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  #301  
Old 04-16-2010, 03:08 AM
nicefig nicefig is offline
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Originally Posted by AClockworkMelon View Post
If the treadmill is going backwards at the same speed the wheels are spinning forward, doesn't that mean that the plane is stationary? And yes, I know that the plane doesn't use the wheels to move forward, but still, the wheel speed would be dependent on how fast the plane is moving.

But if the plane can take off in this situation, why can't it take off while remaining stationary in other situations?
Well that's the thing. It most definitely can. The original puzzle was meant to trap people who had the perception that aeroplanes were propelled by their wheels, when in fact they are propelled by air.

In other words you can introduce a conveyor belt below the craft, but all it does is increase drag in the form of friction at the wheel/belt interface.

Now imagine placing an aircraft on a conveyor belt, but this time you removed the plane's wheels. Now it's just a hunk of metal sitting on the belt. I'm sure we all know nothing is going to take off and fly in this experiment. We assume this because we have prior experience of the difficulty of moving huge objects over rough surfaces, and we intuit that no engine is powerful enough to accelerate an aircraft to takeoff velocity when it's dragging on tarmac. Well what if we used a hypothetical lubricant that reduces the coefficient of friction to 0? Well that plane would definitely take off! Now what we used wheels instead, since we know such a lubricant cannot exist? Sure, the coefficient of friction is not 0 at the moment, but it is sufficiently low enough for the engines to meet and exceed, this surplus being the net force that produces acceleration.

We should all take note that friction caused by the conveyor belt is the key to this riddle. If we do not take friction into account, the aeroplane would always take off...even if the belt was made of sandpaper and moving at the speed of light. The existence of the belt itself would be inconsequential to the riddle.

If we do however take friction into account, then yes it is possible to drive a belt fast enough such that it's friction component overcomes the force output of the craft's engine, such that the plane cannot take off. I believe this is what the original poster was trying to put across. He however grossly overestimated the practicality of such a possibility. Consider that if the presence of wheels of an aircraft decreases its coefficient of kinetic friction to 10% (compared to just the fuselage dragging along on the runway), call it 0.1--this means that the engines have to work out propelled air at an amount of force equal to 10% of the aircraft's weight just to keep it from sliding backwards with the belt.

This is where all the issues should become clear. The amount of counterproductive friction caused by the belt on the plane is a function of the plane's weight and the wheel coefficient of friction. Now even if the belt was moving at the speed of light...the friction caused by it against the plane is still the same amount as ever. Its the same amount the engineers factored into power requirements of the engine they placed on the plane. What this means is that though the fast moving belt will cause the plane to move backwards, whether at -10mph or -100,000mph, the engine would still be able to accelerate the plane back to 0mph (stationary with respect to Earth) and then to +400 or whatever the takeoff velocity is. Because the force required to do either is the same in both cases. It just a matter of time and amount of fuel available, etc.

But if we get into that, I'm not coming back to this thread.
  #302  
Old 04-16-2010, 03:22 AM
nicefig nicefig is offline
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I just want to add that the coefficient of kinetic friction is a function of the plane's weight and so any characteristic of an antagonistic runway moving below it is irrelevant. The plane will always take off.

While I also said that it is possible to manufacture a conveyor belt that COULD in fact prevent an aircraft from taking off, that would however, not be in the spirit of the original question at all since it would require the adding in of various aspects of physics that weren't required for the answering of the question in the first place.

Last edited by nicefig; 04-16-2010 at 03:22 AM.
  #303  
Old 04-16-2010, 08:45 AM
Armchair Aviator Armchair Aviator is offline
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Quote:
Originally Posted by nicefig View Post
Now imagine placing an aircraft on a conveyor belt, but this time you removed the plane's wheels. Now it's just a hunk of metal sitting on the belt. I'm sure we all know nothing is going to take off and fly in this experiment. We assume this because we have prior experience of the difficulty of moving huge objects over rough surfaces, and we intuit that no engine is powerful enough to accelerate an aircraft to takeoff velocity when it's dragging on tarmac. Well what if we used a hypothetical lubricant that reduces the coefficient of friction to 0? Well that plane would definitely take off! Now what we used wheels instead, since we know such a lubricant cannot exist? Sure, the coefficient of friction is not 0 at the moment, but it is sufficiently low enough for the engines to meet and exceed, this surplus being the net force that produces acceleration.


We should all take note that friction caused by the conveyor belt is the key to this riddle. If we do not take friction into account, the aeroplane would always take off...
An airplane faces this belly scenario in flight whenever it is in a headwind. The headwind is essentially acting as the conveyor belt. In a headwind the plane requires more thrust to maintain speed, so would not the plane on the conveyor belt require the same?

Last edited by Armchair Aviator; 04-16-2010 at 08:48 AM.
  #304  
Old 04-16-2010, 09:47 AM
Musicat Musicat is offline
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Quote:
Originally Posted by Armchair Aviator View Post
An airplane faces this belly scenario in flight whenever it is in a headwind. The headwind is essentially acting as the conveyor belt.
No, it it not. One acts on the forward airspeed, the other, on the rotational speed of the wheels. Within practical limits, the rotational speed of the wheels does not affect the forward motion of the plane.

You do know that the wheels aren't powered, like a car, don't you?
  #305  
Old 04-16-2010, 09:55 AM
Armchair Aviator Armchair Aviator is offline
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Using a boat for an example is easier...

Is a boat propelling itself forward against the current not the same as the plane propelling itself forward on the conveyor belt? If so then it would require more thrust for the plane to come up to speed just as it would the boat. This being the case, is there enough thrust available to propel the plane to take off speed?

Last edited by Armchair Aviator; 04-16-2010 at 09:59 AM.
  #306  
Old 04-16-2010, 10:21 AM
ElvisL1ves ElvisL1ves is offline
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No, it is not the same. The boat is being propelled against the water. The airplane is being propelled against the air. Not against the ground.

What do you think moves an airplane after it's in the air? Its wheels?
  #307  
Old 04-16-2010, 10:32 AM
John DiFool John DiFool is offline
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Quote:
Originally Posted by AClockworkMelon View Post
Just popping in to say that I read the article and skimmed most of the thread. This thought experiment is making my brain melt.

If the treadmill is going backwards at the same speed the wheels are spinning forward, doesn't that mean that the plane is stationary? And yes, I know that the plane doesn't use the wheels to move forward, but still, the wheel speed would be dependent on how fast the plane is moving.

But if the plane can take off in this situation, why can't it take off while remaining stationary in other situations?

Ugh, I can't wrap my brain around this.
That was my original take as well (I thought people were saying it would indeed take off while stationary, which is absurd of course). It took several rereadings before I grokked the actual point.
  #308  
Old 04-16-2010, 10:44 AM
Armchair Aviator Armchair Aviator is offline
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Originally Posted by ElvisL1ves View Post
No, it is not the same. The boat is being propelled against the water. The airplane is being propelled against the air. Not against the ground.

What do you think moves an airplane after it's in the air? Its wheels?
You are completely missing the point. A plane propelling itself "against the current" will require more thrust. There has to be some loss due to the conveyor belt moving in the opposite direction of the plane...just as if the conveyor belt was moving in the same direction of the plane it would require less thrust to get up to speed.

example:
  • On pavement a plane requires 100 knots to take off.
  • On a conveyor belt moving forward at 50 knots the plane only need produce 50 knots of thrust to take off...and then it would need to increase another 50 knots to maintain flight once airborne.
  • So would it be logical to assume that on a conveyor belt moving against the plane at 50 knots the plane would require a thrust of 150 knots to take off?

Last edited by Armchair Aviator; 04-16-2010 at 10:47 AM.
  #309  
Old 04-16-2010, 10:59 AM
Irishman Irishman is offline
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Armchair Aviator said:
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Well I guess my question is if you brought the (treadmill) plane up to speed and cut the engines, will it roll the same distance as it would on pavement?
Same distance with respect to what?

The same distance with respect to the ground? No, because the belt is moving the other direction.

The same distance with respect to a spot on the belt? Yes. If the belt is moving at a constant velocity.

AClockworkMelon said:
Quote:
If the treadmill is going backwards at the same speed the wheels are spinning forward, doesn't that mean that the plane is stationary? And yes, I know that the plane doesn't use the wheels to move forward, but still, the wheel speed would be dependent on how fast the plane is moving.
This is the root of the issue. The vague statement about the belt moving backwards at the speed of the wheels moving forward makes this an interpretation problem, not a physics problem.

If you interpret that description to mean the belt keeps the plane from moving forward, then the plane cannot take off because it gets no airspeed.

If you interpret that description to just be an attempt to describe how a treadmill responds with a car on it to keep the car in place, then the belt matches engine output, but the wheels rotate faster. Ergo, the plane moves forward, and can take off.

Quote:
But if the plane can take off in this situation, why can't it take off while remaining stationary in other situations?
Can you answer your second question now?

Armchair Aviator said:
Quote:
An airplane faces this belly scenario in flight whenever it is in a headwind. The headwind is essentially acting as the conveyor belt. In a headwind the plane requires more thrust to maintain speed, so would not the plane on the conveyor belt require the same?
As Musicat said, a headwind has a different interface to the airplane than a conveyor belt. The headwind is pushing on the airframe. The treadbelt is pushing on the bottom of the wheel. The wheel has the ability to rotate, the airframe does not.
  #310  
Old 04-16-2010, 02:16 PM
ElvisL1ves ElvisL1ves is offline
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Quote:
Originally Posted by Armchair Aviator View Post
You are completely missing the point.


Quote:
There has to be some loss due to the conveyor belt moving in the opposite direction of the plane...just as if the conveyor belt was moving in the same direction of the plane it would require less thrust to get up to speed.
A very tiny amount of rolling friction in the wheel bearings, and another very tiny amount from tire deformation, but that's all. Nothing compared to propeller thrust.

Quote:
On a conveyor belt moving forward at 50 knots the plane only need produce 50 knots of thrust to take off
Nope. The wing lift is based on the airplane's speed relative to the air, not the ground. A plane will take off faster into a headwind than a tailwind, though.

Quote:
So would it be logical to assume that on a conveyor belt moving against the plane at 50 knots the plane would require a thrust of 150 knots to take off?
Thrust is a unit of force, knots are a unit of speed. The question is nonsensical.
  #311  
Old 04-16-2010, 02:36 PM
DanBlather DanBlather is offline
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Quote:
Originally Posted by Armchair Aviator View Post
  • On pavement a plane requires 100 knots to take off.
  • On a conveyor belt moving forward at 50 knots the plane only need produce 50 knots of thrust to take off...and then it would need to increase another 50 knots to maintain flight once airborne.
  • So would it be logical to assume that on a conveyor belt moving against the plane at 50 knots the plane would require a thrust of 150 knots to take off?
That would only be true if the wheel brakes were set. If you had a plane stationary on a treadmill and then accelerated it to 50 MPH the plane's momentum would keep it relatively motionless and the wheels would spin.

In the original problem the wheels are not braked, they spin freely and impart just a small amount of motion to the plane from bearing friction.
  #312  
Old 04-16-2010, 02:42 PM
DanBlather DanBlather is offline
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It seems like there are three takes to this question:

1) A person has no idea of how planes work and just makes silly statements.
2) A person realizes that the wheels will only impart a negligible amount of movement to the plane.
3) A person understands the above, but since it is a finite amount of force you can say that there is a speed at which the treadmill's speed could be an issue (ignoring the physics of building a treadmill that can go several thousands of miles an hour)

But in the end it really comes down to whether you understand the difference between how a car moves forward and how a plane does.

Last edited by DanBlather; 04-16-2010 at 02:43 PM.
  #313  
Old 04-16-2010, 03:03 PM
ElvisL1ves ElvisL1ves is offline
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Originally Posted by ElvisL1ves View Post
Thrust is a unit of force ... the question is nonsensical
And so was that statement. Thrust is a synonym for force. Sorry.

Dan, understanding that f = m a would help too, but isn't really necessary.

Last edited by ElvisL1ves; 04-16-2010 at 03:05 PM.
  #314  
Old 04-16-2010, 03:16 PM
Armchair Aviator Armchair Aviator is offline
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Originally Posted by ElvisL1ves View Post


A very tiny amount of rolling friction in the wheel bearings, and another very tiny amount from tire deformation, but that's all. Nothing compared to propeller thrust.

Nope. The wing lift is based on the airplane's speed relative to the air, not the ground. A plane will take off faster into a headwind than a tailwind, though.

Thrust is a unit of force, knots are a unit of speed. The question is nonsensical.

Yes but the plane IS moving at 50 knots on the forward moving conveyor belt before even engaging thrust, thus receiving 50 knots of wind at rest...relative to a bystander it would be moving forward at 50 knots. Anyway this is actually not relevant as the plane in this scenario starts from a stationary position and is not moving backwards.

So the way I see it this entire debate hinges on only two factors:
  • Wheels on a runway are being pulled forward by the planes thrust.
  • Wheels on the conveyor belt are being pulled forward by the planes thrust as well the conveyor belt is slipping underneath them.

If this is of no consequence then the plane will take off the same as on a runway.

Last edited by Armchair Aviator; 04-16-2010 at 03:21 PM.
  #315  
Old 04-16-2010, 03:17 PM
ElvisL1ves ElvisL1ves is offline
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That is of no consequence and the plane will take off the same as on a runway.
  #316  
Old 04-16-2010, 03:22 PM
DanBlather DanBlather is offline
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Quote:
Originally Posted by Armchair Aviator View Post
Y
So the way I see it this entire debate hinges on only two factors:
  • Wheels on a runway are being pulled forward by the planes thrust.
  • Wheels on the conveyor belt are being pulled forward by the planes thrust as well the conveyor belt is slipping underneath them.
Except starting the treadmill moving forward at 50 mph will not move the plane with it due to inertia.
  #317  
Old 04-16-2010, 03:30 PM
Armchair Aviator Armchair Aviator is offline
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Originally Posted by DanBlather View Post
That would only be true if the wheel brakes were set. If you had a plane stationary on a treadmill and then accelerated it to 50 MPH the plane's momentum would keep it relatively motionless and the wheels would spin.

In the original problem the wheels are not braked, they spin freely and impart just a small amount of motion to the plane from bearing friction.
Agreed.
  #318  
Old 04-16-2010, 04:39 PM
Czarcasm Czarcasm is offline
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Originally Posted by DanBlather View Post
But in the end it really comes down to whether you understand the difference between how a car moves forward and how a plane does.
With a car, the wheels cause the vehicle to move. With a plane, the wheels allow the vehicle to move.
Right?
  #319  
Old 04-16-2010, 08:14 PM
Armchair Aviator Armchair Aviator is offline
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Slightly off topic but I have a question.

In a no wind situation a plane needs to reach a speed of 100 kts to create sufficient lift to take off. This would require maximum thrust for the plane in question at full capacity.

In a 50 knot head wind would the same plane still require full thrust to reach 100 kts IAS or 50 kts TAS?

Last edited by Armchair Aviator; 04-16-2010 at 08:15 PM.
  #320  
Old 04-16-2010, 09:22 PM
Xema Xema is offline
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Quote:
Originally Posted by Armchair Aviator View Post
In a no wind situation a plane needs to reach a speed of 100 kts to create sufficient lift to take off. This would require maximum thrust for the plane in question at full capacity.
Note that most aircraft are capable of generating more power than the bare minimum necessary to take off.


Quote:
In a 50 knot head wind would the same plane still require full thrust to reach 100 kts IAS or 50 kts TAS?
It will take the same power from the engine(s) to yield the 100-knot airspeed specified as necessary for takeoff.

Compared to the no-wind situation, it will take less time and less total energy to reach that airspeed.


Note: Your phrasing here indicates that you may not understand the correct meaning of IAS (indicated airspeed) and TAS (true airspeed). In particular, TAS is not the same as groundspeed.
  #321  
Old 04-16-2010, 09:33 PM
Armchair Aviator Armchair Aviator is offline
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Quote:
Originally Posted by Xema View Post

Note: Your phrasing here indicates that you may not understand the correct meaning of IAS (indicated airspeed) and TAS (true airspeed). In particular, TAS is not the same as groundspeed.
Ya I thought I might have TAS and ground speed mixed up...

so in the 50 kts headwind at takeoff the IAS would be 100 kts and the ground speed would be 50 kts.....so what is the TAS?

Last edited by Armchair Aviator; 04-16-2010 at 09:37 PM.
  #322  
Old 04-16-2010, 09:41 PM
Armchair Aviator Armchair Aviator is offline
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Found it.
http://www.csgnetwork.com/tasinfocalc.html

Last edited by Armchair Aviator; 04-16-2010 at 09:42 PM.
  #323  
Old 04-16-2010, 09:56 PM
Xema Xema is offline
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Originally Posted by Armchair Aviator View Post
...so what is the TAS?
Basically, the speed at which air molecules are zipping past the airplane.

IAS is just a bit trickier, since it depends on air density (at a given true airspeed, lower density implies a lower IAS). Basically, IAS has to do with the air's ability to exert force on an aircraft.
  #324  
Old 04-17-2010, 01:35 AM
nicefig nicefig is offline
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Aeroplanes propulsion is from moving air. This has been mentioned a million times. A plane propelled forward on top of a countermoving belt is not the same as a boat propelled forward on top of a countermoving water current.

You can completely stall a boat by throwing at it a water current of equal velocity to the boat's maximum attainable velocity in still water. To stall an aircraft, you would have to throw a headwind at it at the aircraft's maximum attainable velocity in air. Obviously a conveyor belt cannot create such a headwind, unless we are talking viscous flow inside a tube, which really isn't in the spirit of this thought experiment.

I am not discounting the effect of the conveyor belt on the forward movement of the plane. Meanwhile we should not overcount it. There seems to be a wrong perception that an increased belt velocity would require an increased engine output to overcome. This is not the case, as friction caused by the belt is a function of the plane's weight, not the belt velocity. You can increase the belt velocity infinitely but since the friction is not a function of this velocity, the backwards acceleration of the plane is always the same. Guess what? The magnitude of this negative acceleration is exactly the same as the one you would encounter if the plane was on flat ground. After all, the belt is made of the same material as a flat runway, as per the spirit of this thought experiment.

If the aerospace engineers gave the plane an engine that could overcome ground resistance, then the plane can overcome the belt resistance.

I am going to pre-empt a question: "What if the belt is moving at 999,999mph? After awhile, wouldn't the aeroplane be moving backward at say 100,000mph?"

Eventually it would reach 999,999mph, if we disregard alot of real-world physics. This is because the plane is being accelerated backwards by friction at the belt/wheel interface. Yes, the wheels would always be running close to 999,999mph, but the plane would start slow and accelerate slow, and the engine will always manage to overcome this negative velocity and propel the plane forward at take off velocity eventually. This negative acceleration is a constant, like I said, and it is the same if the belt were moving at 50 or 50,000mph. It is also a small value because that's what wheels are supposed to do: keep kinetic friction low. This small value is the exact same value you would encounter if the plane were rolling on a flat runway. This same value was considered by the aerospace engineers who built the plane. ie, If the plane can take off on a runway, it can take off on a countermoving belt moving at any velocity.

Last edited by nicefig; 04-17-2010 at 01:38 AM.
  #325  
Old 04-17-2010, 07:12 AM
Fear Itself Fear Itself is offline
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Originally Posted by nicefig View Post
If the plane can take off on a runway, it can take off on a countermoving belt moving at any velocity.
This is a good point. If an airplane had skids like a helicopter, it would probably have a lot of difficulty overcoming the drag on the runway to begin takeoff, and if it was on a conveyor belt, it would be much harder to reach the airspeed necessary to provide enough lift for take-off. Because it has wheels, that drag is minimized, and forward motion is possible. Any drag from a conveyor belt is likewise minimized.
  #326  
Old 04-17-2010, 09:09 AM
Xema Xema is offline
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Originally Posted by nicefig View Post
To stall an aircraft, you would have to throw a headwind at it at the aircraft's maximum attainable velocity in air.
"Stall" isn't the best word to use here, as it has a specific meaning in connection with winged aircraft that isn't related to retarding motion across the ground.
  #327  
Old 04-17-2010, 03:48 PM
ElvisL1ves ElvisL1ves is offline
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Basically, IAS has to do with the air's ability to exert force on an aircraft.
You can think of IAS as the rate at which air mass is flowing over the wings. That's really what's holding the airplane up, and why IAS at stall is independent of altitude. Lower TAS and higher density can give the same IAS as higher TAS and lower density, if those give you the same mass air flow.
  #328  
Old 04-17-2010, 05:08 PM
John W. Kennedy John W. Kennedy is offline
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If the plane can take off on a runway, it can take off on a countermoving belt moving at any velocity.
Only if you assume that the tires and the bearings don't give out, which they damn well will at 999,999 mph.
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  #329  
Old 04-17-2010, 06:29 PM
Fear Itself Fear Itself is offline
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Originally Posted by John W. Kennedy View Post
Only if you assume that the tires and the bearings don't give out, which they damn well will at 999,999 mph.
If we are operating in a universe with a conveyor belt that can go 999,999 mph, I am sure they also have wheels and bearings capable of withstanding such speeds.
  #330  
Old 04-19-2010, 04:37 PM
Irishman Irishman is offline
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DanBlather said:
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That would only be true if the wheel brakes were set. If you had a plane stationary on a treadmill and then accelerated it to 50 MPH the plane's momentum would keep it relatively motionless and the wheels would spin.
It's a bit of a competition between inertia and friction. If the speed transition is slow, the friction can possibly overcome the inertia and the plane start moving. If the speed transition is quick, inertia wins and the wheels just roll.

Kinda like the old magician's trick of removing a table cloth but leaving the place settings in place. How? Give a quick, solid yank on the table cloth. Inertia keeps the dishes from moving and overcomes the friction with the cloth.

If an airplane is sitting on a conveyor belt with the engine off, and the conveyor belt starts to move, and it accelerates slowly, the plane will probably start moving with the belt. Then start up the plane engine.

If the conveyor belt is moving the plane forward, it is providing forward speed, which translates into airspeed over the wings, so the airplane requires less thrust to get to the takeoff point. However, as soon as it leaves the belt, the engine will need to ramp quickly to proper thrust, or the plane will not maintain airspeed and will drop back onto the belt, have some skidding until the wheels grip and bearings spin in sync, then when proper thrust is achieved the airplane will take off again. So if one doesn't want a bouncy take off, one should get the engine to proper thrust before lifting up rather than going early.

If the conveyor belt is moving the plane backward, it is providing backwards speed, but as soon as the engines start pushing air, the wheels will start spinning and the engine will overcome the belt drag. Then the plane will proceed to take off as normal with the wheels spinning extra fast.
  #331  
Old 04-20-2010, 02:02 PM
Strassia Strassia is offline
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Quote:
Originally Posted by John W. Kennedy View Post
Only if you assume that the tires and the bearings don't give out, which they damn well will at 999,999 mph.
It all comes down to assumptions. If you have a magic treadmill, but a real world plane, you can keep it down. Actually, if you created a treadmill that could apply enough force through the wheels to keep the plane from moving it would not be stationary, it would flip (picture what would happen if you tied a chain to the wheels and hit full throttle). So to keep the plane stationary you need a magic treadmill (impossible speeds and accelerations with no air dragged back over the plane) and a partially magic plane (wheels that don't break down but aren't frictionless, and a profile that puts the wheels in line with the propeller).
  #332  
Old 04-26-2010, 03:30 AM
neomanrex neomanrex is offline
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New here. Reading this whole thread and came to a conclusion. I love science but I wouldn't say I'm an expert. I'm barely a novice. I'm seeing a pattern though.

Originally the point was that if you could make a conveyor belt that exactly matched the plane speed or something. (honestly the math was a bit above me but I got the gist.) That the plane wouldn't move and therefore no airflow therefore no lift therefore no liftoff. Ok fine.

Here's my thing. I think the answers right. I think the question is wrong. It's like Hitchhiker's Guide. The answer to the meaning of life the universe and everything IS 42. The question however is wrong.

Most people seem to be answering the question "would a plane on a treadmill take off." Answer: yes.

The second set of people seem to be answering a different question. Here's the question I think they are answering. "If you nailed a plane to the F****ing ground could the plane take off?" They just seem to be complicating the way in which you manage to nail a plane to the ground. I would use nails. Heck even chains would work. Where they use a really complicated system involving really complicated math and really complicated physics when a simple nail would do.

So basically to me realistically a plane on a treadmill can take off. A plane nailed to the ground(motionless) can't. Whatever method you use to keep it motionless

Last edited by neomanrex; 04-26-2010 at 03:31 AM. Reason: spelling
  #333  
Old 04-29-2010, 06:37 AM
JoelKatz JoelKatz is offline
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I think the problem description is sufficiently precise that only one answer is possible: "This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)." So if the plane is going forward at 30 miles per hour, the conveyer is going backwards at 30 miles per hour. The sole effect of such a conveyer would be a tiny bit of extra friction and extra wear on the wheels.

The trap people fall into is assuming the conveyer's speed will match the linear speed of the wheels. That is not what the problem says. (And if it did, you would truly need a magic conveyer.)
  #334  
Old 05-07-2010, 01:12 PM
TriPolar TriPolar is online now
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unbelievable! mythbusters proved the plane will take off. the wheels of an airplane are free spinning in bearings. there is friction in the bearings, but it is minimal, not considerable. the scenario is no different than a plane with some worn bearings in the wheels. as long as the planes propellor produces enough thrust to overcome the friction in the bearings, it will take off. a plane can take off without wheels if there is a strong enough headwind, or if the plane is on the back of a truck moving fast enough. the only purpose of the wheels is to reduce friction on the ground during the take off. early aircraft used skids instead of wheels, with considerably more friction to overcome, but they flew. i guess people keep forgetting that the free-spinning wheels isolate the plane from the ground.
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Old 05-07-2010, 02:01 PM
zut zut is offline
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Was that in response to any particular post, or just stream-of-consciousness?
  #336  
Old 05-07-2010, 08:00 PM
TriPolar TriPolar is online now
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Quote:
Originally Posted by zut View Post
Was that in response to any particular post, or just stream-of-consciousness?
just tired of hearing about this inane supposition from many sources.
  #337  
Old 11-15-2010, 12:22 PM
jdunlevy jdunlevy is offline
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Alan Molumby comments over at chicagoreader.com:
Quote:
I was wrong in calling Cecil wrong, but he was equally wrong in calling me wrong. I was probably the bigger oaf because I called him out first, but his wit is sharper and his answer even more cocksure than mine. The fact of the matter is, the question we are both responding to can be read two ways. It either asks 1) can a stationary plane on a treadmill take off? or 2) can the action of a treadmill prevent a plane from taking off?
... and suggests that Cecil ignores the point of version 1.
  #338  
Old 11-17-2010, 11:04 AM
Powers Powers is offline
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Quote:
Originally Posted by jdunlevy View Post
Alan Molumby comments over at chicagoreader.com:

... and suggests that Cecil ignores the point of version 1.
But, as we've established, the answer to version 1 is trivial to anyone who understands aerodynamics.


Powers &8^]
  #339  
Old 11-17-2010, 11:15 AM
Powers Powers is offline
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... and, I should point out, nothing in the original question suggests that the plane must be kept stationary! So I see no reason to even consider "version 1", since it's clearly not what the question is asking.


Powers &8^]
  #340  
Old 11-17-2010, 05:25 PM
Irishman Irishman is offline
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As we have beaten to death, the original question is not clear. The part about the treadbelt matching the speed of the plane or the speed of the plane's wheels is misleading/confusing.

If the question is 1, that is stupid. No, if the airplane is chained to the ground, bolted down, or put on a magic treadmill that prevents the fuselage from moving, then the airplane cannot take off.

If the question is 2, there is no treadmill that can prevent the airplane from taking off.
  #341  
Old 01-03-2014, 08:02 AM
SPACKlick SPACKlick is offline
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Ok, looking at the interpretation of the question whereby the conveyor matches the wheelspeed (which leads to a stationary plane)

There are three ways in which the force of the treadmill acts on the plane in a fashion counter to its motion. As it's a physics question putting in relevant formulae will give the answer. Why does nobody turn to the maths.

1) Moment of Inertia. Using a Boeing 747 and information pulled from the internet
The 747's 4 engines produce an approximate thrust of 772,000N
It has 24 wheels, each of which has a radius of 0.7112m and a mass of C.250kg (tyre is 110kg various numbers were found for the wheels but it was hard to be exact on which bits rotate)
This means each wheel has a moment of inertia;
Mass*Radius^2/2 = 63.22568
[This boils down to (thrust/wheels)/(WheelMass/2) so I'm no longer certain this maths is right]

The moment of inertia responds to the acceleration of the belt, not its speed.
Force per wheel is;
Thrust/wheels = 32,166.67N
The equivalent mass at the circumference for the same moment of inertia is;
Mass/2 = 125 kg
Acceleration of belt to counteract the engines
A = F/M = 257.33m/s/s

That acceleration of the belt alone would counter the engines and you get bonus resistance from

2) Friction in the bearings. this is correlated with speed and also vibration and heat.
I don't understand the full physics of bearings but, the speed of the wheel affects the turbulence in the lubricant which affects viscosity and rolling friction (higher speed, higher friction). The heat in the bearing changes the viscosity of the grease and the kinetic friction between the rollers and the axle (higher speed higher friction) the vibration of the bearing affects viscosity, contact friction etc and this will go up as speeds increase due to 3.

3) Deformation of the tyre. The Boeing 747 weighs between 178,750kg and 445,000kg, or 7,445kg to 18,420kg per wheel.
This causes serious deformation of the tyre.
To quote wikipedia
Quote:
Originally Posted by Wikipedia
Factors that contribute to rolling resistance are the (amount of) deformation of the wheels, the deformation of the roadbed surface, and movement below the surface. Additional contributing factors include wheel diameter, speed,[2] load on wheel, surface adhesion, sliding, and relative micro-sliding between the surfaces of contact. The losses due to hysteresis also depend strongly on the material properties of the wheel or tire and the surface.
So as the speed goes up, so does the resistance from factors 2 and 3 allowing acceleration to go down.

As 273m/s/s is an insane acceleration, we can look at how that can be affected. The easiest way is to change the mass of the wheels, I'm not confident in my wheel mass, if it was doubled the necessary acceleration of the belt would be halved.

Without the formulae for The bearings and the rolling resistance due to deformation anyone who rules out the ability of the treadmill to keep the plane stationary is simply being closed minded.

Last edited by SPACKlick; 01-03-2014 at 08:04 AM.
  #342  
Old 01-03-2014, 09:10 AM
Musicat Musicat is offline
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Welcome to the Dope, SPACKlick. You are replying to a 4 year old thread (started 8 years ago). I thought we covered everything.

{sigh} Sometimes (not always) it's a good idea to read the WHOLE thread before replying.

This may be one of those cases.

Last edited by Musicat; 01-03-2014 at 09:11 AM.
  #343  
Old 01-04-2014, 03:32 PM
Xema Xema is offline
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Quote:
Originally Posted by SPACKlick View Post
... anyone who rules out the ability of the treadmill to keep the plane stationary is simply being closed minded.
... or confining his attention to versions of the problem that don't admit magic treadmills.

But you are correct that a treadmill allowed to exhibit continuous, wildly unrealistic acceleration can generate a retarding force on an aircraft similar to when wheels are locked and unable to rotate. And few aircraft have engines powerful enough to take off - or move at all - with locked wheels.
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