CAP Talk

Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

Yes, it will. Ex-plane-ation can be given after other comments posted.  :)

lift has nothing to do with the speed of the wheels.

Nor does thrust come from the wheels rolling on the ground.

No it will not, unless I am missing the fact that there is no relative wind alowing over the wings......

From the scenario you listed the aircraft is not moving through the air, or the air is not flowing over the wings.  Just the wheels are moving.

Yes, it will take off.  Here is a demonstration:  http://mythbustersresults.com/episode97

As was said previously the speed of the wheels has nothing to do with the lift.

Quote from: Al Sayre on February 15, 2010, 01:12:26 PM
Yes, it will take off.  Here is a demonstration:  http://mythbustersresults.com/episode97

As was said previously the speed of the wheels has nothing to do with the lift.

Huh?

You can see the plane is moving, when you look at the background passing by.

The text suggests that the aircraft will fly from a still position because of engine thrust.  That may be true in very limited conditions / scenarios.

But the video shows the airplane moving well before takeoff.

???

What's missing from the OP is the fact that the engines are actually running and producing the normal thrust.   It's not claiming that the treadmill/belt/whatever is generating thrust or lift.

This is a tough one.  If there is an increase in air past the wing it will take off, but if it is moving with no air increase initially it will not??

I must break out the Aerospace book for this one.

Engine thrust does not create lift, it creates the movement to make relative wind over the wing that creates lift.  If the belt increases speed so the aircraft remains stationary on it, then there will be no relative wind or lift from the wings.  The aircraft cannot fly no matter what the thrust. Mythbusters did not replicate this. If the aircraft is allowed forward progress by the belt, then eventually it will fly depending on the lift needed on that aircraft. But really, who cares?  ;D

Quote from: Al Sayre on February 15, 2010, 01:12:26 PM
Yes, it will take off.  Here is a demonstration:  http://mythbustersresults.com/episode97

As was said previously the speed of the wheels has nothing to do with the lift.

The myth busters demonstartated that he treadmill has nothing to do with it...because the thrust comes from the engine/prop not from the wheels pushing against the tarmac.

The only affect the runway has on the aircraft is drag (the friction of the wheels on the ground) and Ground Effect on lift.

Put the plane on a tread mill and it has almost NO effect on the planes ability to fly. (it may change the lenght of the take off roll and that is it.)

Quote from: Thrash on February 15, 2010, 04:07:09 PM
Engine thrust does not create lift, it creates the movement to make relative wind over the wing that creates lift.  If the belt increases speed so the aircraft remains stationary on it, then there will be no relative wind or lift from the wings.  The aircraft cannot fly no matter what the thrust. Mythbusters did not replicate this. If the aircraft is allowed forward progress by the belt, then eventually it will fly depending on the lift needed on that aircraft. But really, who cares?  ;D

That would be true....if the trust was developed by the wheels.  A car on a tread mill goes nowhere because the wheels are giving the car thrust by friction with the ground.  If the ground is moveing at the same rate of the wheels then no trust.

But an airplane's trust is deveoped by the prop or the jet.  It does not push against the ground.  So it does not matter what the tread mill is doing... the plane will fly.

Quote from: lordmonar on February 15, 2010, 05:41:21 PMThat would be true....if the trust was developed by the wheels.  A car on a tread mill goes nowhere because the wheels are giving the car thrust by friction with the ground.  If the ground is moveing at the same rate of the wheels then no trust.

But an airplane's trust is deveoped by the prop or the jet.  It does not push against the ground.  So it does not matter what the tread mill is doing... the plane will fly.

I am not an engineer, but...

It seems to me that the conditions you describe would only apply to an aircraft already in flight - ie, one that already has the weight force canceled out by lift. If an aircraft is flying, and comes into contact with the treadmill, then the wheels will "spin" (assuming that the plane is flying perfectly level and just barely touching the treadmill) and the plane will continue to fly.

When the plane is at rest, the prop has to generate thrust in order to move forward and begin generating lift. But the plane can't simply move forward by pushing air backwards, because it's still being pulled towards the ground, so it has to use the friction of the wheels against the ground in order to generate forward motion. If the plane is already in flight, this isn't an issue, because the weight is already canceled out by lift.

If you put the plane on a treadmill, you remove the friction of the wheels against the ground, and take away the grounded plane's ability to generate forward motion.

No....trust in a prop aircraft is generated by the forward screw of the Prop.  It pushes (and pulls) on the air around the prop and pull the aircraft forward.  The wheels on the ground do nothing for thrust (except resist it through friction).  If the tread mill started moving at the same rate the aircraft moved forward then the wheels would just turn twice as fast...but because the wheels turn freely it would not impeed (much) the thrust (forward motion) of the aircraft.

The trust of the aircraft must overcome the drag induced by the wheels in contact with the ground.....but that is not enough to stop the forward motion of the aircraft.

Once again...unlike a car (whose motion is created by the friction of the wheels pushing against the ground) an air plane's forward motion is competely generated by the air screw or jet thrust of the power plant.  Ground friction is something that must be over come (and inertia) but it is not not enough to keep an air plane from becoming airborn.

Thrust is fine but if the air is not moving over the wings, no lift is generated.  Prop wash is inadequate to generate enough lift for your average airplane to overcome its weight.  Thrust will move the airplane from one end of the airstrip to the other.  If lift is not generated by the movement of the airfoil through the air, the airplane will stay on the ground.   If the airplane is stationary due to a treadmill moving the airplane backwards as fast as the thrust moves the airplane forward - no lift is generated.

Music to my ears.

//s//
DG
Philadelphia Liar

Quote from: lordmonar on February 15, 2010, 08:51:17 PMThe trust of the aircraft must overcome the drag induced by the wheels in contact with the ground.....but that is not enough to stop the forward motion of the aircraft.

Given the problem, it actually would be. Remember, we have a conveyor belt that "is designed to exactly match the speed of the wheels, moving in the opposite direction".

I submit to you, that in order for the airplane to have any forward motion relative to the wind (and thus take off), its wheels must spin faster in the positive than the conveyor belt spins in the negative.

A simple mathematical simulation would bear out that a system including an airplane and the type of conveyor belt theorized in the problem, the speed of both the wheels and the conveyor belt will increase over time until an equilibrium is reached whereby the maximum thrust of the airplane's engine will match the kinetic force of friction on the wheels, resulting in zero forward movement.

And the aircraft will never take off.

Quote from: Short Field on February 16, 2010, 04:44:24 PM
Thrust is fine but if the air is not moving over the wings, no lift is generated.  Prop wash is inadequate to generate enough lift for your average airplane to overcome its weight.  Thrust will move the airplane from one end of the airstrip to the other.  If lift is not generated by the movement of the airfoil through the air, the airplane will stay on the ground.   If the airplane is stationary due to a treadmill moving the airplane backwards as fast as the thrust moves the airplane forward - no lift is generated.

Unless you chain the wings to the ground, the airplane will move forward and fly.  The speed of the treadmill will only affect the speed at which the wheels turn, which the airfoil and engine could not care less about.  You could run the treadmill backwards at speeds approaching c, and the the airplane would still move forward as soon as prop thrust overcomes the wheel bearing friction.

Quote from: Al Sayre on February 16, 2010, 05:27:41 PM
Unless you chain the wings to the ground, the airplane will move forward and fly.  The speed of the treadmill will only affect the speed at which the wheels turn, which the airfoil and engine could not care less about.  You could run the treadmill backwards at speeds approaching c, and the the airplane would still move forward as soon as prop thrust overcomes the wheel bearing friction.

I think you're introducing factors that aren't part of the original problem. Namely, lag between an increase in thrust (and thus increase in wheel spin) and increase in conveyor belt speed. However, the theoretical conveyor belt machine defined in the problem has no such lag. It matches the speed of the wheels exactly.

We need to perform the test.  What squadron commander reading this would volunteer to have their cadets do this experiment?  I'd love to see some real data.....

Quote from: FW on February 16, 2010, 05:36:38 PM
We need to perform the test.  What squadron commander reading this would volunteer to have their cadets do this experiment?  I'd love to see some real data.....

And you hope to get real data on a theoretical problem involving machines that can not exist how?

Well there's an AFA grant for $250 dollars just waiting for a squadron wanting to do a little Aerospace Education

How about it?  Some of that theoretical stuff is what is making airplanes fly today!

Quote from: N Harmon on February 16, 2010, 05:42:47 PM

Quote from: FW on February 16, 2010, 05:36:38 PM
We need to perform the test.  What squadron commander reading this would volunteer to have their cadets do this experiment?  I'd love to see some real data.....

And you hope to get real data on a theoretical problem involving machines that can not exist how?

Um, did we ever hear of models?  :o

I'm sure we have some sharp cadets out there willing to prove a point.  Don't we?

Quote from: FW on February 16, 2010, 06:53:02 PM

Quote from: N Harmon on February 16, 2010, 05:42:47 PM

Quote from: FW on February 16, 2010, 05:36:38 PM
We need to perform the test.  What squadron commander reading this would volunteer to have their cadets do this experiment?  I'd love to see some real data.....

And you hope to get real data on a theoretical problem involving machines that can not exist how?

Um, did we ever hear of models?  :o

I'm sure we have some sharp cadets out there willing to prove a point.  Don't we?

The mythbusters already did it with models and I think they might have even done it with a J-3.

Assume that the wheels of the aircraft are hypothetically frictionless...As if they were perfect ice skates. Since the work being carried out by the AC engine is used to create a compressed column of air to push the AC in the opposite direction ( in accordance with Newtons law) The aircraft accelerates primarily as a function of the amount of energy pushed aft. The "can't fly" analogies are similar to the arguments that the airplane can't take off contrary to the rotation of the earth, since it would have accelerate to the velocity of the Earth's rotation just to break even. We can see this is not true, and the relative airspeed over the wings ( If you are a Bernoullian) or the lift generated by impact against the lower surface of the wings by impact forces in ground effect and later phases of flight (If you are a Newtonian) are the relevant factors in determining lift off.

Reintroducing the friction to the wheels changes things a bit. The frictional losses of the wheels are one of the forces working against the acceleration of the AC to take off speed, but these forces are not constant. The movement of the treadmill under the wheels introduces a small amount of force, but you could probably hold it back  with minimal holding force. As the AC accelerates, the downward forces of gravity are overcome, resulting in lesser friction, resulting in a higher velocity. Of course, the wheels are going to be spinning at an RPM that may not have been foreseen by the manufacturer, and the centrifugal forces could potentially result in a cataclysmic failure of the wheel bearings from excessive heat, but thats not the question, is it?

I think the Mythbuster episode shows it rather eloquently.

Major Lord

Quote from: N Harmon on February 16, 2010, 05:27:26 PM

Quote from: lordmonar on February 15, 2010, 08:51:17 PMThe trust of the aircraft must overcome the drag induced by the wheels in contact with the ground.....but that is not enough to stop the forward motion of the aircraft.

Given the problem, it actually would be. Remember, we have a conveyor belt that "is designed to exactly match the speed of the wheels, moving in the opposite direction".

I submit to you, that in order for the airplane to have any forward motion relative to the wind (and thus take off), its wheels must spin faster in the positive than the conveyor belt spins in the negative.

A simple mathematical simulation would bear out that a system including an airplane and the type of conveyor belt theorized in the problem, the speed of both the wheels and the conveyor belt will increase over time until an equilibrium is reached whereby the maximum thrust of the airplane's engine will match the kinetic force of friction on the wheels, resulting in zero forward movement.

And the aircraft will never take off.

The point I am making is that unless the plane is bolted to the tread mill....it will move forward!  The Prop pushes on the air....Newton's law of motion rules that the plane must move forward.

So if the plane starte moving forward at taxi speed (10mph) and the treadmill moved in the opposite dirction at 10mph then the wheels would simply spin at 20MPH and the plane would still maintain a ground speed of 10MPH.

IF.....IF the trust of the aircraft was generated by friction with the ground (as it is in a car or truck) then the two motions would counter act and the ground speed would remain zero.  But that is not the case.  Thrust is generated by the prop working on the AIRMASS over the runway not on the surface of the runway.

^^^ Good explanation. 

Another way to think of this is to again imagine a car on this hypothetical treadmill.  I think we all agree that the car would not move forward regardless of how fast the car accelerated.  Now imagine attaching a tow rope to the front of the car, and towing the car forward.  Regardless of how fast the treadmill spins, the car will still move forward because it is being pulled forward by an outside force.

Going back to the airplane now, the engine and prop act as that tow rope, so regardless of how fast the treadmill runs, the plane will still always move forward because it is being pulled forward by the prop.

Quote from: N Harmon on February 16, 2010, 05:34:06 PM

Quote from: Al Sayre on February 16, 2010, 05:27:41 PM
Unless you chain the wings to the ground, the airplane will move forward and fly.  The speed of the treadmill will only affect the speed at which the wheels turn, which the airfoil and engine could not care less about.  You could run the treadmill backwards at speeds approaching c, and the the airplane would still move forward as soon as prop thrust overcomes the wheel bearing friction.

I think you're introducing factors that aren't part of the original problem. Namely, lag between an increase in thrust (and thus increase in wheel spin) and increase in conveyor belt speed. However, the theoretical conveyor belt machine defined in the problem has no such lag. It matches the speed of the wheels exactly.

The point being.....the treadmill moves in such a way that the wheels don't move...if the aircarft started moving forward (turning the wheels) the treadmill would have to move in the same direction the aircraft was moving to keep the wheels from turning.  So it the aircraft was accelerating to 90MPH the treadmill would have to accelerat to 90MHP IN THE SAME DIRECTION AS THE AIRCRAFT to keep the wheels stationary.   But the tread mill has no affect on the reletive wings flowing over the wings.....producing lift and thus has not affect on the ability of the aircraft to become airborne.

If any of you guys took the position that it should not fly, please surrender your Yaeger Awards to the appropriate authorities..... ;)

Major Lord

Quote from: Major Lord on February 16, 2010, 07:07:43 PMAssume that the wheels of the aircraft are hypothetically frictionless...

That would be an interesting twist on the original problem. If the wheels were frictionless then they and the conveyor belt's velocity would immediately go to infinity. So then what? I'll have to think about this. :)

QuoteReintroducing the friction to the wheels changes things a bit. The frictional losses of the wheels are one of the forces working against the acceleration of the AC to take off speed, but these forces are not constant. The movement of the treadmill under the wheels introduces a small amount of force, but you could probably hold it back  with minimal holding force.

Actually, you would not be able to. Realizing that the conveyor belt's opposite speed will always be the same as the forward speed of the aircraft's wheels, that holding force will always be equal to the forward force generated by engine thrust.

QuoteI think the Mythbuster episode shows it rather eloquently.

I'm sorry, but some of the "science" shown on Mythbusters is bad...bad...bad.

Quote from: lordmonar on February 16, 2010, 07:16:55 PM
So if the plane starte moving forward at taxi speed (10mph) and the treadmill moved in the opposite dirction at 10mph then the wheels would simply spin at 20MPH and the plane would still maintain a ground speed of 10MPH.

Okay! So you DO agree with me that in order for the plane to take off, it's wheels must spin faster in an opposite direction of the conveyor belt. Right?

Well, remember the conveyor belt we have will match the opposite speed of the wheels exactly. Get that? Exactly. So there is no impulse of the plane moving forward suddenly because the conveyor matches and cancels those impulses precisely.

Quote from: Major Lord on February 16, 2010, 07:24:05 PM
If any of you guys took the position that it should not fly, please surrender your Yaeger Awards to the appropriate authorities..... ;)

I'm thinking a wager here is in order...  >:D

Quote from: N Harmon on February 16, 2010, 07:48:50 PM

Quote from: Major Lord on February 16, 2010, 07:07:43 PMAssume that the wheels of the aircraft are hypothetically frictionless...

That would be an interesting twist on the original problem. If the wheels were frictionless then they and the conveyor belt's velocity would immediately go to infinity. So then what? I'll have to think about this. :)

In a word... no.  Review your basic physics. An absence of friction simply means there won't be a force to slow the wheel down.  You still need to add a force to speed it up.  Newton's first law and all....

Quote from: N Harmon on February 16, 2010, 07:48:50 PM

QuoteReintroducing the friction to the wheels changes things a bit. The frictional losses of the wheels are one of the forces working against the acceleration of the AC to take off speed, but these forces are not constant. The movement of the treadmill under the wheels introduces a small amount of force, but you could probably hold it back  with minimal holding force.

Actually, you would not be able to. Realizing that the conveyor belt's opposite speed will always be the same as the forward speed of the aircraft's wheels, that holding force will always be equal to the forward force generated by engine thrust.

Again, no.  Remember, the wheels on an airplane are just freely spinning.  I've not done the math here, but common sense dictates that you cannot generate enough friction between the moving parts of the wheels to hold an aircraft stationary at takeoff RPM.

Quote from: N Harmon on February 16, 2010, 07:48:50 PM

QuoteI think the Mythbuster episode shows it rather eloquently.

I'm sorry, but some of the "science" shown on Mythbusters is bad...bad...bad.

Yes, yes, yes.

Quote from: N Harmon on February 16, 2010, 07:48:50 PM

Quote from: lordmonar on February 16, 2010, 07:16:55 PM
So if the plane starte moving forward at taxi speed (10mph) and the treadmill moved in the opposite dirction at 10mph then the wheels would simply spin at 20MPH and the plane would still maintain a ground speed of 10MPH.

Okay! So you DO agree with me that in order for the plane to take off, it's wheels must spin faster in an opposite direction of the conveyor belt. Right?

Well, remember the conveyor belt we have will match the opposite speed of the wheels exactly. Get that? Exactly. So there is no impulse of the plane moving forward suddenly because the conveyor matches and cancels those impulses precisely.

Um... no.  The key here is that ultimately, the wheels, the conveyor belt don't matter.  The prop is going to pull the aircraft forward, regardless of how fast the treadmill starts to go.  Basically, if you drew the free body diagram on this particular problem, the force of the prop pulling the aircraft forward is always going to be significantly greater than the force of friction generated by the wheels spinning.  Why the wheels are spinning (the conveyor belt) doesn't matter to the aircraft's forward motion. 

The treadmill can match the speed of the wheels, but that doesn't mean the aircraft won't take off- again, the propeller is pulling it forward, and while the conveyor belt is moving backward in this example, it's not pushing the aircraft backward, just the free spinning wheels.


Okay.  One more tidbit for thought here, if the treadmill is indeed as wide as a normal runway, the treadmill itself will also be generating relative wind favorable to the aircraft taking off.  So, your ground effect is actually going to be higher in this example than it normally would be... thus allowing the aircraft to take off at a lower ground speed than normal.

I weep for the future of our cadets when I think who may be teaching them physics.....I remember one senior member telling cadets that a bullet shot straight up will come back to earth at the same velocity at which it was launched. Crikey! The purpose of assuming a hypothetical is to eliminate factors not intrinsic to the model. As far as the mythbusters being a little slow in the scientific method goes, I won't deny that, but I think that their ACTUALLY running the experiment with a real airplane and a treadmill is sound empirical evidence.

The force required to "hold" the aircraft stationary ( to prevent the aircraft from being carried away backwards by the treadmill) is largely a function of the coefficient of drag of the wheels. Standing off to one side of this treadmill , you could hold the aircraft back with a leash in one hand, as long as the treadmill was already up to speed, preventing you from having to overcome its moment.

Major Lord

Quote from: Pingree1492 on February 16, 2010, 08:18:19 PM

Quote from: N Harmon on February 16, 2010, 07:48:50 PM
That would be an interesting twist on the original problem. If the wheels were frictionless then they and the conveyor belt's velocity would immediately go to infinity. So then what? I'll have to think about this. :)

In a word... no.  Review your basic physics. An absence of friction simply means there won't be a force to slow the wheel down.  You still need to add a force to speed it up.  Newton's first law and all....

Oh, that's good. See, I wasn't even looking at the tire/belt connection being frictionless but rather the wheel/hub connection. But in that case the wheels won't move at all, and neither will the conveyor so it would be the same as a plane on a frictionless runway. I suppose a similar effect would be to have the pilot just lock the brakes and put in enough thrust to skid to take off, but that would be cheating. ;)

QuoteRemember, the wheels on an airplane are just freely spinning.  I've not done the math here, but common sense dictates that you cannot generate enough friction between the moving parts of the wheels to hold an aircraft stationary at takeoff RPM.

See, I think a lot of you are looking at the rolling resistance of the wheels as being a constant, which it is not. Rolling resistance is very much dependent on velocity. It just doesn't change much in the low velocities we normally deal with (a few hundred m/s).

Now, you may argue (or did argue) that you just can't get enough force from rolling resistance to counter thrust. But consider the problem again...We have this amazing conveyor belt that matches the speed of the wheels exactly. To do that, it would have to be capable of some amazing speeds necessary to keep up.

QuoteUm... no.  The key here is that ultimately, the wheels, the conveyor belt don't matter.

Okay, wait wait wait. The wheels of the plane MUST spin faster in opposite of the conveyor belt for the plane to move forward in relation to the ground. Correct?

Quote
Okay.  One more tidbit for thought here, if the treadmill is indeed as wide as a normal runway, the treadmill itself will also be generating relative wind favorable to the aircraft taking off.  So, your ground effect is actually going to be higher in this example than it normally would be... thus allowing the aircraft to take off at a lower ground speed than normal.

Not to mention a lot of drag.

Quote from: Major Lord on February 16, 2010, 08:32:51 PMAs far as the mythbusters being a little slow in the scientific method goes, I won't deny that, but I think that their ACTUALLY running the experiment with a real airplane and a treadmill is sound empirical evidence.

They didn't run this experiment. Did their conveyor match the speed of the wheels (important, wheels not the plane) exactly?

Nathan,

I am not sure what you are arguing here. Of course the tread mill was traveling at the speed of the wheels! It could hardly do otherwise ( without making some godawful skid marks!)

Are you are positing that an aircraft could not take off from a treadmill moving backwards in direct proportion to the forward (ground speed) velocity of the aircraft? If so, I will happily wager the sum  of  $100.00 US Dollars that it can do precisely that.

Major Lord

Quote from: Major Lord on February 16, 2010, 09:20:10 PM
I am not sure what you are arguing here. Of course the tread mill was traveling at the speed of the wheels! It could hardly do otherwise ( without making some godawful skid marks!)

Not necessarily. If the wheels are traveling at speed different from the treadmill, then the aircraft will moving forward/backward in relation to the ground. Think about it like this:

Say you have a firetruck on your home treadmill, and you're sitting in front of it with a rope. The treadmill is running at 5mph, and with the rope you're holding the firetruck steady in relation to the ground. It's wheels are moving at the same speed as the treadmill, just in an opposite direction. The force you extert on the rope is in equilibrium with the force of friction from the rolling wheels on the treadmill.

Now say you pull harder on the rope, moving the toy forward in relation to the ground. For this to happen, it's wheels must turn slightly faster than the treadmill. This excess velocity translates into excess forward motion in relation to the ground.

Let's say you increase the speed of the treadmill, well then you'll find it takes a little more force to keep the firetruck stationary in relation to the ground.

OKAY.

The question here is: Is it possible to have a treadmill powerful enough to spin fast enough to keep you from pulling the firetruck forward? If so, then a treadmill that constantly increases speed to match the speed of the wheels exactly, will be that powerful.

QuoteAre you are positing that an aircraft could not take off from a treadmill moving backwards in direct proportion to the forward (ground speed) velocity of the aircraft? If so, I will happily wager the sum  of  $100.00 US Dollars that it can do precisely that.

No. Remember, the speed of the aircraft in relation to ground is the result of a magnitude difference between the speed of the treadmill and the speed of the wheels. If the treadmill simply matches the aircraft speed, then the wheels are free to move in proportion and the plane will take off.  But if the wheel and treadmill velocities remains equal and opposite, there is no excess difference for the plane to move forward.

"Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"

You are changing the terms. The postulate stated that the treadmill is going exactly the same velocity of the wheels,   We have an aircraft accelerating to a velocity approaching VR, and a treadmill upon which it runs accelerating to and reaching the forward velocity of the aircraft wheels rotation. when the wheels rotational velocity and the treadmills inverse velocity are equal, the airplane should be static. As the thrust of the aircraft overcomes the CD of the wheels, it will start to lift off from the treadmill by the forces being introduced by the engine and prop.

Major Lord

OK...I'll nibble.

If Vr of a plane is 55 knots then the wheels on a conveyor matching the wheel speed (in inverse) only means that the wheels will be spinning as if rolling at 110 knots when the plane rotates and the conveyor is no longer a factor.

It really is that simple. It will fly.

Another view.

Treadmill running forward at 55 knots, plane takes off with no tire movement (0X).
Treadmill at a stand still, plane takes off at 55 knots with 55 knot revolutions on tires (1X).
Treadmill running backwards at 55 knots (the problem in question), plane takes off, tires moving at both the forward speed of the plane and the reverse speed of the treadmill (2X)

This is not a car. There is nothing providing power to the wheels. They free wheel independent of the power which propels the plane forward.

The only thing the treadmill is doing is causing a wheel to spin and generating friction in the wheel bearings which the thrust of the plane easily will overcome until failure of said bearings.

Wow.  This was totally a trick question.  TACP got all of you. 

Everyone went off on variable tangents regarding aerospace mechanics and science.  I urge each of you to read the question over and over this time.  Just imagine a treadmil and the last time you were on one.   

What happens then when you put on rollerblades and duck tape your legs together. Then your argument is more valid.

Now pull yourself forward with your arms. Did you move forward???? See how you moved forward regardless of no power being sent through your legs (aka running)?

If you are running, you are providing power to your legs like a drive train to  wheel.

If you put on rollerblades, duck tape your legs together, you then are like an airplane wheel. Your arms are now like a prop. You can still move forward despite any speed of the treadmill.

Why is this whole thing so complicated?

A plane will lift off at the specified AIR speed based on weight and balance. As far as I know, air speed is the speed of the air flowing thru the wings. If the airplane is running really fast on a treadmill, then the ground speed could be really fast like say 100 knots, but the air speed is still zero.

The only way an airplane will lift off while on a treadmill is if the airplane and the treadmill is pointed into a strong headwind with a wind speed equal or greater than the air speed required for lift off.  ;)

Quote from: Spike on February 16, 2010, 10:43:16 PM
Wow.  This was totally a trick question.  TACP got all of you. 

Everyone went off on variable tangents regarding aerospace mechanics and science.  I urge each of you to read the question over and over this time.  Just imagine a treadmil and the last time you were on one.   

The treadmill has no bearing at all on the aircraft. The wheels rotate because the aircraft is moving from the trust of the power plant.  Any motion of the treadmill forward, back or nothing at all....will only make the wheels rotate faster or slower.  It will not slow the aircraft (or not enough to affect the aircraft's ability to get airborne...there is a little resistance but not much).

The only way that the treadmill can move to counter act the rotation of the wheels is if it were to more in the same direction that the aircraft is moving......so as silvereagle said wheel rotation is zero....but the aircraft is still gaining speed via the power plant, developing lift via air flow over the wings and will eventually become airborne.

Quote from: Major Lord on February 16, 2010, 08:32:51 PM
I weep for the future of our cadets when I think who may be teaching them physics.....I remember one senior member telling cadets that a bullet shot straight up will come back to earth at the same velocity at which it was launched.

Actually, if it goes exactly straight up, and exactly straight down, that is true. Add any horizontal component, and all bets are off.

The bullet starts with a specific amount of kinetic energy when fired, and at the top of its flight it becomes potential, after having been slowed at 32 ft/(sec*sec). It is then accelerated at the same rate until it falls to Earth. Air resistance is effectively cancelled out, since it is present on both parts of the flight.

Boy, I've run pretty fast on a treadmill and have yet to feel any wind on my face as I would if I was outside running around the track.

Lordmonar,

Right you are, but I don't think they will believe you. ( they probably still believe in man-made global warming)We might have to find an Aeronautical Engineer to convince the skeptics.

Major Lord

Quote from: SarDragon on February 17, 2010, 01:03:54 AM

Quote from: Major Lord on February 16, 2010, 08:32:51 PM
I weep for the future of our cadets when I think who may be teaching them physics.....I remember one senior member telling cadets that a bullet shot straight up will come back to earth at the same velocity at which it was launched.

Actually, if it goes exactly straight up, and exactly straight down, that is true. Add any horizontal component, and all bets are off.

The bullet starts with a specific amount of kinetic energy when fired, and at the top of its flight it becomes potential, after having been slowed at 32 ft/(sec*sec). It is then accelerated at the same rate until it falls to Earth. Air resistance is effectively cancelled out, since it is present on both parts of the flight.

Basically, another Mythbusters Episode  ;D

Now the question is: If you add Einsteinian Theory to the equation, does it take longer for it to go up than down?  :o

FW, do you have bullets that go the speed of light? Send me a box.....you can't get them in California!

The science project trick of excluding air densities at various heights and calculating the velocities as if they were all in a vacuum would be great, but the earth sucks and air is thick. (unless you are a climate scientist or a witch doctor)  A bullet fired straight up weighing 120 Grains, at 3000 M/S will fall until it reaches about 300-400 M/S, its terminal velocity. ( Depending on its attitude, sectional density, coefficient of drag, and other magical influences) Still not fun to get hit with, but not the same velocity it was launched at. Okay, that one was too hard: If you put a bird in a space suit, how fast can it fly on the moon?

Major Lord

ps. Don't we have even one full fledged (pun intended) aerospace engineer on this board?

Quote from: RiverAux on February 17, 2010, 01:12:00 AM
Boy, I've run pretty fast on a treadmill and have yet to feel any wind on my face as I would if I was outside running around the track.

Yes...but your thrust is developed from the friction between your feet and the road.  Since the road is moving away from you your net velocity becomes zero......airplanes do not develope their thrust from friction between the wheels and the ground.....but between the prop and the surounding air.  So it will still develope thrust even if the ground is going the other way.

Please read this:
http://tinyurl.com/Stupid-Airplane-On-Treadmill-Q

Where the author of that article claims there is no physical mechanism that would cause the plane to have nonzero speed, I say there is: kinetic friction. And kinetic friction is precisely what stops the treadmill from spinning up to infinity as the thrust of the plane's engine is bounded so is the limit of the speed of the treadmill. If you want to argue against THAT portion of my argument, I would be glad to do so.

Gee Maj., can't a guy have a little fun now and again.  Of course, if you want to be a little serious, timespace (yes, one word) is not dependant on the speed of light.  The further we are from the earth's surface, the more the time rate changes in space.  GPS works because we can calculate this relationship between the time rate differences between the satellites and earth.  It's kind of like "why is there gravity?" 

I know this is tangential to the thread but, I was getting tired of running this treadmill.  ;D

Quote from: FW on February 17, 2010, 02:19:54 AMThe further we are from the earth's surface, the more the time rate changes in space.

That isn't exactly true. It is not the distance from the earth's surface that causes time dilation, but rather differences in inertial reference frames. The reason why objects in orbit pass through time faster then people on the ground is because they are travelling at greater velocities.

Quote from: TACP on February 15, 2010, 06:06:24 AM
Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

Okay, while I was working out the free-body diagram to share with everyone, I realized that I was partially wrong.

Operating on the assumption that the aircraft's engine is on at full power... The plane will take off.  The wheels will not move or spin.  Let me explain.

The conveyor belt is as long as a runway- this was stated for a reason.  The only way for an aircraft's wheels to spin while the aircraft is on the ground is for the aircraft itself to actually move. 

So the plane will be sitting stationary relative to the conveyor belt, but the plane and the conveyor belt will be moving forward at an increasing velocity, until the plane takes off.

Do you guys really need this explained? 

Quote from: lordmonar on February 17, 2010, 02:16:11 AM

Quote from: RiverAux on February 17, 2010, 01:12:00 AM
Boy, I've run pretty fast on a treadmill and have yet to feel any wind on my face as I would if I was outside running around the track.

Yes...but your thrust is developed from the friction between your feet and the road.  Since the road is moving away from you your net velocity becomes zero......airplanes do not develope their thrust from friction between the wheels and the ground.....but between the prop and the surounding air.  So it will still develope thrust even if the ground is going the other way.

The scenario did not say that the planes engine was running...

On the bullet tangent: a bullet fired vertical will not fall at the same velocity it was fired at. A bullets terminal velocity is well below it's muzzle velocity. My best friend and I shoot extreme long range for fun so I've got a better than average grasp on ballistics. If the theory that all the forces are equal going up as going down were true then my bullet would hit the target at 500 yds at the same velocity as I fired it. It hits the target with about half the velocity. I'd explain further but it's late and I'm on my cell phone.

Quote from: RiverAux on February 17, 2010, 03:04:21 AM

Quote from: lordmonar on February 17, 2010, 02:16:11 AM

Quote from: RiverAux on February 17, 2010, 01:12:00 AM
Boy, I've run pretty fast on a treadmill and have yet to feel any wind on my face as I would if I was outside running around the track.

Yes...but your thrust is developed from the friction between your feet and the road.  Since the road is moving away from you your net velocity becomes zero......airplanes do not develope their thrust from friction between the wheels and the ground.....but between the prop and the surounding air.  So it will still develope thrust even if the ground is going the other way.

The scenario did not say that the planes engine was running...

Then the wheels would not be turning and the treadmill would not be moving.  That means "can a parked airplane take off?"   The answer is NO.  ;D

Quote from: davidsinn on February 17, 2010, 03:52:44 AM
On the bullet tangent: a bullet fired vertical will not fall at the same velocity it was fired at. A bullets terminal velocity is well below it's muzzle velocity. My best friend and I shoot extreme long range for fun so I've got a better than average grasp on ballistics. If the theory that all the forces are equal going up as going down were true then my bullet would hit the target at 500 yds at the same velocity as I fired it. It hits the target with about half the velocity. I'd explain further but it's late and I'm on my cell phone.

I stated a very (almost impossible) narrow case. ANY horizontal component will change the result greatly.

Quote from: SarDragon on February 17, 2010, 08:51:51 AM

Quote from: davidsinn on February 17, 2010, 03:52:44 AM
On the bullet tangent: a bullet fired vertical will not fall at the same velocity it was fired at. A bullets terminal velocity is well below it's muzzle velocity. My best friend and I shoot extreme long range for fun so I've got a better than average grasp on ballistics. If the theory that all the forces are equal going up as going down were true then my bullet would hit the target at 500 yds at the same velocity as I fired it. It hits the target with about half the velocity. I'd explain further but it's late and I'm on my cell phone.

I stated a very (almost impossible) narrow case. ANY horizontal component will change the result greatly.

Even pure vertical it would not impact at the same velocity it was fired at. Drag increases exponentially while velocity increases linearly. The bullet will not exceed it's terminal velocity on the way down. That velocity is much lower than muzzle velocity.

Quote from: davidsinn on February 17, 2010, 11:19:12 AM
Even pure vertical it would not impact at the same velocity it was fired at. Drag increases exponentially while velocity increases linearly. The bullet will not exceed it's terminal velocity on the way down. That velocity is much lower than muzzle velocity.

Agreed. The resistance force of atmospheric drag will keep the bullet from returning with muzzle velocity. I might also mention that in a vacuum, even a horizontal component wouldn't really matter. The bullet would travel parabolically and return to the surface with muzzle velocity.

Quote from: N Harmon on February 17, 2010, 01:32:13 PM

Quote from: davidsinn on February 17, 2010, 11:19:12 AM
Even pure vertical it would not impact at the same velocity it was fired at. Drag increases exponentially while velocity increases linearly. The bullet will not exceed it's terminal velocity on the way down. That velocity is much lower than muzzle velocity.

Agreed. The resistance force of atmospheric drag will keep the bullet from returning with muzzle velocity. I might also mention that in a vacuum, even a horizontal component wouldn't really matter. The bullet would travel parabolically and return to the surface with muzzle velocity.

Yup. Most people never get past kinematics in a vacuum and so can't fully grasp this stuff. I never had any actual training past that point myself. All I know about ballistics is self taught. I must be doing something right because I spot for my friend and he can hit a 19" gong at 730 yds with a .308 in squirrelly winds. I myself can hit the same gong just past 500 yds with an AR chambered for 5.56 but shooting .223.

I have an engineering degree (Last year I couldn't even spell engineer, and now I are one.)

All you need to know is two things.

F=MA

and

You can't push on a string.

THE PLANE WILL NOT FLY.

Presuming the treadmill was the only equipment and it was touching the wheels only.  It don't make a split of difference if the wheels are rotating at 110kts, 50kts otr 500kts.

Unless the aircraft has enough revative wind flowing over the airfoil the aircraft will not fly.

Airfcraft speed had nothing to do with the equation, only speed of the relative wind over the airfoil.

The treadmill theory is BUSTED.

Remember relative wind over the airfoil creates lift unless you exceed the angle of attack of the airfoil in which timeyou will stall the lift of the wing.

YES. The Airplane will fly

I don't think anyone is arguing that if the airplane is not actually moving into the wind, the airplane will not take off. If someone is thinking that the wheel RPM makes the airplane fly, they are not thinking clearly.

The overriding question is whether the airplane will continue to accelerate into the wind despite the treadmill rotating its wheels "backwards" in relationship to the forward movement of the aircraft. When the magician slides the table cloth out from under the dinnerware, the dinnerware is not instantly accelerated to the velocity of the tablecloth. The amount of energy coerced onto the dinnerware is a function of the critical coefficient of drag. If introduced too slowly, the frictional forces are sufficient to allow the table cloth to drag the dinnerware off the edge of the table, but if introduced at a rate that is "magic"; That is to say, a rate at which the frictional forces are induced and overcome quickly enough so that inadequate force is transmitted to the plates, the table cloth slides clear.

The force of the counter-rotating treadmill is not sufficient to overcome the thrust of the aircraft, which will accelerate regardless of the tiny amount of additional drag introduced by the counter-rotating treadmill's action on the wheels. The wheels will just roll faster that the aircraft is actually moving forward. The model most of you people in the "Can't fly this way" camp seem to envision sees the counteracting force of the treadmill as a 100% effectively coupled energy source that cancels out the ability of the aircraft to accelerate. If the aircraft was accelerating by virtue of engines turning its wheels directly, you would be right ( a car for instance, would remain static in relation to the treadmill) but since the airplane is driven by a column of compressed air, it matters not how fast the wheels are turning, only that the aircraft is accelerating to the velocity required to achieve lift sufficient to leave the treadmill.

Now, I am an engineer too, but the electronic kind, not the aero type, so I think we need the input of a bona fide aeronautical engineer to put this one to bed, not just another civil engineer. My $100.00 bet is still open. ( first come, first serve)

Major Lord

Quote from: Major Lord on February 17, 2010, 08:16:05 PMThe model most of you people in the "Can't fly this way" camp seem to envision sees the counteracting force of the treadmill as a 100% effectively coupled energy source that cancels out the ability of the aircraft to accelerate.

Did you even read the article I linked to in re: #46?

The problem with the original question is that as stated the question is paradoxical. The plane can't fly because the treadmill will somehow always match the velocity of the wheels. How it does this is not stated in the problem, only that it does it.

You talking to us about movement coming from power to its wheels or power to a column of air...we get it.

I am positing that the paradox may be solved by assuming that the bounds on engine thrust means the treadmill and wheels do not spin to infinity but rather at some pyschotic high speed whereby the rolling resistance of the wheels create enough force in the negative direction to cancel the positive force from the engines.

Nathan,

I fully understand your point, but we are not talking about a frictionless model in a vacuum. There is no "accelerate to infinity" possibility here. I just think you are wrong. I have asked a group of aviators I deal with to find an AE to answer the question in fully real world terms. So you accept my wager?

Major Lord

Wow, you don't understand my point at all.

Quote from: N Harmon on February 17, 2010, 08:49:24 PM

Quote from: Major Lord on February 17, 2010, 08:16:05 PMThe model most of you people in the "Can't fly this way" camp seem to envision sees the counteracting force of the treadmill as a 100% effectively coupled energy source that cancels out the ability of the aircraft to accelerate.

Did you even read the article I linked to in re: #46?

The problem with the original question is that as stated the question is paradoxical. The plane can't fly because the treadmill will somehow always match the velocity of the wheels. How it does this is not stated in the problem, only that it does it.

You talking to us about movement coming from power to its wheels or power to a column of air...we get it.

I am positing that the paradox may be solved by assuming that the bounds on engine thrust means the treadmill and wheels do not spin to infinity but rather at some psychotic high speed whereby the rolling resistance of the wheels create enough force in the negative direction to cancel the positive force from the engines.

Nathan,

You can't solve the paradox....the breakdown is that the wheels freely spin.  The plane moves forward at 5m/s the tread mill moves back at 5m/s....there is not enough Resistance in the wheel bearings to produce enough drag to counter act the thrust of a real airplane.  Because they are designed that way.  In theory you could move the treadmill at sufficient speed that drag from the wheels counter acts the thrust....and keeping the aircraft stationary (or at least keeping below take of speed) but the original question posted that the treadmill only moves at the same speed of the wheels.

Matching the speed of the wheels will only make the wheels turn faster.....it will increase the drag...but not by much (assuming a real aircraft)....it does not take a lot of force to move even a 747 (I have seen iron men pull them on TV!)....because the bearings on the wheels are so efficient.

The treadmill can not go to some high speed because it can only go the same speed at the wheels.  If the take off speed of the plane is 100 KIAS then the relative speed of the wheel and the treadmill will only be 200 Knot....and that is not high enough to induce enough drag to counter act the thrust of the powerplant.....About the only thing that may happen is the wheels would fail under such speed....but let us assume for the sake of argument, these wheels can take those sort of speeds.....the reality of the equation is that the wheels are designed to roll freely and reduce the amount of drag between the ground and the aircraft during the take off roll.  Yes there is drag, yes in theory you could develop enough drag to counter thrust (say you had a ski-plane on tarmack! or you forgot to pull the chocks)....but that is introducing new variable to the problem.

A properly maintained, balanced and loaded, production plane has more then enough thrust to overcome any drag introduced by the wheels in contact with the ground.  If anything the treadmill may actually help the plane get airborn as the backward motion helps reduce the inertia of the wheels themselves and allows the aircraft to use that much more power to accelerate the airplane.

Nathan,

Lets try this as a fundamental step-off point. " The rotational velocity of the wheel is the sum of the velocities of the aircraft and the treadmill" agree , or disagree?

Major Lord

Quote from: N Harmon on February 17, 2010, 02:17:34 AM
Please read this:
http://tinyurl.com/Stupid-Airplane-On-Treadmill-Q

Where the author of that article claims there is no physical mechanism that would cause the plane to have nonzero speed, I say there is: kinetic friction. And kinetic friction is precisely what stops the treadmill from spinning up to infinity as the thrust of the plane's engine is bounded so is the limit of the speed of the treadmill. If you want to argue against THAT portion of my argument, I would be glad to do so.

I looked at this again and I found some errors.

In Case 1 he states that V_b=v_c that is the speed of the bottom of wheel V_b (as it turns) is equal to the speed of threadmill V_c

The problem is that the speed of the bottom of the wheel (v_b) is developed by the forward motion of the aircraft V_w and Resistance with the ground.  If the ground is also moving (v_c) then you have to factor that in as well.  The equation should actually be V_b=(v_w+v_c)*R where R is the coefficient of resistance between the bottom of the wheel and the treadmill.

In Case 3 he wants the tradmill to move a the speed of the sum of the aircraft speed and the speed of the spinning tire V_s=V_b+V_w. 

So the equation would be V_c=V_b+V_w.  However I have already shown that V_b=(V_c+V_w)*R so you end up with an equation where the product of the equation is also one of the variables in the equation V_c=(V_c+V_W)*R+V_w

Therefore the speed of the treadmill develops a positive feedback look.  It will theoretically accelerate to infinity if V_W is anything accept ZERO....which is obviously wrong and violated the basic premise of the paradox.

And all of this has no bearing on the ability of the aircraft to fly...as the only velocity the wings care about is V_w and nothing as been presented that v_c can affect this in any meaningful way.

Excellent work there, my friend. You may keep the coveted Yaeger Aerospace award! :clap:

Major Lord

Oh, so close, yet so far.

Major Lord, if your troll can't even spell Yeager correctly, then would you kindly leave it at home?

Okay, lordmonar. You said,...

Quote from: lordmonar on February 17, 2010, 10:01:21 PM
Matching the speed of the wheels will only make the wheels turn faster.....it will increase the drag...but not by much (assuming a real aircraft)....it does not take a lot of force to move even a 747 (I have seen iron men pull them on TV!)....because the bearings on the wheels are so efficient.

And then you also said,...

Quote from: lordmonar on February 17, 2010, 10:44:14 PM
Therefore the speed of the treadmill develops a positive feedback look.  It will theoretically accelerate to infinity if V_W is anything accept ZERO....which is obviously wrong and violated the basic premise of the paradox.

Now, consider this posit: Small forces like that of your highly efficient ball bearings (which are oiled, right? thus travelling in a fluid, right?) that increases with velocity....become very LARGE forces as a result of very LARGE velocities (large as in,...approaching infinite).

And since the amount of thrust the airplane can provide is finite, then at SOME point, those LARGE velocities scaling small forces into LARGE forces will create a sufficient force equal and opposite of thrust....creating equilibrium.

Oooh, nasty! Didn't know it was your maiden name! Focus on the physics Nathan. I see you have still not accepted my $100.00 wager, so I assume you rest on the courage of your proffered opinion. So you are sticking with the force exerted on the bearings being so large at near infinite velocities, that they overcome the thrust of the aircraft at takeoff  velocities. Check. "Yaeger" or "Yeager"  by the way is the anglicized version of the German name "Jaeger" meaning "Hunter".

Major Lord

A more complete Mythbusters video: http://www.youtube.com/watch?v=YORCk1BN7QY

Major Lord

Who cares if it flies, the most important questions are:

How much does it pay?
How senior will it be?

The obvious answer is that pilots can do anything....just ask one!

Major Lord

^And that, my friends, is the answer to all our questions.  Thanks.  ;D

Quote from: N Harmon on February 18, 2010, 02:41:24 AM
Oh, so close, yet so far.

Major Lord, if your troll can't even spell Yeager correctly, then would you kindly leave it at home?

Okay, lordmonar. You said,...

Quote from: lordmonar on February 17, 2010, 10:01:21 PM
Matching the speed of the wheels will only make the wheels turn faster.....it will increase the drag...but not by much (assuming a real aircraft)....it does not take a lot of force to move even a 747 (I have seen iron men pull them on TV!)....because the bearings on the wheels are so efficient.

And then you also said,...

Quote from: lordmonar on February 17, 2010, 10:44:14 PM
Therefore the speed of the treadmill develops a positive feedback look.  It will theoretically accelerate to infinity if V_W is anything accept ZERO....which is obviously wrong and violated the basic premise of the paradox.

Now, consider this posit: Small forces like that of your highly efficient ball bearings (which are oiled, right? thus travelling in a fluid, right?) that increases with velocity....become very LARGE forces as a result of very LARGE velocities (large as in,...approaching infinite).

And since the amount of thrust the airplane can provide is finite, then at SOME point, those LARGE velocities scaling small forces into LARGE forces will create a sufficient force equal and opposite of thrust....creating equilibrium.

No....an equilibrium will NOT be met....you are forgetting the Three things.  One.....by the original premise the fastest the treadmill can travel is the speed the aircraft is moving.  Two...The feed back loop I describe shows that the math is wrong.  You cannot set up a system with the set up that he describes the math does not support it.  Third...you still assume that there sufficient drag induced through the wheels and the hub bearings to counter act the thrust of the power plant.

As I said....in theory that could be the case....flat tires, seized bearings, float plane pontoons on hard asphalt......but not a properly maintained aircraft.  The plane will have gotten to take off airspeed long before the any drag induced by the treadmill got high enough to noticeably counter act the thrust of the power plant.

Quote from: Major Lord on February 18, 2010, 03:33:06 AM
The obvious answer is that pilots can do anything....just ask one!

Major Lord

Allen,

I am glad to see you finally understand that pilots are "god's".  It sure took you a long time to realize that and, who would of thought that a ground pounder can be taught things.   


;D

Quote from: flynd94 on February 18, 2010, 06:19:33 AM

Quote from: Major Lord on February 18, 2010, 03:33:06 AM
The obvious answer is that pilots can do anything....just ask one!

Major Lord

Allen,

I am glad to see you finally understand that pilots are "god's".  It sure took you a long time to realize that and, who would of thought that a ground pounder can be taught things.   


;D

Yeah.....but with out maintenance.....a pilots is just pedestrian with a lether jacket and cool sun glasses!  ;)

I'm starting to think this is one of those things that we can never really know for sure, since it can't effectively be proven under the circumstances given in the original post...

Quote from: lordmonar on February 18, 2010, 04:04:53 AM
you are forgetting the Three things.  One.....by the original premise the fastest the treadmill can travel is the speed the aircraft is moving.  Two...The feed back loop I describe shows that the math is wrong.  You cannot set up a system with the set up that he describes the math does not support it.  Third...you still assume that there sufficient drag induced through the wheels and the hub bearings to counter act the thrust of the power plant.

One: The original premise is that the treadmill travels at the speed of the wheels, not the aircraft. This is an important distinction because wheel speed is independent aircraft speed (we agree here). Thus, the speed of the wheels is (theoretically) unbounded, as is the speed of the treadmill.

Two: The math mirrors the way the problem is worded. If it creates a paradox in doing so, then that means the problem is paradoxical. It is not evidence that the math is wrong, and by no means evidence that the plane takes off.

Three: I offer it as a possible solution to the paradox. The the "feedback loop" reaches some terminal velocity where the rolling resistance matches engine thrust, and the speed of the wheels and speed of the treadmill stop accelerating. Is it possible? I've found surprisingly little information on how rolling resistance changes with relativistic speeds, so I don't know. But if it isn't possible, then that again, doesn't mean the airplane flies. It just returns us to this paradox where the treadmill is designed to keep the aircraft at zero speed by virtue of spinning the wheels, but doesn't say how.

Your solution to the paradox breaks the premise of the question.

I agree......it is theoretically possible to spin the treadmill fast enough to keep the plane from flying.....but the question says it only goes as fast as the wheels move.  I don't think the 100 MPH that the treadmill is moving will be enough to keep a Cessna from flying! 

The math mirrors the way that question is worded.  That shows that the person asking the question does not understand physics, math or how to word questions.

Either way....the plane will fly.  Mythbusters did it.....even if they too did not understand the physics behind it.

I may be showing off my ignorance here, but I can't help but wonder...

Aren't the speed of the wheels and the speed of the aircraft equal as long as the wheels remain on the ground?

Under normal circumstances they are, but the wheels aren't connected to the driving force, so on a treadmill, their speed is irrelevant to the aircraft speed.

Lt.,

The speed of the wheels in this scenario would be the speed of the treadmill plus the speed of the aircraft, if any. If the aircraft stood still, basically maintaining just enough thrust to stay in one place on the treadmill, the wheel velocity ( To be clear, the speed at which the bottom of the tire travels over the treadmill) would be that of the treadmill.

Major Lord

Quote from: Major Lord on February 18, 2010, 06:43:47 PM
Lt.,

The speed of the wheels in this scenario would be the speed of the treadmill plus the speed of the aircraft, if any. If the aircraft stood still, basically maintaining just enough thrust to stay in one place on the treadmill, the wheel velocity ( To be clear, the speed at which the bottom of the tire travels over the treadmill) would be that of the treadmill.

Major Lord

And the paradox is that the treadmill will always match the speed of the wheels, which is to say for the airplane to have any forward speed then the speeds of the treadmill and wheels won't match...breaking the premise.

Quote from: lordmonar on February 18, 2010, 05:24:17 PM
I agree......it is theoretically possible to spin the treadmill fast enough to keep the plane from flying.....but the question says it only goes as fast as the wheels move.  I don't think the 100 MPH that the treadmill is moving will be enough to keep a Cessna from flying!

If the treadmill is moving at -100 mph, and the Cessna is taking off, then its wheels are traveling >100 mph. But the problem says the treadmill matches the speed of the wheels so the plane taking off breaks the premise.

Quote from: Al Sayre on February 18, 2010, 06:40:29 PM
Under normal circumstances they are, but the wheels aren't connected to the driving force, so on a treadmill, their speed is irrelevant to the aircraft speed.

So, if we disregard the wheels and have a plane doing, say, 70 knots on a treadmill moving at a speed of 70 knots in the opposite direction, what is the effective speed of the aircraft?

Quote from: Major Lord on February 18, 2010, 06:43:47 PM
The speed of the wheels in this scenario would be the speed of the treadmill plus the speed of the aircraft, if any. If the aircraft stood still, basically maintaining just enough thrust to stay in one place on the treadmill, the wheel velocity ( To be clear, the speed at which the bottom of the tire travels over the treadmill) would be that of the treadmill.

What makes your situation any different that the original question?  You have a plane "maintaining just enough thrust to stay in one place on the treadmill," but the question postulates a treadmill that is maintaining just enough resistance to keep the plane stationary.  Isn't the end result the same?

My turn. 

I saw that Mythbusters and they didn't bust or confirm anything, since despite the assertion of the announcer, the "treadmill's" speed clearly did not match the aircraft's speed - you can see the aircraft physically move forward and continue to accelerate in the opposite direction faster than the treadmill was moving, as evidenced by forward motion.

http://www.youtube.com/watch?v=YORCk1BN7QY

1) An airplane flies because of the motion of air over the wings which creates lift.  Forward velocity is irrelevant to flight except in that the physics of an airfoil require "x" air at "x" speed to pass over to provide lift.  The only way to get that amount of air is forward motion of the aircraft, which is caused by the propeller pulling it forward.  The propeller does not provide lift air over the wings, only forward velocity.

2) In the right theoretical conditions, a given airplane, especially one like a Cessna, could "hover" with a headwind balanced to the power of the engine.  Any discussions that involve vacuum are irrelevant because an aircraft cannot fly in a vacuum.

3) An aircraft tethered to the ground with a source (i.e. huge fan) of air pressure high enough could be made to hover in place with no forward velocity.

4) Any device which impedes forward velocity and thus prevents air from flowing over the wings, would prevent the aircraft from flying.

Thus, the aircraft would not fly, if properly situated on a treadmill which prevented it from achieving forward velocity.

^^^ I agree with what Eclise said above, makes sense.
To quote myself in an earlier reply...  >:D

Quote from: vento on February 16, 2010, 11:43:49 PM
Why is this whole thing so complicated?

A plane will lift off at the specified AIR speed based on weight and balance. As far as I know, air speed is the speed of the air flowing thru the wings. If the airplane is running really fast on a treadmill, then the ground speed could be really fast like say 100 knots, but the air speed is still zero.

The only way an airplane will lift off while on a treadmill is if the airplane and the treadmill is pointed into a strong headwind with a wind speed equal or greater than the air speed required for lift off.  ;)

QuoteI agree with what Eclipse said above, makes sense.

Which really scares me.

The only time a treadmill impedes the forward velocity of the plane is when the speed exceeds the ability of the bearings in the wheels to overcome the friction interior to the bearing. By design, this friction coefficient is many times less than the velocity the plane requires to be air born. The only reason for wheels on planes in the first place is to reduce the friction of the plane on the surface for the plane to become air born and to make it more pleasant on the plane and passengers when the plane lands.

Heck, lets put a plane that requires only 50 knots airspeed to fly on floats and put it in a river flowing in the opposite direction (a pseudo treadmill) at 50 knots. Who cares that the friction of the water passing the floats is far more than tires on a treadmill.

With the planes prop not turning, the plane will float down stream. Turn on the engine and with little effort, the plane will be up on the step of the floats and will then look as though it is sitting still in the water relative to a fixed observer on the shore, effectively balancing the force of the thrust against the friction of the water passing under the floats.

Go full power and it will accelerate. As it gets to 50 knots AIRSPEED it flies. The floats however feel as though they are running though the water at 100 knots (50 from the current, 50 from the forward motion of the plane......equal).

If your explanation above were true, then any plane that needs only 50 knots to fly that is landing at 100 knots would simply stop the instant it hit the ground rather than rolling 1000+ feet to a stop. And that is with the engine at idle.

So where, in a world where the wheels on a plane are FREE SPINNING, does it state that the treadmill is impeding the forward velocity of the plane????

The speed of the wheels (which is matched by the treadmill as stated in the problem) has no required dependency on speed of the plane. They just happen to correlate when the plane is rolling down the runway before take off. Once off, no correlation at all.

A plane in flight with the wheels retracted has a wheel speed of 0. Get them hanging in the slipstream and they may turn a little but not much. So here we have a plane in the air with the wheels not turning.

For those that are stuck on the idea that wheel speed and forward velocity of the plane are related, planes should be falling out of the air all over.

I agree with the wheels part of this - they are irrelevant, so the treadmill itself is really a red herring. I would think someone with "skillz" could create a computer model that would prove it once and for all.  Forward velocity has to be completely blocked for this to be a proper test.

But I don't agree on the water, or anything else which impedes forward velocity.  However you prevent forward motion, whether the ground equals the plane, the water equals the plane, or the plane is sitting on ice, as long as the aircraft cannot achieve forward velocity, and thus air pressure over the wings, it will not fly.

Anything that allows the airplane to attain forward velocity, means your test isn't working properly.

Absent the velocity necessary to induce the air pressure, or artificially induced air pressure (big fan), an airplane is not going to just
pop up in air because the prop is spinning.

OK, what makes a wheel spin on a plane that is on the ground?

Forward Velocity.

If then a plane is on the ground rolling because of forward velocity, causing the wheels to spin, what would be the effect of the treadmill matching the spin speed of the wheels. A doubling of the wheel spin rate. So a 50 knot Vr would simply mean that the wheels were spinning at 100 knots.

If no forward velocity, then no wheel spin then no movement of the treadmill. Of course it won't fly. It is no different than a plane sitting on the runway.

But to satisfy the question in the problem, it has to include forward velocity in order to get a wheel that is spinning for the treadmill to match.

So any model that does not include a forward velocity component is simply showing a plane sitting on a treadmill with zero motion. I can model that any day.

Once again, the original question:

" Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"

The hypothetical does not state that the airplane cannot move forward, only that the speed (rotation) of the wheels is exactly matched by the treadmill. No one is arguing that the airplane will fly without forward motion into the wind.

Major Lord

Quote from: Eclipse on February 18, 2010, 08:06:21 PM
My turn. 

I saw that Mythbusters and they didn't bust or confirm anything, since despite the assertion of the announcer, the "treadmill's" speed clearly did not match the aircraft's speed - you can see the aircraft physically move forward and continue to accelerate in the opposite direction faster than the treadmill was moving, as evidenced by forward motion.

http://www.youtube.com/watch?v=YORCk1BN7QY

1) An airplane flies because of the motion of air over the wings which creates lift.  Forward velocity is irrelevant to flight except in that the physics of an airfoil require "x" air at "x" speed to pass over to provide lift.  The only way to get that amount of air is forward motion of the aircraft, which is caused by the propeller pulling it forward.  The propeller does not provide lift air over the wings, only forward velocity.

2) In the right theoretical conditions, a given airplane, especially one like a Cessna, could "hover" with a headwind balanced to the power of the engine.  Any discussions that involve vacuum are irrelevant because an aircraft cannot fly in a vacuum.

3) An aircraft tethered to the ground with a source (i.e. huge fan) of air pressure high enough could be made to hover in place with no forward velocity.

4) Any device which impedes forward velocity and thus prevents air from flowing over the wings, would prevent the aircraft from flying.

Thus, the aircraft would not fly, if properly situated on a treadmill which prevented it from achieving forward velocity.

How would the treadmill impeed forward motion?  That is the crux of the problem.

Quote from: lordmonar on February 19, 2010, 01:01:34 AM
How would the treadmill impeed forward motion?  That is the crux of the problem.

It actually prevents it, and causes the airplane to be moving virtually backwards.

Picture this:

Run the treadmill without a motor on the plane.
The plane would move backwards until it hit the end of the runway - no flight.

Engage the engine to the point of equilibrium to the treadmill and the aircraft would stand still - no flight.

Increasing the throttle to exceed the speed relative to the treadmill (as they did on Mythbusters) causes pressure on the wings  - flight - but negates the terms of the test.

You can't compare this action of the aircraft on the ground to it in the air - once airborne, the assumption is a balance of forward velocity and air pressure for lift, but in order to attain that forward velocity, the aircraft has to break gravity, friction, and inertia in order to get the
air moving over the wings in the first place.

The net effect of the treadmill is negative forward motion, thus no lift.

Here's another example - an aircraft can take off from a carrier because it is pushed from behind hard enough for the air pressure to increase enough to lift the airplane (and anyone who has watched a launch knows it's usually right at the edge of stalling).

If the carrier was able to move at the same speed as the steam trolley (in the opposite direction), there would be no actual forward motion of the aircraft, and the plane would just drop into the water like Wile E. Coyote.

(http://i191.photobucket.com/albums/z13/AmandaReconwith/GravityLessons.jpg)

Now one question I'd have about a jet is whether its takes off based more on Newton's law of motion vs. a prop plane which
gets its velocity from Bernoulli's principle. If its the former, then forward motion is more like a rocket than a plane, and I don't know whether that makes a difference to this discussion, since rockets don't really "fly" in the Bernoulli sense.

Quote from: SilverEagle2 on February 19, 2010, 12:31:40 AM
If no forward velocity, then no wheel spin then no movement of the treadmill. Of course it won't fly. It is no different than a plane sitting on the runway.

But to satisfy the question in the problem, it has to include forward velocity in order to get a wheel that is spinning for the treadmill to match.

I think we are having a violent agreement or disagreement of some sort. We both agree that AIRSPEED is what makes an airplane fly, no questions here.

I also agree that forward velocity is needed to move the wheels and make the whole airplane move. What we don't seem to agree is that I think the treadmill that the OP proposed will counteract whatever forward velocity there is. So we will have an airplane with the wheels spinning really fast but the plane is in the same spot (Zero ground speed) and it will not fly. This is quite different than your idea of being the same as the airplane sitting on the runway.

That's why I think, the airplane will only fly (float, or lift off, or whatever we call it) if it is pointed into a headwind of equal or greater wind speed than it's required Vr AIRSPEED. The headwind blowing across the wind surface is what creates the lift for the plane to fly, not the speed the wheel is turning. And I think we also agree on this by reading from different segments of your post.

The major disagreement among all of us, is the effect of the treadmill. Some try to explain that the treadmill will never match the airplane in motion and therefore the airplane will eventually accelerate and move forward from the spot of the treadmill, while some argue that the airplane would remain in the same spot, some think differently if in the vacuum, etc. I simply took at as the force that counteracts against the forward movement of the plane and thus keeping the airplane at ZERO GROUND speed regardless of how fast the wheels turn.

My two cents worth...  :angel:

^ I agree.  Unless there is a head wind exceeding Vr, the aircraft will not fly.  Case in point.  I recently watched a Gulfstream taxi a little to close in front of a stationary C172.  It was the first time I saw a Cessna go Vertical..... Enough hot air and, up it goes. ;D

Quote from: Eclipse on February 19, 2010, 01:42:54 AM

Now one question I'd have about a jet is whether its takes off based more on Newton's law of motion vs. a prop plane which
gets its velocity from Bernoulli's principle. If its the former, then forward motion is more like a rocket than a plane, and I don't know whether that makes a difference to this discussion, since rockets don't really "fly" in the Bernoulli sense.

Huh???

The aerodynamics of flight are essentially independent of how an aircraft acquires its forward motion to generate lift.

Propulsion

A. Prop plane - big fan in the front (or back - B-36, C-337) drags the plane through the air fast enough for the wings to produce lift

B. Pure jet - suck, squeeze, bang, blow; hot combustion gas pushes on the back of the power turbine and pushes the plane through the air fast enough for the wings to produce lift

C. Turbofan - a combination of A and B above.

D. Rocket - B minus the suck and squeeze, has its own fuel and oxidizer; hot combustion gas pushes on the forward end of the combustion chamber and pushesthe plane through the air fast enough for the wings to produce lift

Now let's talk about airframes.

1. Airplane - wings sticking out the sides, with additional airfoils as needed to maintain control (V-stab, H-stab, etc); may be propelled by A - C-182, B - F-4, C - B-747, and the all important D - X-15. Yes- it is an airplane, because you can fly it just like the other three examples.

2. Rocket - wings (fins) in the back for stability; 2.75 FFAR, point and shoot, unguided (ballistic)

3. Missile - wings (fins) in the back for stability and control, and possibly vectored thrust from rocket style propulsion; Saturn V, not usually controlled in flight by the people flying in it

Move a wing fast enough through the air, and it will generate lift. It doesn't matter what the motive force is.

Fling-wings are left of another discussion.

My point was that an airplane won't fly without a wing, but a rocket can (since it doesn't really "fly") its just pushed forward really fast and hard.  Bernoulli has little to do with rockets you don't care about steering.

Quote from: Eclipse on February 19, 2010, 01:42:54 AM
It actually prevents it, and causes the airplane to be moving virtually backwards.

Picture this:

Run the treadmill without a motor on the plane.
The plane would move backwards until it hit the end of the runway - no flight.

Okay...I agree with this. As the treadmill moves back....the aircraft offers it no resistance and so the wheels stay stationary and the entire planes moves to the back with the treadmill.

Quote from: Eclipse on February 19, 2010, 01:42:54 AM
Engage the engine to the point of equilibrium to the treadmill and the aircraft would stand still - no flight.

Increasing the throttle to exceed the speed relative to the treadmill (as they did on Mythbusters) causes pressure on the wings  - flight - but negates the terms of the test.

Nope.....it illustrates the exact point of the test.  People think that a plane is a car.  That the interface between the ground and the wheels is as important to the plane as it is in a car.

Quote from: Eclipse on February 19, 2010, 01:42:54 AMYou can't compare this action of the aircraft on the ground to it in the air - once airborne, the assumption is a balance of forward velocity and air pressure for lift, but in order to attain that forward velocity, the aircraft has to break gravity, friction, and inertia in order to get the air moving over the wings in the first place.

The net effect of the treadmill is negative forward motion, thus no lift.

But the speed that you would have to move the treadmill to counteract forward motion of the aircraft would be astronomical which is defiantly a violation of the terms of the test.

Quote from: Eclipse on February 19, 2010, 01:42:54 AMHere's another example - an aircraft can take off from a carrier because it is pushed from behind hard enough for the air pressure to increase enough to lift the airplane (and anyone who has watched a launch knows it's usually right at the edge of stalling).

If the carrier was able to move at the same speed as the steam trolley (in the opposite direction), there would be no actual forward motion of the aircraft, and the plane would just drop into the water like Wile E. Coyote.

That is absolutely true....That is because the steam trolly is hardwired to the airplane and for that .02 seconds is the only source of thrust.  So if you are travelling over the water with a tail wind of 100Kts and the catapults shoots you forward at 100Kts your IAS will be zero, no lift, no flying, big splash.

But here is the kicker......it is because you simply pulled the runway out from under the plane.   In the plane on the treadmill test....the question is whether the ground of surface of the ground has any affect on the plane.  The answer is yes.  Friction will tend to slow the plane and resists its forward motion.  But the facts is because the wheels are specifiably designed to reduce this friction and allow the plane to travel over rough asphalt and other terrain.    Once the powerplant is running it will quickly over come the resistance of the bearings and the interface between the treadmill and the wheels and start moving forward.   

Quote from: Eclipse on February 18, 2010, 08:06:21 PM
My turn. 

I saw that Mythbusters and they didn't bust or confirm anything, since despite the assertion of the announcer, the "treadmill's" speed clearly did not match the aircraft's speed - you can see the aircraft physically move forward and continue to accelerate in the opposite direction faster than the treadmill was moving, as evidenced by forward motion.

Thus, the aircraft would not fly, if properly situated on a treadmill which prevented it from achieving forward velocity.

You don't get it.

Refer to the guidance hereinabove "The hypothetical does not state that the airplane cannot move forward, only that the speed (rotation) of the wheels is exactly matched by the treadmill. No one is arguing that the airplane will fly without forward motion into the wind."

Quote from: SilverEagle2 on February 19, 2010, 12:31:40 AM
OK, what makes a wheel spin on a plane that is on the ground?

Forward Velocity.

I look at it as the wheel is spun by a difference between aircraft speed and treadmill speed. After all, if the treadmill and airplane are traveling at the same forward velocity, the wheel speed is zero. Further, if the treadmill and airplane are both traveling backward at different speeds, you will have wheel spin.

Quote from: lordmonar on February 19, 2010, 05:46:48 AMFriction will tend to slow the plane and resists its forward motion.  But the facts is because the wheels are specifiably designed to reduce this friction and allow the plane to travel over rough asphalt and other terrain.    Once the powerplant is running it will quickly over come the resistance of the bearings and the interface between the treadmill and the wheels and start moving forward.

The question is can the power plant overcome the rolling resistance in the wheels at any speed? We can posit that if the treadmill were moving backward at a low speed, the aircraft could apply a small amount of thrust to remain stationary in relation to something not on the treadmill. Apply a little more treadmill speed, and you'd need a little more thrust to remain stationary. Rinse, repeat. At some point you're going to reach a limit. The thrust of the power plant is bounded, but the speed at which our theoretical treadmill can spin is not bounded.

Quote from: lordmonar on February 19, 2010, 05:46:48 AM
Nope.....it illustrates the exact point of the test.  People think that a plane is a car.  That the interface between the ground and the wheels is as important to the plane as it is in a car.

The interface between the ground and the plane IS as important to the plane as it is to a car as long as the plane remains on the ground.

You and others have made the point that a plane is different from a car because the car transmits thrust directly to the wheels while the plane does not.  You're absolutely right, but HOW the thrust is transferred to the wheels is beside the point, because as long as the plane remains on the ground, those wheels are the only things transferring thrust to the immediate force of resistance (the ground).

Consider a plane doing a run-up before taking the active runway.  The pilot engages the wheel brakes and goes to full throttle.  The plane lurches forward a bit because the thrust is acting on the airframe, yet the plane remains stationary.  Why?  Because the wheels are locked, rendering the plane's effective speed zero.

You can apply the same principle to the perfect treadmill assumed by the original question.  If the treadmill is able to match the plane's ground speed, the plane's effective ground speed is zero, leaving the plane motionless and unable to rotate into it's natural environment.

Quote from: DG on February 19, 2010, 01:27:25 PM
Refer to the guidance hereinabove "The hypothetical does not state that the airplane cannot move forward, only that the speed (rotation) of the wheels is exactly matched by the treadmill. No one is arguing that the airplane will fly without forward motion into the wind."

Then this is a waste of time - if the plane can move forward, its not a test of the actual idea, just a longer runway.

Can anyone explain exactly how the treadmill produces force on the airplane once the wheels start moving. It would need to create a force in the opposite direction of the thrust in order to prevent the airplane from accelerating forward.

As noted previously in the thread, the treadmill moving at the same (but opposite) speed as the thrust of the A/C is the exact same as the A/C having the brakes locked and running up the engine.  The A/C will not fly as there is no relative wind travelling over the wings to induce lift..  Some people are trying to overthink this problem..  The A/C will not lift until the A/C is allowed to travel faster than the treadmill, thereby moving on the treadmill, thereby causing relative wind, hence lift..  Thrust and drag are two forces working on the A/C, but they are unimportant in this situation because we need relative wind to generate lift.  Thrust and drag will be used to determine how fast the A/C will fly once airborn..

Its a hard idea for people to wrap their minds around. You are quite right, there is no way in the real world that a treadmill could introduce enough force to make the airplane static, or to prevent it from accelerating. The arguments fall into two camps: The first camp believes that the airplane cannot accelerate over the treadmill, because in order for the wheels to be going at the same speed of the treadmill, the aircraft would be standing still. No one believes that the airplane would fly by itself absent forward velocity) ( Although an Aircraft with enough thrust to weight ratio could do exactly that, that rare exception is clearly not what the original questioner poses)

The "it can fly" camp generally takes the position that the airplane will accelerate to takeoff velocity over the treadmill, even if the treadmill exceeds the velocity of the wheels. ( which would be against the rules of the question) One area of ambiguity is that in real life, the treadmill and the airplane both require time to change velocities. As the airplane increase in speed going down the runway, the treadmill introduces an equal but opposite increase in velocity but because the aircraft wheels are in contact with the runway ( as long as their coefficient of friction, i,e, traction holds) they will be rotating the speed of the treadmill plus the forward velocity of the aircraft. Now the original question states that the treadmill will automatically change speed to match the velocity of the tires, and in some peoples minds this is a paradox.

Major Lord

Quote from: bte on February 19, 2010, 05:43:11 PM
Can anyone explain exactly how the treadmill produces force on the airplane once the wheels start moving. It would need to create a force in the opposite direction of the thrust in order to prevent the airplane from accelerating forward.

There a few different ways that it could. The resistance torque of the wheels would create a negative force on the aircraft while they are being accelerated by the treadmill. As would the rolling resistance of the tire against the conveyor belt. And as would the fluid drag of the oiled ball bearings in the wheel hub.

According to the scenario given, although the wheels and the treadmill are moving and have overcome inertia, the fact that they are moving in opposite directions at the same speed means that the A/C has not overcome inertia in relationship to the earth and hence is not moving forward and will not create lift as there will be no relative wind between the earth and the A/C.. It seem so easy and I have explaned it many times in groundschool, but some people are trying to introduce quantum physics into a simple equation..  If the A/C is not moving in relationship to the earth, there will be no lifting, no flying, nada..  The wheels and threadmill are status quo and cancel each other out..

Nobody is introducing quantum physics into anything. This is simple high-school level newtonian mechanics. Quite simply, work equals force times distance...

W = F * d

The positive force in this equation is the force produced by the aircraft's engine. The negative force is the force produced by friction in the wheels. Remove the distance component, as if the aircraft was sitting still on a conventional runway, and it's just a battle of forces with the aircraft engine winning.

But the situation we have here is that the negative force produced by the friction in the wheels is multiplied over a MUCH greater distance than the distance of the engine. And at some point the Work/Distance function of the wheels intersects the Work/Distance function of the engines.

And that has nothing to do with lift or flight.  You may have force in the engine, but if the A/C is standing still and not moving down the threadmill, then you have no distance and thus no work.. if the threadmill is going south at 60 miles and hour and the wheels are rolling north at 60 miles an hour, the A/C is not moving in relation to the earth and there is no relative wind and no lift..  The wheels and the treadmill are a distraction in this problem because without relative wind over the wing (and I don't mean propwash) there just ain't no lift..

Quote from: AirAux on February 19, 2010, 07:09:54 PMif the A/C is standing still and not moving down the threadmill, then you have no distance and thus no work.

Not exactly... http://en.wikipedia.org/wiki/Thrust#Thrust_to_power_2

QuoteImagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

No where does the question state the plane is stationary. We all agree that a stationary plane will not fly. What we do not agree is that the plane remains stationary.

It will not.

The treadmill and wheels would have to be spinning at a very high rate of speed in order to produce enough friction to keep a fully throttled up airplane static in relation to the earth/wind/air mass.

After all, what are wheels for? To remove/reduce friction of the plane as it moves forward over the ground.

Otherwise the treadmill would only have to be as long as the wheelbase of the plane. The question states it is a conveyor the size of the runway.

If there is no forward motion of the plane on the ground then there is no wheel speed for the conveyor to match. It must move forward to activate the question.

As the plane approaches Vr, the speed of the wheels is simply 2xVr. It really is that simple.

Quote from: SilverEagle2 on February 19, 2010, 08:29:36 PM
If there is no forward motion of the plane on the ground then there is no wheel speed for the conveyor to match. It must move forward to activate the question.

I think the way the problem presents it is that the treadmill starts at the exact time the aircraft's engine applies a force. But otherwise you would be correct.

So?

The plane still can accelerate down the belt, up to the point where the friction/drag equals thrust.

It will be long off the ground before that point.

Consider this, if you had an A/C on an Aircraft carrier.  If the A/C had to reach 100 mph to take off and the Aircraft carrier was travelling in the oposite direction at 100 mph, would the A/C take off??  There would be no relative wind traveling over the airfoil to produce lift.  That is why an Aircraft carrier heads into the wind for take offs and landings..  I am not talking about acceleration, I am talking about constant speeds of both items.. They cancel each other out..

These are not the same. To many factors have been altered. The constants are no longer constants on a carrier.

Your logic is flawed as the start of the problem has the airplane sitting on the deck of a fast moving carrier.

Observer standing on the shore of the ocean looks out at a carrier and sees carrier and plane moving together. Catapult is then countering the carrier and the plane then looks static to the observer.

Observer turns around and sees plane static and the belt moving. Plane hits the throttle and then moves down the belt with high wheel speed.

They are not the same.

Quote from: SilverEagle2 on February 19, 2010, 08:39:22 PM
The plane still can accelerate down the belt, up to the point where the friction/drag equals thrust.

Somehow I think you're missing the premise of the question where the treadmill matches wheel speed exactly. Or are you arguing something else?

How...even if the plane is accelerating, is the distance that each revolution of the tire makes, not covering the same distance on the treadmill? They are equal.

Quote from: SilverEagle2 on February 19, 2010, 09:04:56 PM
How...even if the plane is accelerating, is the distance that each revolution of the tire makes, not covering the same distance on the treadmill? They are equal.

Because the speed of the wheels is the speed of the aircraft minus the speed of the treadmill. But since the premise of the problem says the speed of the treadmill is equal and opposite the speed of the wheels, we find that the speed of the wheels is the speed of the aircraft plus the speed of the wheels. This just doesn't work out for any nonzero aircraft speed.

The point is the speed of the wheels is equal to the speed of the belt.  The A/C has no speed as it has no traction (in effect).  The premise was that the wheels and the belt travelled at the same speed.  So the faster teh wheels travel, if they do accelerate, the faster the belt would travel, causing no A/C speed and the A/C would be sitting in one location, not moving down the belt.  There is no need for the belt to be as long as a runway, it could be the lenght of the A/C in teh scenario.  The only way she will fly is "if" the wheels begin to move faster than the belt to allow air to flow over the wings and then you blow the premise of the wheels travelling the same speed as the belt.  If I read teh premise correctly (And I am now so dazed and confused, I am not sure of anything..)   

Before I concede your point...which is true...the question leaves out a vital point.

Since Speed or Velocity is the measurement of Distance/Time it is important to know in relation to where the observer is.

If the observer is outside the plane, then yes, the only time the conveyor speed and the wheel speed is equal is when they are at zero...no flight.

If you are the pilot in the cockpit and the equation is in relation to your position, you can get to Vr of 50 knots and see the ground under you going by at 100 knots with a wheel and conveyor speed of 100 knots. Since the pilot/observer is already at 50, his relative speed is to the plane is 0 but to the ground moving below him he is moving at 100 knots and his equation balances.

Since I am a pilot, I ran the equation from inside the plane. It appears that you are running it from outside the plane. Your answer is correct. So is mine.

It is all about where the observer is.

Tricky.

If you're in the pilot's seat, traveling at 50 knots in relation to the stationary ground (not the treadmill), and the treadmill is moving backward at a speed of 50 knots in relation to the stationary ground but 100 knots in relation to you,... then what speed would your wheels be at....

I need to think about this some more...

Nope, still wrong!  The aircraft is only incidentally rolling: it is primarily an object propelled through space by compressed air from the prop. The wheels are just dragging along at the speed of the aircraft Plus not Minus the treadmill speed. As the aircraft increases in speed to reach VR, the belt will increase in speed to match the speed of the wheels, but it won't dramatically effect the speed over ground of the aircraft. The presence of the observer is irrelevant. The model of this as a hamster running in a cage or walking in place on an escalator is just not accurate, these models only apply to operations on treadmills wherein the motion is imparted by the wheels ( or legs, in the above cases) rather than by being pushed by a frictionally unrelated power source.   In fact, I doubt you could even cause an aircraft at full power to stand static like this on a treadmill if you tried, since the rolling resistance is so slight, that any amount of throttle, high or low, would cause you to drift forwards or backwards.

Major Lord

Quote from: N Harmon on February 19, 2010, 09:47:56 PM
If you're in the pilot's seat, traveling at 50 knots in relation to the stationary ground (not the treadmill), and the treadmill is moving backward at a speed of 50 knots in relation to the stationary ground but 100 knots in relation to you,... then what speed would your wheels be at....

I need to think about this some more...

The wheels move because the thrust of the aircraft is converted to rotation by the friction with the ground.

If the plane is stationary and held in place by rope....and the treadmill moves (V_c)...the wheels will turn...(V_b) thus V_b=V_c.  If The ground is stationary and the plane move V_w then the wheels will turn and give you V_b=V_w. 

That is how the wheels turn....and give you wheel speed.  The do not turn on their own.  They only turn when either the ground moves or the plane moves.

So basically the speed of the wheels is V_b=V_W+V_c

So the premise says....the treadmill moves at the same speed (but opposite direction) of the wheels V_c=V_b.  But if the ground moves that movement increases the movement of the wheels...which increases the movement of the ground...and so on...until in theory treadmill speed goes to infinity....even if the wheels only turn a fraction of an inch...so long as it maintains the initial speed then the treadmill will ramp up to light speed in a fraction of a second (assuming instantaneous feed back)....that is the problem with a positive feedback loop.  V_c=V_w+V_c

You cannot solve for V_c unless everything is zero. 

It is mathematically impossible.

It is practically possible....because there in always some lag in the feedback loop.  The speed of the lag will determine what will happen.  If the lag is slow....the airplane will get airborne and fly away.  If the lag is fast then the speed of the treadmill and the speed of the wheels will increase to a point where something will fail and break apart before the aircraft has enough air speed to get airborn.  If the lag is instantanious the threadmill goes to light speed and create a black hole and then just suck everything in and that will be the end of the experiment!

I think what our problem is.....is that we are reading too much into the premise.  The guy who wrote it was probably trying to see if people knew how an aircraft developed forward motion.  In a car you can do this treadmill thing because thrust comes from engine to the axle and then resistance between the tire and the ground pushes the car forward.  A treadmill moving backwards will absorb the energy (that is the law of conservation of energy) and the car will remain stationary.  If you are trying to catch people into not thinking where a planes thrust comes from....they would assume that if a car stay stationary then a plane must do so also.  But that is not the case.  A plane's thrust comes from the prop pulling on the air in front of it....or a jet/rocket directing its blast to the rear of the aircraft.  The treadmill has no effect on either of these things.  So the only affect if could possible have on the aircraft is through friction with the wheels.


Mathematically in can't fly.....but that is because the premise of the math equations is only solveable where the velocity is zero.  It is a faulty math problem.  In reality it will fly.  The wheels will freely turn no matter what anything else is doing.  The feedback lag will be slow enough for the plane to get airborn or at the very most something will explode in an orgy of sparks and burning rubber.

This reminds me of the old mathematics problem of the turtle that is 100M away from his home and covers half the distance between itself and home every second.....How long does it take him to get home.

Mathematically the answere is never....but in reality the distance is so small we just say "Lucy I'm home!".

Same thing here.  Mathematically we instantaneously spin the wheels to the speed of light and the universe comes to an end.....in reality the plane takes off and flies away, because a bunch of engineers made some good bearings and high strength rubber tires.

This is a "How many angels can dance on the head of pin" type question.....

Quote from: Short Field on February 21, 2010, 09:56:07 PM
This is a "How many angels can dance on the head of pin" type question.....

That one is easy....measure the dance area of an angle.....measuer the area of the head of a pin....divide one into the other.....QED

Quote from: lordmonar on February 20, 2010, 09:57:27 AM

Quote from: N Harmon on February 19, 2010, 09:47:56 PM
If you're in the pilot's seat, traveling at 50 knots in relation to the stationary ground (not the treadmill), and the treadmill is moving backward at a speed of 50 knots in relation to the stationary ground but 100 knots in relation to you,... then what speed would your wheels be at....

I need to think about this some more...

The wheels move because the thrust of the aircraft is converted to rotation by the friction with the ground.

If the plane is stationary and held in place by rope....and the treadmill moves (V_c)...the wheels will turn...(V_b) thus V_b=V_c.  If The ground is stationary and the plane move V_w then the wheels will turn and give you V_b=V_w. 

That is how the wheels turn....and give you wheel speed.  The do not turn on their own.  They only turn when either the ground moves or the plane moves.

So basically the speed of the wheels is V_b=V_W+V_c

So the premise says....the treadmill moves at the same speed (but opposite direction) of the wheels V_c=V_b.  But if the ground moves that movement increases the movement of the wheels...which increases the movement of the ground...and so on...until in theory treadmill speed goes to infinity....even if the wheels only turn a fraction of an inch...so long as it maintains the initial speed then the treadmill will ramp up to light speed in a fraction of a second (assuming instantaneous feed back)....that is the problem with a positive feedback loop.  V_c=V_w+V_c

You cannot solve for V_c unless everything is zero. 

It is mathematically impossible.

It is practically possible....because there in always some lag in the feedback loop.  The speed of the lag will determine what will happen.  If the lag is slow....the airplane will get airborne and fly away.  If the lag is fast then the speed of the treadmill and the speed of the wheels will increase to a point where something will fail and break apart before the aircraft has enough air speed to get airborn.  If the lag is instantanious the threadmill goes to light speed and create a black hole and then just suck everything in and that will be the end of the experiment!

I think what our problem is.....is that we are reading too much into the premise.  The guy who wrote it was probably trying to see if people knew how an aircraft developed forward motion.  In a car you can do this treadmill thing because thrust comes from engine to the axle and then resistance between the tire and the ground pushes the car forward.  A treadmill moving backwards will absorb the energy (that is the law of conservation of energy) and the car will remain stationary.  If you are trying to catch people into not thinking where a planes thrust comes from....they would assume that if a car stay stationary then a plane must do so also.  But that is not the case.  A plane's thrust comes from the prop pulling on the air in front of it....or a jet/rocket directing its blast to the rear of the aircraft.  The treadmill has no effect on either of these things.  So the only affect if could possible have on the aircraft is through friction with the wheels.


Mathematically in can't fly.....but that is because the premise of the math equations is only solveable where the velocity is zero.  It is a faulty math problem.  In reality it will fly.  The wheels will freely turn no matter what anything else is doing.  The feedback lag will be slow enough for the plane to get airborn or at the very most something will explode in an orgy of sparks and burning rubber.

This reminds me of the old mathematics problem of the turtle that is 100M away from his home and covers half the distance between itself and home every second.....How long does it take him to get home.

Mathematically the answere is never....but in reality the distance is so small we just say "Lucy I'm home!".

Same thing here.  Mathematically we instantaneously spin the wheels to the speed of light and the universe comes to an end.....in reality the plane takes off and flies away, because a bunch of engineers made some good bearings and high strength rubber tires.

Ahhhh......,

were you doing undercover work, in Mendocino County?

Quote from: lordmonar on February 20, 2010, 09:57:27 AM
So basically the speed of the wheels is V_b=V_W+V_c

So the premise says....the treadmill moves at the same speed (but opposite direction) of the wheels V_c=V_b.  But if the ground moves that movement increases the movement of the wheels...which increases the movement of the ground...and so on...until in theory treadmill speed goes to infinity....even if the wheels only turn a fraction of an inch...so long as it maintains the initial speed then the treadmill will ramp up to light speed in a fraction of a second (assuming instantaneous feed back)....that is the problem with a positive feedback loop.  V_c=V_w+V_c

Right, but from the perspective of the pilot V_w is always zero, right? I mean, unless the guy is walking to or from the lavatory, the relative velocity of the pilot and airplane is zero. Or are we missing something?

Quote from: N Harmon on February 22, 2010, 03:26:17 AM

Quote from: lordmonar on February 20, 2010, 09:57:27 AM
So basically the speed of the wheels is V_b=V_W+V_c

So the premise says....the treadmill moves at the same speed (but opposite direction) of the wheels V_c=V_b.  But if the ground moves that movement increases the movement of the wheels...which increases the movement of the ground...and so on...until in theory treadmill speed goes to infinity....even if the wheels only turn a fraction of an inch...so long as it maintains the initial speed then the treadmill will ramp up to light speed in a fraction of a second (assuming instantaneous feed back)....that is the problem with a positive feedback loop.  V_c=V_w+V_c

Right, but from the perspective of the pilot V_w is always zero, right? I mean, unless the guy is walking to or from the lavatory, the relative velocity of the pilot and airplane is zero. Or are we missing something?

I don't know where  you are going on this at all?

If you want to bring reletivity into this......okay....but why?

The airplane and the wheels will be pulled forward by the power plant as soon as it developes enough thrust to break the friction of the wheels.  The treadmill will not induce enough drag through the wheels to prevent the power plant from moving the airplane forward.

Reletive speeds and frames of references have very little do with the problem.

Quote from: lordmonar on February 22, 2010, 07:04:13 AM
If you want to bring reletivity into this......okay....but why?

Woah. Don't blame me! The issue of relativity was brought up by SilverEagle2 at the end of page 6.  :angel:

My mistake. It was a long day of frustrating circumstances which led to the thought. It won't happen again.

The effective speed of the treadmill is increased by the forward motion of the plane. Adding the planes velocity to the speed of the treadmill, it will equal the speed of the wheel rotation.

But then that will be argued as invalid by those that say it is not matching the wheel speed despite the continued 1 to 1 distance of the tire rotating across the surface of the treadmill.

Those who would argue that the invalidity of the premise could  reread the beginning premise:

"The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction."

In the real world, both the airplane and the treadmill need time to accelerate, but the premise of the question shows us that the treadmill will adjust itself to the speed of the wheels, and so we accept that as a fixed factor. We cannot assume that the velocity changes of the treadmill and the wheels happens instantaneously, because that does not happen in the real world. The wheel velocity on the other hand, is for the most part, a direct function of the treadmill velocity plus the aircraft forward velocity, their inertia and friction is one of the limiting factors on the ability of the treadmill to change velocity.

Major Lord

Ok, my turn to join the masses of the yes people. That and post on this thing again after something like a year-absence, haha! (Had to update my signature entirely, not even an AEO anymore, heh)

Anyways, here's why it is yes, and this explaination probably has already been posted, but it's 3 am and I don't want to do math at this time of the morning.

Ok, as was stated before, airplane wheels are not directly powered. They only move because the prop pulls the plane forward and they move against the ground due to friction, electron repulsion on the atomic level, and invisible little green men :-P

So, let's say that the wheels are rotating at a factor of 10 kts. This hypothetical perfect treadmill is therefore instantly rotating at -10 kts relative to the same direction, since it's moving in the opposite direction. Ok so now the wheels will no longer be rotating since they have lost their rotational velocity. However since they don't directly influence the plane, they are just "support and cushioning", the plane will continue to accelerate by the action of the prop pulling the plane through the air. The treadmill will increase in speed to keep the wheels at 0 kts, but again this doesn't matter. The plane will continue to accelerate. Your wheels may leave skidmarks and may even burn off some, and the plane may end up with a higher VR, but once it reaches that VR, physics says lift will overcome weight to the degree that the plane will fly.

Okay, if the airplane is stationary, absolute and the treadmill is going backwards suddenly at 60kts.

Is the air moving over the wings at 60 kts?

Thats the part of this I just don't get. The TV clip definitely showed the airplane moving forward. In which all they did was accomplish a really short field take off somehow.

Unless the power plant is run up at the same constant that the treadmill runs backwards, the airplane will not stay in the same place, and the moment it comes off the treadmill it has to go forward or it will just come back to the ground.

But again, the air flow has nothing to do with the treadmill movement.

The myth busters episode had some serious flaws.  If the plane was on a true tread mill that equally matched the speed as the tires rolled, the airplane would not gain any forward airspeed.  Gents.....unless your a Harrier, a helicopter or an F-35, your not flying without forward airspeed.

Mythbusters used the argument that because the power of the airplane is not tied the the wheels like they are in a car, that it is possible for a plane on a treadmill to fly.  In that segment, the airplane was accelerating forward because the ground under the tarp they were pulling was still providing enough friction for the airplane to gain forward motion.  On a true treadmill, where the tread mill exactly matches the speed of the rolling tires, the plane would go nowhere.

Flying Pig.

The plane will move!  The power plant pulls the aircraft forward.  Unless the friction/drag from the tread mill is so great that it will counter act the thrust of the power plant it will move.

The way the OP question was posted....the treadmill only moves as fast as the wheels.

In that scenio it is either talking about speed of the rotating tire....in which you end up with a positive feedback loop that will quickly go to the speed of light (mathmatically) or it matches the speed of the axil as it moves forward...in which case...it is moving forward which implies air flow...and the plane will fly.

The other way the treadmill can move is in the same direction as the aircraft (keeping the wheels from turning).  In that case the airplane is still moving foward through the airmass, generating lift.

So....bottom line.  The only way to keep the plane from flying is to move the treadmill so fast that it overcomes the thrust of the engine.  The speed to do this would be much greater then the speed of the tires that the OP has stipulated in his original question......so one again....the plane will eventually overcome the drag from the treadmill and gain enough airspeed to take off.

paraphrased from another site:   The airplane on a treadmill problem contains a basic ambiguity, and people resolve it one of a couple different ways. The tricky thing is, each group thinks the other is making a very simple physics mistake. So you get two groups each condescendingly explaining basic physics and math to the other. This is why, for example, the airplane/treadmill problem is a banned topic on some forums (along with argument about whether 0.999... = 1).

Can anyone explain how the treadmill can exert any force on the airframe which can at all counteract the thrust developed by the powerplant/propeller?

That is going to be the only way that it can keep the airplane from flying.

By the way, be specific. If you say it is friction, be specific about the source, how it gets transferred to the plane, , the direction, and the magnitude.

There is really no ambiguity about it, other than those introduced by persons introducing completely theoretical factors. Wheels spinning to infinity, frictionless environments, changes in velocity occurring outside of time, etc. etc. One group is thinking like theoretical physicists, ardently arguing that bees can't fly, and if they do in real life, its merely because we engineers are too dumb to understand the physics, or that we gamed  the question and now duck the math. The other group sees the problem as just how it was initially posed, and the answer ( as is so often the case when the question is fully understood before seeking the answer) is that of course the airplane can take off. To take a liberty with the initial question, in the real world ( no vacuums, magic, frictionless loops, or Heisenberg uncertainties) could you possibly create a situation in which you could cause an aircraft ( or lets call it a propeller driven car if you prefer) to stand perfectly static on a treadmill as the power of the propeller thrust is increased? Not a chance. The lag time between treadmill response and vehicle thrust would cause some degree of fore or aft motion. How about this;  If you landed your plane on a treadmill that exactly matched the reciprocal speed of the wheels of the aircraft, would the plane instantly stop because the wheels were accelerating to the velocity of the treadmill? Nonsense.

BTE, No one can explain to you how the treadmill can exert the force necessary without using introducing a religious argument to do so.

The funny thing is in this whole durn organization of aviation enthusiasts we don't seem to have a single real aerodynamics engineer. We should all just join the Coast Guard Aux, cause fluid dynamics is easier with water than air......

Major Lord

This isn't an engineering question. It's a physics/logic question, and there is a huge ambiguity to it.

Quote from: bte on March 11, 2010, 07:49:25 PM
Can anyone explain how the treadmill can exert any force on the airframe which can at all counteract the thrust developed by the powerplant/propeller?

You asked this on page 6, and I answered it (http://captalk.net/index.php?topic=9902.msg180674#msg180674). As for being specific, which one would you like to discuss first?

Quote from: N Harmon on March 12, 2010, 05:34:03 PM
This isn't an engineering question. It's a physics/logic question, and there is a huge ambiguity to it.

Quote from: bte on March 11, 2010, 07:49:25 PM
Can anyone explain how the treadmill can exert any force on the airframe which can at all counteract the thrust developed by the powerplant/propeller?

You asked this on page 6, and I answered it (http://captalk.net/index.php?topic=9902.msg180674#msg180674). As for being specific, which one would you like to discuss first?

Yes I did ask before, but I have to admit that your answer did not actually answer my question. I really want to know how the forces can be exerted by the treadmill in such magnitude and direction to counteract the force provided by the propeller.

Quote from: bte on March 12, 2010, 05:40:50 PM
Yes I did ask before, but I have to admit that your answer did not actually answer my question. I really want to know how the forces can be exerted by the treadmill in such magnitude and direction to counteract the force provided by the propeller.

It would be simple mechanical advantage, where the force of friction is multiplied over the huge distances developed by the treadmill to create a huge amount of work (http://en.wikipedia.org/wiki/Work_%28physics%29). Since there is a limited amount of mechanical advantage available to the propeller, and by definition of the problem, an unlimited amount of advantage available to the treadmill, the treadmill at some point should be able to counteract the force produced by the propeller.

Of course, this assumes all sorts of things in the problem that could be perceived differently by different people, thus the problem of ambiguity.

Okay......Simple machines.

The axle and wheel.

The Wheel works in two ways.

One it reduced the amount of friction between the load and the surface.  Say a 10'X10' load weighing 2000lbs sitting on the tarmack.....you can push all day and it will not budge.

But put it on 6" wide tricycle gear wheels and the area in contact with the ground is GREATLY REDUCED.

They also reduce friction by transferring it to the axle.

The weight of the load is not sitting on the rough ground....but on the ultra smooth surface of the axle bearings.  The bearing have an even smaller surface area then the outside of the tires....again greatly reducing friction.

The other way wheels work is by acting as a lever.  The longer the lever the less force it takes to move a particular load a set distance.

This is how you can get those iron men who can move 747's!

Now.....with this in mind.  If you want specific numbers we would have to know a whole lot of details that are just not provided.

We would have to know the resistive properties of the tradmill....it is Teflon, rubber, concrete, glass, polished steel?  The make up of the surface material has a lot to do with this problem.  Teflon is specifically designed to be low friction. but we use rubber mats in our bath to keep from slipping on the porcelain tub.

Then we would have to know about the properties of the wheels themselves.  Some tires are designed to have a lot of grip.  Take drag racing.....lots of surface area with very soft rubber.....they WANT a lot of traction between the road and the tire......airplanes tires are ususally designed with two things in mind.  Reducing friction on taxi and take off.....but having enough friction to stop the aircraft on landing or during an abort. 

We also need to take into account the size of the tires. The larger the diameter of the tire the less force it take to move the load. But larger tires weigh more too. Big Fat tires are good in very rough terrain...that is why bush planes has like the husky and cubs have big fat donut tires.  These tires are not so good on asphalt as they are too soft and get eaten up by the tarmac and they add additional weight to the aircraft.

Next we have to look at the efficiency of the axle/bearings.  The bearing/axle interface is critical.  Seize a bearing and you can lock up a wheel.

The next issue we would have to look at is the power plant and propeller....how much static thrust do they generate and how much total thrust do they generate at take off speed.

So.....to answer your question....we cannot answer specific questions about the total induced drag because we don't know any of the many, many, many variable in the problem. (I did not even go through things like density altitude, head winds, tail winds, crosswinds.  gross take off weight, ramp weight etc ET AL.)

My GUT tells me that unless I am missing something very basic.....the treadmill can't generate enough drag to counter act the thrust of a 182's engine/prop combination.  The wheels are too efficient.

Let's go back to the original post shall we?

Quote from: TACP on February 15, 2010, 06:06:24 AM
Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

Picture the airplane sitting on the conveyor 36/18 if it were a runway. Advance the throttle and the thrust of the engine moves me forward to the north at one knot and the conveyor matches my speed at one knot to the south so the wheels are spinning at the equivalent of two knots. Let's say my lift of speed is 60 knots so at 60 knots forward speed on the aircraft the conveyor is moving at 60 knots in the other direction and the wheels are spinning at 120 knots. I now lift off and leave the conveyor. There is nothing that will stop me from moving. If the airplane's speed is zero then the conveyor is at zero as well because I haven't caused the wheels to spin yet. I can only cause the wheels to spin by moving the aircraft and I just demonstrated that the conveyor will not exceed my forward speed and the amount of friction in the system should not come anywhere near the amount needed to keep me from moving forward. The reason the hypothetical conveyor is the length of a runway is because it assumes the aircraft is moving forward to gain airspeed.

Where do you get to intercede that the wheels are moving at 2 knots and not at 1 knot as the premise states??  The thrust of the engine (as measured by the speed of the wheels)  and the speed of the conveyor belt match so you are not moving anywhere and you will not fly.  No air moving over the wing and no lift..No Flying..  The only way would be "if" the engine could create enough power to move enough air over the wing to lift it straight up, ie, creating airspeed while stationary...   

Quote from: davidsinn on March 12, 2010, 10:16:49 PM
Picture the airplane sitting on the conveyor 36/18 if it were a runway. Advance the throttle and the thrust of the engine moves me forward to the north at one knot and the conveyor matches my speed at one knot to the south so the wheels are spinning at the equivalent of two knots.

Stop right there. Your situation violates the premise of the original post. Here it is again (emphasis mine):

Quote from: TACP on February 15, 2010, 06:06:24 AM
Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

The premise of the original post is in no way violated. The rotational velocity ( the speed at which the wheels surface moves over the ground) is exactly the sum of the velocity of the aircraft and the velocity of the treadmill. Without breaking traction, how could it be otherwise? Nathan, Did you interpret the premise of the original post to mean the actual forward velocity of the wheels, regardless of their rotational velocity, as if they were non-rotating objects dragged over the treadmill, but moving in some frame irrespective of of rolling? Are these magic wheels, to paraphrase Joe Pesci, sold by the Guy who sold Jack the beans to grow the beanstalk, or a magical universe in which non-instant grits are cooked in seconds?

Major Lord

Quote from: AirAux on March 12, 2010, 10:51:26 PM
Where do you get to intercede that the wheels are moving at 2 knots and not at 1 knot as the premise states??  The thrust of the engine (as measured by the speed of the wheels)  and the speed of the conveyor belt match so you are not moving anywhere and you will not fly.  No air moving over the wing and no lift..No Flying..  The only way would be "if" the engine could create enough power to move enough air over the wing to lift it straight up, ie, creating airspeed while stationary...

If you can explain how you can acheive this I would listen to it.

How can you move the conveyor belt in a way that is exactly matches the speed of the wheels......with out affecting the speed of the wheel.

The treadmill either moves in the same direction as the aircraft......keeping the wheels stationary.....but the plane still has forward motion and will lift off.   Or....the treadmill moves in the opposite direction.....INCREASEING the speed of the wheels....which violates the premeis of the problem......and again not inducinging enough drag to prevent flight.

I just spent the better part of two hours drawing some pretty pictures and another 30 min typing this post, to put this one to bed once and for all.

First let's review the four forces at work on an aircraft: Money, red tape, politics... ;D

Seriously: Lift, Drag, Thrust, and Gravity.

If Thrust>Drag and Lift>Gravity then the bird will fly. There is no denying that.

Let's set up our scenario. The observer(you) is on the ground. All velocity's are relative to the ground not the treadmill.
(http://www.majhost.com/gallery/davidsinn/CAP/AE/static.jpg)

The aircraft is static. No thrust, no drag, 1g of gravity and 1g of lift due to the treadmill pushing up on the aircraft.

There are two possible ways for this to work. The treadmill can move to the right or it can move to the left. I will address a right moving treadmill first.

(http://www.majhost.com/gallery/davidsinn/CAP/AE/10kt-a.jpg)

Case one. I apply power and Sir Newton says that unless my aircraft is tied to the ground the thrust of the engine will move it to the right. At this point I have 10 kts of velocity relative to the ground. Since the treadmill is matching my wheel speed exactly and for this one I decided the treadmill is moving to the right it's velocity is 10 kts and my wheels have zero RPM. I have a little drag due to aerodynamics. Lift=gravity.
(http://www.majhost.com/gallery/davidsinn/CAP/AE/60kt-a.jpg)

A little while later my aircraft is at 60 kts relative to the ground which gives me 60 kts of airspeed. My treadmill is still matching my wheels so it's at 60 kts and my wheels still have no rotation. Lift>gravity so I lift off. Drag is higher but still well below my thrust.

Case 2 Treadmill moves to the left.
(http://www.majhost.com/gallery/davidsinn/CAP/AE/10kt-b.jpg)
I apply power and Sir Newton says that unless my aircraft is tied to the ground the thrust of the engine will move it to the right. At this point I have 10 kts of velocity relative to the ground. Since the treadmill is matching my wheel speed exactly and for this one I decided the treadmill is moving to the left it's velocity is 20 kts and my wheels have 200 RPM. I have a little drag due to aerodynamics and a little drag due to wheel bearing friction. Lift=gravity.
(http://www.majhost.com/gallery/davidsinn/CAP/AE/60kt-b.jpg)
A little while later my aircraft is at 60 kts relative to the ground which gives me 60 kts of airspeed. My treadmill is still matching my wheels so it's at 120 kts and my wheels are at 1200 RPM. Lift>gravity so I lift off. Drag is higher but still well below my thrust.

Any questions?

Quote from: Major Lord on March 12, 2010, 11:08:53 PM
The premise of the original post is in no way violated. The rotational velocity ( the speed at which the wheels surface moves over the ground) is exactly the sum of the velocity of the aircraft and the velocity of the treadmill. Without breaking traction, how could it be otherwise? Nathan, Did you interpret the premise of the original post to mean the actual forward velocity of the wheels, regardless of their rotational velocity, as if they were non-rotating objects dragged over the treadmill, but moving in some frame irrespective of of rolling? Are these magic wheels, to paraphrase Joe Pesci, sold by the Guy who sold Jack the beans to grow the beanstalk, or a magical universe in which non-instant grits are cooked in seconds?

Major Lord

Take a wheel with a circumference of 4 feet. If it rolls on a stationary treadmill at 5 RPMs, then it's speed is ( 4 feet * 5 RPM ) 20 feet per minute. Now, if the treadmill is moving backward at a speed of 20 feet per minute, then the wheel will appear to be stationary from an observer on the ground. If the wheel is not stationary, then it's speed is not the same at the treadmill. If it is moving forward in relation to the ground, it's speed is greater than 20 feet per minute. If backward, it's less than 20 feet per minute.

Can we agree on that?

Quote from: davidsinn on March 13, 2010, 03:35:37 AM
Any questions?

How did you arrive at your force figures? And did you multiply them over the distance to find the amount of work they performed?

Quote from: N Harmon on March 13, 2010, 04:37:19 AM

Quote from: Major Lord on March 12, 2010, 11:08:53 PM
The premise of the original post is in no way violated. The rotational velocity ( the speed at which the wheels surface moves over the ground) is exactly the sum of the velocity of the aircraft and the velocity of the treadmill. Without breaking traction, how could it be otherwise? Nathan, Did you interpret the premise of the original post to mean the actual forward velocity of the wheels, regardless of their rotational velocity, as if they were non-rotating objects dragged over the treadmill, but moving in some frame irrespective of of rolling? Are these magic wheels, to paraphrase Joe Pesci, sold by the Guy who sold Jack the beans to grow the beanstalk, or a magical universe in which non-instant grits are cooked in seconds?

Major Lord

Take a wheel with a circumference of 4 feet. If it rolls on a stationary treadmill at 5 RPMs, then it's speed is ( 4 feet * 5 RPM ) 20 feet per minute. Now, if the treadmill is moving backward at a speed of 20 feet per minute, then the wheel will appear to be stationary from an observer on the ground. If the wheel is not stationary, then it's speed is not the same at the treadmill. If it is moving forward in relation to the ground, it's speed is greater than 20 feet per minute. If backward, it's less than 20 feet per minute.

Can we agree on that?

Yes. You're however missing the fact that the wheel is only spinning because the prop is pulling it forward.

Quote

Quote from: davidsinn on March 13, 2010, 03:35:37 AM
Any questions?

How did you arrive at your force figures? And did you multiply them over the distance to find the amount of work they performed?

The g force and lift are what they are. I made the thrust and drag up to illustrate the point. The concept is sound. The logic is undeniable.

Quote from: davidsinn on March 13, 2010, 01:31:26 PMYes. You're however missing the fact that the wheel is only spinning because the prop is pulling it forward.

I'm not missing that fact at all. What makes you think that?

QuoteThe g force and lift are what they are. I made the thrust and drag up to illustrate the point. The concept is sound. The logic is undeniable.

You didn't say why you only calculated forces and not work.

Quote from: N Harmon on March 13, 2010, 04:23:34 PM
You didn't say why you only calculated forces and not work.

Because work is irrelevant. It is the force that leads to acceleration to speeds at which the aircraft can take-off.

This is too over thought.  The wheels on an aircraft are irrelevant.  If they were so important to reaching Vr, the the whole premise behind skis or floats would be impossible.  The propeller will move the aircraft forward regardless of what the wheels are doing (exception being the brakes).  I agree with what was posted earlier: If you think the aircraft will sit like a brick, you should turn in your Yeager award, and I'm thinking that the pilot they used on mythbusters should consider turning in his certificate...

Quote from: N Harmon on March 13, 2010, 04:23:34 PM

Quote from: davidsinn on March 13, 2010, 01:31:26 PMYes. You're however missing the fact that the wheel is only spinning because the prop is pulling it forward.

I'm not missing that fact at all. What makes you think that?

QuoteThe g force and lift are what they are. I made the thrust and drag up to illustrate the point. The concept is sound. The logic is undeniable.

You didn't say why you only calculated forces and not work.

I said that because you are completely failing to grasp the concepts at work here. Until the aircraft starts to move forward the wheel and thus treadmill are static. Once the airframe starts to move then everything goes into action. As a consequence of that the treadmill will not exceed the velocity of the aircraft over the ground. It will either force the wheel to stay at zero rotation and move in concert with the aircraft or it's vector will be 180 degrees opposite the aircraft's velocity and equal which through simple addition will cause the wheel to spin at V*2. I pulled the thrust and drag out of my FPOC to illustrate the concept. One g is a given unless you want to start talking about different planets.

Quote from: tsrup on March 13, 2010, 09:56:16 PM
This is too over thought.  The wheels on an aircraft are irrelevant.  If they were so important to reaching Vr, the the whole premise behind skis or floats would be impossible.  The propeller will move the aircraft forward regardless of what the wheels are doing (exception being the brakes).  I agree with what was posted earlier: If you think the aircraft will sit like a brick, you should turn in your Yeager award, and I'm thinking that the pilot they used on mythbusters should consider turning in his certificate...

Dude! I suggested that anyone who thought it could not lift off should turn in their Yeager too! I also offered a wager of $100.00 to Nathan, but he has not bit......I don't think there is any way to convince the people who believe in magic that it will fly. I guess we are just going to have to build one great big treadmill and find a pilot willing to "risk" his life with a daring, high wheel RPM, normal speed takeoff! Where do they find such men?

Major Lord

I still believe that the aircraft will not fly.

In a no wind situation, a treadmill working against the force on the propeller, at the exact same speed, the relative speed of the aircraft will be ZERO.

Now can someone tell e how much relative wind is moving over the airfoil (wing) with a relative speed of Zero?

The premise of the question in my understanding is that the treadmill speed was matched by the wheels of the aircraft.  Equal forces applied, Does the aircraft move anywhere? No it does not.

I'll take the $100, and keep my Yeager.

Quote from: CadetProgramGuy on March 14, 2010, 03:07:00 AM


In a no wind situation, a treadmill working against the force on the propeller, at the exact same speed, the relative speed of the aircraft will be ZERO.

I fail to see how a treadmill has anything to do with a propeller.

Major Lord isn't interested in any serious conversation on the subject and is just trolling.

Quote from: davidsinn on March 14, 2010, 01:26:21 AM
I said that because you are completely failing to grasp the concepts at work here. Until the aircraft starts to move forward the wheel and thus treadmill are static. Once the airframe starts to move then everything goes into action. As a consequence of that the treadmill will not exceed the velocity of the aircraft over the ground. It will either force the wheel to stay at zero rotation and move in concert with the aircraft or it's vector will be 180 degrees opposite the aircraft's velocity and equal which through simple addition will cause the wheel to spin at V*2. I pulled the thrust and drag out of my FPOC to illustrate the concept. One g is a given unless you want to start talking about different planets.

This is the second time you have said the wheels will spin faster than the treadmill, which is NOT what the original problem said the treadmill is designed to do. The original problem said the treadmill will "exactly match the speed of the wheels, moving in the opposite direction". It doesn't say it will match them "once the airframe starts to move", or at half of the speed of the wheels. It says it will MATCH the the speed, EXACTLY.

I would appreciate if you, and some of you others tone down the condescending "you are completely failing to grasp the concepts at work here". I do grasp them. You are violating the conditions of the original problem by saying the velocity magnitude of the wheels and treadmill are unequal.

Quote from: tsrup on March 14, 2010, 03:09:56 AM
I fail to see how a treadmill has anything to do with a propeller.

The treadmill performs work on the wheels, which exert a negative force on the aircraft in the opposite direction of the force exerted by the propeller. The work performed by the propeller is bounded, whereas the work performed by the treadmill, given the premise of the question, is unbounded. A bounded and unbounded force working against each other. Guess which one will win?

Quote from: Major Lord on March 14, 2010, 02:28:05 AM

Quote from: tsrup on March 13, 2010, 09:56:16 PM
This is too over thought.  The wheels on an aircraft are irrelevant.  If they were so important to reaching Vr, the the whole premise behind skis or floats would be impossible.  The propeller will move the aircraft forward regardless of what the wheels are doing (exception being the brakes).  I agree with what was posted earlier: If you think the aircraft will sit like a brick, you should turn in your Yeager award, and I'm thinking that the pilot they used on mythbusters should consider turning in his certificate...

Dude! I suggested that anyone who thought it could not lift off should turn in their Yeager too! I also offered a wager of $100.00 to Nathan, but he has not bit......I don't think there is any way to convince the people who believe in magic that it will fly. I guess we are just going to have to build one great big treadmill and find a pilot willing to "risk" his life with a daring, high wheel RPM, normal speed takeoff! Where do they find such men?

Major Lord

Yes, I believe it was your post that I was referencing ;D

I'm sure I would be fine "risking" life and limb in this daring pursuit of science.  I better check my POH first to find out what published max wheel speed is. 

[darn] me for even mentioning it, I can see the new AD now..

"As per CFR XXX-XX wheels on the cessna 182T aircraft are limited to XXRPM.  Placard shall be placed in the middle of the windscreen in Bright neon pink on brown background no smaller than 3" by 8" "   

I would like to point out that the conditions of the original problem are impossible to replicate in the real world. That might be the biggest impediment to understanding here.

Thanks Capt!!

Unless you have a force that will counteract the force of the treadmill, the aircraft will move backwards.  The propeller will counteract that force.

Quote from: N Harmon on March 14, 2010, 03:12:20 AM

Quote from: tsrup on March 14, 2010, 03:09:56 AM
I fail to see how a treadmill has anything to do with a propeller.

The treadmill performs work on the wheels, which exert a negative force on the aircraft in the opposite direction of the force exerted by the propeller. The work performed by the propeller is bounded, whereas the work performed by the treadmill, given the premise of the question, is unbounded. A bounded and unbounded force working against each other. Guess which one will win?

I think I read someone else who put it best. 
Stand on a treadmill wearing roller blades, then using your arms pull yourself forward.  Guess what, you will move forward.  You can play with the speeds all you want, but the outside force will over come the two opposing forces.

Simple physics.  You have two opposing forces in equilibrium, as soon as you introduce a third, equilibrium will cease to exist.  The treadmill will never be able to compensate for the propeller because the wheels negate it immediately (provided we don't start dealing with friction). 

Quote from: CadetProgramGuy on March 14, 2010, 03:07:00 AM
I still believe that the aircraft will not fly.

In a no wind situation, a treadmill working against the force on the propeller, at the exact same speed, the relative speed of the aircraft will be ZERO.

Now can someone tell e how much relative wind is moving over the airfoil (wing) with a relative speed of Zero?

The premise of the question in my understanding is that the treadmill speed was matched by the wheels of the aircraft.  Equal forces applied, Does the aircraft move anywhere? No it does not.

I'll take the $100, and keep my Yeager.

The thing is that the treadmill cannot "work against the force of the propeller."

In order for the treadmill to move at the same rate as the wheels, there must be zero velocity (relative to an observer not in the plane and not on the treadmill.) That means the net force on the plane is zero.  If power is applied creating force in the forward direction, something has to apply force in the opposite direction. However, the treadmill cannot be the source of this force. The force being applied by the treadmill is being used to turn the wheels. It is not being used to hold back the aircraft. So something else must be holding back the aircraft. So technically, the airplane will not fly, but something other than the treadmill is to blame.

Let me try to make my answer simpler.  Let us propose the following:

The four forces on an airframe in level unaccelerated flight are Lift vs Weight (gravity), Thrust vs drag.

The treadmill is drag on the airframe.
in aviation to fly, one needs to counteract drag with thrust.

Drag (treadmill) is 60kts.

To acheive equilibrum thrust needs to be 60kts.

To acheive flight lift must be created by wind flowing over the wing.  It must be sufficient lift to overcome the weight of the aircraft or gravity. The wing cannot create lift if it is standing still with no wind flowing over it.

Quote from: tsrup on March 14, 2010, 03:24:37 AMThe treadmill will never be able to compensate for the propeller because the wheels negate it immediately (provided we don't start dealing with friction).

Ah hah!  ;D

See, some of us are dealing with friction, and some of us are not. Yet another reason why the original problem sucks.

Quote from: bte on March 14, 2010, 03:28:25 AMThe force being applied by the treadmill is being used to turn the wheels. It is not being used to hold back the aircraft. So something else must be holding back the aircraft. So technically, the airplane will not fly, but something other than the treadmill is to blame.

Are you asserting that if the propeller was not turning, and the treadmill began turning,... the aircraft would remain stationary and only its wheels move? If so, you may be assuming zero friction at the wheels, which is not part of the problem.

Quote from: N Harmon on March 14, 2010, 03:31:53 AM

Quote from: tsrup on March 14, 2010, 03:24:37 AMThe treadmill will never be able to compensate for the propeller because the wheels negate it immediately (provided we don't start dealing with friction).

Ah hah!  ;D

See, some of us are dealing with friction, and some of us are not. Yet another reason why the original problem sucks.

Null factor, The propeller was designed to overcome the friction from a start on a stationary surface therefore it doesn't factor in to the problem. 
friction is only an issue if the treadmill was started before the engine.  In that case the plane, as pointed out before, would simply move backwards until the engine is started.

No, I am saying if the wheels are turning at the same speed as the treadmill, something else must be acting on the airplane other than the treadmill.

Quote from: N Harmon on March 14, 2010, 03:34:02 AM

Quote from: bte on March 14, 2010, 03:28:25 AMThe force being applied by the treadmill is being used to turn the wheels. It is not being used to hold back the aircraft. So something else must be holding back the aircraft. So technically, the airplane will not fly, but something other than the treadmill is to blame.

Are you asserting that if the propeller was not turning, and the treadmill began turning,... the aircraft would remain stationary and only its wheels move? If so, you may be assuming zero friction at the wheels, which is not part of the problem.

You'll find that when dealing with physics problems the norm is to assume a non friction environment.  It helps simplify the problem and is usually not necessary until dealing with applied physics anyways. 

Quote from: tsrup on March 14, 2010, 03:37:36 AM
You'll find that when dealing with physics problems the norm is to assume a non friction environment.  It helps simplify the problem and is usually not necessary until dealing with applied physics anyways.

I didn't find that in my physics classes. When we were dealing with mechanics, once we learned how to include friction in our calculations we included friction quite regularly. In fact, we were not allowed assume a frictionless environment unless the problem stated as such. YMMV, obviously.

Quote from: tsrup on March 14, 2010, 03:35:45 AM
The propeller was designed to overcome the friction from a start on a stationary surface therefore it doesn't factor in to the problem. friction is only an issue if the treadmill was started before the engine.  In that case the plane, as pointed out before, would simply move backwards until the engine is started.

The propeller, while able to overcome friction on a stationary surface, may not be able to overcome friction on a moving surface, especially when the velocity limit of that surface is not bounded.

Say we have a Cessna 182 with a Lycoming engine that puts out 230 horsepower. Let's also say that its wheels require 50 pounds force (lbf) to keep it rolling.

Assuming a ideal prop, I simply need to run my treadmill at -1,725 miles per hour, to keep the aircraft stationary (http://www.google.com/#hl=en&safe=off&q=%28+50+pounds+force+*+-1725+miles+%2F+hour+%29+to+horsepower&aq=f&aqi=&aql=&oq=&fp=22b4dcbb1403dc0f). Less if the prop is not ideal.

Quote from: N Harmon on March 14, 2010, 03:58:52 AM


The propeller, while able to overcome friction on a stationary surface, may not be able to overcome friction on a moving surface, especially when the velocity limit of that surface is not bounded.

Actually it would take less effort to overcome friction on the treadmill than it would on a stationary surface since the treadmill would already be working toward breaking the friction of the wheels. 

Quote from: N Harmon on March 14, 2010, 04:08:39 AM
Say we have a Cessna 182 with a Lycoming engine that puts out 230 horsepower. Let's also say that its wheels require 50 pounds force (lbf) to keep it rolling.

Assuming a ideal prop, I simply need to run my treadmill at -1,725 miles per hour, to keep the aircraft stationary (http://www.google.com/#hl=en&safe=off&q=%28+50+pounds+force+*+-1725+miles+%2F+hour+%29+to+horsepower&aq=f&aqi=&aql=&oq=&fp=22b4dcbb1403dc0f). Less if the prop is not ideal.

Umm not to nitpick, but your answer is in the negative.....

Quote from: CadetProgramGuy on March 14, 2010, 01:35:47 PM
Umm not to nitpick, but your answer is in the negative.....

It's a power vector in the opposite direction the aircraft's engine power is being directed.

Quote from: tsrup on March 14, 2010, 09:58:40 AM
Actually it would take less effort to overcome friction on the treadmill than it would on a stationary surface since the treadmill would already be working toward breaking the friction of the wheels. 

Except the work being performed by the treadmill is in the opposite direction as the work being performed by the propeller. So, the treadmill isn't taking work away from the propeller, but adding to it's burden.

Quote from: N Harmon on March 14, 2010, 03:12:20 AM
Major Lord isn't interested in any serious conversation on the subject and is just trolling.

Quote from: davidsinn on March 14, 2010, 01:26:21 AM
I said that because you are completely failing to grasp the concepts at work here. Until the aircraft starts to move forward the wheel and thus treadmill are static. Once the airframe starts to move then everything goes into action. As a consequence of that the treadmill will not exceed the velocity of the aircraft over the ground. It will either force the wheel to stay at zero rotation and move in concert with the aircraft or it's vector will be 180 degrees opposite the aircraft's velocity and equal which through simple addition will cause the wheel to spin at V*2. I pulled the thrust and drag out of my FPOC to illustrate the concept. One g is a given unless you want to start talking about different planets.

This is the second time you have said the wheels will spin faster than the treadmill, which is NOT what the original problem said the treadmill is designed to do. The original problem said the treadmill will "exactly match the speed of the wheels, moving in the opposite direction". It doesn't say it will match them "once the airframe starts to move", or at half of the speed of the wheels. It says it will MATCH the the speed, EXACTLY.

I would appreciate if you, and some of you others tone down the condescending "you are completely failing to grasp the concepts at work here". I do grasp them. You are violating the conditions of the original problem by saying the velocity magnitude of the wheels and treadmill are unequal.

Quote from: tsrup on March 14, 2010, 03:09:56 AM
I fail to see how a treadmill has anything to do with a propeller.

The treadmill performs work on the wheels, which exert a negative force on the aircraft in the opposite direction of the force exerted by the propeller. The work performed by the propeller is bounded, whereas the work performed by the treadmill, given the premise of the question, is unbounded. A bounded and unbounded force working against each other. Guess which one will win?

I never stated the wheels spin faster than the treadmill. Unless the wheels are in a skid that's not possible. The tangential velocity of the wheels always exactly matches the velocity of the treadmill. I stated that the only way to make the wheels spin at all is to move the airframe via thrust from the prop. Thus I have imparted forward rotation to the wheel at a tangential velocity of X. Since common sense as well as every physics problem I have ever seen states that the wheel the surface they run over are always matched unless in a skid the only way to meet the premise of the problem is to make the treadmill's velocity be X in the opposite direction which leads us to a wheel tangential velocity of 2X.

You need to remember that the only way to add any kind of velocity into the system at all is for the airframe to start moving in reaction to prop thrust. You are missing that point.

Quote from: N Harmon on March 14, 2010, 03:18:27 AM
I would like to point out that the conditions of the original problem are impossible to replicate in the real world. That might be the biggest impediment to understanding here.

Well, if by this, you mean there is no way an actual experiment could be conducted that would validate your findings, I would have to agree. As for your "Troll" comment, I think you may want to have a chat with your professor ( or high school physics teacher) about your position on this particular test question. My experience leads me to believe the madder you get, the more likely you are to be wrong,  and its time to reconsider the problem without emotion. Chill.

Major Lord

The question as originally posed:

Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

Quote from: davidsinn on March 14, 2010, 03:21:19 PMI never stated the wheels spin faster than the treadmill. Unless the wheels are in a skid that's not possible. The tangential velocity of the wheels always exactly matches the velocity of the treadmill.

What? You did too state the wheels spin faster than the treadmill. You even stated it again in this very post; in the final sentence of your first paragraph (underline mine)...

QuoteSince common sense as well as every physics problem I have ever seen states that the wheel the surface they run over are always matched unless in a skid the only way to meet the premise of the problem is to make the treadmill's velocity be X in the opposite direction which leads us to a wheel tangential velocity of 2X.

I'm afraid that I simply can not follow your reasoning here. You seem to be contradicting the problem in one instance while contesting you are not in another.

Are you measuring the tangential velocity of the wheels relative to the treadmill, and comparing that to the velocity of the treadmill relative the ground? In other words, are you using different points of reference for each velocity and from that concluding the premise of the question, that the treadmill is designed to match the speed of the wheels, is satisfied?

If so, then I would have to say your interpretation does not seem at all reasonable to me. While I will gladly lay the blame for this on the poor wording of the original problem, it would go far in bringing us together to realize that most of us took that to mean that the treadmill would match the speed of the wheels as both are compared to the ground.

QuoteYou need to remember that the only way to add any kind of velocity into the system at all is for the airframe to start moving in reaction to prop thrust. You are missing that point.

Not really. Forces can be introduced without the airframe starting to move, causing the wheels and treadmill to spin. Remember the premise of this question has all of this occurring instantaneously.

ok, let me ask this question. In order for the airplane to fly, you need lift.  Where is your lift created in this theory?

Quote from: N Harmon on March 14, 2010, 02:14:43 PM

Quote from: tsrup on March 14, 2010, 09:58:40 AM
Actually it would take less effort to overcome friction on the treadmill than it would on a stationary surface since the treadmill would already be working toward breaking the friction of the wheels. 

Except the work being performed by the treadmill is in the opposite direction as the work being performed by the propeller. So, the treadmill isn't taking work away from the propeller, but adding to it's burden.

Wrong, If you want to talk about friction then you have to isolate the wheels and the treadmill, as soon as the treadmill starts running it will try to break the friction of the wheels.  Just as a powered wheel tries to break the friction of the ground, the powered ground will try to break the friction of the wheel 

Quote from: N Harmon on March 14, 2010, 02:14:43 PM

Quote from: CadetProgramGuy on March 14, 2010, 01:35:47 PM
Umm not to nitpick, but your answer is in the negative.....

It's a power vector in the opposite direction the aircraft's engine power is being directed.

Quote from: tsrup on March 14, 2010, 09:58:40 AM
Actually it would take less effort to overcome friction on the treadmill than it would on a stationary surface since the treadmill would already be working toward breaking the friction of the wheels. 

Except the work being performed by the treadmill is in the opposite direction as the work being performed by the propeller. So, the treadmill isn't taking work away from the propeller, but adding to it's burden.

What I am failing to understand is for an aircraft to remain stationary on the treadmill at full power, the treadmill must be running at Mach 3ish.....(1700 MPH)

Quote from: CadetProgramGuy on March 14, 2010, 06:20:24 PM
What I am failing to understand is for an aircraft to remain stationary on the treadmill at full power, the treadmill must be running at Mach 3ish.....(1700 MPH)

Think of it like this: Every second that 230 horsepower engine does 171.5 Kilojoules of work to make the plane go forward, meanwhile the treadmill is doing 171.5 Kilojoules of work to make the plane go backward. To argue that the plane goes forward is to argue against the conservation of energy.

Quote from: tsrup on March 14, 2010, 06:13:32 PM
Wrong, If you want to talk about friction then you have to isolate the wheels and the treadmill, as soon as the treadmill starts running it will try to break the friction of the wheels.  Just as a powered wheel tries to break the friction of the ground, the powered ground will try to break the friction of the wheel 

Breaking the friction usually means going from static friction to sliding friction. A rolling wheel is not sliding friction, it's static friction, so there is no friction to break. You may be thinking of the wheels' moment of inertia, and while the treadmill would help break the moment of inertia, that still translates as a negative force to the airframe.

Nat, you must remember that all of the Physicists that the opposition want to mention were the very ones that said the bumble bee couldn't fly..  By complicating the original supposition, that the wheels and threadmill are going the same speed in opposite directions, they miss the whole premise.  The A/C is not moving in relation to the ground, ergo, no airspeed, no airflow, no lift, no flying..  It really is simple..Isn't it..  Given the parameters we have in the original question, we are right.  Adding exterraneous stuff that is not in the original is not allowed..  Geesh, it just doesn't get any simpler..

+1

Thanks capchiro!!  Exactly what I have been trying to say.

The argument that you are making for the non-flight side is that the treadmill will prevent the aircraft from accelerating.

No one in their right mind believes that the aircraft will take flight due to the AC/s wheels spinning at takeoff velocities if the airplane is not moving forward into the wind. (stop me if anyone in their right mind thinks it will leap off the runway)

The argument from the flight side is fundamentally that the aircraft will accelerate as a function of the thrust generated by the propeller, moving the airplane forward. Because the problem stipulates that the treadmill will change to match the velocity of the wheels, the forward motion of the aircraft plus the backwards motion of the treadmill determine the specific velocity (RPM) of the wheels, but not the forward velocity of the aircraft, which is primarily a result of the forces in play created by the propeller.

Yes, the additional drag created by the treadmill will act to slow the plane, through the minor additional frictional forces imparted by the treadmill working against the wheels, but unless the treadmill is going (as someone pointed out) Mach 2.8, the forces won't be enough to slow the plane.

This can't happen in this situation, because the problem stipulates that the treadmill can accelerate only to the velocity of the airplanes' wheels, which with any aircraft, will be well below Mach anything!

As the aircraft adds power, it begins to move forward ( although many of you doubt this apparently) and the treadmill accelerates to the velocity of the wheels. This does not substantially reduce the aircrafts' forward speed, but it sets up a loop of cause and causation: As the airplane picks up forward speed, the treadmill picks up rearward speed. No amount of treadmill force can effectively counteract the airplane's thrust, because the treadmills speed is limited to the absolute maximum velocity of the aircraft's forward speed, which determines the initial wheel RPM.

Imagine if this aircraft had ice skates, and it was trying to take off from a perfectly flat glacier sliding away in the opposite direction that the aircraft is attempting to accelerate. Do you think the glacier would prevent the airplane from accelerating? Can you construct an experiment that will do this?

The Mythbusters constructed both a model, using an actual home treadmill, and a toy aircraft. It took off. Since doubt was still present, they dragged a sheet of canvas across an airfield to replicate the treadmill, and had a light sport aircraft of some breed try and take off. It accelerated without problems and took flight perfectly.

You say it won't roll, we say it will. I will leave my $100.00 on the table and will walk around with a hole in my Ribbon rack where my Gen. CY award is supposed to sit if you can prove the treadmill will prevent takeoff. Absolutely no way in the real world can this happen. 

Major Lord

Quote from: CadetProgramGuy on March 14, 2010, 06:12:22 PM
ok, let me ask this question. In order for the airplane to fly, you need lift.  Where is your lift created in this theory?

Okay.

The wheels must turn.....the orginal question says the wheels turn.  The treadmill's speed is set by the speed of the wheels.


How do the wheels turn on an air plane?

When the powerplant generates enough thrust to overcome inertia and the resistance of the bearings and the reisistance of the ground.....it moves the whole aircraft forward.  The wheels turn because the plane is moving forward.

As the plane gains speed it generates lift.

and I agree that if the airplane can create FORWARD movement it will fly.  No doubts about it.  but the question was for a treadmill and wheels.  No movement of the airplane.

Why is anyone taking the time to discuss this?  It's been done to death.  The treadmill has no effect on the plane.

S. Morgan

Quote from: Swampfox on March 15, 2010, 03:27:26 AM
Why is anyone taking the time to discuss this?  It's been done to death.  The treadmill has no effect on the plane.

S. Morgan

Did you register on here just to post this?

^^^^^

What S Morgan said!! :clap: :clap: :clap: :clap: :clap:

Well, it beats discussing uniforms, that's for sure.

^^^^

There is that!!

Although the "will fly" group seems to outnumber the "won't fly" group, I don't think the question has been definitively  answered. ( Hey, until a few months ago, "reputable" scientists believed in man-made global warming and the benefits of the Acai Berry, whatever the heck that is!) We could just drop it, conduct an experiment, or find an expert that everyone would acknowledge as acceptable. ( fat chance!) Trial by Combat seems the only practical answer. We will take Chuck Norris, who do you guys want?

Major Lord

Quote from: N Harmon on March 15, 2010, 06:37:10 PM

Quote from: Swampfox on March 15, 2010, 03:27:26 AM
Why is anyone taking the time to discuss this?  It's been done to death.  The treadmill has no effect on the plane.

S. Morgan

Did you register on here just to post this?

No, but thanks for the warm welcome to CAP and exemplary mentoring.

Quote from: Swampfox on March 15, 2010, 11:55:23 PM
No, but thanks for the warm welcome to CAP and exemplary mentoring.

Well, this is the only thread to be graced by your input. It is odd to see a new member jump into a 10 page thread, and declare it done to death while putting in his/her two cents.

It is more typical of people who have been here longer. ;)

I might be interested in how you arrived at the conclusion that the treadmill has no effect on the plane, if it is a reason we have not touched on already. Or perhaps you have a better insight into one of the already discussed reasons?

Quote from: Swampfox on March 15, 2010, 11:55:23 PM
No, but thanks for the warm welcome to CAP and exemplary mentoring.

Part of mentoring is that the Protoge (that's you) actually takes the time to listen to the advice of the mentor (that would be us).

So....begins the lesson.

If you are going to jump into a discussion that is long lived and has two very opposed view points.  Saying "Why are you arguing....you're wrong!" is NOT the way to gain friends and influence people.

Asking a question (even if it has been asked before) or adding some new information is always welcomed.  No one likes to be told that "they are wrong...shut up".....that is considered poor feed back.  Be specific, offer corrective advice and then observe if the person has learned from the feed back.

Thank you.....may return to your previously scheduled argument!  :D

Quote from: N Harmon on March 16, 2010, 12:06:12 AM

Quote from: Swampfox on March 15, 2010, 11:55:23 PM
No, but thanks for the warm welcome to CAP and exemplary mentoring.

Well, this is the only thread to be graced by your input. It is odd to see a new member jump into a 10 page thread, and declare it done to death while putting in his/her two cents.

It is more typical of people who have been here longer. ;)

I might be interested in how you arrived at the conclusion that the treadmill has no effect on the plane, if it is a reason we have not touched on already. Or perhaps you have a better insight into one of the already discussed reasons?

Sorry, obviously not a good way to provide a first post.

I could be wrong but I was assuming that this forum is not the only source of information on the topic.

A quick search on Google, searching for "airplane treadmill argument" found 1,340,000 hits.  Please note that many of these multiple hits are copied from other sites making the number a little lower.  Also, please consider that the Google search engine probably stopped after the first 1,340,000 items were found.

For example:

http://www.airplaneonatreadmill.com/2008_01_01_archive.html

http://pogue.blogs.nytimes.com/2006/12/11/the-airplane-treadmill-conundrum/

http://blog.xkcd.com/2008/09/09/the-[stupid]-airplane-on-the-[stupid]-treadmill/

http://answers.google.com/answers/threadview?id=428718

http://www.airplaneonatreadmill.com/

http://boingboing.net/2008/01/28/mythbusters-tackles.html


Since I have seen this argument for many years now, I was surprised that it is still going on.  It has been done to death on aviation forums, physics classes, etc.  The answers are available.

Just curious, are there any pilots saying the airplane won't fly?

S. Morgan

yes there is, me for one.

One cannot prove to me that a stationary airplane will take off unless there is significant airflow over the wings to create lift.  The only way that can happen is if the airplane is moving forward - or - an outside source is providing the lift.   That was never in the premise of the original question.

Quote from: CadetProgramGuy on March 16, 2010, 09:24:58 PM
yes there is, me for one.

One cannot prove to me that a stationary airplane will take off unless there is significant airflow over the wings to create lift.  The only way that can happen is if the airplane is moving forward - or - an outside source is providing the lift.   That was never in the premise of the original question.

Sorry...but it was a prmise in the original question.

QuoteImagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?

The treadmill moves at the same speed as the wheels........HOW DO THE WHEELS MOVE?!?!?!

The only way for the wheels to move is for the aircraft to be propelled forward by the powerplant....i.e. thrust! 

IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

Quote from: AirAux on March 16, 2010, 10:21:53 PM
IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

Please explain how the prop has anything to do with the wheels?

Quote from: AirAux on March 16, 2010, 10:21:53 PM
IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

No....

Plane is at rest.....prop at 1200 RPM brakes set....Wheel speed is 0 treadmill speed is 0.
Release the brakes, advance the throttle....wheels move at say 10 Kts threadmill moves at 10Kts in opposite direction.....the wheels will rotate twice as fast.

Speed picks up to 60 Kts the treadmill is moving at 60 Kts....wheels are rotating as if they were moving at 120 Kts.

Plane speeds up to 100 Kts.......treadmill is moving at 100 kts.....wheels are rotating as if the were moving at 200 kts.....plane lifts off.

This is counter inutitive to what we experince walking on a treadmill or driving a car on test stand....because the thrust in walking or driving a car comes THROUGH the axel to the wheels....so as you thrust forward the ground moves away you do not generate any friction and the car/or person goes no where.

On a plane the thrust is from the power propeller.  It pushes on the air and nothing else.  It does not matter what the ground is doing.

Quote from: lordmonar on March 16, 2010, 11:40:37 PM

Quote from: AirAux on March 16, 2010, 10:21:53 PM
IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

No....

Plane is at rest.....prop at 1200 RPM brakes set....Wheel speed is 0 treadmill speed is 0.
Release the brakes, advance the throttle....wheels move at say 10 Kts threadmill moves at 10Kts in opposite direction.....the wheels will roate twice as fast.

Speed picks up to 60 Kts the treadmill is moving at 60 Kts....wheels are rotating as if they were moving at 120 Kts.

Plane speeds up to 100 Kts.......treadmill is moving at 100 kts.....wheels are rotating as if the were moving at 200 kts.....plane lifts off.

This is counter inutitive to what we experince walking on a treadmill or driving a car on test stand....because the thrust in walking or driving a car comes THROUGH the axel to the wheels....so as you trust forward the ground moves away you do not generate any friction and the car/or person goes no where.

On a plane the thrust is from the power propeller.  It pushes on the air and nothing else.  It does not matter what the ground is doing.

I drew what the major is explaining. It's a few pages back.

Once the wheels start moving faster than the treadmill, you have broken the premise of the problem. Remember that the premise of the problem is that the treadmill is moving at the same speed as the wheels. As I interpret it, it means the edge of the tire is moving at the same speed as the treadmill. If this is the case, then the airplane will not move relative to the stationary airport. It will not fly.

Once the airplane does move forward, the wheels and the treadmill are no longer moving at the same speed, so even if the airplane does fly, it doesn't contradict the statement of the problem since the premise is no longer in play.

The problem with the question is really if there is any possible way for the treadmill to prevent the airplane from moving forward if the airplane is under full power. My contention is that there is not.

Quote from: lordmonar on March 16, 2010, 11:40:37 PM
On a plane the thrust is from the power propeller.  It pushes on the air and nothing else.  It does not matter what the ground is doing.

Yes, but what the wheels are doing does matter, as they indirectly transfer the propeller's thrust to the ground.  What happens when you lock the wheel brakes and run the engine up to full throttle?  The aircraft wants to move forward, but the thrust is unable to overcome the resistance generated by the brakes.  You have plenty of thrust, but your ground speed is zero.  As long as that remains true, you're going to remain grounded and stationary.

Put that same plane on the postulated treadmill and it will act the same way.  The thrust of the aircraft is negated by the opposing motion of the treadmill, leaving you with an effective ground speed of zero.

Quote from: NC Hokie on March 17, 2010, 12:08:25 AM

Yes, but what the wheels are doing does matter, as they indirectly transfer the propeller's thrust to the ground. 

I beg to differ. The wheels merely provide a way to reduce friction between the aircraft and the ground with some limited cushioning being provided by the wheels themselves.

Wheels are not required in order to transfer propeller thrust to the ground, as there is no need for the thrust to work against the ground (cf. the Wright Flyer of 1903 which was on skids, or the myriad float and ski planes). Sir Isaac Newton said famously, "For every action, there is an equal and opposite reaction." The propeller accelerating a column of air rearward is sufficient to impart forward motion to the aircraft. This can also be seen by increasing the throttle on an airplane at 10,000 feet and noting, all other things being equal, the acceleration of the aircraft, even though the ground is nearly 2 miles away.

I would submit, that in the original question, the aircraft would fly away from the treadmill even as the wheels have no rotation. The airplane will be stationary relative to the treadmill, but at flying speed relative to the earth and surrounding air.

Agreed, however, that if you lock the brakes and don't have sufficient thrust to overcome the huge increase in friction, the airplane will remain stationary.


v/r

Quote from: bte on March 17, 2010, 12:05:08 AM
Once the wheels start moving faster than the treadmill, you have broken the premise of the problem. Remember that the premise of the problem is that the treadmill is moving at the same speed as the wheels. As I interpret it, it means the edge of the tire is moving at the same speed as the treadmill. If this is the case, then the airplane will not move relative to the stationary airport. It will not fly.

Once the airplane does move forward, the wheels and the treadmill are no longer moving at the same speed, so even if the airplane does fly, it doesn't contradict the statement of the problem since the premise is no longer in play.

The problem with the question is really if there is any possible way for the treadmill to prevent the airplane from moving forward if the airplane is under full power. My contention is that there is not.

Its clear though that you have misinterpreted the premise of the question. The premise stated that the treadmill will travel in a direction opposite, but directionally proportionate to, the aircraft wheels.  The premise tells us that the Treadmill MATCHES the speed of the WHEEL. The treadmill will always be either at the fixed velocity of the wheels, or increasing or decreasing in velocity to accommodate the speed of the aircraft wheel.

The mental image generated by an incomplete reading of the premise implies in some minds, the idea of a man walking against an escalator, If them man walks faster, and the escalator speeds up at the same rate and absolute velocity, the man stays stationary, like an hamster in a wheel. These models are not what the original premise tendered. The forces used to accelerate the airplane are not a function in any significant fashion of the rotational velocity of the wheels, but only of the true forward motion of the aircraft. The wheel velocity according to the premise will always be 2X the forward velocity of the aircraft. The idea that the treadmill's opposing force is sufficient to decelerate the aircraft to a static position is a red herring.

If we restate the problem as making the wheels match the treadmills speed, instead of vice-versa, you might be able to create a static airplane on a treadmill, but there is no way on Gods' green earth you could make it happen the other way around.

Major Lord

Quote from: AirAux on March 16, 2010, 10:21:53 PM
IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

EXACTLY!!!!!!

Quote from: CadetProgramGuy on March 17, 2010, 01:43:36 AM

Quote from: AirAux on March 16, 2010, 10:21:53 PM
IF the treadmill has a powerplant that is moving the treadmill in the opposite direction as the powerplant is moving the AC and at the same speed, ergo, wheels are rolling at the same speed, the AC will not reach flying speed and will in fact be stationary to mother earth..

EXACTLY!!!!!!

Please see my post at #205 above. The wing of the airplane cares not a whit about the speed that the wheels are rotating (either at 0 knots or 2xFlying Speed, depending on how you interpret the ambiguous wording of the original question). The airplane will accelerate forward (relative to the earth, even while remaining stationary [or moving 2x flying speed, again based on your interpretation of the original question] relative to the treadmill). To posit that wheels are necessary for takeoff, regardless of their rotational velocity, does a great disservice to aircraft that have skids, floats and skis for landing gear and to flying boats with no landing gear at all.

v/r

Are you people really still perplexed by this??? When the air speed reaches 60......somethin' funny is gonna happen.  Reguardless how fast the little wheels turn, how fast the snow is moving under the ski or how fast the current is moving under the float. Something funny is gonna happen. 

What airspeed?  The airplane is not moving........

Quote from: bte on March 17, 2010, 12:05:08 AM
Once the wheels start moving faster than the treadmill, you have broken the premise of the problem. Remember that the premise of the problem is that the treadmill is moving at the same speed as the wheels. As I interpret it, it means the edge of the tire is moving at the same speed as the treadmill. If this is the case, then the airplane will not move relative to the stationary airport. It will not fly.

I addressed this earlier......the only way that the treadmill can move that would make the wheels NOT move (that is rotate) is to move in the same direction that the plane is moving.....in which case the plane still has forward motion, AKA air speed, and will fly.

QuoteOnce the airplane does move forward, the wheels and the treadmill are no longer moving at the same speed, so even if the airplane does fly, it doesn't contradict the statement of the problem since the premise is no longer in play.

I brought that up also.....depending on the lag between the wheels gaining speed and the treadmill matching that speed......if you assume a ZERO time lag the only states (mathmatically) of the wheels are zero and infinity!

QuoteThe problem with the question is really if there is any possible way for the treadmill to prevent the airplane from moving forward if the airplane is under full power. My contention is that there is not.

The answer is yes...there is a way for the treadmill to move that would induce enough drag that would prevent the plane from gaining lift off speed....but that speed would be much greater then the foward speed of the aircraft, and the wheels which the original question stated was not the case.

Quote from: NC Hokie on March 17, 2010, 12:08:25 AMYes, but what the wheels are doing does matter, as they indirectly transfer the propeller's thrust to the ground.

No they don't.  The wheels and the ground induce drag that fight against the thrust of the aircraft.  Thrust is NOT transferred to the ground via the wheel in an aircraft.

QuoteWhat happens when you lock the wheel brakes and run the engine up to full throttle?  The aircraft wants to move forward, but the thrust is unable to overcome the resistance generated by the brakes.  You have plenty of thrust, but your ground speed is zero.  As long as that remains true, you're going to remain grounded and stationary.

Absolutely true....but once you release the breaks and it moves forward and the treadmill moves backward you no longer have that resistance because you have removed the brakes from the equation.

QuotePut that same plane on the postulated treadmill and it will act the same way.  The thrust of the aircraft is negated by the opposing motion of the treadmill, leaving you with an effective ground speed of zero.

Not necessarily true.  IF the treadmill was moving at a very high rate of speed then it would induce enough drag into the equation to prevent flight.....but that speed would be much higher then the speed of the wheels.....which is the upper limit of the original premise.

Quote from: CadetProgramGuy on March 17, 2010, 06:01:14 AM
What airspeed?  The airplane is not moving........
[/quot

Again...what is preventing the air craft from moving.

There are only two possiblities of the premise.

a) The definition of "the speed of the wheels" is the speed of the surface of the wheel as it turns which can be expressed as RPM.

b) The dfinition of "the speed of the wheels" is the speed of the axle or hub as it is moved foward by the propeller.

If it is case a....then the onlly outcome is that the as the plane moves forward and the treadmill moves backward the speed of the wheel induces a positive feed back loop that quickly spins the wheel (and the treadmill) to something close to the speed of ligh and a black hole is created (assuming indestructable wheel and treadmill).

If it is case b....then the wheel just spins twice as fast as it would normally spin as the plane accelerated down the run way.

The treadmill could move in a way to induce enough drag to stop the plane from moving forward but that would be greater then the speed of the wheels (by either definition) and a violation of the premis.

The only way the treadmill could move that would negate the movement of the wheel (as in case a) would be to move in the same direction of as the moving aircraft....again a violation of the original premis.

Quote from: CadetProgramGuy on March 17, 2010, 06:01:14 AM
What airspeed?  The airplane is not moving........

It must move.

The premise clearly states that the treadmill matches the speed of the wheels.  The only way for the wheels to move is for the whole aircraft to move.  The only way for the treadmill to keep the aircraft from moving forward is if it was moing in such a way to induce the same amount of drag as a set of chocks or the break....and that would require the treadmill to move at significantly higher speeds then the the whees are moving.

Quote from: lordmonar on March 17, 2010, 08:25:33 AM
The only way for the wheels to move is for the whole aircraft to move.  The only way for the treadmill to keep the aircraft from moving forward is if it was moing in such a way to induce the same amount of drag as a set of chocks or the break....and that would require the treadmill to move at significantly higher speeds then the the whees are moving.

So it seems like there isn't a whole lot of disagreement between us, except for our interpretation of "the speed of the wheels". You take it as meaning the distance displacement of the whole wheel in some time, which makes the wheel speed the same as the aircraft speed in all situations. In that case the problem is exactly the same as your conventional "plane on a treadmill" problem, and the aircraft flies.

However, some of us took "the speed of the wheels" as meaning the wheel's circumference multiplied by its angular velocity (RPMs). Basically, what a speedometer attached to the wheels would measure. If the treadmill matches this speed exactly, it will produce enough rolling resistance to counter the power output of the power plant, and prevent the aircraft from flying.

I think it is probably a waste of time arguing which interpretation is correct, since the problem itself is ambiguous. But the details of the problem are interesting to discuss as they provide a good refresher of basic mechanics.

Quote from: N Harmon on March 17, 2010, 11:52:33 AM

Quote from: lordmonar on March 17, 2010, 08:25:33 AM
The only way for the wheels to move is for the whole aircraft to move.  The only way for the treadmill to keep the aircraft from moving forward is if it was moing in such a way to induce the same amount of drag as a set of chocks or the break....and that would require the treadmill to move at significantly higher speeds then the the whees are moving.

So it seems like there isn't a whole lot of disagreement between us, except for our interpretation of "the speed of the wheels". You take it as meaning the distance displacement of the whole wheel in some time, which makes the wheel speed the same as the aircraft speed in all situations. In that case the problem is exactly the same as your conventional "plane on a treadmill" problem, and the aircraft flies.

However, some of us took "the speed of the wheels" as meaning the wheel's circumference multiplied by its angular velocity (RPMs). Basically, what a speedometer attached to the wheels would measure. If the treadmill matches this speed exactly, it will produce enough rolling resistance to counter the power output of the power plant, and prevent the aircraft from flying.

I think it is probably a waste of time arguing which interpretation is correct, since the problem itself is ambiguous. But the details of the problem are interesting to discuss as they provide a good refresher of basic mechanics.

Nathan, you beat me to it. I was about to post a similar post. We finally agree on something in this thread.

We probably still disagree on whether or not the treadmill can in fact prevent the airplane from accelerating, but we do not need to discuss it further.

Quote from: bte on March 17, 2010, 12:12:17 PM
We probably still disagree on whether or not the treadmill can in fact prevent the airplane from accelerating, but we do not need to discuss it further.

Nah, who needs to discuss anything on here? :P  But it is a good refresher for basic physics understanding.

I'm curious how you see the airplane still accelerating.

The wheels go round and round..They are moving, but only in relationship to the treadmill and not to the ground.  As long as the wheels and treadmill are moving in opposite directions at the same speed, there will be no movement of the AC on the treadmill.  No movement of the AC, no lift..  It is, as was mentioned above, but somehow misconstrued, the same as a person walking on a treadmill.  the person is not moving in relationship to the ground and has no ground speed..  The AC is the same..it has no ground speed, it has no airspeed, it has no lift, it has no way possible to fly..  But, the wheels go round and round..

The wheels on the bus go round and round.
round and round.
round and round.
The wheels on the bus go round and round,
all through the town!

The people on the bus go up and down.
up and down.
up and down.
The people on the bus go up and down,
all through the town!

The horn on the bus goes beep, beep, beep.
beep, beep beep.
beep, beep, beep.
The horn on the bus goes beep, beep, beep.
all through the town!

The wipers on the bus go swish, swish, swish.
swish, swish, swish.
swish, swish, swish.
The wipers on the bus go swish, swish, swish,
all through the town!

The signals on the bus go blink, blink, blink.
blink, blink, blink.
blink, blink, blink.
The signals on the bus go blink, blink, blink,
all through the town!

The motor on the bus goes zoom, zoom, zoom.
zoom, zoom, zoom.
zoom, zoom, zoom.
The motor on the bus goes zoom, zoom, zoom,
all through the town!

The babies on the bus go waa, waa, waa.
waa, waa, waa.
waa, waa, waa.
The babies on the bus go waa, waa, waa,
all through the town!

The parents on the bus go shh, shh, shh.
shh, shh, shh.
shh, shh, shh.
The parents on the bus go shh, shh, shh,
all through the town!

The mommy on the bus says, I love you.
I love you, I love you
The daddy on the bus says, I love you, too.
All through the town.



For some reason I couldn't resist.

Quote from: AirAux on March 17, 2010, 01:08:40 PM
It is, as was mentioned above, but somehow misconstrued, the same as a person walking on a treadmill.  the person is not moving in relationship to the ground and has no ground speed..  The AC is the same..it has no ground speed, it has no airspeed, it has no lift, it has no way possible to fly..  But, the wheels go round and round..

Again, I beg to differ. About the only thing in common a person walking on a treadmill has with the original question is that a treadmill is present in both.

In order to move forward by walking, your feet, aided by friction, push against the ground to generate motive power. This is why walking on a nearly frictionless ice surface is so difficult. However, an airplane generates motive force by moving a column of air generally independent of the ground.

Although still imperfect, a better analogy would be to have the person on the treadmill reach forward on the hand rails and pull himself forward while dragging his feet lightly on the treadmill. In this case, the person's arms will replicate the action of the propeller and the hand rails will stand in for the surrounding air mass, both of which are unaffected by either the action of the treadmill or his lightly dragging feet. This person will move forward, both relative to the treadmill and, most importantly, relative to the ground.

The notion that an airplane needs its wheels to act against the ground to produce forward motion can be seen to be false by the fact that, if an airplane is in a steady-state flying condition at an altitude greater than 0' AGL (straight and level and constant airspeed in a still air mass of consistent temperature) and the throttle is advanced, the aircraft will accelerate without any interaction with ground. This same fact can be seen by watching ski planes and float planes accelerate and take off from the surface where the landing gear can only provide support for the weight of the aircraft prior to the wings taking the weight.

In my mind the only question is whether or not the aircraft will be stationary relative to the treadmill or moving at 2 times the flying speed when the airplane takes off, and that answer is wholly dependent on how you interpret the arguably ambiguous wording of the original poster's proposal. In both cases, the airplane will be accelerating relative to the earth (to include the airmass) and reach a speed sufficient to sustain flight, assuming it could fly if the treadmill were not present.

v/r

Quote from: N Harmon on March 17, 2010, 11:52:33 AMSo it seems like there isn't a whole lot of disagreement between us, except for our interpretation of "the speed of the wheels". You take it as meaning the distance displacement of the whole wheel in some time, which makes the wheel speed the same as the aircraft speed in all situations. In that case the problem is exactly the same as your conventional "plane on a treadmill" problem, and the aircraft flies.

QuoteHowever, some of us took "the speed of the wheels" as meaning the wheel's circumference multiplied by its angular velocity (RPMs). Basically, what a speedometer attached to the wheels would measure. If the treadmill matches this speed exactly, it will produce enough rolling resistance to counter the power output of the power plant, and prevent the aircraft from flying.

I disagree that the treadmill will produce enough rolling resistance to counter the thrust.

This reminds me of a discussion we had many, many years ago on the USENET group rec.skydiving about spotting, exit order and separation for skydivers jumping from an aircraft in flight.  The two basic camps were "ground speed matters more than airspeed" and "airspeed is key, ground speed is not" and there was tons of handwaving around the descriptions of the subjects and conditions.   (Very similar to what I've read here so far, BTW) 

The entire idea was to find the most effective and safe solution that would naturally and logically deconflict differing groups of jumpers (both in terms of size and fall rate) such that there was sufficient horizontal separation and also induced time and vertical separation that was helpful versus harmful to the overall equation.  Nobody liked the idea of tracking off a skydive to find someone from the previous group deploying in your face, or having someone from a following group come burning thru yours at breakoff...  usually results in what NASA commonly understates as a "bad day."

There was always this "well, the wind at 12,000 ft is this, and the airspeed of the plane is this, so it makes the ground speed this, but the wind at 8,000 ft is this.." and then there would be wildly divergent offshoots talking about ground speed versus airspeed, the jumper's forward throw after exit, the effect of body position on terminal velocity, the tendency for freeflyers to carve around the sky rather than describe a substantially vertical path, a column of air moving at xspeed, etc, etc. 

Someone would always say "Imagine that you're jumping from a balloon tethered to the ground and the wind doing y knots..."  and all these hypotheticals and variables.  One description, as I recall, using the balloon and wind analogy involved "hooking the DZ up to a tractor and dragging it along the earth.." to simulate ground speed.   Thereafter, every time this would come up again, I'd always say "I'm not getting into this again, I just volunteer to drive the tractor."

Finally, two kind gents named Winsor Naugler and John Kallend got together and did a couple presentations at the World Freefall Convention in Qunicy, IL on the subject and John, being a PhD in something, really put together a number of cool simulations to graphically explain the whole thing.  Finally, everybody "got" what was being posited and several years of heated discussions sort of evaporated.   Maybe someone smart/skilled can do the same here?

BTW, you can check out John Kallend's trajectory simulations right here: http://mypages.iit.edu/~kallend/skydive/

Quote from: NIN on March 17, 2010, 04:50:51 PM
This reminds me of a discussion we had many, many years ago on the USENET group rec.skydiving about spotting, exit order and separation for skydivers jumping from an aircraft in flight.  The two basic camps were "ground speed matters more than airspeed" and "airspeed is key, ground speed is not" and there was tons of handwaving around the descriptions of the subjects and conditions.   (Very similar to what I've read here so far, BTW) 

The entire idea was to find the most effective and safe solution that would naturally and logically deconflict differing groups of jumpers (both in terms of size and fall rate) such that there was sufficient horizontal separation and also induced time and vertical separation that was helpful versus harmful to the overall equation.  Nobody liked the idea of tracking off a skydive to find someone from the previous group deploying in your face, or having someone from a following group come burning thru yours at breakoff...  usually results in what NASA commonly understates as a "bad day."

There was always this "well, the wind at 12,000 ft is this, and the airspeed of the plane is this, so it makes the ground speed this, but the wind at 8,000 ft is this.." and then there would be wildly divergent offshoots talking about ground speed versus airspeed, the jumper's forward throw after exit, the effect of body position on terminal velocity, the tendency for freeflyers to carve around the sky rather than describe a substantially vertical path, a column of air moving at xspeed, etc, etc. 

Someone would always say "Imagine that you're jumping from a balloon tethered to the ground and the wind doing y knots..."  and all these hypotheticals and variables.  One description, as I recall, using the balloon and wind analogy involved "hooking the DZ up to a tractor and dragging it along the earth.." to simulate ground speed.   Thereafter, every time this would come up again, I'd always say "I'm not getting into this again, I just volunteer to drive the tractor."

Finally, two kind gents named Winsor Naugler and John Kallend got together and did a couple presentations at the World Freefall Convention in Qunicy, IL on the subject and John, being a PhD in something, really put together a number of cool simulations to graphically explain the whole thing.  Finally, everybody "got" what was being posited and several years of heated discussions sort of evaporated.   Maybe someone smart/skilled can do the same here?

BTW, you can check out John Kallend's trajectory simulations right here: http://mypages.iit.edu/~kallend/skydive/ (http://mypages.iit.edu/%7Ekallend/skydive/)

I already did pictures. What more can we do? I'll do equations next I guess.

Quote from: davidsinn on March 17, 2010, 04:56:15 PM
I already did pictures. What more can we do? I'll do equations next I guess.

My bad. I read pages 1, 11 & 12.  All that middle stuff? "Too long, did not read." :)

Quote from: NIN on March 17, 2010, 05:16:08 PM

Quote from: davidsinn on March 17, 2010, 04:56:15 PM
I already did pictures. What more can we do? I'll do equations next I guess.

My bad. I read pages 1, 11 & 12.  All that middle stuff? "Too long, did not read." :)

Back at post #147 (http://captalk.net/index.php?topic=9902.msg183875#msg183875) It kind of feels like an argument with moon landing deniers.

Guess I will have to go get a model airplane and a treadmill.....

My point is somehow getting complicated.  I agree if the wheels on the airplane were not in motion, the treadmill would pull the aircraft backwards.

I also agree that to keep the wheels of the aircraft moving at 60kts IAS, without the treadmill, the airplane will have to move forward.

Now if the treadmill was moving at 60kts, IAS, and the airplane was matching the 60kts IAS under power, the aircraft is not moving forward, or the ground speed is 0, and the airspeed indicator reading through the pitot tube would also be 0, would it not?

I realize and agree with the premise that the airplane would have to be moving forward to counteract the treadmill, but if equal speeds are present, then you are on a highway to nowhere.

Quote from: CadetProgramGuy on March 17, 2010, 06:41:06 PM
Guess I will have to go get a model airplane and a treadmill.....

My point is somehow getting complicated.  I agree if the wheels on the airplane were not in motion, the treadmill would pull the aircraft backwards.

I also agree that to keep the wheels of the aircraft moving at 60kts IAS, without the treadmill, the airplane will have to move forward.

Now if the treadmill was moving at 60kts, IAS, and the airplane was matching the 60kts IAS under power, the aircraft is not moving forward, or the ground speed is 0, and the airspeed indicator reading through the pitot tube would also be 0, would it not?

I realize and agree with the premise that the airplane would have to be moving forward to counteract the treadmill, but if equal speeds are present, then you are on a highway to nowhere.

No....you are supposing that the treadmill is pulling back at some rate that would resist the thrust of the propeller at an RPM that should be propelling the aircraft at 60 Kts.

This is possible.....but not within the parameters set by the original premis.

Here is why.

The plane's throttle is set at say 2000 RPM....enough that it normally would give you 60 Kts IAS in still winds on an asphalt runway.

If the treadmill was only going 60 Kts it would not induce enough drag to stop the aircraft.

Here is the proof.

If the treadmill was stationary and the plane accellerated to 60 kts there is NOT ENOUGH DRAG to stop the aircraft.

So....the treadmill MUST move at a significantly higher speed....much higher then the top speed of the aircraft.

So.....it is possible to build a machine to do this.....they are called chocks and breaks  :D.

So you would have to build a treadmill that moved at a speed high enough that it induced the same amount of resistance as the brakes or chocks do.....and that speed would have to be very high....not the "same speed as the wheels" that the original premise stipulates.

Quote from: CadetProgramGuy on March 17, 2010, 06:41:06 PM
Guess I will have to go get a model airplane and a treadmill.....

My point is somehow getting complicated.  I agree if the wheels on the airplane were not in motion, the treadmill would pull the aircraft backwards.

I also agree that to keep the wheels of the aircraft moving at 60kts IAS, without the treadmill, the airplane will have to move forward.

Now if the treadmill was moving at 60kts, IAS, and the airplane was matching the 60kts IAS under power, the aircraft is not moving forward, or the ground speed is 0, and the airspeed indicator reading through the pitot tube would also be 0, would it not?

I realize and agree with the premise that the airplane would have to be moving forward to counteract the treadmill, but if equal speeds are present, then you are on a highway to nowhere.

Using your 60 Kts treadmill speed:

If the wheels are moving in contact with the treadmill BUT the aircraft has no forward motion relative to the earth then:

     The wheels are moving at 60 kts rotational velocity (Vww), 0kts ground velocity(Vg), and 0 kts
          Indicated Air Speed(IAS). 
     The aircraft wing is moving at 0 + Vv (Wind Velocity vector * calibration factor) Calibrated Air Speed   
     The treadmill is moving at -60kts Vwt and 0kts Vg

If the wheels are in contact with the treadmill, AND the aircraft has motion relative to the earth, then:

     The wheels are moving at (60+X) Kts Vww  and X kts Vg.  Where X=Vectoral Sum of Vv + Calibrated Air Speed (CAS). 
     The aircraft wing is moving at X Vg and CAS
     The treadmill is moving at -(60+X) Vwt and 0 Vg

When the CAS exceeds Vr (rotation velocity of the wing)  (CAS>Vr) the aircraft will become airborne.


The point of all this is that Vwt and CAS are independent variables and the problem cannot be solved with the information given

If the treadmill is moving at 60 Kts IAS, it is airborne attached to the aircraft, hence Vwt and Vww are moot since the aircraft is airborne.   >:D