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airplane-treadmill problem


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EDIT 3: Screw it, I think it can take off. I don't care anymore. I'm done editing this post. I should just delete this whole thing.

EDIT AGAIN: So I thought about it some more. I actually don't think it would take off the more I think about it. It is possible for a plane to sit on the ground with it's engines at full blast but the brakes are on, and therefore the plane doesn't move. So on a treadmill, the plane is still stationary in relation to the outside world. Since the plane isn't moving against the air around it, there's no lift on the wings, and I don't think it would take off.

EDIT: I take what I wrote below back. I was thinking of power being driven to the wheels like in an automobile. In this case the wheels only move because the thrust of the engine is pushing the plane forward. So in reality, I don't know.

Definitely not. It's the equivalent of putting the plane on a dyno machine. It just sits there and the wheels move, nothing else. Even though engines provide thrust and move air, an engine can't fly on it's own. You need wings and airflow over/under the wings. When the plane is sitting there, there's no airflow around the wings. Nothing to lift it up.

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If the conveyer belt is going the same speed as the plane, it wouldn't. It would be like saying 6 + (- 6) does not equal 0. The plane isn't moving for air to move to create a lift on the wings. It's stationary.

Either way, get Adam and Jamie on it.

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lol...thx chris. i needed that!

btw, i remain firm in my assertion that it cannot take off. it's funny, if you actually read about this, there's tons of smart folk who swear that the whole thing is dumb and that of course it can take off and they back it up with backgrounds in physics and aviation. smart and wrong, that's what they are...

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My evidence:

A bowling ball placed on a moving platform will not stay stationary, the same with anything with wheels, there will be a 'backwards' force exerted on the wheel/ball.

therefore the plane can be moved backwards by a the treadmill.

1) If the treadmill matches the foward speed of the plane, it will probaly not be moving enough to prevent the plane from taking off. Therefore the plane will take off.

2) If the treadmill is programed to prevent froward motion through any means nesicary, the plane will not move froward. The engines can only put out so much thrust, but the treadmill is infinite. Therefore the plane will not take off.

someone needs to do an expirement. A tiny cart on a treadmill, with a magnet on it, and another pulling it to emulate the engine. Who has a hotwheel and a tredmill at home?

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The experiment can be tested in real life, just not in full scale.

You need a variable speed belt sander (to act as the treadmill) and a gas powered RC airplane. Just scale it down. The tricky part will be in attempting to control the speed of the treadmill.

Substituting any component, as suggested above, makes the experiment invalid.

WIll it fly? I can't answer that as it would be pure speculation. Anyone stating that it will or won't is only guessing. Nobody can say for a fact either way unless they have tested it and can reproduce the same results everytime.

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not that anyone asked, but here's my take on it: first you gotta define what makes an airplane fly. everyone knows it's lift. what causes lift? higher pressure under the wing than over it. how does a wing get higher pressure under it than above it? 2 things: the shape of the wing and air passing over it. what causes air to pass over a wing? the thrust of an airplane. what does the thrust do? it moves the plane forward so it can reach a great enough speed to cause high enough pressure under the wing to achieve lift. so...

the jets fire and create thrust. the real question in this puzzle is: does the plane move forward? well, the wheels are independent and not attached to any motor. without the wheels, the plane can't roll forward. but, the treadmill counteracts the movement of the wheels. the wheels spin in place without going forward. with no forward motion, there can be no lift. no lift, no fly. period.

there will be a test on this...

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See the plane taking off and the plane moving forward are 2 different things. The lift is still going to occur because the engine force air under the wing. The plane will take off. The wheels exist to prevent frictional damage to the plane because the forward movement is a consequence of the engine firing. The air doesn't go under the wing because of the plane's forward movement.

An older style plane with a propeller at the nose wouldn't take off as easily because there is no thruster under the wings. Those planes require ground speed to build pressure under the wings. Don't quote me on this though.

EDIT: Total inversion of aerodynamics :o Plane flies because air goes over wings... :x

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Thrusters?? This isnt a space ship. A jet engine isnt much different from a propeller realy, A jet engine generally produces more force, and rather then using an airfoil to stay aloft, it kinda just angles its wing because its going faster. It still utilizes pressure (unless its a 'jump jet')

What the argument really boils down to is if the plane could move froward. Thats how planes take off, its not just ironic that they need a runway. They are not two different things (they are but if the plane moves at any speed, it follows that it oculd take off eventually)

See the plane taking off and the plane moving forward are 2 different things. The lift is still going to occur because the thrusters force air under the wing. The plane will take off. The wheels exist to prevent frictional damage to the plane because the forward movement is a consequence of the thrusters firing. The air doesn't go under the wing because of the plane's forward movement.

An older style plane with a propeller at the nose wouldn't take off as easily because there is no thruster under the wings. Those planes require ground speed to build pressure under the wings. Don't quote me on this though.

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Sorry I meant the jet engine.

EDIT: Total inversion of aerodynamics :o

EDIT 2: I guess you're right. It shouldn't take off. The explanation Cecil Adams gives is suspect. The wheels rotate at 2x the speed only if you assume that the plane is moving forward.

If the plane is moving forward at 5 mph the wheels rotate at 2pix18/(5x1.6x5)xr rps (r being the radius of the wheel in m). The wheels will spin at 2x this rate only if the plane continues to move forward at 5mph while the conveyor belt moves backwards at 5mph.

He has forgotten about relative motion. The motion of the plane is 5mph forward is actually its relative motion with regard to the conveyor belt. Hence for the plane to actually move forward at 5mph it has to move at 10mph w.r.t an observer on the Earth not standing on the belt. At 5mph wrt an observer not on the belt, it will not actually move forward, it will stay it place.

Since the belt is moving backwards, the engine does work in overcoming the static friction of the belt, and not of the Earth - hence it does not move forward wrt the ground and so does not displace additional air. So if the belt does match the plane's speed at all times (i.e. accelerates at the same rate) I agree that the plane technically shouldn't take off.

EDIT 3: Well the question states that the belt matches wheel speed all the time. The wheel speed is dependent on the plane and the conveyor belt's speed. Hence it can't actually match the wheel speed unless the plane does not move (wrt belt, i.e moves backwards with the treadmill). So there is no question of switching on the engine because the minute you do, the treadmill has to accelerate to an infinite speed. Then the whole situation breaks down.

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I get paid 15 bucks per hour for being a supplementary instructor for Physics I at my university. I'd get fired if I said the plane stayed still.

The funny thing to think about would be, if the treadmill was moving in the opposite direction, would the plane go faster? Nope.

The fallacy in most peoples' reasoning begins in the fact that in cars (which is what most people relate to), the car moves because of a torque on the wheel. On a jet engine, there's no applied torque to the wheels.

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here's another way to look at this: turn off the engines and start the treadmill. what happens? the wheels do not move and the plane moves backwards. now start the engines and apply enough thrust to counteract the treadmill. the wheels start turning and the plane stands still, right? if the thrusters can counteract the treadmill, does this mean that the treadmill can counteract the thrusters? i think the answer has to be, 'yes' as the spirit of the puzzle assumes the existence of a hypothetically totally-frictionless treadmill.

thinking is fun!

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this problem is stupid. i remember seeing it as an article for deletion on wikipedia, there was a massive debate on the articles talk page the same way.

it doesnt matter what you do to the damn wheels, the thing that makes the plane fly are the engines which work purely through the air. the most you will get is extra hot tires as there is excess friction.

Shmengie, if the brakes are on, the plane will move backwards. Otherwise the plane will slowly begin to move backwards due to friction on the axles of the plane, but the wheels will roll forwards.

this is truly close to the worlds stupidest paradox, the stupidest being found here:

http://www.logicalparadoxes.info/hempelsravens.html

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I get paid 15 bucks per hour for being a supplementary instructor for Physics I at my university. I'd get fired if I said the plane stayed still.

The funny thing to think about would be, if the treadmill was moving in the opposite direction, would the plane go faster? Nope.

The fallacy in most peoples' reasoning begins in the fact that in cars (which is what most people relate to), the car moves because of a torque on the wheel. On a jet engine, there's no applied torque to the wheels.

By that reasoning, the jet, with its engines off and the treadmill on will stay stationary because of its inertia. Inertia is a force after all, opposing any motion.

But the plane WILL begin to roll back.......

Your thinking like a physicist with pretty frictionless parts, think like an engineer :P

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Shmengie, if the brakes are on, the plane will move backwards. Otherwise the plane will slowly begin to move backwards due to friction on the axles of the plane, but the wheels will roll forwards.

hmmm...i think you're almost right. i forgot to apply total-frictionlessness to the axles of the wheels. damn, maybe that damn plane will move damnedly forward...

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I think it would move foward, but I question whether or not it would actually take off. I think the resistance would prevent the plane from getting enough speed & air flow to get off the ground, unless we are referring to a powerful jet fighter type plane. But I believe a commercial air liner would not make it off the ground.

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totally wrong as always :)

the thing most people seem to be forgetting is yes, the wheels are moving faster, but there is not that much resistance in them to slow down the plane, since we need brakes to stop a plane. Stop confusing the wheels travelling twice as fast with the plane travelling twice as fast, instead imagine a plane that is flying with gear up, with added resistances (someone left a flag sticking out of the wing, i dunno), since it is equivalent to the resistance of the extra speed, yet its too small to affect the total power generated by the engines to reach the necessary take off speed.

i believe that is the most i've ever typed in one post...and yet peter and rh explain it so much better on that page

if you want something you can imagine better, imagine a car that is on the road, and has two extra wheels attached to the doors, which are touching conveyer belts. If the belts go backward at the same speed as the four main wheels, will the car ever move forward?

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NO! YOU'RE WRONG!!! :mad:

;)

I'm so confused about what people are arguing about. It's not like it would make a difference, would we see airports start using runways out of giant conveyor belts if it's possible and would it revolutionize the way we think about traveling, airplanes, or building airports? No.

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