Answer is yes, but those wheels will be smoking!

Think of it this way. Thrust is applied that would make the plane move 20 mph. Because it is on the ground, it rolls at 20 mph. If the ground is holding still, the plane will also move at 20 mph relative to the air around it. When you put it on the conveyor, the ground (conveyor) is moving backwards at 20 mph (relative to the air), and the planes thrust makes it move forward at 20 mph (relative to the ground). The plane will be moving forwards, but the grround will also be moving backwards. The velocity relative to the air is zero, thus no lift is created. The wheels are relveant b/c they are what lets the plane move on the ground without minimal friction. Without the wheels, the plane is sitting on the ground with jets blasting, trying to create enough thrust to slide the belly of it along the ground.

I can't understand why you think the wheels can't just turn faster. The plane's engine will push it forward and the wheels will turn. If the conveyor moves the opposite direction, the wheels will just spin faster, but the plane will continue to move forward due to the thrust of the engines. It doesn't seem complicated to envision the wheels spinning at conveyor + plane speed, so the plane is moving forward and takes off. Is there something to keep the wheels from moving faster to accommodate all influences?

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The plane will be moving forwards, but the grround will also be moving backwards. The velocity relative to the air is zero, thus no lift is created. The wheels are relveant b/c they are what lets the plane move on the ground without minimal friction. Without the wheels, the plane is sitting on the ground with jets blasting, trying to create enough thrust to slide the belly of it along the ground.

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This is wrong. First, the plane's airspeed has nothing to do with the ground. If the plane is moving forward, it is moving forward no matter what direction the "ground" is moving. You can not say that because the ground is moving backwards and the plane is moving forward the airspeed is zero. Under this logic, if a plane already in the air flies over said conveyor it would immediately lose lift because it's forward motion is canceled out by the backward motion of the conveyor. This is just not good reasoning.

The wheels are important yes, because they serve to reduce the friction force that is acting on the plane by the runway. This is the only force opposing thrust (save air resistance, but this is negligible until the plane achieves a decent speed). The wheels effectively cancel out the friction force opposing the thrust (yes there is some friction force in the thrust direction remaining, this is the friction between the wheel and the axle it rotates around, but this can be minimized with oil, etc.) THERE IS NO OTHER FORCE OPPOSING THRUST OTHER THAN THIS FRICTION FORCE. Yes a plane trying to take off on it's belly will have one hell of a time, but if the thrust is greater than the frictional force (and the runway is long enough!) THIS PLANE CAN STILL TAKE OFF! Not all planes have wheels, some have skids, and some have pontoons which they land on in water. If wheels are the reason planes take off then any plane without wheels will never take off. This, too, is wrong.

So, by your reasoning, if you have a plane on a conveyor, and the plane's engines are off, when you start the conveyor, the plane will not move. Rather the wheels will just start spinning backwards to match the conveyor's speed. Does that make any sense to you?

And don't be silly about wheels being required for takeoff. Show me a plane that can start off on the ground with it's landing gear up and takeoff. Planes on the water work fine, b/c the water doesn't create enough friction to hold the plane back. On the ground though (keeping it RELEVANT to the question), you need something to reduce friction with the ground. In this case, wheels.

Part of the question set up was that the conveyor would match the plane's speed. Now, while the plane is on the ground, it IS dependent on the wheels, not for thurst, but to reduce friction with the ground enough to allow the plane to move. So it's more the bearings that it needs to reduce friction. But, the wheels are still "stuck to the ground" in the the sense when the ground moves backwards, the plane will also. In a frictionless world, a nearly massless plane, or a zero gravity world, the *2 wheel spinning theory holds more water.

When you go to Sun & Ski Sports and you see the ski lesson place think about this problem. We'd have to change some conditions, to match this but hear me out. First, measure you speed and have the conveyor match it, and wear rollerblades. I maintain that you will hold your place, relative to the air, provided that the conveyor matches your speed. You will be constantly accelaerating due to gravity. This is a decent comparison b/c the main factors are the same. Wheels to reduce friction with the ground, thrust is applied independently of the wheels, the conveyor matches your speed.

The only wildcard here is the friction of the wheels between themselves and their axle on the plane. For the purposes of this argument, I have been considering that yes, the bearings have physical limitations that would provide some counter to the thrust of the engines, but so does the conveyor belt. I think to solve the physical problem, you have to count those as a wash. Otherwise, you would have to know the coefficient of friction, the max speed of the conveyor, max thrust of the airplane, the plane's coeefficient of friction, etc. No, there is not zero-friction in the axle, but there is also not a conveyor belt that can spin past a certain speed.

Your roller blade example is relevant in that you have an external force and wheels countering an opposing force. I still say assuming infinitely capable wheels and conveyor belt, you couldn't spin that conveyor belt fast enough to keep you from coming down. In fact, making those assumptions, you would come down according to gravity constant and the slope without regard for the wheels or the conveyor. Same is true of the plane. The conveyor and wheels are non-events unless you don't assume they're both of infinite capabilities.

Lastly, if the plane was at rest and you cranked up the conveyor belt, yes it would try to remain at rest as much as the friction in the axles would allow it. It would begin to move, but the wheels would spin much faster than the plane would move. Inertia: bodies at rest remain at rest unless a force acts on them. That force is friction from the axles, not the speed of the conveyor belt, although there will a direct correlation between the two due to the correlation between friction and rotational velocity.

If the conveyor belt moved fast enough backwards that the friction in the wheels became really significant, it wouldn't take long for the wheels to melt and the aircraft fall crashing onto the conveyor belt.

I would expect the speed required to achieve that much friction in the wheels would be much greater than twice any speed an aircraft would normally encounter on take-off or landing.

Also, consider the following scenarios:

• The aircraft is landing on the conveyor belt running in reverse at the exact speed as the aircraft is moving forward.
• There is zero friction in the wheels and the tires can handle any rotational speeds necessary. Instead of the conveyor belt matching the speed of the aircraft forward, it is running at a constant 500 mph backwards. With no friction in the wheels, the aircraft would sit still until either power or brakes are applied.
• The conveyor belt is set to run forward at the same speed as the aircraft is moving forward.

What would happen in each of them?

I thought nerds would get this....

The most important fact is that the speed of the conveyor is linked to the speed of the plane. If the plane is not moving, then the conveyor isn't. The relative speed of the wheels does not matter at all in this case. The plane doesn't care what is going on with the ground.

However, Even a car could accelerate under these conditions. The conveyor belt is driven as a set speed (according to that of the car). Lets assume that the belt is running at 50 mph (which differs from our problem statement). The cars speedometer would also read 50, but lets also assume that it has a GPS speed read out, which will read zero. If you accelerate the car (add force to the wheels), the belt will provide the necessary reaction force to allow the car to accelerate. And the speedometer would read 51, while the GPS only read 1. Now lets say we changed the belt speed to match, 51 mph hour. The car would slow down if we didn't do anything, but we could apply more gas and thus increase the force again, and the car would then read 52 on the speed and still 1 on the GPS. Apply more gas, the car reads 53 and GPS reads 2 and so on.

The belt is not frictionless, its limited in speed. The plane has no direct affect on its speed, only what the computer (reading the planes speed) tells it to run at.

The belt does not speed up on its own to negate any forward motion. It is DIRECTLY linked to the planes airspeed. The only variable that changes the speed of the conveyor is the speed of the plane. Sure, you could speed the conveyor up until the force of friction overcomes the force of the engines (or for our car, outdoes the cars top speed), but in our case, the speed of the conveyor is directly limited by the speed of the plane. No movement of the plane = no movement of the conveyor.

Moral of the story, try to understand what other people are posting and analyze it. Then give the right answer.

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So, by your reasoning, if you have a plane on a conveyor, and the plane's engines are off, when you start the conveyor, the plane will not move. Rather the wheels will just start spinning backwards to match the conveyor's speed. Does that make any sense to you?

And don't be silly about wheels being required for takeoff. Show me a plane that can start off on the ground with it's landing gear up and takeoff. Planes on the water work fine, b/c the water doesn't create enough friction to hold the plane back. On the ground though (keeping it RELEVANT to the question), you need something to reduce friction with the ground. In this case, wheels.

Part of the question set up was that the conveyor would match the plane's speed. Now, while the plane is on the ground, it IS dependent on the wheels, not for thurst, but to reduce friction with the ground enough to allow the plane to move. So it's more the bearings that it needs to reduce friction. But, the wheels are still "stuck to the ground" in the the sense when the ground moves backwards, the plane will also. In a frictionless world, a nearly massless plane, or a zero gravity world, the *2 wheel spinning theory holds more water.

When you go to Sun & Ski Sports and you see the ski lesson place think about this problem. We'd have to change some conditions, to match this but hear me out. First, measure you speed and have the conveyor match it, and wear rollerblades. I maintain that you will hold your place, relative to the air, provided that the conveyor matches your speed. You will be constantly accelaerating due to gravity. This is a decent comparison b/c the main factors are the same. Wheels to reduce friction with the ground, thrust is applied independently of the wheels, the conveyor matches your speed.

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kb2001 - UNLESS the friction in the wheels is huge, the plane will take off. If the engines were off, and the conveyor started up, the first thing that would happen is that the wheels would start to spin and the plane would barely move. That's because the planes mass is very high (mass has inertia). But the wheels aren't frictionless so the plane would start to move in the same direction as the conveyor belt.

I think we should assume the engines have enough thrust to more than comfortably exceed takeoff requirements. That should probably be far more than required to overcome the friction of wheels and tires spinning as if the plane were traveling 125 MPH. After all - car wheel bearings, etc. can easily spin at those speeds. We know planes land at speeds above 100 MPH and the plane will not stop in a reasonable distance without air brakes and reverse thrust.

One point not included in the problem is the length of the conveyor belt. Probably because it doesn't matter. If it were 10,000 feet long the plane takes off. If it were 1000 feet long it will take off quicker.

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I have been considering that yes, the bearings have physical limitations that would provide some counter to the thrust of the engines, but so does the conveyor belt. I think to solve the physical problem, you have to count those as a wash.

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The setup for the question said that the conveyor would match the speed, so the friction is applied before. This is not a wash for this reason. The conveyor's ability to go as fast as it wants was an assumption, when it was stated that it will match the plane's speed.



I think this is one for Mythbusters. There are too many factors involved to estimate it, and I don't even want to begin setting up a problem to calculate it, if I even remember how to. Both sides make sense when you ignore certain elements. I think from a standstill if you kicked on the conveyor, the plane would only remain in place if it was a hard kick start, enough to break the static coefficient of friction of the wheels. If it accelerated slowly, static friction on the bearings would be too much for them to start moving, IMO. I see both sides as feasible, but too many unknowns to make a reasonable determination.

Eric76-

For yours,

• momentum carries the plane forward. It just deccelerates faster. The friction on the wheels cannot generate enough force to stop that much momentum quickly. Key factor there is momentum.
• In a frictionless world, yes. Once force is applied forward, the plane would move forward, provided the conveyor speed remains constant. Same for brakes applied.
• This is part of the question's setup. Although a true impossibility unless each has zero speed, I think it's clear that the conveyor will move as fast as the plane would be moving if the ground were to stand still. See two very long threaeds for your answer.

[This message has been edited by kb2001 (edited 12/5/2006 5:17p).]

Another way to look at it.

You have a wagon rolling on a moving tread mill. The tread mill is set to exponentially increase to counteract the movement of the wagon. You are holding the wagons handle. You start to move the wagon forward and the belt speeds up. (assume all parts can handle the strains required and that the belt can move up to an infinite speed if necessary.

Are you telling me that you don't think that you could pull that wagon off of the treadmill without much effort, even if the wheels melted?

Now apply that to the plane. Switch the force of the pull on the handle, with the thrust provided by the engines and you have a plane that gains forward airspeed and takes off.

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I think this is one for Mythbusters.

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No it's not. No manufacturer in the world has ever created a wheel/axle system for a plane that could produce enough forward resistance (in the form of a frictional force between the wheel and the axle) to completely negate an opposing force that is the thrust from an engine. And even if they did that would be completely pointless, a plane might as well take off on skids (hmmm...oh wait sometimes they do this!) Coefficients of friction just don't exist that high in the real world. Look at the wagon wheel example above. A more realistic scenario to increase that frictional force would be to have the conveyor move at an INFINITE speed to compensate for a low coefficient of friction.

Take any wheel/axle system used in planes today and you will find that they can spin with little to know effort. To say that a jet engine can't spin that wheel is just ridiculous, just like it would be ridiculous to say you couldn't pull the wagon off the treadmill (nice example by the way)

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To say that a jet engine can't spin that wheel is just ridiculous, just like it would be ridiculous to say you couldn't pull the wagon off the treadmill (nice example by the way)

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That's not what I was saying. I was referring to the treadmill starting slowly or quickly. Too many theories and too mnay unknowns to make an accurate estimate. I think the wagon is a good example, only if you are floating above the ground. You are anchored on the ground. If a person who can easily lift 20 tons were standing on the ground next to the airplane, I'm sure he could pull the plane off the conveyor as well.

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momentum carries the plane forward. It just deccelerates faster. The friction on the wheels cannot generate enough force to stop that much momentum quickly. Key factor there is momentum.

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It would make for a lot more wear and tear on the brakes and tires.

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In a frictionless world, yes. Once force is applied forward, the plane would move forward, provided the conveyor speed remains constant. Same for brakes applied.

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The point of that scenario was that you wouldn't even have to have conveyor belt match the speed of the aircraft. Without friction and without having to worry about the tires, the speed of the conveyor belt would make no difference at all.

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This is part of the question's setup. Although a true impossibility unless each has zero speed, I think it's clear that the conveyor will move as fast as the plane would be moving if the ground were to stand still. See two very long threaeds for your answer.

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Huh?

Actually, in the third scenario, the wheels would never need to roll since the conveyor belt would autmagically adjust speed based on the application of power to the engine. Relying only on brakes to abort takeoff would be a big problem, though since the wheels wouldn't be rolling at all.

[This message has been edited by eric76 (edited 12/5/2006 7:18p).]

If the conveyor negatively matched the speed of the wheels of the plane while it is trying to get to lift off speed, the plane will sit still as far as the air is involved. Only if the air is moving over the wings will a plane take off. Why would it not be that simple?

A wind tunnel would be different and what is needed for the plane to stay in one place but lift off.

http://www.google.com/search?sourceid=navclient&ie=UTF-8&rls=GGLD,GGLD:2003-49,GGLD:en&q=can+a+plane+take+off+while+sitting+on+conveyor

The engines do not drive the wheels.

The engines move the aircraft directly.

The aircraft does not stay stationary.

The problem is that you are looking at aircraft like you do at a car. In a car, the engine propels the car forward by driving the wheels.

There is a big difference.

It must be true - it's on YouTube and they are playing "Airplane!" music in the background.
http://www.youtube.com/watch?v=IZGdUAiMcPs

One more:
http://www.youtube.com/watch?v=mAA_WbgyD8I&mode=related&search=

I'm amazed that some of you, that I assume are aggie engineers, are still arguing that the plane wouldn't take off.

Draw the free body diagram and tell me what the opposing force for the thrust of the engine is.

The only available force is friction. Lets assume we have a 100 lb thrust engine that matches the max friction available. Since we can always add a bigger engine, the next force will cause acceleration leading to airspeed leading to lift.

It's like black magic, this physics stuff...

This is so blasted simple. The wheels don't have anything to do with the plane taking off. They have no effect unless they don't spin. ANY plane takes off because of airflow on the wings. The conveyor belt doesn't affect that at all. The propellor or jet works against the air, which is stationary and unaffected by the conveyor.

The plane takes off!

Thank you Spicewood!! But apparently some people just don't get this, and it absolutely blows my mind.

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If a plane is moving thru the air at 100mph and a convery it lands on it moving at 100mph in the opposite direction, does it roll off the convery or remain in place?

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Assuming no friction in the wheel bearings, the plane keeps going forward at 100mph, its wheels accelerating to 200mph.

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Think of it this way. Thrust is applied that would make the plane move 20 mph. Because it is on the ground, it rolls at 20 mph. If the ground is holding still, the plane will also move at 20 mph relative to the air around it. When you put it on the conveyor, the ground (conveyor) is moving backwards at 20 mph (relative to the air), and the planes thrust makes it move forward at 20 mph (relative to the ground).

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That's where you mess up. Planes don't move relative to the ground, they move in relation to the air.

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The plane will be moving forwards, but the grround will also be moving backwards. The velocity relative to the air is zero

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Wrong assumption, it makes no difference what the ground is doing.


Think about this. A plane sitting on frictionless wheels would react exactly like a plane in flight. (For this example, we're not worrying about turning or cross winds.)

Assume no wind, a plane that can fly at 50mph. It takes off, and flies with the wheels 6 inches off the ground, at 50mph. Will you agree that this is exactly the same as rolling on the ground at 50mph, with frictionless wheels? (It is.) So our "conveyor" is moving opposite to our direction of flight at 50mph, and we are still flying.

A could front blows in, with winds of 50mph. The plane's speed through the air remains 50mph, according to the pilots airspeed indicator. But if you look at the speed of the plane over the ground, it is ZERO. Those wheels are still 6 inches off the ground, but they are not moving in relation to the ground. Our conveyor is stopped, and we are still flying.

Now the winds increase to 100mph. The pilot keeps the airspeed indicator at 50mph, he's still moving through the air at 50mph, but because the mass of air in which he's flying (just like a fish in a river) is moving at 100mph opposite his direction of flight, and he is moving 50mph in the direction of flight through the air, the net effect is that he is moving 50mph over the ground BACKWARDS. Our "conveyer" is going 50mph in the direction of flight, and we are still flying, and we are moving opposite to the direction out "conveyor" is going.

Confused?

http://duggmirror.com/videos_comedy/Plane_and_a_Treadmill_Problem_Explained_by_a_Canadian/

this kid explains it in a way that everyone can understand...

Good video find slim
Now I believe the plane will take off - but I don't think he's Canadian!

are we all computer nerds and completely devoid of aeronautical or mechanical engineers here? Somebody with a MS ME identify yourself and tell us the answer already!

I took Aero101 and had my highest grade while at A&M while taking it. It was all physics, but more lauching of satellite stuff. It was also my last Aero class also.

Now I'm a computer guy.
I promise I won't build airplanes if you leave my PCs alone.

well, if you were just enlightened enough to get a Mac, you would never have any trouble with the computer or any of its applications. Then nobody would ever need to touch your computer.

I'm just an stupid ChemE coming in at the end of the conversation, but I just wanted to pose a counter-example:

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he problem is that you are looking at aircraft like you do at a car.

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Okay. Let's stick wings and an jet engine on a car. Take-off would occur in two discrete intervals. First off, the car's natural engine would mechanically move the car relative to the air and the ground up to the airspeed required for takeoff. The car may lift a little bit in the air at that speed, but since its thrust has been, to this point, provided by the wheels and the wheels don't have anything solid to push against, that force is now zero. Therefore, we instantaneously engage our jet engine and instantaneously bring our car to the required air speed and we fly off.

The point is that if we put this car-plane on the conveyor belt and the conveyor belt's speed always matched the speed of the car (in an equal and opposite fashion), the speed of the car relative to the ground and the air would be zero and the vehicle would never reach takeoff speed. And that's because the wheels in this case are translating the motion of the car. Conversely, the wheels in the initial case aren't translating any movement, if the axles are frictionless. They're just spinning and providing a soft, elevated takeoff spot.

Like I said, I'm jumping in late.

[This message has been edited by SuperDave03 (edited 12/6/2006 10:16a).]

meh, trying to introduce driven wheels is a wild goose chase. In your example, the best thing you can do is put it in neutral and let the jet engine do what it would do for the plane. Your wheels are 100% countered by the conveyor in the problem.

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meh, trying to introduce driven wheels is a wild goose chase.

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I'm not chasing the answer to the initial question.

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Your wheels are 100% countered by the conveyor in the problem.

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Um, exactly. That's the point.

[This message has been edited by SuperDave03 (edited 12/6/2006 10:24a).]

The way I see it, there are two ways to frame the argument to this problem.

You could affirm the fact that the plane does take off and go into a detailed discussion regarding the physics...

or

You could provide the exception to when the plane would NOT take off and then easily show how that IS the exception to the normal system.

I think the latter is easier for people to get, since they usually have more experience with cars and feet and little experience with frictionless axles.

[This message has been edited by SuperDave03 (edited 12/6/2006 10:30a).]

SD, the driven wheels would result in an airspeed of 0 and relative to the ground of 0 as well because the conveyor would have you standing still; literally and metaphorically spinning your wheels. Plus, when you did kick in the jet engine, the fixed gear ratios of your transmission would allow the conveyor to continue to control your forward motion. Now your engine is acting as a brake against the thrust. The driven wheels would only be a hinderance to taking off and would afford no positive effect.