A jet plane on a large treadmill

FUCK THIS THREAD!!!

AAGGGGH.

HOW CAN YOU ALL BE SO STUPID.

The only way the plane can be held stationary by moving a conveyor belt (putting aside the awesome calculation of the small friction created by the friction of the wheel bearings) is by applying the wheel brakes of the plane.

OTOH. IF YOU APPLY THE WHEEL BRAKES ON THE PLANE, YOU DON"T EVEN NEED THE CONVEYOR TO HOLD THE PLANE STATIONARY.

sorry for shouting, but this thread is so stupid, and the question was correctly answered many pages ago.

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Originally Posted by Core Shot

HOW CAN YOU ALL BE SO STUPID.

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Pretty much. I guess some people just don't get physics.

edg..... Wrong

J>=C because C is only provided by air resistance to the plane's forward motion and the friction inherent in the landingear rolling on the surface. At very low thrusts, the plane might not be able to overcome the friction in the wheels, but as soon as that threshold is past, the plane will accelerate unless it's tied down.

Here's a different angle.

You are on a pair of rollerblades standing on a treadmill.
You hold onto a tow rope and I gun the throttle of my motorcycle which is not on the treadmill (just like the thrust of the airplane engine is independent of the treadmill).

No matter how fast the treadmill spins underneath you, you cannot be held stationary.

I will pull you forward, just as the planes engines will push it forward, independent of the speed of the treadmill.
The treadmill does nothing.
It is a trick question.
The treadmill is irrelevant.

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Originally Posted by Core Shot

Here's a different angle.

You are on a pair of rollerblades standing on a treadmill.
You hold onto a tow rope and I gun the throttle of my motorcycle which is not on the treadmill (just like the thrust of the airplane engine is independent of the treadmill).

No matter how fast the treadmill spins underneath you, you cannot be held stationary.

I will pull you forward, just as the planes engines will push it forward, independent of the speed of the treadmill.
The treadmill does nothing.
It is a trick question.
The treadmill is irrelevant.

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I think somebody needs to actually test this in real life. Who's up for it?

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Originally Posted by Telenater

Pretty much. I guess some people just don't get physics.

edg..... Wrong

J>=C because C is only provided by air resistance to the plane's forward motion and the friction inherent in the landingear rolling on the surface. At very low thrusts, the plane might not be able to overcome the friction in the wheels, but as soon as that threshold is past, the plane will accelerate unless it's tied down.

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More importantly, I just realised that the conveyor doesn't exert a force on the plane (well, negligible), but only spins the wheels.

edg

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Originally Posted by Core Shot

The only way the plane can be held stationary by moving a conveyor belt (putting aside the awesome calculation of the small friction created by the friction of the wheel bearings) is by applying the wheel brakes of the plane.

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Dude, we can fucking read, how can you be so fucking stupid? Every argument for it taking off assumes (in a more physically correct manner) it can move relative to the treadmill (which is true, the friction free wheels don't transmit force to the plane). The only problem is the problem states it can't move relative to the treadmill. The argument is framed improperly

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Originally Posted by Cornholio

In my mind, and using the free-body diagrams I've sketched, there is no way the plane ever moves forward.

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Wow, how did I miss this thread for so long!

I'm not going to trudge through the rest of this thread, bu Cornholio is 100% correct. The only reason an airplane moves forward on a runway (therefore producing lift over the wings) is because the thrust of the engines causes the tires to roll against the ground. The equal and opposite force is transferred to the ground. On a perfect (i.e., no loss due to friction) treadmill this force will cause the treadmill to travel with exactly the same speed in the opposite direction and the airplane will not move. No movement means no lift and the airplane will NOT takeoff.

Core,
The treadmill's properties are THE key to the problem.

As the original problem was written, the treadmill would speed up to the point where the (admitedly small in real life) friction of the rolerblade wheels & bearings would counteract the forward pull from the bike, holding the blader (& attached bike) in place. Treadmill speed would go incredibly high, but it is by definition high enough to prevent the rollerblader from achieving ANY forward motion (speed).

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Originally Posted by Core Shot

Here's a different angle.

You are on a pair of rollerblades standing on a treadmill.
You hold onto a tow rope and I gun the throttle of my motorcycle which is not on the treadmill (just like the thrust of the airplane engine is independent of the treadmill).

No matter how fast the treadmill spins underneath you, you cannot be held stationary.

I will pull you forward, just as the planes engines will push it forward, independent of the speed of the treadmill.
The treadmill does nothing.
It is a trick question.
The treadmill is irrelevant.

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Originally Posted by cj001f

The only problem is the problem states it can't move relative to the treadmill.

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Where does it say that the plane cannot move relative to the ground/treadmill? That seems to be the premis of your argument.

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Originally Posted by The Big One

A plane (747 passenger jet) is sitting on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the planes speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction).

The question is:

Will the plane (747 passenger jet) take off or not?

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We have some stated premises.
"The plane moves in one direction"
"conveyor moves in the opposite direction" I think that it's safe to assuem that they're referring to the surface of the conveyor belt moving, not the conveyor it'self (though it doesn't really matter).
"tracks the planes speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction)"

From these we get the following.
Vplane can be nonzero (it states that it's moving and thus not tied to the ground).

Vplane = -Vconveyor
Aplane = -Aconveyor

However, Because the plane is using jet engines, unless it's tied down (which it isn't) it will have a thrust that accelerates the plane forward as long as the force of the thrust more than balances out any drag from the landing gear and air resistance.

We know that the force of friction on a wheel is essentially constant with respect to its speed. We also know that the jet's engines can overcome air resistance under normal circumstances. The only variable that chages since the plane's speed with regards to the air would be the same as under normal thrust is the friction from the wheels which being constant is the same as before regardless of the wheel speed. Therefore (and listen carefully here), the only difference from a normal take off would be that the wheels are spinning twice as fast.

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Originally Posted by The AD

On a perfect (i.e., no loss due to friction) treadmill this force will cause the treadmill to travel with exactly the same speed in the opposite direction and the airplane will not move. No movement means no lift and the airplane will NOT takeoff.

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No, no, no, no...... edg got it. This would be true if the plane were accelerating using it's wheels. Then the equal and opposite reaction would apply to the treadmill. In this case, the plane is accelerating with it's jet engines. the equal and opposite reaction is applied to the air mass surrounding the jet. In an environment where the only friction is the rolling friction of the planes's wheels on the conveyor, it the conveyor would not move at all.


Yes, I'm a glutton of punishment.

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Originally Posted by Telenater

We know that the force of friction on a wheel is essentially constant with respect to its speed. .

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It is?

Surely the rolling resistance of the tire and friction of wheel bearing continually increase with speed.

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Originally Posted by TomK

Core,
The treadmill's properties are THE key to the problem.

As the original problem was written, the treadmill would speed up to the point where the (admitedly small in real life) friction of the rolerblade wheels & bearings would counteract the forward pull from the bike, holding the blader (& attached bike) in place. Treadmill speed would go incredibly high, but it is by definition high enough to prevent the rollerblader from achieving ANY forward motion (speed).

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You are missing the point that there is a difference in how speed is measured.
In each hypothetical, there are two different speeds.

If I pull you at 10mph on my bike, the treadmill will turn at 10mph.
You, however, will move 10mph forward (as am I, since I am pulling you with my bike which is not attached to the treadmill). There is not enough wheel bearing friction at 10mph to slow you down at all.

In the plane example, the plane measures airspeed and has air thrust.
The Treadmill measures ground speed, and (other than the scant friction of the bearings) cannot exert force on the plane.

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Originally Posted by cj001f

the problem states it can't move relative to the treadmill. The argument is framed improperly

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I am really not trying to be obtuse, but where does the original problem state that the plane can't move relative to the treadmill? I think it just says it matches the speed of the plane in the opposite direction. Obviously if the plane can't move forward, there won't be airflow and it can't take off... but 99.9% of the male population knows this. Not a very interesting question.

edit: oops, I type slow or something.

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Originally Posted by The AD

The only reason an airplane moves forward on a runway (therefore producing lift over the wings) is because the thrust of the engines causes the tires to roll against the ground. The equal and opposite force is transferred to the ground.

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WRONG.

Airplanes push air. The force from the engines pushes air. There is no force transfered to the ground. This is where the non-flyers are missing the point.

According to your argument, airplanes cannot fly, once they leave the ground, there is no force pushing against the plane.

I was thinking about it a little wrong initially, but I still stick to my original view that the plane will not take off.

Imagine it this way. What if the treadmill starts rolling before the airplane's engines are fired up? In this case the airplane will roll off the back end of the treadmill unless it's engines are fired up to provide a reacting force to the treadmill. So if the engines are fired up and the airplane is then able to maintain its position, or move forward, the treadmill can turn faster to cancel out that force.

You're going to have some very hot wheel bearings, though, because all the planes thrust needs to be dissipated by rolling friction.

That's my position and I'm sticking to it.

at least for now...

The bike does not pull the blader forward at 10MPh, it exerts a force that in the absence of other forces WOULD tow the blader at 10MPh.
But...since the treadmill speed is by definition high enough to use the friction provided by the rollerblade wheels & bearings to prevent any forward motion of the blader getting started in the first place, the motorbike's wheel would spin in place generating a lot of smoke, but there would be no forward motion relative to the surface of the earth. So, the blader stays in place while the treadmill spins underneath.

Think about what would have to happen to get the blader (or plane) moving relative to an outside the sytem observer in the first place. Since the treadmill's speed exactly cancels ALL "plane speed", it must be able to counteract any other forces trying to overcome inertia.

Real world limits and relative power would easily overcome the counteracting forces, but not in this "no limits" thought experiment.

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Originally Posted by Core Shot

You are missing the point that there is a difference in how speed is measured.
In each hypothetical, there are two different speeds.

If I pull you at 10mph on my bike, the treadmill will turn at 10mph.
You, however, will move 10mph forward (as am I, since I am pulling you with my bike which is not attached to the treadmill). There is not enough wheel bearing friction at 10mph to slow you down at all.

In the plane example, the plane measures airspeed and has air thrust.
The Treadmill measures ground speed, and (other than the scant friction of the bearings) cannot exert force on the plane.

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Originally Posted by DJSapp

WRONG.

Airplanes push air. The force from the engines pushes air. There is no force transfered to the ground.

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Only true if you neglect friction and nowhere in the problem is that stated as an assumption. As long as the tires are in contact with the ground there will be a frictional force opposing the engine thrust. If the treadmill were free-spinning the friction would be << than the engine thrust and the plane could still take off, but since the treadmill is powered it can theoretically turn the belt fast enough to create a static condition between engine thrust and friction.

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Originally Posted by TomK

But...since the treadmill speed is by definition high enough to use the friction provided by the rollerblade wheels & bearings to prevent any forward motion of the blader getting started in the first place

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Where does the question state this?

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Originally Posted by PNWbrit

It is?

Surely the rolling resistance of the tire and friction of wheel bearing continually increase with speed.

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Close, but not quite. In a non defomational system the force applied by friction is defined as having a maximum of the load times the coefficient of friction. The speed of movement doesn't directly apply. However, other events that accompany the increase in speed can effect it as the objects properties(and therefore coefficient of friction) change. ie as the friction will increase witing a bearing supported axle as the heat of the bearings increases, and as turbulence in the lubricant around the bearings increases, or as bearings rub against one another instead of just the traces. In most situations where you have a wheel attached to bearings, small variations in the weight distribution of the wheel become a problem before friction in the hub does.

frictional losses of the tire on the road due to slippage or deformation are far more difficult to model and I don't have any direct information on it. I made the assumption that the change in friction of the tire on the surface due to speed was similare enough per distance traveled that it would also be close to flat.

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Originally Posted by The AD

If the treadmill were free-spinning the friction would be << than the engine thrust and the plane could still take off, but since the treadmill is powered it can theoretically turn the belt fast enough to create a static condition between engine thrust and friction.

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But, the treadmill is limited to exactly the speed of the plane.

While I cannot rule out that wheel friction could become an issue below 2x the take off speed, I suspect that the friction provided even at 2x normal take off speed is still significantly less than that of the jet's thrust. So, losses due to wheel friction might make it take longer to reach takeoff, but it would not prevent it.

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Originally Posted by The AD

Only true if you neglect friction and nowhere in the problem is that stated as an assumption. As long as the tires are in contact with the ground there will be a frictional force opposing the engine thrust. If the treadmill were free-spinning the friction would be << than the engine thrust and the plane could still take off, but since the treadmill is powered it can theoretically turn the belt fast enough to create a static condition between engine thrust and friction.

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AD, see a previous post of mine regarding friction; it's too small to matter here, 747's can take off with the brakes locked (provided the wheels don't explode).

As for the rest of your argument, you are measuring the plane's speed relative to the conveyor. This creates a circular logic loop. By measuring the speed relative to the conveyor, the plane cannot begin moving without violating the statement that the belt speed equals the aircraft speed.

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Originally Posted by Telenater

But, the treadmill is limited to exactly the speed of the plane.

While I cannot rule out that wheel friction could become an issue below 2x the take off speed, I suspect that the friction provided even at 2x normal take off speed is still significantly less than that of the jet's thrust. So, losses due to wheel friction might make it take longer to reach takeoff, but it would not prevent it.

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The tires will blow up before friction is an issue. Rubber cannot hold together at those speeds. I mean, gonzo has a router that can do 30,000 rpm fer christs sake

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Originally Posted by DJSapp

AD, see a previous post of mine regarding friction; it's too small to matter here, 747's can take off with the brakes locked (provided the wheels don't explode).

As for the rest of your argument, you are measuring the plane's speed relative to the conveyor. This creates a circular logic loop. By measuring the speed relative to the conveyor, the plane cannot begin moving without violating the statement that the belt speed equals the aircraft speed.

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Clarification:

Airspeed = 1 to begin moving
conveyor = 1 to match
Wheelspeed = airspeed + conveyorspeed

according to 'stay still' arguments:

wheelspeed = conveyorspeed

Therefore according to this, the conveyor cannot start moving. The logic is flawed.

I drew a diagram representing my logic. Correct? Incorrect?

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Originally Posted by dbp

I drew a diagram representing my logic. Correct? Incorrect?

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The setup is correct, the question is where speed is measured from.

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Originally Posted by dbp

I drew a diagram representing my logic. Correct? Incorrect?

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I'd say completety incorrect because the motorcycle is pushing against the ground and that's what's causing its forward speed. How about replace the cycle with a really big RC airplane and that's more like it. With this scenario can't you imagine the treadmill spinning fast enough such that both the rollerblader and RC plane are stationary WRT the ground?

Really nice diagram, though, other than that! :)