experience a net forward motion per Newton's laws. Now, let's envision that a conveyor belt underneath the plane, but not touching it, starts to move in an equal and opposite direction to the net forward motion of the plane. Obviously, unless it was in contact with the plane, the conveyor belt would do nothing to affect the net forward momentum of the aircraft.

Now let's add the wheels back into the mix. As long as the wheels imparted negligible friction, the conveyor belt would do little to affect the plane's forward speed. The conveyor belt might as well be made of teflon or ice.

[Velocity211]

wasn't this part of the joy of tech comic?

[f1000]

Originally Posted by JohnM15141 

But that is not what is going on in the question, unless..ha ha!..you are eliminating gravity from the picture... However gravity is assumed since it as well as friction, are not specifically eliminated. i.e. all airplanes sitting on a runway are held in place by gravity, friction and inertia...the "givens" in our equation, regardless of whether its an asphalt runway or a giant imaginary conveyor belt. So thrust is required to overcome the inertia and friction of the wheels on the runway, the thrust of the aircraft engine will overcome the inertia of the airplane, friction of the wheels will be eliminated once lift is created and the wheels leave the runway, but lift will not be created until the aircrat begins moving through the airmass, the aircraft will not move through the airmass because the conveyer belt is increasing with the tire speed to keep the aircraft stationary relative to a stationary object next to the runway.

You're misreading the problem. The problem doesn't state that the conveyor belt moves at such a velocity as to zero the axles' net forward motion with respect to a stationary observer. For this to happen, the conveyor belt would have to slide by at some absurdly high speed to generate enough total friction to counteract the tremendous forward thrust of the plane's jet engines.

What the problem actually states is that the conveyor belt merely moves at such a velocity as to simply match that of the wheel axles' net forward motion, but in reverse. The total effect on the plane should be negligible other than to double the plane's relative velocity to the surface immediately beneath it and to slightly reduce its forward velocity with respect to the air around it. Our hypothetical conveyor-belt runway would simply cause our plane to take a little longer to reach takeoff speed.

[JohnM15141]

No you're reading more into it then is actually stated, there is no absurd speed limit imposed in the problem. The rate the conveyer belt moves can be as "absurdly" high as it needs to be to match the forward velocity of the wheels axle. As stated. If you want to add limits to the problem because it "seems" absurd, then the entire idea of a conveyer belt as big as a Runway is absurd. Thus the entire question is absurd and unanswerable. But, that is not the case here, just answer the question as presented...The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction..no limit is imposed like you are imposing into the question. There is no negligible effect, the conveyer belt simply cancels out all forward veleocity of the airplane relative to a stationary object as you said yourself: "the conveyor belt merely moves at such a velocity as to simply match that of the wheel axles' net forward motion"

Originally Posted by f1000 

You're misreading the problem. The problem doesn't state that the conveyor belt moves at such a velocity as to zero the axles' net forward motion with respect to a stationary observer. For this to happen, the conveyor belt would have to slide by at some absurdly high speed to generate enough total friction to counteract the tremendous forward thrust of the plane's jet engines.

What the problem actually states is that the conveyor belt merely moves at such a velocity as to simply match that of the wheel axles' net forward motion, but in reverse. The total effect on the plane should be negligible other than to double the plane's relative velocity to the surface immediately beneath it and to slightly reduce its forward velocity with respect to the air around it. Our hypothetical conveyor-belt runway would simply cause our plane to take a little longer to reach takeoff speed.

[Gossamer]

Originally Posted by JohnM15141 

But that is not what is going on in the question, unless..ha ha!..you are eliminating gravity from the picture... However gravity is assumed since it as well as friction, are not specifically eliminated. i.e. all airplanes sitting on a runway are held in place by gravity, friction and inertia...the "givens" in our equation, regardless of whether its an asphalt runway or a giant imaginary conveyor belt. So thrust is required to overcome the inertia and friction of the wheels on the runway, the thrust of the aircraft engine will overcome the inertia of the airplane, friction of the wheels will be eliminated once lift is created and the wheels leave the runway, but lift will not be created until the aircrat begins moving through the airmass, the aircraft will not move through the airmass because the conveyer belt is increasing with the tire speed to keep the aircraft stationary relative to a stationary object next to the runway.

The airplane moves because the jet engines create force. The conveyer belt can in no way impede the plane's ability to move relative to an outside object.

[JohnM15141]

So, you are saying, a man running on a treadmill moves because his muscles create force and the treadmill in no way impedes his ability to move relative to an outside object?

So for example, me(stationary object,) standing next to him, am wondering why(based on what you have said) he does not move? Since the treadmill should as you say in no way impede his his ability to move, yet he does not move?

However you are right, the jet engine creates a force that results in work being done, the work in this case is to move the "jet" across the surface of the conveyor belt. And, as stated in the problem, is equal to and opposite of the conveyor belt: net result equaling zero movement...

Originally Posted by Gossamer 

The airplane moves because the jet engines create force. The conveyer belt can in no way impede the plane's ability to move relative to an outside object.

[Gossamer]

Originally Posted by JohnM15141 

So, you are saying, a man running on a treadmill moves because his muscles create force and the treadmill in no way impedes his ability to move relative to an outside object?

So for example, me(stationary object,) standing next to him, am wondering why(based on what you have said) he does not move? Since the treadmill should as you say in no way impede his his ability to move, yet he does not move?

However you are right, the jet engine creates a force that results in work being done, the work in this case is to move the "jet" across the surface of the conveyor belt. And, as stated in the problem, is equal to and opposite of the conveyor belt: net result equaling zero movement...

The man relies on friction between his shoes and the treadmill to move. An airplane does not rely on that. Attach a jet engine to a man. He'll move forward no matter how fast or slow his legs are running on the treadmill.
Once again, it's like a skate on a treadmill being pulled by a string. The force moving the skate is independent of the surface of the treadmill.

[JohnM15141]

Just as the friction between the Airplanes wheels and the conveyor belt(and its inertia) are moving the jet backwards, the work being done by the jet engine moves it forward(relative to the conveyor belt) and overcoming the friction so...

...as the man is propelled backwards by friction he pushes against the friction with his shoes on the treadmill with his muscles to propel himself forward relative to the conveyor belt...there is little difference between pushing against the friction of the treadmill and creating thrust to be propelled forward to overcome friction...

the only difference is the man is using the friction to work for him by pushing against it(at a rate equal to the conveyor belts opposite movement) propelling himself forward, the Airplane is using thrust(equal and opposite reaction) opposite to the direction of the conveyor belt, to overcome the same friction.

Adding a string tied to stationary object changes the entire problem and doesnt fit this problem...the airplane is not being towed. Your analogy doesnt fit.

Originally Posted by Gossamer 

The man relies on friction between his shoes and the treadmill to move. An airplane does not rely on that. Attach a jet engine to a man. He'll move forward no matter how fast or slow his legs are running on the treadmill.
Once again, it's like a skate on a treadmill being pulled by a string. The force moving the skate is independent of the surface of the treadmill.

[f1000]

John, when the ground is stationary, the tangential speed of the plane's wheels will equal their linear velocity. In the case of our moving conveyor belt runway, however, the tangential speed of the plane's wheels can greatly exceed their linear velocity.

It's somewhat absurd to interpet "wheel speed" as meaning tangential speed. If we did so, then we'd find that our conveyer belt runway could never match the tangential speed of an already moving wheel. As the conveyor belt began to move, the wheel would spin faster, thereby always remaining beyond the belt's reach. Our conveyer belt would only be able to maintain reverse tangential speed if the wheel's axle were stationary in the first place; thus, it's only logical that we interpret wheel speed to mean linear velocity (relative to our stationary observer).

[Gossamer]

Originally Posted by JohnM15141 

Just as the friction between the Airplanes wheels and the conveyor belt(and its inertia) are moving the jet backwards, the work being done by the jet engine moves it forward(relative to the conveyor belt) and overcoming the friction so...

...as the man is propelled backwards by friction he pushes against the friction with his shoes on the treadmill with his muscles to propel himself forward relative to the conveyor belt...there is little difference between pushing against the friction of the treadmill and creating thrust to be propelled forward to overcome friction...

the only difference is the man is using the friction to work for him by pushing against it(at a rate equal to the conveyor belts opposite movement) propelling himself forward, the Airplane is using thrust(equal and opposite reaction) opposite to the direction of the conveyor belt, to overcome the same friction.

Adding a string tied to stationary object changes the entire problem and doesnt fit this problem...the airplane is not being towed. Your analogy doesnt fit.

Okay, change 'string on front' to 'rod on back.' The plane is being propelled by a force completely and totally independent of the conveyer belt and its friction.

[f1000]

Originally Posted by f1000 

Our conveyer belt would only be able to maintain reverse tangential speed if the wheel's axle were stationary in the first place.

To expand upon this point further, interpreting "wheel speed" as meaning tangential speed sets up a tautology. Since the only way a conveyor belt could maintain reverse tangential speed with a spinning wheel is when that wheel has no initial linear velocity, then of course the plane will never achieve forward motion from such a starting situation. We've already locked the plane into a stationary position mathematically, the physics be damned.

[f1000]

Originally Posted by JohnM15141 

It does not say that...there is no forward motion in the example. If the conveyor belt matches the linear speed of the tire then the the conveyer belt moves backwards 1 mile as the Tire translates forward 1 mile, thus no motion relative to a stationary object.

No, the tire could translate forward 1 mile but ROTATE at twice the rate to accomodate the conveyor belt's moving backward 1 mile. This is the point that you keep missing: the linear velocity of the tire (as measured at the axle) does not necessarily equal the tangential velocity of the tire.

[f1000]

Originally Posted by BRussell 

I personally don't see how it could take off, but all the "smart" answers on the internet seem to suggest that it does take off. Here's an example.
That doesn't make any sense to me, but there it is.

I just read your link. Cecil explains the problem and its solution in layperson terms clearly. He even begins to point out the tautology that I stated above, but neglects to mention the special case of a wheel with no initial linear velocity.

Count this physicist retired from this thread.