Physics Question for you.....

[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.

[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.

[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?

[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

[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]

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

[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]

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

[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.

[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.

[Anna]

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.

[williamr]

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 free spinning.

There is no question there is an initial influence -- but then you are right the influence rapidly dwindles to small significance.

Once you get a short time beyond the startup phase the plane is working in it's native media -- the fluid air... i.e once the "inertia" of the plane is overcome -- friction of the wheels etc... So a second or two or three (and even if it's 10 -- it doesn't affect the final outcome) after windup and the brakes are released...

Maybe you should do the force vector analysis for all of us -- and show that the vectors are working (primarily) in a fluid media. <grin>

I think that's the difficulty with the analysis for most.

---
will

[Russianwolf]

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.

[williamr]

William, I know it's really tempting to turn this into a Second Law problem, but it's really a kinematics problem.

And although it's been three years since I last taught calculus physics, I think I can probably handle the equations and free body diagrams just fine.


P.S. Husband's comment: "Is there a pilot in the plane? Because, you know, whether the conveyor belt matches the plane's speed or not, the FAA won't allow the plane to take off."

And it's been about the same since I taught docs, and post docs in eng. math <grin> -- so we're even there. lol The only reason I responded was I thought -- that person knows how to present a analysis -- and clearly that's true -- I actually admired your case.

Regardless -- I will go for the guy from Boeing and his solution. (mpc)

And I feel better since I read all his posts -- I got suckered for a few minutes too -- till I remembered the plane is sitting in air, the engines work in the fluid system of the air, and the conveyor and the wheels are just a distraction for the real issue...

There is nothing wrong with your conveyor analysis. I stand by the statement that it is "the wrong problem space".

As to you husbands comment -- he's probably right -- so all the science in the world don't matter. FAA has grounded "The Flight of the BT3" -- end of discussion.

And I still won't do math today. And I will stick to NP problems from now on -- simpler to wrap your head around. :-) :-)

---
Will

[Anna]

William, I know it's really tempting to turn this into a Second Law problem, but it's really a kinematics problem.

And although it's been three years since I last taught calculus physics, I think I can probably handle the equations and free body diagrams just fine.

One last attempt, then I'll call it a day.

When an object "moves," it's usually relative to something. We have three components in our system: the plane, the ground, and the conveyor belt. We're assuming that the air is "still" with respect to the ground, where most of us are watching.

Case 1: Conveyor belt does not move. This is the same case as when the belt does not exist at all, and the plane taxies off the ground.

For the plane to take off, it has to move with respect to the ground in order to create a lift. That is, the motion of the plane allows the air to move against the plane (although to us sitting on the ground, the air is still not moving) which allows the plane to fly.

Does it matter if the plane has wheels or skids or pontoons? Not really because what's important is the relative motion of the plane to the ground. With still air, the speed of the plane is also its air speed, and when it reaches a critical air speed, it takes off.

Case 2: The conveyor belt is moving. This is basically when the "ground" on which the plane is sitting on is moving in the opposite direction.

If the speed of the plane is matched by the conveyor belt but in the opposite direction, then the resulting motion is zero. Honest. Go ask your physics teacher. It doesn't matter if the plane is going full throttle, as long as the conveyor belt is going full throttle in the opposite direction. It's still zero.

The only way that the plane will take off with respect to the ground is if the speed of the plane is greater than the speed of the belt. But the statement of the problem denies that.

In the Mythbusters episode, the acceleration of the plane beat the acceleration of the truck. The instantaneous speed of the plane was therefore different from that of the truck, and there's a net speed for the plane. Therefore, it moved with respect to the ground with enough speed to take off.

Another important point: we're talking about matching speeds between the conveyor belt and the plane. If the conveyor belt runs at CONSTANT speed, it loses because there is a net force on the plane, and therefore a net acceleration. Constant speed implies ZERO net force (or zero acceleration). So the case with the matchbox or car or whatever is not the same as the original problem either.

Okay, that's all for me. I don't really know how many other ways to explain that there is no relative motion to the ground and therefore no relative motion to the air with the way the problem is originally defined. I don't buy the wheels-have-nothing-to-do-with-motion argument either. Well, it's really not an argument. And it's pretty common to conflate motion with forces.

P.S. Husband's comment: "Is there a pilot in the plane? Because, you know, whether the conveyor belt matches the plane's speed or not, the FAA won't allow the plane to take off."