Plane on a Treadmill

[heliodoc]

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!

[FW]

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? 

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

[davidsinn]

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? 

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.

[Major Lord]

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

[lordmonar]

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.

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.

[Pingree1492]

^^^ 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.

[lordmonar]

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.

[Major Lord]

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

Major Lord

[N Harmon]

Assume 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.

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.

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.

I think the Mythbuster episode shows it rather eloquently.

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

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.

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... 

[Pingree1492]

Assume 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....

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.

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.

I 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.

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.

[Major Lord]

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

[N Harmon]

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.

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.

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.

Um... 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?

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.

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.

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

[Major Lord]

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

[N Harmon]

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.

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.

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.

[Major Lord]

"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

[SilverEagle2]

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.

[Spike]

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.   

[SilverEagle2]

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.

[vento]

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. 

[lordmonar]

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.