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  #1  
Old 12-07-2005, 03:19 PM
bouv bouv is offline
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Will a plane on a treadmill take off?

OK, I have seen this question posted on a couple other message boards I go to, but seeing asd most of the people at those messageboards don't have a large knowledge of physics, I am posting here in hopes to get the correct answer.

Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

Can the plane take off?

I say no, because the plane will not move relative the the ground and air, and thus, very little airflow will occur over the wings (the engines will create a small amlunt, but not enough.) However, other peopel are convinced that since the wheels of a plane are free spinning, and not powered by the engines, and the engines provide thrust against the air, that somehow that makes a difference and air will flow over the wing.

So what's the real answer here>
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  #2  
Old 12-07-2005, 03:24 PM
Shagnasty Shagnasty is offline
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You need to reassure me that the other people were joking or we are going to start taking away voting rights.

Airspeed is the only thing that matters to an airplane. The speed of the wheels has nothing to do with anything. You need air flowing very quickly over the wings and tail to generate lift.

The only time an airplane can take off from a very low groundspeed if it was facing into a very strong headwind. Some small planes have been know to hover relative to the ground if they are flying directly into a very strong wind.
  #3  
Old 12-07-2005, 03:29 PM
pmwgreen pmwgreen is offline
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Quote:
Originally Posted by bouv
The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
How would that work? Would you have a sensor that monitors the rotational speed of the wheels and runs the conveyer accordingly? Let's say you pulled the plane forward using a rope attached to a truck not on the treadmill. Wouldn't this cause feedback between the wheels and the treadmill to cause the treadmill to speed up to infinity? And beyond?
  #4  
Old 12-07-2005, 03:29 PM
bouv bouv is offline
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Yeah, that's what i thought. but some of these peopel almost seemed to know what they were talking about. Well, not so much the "thrust is from the engine and has no effect on the wheels" people, but there was another line of reasoning for why it could take off.

OK, I found someone's explaination:
Quote:
The airplane moves forward in one direction, the surface of the runway moves backwards in another direction without impeding the forward movement of the airplane, and the airplanes wheels spin like mad. The only influence the runway has on the airplanes normal forward acceleration is that it roughly doubles the amount of rolling friction that the wheels need to overcome. Rolling friction is a small, even negligible, force hardly worth mentioning in comparison to the other forces that aircraft normally overcome to achieve flight.
So basically they are saying that even though the magic runway matches the speed of the wheels on the opposite direction, that dosen't matter, because it merely makes it slightly harder for the plane to move, but the plane will still move forward.
  #5  
Old 12-07-2005, 03:32 PM
tanstaafl tanstaafl is offline
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The plane would not sit there on a treadmill with just its wheels spinning either. It is the thrust of the engines that moves the plane forward, not the effect of its wheels on the ground. The wheels wouldn't exert any backwards force on the treadmill, so it wouldn't start to move. The plane would just move forward off the treadmill (and would eventually take off as normal).
  #6  
Old 12-07-2005, 03:35 PM
Finagle Finagle is offline
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Quote:
Originally Posted by bouv
Yeah, that's what i thought. but some of these peopel almost seemed to know what they were talking about. Well, not so much the "thrust is from the engine and has no effect on the wheels" people, but there was another line of reasoning for why it could take off.

OK, I found someone's explaination:


So basically they are saying that even though the magic runway matches the speed of the wheels on the opposite direction, that dosen't matter, because it merely makes it slightly harder for the plane to move, but the plane will still move forward.
That sounds right to me. The wheels aren't the things that are accelerating the plane, so the treadmill doesn't really do anything except spin them faster as the plane takes off.
  #7  
Old 12-07-2005, 03:39 PM
Shagnasty Shagnasty is offline
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I need names and voting jurisdiction. This is too unbelievable for words. I can actually relate to those Snopes type things a lot better than this.
  #8  
Old 12-07-2005, 03:39 PM
Ethilrist Ethilrist is offline
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That Newton. What a kidder.

The engines, wings, and air don't know a thing about the conveyor belt. The engines push, the plane moves forward and continues to do so unless acted upon by some other force. The engines push harder, the plane moves faster, and eventually it takes off, while the wheels (and the conveyor belt) are moving at some multiple of the plane's takeoff speed, how fast depends on how much acceleration the conveyor belt has behind it.
  #9  
Old 12-07-2005, 03:41 PM
Dante Dante is offline
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Quote:
Originally Posted by bouv
Quote:
The airplane moves forward in one direction, the surface of the runway moves backwards in another direction without impeding the forward movement of the airplane, and the airplanes wheels spin like mad. The only influence the runway has on the airplanes normal forward acceleration is that it roughly doubles the amount of rolling friction that the wheels need to overcome. Rolling friction is a small, even negligible, force hardly worth mentioning in comparison to the other forces that aircraft normally overcome to achieve flight.
Please go find this person and take away the ballpeen hammer with which they're hitting themselves in the forehead.

In your OP, basically you'd have a very loud, very big machine standing very still (relatively speaking). Just go back into that other thread, scream BERNOULLI! at them, and leave. Let them figure it out.
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  #10  
Old 12-07-2005, 03:47 PM
Finagle Finagle is offline
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Quote:
Originally Posted by Shagnasty
I need names and voting jurisdiction. This is too unbelievable for words. I can actually relate to those Snopes type things a lot better than this.
But you seem to be thinking that the conveyor build is actually conveying the airplane backwards at the same speed as the engines are moving it forward. But that shouldn't be the case unless the pilot has the brakes on. Otherwise, it's fairly easy to move the airplane against the force of the treadmill.

A thought experiment. Suppose you're on the treadmill at the gym and someone sets the speed to "WHOAH!". You're going to go flying backwards. Now, suppose you have rollerblades on. With just one finger wrapped around the handbar, you'd be able to resist the force of the treadmill no matter what the speed was set to (up until the bearings on the rollerblades started smoking.)

Now, imagine someone gave you a Wile E. Coyote-style Acme rocketpack and lit it off. What direction do you think you'd go?
  #11  
Old 12-07-2005, 03:47 PM
pmwgreen pmwgreen is offline
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I still want an explanation of the feedback between the wheels and the treadmill. It sound like any foward motion will cause the treadmill to speed up to the point where it bursts into flames. How does the plane take off from a high speed flaming conveyer belt? Unless the speed of the belt generates a headwind sufficient to let the plane take off vertically... yeah, that might work...
  #12  
Old 12-07-2005, 03:58 PM
Dag Otto Dag Otto is online now
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All I know is that when I fly, the plane has to touch down every so often in order to regain speed.
  #13  
Old 12-07-2005, 04:07 PM
scr4 scr4 is offline
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I'm with pmwgreen on this.

If it were an automobile on the treadmill, you can program the treadmill to match the speed of the wheels and make the vehicle. It's possible because the vehicle is trying to move by pushing on the treadmill surface, and you're moving the treadmill surface so it can't be pushed.

If you put an airplane on the treadmill, the airplane accelerates by pushing on the air, not the treadmill surface. If the treadmill is programmed to try to keep the plane in one spot, it will move faster and faster to try to stop the plane, but fail to do so. The plane will still move and take off. Unless the treadmill can move so fast that it overheats the wheel bearings of the airplane and causes them to fail.
  #14  
Old 12-07-2005, 04:07 PM
Hombre Hombre is offline
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I agree that the jet would surely take off, but as a thought experiment the belt is confusing.

Suppose for this thought experiment that a laser was monitoring the jet wheels and the throttle on the belt. Every little forward movement of the wheels caused an equal increase in belt speed.

Given that the jet would take off, how would the wheel/belt situation resolve itself?
  #15  
Old 12-07-2005, 04:08 PM
Finagle Finagle is offline
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Quote:
Originally Posted by pmwgreen
I still want an explanation of the feedback between the wheels and the treadmill. It sound like any foward motion will cause the treadmill to speed up to the point where it bursts into flames. How does the plane take off from a high speed flaming conveyer belt?
Well, yeah, the physics of the conveyor belt don't really work out unless the wheels are the only thing driving the plane. Otherwise you're going to have to spin the conveyor belt at infinite speeds. (Or, in real world, fast enough so that the wheels would start slipping, because there's only so fast you can drive them. The plane would take off amidst burning rubber and smoke. Landing would be a real problem.)
  #16  
Old 12-07-2005, 04:11 PM
Ike Witt Ike Witt is online now
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The question that needs to be asked is what is going to generate the lift?
  #17  
Old 12-07-2005, 04:11 PM
Hombre Hombre is offline
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Quote:
Originally Posted by Hombre
Every little forward movement of the wheels...
Wait, scratch that. "With every detected increase in wheel speed..."

Sorry. I'm confused.
  #18  
Old 12-07-2005, 04:14 PM
kanicbird kanicbird is offline
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Quote:
Imagine a plane is sitting on a massive conveyor belt, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.

Can the plane take off?
The bold is the technicality here, if the 2 match exactly the plane can't move unless there is skidding. I suspect within a foot of travel the belt would be traveling a good portion of the speed of light however. Practically the tires would blow, the wheel bearings would overheat, seize (both giving a great deal of resistance to the forward motion).

Perhaps the belt can generate a wind high enough for the plane to lift off at zero speed.
  #19  
Old 12-07-2005, 04:14 PM
Valgard Valgard is offline
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Quote:
Originally Posted by Dante
Please go find this person and take away the ballpeen hammer with which they're hitting themselves in the forehead.

In your OP, basically you'd have a very loud, very big machine standing very still (relatively speaking). Just go back into that other thread, scream BERNOULLI! at them, and leave. Let them figure it out.
No, you'd get a plane taking off from a big loud treadmill.

The plane is driven forward by the jet exhaust - tons of air moving at high speed, not by the action of the wheels. You can work it out from conservation of momentum or by keeping the center of mass of the system (plane + exhaust) constant, but no matter how you look at it the plane will move forward.

Suppose that the plane was being towed forward with a rope (the towing mechanism being located on solid ground, not on the treadmill). It'd certainly move forward no matter how fast you ran the treadmill, right? Same thing.

And IIRC the Bernoulli equation isn't really what's keeping a plane aloft, it's conservation of momentum of the fluid flow over inclined planes (wings/flaps).
  #20  
Old 12-07-2005, 04:18 PM
Quercus Quercus is offline
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Thanks Dag Otto. But just in case that's not enough:

OK, instead of a treadmill -- which as people have pointed out, has some problems with infinite speed -- consider that you have a perfectly smooth, flat, and slippery surface. For a car, that has the exact same effect as the treadmill -- if you rev the engine the car spins its wheels and doesn't move, right?

Now, what would happen to a plane on that surface? Just to make it easier, call the surface 'ice'

Or, as Otto might have said "All I know is that skiplanes, floatplanes and other planes without wheels can never possibly get off the ground."
  #21  
Old 12-07-2005, 04:29 PM
robby robby is offline
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The plane will take off.

If it makes you feel any better, it took me moment to figure this out.

To simplify, let's assume there is no wind and the plane's wheels can turn on frictionless bearings. The pilot fires up the engines. Let's figure out the net force on the plane. The engines are producing a force on the plane in the direction of travel. The plane is not yet moving, so there is no drag. Because there is a net force on the plane due to engine's thrust, the plane accelerates in the direction of travel relative to the ground (and the air). As the plane starts moving relative to ground (and the air), the treadmill kicks up. However (and this is very important), because I have frictionless bearings, no force is exerted on the plane by the motion of the treadmill. The motion of the treadmill just makes the wheels spin twice as fast as they would normally.

The plane continues to accelerate relative to the ground and the air until it reaches takeoff speed, at which point it takes off. If takeoff speed is 100 mph, then the plane is moving relative to the ground (and the air) at 100 mph. At the same time, the treadmill is rolling backwards at 100 mph, so the relative speed difference between the plane and the treadmill surface at takeoff is 200 mph.

The real-world situation (with friction in the wheel bearings) simply means that the plane has to overcome a bit more friction to accelerate itself to takeoff speed.

All of you folks trying to figure out how this would work in the real world need to relax, IMHO. It's a thought experiment, for crying out loud.

And all of you folks who think that the treadmill somehow is exerting a backwards force on the plane are apparently thinking that the plane's brakes are on, or that the plane is bolted to the treadmill surface.
  #22  
Old 12-07-2005, 04:34 PM
ElvisL1ves ElvisL1ves is offline
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You got that here, right? Short answer: The conveyor belt doesn't matter. ll it will do is make the tires spin faster. The plane is pulling against the air, not the pavement. Its propulsion comes from the propeller, not the tires.
  #23  
Old 12-07-2005, 04:40 PM
Ike Witt Ike Witt is online now
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Quote:
Originally Posted by robby
The plane continues to accelerate relative to the ground and the air until it reaches takeoff speed, at which point it takes off. If takeoff speed is 100 mph, then the plane is moving relative to the ground (and the air) at 100 mph. At the same time, the treadmill is rolling backwards at 100 mph, so the relative speed difference between the plane and the treadmill surface at takeoff is 200 mph.
Again, what is genertating lift? If the plane isn't moving and there isn't flow of air over the wings what is going to get the plane into the air?
  #24  
Old 12-07-2005, 04:42 PM
robby robby is offline
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If it helps, let's now compare our plane to an automobile.

Planes accelerate due to their engines, which exert a net force on the plane due to their thrust.

Automobiles accelerate because the contact pad on the tire exerts a force on the ground, and the ground therefore exerts a reactive force on the tire. This is why cars do not accelerate well on ice, for example. Planes, however, will take off just fine on ice, because their acceleration is not dependent on ground friction.

OK, let's put our automobile on the treadmill now. The driver steps on the gas, and car begins to roll forward. As the car's wheels begin to turn, the treadmill starts up. In this situation, indeed, the car remains stationary with respect to the ground (and the air, for that matter).

The difference, folks, is that airplanes have engines that produce a net force on the plane irrespective of whether it is on the ground, on a treadmill, or in the air!

Does this help?
  #25  
Old 12-07-2005, 04:56 PM
ElvisL1ves ElvisL1ves is offline
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Quote:
Originally Posted by adam yax
Again, what is genertating lift? If the plane isn't moving and there isn't flow of air over the wings what is going to get the plane into the air?
The plane is moving, once the propeller starts turning and pushing air aft. Equal and opposite reaction, ya know. The plane's accelerating motion relative to the air generates increasing lift until it equals weight. What do you think happens normally?
  #26  
Old 12-07-2005, 04:57 PM
Xema Xema is online now
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The limitation due to tires gives the "won't take off" faction their best claim to being correct. Airliners' tires have maximum speeds, which generally are only a bit (say, 10%) faster than their low-wind, maximum-gross-weight, hot-weather, high-altitude takeoff speed. With the treadmill, the wheels will likely be turning faster than the tires can handle. The tires will fail and the plane will thus not take off.
  #27  
Old 12-07-2005, 04:57 PM
robby robby is offline
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Quote:
Originally Posted by adam yax
Again, what is genertating lift? If the plane isn't moving and there isn't flow of air over the wings what is going to get the plane into the air?
The plane is moving relative to the ground and the air. There is a flow of air over the wings.

From the website noted above:

Quote:
...more rational heads prevailed, pointing out that the airplanes do not apply their thrust via their wheels, so the conveyor belt is irrelevant to whether the airplane will takeoff.
Any analogy that you make, such as a automobile on the treamill, or a runner on a treadmill, is not a valid comparison because in those situations, the auto or the runner accelerate themselves due to action/reaction frictional forces with the surface of the treadmill. Airplanes do not accelerate themselves with their wheels!

A better analogy would be a car with a rocket engine on the back and free-spinning wheels. Such a car will accelerate just fine relative to the ground, because it's not acclerating via its wheels.

Another analogy would be a person on roller blades with a huge fan. Again they're not accelerating themselves via their wheels.
  #28  
Old 12-07-2005, 05:03 PM
robby robby is offline
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Quote:
Originally Posted by Xema
The limitation due to tires gives the "won't take off" faction their best claim to being correct. Airliners' tires have maximum speeds, which generally are only a bit (say, 10%) faster than their low-wind, maximum-gross-weight, hot-weather, high-altitude takeoff speed. With the treadmill, the wheels will likely be turning faster than the tires can handle. The tires will fail and the plane will thus not take off.
Again, this whole discussion is a thought experiment intended to enhance our understanding of physics, OK?

Einstein never actually got on a rocket travelling near the speed of light, either.

However, by thinking about what would happen if he were on a rocket travelling near the speed of light, he came up with the theory of relativity.
  #29  
Old 12-07-2005, 05:04 PM
AndrewL AndrewL is offline
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The fundamental problem here is that the original questing is sufficiently vause as to not make it clear if the airplane can move or not. Those who say the plane will not take off are reading it to mean that the treadmill will somehow be able to keep the plane from being able to move. I don't believe that this is a correct interpretation, or for that matter even physically possible.
  #30  
Old 12-07-2005, 05:13 PM
robby robby is offline
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Quote:
Originally Posted by AndrewL
The fundamental problem here is that the original questing is sufficiently vause as to not make it clear if the airplane can move or not. Those who say the plane will not take off are reading it to mean that the treadmill will somehow be able to keep the plane from being able to move. I don't believe that this is a correct interpretation, or for that matter even physically possible.
It's pretty clear to me that the people who think the airplane will remain in one place relative to the ground (and not take off) are thinking of how an automobile would act in such a situation, whether they realize it or not.
  #31  
Old 12-07-2005, 05:20 PM
robby robby is offline
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Quote:
Originally Posted by robby
It's pretty clear to me that the people who think the airplane will remain in one place relative to the ground (and not take off) are thinking of how an automobile would act in such a situation, whether they realize it or not.
People may also be thinking of a runner on a treadmill, to wit: runners don't move relative to the ground, so neither would the plane, so therefore the plane won't take off.

The mistake, of course, is thinking that the runner on a treadmill and the plane on a treadmill are valid comparisons. They are not.
  #32  
Old 12-07-2005, 05:30 PM
pmwgreen pmwgreen is offline
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Quote:
Originally Posted by Xema
The limitation due to tires gives the "won't take off" faction their best claim to being correct. Airliners' tires have maximum speeds, which generally are only a bit (say, 10%) faster than their low-wind, maximum-gross-weight, hot-weather, high-altitude takeoff speed. With the treadmill, the wheels will likely be turning faster than the tires can handle. The tires will fail and the plane will thus not take off.
Well, if the belt is matching the forward speed of the plane, (which is probably what was intended) the wheels are forced to spin at precisely twice that. So, ignoring wind, what is the ratio of the maximum-gross-weight, hot-weather, high-altitude takeoff speed to the unloaded, cold dry air, sea-level takeoff speed? If it's higher than 2:1, the plane should be able to take off before the wheels melt if you do it in Boston, in December.
  #33  
Old 12-07-2005, 05:32 PM
Xema Xema is online now
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Quote:
Originally Posted by robby
Again, this whole discussion is a thought experiment intended to enhance our understanding of physics, OK?
Definitely okay with me.

My first thought was that the plane will obviously take off because there's no way for the treadmill to exert a force to match that supplied by the engines. Engine force => acceleration => airspeed => flight.

My second thought was that there's more than one way for the treadmill to interfere with a takeoff - such as by causing tires to fail.
  #34  
Old 12-07-2005, 05:32 PM
Rick Rick is offline
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In my sick twisted mind I found it easiest to compare the airplane to a water skier on a river.
Assume that the skier can swim (ski off course) @ 3mph.
Current is 3 mph
What happens if he tries to swim upstream? He goes no where because 3-3 = 0
Now he puts on his ski and grabs the the rope. The boat takes off up stream. Does the skier stay in the same place? No because he is being towed by the rope. Change the rope for a jet engine and you have your answer.
  #35  
Old 12-07-2005, 05:39 PM
Xema Xema is online now
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Originally Posted by pmwgreen
the plane should be able to take off before the wheels melt if you do it in Boston, in December.
In a good stiff headwind (by no means rare in December, in Boston).

Note that the wheels don't melt - the tires fail (which admittedly can lead to wheel damage - or worse).
  #36  
Old 12-07-2005, 05:43 PM
robby robby is offline
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Quote:
Originally Posted by Xema
...My second thought was that there's more than one way for the treadmill to interfere with a takeoff - such as by causing tires to fail.
It's realists like yourself who make life hard for physics teachers.

Back when I taught college physics, I took pains to always state any simplifying assumptions on tests and quizzes to head off such questions, such as assuming free-fall, or a frictionless surface, or frictionless pulleys, etc. Not doing so, IMHO, was just sloppy test-writing.
  #37  
Old 12-07-2005, 05:44 PM
Hombre Hombre is offline
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Quote:
Originally Posted by Rick
In my sick twisted mind I found it easiest to compare the airplane to a water skier on a river.
Assume that the skier can swim (ski off course) @ 3mph.
Current is 3 mph
What happens if he tries to swim upstream? He goes no where because 3-3 = 0
Now he puts on his ski and grabs the the rope. The boat takes off up stream. Does the skier stay in the same place? No because he is being towed by the rope. Change the rope for a jet engine and you have your answer.
Except the river doesn't accelerate.

I get the jet being towed analogy. It will take off. What I'm having trouble picturing is the concept that if the wheels move forward then the belt isn't matching the speed of the wheels.
  #38  
Old 12-07-2005, 05:53 PM
ElvisL1ves ElvisL1ves is offline
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Quote:
Originally Posted by Xema
Note that the wheels don't melt - the tires fail (which admittedly can lead to wheel damage - or worse).
If aircraft tires get hot enough, there's a plug of rubber, made to melt at a lower temperature than the carcass, which will let the air deflate gradually and, in theory, prevent an explosive blowout. That is usually only a consideration on heavy braking, though.
  #39  
Old 12-07-2005, 05:55 PM
Fish Fish is offline
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Hmm. Let me see if I understand this.

Let's say takeoff speed is 300 kph. The circumference of the tires is 5 m.

300 kph = 300,000 m/hr = 5,000 m/min.

The wheels would therefore be turning at 1,000 rpm across normal, level ground at takeoff speeds.

If you were to take a giant invisible hand (or a jet engine) and force the plane forward, the wheels would begin turning at a higher RPM, but the plane would still move.

When the wheels turn at a higher RPM, the conveyor belt moves faster to compensate. . . but the plane still moves. When the plane reaches takeoff velocity, the wheels would be moving at 2,000 rpm which, over level ground, would ordinarily equate to 600 kph. . . but the plane would still move forward at takeoff speed as specified.

We might see feedback between conveyor and wheel RPMs, depending on how the conveyor matches speeds: as one accelerates, the other accelerates farther to compensate. With frictionless bearings this is immaterial, at least until the plane's wheels leave the treadmill at 2,000 rpm and hit level ground. (With a treadmill long enough for takeoff, even this is immaterial.)

Have I got it right?
  #40  
Old 12-07-2005, 05:58 PM
A.R. Cane A.R. Cane is offline
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INA aeronautical engineer, but I doubt that a prop driven plane will generate enough airflow over the wings to create lift. I am sure that a jet would not take off. No forward movement, no airflow, no lift, no flight. The wheels have absolutely nothing to do with it. Try this another way. You have a very long cable secured to the tail end of a jet aircraft and secured to an immovable object, if you believe that a plane can take off from a treadmill (w/ no forward movement), then the jet on the tether will also take off? I don't think so. Again, no airflow, no lift, no flight.
Maybe a small prop plane w/ a very powerful engine might take off, but this would be from the airflow generated by the engine. Think about this, when a jet lands on a carrier the pilot immediately applies full power in case he/she misses the trap and doesn't reduce power until the aircraft is almost at a standstill.
  #41  
Old 12-07-2005, 06:01 PM
Xema Xema is online now
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Quote:
Originally Posted by ElvisL1ves
If aircraft tires get hot enough, there's a plug of rubber, made to melt at a lower temperature than the carcass, which will let the air deflate gradually and, in theory, prevent an explosive blowout. That is usually only a consideration on heavy braking, though.
Right. My understanding is that the overspeed failures are mostly from centrifugal force, not heat. I was told this by a guy who flew the Concorde. He said you had to be quite careful to rotate and lift off the runway at the right speed, as there was often less than 10kts of safety margin for tire failure.
  #42  
Old 12-07-2005, 06:01 PM
RipCurl RipCurl is offline
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Quote:
Originally Posted by AndrewL
The fundamental problem here is that the original questi[o]n is sufficiently vau[g]e as to not make it clear if the airplane can move or not. Those who say the plane will not take off are reading it to mean that the treadmill will somehow be able to keep the plane from being able to move.
Bingo. I'm a member on the board where this question (to my knowledge) was originally posted, before the avweb guys caught wind of it. It is a pilot forum, flightinfo.com. Anyways, there are 2 types of people who read this question.

Person A reads it as: airplane moves forward at 5 knots (with reference to a stationary object), belt moves backward at 5 knots, wheels turn at ten knots. The airplane will take off shortly.

Person B reads it as: airplane begins to move forward (again, with reference to a stationary object), the belt speeds up to the point where friction from the wheel bearings equals the airplane's thrust. Obviously, this is practically impossible, but if the belt is infinitely fast and the wheels and bearings are infinitely strong, the airplane goes NOWHERE.

The whole debate is confused because half of the people are talking speeds and the other half are talking forces. Seeing as how we are talking about a 200' wide conveyer belt that is capable of infinite speed, I'm going to say that we can also have superwheels and superbearings, and as a result I take side with the force people.
  #43  
Old 12-07-2005, 06:03 PM
robby robby is offline
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Quote:
Originally Posted by Hombre
...What I'm having trouble picturing is the concept that if the wheels move forward then the belt isn't matching the speed of the wheels.
Assuming no skidding, the belt does match the speed of the wheels.

More precisely, at the point of contact between a wheel and the surface of the treadmill, there is no relative motion between the wheel and the surface. That's how wheels work.

To illustrate, take the treadmill out of the situation, and consider a wheel on normal pavement. If a car (or plane) is moving forward at 30 mph, then the linear velocity of the wheel at the point of contact is -30 mph (30 mph backwards) relative to the car. Relative to the ground, the linear velocity of the tire at the point of contact is zero (30 mph due to the forward motion of the auto minus 30 mph due to the rotation of the wheel, which is backwards relative to the car at the point of contact).

Note that the linear velocity of the top of the tire is 30 mph forward relative to the car, and as the car's velocity is 30 mph, the linear velocity of the top of the tire is 60 mph forward relative to the ground.
  #44  
Old 12-07-2005, 06:04 PM
Xema Xema is online now
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Quote:
Originally Posted by A.R. Cane
INA aeronautical engineer, but I doubt that a prop driven plane will generate enough airflow over the wings to create lift.
True - but it doesn't need to. It simply uses its engine to accelerate to a normal takeoff airspeed. The fact that the wheels are spinning unusually rapidly is, to a first approximation, irrelevant.
  #45  
Old 12-07-2005, 06:13 PM
Frylock Frylock is online now
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Here's another way to explain why the plane will move and will take off.

Imagine the conveyer is designed, not just to meet, but to exceed the plane's wheels' speed. So even when the plane is standing still, the conveyer is moving.

(As has been mentioned, frictionless wheel mechanisms should be assumed here to stay within the spirit of the thought experiment.)

Will the conveyer's movement cause the plane to go backwards when the plane's engine is not providing thrust? No--the plane's wheels will turn but the plane itself will stay in place.

This means the movement of the conveyer belt has no effect on the motion of the plane.

And nothing changes about this fact just because the engine starts up and provides forward thrust.

(BTW I started out thinking the plane would stay still but posts on this thread showed me otherwise.)

-FrL-
  #46  
Old 12-07-2005, 06:18 PM
robby robby is offline
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Quote:
Originally Posted by RipCurl
Bingo. I'm a member on the board where this question (to my knowledge) was originally posted, before the avweb guys caught wind of it. It is a pilot forum, flightinfo.com. Anyways, there are 2 types of people who read this question.

Person A reads it as: airplane moves forward at 5 knots (with reference to a stationary object), belt moves backward at 5 knots, wheels turn at ten knots. The airplane will take off shortly.

Person B reads it as: airplane begins to move forward (again, with reference to a stationary object), the belt speeds up to the point where friction from the wheel bearings equals the airplane's thrust. Obviously, this is practically impossible, but if the belt is infinitely fast and the wheels and bearings are infinitely strong, the airplane goes NOWHERE.

The whole debate is confused because half of the people are talking speeds and the other half are talking forces. Seeing as how we are talking about a 200' wide conveyer belt that is capable of infinite speed, I'm going to say that we can also have superwheels and superbearings, and as a result I take side with the force people.
Person B's interpretation does not match the problem as stated in the OP, though:
Quote:
Originally Posted by bouv
...The conveyer belt is designed to exactly match the speed of the wheels at any given time [emphasis added], moving in the opposite direction of rotation.
The problem as stated in the OP said nothing about an infinitely fast belt. It said that it exactly matched the speed of the wheels. And since real airplanes do not have to travel infinitely fast to take off, this seems like a silly interpretation of the problem.

In any event, I don't get the impression that anyone in the discussion so far pictured the situation as depicted by Person B.

IMHO, it's much more likely people are imagining how an automobile or a runner acts on a treadmill, which is not a valid comparison, as I noted previously.
  #47  
Old 12-07-2005, 06:30 PM
robby robby is offline
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Quote:
Originally Posted by A.R. Cane
INA aeronautical engineer, but I doubt that a prop driven plane will generate enough airflow over the wings to create lift.
First of all, propellor planes do not fly because they blow air over the wings. They work because the propellor accelerates air backwards, producing a reactive force forwards. Have you ever seen a plane with the propellor at the rear of the plane? How do you think those work?

Quote:
Originally Posted by A.R. Cane
I am sure that a jet would not take off.
I'm am sure that you are incorrect.

Quote:
Originally Posted by A.R. Cane
No forward movement, no airflow, no lift, no flight.
Why do you think there is no forward movement?

Quote:
Originally Posted by A.R. Cane
Try this another way. You have a very long cable secured to the tail end of a jet aircraft and secured to an immovable object, if you believe that a plane can take off from a treadmill (w/ no forward movement), then the jet on the tether will also take off? I don't think so.
Why do you think that these two situations (a tether and the treadmill) are analogous?

Quote:
Originally Posted by A.R. Cane
Think about this, when a jet lands on a carrier the pilot immediately applies full power in case he/she misses the trap and doesn't reduce power until the aircraft is almost at a standstill.
What does this have to do with anything?
  #48  
Old 12-07-2005, 06:53 PM
A.R. Cane A.R. Cane is offline
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Quote:
Originally Posted by robby
First of all, propellor planes do not fly because they blow air over the wings. They work because the propellor accelerates air backwards, producing a reactive force forwards. Have you ever seen a plane with the propellor at the rear of the plane? How do you think those work?


I'm am sure that you are incorrect.


Why do you think there is no forward movement?


Why do you think that these two situations (a tether and the treadmill) are analogous?


What does this have to do with anything?
I think many posters are misunderstanding the OP and complicating the problem w/
such things as wheel failure.
I believe the basic hypothesis is that the forward thrust of the engine(s), whether prop
or jet, is being negated by the treadmill. I maintain that an aircraft, assuming no wind
factor, needs forward movement, provided by the engine(s) thrust, to create an
airflow over the wings, thereby providing the lift necessary for flight. If the aircraft
remains stationary, relative to the ground AND the ambient air, then no lift will be
created and no flight is possible.
My aircraft carrier analogy points out that the maximum thrust of the jet engines is
insufficient to create lift because the aircraft is prevented from forward movement by
the arresting cable.
Don't we have any aeronautical engineers on the board?
  #49  
Old 12-07-2005, 07:04 PM
Weirddave Weirddave is offline
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Quote:
Originally Posted by robby


What does this have to do with anything?
It's really cool.
  #50  
Old 12-07-2005, 07:06 PM
Valgard Valgard is offline
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Quote:
Originally Posted by A.R. Cane
No forward movement, no airflow, no lift, no flight. The wheels have absolutely nothing to do with it.
If there was no forward movement then you would certainly be correct, however there will be forward movement and so the plane can fly.

Again, you must keep in mind that because the rotation of the wheels is NOT what moves the plane around, the wheels can spin at any speed, totally independent of how fast the plane is moving with respect to the fixed earth.

The jet engine produces a certain amount of force which pushes the plane forward, and this force is completely unrelated to how fast the treadmill is spinning. That's why I used the analogy of a cable pulling the plane forward rather than the exhaust "shoving" it forward, it's a little easier to visualize.

Here's a more familiar example to show why the wheels can spin at any speed you want, so long as they are not providing the force that moves the vehicle.

Get your roller blades (Perfect Physics rollerblades...no friction in the wheel bearings) and go over to the gym. Put on the skates and hop on a level treadmill. Turn on the treadmill.

No matter how fast the treadmill is spinning, you won't go anywhere - the wheels spin at the same speed as the treadmill surface and you stay at 0mph with respect to the fixed floor.

In other words, it's EXACTLY like you were standing on a smooth, frictionless surface. Play with the treadmill speed all that you want, it makes no difference, you don't move. There is NO FORCE causing you to move backward. Set the treadmill to 1mph or 100mph, you don't go anywhere, even though the skate wheels will be spinning like mad.

Now let's apply some forward thrust. Your buddy comes up behind you, standing on the floor, and starts to shove you forward. You begin to move up the treadmill at exactly the speed he is pushing. If he pushes you at 1mph, you move at 1mph, even though you've got the treadmill moving at 100mph.

And that's exactly what happens with the airplane on the conveyor belt - it's just a plane on a frictionless runway. The jet engine provides thrust which causes forward motion regardless of how slippery the runway is. The wheels can revolve at 1mph, 100mph or 1000mph, it makes no difference at all.
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