Ultimate brain teaser......

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bigblockmatt
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Post by bigblockmatt » Mon Apr 16, 2007 3:58 pm

ok, tristan...i still dont get it. how can the air move over if the plane isnt moving? (or am i not reading it correctly)?
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Post by bubba » Mon Apr 16, 2007 5:11 pm

Ok, got to BS'n about this at work with a couple other guys who got this in an email. We (after an hour or so of going back and forth) started to look at the question real close.

The question says that the conveyor takes into account the planes speed then goes in the opposite direction at the same speed instantly.

Now, the conveyor (for talking purposes) is the same length and FIXED to the ground.

now, the plane is setting on the conveyor its on its wheels ready to take off and setting centered on the conveyor front to back and side to side.

Nothing is moving everything at zero.

Now the pilot applies throttle, witch then creates thrust, witch creates movement witch creates speed. plane starts forward movement on the WHEELS (the plane will not move independent of the wheels until in the air). Instantly (as per the original question) the conveyor then matches the forward movement but going reverse.

Now with forward and reverse movement being equal and opposite, and the plane still on its wheels on the conveyor there should be NO difference in the relationship of the plane and the conveyor.

With no forward movement the plane will then still be centered on the conveyor, witch means no real forward movement off the conveyor and no lift.
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Post by bigblockmatt » Mon Apr 16, 2007 5:57 pm

ya, thats what im seeing in my brain. If the plane were somehow to move, then it would be off of the conveyor.
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Post by TristanM » Mon Apr 16, 2007 6:19 pm

bigblockmatt wrote:ya, thats what im seeing in my brain. If the plane were somehow to move, then it would be off of the conveyor.
Let's go back to my rollerskates example -

You stand on a treadmill, not moving, and the treadmill is still. If you start the treadmill, you will (due to rolling friction) be pushed off the back of the treadmill.

However, if you hold on to the bar at the front, it won't take very much force to hold you in place. Agreed so far? This small amount of force would be the equivalent of a small amount of thrust from the plane's engines.

Since this amount of thrust is enough to compensate for the rolling friction, and rolling friction does not increase with the speed of the rolling wheels, regardless of how much faster the wheels spin (or the treadmill makes them spin) the plane will start to move forward relative to the treadmill if additional thrust is applied. This would be the equivalent of pulling yourself forward on the treadmill on your rollerskates even though the wheels are going like mad.

So, in the end, the plane will start to move forward relative to the earth, air will move over the wings, low pressure will be created above the wing and higher pressure beneath, and the plane will lift off the ground. It may require slightly more thrust initially to start moving, but you will take off. Just as if you pull the bar on your rollerskating treadmill hard enough you might launch yourself over it and cause yourself injury.

I had an excellent link at one point which explains it better, I'll see if I can find it again. The key to the question is understanding that an airplanes wheels have nothing to do with moving it down the runway. The thrust is being applied backward against the air the same way as it is whilst in flight.

Another way to think of it - You have a treadmill and a toy car with freely rolling wheels. Put one finger behind the car and turn the treadmill on, no matter how fast the treadmill moves, the force that you are required to apply to the back of the car to hold it in place doesn't change, i.e. - you don't have to push harder the faster the wheels spin. If you do push harder, the car will move forward with relation to the amount of force you apply and will reach the other end of the treadmill. This, I'm sure, can be demonstrating mathematically, but I am currently without any of my old high school physics notes so I won't be able to show you the equations involved.

Edit - Actually, I found that link, but I think I've made it more clear - here it is anyway, if you'd like to have a look - http://tinyurl.com/qsdu4

Edit 2.0 - In fact, I used a similar example to his, but again I think mine is more clearly stated.

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Post by Alathald » Mon Apr 16, 2007 7:38 pm

here's a very simple way to think about it:

An outside observer with a radar gun measures the speed of the airplane, which must equal the speed of the belt...Agreed?

If the radar clocks the belt at 0mph, according to the problem he must also clock the plane at 0mph...Agreed?

If the radar clocks the belt at 1mph, according to the problem he must also clock the plane at 1mph (but in the opposite direction to the belt)...Agreed?

This continues so if the radar clocks the belt at 100mph, according to the problem he must also clock the plane at 100mph (but in the opposite direction to the belt)...

And finally if the radar clocks the belt at takeoff speed, according to the problem he must also clock the plane at takeoff speed...meaning the plane is in the air!!!

Ok, I think the flaw in your logic is that the belt prevents the plane from moving but let me ask you this, If the plane doesn't move, how can the belt move to stop the plane from moving? It's a classic catch-22...

While it's true that more force (thrust) is needed because the belt is moving backward relative to the plane and there is a rolling friction, the rolling friction is not going to amount to enough to prevent the plane from reaching takeoff speed.

BTW bubba, the equal and opposite thing, is called Newton's 3rd Law and it only applies to force's, not velocities.
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Post by elkmanwsu » Tue Apr 17, 2007 2:02 am

For those of you who think the plane will take off what do you suppose will happen as soon as their is lift. You think that the plane can be on a conveyor belt essentially going nowhere to taking off full speed as soon as it gets off the ground?
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Post by TristanM » Tue Apr 17, 2007 2:51 am

:shock: :-s :| :roll: are you serious?

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Post by bubba » Tue Apr 17, 2007 4:34 am

Alathald wrote:BTW bubba, the equal and opposite thing, is called Newton's 3rd Law and it only applies to force's, not velocities.
I know, still don't think it will take off. you get speed from the forward movement of the plane, thrust vrs the speed of the tread mill have no link.

Take the wheels and turbines out, or don't pay attention to them at east, if forward movement of the plane is whats being compensated for, keeping the plane in the same spot on the treadmill, then it can't move.

I just someone that has an RC plane and a tread mill, so we can have our selves a redneck mythbusters :lol:
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Post by Illuminati » Tue Apr 17, 2007 7:07 am

bigblockmatt wrote:so, it the plane is standing still, no air is moving over the wings, no lift is produced, no flying plane - just wasted jet fuel.
The plane is moving. Nothing in the teaser said the plane is standing still. Just that if the plane is moving forward at 100MPH, then the conveyor belt is moving 100MPH in the oposite direction. So the wheels are effectively moving at 200MPH. The conveyor belt is doing nothing to prevent the forward motion provided by the jets which will get the plane up to speed as if the conveyor belt were not even there. So there will be lift on the wings just as if the conveyor belt were not even there.
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Post by bubba » Tue Apr 17, 2007 10:33 am

someone already did the RC plane on a conveyor.

http://www.youtube.com/watch?v=Tmbsd_o5 ... ed&search=
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Post by Illuminati » Tue Apr 17, 2007 12:27 pm

bubba wrote:someone already did the RC plane on a conveyor.

http://www.youtube.com/watch?v=Tmbsd_o5 ... ed&search=
Ah yes... notice how he couldn't keep the plane stationary while the belt was moving. its impossible. there are a few other related youTube videos demonstrating this as well once you watch this one.
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Post by bubba » Tue Apr 17, 2007 1:02 pm

Once the wheels matched the speed then the plane was stationary, once the plane met the same speed it moved forward.
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Re: Ultimate brain teaser......

Post by vicaphit » Tue Apr 17, 2007 1:56 pm

A plane is standing on a runway that can move (like a giant conveyor belt). This conveyor has a control system that tracks the plane’s speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction) instantly.
"Objects in motion stay in motion UNLESS acted upon by an outside force"

the conveyor is the outside force, and always moves in the opposite direction at the same sped as the plane. Therefore the plane is never in motion (except the motion of the wheels turning)

so...the plane is flying -> at 100mph, the conveyor goes the same speed in the opposite direction <- at 100mph... therefore the plane is NOT moving with respect to anything off of the conveyor. Therefore: no air is moving accross the wing, and no lift will occur.

I suppose if the wind was strong enough and the plane was pointing into the wind it would get lift and then be able to take off since the conveyor was no longer working in the opposite direction.

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Post by Alathald » Tue Apr 17, 2007 2:25 pm

Illuminati wrote:
bigblockmatt wrote:so, it the plane is standing still, no air is moving over the wings, no lift is produced, no flying plane - just wasted jet fuel.
The plane is moving. Nothing in the teaser said the plane is standing still. Just that if the plane is moving forward at 100MPH, then the conveyor belt is moving 100MPH in the oposite direction. So the wheels are effectively moving at 200MPH. The conveyor belt is doing nothing to prevent the forward motion provided by the jets which will get the plane up to speed as if the conveyor belt were not even there. So there will be lift on the wings just as if the conveyor belt were not even there.
Precisely, the problem doesn't say the speed of the conveyor belt equals the speed of the wheels, it says the speed of the conveyor belt equals the speed of the plane...Bubba (or anyone for that matter) if you can give me a good answer to my question, I'll reconsider your POV...If the plane doesn't move, how can the belt move to stop the plane from moving?

Remember, one of the key words in the question is instantaneous...

On a side note, this is a truely mature forum, we've got a somewhat heated debate here and not a single flame yet =D>
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Post by Illuminati » Tue Apr 17, 2007 3:35 pm

Bubba, in that video, the controller was feathering the throttle to keep the plane in 'about' the same place on the conveyor belt, but the plane was still doing a lot of forward and backward movement with respect to a stationary point. if the controller would not have been feathering the throttle and always had just a little bit of power, the plane always moved forward.

This video may better show what will happen...
http://www.youtube.com/watch?v=eSxUHHcf ... ed&search=

ok, I'll try one more time. :)

If this were a car, we would all be in agreement that the car would not move anywhere. The reason being, when you push the gas pedal in a car, the engine spins the car's wheels to provide the forward motion. The conveyor belt would be able to counter that force and keep the car effectively in the same place. The key here is that the wheels spin to move the car forward.

Now back to the plane... during take-off, the wheels of a plane do nothing more than provide a means of not just dragging the bottom of the plane on the ground.... ie, remove as much friction as possible.... the wheels are free rolling... meaning they have no engine like a car that provide force to spin the wheels. The force that allows a plane to pick up enough speed for take off are the turbines in the jets on the wings of the plane. Since the jets do not touch the moving conveyor belt, these forces are independent of each other. When a turbine starts spinning, it propels the air through the jet which propels the plane forward. Since the air around the plane also is independent of the speed of the conveyor belt, as the turbine spins faster, the plane is going to move forward regardless of the speed of the conveyor belt.

I suppose another way to explain my point of view is to modify the original teaser... (now I don't claim to be knowledgeable in the details of aeronautics, so I'm not claiming that this scenario is 100% possible)...
Say a plane is flying over St. Louis on its way to Kansas City at a speed of 100 MPH (small plane). While the plane is over Jefferson City, it encounters sustained 100 MPH winds in the opposite direction in which it is traveling. Will it ever get past Jefferson City?

(I'm assuming that the head winds still provide enough lift to prevent the plane from crashing, but since the wind speed is equal to the speed at which air is being forced through the jet, the plane will effectively be stationary over Jefferson City.)

make sense? or just more confusing?
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Post by TristanM » Tue Apr 17, 2007 3:51 pm

I give up trying to explain this one for now - but I have feelers out with some mathematical/physics types for a proper mathematical proof. I also suggested to Mythbusters that they do a show on it. I've sunk to embarrassing new lows to prove my point...

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Post by bigblockmatt » Tue Apr 17, 2007 4:32 pm

well, i think i see it now in my brian why it would take off. i wont try explaining it because i wouldnt to a good job.

thanks though for the GREAT explanations!!!
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Post by Alathald » Tue Apr 17, 2007 5:25 pm

Illuminati wrote:If this were a car, we would all be in agreement that the car would not move anywhere. The reason being, when you push the gas pedal in a car, the engine spins the car's wheels to provide the forward motion. The conveyor belt would be able to counter that force and keep the car effectively in the same place. The key here is that the wheels spin to move the car forward.
Even if it were a car on the belt it would still move, the trick is in the wording. Replaceing plane with car, the problem implies that the velocities (not the forces, force has nothing to do with this problem) will always be equal and opposite. So, if the car is traveling northbound at 100mph and the belt is southbound at 100mph, the speedometer in the car would read 200mph but the absolute speed of the car would be 100mph. You have to get the idea of anything 'canceling' each other out of your head because the only postulate (something that must remain true at all times) is that the velocities are equal. This means that belt can't be going 100mph and the car/plane be going 0mph because that would violate the postulate.

Lets say that were to happen and the belt is going 100mph(relative to the ground) and the car/plane be going 100mph(relative to the belt so 0mph relative to the ground). Here is the problem, you have to measure the velocities from the same reference frame. Let's measure relative to the ground, the belt moves at 100mph and the car/plane moves at 0mph; no good as it violates our postulate. OK let's try measuring the velocity relative to the belt, the car goes 100mph but the belt's speed relative to itself is always zero. That's no good because once again the postulate is violated. So, if the belt is moving 100mph relative to the ground the car/plane must also be moving relative to the ground...with a small leap of logic we can say if the belt is moving relative to the ground, the car/plane must also be moving relative to the ground.

So if the velocities must be equal and opposite and both are measured in the ground's frame of reference, when the belt is moving Xmph northbound, the car/plane must be moving Xmph southbound; the car's speedometer will read 2X and the plane will takeoff when X=takeoff speed.

Hope this helps

Remember to be consistent with your frame of reference
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Post by TristanM » Tue Apr 17, 2007 5:34 pm

Nice one Alathald. I have seen this question a few times, and it always ends in a massive thread with people on one side or the other. Then there is always a group that claims the question is worded incorrectly etc. so on, and sor forth ad nauseum. Try typing "airplane on a treadmill" into Google and see how many forums come up - unbelievable. The problem is no-one has managed to show an exact, scientific proof based in either mathematics or empirical evidence - at least not that I can find. This debate has started to bother me so much that I spent a few hours searching the internet for some properly executed experiment to answer the question once and for all - but if it's there, it's so lost amongst the arguiing that I can't find it. So back to the original point - nice one, thats the closest to the math that I've seen so far. I'll see if any of the math/physics guys come up with anything more specific...

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Post by bubba » Tue Apr 17, 2007 5:49 pm

I not saying that it won't take off, I'm saying that both instances can happen.

Instance 1. Wheel speed and conveyor speed same, witch means that there is just enough thrust to keep the plane in one spot, like holding the skate in place with your finger, but instead of the finger its enough thrust to act as the finger.

Instance 2. plane speed is increased to match the conveyor, witch means the wheels are no longer the determining factor and you get forward movement of the plane and it will take off. Like pushing the skate with your finger.

I for one would like to see this on the Mythbusters, I think it would make for a good show. I want to see the rigs they would come up with to test it, and I think they would be split just like everyone I have talked to about this.
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