Plane Physics Question

This is a discussion topic from another message board, that was originally posted on another message board before that - it has caused quite an argument on both, so I thought it might be fun to discuss it here too:

[quote:0060107e3c]A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

The question is:

Will the plane take off or not? [/quote:0060107e3c]

Of course. The plane isn't pushed forward by the wheels. It's pulled forward by the engines. The wheels can spin back just as fast as the plane's moving forward, but the plane will continue to move forward. The drag on the wheels would be inconsequential.

I'm the worst person ever to try this but I'll just give it a go to kick it off...

If you imagine the plane's coordiantes on a map, it doesn't move at all (in terms of lines of latitude, so to say) because of the runway, right? What it needs though to take off is the wind uner it's wings, not the speed of its wheels. So, I say, it doesn't take off.

In reply to Ba: If I got Mal's quote right, we are to imagine that no matter how much speed the plane gains - by mentioning the wheels I didn't mean I see them pushing the plane- the runway relates it. Right or wrong?

But the plane doesn't stop. The wheels simply spin twice as fast. That's not enough to stop the plane.

Now, there is a way to do this so that it would stop the plane. The runway would have to move back enough to counteract the [i:be526290de]force[/i:be526290de] of the plane moving forward, not simply match the speed. This would require it moving many thousands of miles per hour, but it's conceivably possible to do, imparting enough momentum to the wheels to check the plane's forward progress. But that's not the problem as Mal phrased it.

Well, as hinted, I completely lack expertise, so for all I know Ba could be right. That leaves me with one final question before I leave the ring to the more competent people (in regard to the laws of physics, that is):
If it would be as Ba has pointed out, why don't plane companies spare a lot of room by inventing those runways and let two planes at a time start from the ground that is now needed by just one?

(Also, if rubbing a cat's fur against acrylic rods creates electircity, why don't they have power plants where thousands of cats are shood back and forth under an acrylic grating?)

Because, Hsing, it doesn't actually change the distance the plane must travel to get off the ground. The point is that the plane isn't going to stop. It's going to continue forward despite the ground beneath it moving back. The wheels move twice as fast because the plane continues forward even as the ground moves back. There isn't enough drag or momentum imparted to the wheels to stop it.

That doesn't answer my cat question.

Because hamsters on little wheels work cheaper.

Ah, but see, there's nothing keeping the plane from moving forward. The mobile tarmac may go backwards, but it's not enough to pull the plane with it against the force of the engines.

Think of it like this. One is on a treadmill, wearing a pair of rollerblades. There's a rope on the wall ahead. One uses the rope to pull oneself forward. For every inch one goes forward, the treadmill goes back an inch. One would still move forward. The only effect is that the wheels would have to turn twice as much.

This conveyer belt is not pulling the plane back that strongly, even if it is going as fast as the plane is. Remember, wheels are there to lower the amount of resistance involved in moving across the ground. The friction is negligible. There would be a bit of momentum imparted when the ground moved back, but that wouldn't be enough to keep the plane in place either. The plane would still move forward. Not just in relation to the ground, but, and this is important, in relation to the air around it. That's what the plane is pulling against. That's what it needs to move against to gain lift. The ground doesn't matter.

Right, Ba made a few simple diagrams. Simply pretend they resemble in some way a plane on a treadmill.

Image One

This shows the starting position. The plane is at one end of the ramp. Now, what happens when the engines are started? (Pretend there are engines. Come on, exercise those imaginations!)

Image Two

Gasp! It's moved forward. This is because it isn't pulling along the ground to move forward. It pulls on the air instead. The treadmill has moved back the same distance as the plane. The wheels have moved twice as far as either the plane or the treadmill. This is because they're the only part of the plane touching the treadmill. Thus, they're the only part affected. They move twice as far, and thus twice as fast. This doesn't affect of the plane much, however. It certainly isn't enough to cancel the forward momentum from the engines.

What people think is happening is that the movement of the plane would somehow be X+Y, or 1+(-1), which would equal zero. If the wheels were pulling the plane forward, this would be true. But they're not. Forward movement of the plane simply equals X. Y only moves the wheels faster. The wheels aren't propelling the plane. For any reasonable speed (a plane doesn't need that much speed before it's no longer touching the ground), the friction and backward momentum they produce is negligible. The treadmill would need to be moving backwards much, much faster than the plane is moving forward to impart enough momentum to the wheels to halt the plane.

When it's moving fast enough, the lift will be sufficient for the plane to leave the ground. End of story.

Incidentally, anyone know Bournelli's principle, and how it's been misleading students for ages?

That's the one. Ba can never get it spelled quite right. It's often used wrongly to explain the lift of an airplane wring. It's not that it isn't involved in lift, because it is. It's just that incorrect information is often used. Like the idea that the air travelling on the top must reach the end of the wing at the same time as the air travelling on the bottom. In fact, even though it has to travel farther, the air travelling over the top gets their much quicker. There are other factors involved as well, such as Newton's laws of motion. It's much more complicated than most people realize.

It just had a thought that perhaps we shouldn't get to fixated on the conveyor belt, which merely serves the purpose of illustrating that the plane can't move forwards as it would nomally. What if the wheels had steel rollers under them instead that matched the forward speed of the aircraft? I mean that's how I read it anyway.

Still wouldn't stop the plane. The surface the plane is resting on isn't enough to keep the plane still. The plane is pulling the air, not the ground.

Again, back to the rollerskates analogy. If one is on rollerskates, on those steamrollers, with a rope attacked to a wall in front, then one can simply pull oneself forward with the rope. The streamrollers can turn all they like. All they'll do is make the ride a bit bumpier.

It helps to remember that the wheels aren't really attached to anything. That is, there's nothing about them connected to a motor or other method of turning. They spin freely, independant of the plane's motion. Only because they touch the ground does their spin match the plane's speed. If the ground moves back, the wheels move forward. But just as the plane's speed doesn't directly impact them, neither do they impact the plane's speed. It doesn't matter how fast the wheels spin, for all practical purposes.

What if we had an arm at right angles to the plane which held it securely in place so it can't go forwards or backward but can go up and down.

If there was a big fan in front of the plane with the arm attached, like in a wind tunnel, then obviously it would rise up into the air. Would the same thing happen just using the plane's engine/s?

Well, if the plane can't move relative to the air around it, then it doesn't lift off. That's the crux of all this. The ground moving beneath it doesn't stop its forward progress in relation to the air. Keep it bolted down, and it doesn't move quick enough in relation to the air.

The engines don't provide lift on their own. What they do is pull air back, which pulls the plane forward. This pulls air over the wings, which, because of various things like Bernoulli's principle and Newton's laws of motion, lifts the plane up. Without that air moving across the wings, there's no lift.

But that's not the same as this problem, where there's nothing actually keeping the plane from moving forward into the wind.

And Ben's right too, of course. Either the arm would snap or the engines would tear off of the wing. Or the entire wing would come off. There's a lot of force involved.

I don't think anything would break. And besides you don't have to assume it's a 747 we're talking about, it could just as easily be a model aircraft with a little 12 cc engine and a single prop. - the principle is the same. We could set up a test if anyone has a model plane.