Physics Question for you.....

[Anna]

Anna, in your second case you are assuming that the speed of the plane is influenced by the contact with the conveyor. Why would this be the case?

The airplane is not driven forward by it's wheels. It is the engine pushing against the air behind it that moves the plane. The wheels are freespinning.

What I'm thinking right now is a bike on a downhill ride. The propulsion is due to gravity, you're not pedaling, but the bike's wheels still spin. Technically, the wheels are freely spinning, but the bike is moving because the wheels are moving. The wheels can be spinning "perfectly" in which case the point of contact between the wheel and the ground has a speed of zero, or the wheels can be sliding. In either case there's friction: in the first case, it's static friction, and in the second case, it's kinetic friction. Both will tend to retard the motion of the bike.

A plane in contact with the ground is the same way. It doesn't matter where the propulsion comes from: whether it's the propeller, jets, or a giant truck that's pulling on the plane to the hangar, or a dozen crazy guys with sturdy ropes pulling on it. The plane moves because the wheels roll on the ground. Once the wheels start rolling, or even sliding, there's friction, which means you have to pull harder to get the thing going.

The only time that the conveyor belt will have no effect on the motion of the plane is when the plane is not in contact with the belt, in which case it's already flying anyway, or when the belt is frictionless. My assumption, in my long posts, is that the plane stays in contact with the belt and the belt is not frictionless.

I'll concede that once you assume otherwise, then the plane will take off. But at least I can now see how and why.

[JeffG78]

But, it doesn't need hypothetical frictionless bearings. A regular plane with regular bearings will accelerate down the conveyor runway and take off in nearly the identical distance as a plane on a regular runway. The friction of the tires and bearings stopping an airplane has about the same chance as a car on the highway being slowed by a bug hitting the windshield. The friction of the wheels is insignificant compared to the power of the plane's engine. A plane on a normal runway must overcome the friction just like the conveyor plane does. The only difference is the wheel speed at takeoff. The plane on a conveyor will have twice the wheel speed as a plane on a normal runway. The rolling friction of a bearing is much less than the breakaway friction and in both cases, they must overcome the same breakaway friction. The higher wheel speed at takeoff will increase the rolling friction, but it will have little effect.

I would be willing to bet that the distance to takeoff would be within standard tollerance between the two conditions.

[williamr]

Well, as usually the case, I can't stay away from a good debate unless I completely turn the computer off. So here goes:

I've been thinking about the proposition that planes act on the air around them and not on the ground. And that's true... when the plane is in flight.

In our case, the plane is in contact with the ground. Now there are two cases:

1. The "real world" case where the plane's wheels roll on the ground which means there's friction, which means there's a force in the opposite direction to the plane's thrust, which can make the plane's effective acceleration zero. Hence no motion. That's what I've been proposing because I assumed that the plane's wheels kept in contact with the ground. After all, if it's not in contact with the ground, it's already in flight and what's the point of all the argument anyway?

2. The second case is a completely frictionless system. Imagine the plane on ice skates and the conveyor belt is made of ice. Either that or the air already rests on a cushion of air (like the super trains in Japan). In this case, there is no drag to the plane's motion when the jets or props are fired up, and the plane flies! This is the same scenario as when the wheels have no traction on the ground or conveyor belt. In other words, the net force on the plane is equal to the thrust, and the plane accelerates.

So, I think all this debate is really based on two different assumptions. I assumed a real-world case where the plane's wheels stay in contact with the ground without slipping. I think the others assumed that everything is frictionless.

Seen that way, everyone is right. Although, being a woman and all, I'll have to say I'm never wrong.

Women are never wrong. That much I accept as axiomatic. :-)

Now that you can see I have been well trained...

Keep in mind that if you were to do a set of calculations you would have to calculate the following...

1. The behavior and thrust of the jet engine in air -- and come up with a thrust vector.

2. The behavior of frictionless wheels with a thrust vector being applied at the bottom of the wheels.

For the conveyor argument to be correct you only have to prove that you can apply enough thrust at the outside radius of the frictionless wheels to overcome the thrust of the jet engines. That's tough to show I think.

Once you have done that -- redo the calculations with "less-than-perfect" wheels and you should still end up with a moving plane.

So having said that, first assumption might bear looking at.... It may need a little refinement. Only refinement mind you because if I accept that women are always right, it could only be your expression of your correctness that is escaping me... due to male fallibility of course. :-)

Let's look at the proposition that the engine acts on the fluid media of air only -- as other claim and do I. If you could suspend the engine via anti-gravity and spin it up -- it would thrust forward. Add a wheeled suspension and it will still do so.

Ignore the wing.

Now work the rest of the argument from there -- adding friction from the ground, add additional drag due to a conveyor. Can the engine still thrust forward -- through the air -- regardless of drag produced by "frictionless" wheels. (We both know they aren't frictionless -- but the ratio of engine thrust to landing gear drag is pretty high. So do the math professor thing and ignore small contributions to the overall sums... )

Next question: Can a properly functional set of landing gear produce more drag than the engine can produce thrust? Brakes -- maybe?

For all intents and purposes the wheels spin -- but produce little enough drag to be ignored.

Assuming that the plane accelerates despite the conveyor, then the drag component due to ground contact becomes vanishingly small as the wing generates lift. (Same as pontoons with planing hulls -- the only kind that work.)

Then the air flow over the landing gear produces drag until the gear is stowed. Again, drag is much smaller than engine thrust -- although drag in the fluid media of air becomes very significant with respect to efficiency if you leave the gear down.


---
Will

[Anna]

Will, you are making it too complicated. Forget the force diagrams. Let's make an equivalence here: Since F = ma, and the plane's thrust is not zero, then there should be a corresponding acceleration that makes the plane move.

So now let's just look at it as the plane starting to move, without regard to the amounts of force acting on it (since we already applied F = ma). As long as the wheels are in contact with the conveyor, any motion that the plane makes is relative to the conveyor. If the conveyor is stationary, then the plane moves forward. But the conveyor is not stationary. For every motion forward that the plane makes, the conveyor moves backwards taking the plane with it as long as the wheels stay in contact with the conveyor. If the plane's forward motion is perfectly countered by the conveyor's backward motion, then the plane is stationary with respect to an observer on the ground.

For someone on the plane, though, the plane is indeed moving with respect to the conveyor belt.

Now, in the second case with a completely frictionless system, if the plane's engines are off and the conveyor starts to move, the plane will stay still with respect to our ground observer. It's the same as Cabinetman's tablecloth experiment, only more successful. That is, there are no horizontal forces acting on the plane. If the conveyor is not frictionless, then the plane starts moving backwards with the conveyor because of static friction.

Back to the frictionless system. When the plane's engines fire up, no matter how fast the conveyor belt is moving, the plane will move forward.

Like I've said, the first case is really a kinematics problem because the assumption is that the plane and the conveyor belt are continuously in contact with each other. Take that assumption away, then the problem changes.

As for thrust acting on air, etc: What happens when you lock the wheels (the wheels do have brakes, don't they?) and start the jets? You can in fact keep the plane stationary with the engines running up to a point where the engine's thrust overcomes the static friction force on the wheels, and the wheels just start sliding down the tarmac. I guess that's just my way of saying you can have your jets acting on the air around it and still have no motion at all.

Oh, and congratulations on your training. I'm sure your wife is very happy.

[williamr]

What I'm thinking right now is a bike on a downhill ride. The propulsion is due to gravity, you're not pedaling, but the bike's wheels still spin. Technically, the wheels are freely spinning, but the bike is moving because the wheels are moving. The wheels can be spinning "perfectly" in which case the point of contact between the wheel and the ground has a speed of zero, or the wheels can be sliding. In either case there's friction: in the first case, it's static friction, and in the second case, it's kinetic friction. Both will tend to retard the motion of the bike.

A plane in contact with the ground is the same way. It doesn't matter where the propulsion comes from: whether it's the propeller, jets, or a giant truck that's pulling on the plane to the hangar, or a dozen crazy guys with sturdy ropes pulling on it. The plane moves because the wheels roll on the ground. Once the wheels start rolling, or even sliding, there's friction, which means you have to pull harder to get the thing going.

The only time that the conveyor belt will have no effect on the motion of the plane is when the plane is not in contact with the belt, in which case it's already flying anyway, or when the belt is frictionless. My assumption, in my long posts, is that the plane stays in contact with the belt and the belt is not frictionless.

I'll concede that once you assume otherwise, then the plane will take off. But at least I can now see how and why.

Anna -- hypothetical ...

Remove the wheels on the bike. Replace it with an (imaginary) anti gravity engine that will maintain a constant distance between the centre of mass and the bicycle system - bike rider and whatever. Or use an air cushion generator if you don't like my new ant-grav unit. It's more conventional and doesn't cause air -sickness. :-)

Will the bike go down the hill? Just like it had wheels? Yes. Gravity rules here. Reduced by the angle of the hill. Simple vector calculation. Which you essentially stated.

I admit that using wheels is simpler though. :-)

In the limit, a vertical cliff, the wheels are redundant -- gravity is seen to be dominant -- you fall at a a velocity dictated by the acceleration due to gravity, and the distance traveled -- impeded only by the air.

The plane does not move because the wheels roll. Remove the planes suspension. Spin up the engines to full thrust. Does the plane move? If the engines can supply more thrust -- in the air media (system 1) -- than the (negative) thrust produced due to drag on the ground (system 2) -- and I'm betting yes -- then the plane moves. The wheels are a system to reduce drag, just like the bicycle, and they play a roll in allowing airflow around the wing -- once the plane is moving.

In the above we are ignoring gravity (vector system 3) since we just want to get the plane moving forward. It comes in to play when we talk about the "real-world" behaviour of those not-so-frictionless wheels, and the lift of the wings -- but we aren't ready to fly yet. Maybe tomorrow... :-) Just a little more time in the simulator...

Motion is due to the sum of _all_ the vectors. The greatest thrust vector acting on an aeroplane -- in normal operation -- is the engines. Not the wheels.

I still think NP problems are simpler. :-)

Good night and be well.

---
Will

[JeffG78]

If the conveyor is stationary, then the plane moves forward. But the conveyor is not stationary. For every motion forward that the plane makes, the conveyor moves backwards taking the plane with it as long as the wheels stay in contact with the conveyor. If the plane's forward motion is perfectly countered by the conveyor's backward motion, then the plane is stationary with respect to an observer on the ground.

Wrong, wrong, wrong Anna. The conveyor speed does not matter! The plane will move forward when viewed from the control tower whether the conveyor is stationary, moving at the same speed as the plane or moving at 10 times the speed of the plane. It simply does not matter! Watch this video http://www.youtube.com/watch?v=-EopV...eature=related and you will see what happens. The scale test that this guy does clearly shows that even when the conveyor moves faster backwards that the top speed of the plane, the plane still accelerates down the "runway".

[williamr]

Will, you are making it too complicated. Forget the force diagrams. Let's make an equivalence here: Since F = ma, and the plane's thrust is not zero, then there should be a corresponding acceleration that makes the plane move.

So now let's just look at it as the plane starting to move, without regard to the amounts of force acting on it (since we already applied F = ma). As long as the wheels are in contact with the conveyor, any motion that the plane makes is relative to the conveyor. If the conveyor is stationary, then the plane moves forward. But the conveyor is not stationary. For every motion forward that the plane makes, the conveyor moves backwards taking the plane with it as long as the wheels stay in contact with the conveyor. If the plane's forward motion is perfectly countered by the conveyor's backward motion, then the plane is stationary with respect to an observer on the ground.

For someone on the plane, though, the plane is indeed moving with respect to the conveyor belt.

Now, in the second case with a completely frictionless system, if the plane's engines are off and the conveyor starts to move, the plane will stay still with respect to our ground observer. It's the same as Cabinetman's tablecloth experiment, only more successful. That is, there are no horizontal forces acting on the plane. If the conveyor is not frictionless, then the plane starts moving backwards with the conveyor because of static friction.

Back to the frictionless system. When the plane's engines fire up, no matter how fast the conveyor belt is moving, the plane will move forward.

Like I've said, the first case is really a kinematics problem because the assumption is that the plane and the conveyor belt are continuously in contact with each other. Take that assumption away, then the problem changes.

As for thrust acting on air, etc: What happens when you lock the wheels (the wheels do have brakes, don't they?) and start the jets? You can in fact keep the plane stationary with the engines running up to a point where the engine's thrust overcomes the static friction force on the wheels, and the wheels just start sliding down the tarmac. I guess that's just my way of saying you can have your jets acting on the air around it and still have no motion at all.

Oh, and congratulations on your training. I'm sure your wife is very happy.

My wife feels that my training could still be better. I am sure she appreciates your contribution.

The rotation of the wheels should be considered frictionless.

What you are suggesting would only work if the the turning of a planes landing wheel could exert lateral force on the jet to overcome engine thrust. A tough proposition.

If you lock the brakes the ground certainly does provide equal and opposite thrust. Accepted. So, to the point the engines overcome the brakes -- no motion. If you lock the brakes on the conveyor -- then the plane will do the same as if you had done so on the tarmac -- and possibly get shoved off the conveyor back on to the tarmac. Then all bets are off as to where the thrust vectors go. :-)

The thrust of a jet engine _still_ comes from the action of the engine in the fluid media of air and it happens to be attached to the body of the jet plane. It does not depend on wings or wheels to generate thrust through the air fluid. If you accept that we can unlock the brakes and allow the wheels to turn on the conveyor, and that they are essentially frictionless, then it is tough to argue that the plane won't fly.

I must report for twenty lashes and re-training.

---
Will

[leehljp]

[i]"It does not depend on wings or wheels to generate thrust through the air fluid. If you accept that we can unlock the brakes and allow the wheels to turn on the conveyor, and that they are essentially frictionless, then it is tough to argue that the plane won't fly."[i]

Why will the plane fly? FLYING takes place when there is lift over wings. Rockets don't "fly"! Inertia and power keep it up, not flying.

Again, why will it fly? The engines purpose is to generate enough thrust to move forward to create lift to make it fly. EVERYONE who says it will take off, ignore the fact that no wind is flowing over the wings. IF it will go on engine thrust alone, then no wings are needed.

So what is the purpose of wings - except to slow it down for landing? I am curious as to what I am missing.

I have mentioned this before, but not will will address this fact? Anyone brave enough to tackle this?

[Alex Franke]

I have to agree with Anna here. (And I've never taught physics to anyone.)

Suppose the wheels are so far from ideal (maybe the brakes are stuck engaged a bit) that the conveyor belt would have a significant impact on the plane -- sit the plane on the conveyor, turn the conveyor on, and the plane starts to move. The conveyor is tuned to go as fast as it needs to go in order to keep the plane from moving relative to someone standing next to the conveyor. Suppose the conveyor doesn't pull any air along with it, so it's not generating any wind. I can't see the far-less-than-perfect wheels of the plane ever getting off the ground because they will continue to be affected by the conveyor.

Granted, as I mentioned before, for a real plane that conveyor would have to be going insanely fast to have even a noticeable effect because the wheel is a pretty genius concept.

Now float the plane over a magnet, or use some decent wheels. I don't think anyone's questioning that the plane will accelerate (to the observer on the tarmac) and take off -- regardless of what the conveyor might be doing. It's relativly immaterial.

The more friction you have to overcome, the more thrust you need from your engines to start moving forward, and you can't lift off until you start moving and get some air hitting the wings. Floating over a magnet is great. Wheels are nearly as good. Overcoming water maybe not so easy. Overcoming the brakes even harder still.

But if the conveyor can somehow, someway keep a plane from moving relative to the observer on the tarmac, then it simply will not move relative to the observer on the tarmac. No movement = no wind. No wind = no lift. No lift = still affected by the ground in some way.

[JeffG78]

But Hank, there IS air over the wing since the plane is moving down the runway (as seen from the control tower) just like when there is no conveyor. Nobody is saying that the plane will fly if it is standing still. The whole point of the question is not whether or not the plane will fly, but rather if the plane will move down the runway when viewed from a fixed position like the control tower. The video clearly shows that the plane does move down the runway rather than sitting in one place.

[JeffG78]

Alex, what does holding the brakes on have to do with anything? The brakes would have to be held on the same amount on a stationary runway to have the same effect. The question isn't whether of not a plane can be kept from flying while holding the brakes on.

Like you said, wheels have very low friction relative to the power of an engine. The only difference the moving conveyor makes is the speed of the tires. More speed equals slightly more friction, but the difference isn't enough to matter.

[leehljp]

But Hank, there IS air over the wing since the plane is moving down the runway (as seen from the control tower) just like when there is no conveyor. Nobody is saying that the plane will fly if it is standing still. The whole point of the question is not whether or not the plane will fly, but rather if the plane will move down the runway when viewed from a fixed position like the control tower. The video clearly shows that the plane does move down the runway rather than sitting in one place.

This is where the difference is in questions.

Original question on this forum 2 years ago: A plane is standing on 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).

Rephrasing the question was: IF the speed of the rolling runway matches the speed of the plane, will it take off?

IF they matches each others speed, the air speed relative to ground (control tower) is "0".
ZERO speed of air equals no flight!

IN the Myth Busters, the plane was going forward faster than the rolling runway was going backwards. If the plane moves FORWARD of its starting position as much as 1 foot, then it is going forward faster than the runway is going backwards. In this case, if the speeds are not matched, then that fact nullifies the point of the question above.

Again, the question was - If both are going the same speed in opposite directions . . .

It seems to me that some people want to visualize the plane moving forward at some point in which it could take off, but at that point the two objects would not be going equal speeds in opposite directions.

For the life of me, I can't see what people are talking about saying it can take off under these conditions. Myth Busters did not meet these conditions.

I do get the point that once inertia takes over and it does start moving forward as much as one inch, then it doesn't matter if the rolling runway is going 1000 mph, the plane will not be dependent on the speed of the runway/wheel, but rather its own inertia and power - and it will take off!

[JeffG78]

This is where the difference is in questions.

The question was: IF the speed of the rolling runway matches the speed of the plane, will it take off?

IF they matches each others speed, the air speed relative to ground is "0".
ZERO speed of air equals no flight!

But the original question states that the conveyor matches the plane's speed, it does not say it matches the speed of the plane's tires. The plane accelerates down the runway with relation to the control tower and the conveyor accelerates at the same rate. When the plane reaches X speed to take off, the conveyor's speed would be exactly the same. Now, if the original question said that the conveyor EXACTLY matches the plane's tire's speed, then both the tires and the conveyor would need to be stopped because as soon as the engine was revved up, the plane would begin to move down the runway meaning that the tires are going faster than the conveyor. Since the tires are assumed to not skid, the only time that the speeds could match would be when the tires and conveyor are both going zero. The only rational way to measure a plane's speed is either via the plane's airspeed indicator or a radar gun. Neither of which uses wheel speed. Knowing what a plane's wheel speed is, is rather useless.

[Alex Franke]

Alex, what does holding the brakes on have to do with anything? The brakes would have to be held on the same amount on a stationary runway to have the same effect. The question isn't whether of not a plane can be kept from flying while holding the brakes on.

That's not my point anyway. My point is this: If there's enough friction in the system (wheels, water, ice, magnet, whatever) dragging the plane backward at a rate that effectively cancels out its forward movement (so that the plane appears stationary from the tower) then I can't see the plane flying. If the plane appears stationary from the tower, then it will not lift off the ground. The original question -- to me -- suggests that the plane will appear stationary from the tower throughout the experiment.

If, however, the plane can muster enough thrust to overcome the friction and propel the plane forward (relative to the tower) along the runway (or magnet, or river, or whatever) then it can lift off. Now I'm sure any real plane can surely overcome the friction in a wheel, but a hypothetical plane on a hypothetical conveyor with hypothetically far-from-ideal wheels would be dragged backward by the conveyor, and if it were accelerated backward by the conveyor at the rate it's accelerated forward by the engines, then it will appear stationary to the tower and won't lift off.

So, if this magical conveyor could somehow keep the plane stationary to the tower, then would the plane still take off? "Tuning the speed to be exactly the same but in the opposite direction", to me, means that the plane somehow, some way, appears stationary to the tower.

[Anna]

I don't really know much about planes, so the suggestion that the plane's wheels are freely spinning threw me off a bit. Having thought about this some more, doing the requisite free body diagrams, and learning a little more about planes and their vital statistics in the process... I have to concede.

The plane will take off.