#271034 - 05/12/2005 02:18
Re: Will the plane fly?
[Re: JBjorgen]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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Quote:
Wrong. I know I was saying the same thing earlier in the thread, but it's not true. The belt always matches the wheels. The wheels have a mechanical limit to how fast they will spin due to friction, etc... The two speeds are 0 and the limit of the wheels.
Assuming, the point, Consider that the conveyor runs on wheels too. Far far more of them than the plane. The conveyor is going to fail far sooner than the plane's wheels.
_________________________
Glenn
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#271035 - 05/12/2005 02:51
Re: Will the plane fly?
[Re: JBjorgen]
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carpal tunnel
Registered: 12/11/2001
Posts: 7738
Loc: Toronto, CANADA
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Wow, I was going to comment on this thread when it was only at one page but I thought it would quickly die out once people realized it was just a bit of a mind teaser (the wheels have absolutely nothing to do with the answer).
If a plane crashed on the Canadian-US border, in which country would the survivors be burried?
Imagine a toy car, being held by your hand, with its wheels touching the surface of a motorized treadmill. Now imagine that treadmill moving as slowly or as fast as it can (or you want) in either direction (it doesn't matter). You can hold the car in one place, move it forward or move it backward. The force of your hand controlling the position of the car is analogous to an engine on a plane creating thrust. It moves independent of what its wheels or the treadmill are doing. It doesn't matter what color the car is, nor whether it has plastic bushings or bearings for its axles. That falls completely outside the simple scope of the original question.
I didn't read all the pages, but did anyone confirm if the plane was a private affair with an empeg installed?
Bruno
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#271036 - 05/12/2005 08:40
Re: Will the plane fly?
[Re: music]
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addict
Registered: 23/12/2002
Posts: 652
Loc: Winston Salem, NC
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Quote:
The other group thinks the question means the belt moves against the plane, in an attempt to keep the center of mass of the plane stationary.
This is how I interpreted the question. In order to take off, the plane must have some sort of airflow under the wings. With no wind present, the plane must create thrust in order to achieve air flow. If the purpose of the conveyor belt is cause the plane from thrusting forward (independent of the wheels or friction or whatever)--in other words, if the backward speed of the conveyor belt is inversely proportionate to the forward thrust of the plane--I don't think the plane would take off.
Ultra-simplified example:
Airplane’s forward speed (500 mph) - conveyor belt’s inverse speed (500 mph) = the plane is essentially stationary.
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#271037 - 05/12/2005 09:06
Re: Will the plane fly?
[Re: Cybjorg]
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carpal tunnel
Registered: 13/07/2000
Posts: 4172
Loc: Cambridge, England
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Quote:
If the purpose of the conveyor belt is cause the plane from thrusting forward (independent of the wheels or friction or whatever)--in other words, if the backward speed of the conveyor belt is inversely proportionate to the forward thrust of the plane--I don't think the plane would take off.
But the forward thrust is a force, and the backward speed of the conveyor is a speed -- they can't be directly compared.
Quote:
Ultra-simplified example:
Airplane’s forward speed (500 mph) - conveyor belt’s inverse speed (500 mph) = the plane is essentially stationary.
The plane's engines don't cause "speed" directly, they cause force. Like Newton said, force is mass times acceleration. The forces acting on the plane are thrust (forwards), friction (backwards), weight (downwards), and lift (upwards). If the forwards thrust exceeds the friction, the net forwards force is nonzero and so the acceleration is also nonzero. The plane moves relative to the rest of the airport, and so also relative to the belt. The belt simply can't apply enough force to the plane to counteract the forwards force of the engines, especially as the effective friction force on the plane does not increase with the speed of the belt. As the plane speeds up, the lift also increases until it exceeds the weight, at which point the net vertical force is upwards and the plane takes off.
Peter
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#271038 - 05/12/2005 11:02
Re: Will the plane fly?
[Re: Cybjorg]
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carpal tunnel
Registered: 14/01/2002
Posts: 2858
Loc: Atlanta, GA
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Quote:
in other words, if the backward speed of the conveyor belt is inversely proportionate to the forward thrust of the plane--I don't think the plane would take off.
The problem states that the conveyor would match the speed of the WHEELS, not the thrust of the plane. The wheels don't have to turn at all for the plane to move foward. The only reason wheels turn is due to friction, but once there is enough force the place is going to move foward no matter what is going on with the wheels. At this point the belt will be matching the speed of the wheels, but not the speed of the plane. The plane moves foward and it takes off.
_________________________
-Jeff
Rome did not create a great empire by having meetings; they did it by killing all those who opposed them.
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#271039 - 05/12/2005 18:28
Re: Will the plane fly?
[Re: JBjorgen]
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Anonymous
Unregistered
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Quote:
Quote:
The only possible speeds that the belt can match the wheels are zero and infinity. There´s no inbetween, so it´s pointless to talk about friction.
Wrong. I know I was saying the same thing earlier in the thread, but it's not true. The belt always matches the wheels. The wheels have a mechanical limit to how fast they will spin due to friction, etc... The two speeds are 0 and the limit of the wheels.
Well I figured if we have a magical conveyor belt that can accelerate to infinity then the airplane wheels could be frictionless.
The point is that the conveyor belt is impossible to build. Either something will break (the belt or the airplane wheels) or the wheels will turn faster than the belt, which means the belt failed its task.
The whole problem is a catch-22.
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#271040 - 06/12/2005 02:10
Re: Will the plane fly?
[Re: Cybjorg]
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carpal tunnel
Registered: 12/11/2001
Posts: 7738
Loc: Toronto, CANADA
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Only if the plane was bolted to the conveyor. Since it isn't, and since a plane is not propelled by its wheels, the conveyor would have no effect on the plane because it would have no effect on the thrust of its engines and therefore no effect on it forwarrd movement through the air.
It's just a simple question with the wheel business thrown in to make people forget that planes are not wheel-driven.
Direct from South Park: Nothing to see here, move along.
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#271041 - 06/12/2005 11:27
Re: Will the plane fly?
[Re: hybrid8]
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Anonymous
Unregistered
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Quote:
It's just a simple question with the wheel business thrown in to make people forget that planes are not wheel-driven.
There´s no question that the plane will gain air speed and take off due to the thrust from the engines. The confusing part is the impossibility of the conveyor belt matching the speed of the wheels.
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#271042 - 06/12/2005 11:30
Re: Will the plane fly?
[Re: hybrid8]
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veteran
Registered: 25/04/2000
Posts: 1522
Loc: Arizona
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Quote:
Only if the plane was bolted to the conveyor. Since it isn't, and since a plane is not propelled by its wheels, the conveyor would have no effect on the plane because it would have no effect on the thrust of its engines and therefore no effect on it forwarrd movement through the air.
It's just a simple question with the wheel business thrown in to make people forget that planes are not wheel-driven.
Direct from South Park: Nothing to see here, move along.
The problem is not that the plane is not wheel-driven, but whether or not the plane would have any forward velocity with respect to the surrounding air. The only reason a plane flies is because of the airflow around the airfoils (wings), which creates the pressure differential, which creates lift. With no velocity relative to the air, lift cannot be created. The whole problem boils down to, does this conveyor belt keep the plane stationary with respect to the air?
- Tim
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#271043 - 06/12/2005 13:05
Re: Will the plane fly?
[Re: Tim]
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carpal tunnel
Registered: 12/11/2001
Posts: 7738
Loc: Toronto, CANADA
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The conveyor does nothing. It's a fictitious monkey wrench. The conveyor would have to move faster to match the rotation of the wheels, but would also be adding to the rotation speed as it moved. So the effective ground "speed" (the amount of conveyor passing under wrt to the plane) would be insane. But, since the air over the wings and the plane thrust are completely independent of the ground and wheels, it will still have forward velocity and will therefore take off. The conveyor is not moving the plane backwards (and negating its propulsion/movement).
As mentioned, forget about the conveyor and the wheels - they're just there to get people down the wrong path. As can be seen by most of the posts in the thread and no doubt the dozens in the other forums where this has been posted. Reading too much into the question.
Quote:
The whole problem boils down to, does this conveyor belt keep the plane stationary with respect to the air?
The simple answer to this is NO. So we shouldn't even bother to think about seized wheels, hub friction or anything else. This is not the same as having no wheels on the plane where it rests on the conveyor. Nor having a pontoon plane on a fast current that's moving the plane backwards (so it would have to produce enough thrust to compensate for its reverse movement before it even generates positive/forward movement wrt to standing air.
I think I'll send this question out to a few dozen people at work on my last day... 
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#271046 - 06/12/2005 17:29
Re: Will the plane fly?
[Re: ithoughti]
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addict
Registered: 09/06/1999
Posts: 558
Loc: Newfoundland, Canada
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Seems so simple to me that I can't believe there is this much debate going on.
My father's Cessna has a set of skis and floats as well as wheels. The floats and skis don't rotate whatsoever but the plane will still take off. If it was sitting on a convevor belt travelling the same speed as the skis/floats then it would be that much easier for the plane to take off as the skis/floats wouldn't have any drag (other then air resistance) to hold back the plane.
In this situation I see it as being basically the same as locking up the brakes on the wheels. If the conveyor belt is to match the speed of the wheels then the wheels do not need to be rotating. The belt will simply speed up at the same rate as the plane does with it's thrust provided by the prop.
I think the question is tricking people to some degree (duh!). The runway is moving in the opposite direction of rotation compared to the wheels... however, the wheels would not actually be rotating but will still gain forward speed.
Fun question!
Rene
_________________________
12 gig empeg Mark II, SN: 080000101 30 gig RioCar SN: 30103114 My blog
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#271047 - 06/12/2005 23:15
Re: Will the plane fly?
[Re: ShadowMan]
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addict
Registered: 25/06/2002
Posts: 456
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Quote:
Seems so simple to me that I can't believe there is this much debate going on.
[...]
If it was sitting on a convevor belt travelling the same speed as the skis/floats then it would be that much easier for the plane to take off as the skis/floats wouldn't have any drag
Again, people have interpreted this badly-worded question in two ways.
You are in the first group (i.e., you think the conveyer moves with the plane).
I think that EVERYONE who interprets the question in the way you do agrees with each other:
I.e., "the question is simple, there is no debate, the plane takes off, it is totally obvious, I know planes are driven forward by their engines and not their wheels, please don't waste my time."
It is for the other group of people that this question is even remotely interesting.
I.e., the people who believe the question is asking what happens if the conveyer moves against the plane. Those are the people who can get into debates about infinitely fast belts, wheel friction, etc.
If you are not in the second group then the question is so ridiculously obvious to everyone within about 5 seconds that there is no point even talking about it.
If you are in the second group, then you have to make various assumptions about whether or not this magical belt moving against the plane could somehow "hold back" the plane against the force of the plane's engine.
Some of the noise of this debate is due to the fact that not everyone is attempting to answer the same question!
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#271048 - 06/12/2005 23:52
Re: Will the plane fly?
[Re: music]
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pooh-bah
Registered: 12/02/2002
Posts: 2298
Loc: Berkeley, California
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I'm with bruno on this one. The plane takes off.
Unideal plane, unideal conveyor belt - the belts going to fall to pieces before it has a chance of increasing the rolling resistance enough to slow the plane down. Ideal plane, ideal conveyor belt, the belt has no effect, as the plane obviously has frictionless wheels. The only way the plane doesn't take off is if you've got an unideal plane, and an ideal conveyor belt, which just isn't fair.
Matthew
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#271049 - 07/12/2005 00:00
Re: Will the plane fly?
[Re: music]
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carpal tunnel
Registered: 20/12/1999
Posts: 31565
Loc: Seattle, WA
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Quote:
If you are in the second group, then you have to make various assumptions about whether or not this magical belt moving against the plane could somehow "hold back" the plane against the force of the plane's engine.
In the other versions of the question, the ones that are worded more clearly, the wheel speed isn't even mentioned, nor is wheel rotation. They just say that the belt moves in the opposite direction of takeoff, at the same speed as the plane. (Making it obvious what they meant).
In that case, even taking into account friction, it's not a big deal because the relative speed between plane and belt doesn't need to approach infinity. The relative speed ends up being twice the plane's takeoff speed, and the plane's wheels are most likely rated for that speed because sometimes it's gotta land pretty close to that fast.
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#271050 - 07/12/2005 17:59
Re: Will the plane fly?
[Re: tfabris]
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addict
Registered: 25/06/2002
Posts: 456
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Quote:
In the other versions of the question, the ones that are worded more clearly, the wheel speed isn't even mentioned, nor is wheel rotation. They just say that the belt moves in the opposite direction of takeoff, at the same speed as the plane. (Making it obvious what they meant).
Tony, I like that version much better!
It doesn't have the ambiguities of the version here, and it avoids the need for infinities and concerns about friction and wheel rotation.
Best of all, it has one clear and unambiguous answer.
And that answer is YES. 
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#271051 - 08/12/2005 11:04
Re: Will the plane fly?
[Re: tfabris]
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Anonymous
Unregistered
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Quote:
even taking into account friction, it's not a big deal because the relative speed between plane and belt doesn't need to approach infinity. The relative speed ends up being twice the plane's takeoff speed
Tony, you´re wrong on that point. If the plane has a positive earth-ground speed, then the wheels are rotating faster than the conveyor belt.
The conveyor belt can be seen as a giant wheel attached to the earth and the plane wheels are of course attached to the plane, so we have two sets of wheels rolling against eachother. If both sets of wheels turn at the same speed (not RPM´s, but the speed of the outside diameter of the wheels) in opposite directions, then the objects they are attached to will remain stationary in relation to eachother. So that means the earth and the airplane must be stationary in relation to eachother for the plane wheels and the conveyor belt to move at the same speed in opposite directions. But of course, as we all agree, the plane WILL move forward in relation to the earth (and the air), due to the thrust from the engines, so it´s impossible for the conveyor belt to match the speed of the plane wheels.
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#271052 - 08/12/2005 11:23
Re: Will the plane fly?
[Re: ]
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Anonymous
Unregistered
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CBS = conveyor belt speed
WS = wheel speed of the airplane
AS = airplane speed in relation to the earth (which we´ll assume is the same as the air-speed, since there is no wind)
The following is a stipulation of the original problem; the conveyor belt is designed to match the speed of the wheels in the opposite direction:
CBS = -WS
The conveyor belt is what drives the free-rolling airplane wheels, so for every inch the conveyor belt moves, the wheels move an inch in the opposite direction. The wheels are also fixed to the landing gear of the airplane and the conveyor belt is fixed to the earth, so for every inch the plane moves in relation to the earth, the wheels will move forward one inch on the conveyor belt. So:
WS = -CBS + AS
So if we substitute the conveyor belt speed (CBS) with the first equation, then we have:
WS = -(-WS) + AS
or
WS = WS + AS
So if the earth/air speed of the plane (AS) is not zero, then you can clearly see that the above equation is impossible.
The impossibility comes from the equation to determine the conveyor belt speed (CBS = -WS) which was a stipulation of the original problem -- that the conveyor belt is designed to match the speed of the wheels at all times. So this conveyor belt is impossible to build, unless you can build it so that it accelerates from zero to infinity instantaneously, since zero and infinity are the only valid values for WS and CBS.
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#271053 - 08/12/2005 12:43
Re: Will the plane fly?
[Re: ]
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pooh-bah
Registered: 20/01/2002
Posts: 2085
Loc: New Orleans, LA
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Billy, He's saying that the question is worded so that the belt matches the PLANE's speed relative to the earth, not the wheels' speed. In that case, the wheels would simply be moving twice as fast.
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#271054 - 08/12/2005 13:25
Re: Will the plane fly?
[Re: lectric]
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Anonymous
Unregistered
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Ah, I see. Well then. I'd like to find whoever worded the original question and punch him in his stupid face.
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#271055 - 08/12/2005 13:47
Re: Will the plane fly?
[Re: ]
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pooh-bah
Registered: 20/01/2002
Posts: 2085
Loc: New Orleans, LA
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That being said, the question as it was worded HERE is talking about the wheels of the plane, in which case you'd be right.
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#271056 - 09/12/2005 05:14
Re: Will the plane fly?
[Re: ]
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carpal tunnel
Registered: 20/12/1999
Posts: 31565
Loc: Seattle, WA
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Quote:
Tony, you´re wrong on that point. If the plane has a positive earth-ground speed, then the wheels are rotating faster than the conveyor belt. (...) so it´s impossible for the conveyor belt to match the speed of the plane wheels...
And as I said before, in the properly-worded versions of the question, the unambiguous ones, they never talked about the conveyor having to match the wheel speed. Just the plane's speed. In that version of the question, the plane's wheels only have to spin at twice normal takeoff speed before it lifts off. My only point for bringing this up is so that the friction - infinity camps don't have to keep debating those issues.
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#271057 - 09/12/2005 06:09
Re: Will the plane fly?
[Re: tfabris]
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carpal tunnel
Registered: 13/02/2002
Posts: 3212
Loc: Portland, OR
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Quote:
My only point for bringing this up is so that the friction - infinity camps don't have to keep debating those issues.
Ah... what about the camp which figures that, as long as we have such a magical conveyor belt, we might as well also assume that other magical physics property of it being frictionless, as well?
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#271058 - 09/12/2005 16:04
Re: Will the plane fly?
[Re: canuckInOR]
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carpal tunnel
Registered: 20/12/1999
Posts: 31565
Loc: Seattle, WA
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I'm saying those discussions are moot when the question is worded properly.
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#271059 - 06/02/2006 03:32
Re: Will the plane fly?
[Re: ithoughti]
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carpal tunnel
Registered: 20/12/1999
Posts: 31565
Loc: Seattle, WA
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#271060 - 06/02/2006 04:04
Re: Will the plane fly?
[Re: tfabris]
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carpal tunnel
Registered: 17/12/2000
Posts: 2665
Loc: Manteca, California
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Fabulous, We finally hear from an expert! IE someone from more than 50 miles away with a briefcase. Or would that be since it's written on the web, it must be right. 
_________________________
Glenn
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#306717 - 31/01/2008 21:08
Re: Will the plane fly?
[Re: ithoughti]
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carpal tunnel
Registered: 25/12/2000
Posts: 16706
Loc: Raleigh, NC US
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Mythbusters did this in the most recent episode. Their experiment confirmed our conclusion: that it had little to no effect on the plane's takeoff.
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Bitt Faulk
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#306732 - 01/02/2008 13:53
Re: Will the plane fly?
[Re: wfaulk]
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addict
Registered: 11/01/2002
Posts: 612
Loc: Reading, UK
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I am repeatedly stunned by the amazing confusion about basic physics that so many people display in this kind of analysis.
If this level of science confuses people then it does help me to understand the popularity of 'faith' as a means of explanation of the world around us.
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LittleBlueThing
Running twin 30's
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#306737 - 01/02/2008 14:08
Re: Will the plane fly?
[Re: wfaulk]
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carpal tunnel
Registered: 08/03/2000
Posts: 12318
Loc: Sterling, VA
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Mythbusters did this in the most recent episode. Their experiment confirmed our conclusion: that it had little to no effect on the plane's takeoff. The only problem I had with their tests is that they didn't replicate the circumstances. In their small and large-scale tests, the plane was not matching the speed of the belt, did it? Otherwise it wouldn't move forward relative to the ground until it took off, right? I'm sure I'm missing something.
_________________________
Matt
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