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September 29, 2007 9:47 PM   Subscribe

Here's a seemingly simple physics problem: an airplane taxis in one direction on a moving conveyor belt going the opposite direction. Can the plane take off? The debate rages on and on and on....
posted by zardoz (248 comments total) 22 users marked this as a favorite

 
If the plane is moving fast enough in relation to the conveyor belt, yes. Next question?
posted by dirtynumbangelboy at 9:51 PM on September 29, 2007


I don't know, but a plane can sure land on a moving runway.
posted by blaneyphoto at 9:54 PM on September 29, 2007 [1 favorite]


All this will be academic until somebody puts this to the test. And I'll sooooooo be there for that.
posted by Kattullus at 9:55 PM on September 29, 2007 [1 favorite]


Oh fuck, not this again. Why does this question give so many people a hard time?
posted by Mikey-San at 10:06 PM on September 29, 2007 [3 favorites]


If the plane is moving fast enough in relation to the conveyor belt, yes. Next question?

Then how does it get lift?
posted by Eekacat at 10:07 PM on September 29, 2007


I vote the plane can take off, but I do agree the only way to be sure is for someone to try it.
posted by TheOnlyCoolTim at 10:07 PM on September 29, 2007


Fast enough relative to the air. The conveyor belt isn't really relevant, except in that it reduces the speed of the plane relative to the air.
posted by spaceman_spiff at 10:08 PM on September 29, 2007


The question doesn't really make any sense.

If you put a jet on a conveyor belt and fire it up, the conveyor belt isn't going to keep the plane from going forward. It will just make the wheels spin extra fast.
posted by Mr. President Dr. Steve Elvis America at 10:11 PM on September 29, 2007 [2 favorites]


Actually this is typical of physics questions. You're given a bunch of information, and you need to solve a problem. You have to decide which information is important and go from there. One of my favorites is if you shot and drop identical bullets at the same time, which hits the ground first?

The answer, of course, is that they hit the ground at the same time.
posted by Eekacat at 10:11 PM on September 29, 2007


*Waits for the diamond car hitting the diamond wall post.*
posted by SansPoint at 10:12 PM on September 29, 2007


IANASAVAGE, but it seems to me that all the treadmill does is make the wheels spin while the prop or jet moves the plane forward as usual.
posted by stavrogin at 10:12 PM on September 29, 2007


The controversy boils down to an unclear definition of how fast the conveyor belt is moving.

Assuming that the wheels aren't frictionless the conveyor belt is going to impart some force f to the plane opposing the thrust of the engines. If they conveyor belt moves fast enough that it always balances out the thrust of the engines then no, the plane cannot take off. Since the plane has to be moving relative to the air for the wings to generate lift. No net force == no accelleration == no fly.

If on the other hand the conveyor belt simply moves at an equal and opposite velocity to the plane, then the plane will take of since the force applied to the plane by the conveyor belt will never be enough to fully oppose the thrust of the engines, and the plane will eventually accelerate to takeoff speed.
posted by Grimgrin at 10:12 PM on September 29, 2007 [8 favorites]


Well, unless you shot the bullet directly into the ground. The bullet is fired horizontally to the surface of the ground. Duh
posted by Eekacat at 10:13 PM on September 29, 2007 [2 favorites]


Grimgrin, that made no sense whatsoever.
posted by Eekacat at 10:15 PM on September 29, 2007


One of my favorites is if you shot and drop identical bullets at the same time, which hits the ground first?

How fast is the conveyor belt beneath the bullets moving?
posted by Mikey-San at 10:16 PM on September 29, 2007 [7 favorites]


One of my favorites is if you shot and drop identical bullets at the same time, which hits the ground first?

How fast is the conveyor belt beneath the bullets moving?


REALLY REALLY FAST. Like the top speed of a Ford Pinto, or the speed of light. Whichever is faster.
posted by Eekacat at 10:19 PM on September 29, 2007


Actually Grimgrin that made perfect sense and I don't feel like an idiot for not getting this problem anymore.
posted by afu at 10:21 PM on September 29, 2007 [1 favorite]


Literal viking.

Wait.
posted by CitrusFreak12 at 10:25 PM on September 29, 2007 [3 favorites]


Well, this is just off the top of my head, but it's not a simple problem. You have to ask: in what sense is the conveyor belt pushing the plane backwards? There's a complicated and perhaps faulty premise built into the question.

Basically, the question assumes that moving the runway backward under the plane while it is accelerating forward will cancel out its forward motion. But that's not necessarily true. The degree to which this is possible is the degree to which there's friction between the wheels and their axles. In a frictionless environment, it doesn't matter what the runway is doing.

Looking at it from the opposite extreme, if the runway can push back on the plane exactly as much as the engines are pushing forward, the plane will stand still. Rather than needing any fancy conveyor belt system, you could just put big blocks in front of the wheels. :)

Does this mean that the plane won't take off? Well, probably. You might want to think that the engines, as they push the air over the wings, will produce some lift, and I guess that this is true at least minimally, but the real lift generated by the wings is the relative motion between them and the air through which they move. Without forward motion, you don't have that lift. I doubt the engines could run fast enough to even generate enough lift to bring it off the runway at all.

So, the bottom line is that this isn't a hard problem if you understand that a plane flies because the wings generate lift as they move through the air, not merely because the engines push air over the wings. The engines push air over the wings in some cases just because it's a convenient design. The purpose of the engines to propel the plane forward. They can be anywhere in relation to the wings (well, excepting worrying about turbulence and stuff).

A more complete answer is that if you attempted this experiment, what would happen is that only at first would the conveyor belt cancel out the engines push forward. But very quickly, that small friction of the wheels wouldn't matter. The plane will move forward regardless of how fast the conveyor belt is moving backward. So the plane will just be slightly slow to start moving, then once it does, it will quickly act like any other plane taking off.

Alternatively, assuming you really could apply a backward motion equal to the forward propulsion of the engines, then the plane wouldn't take off. It'd sit there as the engines ran faster and faster because the engines aren't what generate lift. And the fancy backward-moving conveyor belt is a distraction, because you can get the same effect by just locking the plane against forward motion.

I am certain these are the correct answers, and I didn't look at the links. Anyone who says otherwise is wrong. :)

“One of my favorites is if you shot and drop identical bullets at the same time, which hits the ground first?”

What, shot one bullet parallel to the ground? They'd hit the ground at the same time. That's just high school physics. More interesting is what happens if you shoot something that is higher than you that begins to fall just as you shoot at it. What do you aim for?

And, of course, I'm the expert on the Monty Hall Problem.
posted by Ethereal Bligh at 10:31 PM on September 29, 2007 [1 favorite]


Yeah, basically if you take the question to mean that the plane cannot move foward, then no it won't take off. But, because the plane uses air propulsion, not ground friction to move foward, a conveyor belt would not be able to keep the plane stationary, and it would fly.
posted by brevator at 10:31 PM on September 29, 2007


If you replace the conveyor belt with a moving aircraft carrier, then you have a real world application.
posted by randomstriker at 10:34 PM on September 29, 2007 [3 favorites]


I think the real question here is this: Can the plane's thrust alone cause enough airflow over the wings to generate lift?
posted by BeerFilter at 10:35 PM on September 29, 2007


What Ethereal is trying to say is that if the conveyor belt could move wicked fast, it could stop the plane... by causing the wheels to spin so fast that they generated enough drag to cancel out the engine thrust.

It is very unlikely that any wheel could spin that fast without disintegrating. :)
posted by Malor at 10:37 PM on September 29, 2007 [3 favorites]


Lift + thrust = Drag + weight

All heavier than air powered flight is described, essentially, by the above equation. Just plug in the values for the plane of interest to see whether the case is true or false.

If the plane had an engine with enough thrust that it needed an incredibly short runway, essentially zero, it could take off. Your average Cessna 172, not likely. The Cessna uses a little over 1,000 feet of runway (at sea level, 835 feet to V1 rotation speed, and a bit more for lift off), to build up lift along the entire length of its wing. NO power setting you can apply to a stock Cessna 172 will cause it to lift from the ground instantly. The Cessna would fail to fly, and if the conveyor continued to accelerate past V1, would wind up in the weeds behind the conveyor.

However, if you're piloting an F-100 fighter, with a couple of JATO assist units, you could take off, no matter how fast, or slow, the damned conveyor was going. The F-100 with the JATO units is so massively over thrust on takeoff, it needs ZERO lift to fly, until the JATOs burn out.
posted by paulsc at 10:48 PM on September 29, 2007 [2 favorites]


I think the real question here is this: Can the plane's thrust alone cause enough airflow over the wings to generate lift?

No, that isn't the question at all, Beerfilter. Planes don't do that, ever. In cases where the engines are used to directly generate lift, that happens by pointing them at the ground, like the British Harrier jets.

All other planes I'm aware of use rear-facing thrust to cause forward motion, and the forward motion of the plane causes lift, because of how the wings are shaped. A plane that could generate lift directly with the engines over the wings would not need a runway, like the Harriers.

Any normal conveyor belt will not stop the plane from accelerating; the wheels will just spin twice as fast while the plane moves forward. Wheels on a plane are designed to decouple it from ground friction during takeoff; a backward-moving belt just makes them spin faster, and only increases drag marginally.

As Ethereal tried to say above, if the conveyor belt was incredibly, unbelievably fast, it could spin the wheels so enormously quickly that it ended up causing a backward thrust, but it would have to move at such high velocity that any airplane tire would disintegrate almost immediately.

The real, true answer would be: "Yes, the conveyor belt can prevent a successful takeoff, if it moves fast enough to destroy the wheels first."
posted by Malor at 10:48 PM on September 29, 2007 [1 favorite]


Cecil settled the question in links 1 & 2. I'm surprised by the confusion here.
posted by bhnyc at 10:49 PM on September 29, 2007


“Grimgrin, that made no sense whatsoever.”

No, it made sense. He was more concise than I was.

Planes fly because as they move through the air, the wings give them lift. That's an upward force. The engines don't cause that force, they only push the plane forward through the air. Can a conveyor belt push backward on the plane exactly as much as the engines are pushing forward? Not any real-world plane, because the whole point of wheels are that they have little friction preventing them from greatly impeding the plane's forward motion. Rolling the "ground" underneath the wheels will, because there's always some friction in the world, push back on the plane a little bit, but not much. Because we know that planes are able to take off without too much trouble, we already know that this small friction is pretty much negligible. So, in the real world, the conveyor belt will have little effect.

But, if we try to get at what the problem is aiming for, then we can just postulate some mechanism that really does push back on the plane just exactly as much as the engines push forward. What happens then? D'uh, the plane stands still. The engines are pushing a lot of air backward and generating a lot of force (which is being canceled out by whatever is keeping the plane still), but that air and force aren't what make a plane fly into the air. The plane need the air to be moving over the wings at a certain rate all across their length to get enough lift to take off. So, a real-world example with something modified to account for the conveyor belt's intended action would result in a plane that wouldn't take off.

Finally, maybe someone wanted to think that pushing all that air by the engines generates lift. Well, it mostly doesn't, but that doesn't mean that it couldn't. If you had powerful enough engines and everything was light enough, they could do it. What such a structure would amount to would be an inefficient helicopter system, where the wings merely redirect the air put in motion by the engines, pushing downward, causing the plane to move upward. Most people don't understand how wings generate lift1 and thus think this is what wings do anyway. But they don't. You'd need a huge amount of power to get much lift this way. And what would happen is that the plane would move slightly upward, and then, unrestrained from forward motion, it'd take off forward like a rocket, quickly generating real lift from the wings and it'd fly off into the sunset, before the engines overheat and melt.

Stuff like this is my bread-and-butter. I love it not because I like knowing the right answer to a physics problem (or a math problem in the case of the MHP), but because I'm absolutely fascinated by how people comprehend and miscomprehend things. That's the reason for my long explanations above: you can answer the question simply, but then you're not really answering it for many people because, basically, they understand the question differently than you do. This is very true with the MHP where you have to carefully work through things so that everybody is on the same page about what is actually happening. Otherwise, the right answer isn't actually right when it's applied to a question that the other person thinks (wrongly) is being asked. You have to understand how other people think about things before you can help them understand stuff. That's the neat part.

On Preview: I think I answer BeerFilter's version. And Malor is right, except that I don't think wheels could ever generate enough friction to keep the plane from moving forward. They're wheels, after all.
posted by Ethereal Bligh at 10:49 PM on September 29, 2007


What confuses me is why anybody finds this confusing. Well, I guess there's a good selection of the uneducated who think that jet engines make a plane fly.

Planes fly by moving forward, forcing air over the wings via relative motion, causing lift. A plane will fly with a single impulse acceleration, like from a catapult. I mean, a paper airplane doesn't have an engine, and it flies for a ways. You only need the engines to sustain your velocity against the zillions of things robbing you of it (drag and friction being the biggies).

If the conveyor cancels out forward acceleration of the plane, it's not going anywhere... least of all up. There's no air moving over the wings.
posted by Netzapper at 10:49 PM on September 29, 2007 [4 favorites]


Oh, I forgot my footnote. Apparently, the matter of lift is still an open question. It is mostly the Bernoulli Principle, I think, but I dimly remember somewhere that someone is arguing that the simple lift of redirected air actually makes a substantial contribution to the lift of real-world airplanes.

What's really going on is turbulent, complex physics so anyone who wants easy answers isn't likely to get them. So, for the layperson, it's best to just go with the BP.
posted by Ethereal Bligh at 10:53 PM on September 29, 2007


paulsc, this is one of the few times I've seen you get it wrong. A backward-moving conveyor just creates more drag at the wheels; the drag would have to be sufficient to prevent the plane from reaching takeoff speed. You'd have to have a very wimpy engine, or an unrealistically fast conveyor belt, for that to happen.
posted by Malor at 10:53 PM on September 29, 2007


If the conveyor belt moved fast enough, friction between the belt and the air would generate significant airflow parallel to the belt and over the wings, allowing the plane to lift off at least a little bit. Exactly how high would be limited by the boundary of turbulent air flow, depending on the length, width, air-friction coefficient, and speed of the conveyor.
posted by metaplectic at 10:53 PM on September 29, 2007


“If the conveyor cancels out forward acceleration of the plane, it's not going anywhere... least of all up. There's no air moving over the wings.”

Which is why paulsc's explanation is confusing, though in practice it's true. Planes with short take-offs don't manage it by going straight up, they still do it by the combination of very optimized wings which generate a lot of lift per relative motion to the air and (mostly) accelerating to a high forward motion very quickly.

It's forward motion relative to the air. Period.
posted by Ethereal Bligh at 10:55 PM on September 29, 2007


Yeah, paulsc is wrong about the Cessna.
posted by Ethereal Bligh at 10:56 PM on September 29, 2007


Yeah, that's a good point, metaplectic. But we're really getting to the outward fringes with that scenario. It'd matter quite a bit, for example, what kind of surface the belt had. That's such an indirect force, I doubt anyone has it in mind.
posted by Ethereal Bligh at 10:58 PM on September 29, 2007


I thought that wings don't "generate lift," in any meaningful sense.
posted by Kwantsar at 11:01 PM on September 29, 2007


I still want to see it on Mythbusters just for the hell of it.
posted by Foosnark at 11:02 PM on September 29, 2007


".... You'd have to have a very wimpy engine, or an unrealistically fast conveyor belt, for that to happen."
posted by Malor at 1:53 AM on September 30

Exactly. A Cessna 172's engine is "wimpy," simply because its no great inconvenience to private pilots to find a runway long enough to let them build up the 62 mph V1 speed the plane takes to try to fly. No way the standard Continental O-360 engine can create that amount of lift instantaneously. The wash from the standard 2 bladed fixed pitch props doesn't even cover 50% of the wing surface. You need developed speed to take off in the "underpowered" Cessna, and most "practical" aircraft.

But you don't in JATO assisted F-100. You push full afterburner, and hit the JATO lighters, and you will fly. In the first few seconds of that flight, your control surfaces will be entirely ineffective, because your airspeed won't be great enough to have them generating any force, which is why the "zero runway" programs were terminated. But, in your JATO assisted F-100, you surely will go UP, as long as your JATOs are pointed DOWN, because

"Lift + thrust" is much greater than "Drag + weight"
posted by paulsc at 11:05 PM on September 29, 2007


Damn Ethereal Bligh. That's a lot of words to say no it won't fly. I think the confusion lies in the givens of the problem. My assumption is that the conveyor is equal and opposite to the thrust of the engine. It's like one of those mythical frictionless planes used that anyone who has ever taken a physics class knows about.

And no shit Malor, an Harrier will take off, but imagine a giant gorilla pushing down on it which has infinite force to draw from, and so it can only use forwards momentum to lift off because the gorilla can't overcome lift generated from wings.
posted by Eekacat at 11:06 PM on September 29, 2007


LIFT. Understand?
posted by SkinnerSan at 11:09 PM on September 29, 2007


Malor typed: No, that isn't the question at all, Beerfilter. Planes don't do that, ever. In cases where the engines are used to directly generate lift, that happens by pointing them at the ground, like the British Harrier jets.

All other planes I'm aware of use rear-facing thrust to cause forward motion, and the forward motion of the plane causes lift, because of how the wings are shaped. A plane that could generate lift directly with the engines over the wings would not need a runway, like the Harriers.


That's exactly what I was trying to clumsily illuminate, Malor. Rockets "fly" because they have thrust enough to overcome gravity. Planes fly because the airfoil moves through the the air fast enough to generate lift. Fire off a pure (sans airfoil and lifting body) rocket parallel to the ground and it will drop at 9.8 m/s. The plane on the hypothetical magic treadmill won't fly because it won't move forward through the air fast enough.

BUT... Since we're all playing, I think we can all agree a plane that takes off at 100 MPH airspeed COULD take off in a 100 MPH headwind, while remaining in place reletive to the ground.

Right?
posted by BeerFilter at 11:13 PM on September 29, 2007


Answer: nobody cares.
posted by Avenger at 11:21 PM on September 29, 2007


Since this is a physics problem I think everyone should assume the wheels are frictionless.
posted by TheOnlyCoolTim at 11:23 PM on September 29, 2007


But I think you're still missing something, paulsc. I don't understand why you think that a Cessna engine needs to generate enough speed for lift instantly. It doesn't.

You're still assuming that it makes sense to say that the backward-moving conveyor built will actually push the plane backward just exactly as much as the engine pushes the plane forward. But that's just not going to happen. We know this isn't going to happen because the Cessna starts managing to roll forward normally without the conveyor belt. It's plausible that, except for extremely high rotational speeds, the greatest amount of friction between the wheel and the axis is from zero rotation to something rotation. If the engine can overcome that, then I'd wager that long before some effect causes the wheels high rotation to actually begin to matter relative to the engine, the plane will already have reached sufficient forward motion to have enough lift to take off.

Basically, with actual wheels and an actual conveyor belt, the conveyor belt doesn't matter at all, except perhaps at very low engine power. The planes will take off almost completely normally.

The aircraft carrier is a bit more complicated. There's two additional factors to consider, one theoretical and one practical.

The practical consideration is that a carrier can't accelerate like a jet can, so it couldn't move its runway exactly backward to counteract the plane's forward motion.

If it could, though, then we have the theoretical complication that an aircraft carrier runway is limited in length. And that's so short and jets have to move so fast, that basically this scenario would mean the carrier would drop out from underneath the jet before it generated hardly any forward motion. And they're not that high off the water, either, so the jet would probably crash.
posted by Ethereal Bligh at 11:23 PM on September 29, 2007


The force generated by the thrust of the plane is applied to the air, not the rotation of the wheels. An analogous question is this. Suppose you're on a treadmill while wearing rollerskates, holding onto a rope attached to the wall, and you start to pull on the rope. The treadmill speeds up to exactly match the forward speed caused by you pulling on the rope. Would you ever be able to pull yourself forward?
posted by Nquire at 11:26 PM on September 29, 2007 [6 favorites]


“BUT... Since we're all playing, I think we can all agree a plane that takes off at 100 MPH airspeed COULD take off in a 100 MPH headwind, while remaining in place reletive to the ground.”

Of course.

“Since this is a physics problem I think everyone should assume the wheels are frictionless.”

Yes, except that the phrasing of the question and its nature strongly implies some backward force. You only get that with friction from the wheels on the axles. If the wheels are frictionless, then the motion of the belt doesn't matter whatsoever. The plane will act completely normally, with “normally” being a plane that has frictionless wheels.

Nquire: good analogy. And the answers are the same: yes, unless someone really, really wants to find some way of that treadmill pushing back on you exactly as much as you pull on the rope. In which case, no. :)
posted by Ethereal Bligh at 11:28 PM on September 29, 2007


Fucking gorillas. Always keeping mankind down.
posted by Lord_Pall at 11:29 PM on September 29, 2007 [1 favorite]


"Yeah, paulsc is wrong about the Cessna.
posted by Ethereal Bligh at 1:56 AM on September 30

If I were "wrong" about the Cessna, no Cessna 172 pilot could keep his plane headed straight down the runway long enough to get to V1 velocity. What keeps you able to steer the plane during the takeoff roll, and what would keep it controllable on any real world conveyor, is a combination of nose wheel friction with the runway, and, increasingly, as you build up speed in the take off roll, rudder influence. If you mistakenly lift the nose of the plane early, around 55 mph, when first it will let you, you stand a good chance of winding up in the weeds, to your left or right, depending on any crosswind influence of the day, because the total available rudder influence at 55 mph and less isn't enough to steer the plane against the forces it creates itself, much less those that are wind influenced, from cross winds.

In the case of a conveyor belt working on a windless day, as soon as you rotate at V1, you lose the nose wheel steering, and have only prop wash for rudder control (for single engined prop planes like the Cessna 172), and you suddenly head to the left, and shortly, you're flung by the conveyor into the weeds behind and to the left of you. Pilots of Cessna 172 know this, and always apply right rudder in normal takeoffs, to counter prop effects [slow link, wait for it if you want the technical background] during normal (non-crosswind) takeoff. But no amount of right rudder applied to a Cessna on a conveyor belt would work, because there is no developed airstream, other than pure prop wash, for the rudder to apply.

Trust me, and a professional pilot, on this one.
posted by paulsc at 11:31 PM on September 29, 2007


Since this is a physics problem I think everyone should assume the wheels are frictionless.

Also that the plane is a sphere.
posted by thecaddy at 11:31 PM on September 29, 2007 [5 favorites]


If the shape of the wings creates lift, how do planes fly upside down?
posted by Henry C. Mabuse at 11:31 PM on September 29, 2007


I believe you have to compensate. it's the same as trimming your aelierons so you don't go up
posted by Lord_Pall at 11:33 PM on September 29, 2007


My assumption is that the conveyor is equal and opposite to the thrust of the engine.

It's not the problem's fault you can't make correct assumptions or form sentences that make sense.

Read the damn problem, people!
"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 the opposite direction). Can the plane take off?"

Where does this "unbelievably fast-moving conveyor belt" crap come from? The wheels have to spin exactly twice as fast as they normally would. That's it. Do the engines have enough power to overcome the extra friction? Unless they are powered by wound up rubber bands, the answer is yes, they do.
Why is it so hard to understand?
posted by c13 at 11:33 PM on September 29, 2007


Look. This is really stupid.

The problem as described cannot actually occur in the real world, even approximately.

No such unit can exist. If I put power into the model, in a short time the conveyor belt is running faster than the speed of light. In order to set up the very conditions of the problem, you have to break the rules of physics.

At that point, you're perfectly entitled to claim that bunny rabbits swoop down and carry the plane off, or whatever you like, since we're in magic-land anyway.

(btw, this has a lot of similarity to the question: "Can God make a stone so big that he can't lift it?")
posted by lupus_yonderboy at 11:34 PM on September 29, 2007 [1 favorite]


Henry: Angle of attack. They point the nose towards the sky when inverted.
posted by BeerFilter at 11:36 PM on September 29, 2007


"... If the engine can overcome that, then I'd wager that long before some effect [emphasis added] causes the wheels high rotation to actually begin to matter relative to the engine, the plane will already have reached sufficient forward motion to have enough lift to take off. ..."

What "effect," Ethereal Bligh? You've got 4 to choose from:

Lift, drag, weight, thrust. If Lift + thrust > Drag + weight, you fly. Otherwise, you wind up in the weeds. Every time.
posted by paulsc at 11:39 PM on September 29, 2007


I hate this question so much. There are two right answers depending on how you choose to decipher the poorly conceived thought experiment.

If you decide that the questioner meant to create a scenario where the engines were running at full speed without air moving over the wings, then of course the answer is, for conventional planes, no, it will not take off.

If you decide that the questioner meant to create a scenario where the wheels could not push forward, like a car on a testing track, then of course the answer is that the wheels have nothing to do with the generation of thrust, and of course the plane will take off.

All of the arguments are over which of these interpretations of the question is correct, not over the actual outcome.

If you were to actually create this experiment, the actual result would depend on whether the wheels or conveyor belt failed before you reached the maximum energy you had available to power the conveyor. If they did, everything would be a mess. If they did not, the plane would take off.

(The moving conveyor would also quickly create a very fast moving sheet of air above it, which might be enough to get the plane in the air, but it would be so turbulent, and the shear so great as altitude increased, that the plane would probably crash very quickly.)
posted by Nothing at 11:44 PM on September 29, 2007 [6 favorites]


Fun thread. I've learned a lot. :)
posted by BeerFilter at 11:45 PM on September 29, 2007


“But no amount of right rudder applied to a Cessna on a conveyor belt would work, because there is no developed airstream, other than pure prop wash, for the rudder to apply.”

You keep completely missing the point. There would be a developed airstream because the conveyor built wouldn't prevent the prop from pushing the plane forward. The end.

Postscript: and if the conveyor belt could push the plane backward enough to prevent a “developed” airstream, then a jet (without a downward projected thrust of some kind) couldn't take-off and a plane wouldn't take off.

“‘Where does this "unbelievably fast-moving conveyor belt’ crap come from? The wheels have to spin exactly twice as fast as they normally would. That's it. Do the engines have enough power to overcome the extra friction? Unless they are powered by wound up rubber bands, the answer is yes, they do.

Why is it so hard to understand?”


You're the one missing something. Why do you think that the backward moving conveyor belt exerts a force exactly equal to the engines, proportional to speed? It won't. Why won't it? Because, you know, wheels are designed to minimize friction. All the conveyor belt has to work with, pushing backward, is that small friction of the wheels against their axles. None of us know exactly how much friction that is, but those of us who understand the problem know that it's very small relative to the other forces involved. (How do we know that? Because planes can take off in the first place). Therefore, the conveyor belt, to manage to do what the problem assumes it does, would have to go backward much faster relative to the plane to impede its forward motion relative to the air than does a normal plane need to move relative to a stationary runway and the around above it. That's where people are coming up with the “unbelievably fast-moving conveyor belt”. Please don't be condescending unless you are actually right.

What ‘effect,’ Ethereal Bligh? You've got 4 to choose from...”

Paulsc, just as in my comment to c13 above, the only thing that matters with regard to the conveyor belt and the wheels is the small amount of friction between the wheels and their axles. We can assume infinite friction between the wheels and the belt surface for the purposes of this problem. Which, arguably, implies that we should assume zero friction between the wheels and their axles. If we do that, then the freakin' conveyor belt doesn't matter whatsoever and the plane will take off normally (again, where “normal” means how a plane takes off with wheels on frictionless axles).
posted by Ethereal Bligh at 11:47 PM on September 29, 2007


I need to change what I wrote to c13. Rereading, I see that he's not assuming (as others are) that the backward moving belt exerts much force. And, as the problem is stated (and not trying to guess what the problem intended), then the backward moving conveyor belt doesn't matter at all. How fast will it be moving backward? As stated in the problem. And that means the wheels will be turning twice as fast. Not that that will matter.
posted by Ethereal Bligh at 11:50 PM on September 29, 2007


the answer is one, but the plane really has to want to takeoff.
posted by blue_beetle at 11:54 PM on September 29, 2007


“No such unit can exist. If I put power into the model, in a short time the conveyor belt is running faster than the speed of light.”

This is a strange statement to me because it's true only for a small range of assumed values of friction between the wheels and their axles. But those values could be anything. They aren't necessarily in your range.

Anyway, though, as c13 points out, the problem as stated doesn't postulate a force equal and opposite that of the engines; instead, it postulates a specified backward speed of the conveyor belt, which implies a backward force...a force which really wouldn't exist. So part of the problem with the problem is that it is misleading. So, as written, you're wrong. The belt will just accelerate backward equal to the plane's forward motion (making their relative motion twice the plane's forward motion).
posted by Ethereal Bligh at 12:00 AM on September 30, 2007


Rereading, I see that he's not assuming (as others are) that the backward moving belt exerts much force.

What justification would I have to assume it? The only things that generate extra friction are the bearings and the tires. No other forces are mentioned or implied in the problem.
I don't mean to be condescending, but like I said, one has to read the problem correctly before answering it and be able to justify all of the assumptions. Otherwise you're answering a different question. In the present case, if you assume that you can just disregard the limitation on the belt speed, why can't you also assume that the brakes are on, for example?

I've got a good lesson about the dangers of unjustified assumptions on a med micro exam last Monday...
posted by c13 at 12:08 AM on September 30, 2007


"There would be a developed airstream because the conveyor built wouldn't prevent the prop from pushing the plane forward.

Not if the conveyor was able to run up to - 62 MPH (that's minus 62 MPH), in the case of our Cessna. At that indicated ground speed the Cessna's airspeed would be 0. All Cessna's have airspeed indicators, few have actual ground speed indicators, but it's trivial to hook up a speedometer to one of the wheels. Presume I have, for a minute.

On your conveyor, at 62 MPH indicated ground speed, which is V1, I try to lift the nose to rotate, and lose nose wheel steering effect. There is 0 airspeed over the ailerons at the ends of the wings, because I've built no relative motion to the ground and the still air above it, if your conveyor is working right. The prop wash doesn't extend that far along the Cessna's wings, nearly, believe me, although every time I've stalled a Cessna, I wished, like Hell, it did. There is 0 induced lift from the takeoff "roll," because I haven't "rolled" anywhere, relative to the rest of the world, thanks to your conveyor, so all I've got for lift is the pitiful amount of lift I get from prop wash at full power, which the Cessna 172's tiny brakes can overcome, at every pre-flight run up. And then, you want me to rotate, and fly.

Well, OK, I'm a sport, and I pull back the yoke, and maybe, just barely, the nose lifts, because of massive elevator angles (which are in the full wash of the prop, as is the smaller area rudder) I've induced with the yoke, and immediately, the nose wheel steering goes away, and without developed airspeed (still 0, because of the conveyor), I don't have enough rudder control to oppose the loss of nose steering, or any aileron, to counter prop effect. I'm seriously screwed, in the weeds, and answering FAA inquiries about my airmanship, as quick as your conveyor can throw me there.

No, thanks.

If I'm going to be the pilot in your thought experiment, I want the F-100 with the JATO units. It'll be a crappy, wobbly flight out, but I'll damn sure fly off your conveyor, because, worst case:

Lift + thrust > Drag + weight
posted by paulsc at 12:15 AM on September 30, 2007


Again, sorry for misunderstanding you, c13. Those of us who are going beyond the problem as written are just trying to answer the problem the problem seems to intend, as opposed to merely the problem as explicitly asked.

To sum up...

1) What matters for lift is forward motion. So the plane only needs to be moving forward enough relative to the air around it to take off.

2) The engines act to push the plane forward, not push the plane up into the air.

3) The problem as stated just postulates a backward moving conveyor belt equal to the plane's forward motion. The implication is that this impedes the plane's forward motion. But it wouldn't, because the only mechanism for the transmission of this supposed force is through the wheels on their axles. And wheels, being the whole point of wheels, have relatively low friction in this area. A plane's engine easily overcomes that friction in comparison to how much it must work to actually get the plane airborne. So that friction of the wheels against their axles is so small, that it's pretty much negligible. Which means that since the problem specifies exactly a backward speed of the conveyor belt, then the plane will appear to take off normally, excepting that it might move backward a little bit right at first and the wheels will be turning twice as fast.

4) Some people misinterpret the problem to mean that the belt moves backward enough, whatever the amount of friction between the wheels and their axles, to cause the plane to have no forward motion. This isn't the case as the problem is stated; but assuming it is, then we're just saying the plane won't move forward. And if the plane isn't moving forward, it won't take off because of points 1 and 2.

5) An aircraft carrier in place of the conveyor belt would be exactly the same if it had sufficient length for the plane to take off. But, in reality, it doesn't. The deck would drop out under the plane before it had enough forward motion to take off. However, an aircraft carrier couldn't accelerate that quickly anyway.

6) Some quirks of the problem are that a sufficiently powerful engine could generate some lift (not through the Bernoulli Principle, but just like a rocket does, with some of the thrust directed downward via the obstruction of the wings). But this is silly, it's like asking if a helicopter or a rocket could take off under these circumstances. Off course they could. The other quirk is that one can speculate that a sufficiently fast backward-moving belt (probably not one merely going backward as fast as the plane is moving forward, though) might itself drag enough air along with it such that the plane ends up getting lift on its wings to take off. But this is silly, because we're talking in this case about a really inefficient wind tunnel. And we know planes can fly in wind tunnels.

I think that covers everything.
posted by Ethereal Bligh at 12:17 AM on September 30, 2007


“Not if the conveyor was able to run up to - 62 MPH (that's minus 62 MPH), in the case of our Cessna. At that indicated ground speed the Cessna's airspeed would be 0.”

No, darnit, because the belt would never push backward that much on the Cessna. It wouldn't happen. That's the part you're not getting.
posted by Ethereal Bligh at 12:20 AM on September 30, 2007


Lift + thrust > Drag + weight

this is dumb. stop repeating it like it's true. lift/weight point in the vertical direction; drag/thrust point in the horizontal direction. they are totally orthogonal to each other, and while they may bear some relation to each other in normal flight, clearly a plane on a conveyor belt is not normal flight.

the question of "will a plane take off" boils down to "is the lift greater than the weight?"

the lift is a function of the relative velocity between the air and the wings.

the relative motion between the ground and the wheels has nothing to do with it, nor do the forces acting on the plane in the horizontal direction.
posted by sergeant sandwich at 12:25 AM on September 30, 2007


For those having trouble with this, I found the best way to think of this is to compare a conventional petrol/diesel car in gear driven by the engine, and a car in neutral being pushed by a force on the boot.

In gear, the car relies on friction between the ground and the tyres in order to move. There is high friction between the wheels/axle and the drivetrain (due to the clutch). Moving the ground backwards, because of the friction with the tyres will move the wheels backwards. As the wheel axles have a high friction with the rest of the drivetrain, that motion acts a counter force on the drivetrain, and thus the rest of the car. In order to stop going backwards on a moving conveyer, a car engine has to counter the backwards force of the conveyer (applied through the high-friction drivetrain) plus air resistance, plus the rolling resistance in the wheels - all just to stand still relative to a fixed point. The faster the conveyer, the more force the engine will have to apply just to stand still in a direct relationship.

A car in neutral, or the clutch disengaged, with no handbrake applied has the wheels in (mostly) free rotation. The wheels can rotate independently of the motion of the rest of the car. Imagine a car up on jacks in neutral, with you spinning the wheel. It won't cause the car to move and fall of the jack! There is a small force applied due to the friction in the wheel bearings, but this is very very small compared to the friction from the clutch or handbrake. A car like this on a conveyer belt will move backwards, but only slowly due to the bearing friction - the wheels will rotate faster and faster as the belt speeds up, but the rotation of the wheels is not coupled to the motion of the rest of the car. Just as you can push a car with one hand when it's in neutral, so could a small force pushing the car on the boot when the wheels are free rotating push it forward even on a moving conveyer (assuming the man pushing on the boot isn't also standing on the conveyer!)

A plane does not move because it applies force to the wheels and rotates them against the runway, as a car in gear does. It moves because a force is being applied against its body* while the wheels move independently of the rest of the plane (apart from that very small bearing friction), like a car in neutral.

As others have said, taking off from a moving conveyer will only stop the plane taking off if the force from the bearing friction is sufficiently large to make the overall drag big enough to overcome lift+thrust.
That would have to be a very very fast moving conveyer, as bearing friction is tiny compared to say, clutch and drivetrain friction.


*how the force applied to the plane in the horizontal direction by the engines is converted into lift in the vertical direction by the wings is rather irrelevent. What matters is how much horizontal force is countered by the ground normally vs a conveyer belt going counter to the plane's horizontal motion, i.e. the question is how much bigger is drag than normal, so how much thrust is 'lost' to friction. As has been shown, with the wheels in free rotation, the answer is 'not much'.
posted by ArkhanJG at 12:31 AM on September 30, 2007


"No, darnit, because the belt would never push backward that much on the Cessna. It wouldn't happen. That's the part you're not getting."
posted by Ethereal Bligh at 3:20 AM on September 30

A Cessna's landing gear is about 12 feet long, from the nose wheel to the other two wheels. Let's say your conveyor is 15 feet long, and matches the Cessna's ground speed indicators perfectly. Any time the Cessna manages to generate a forward roll of any kind, your conveyor exactly opposes that, so as to keep the Cessna centered in that magic 15 feet of conveyor belt.

Because, if the conveyor couldn't, the Cessna would no longer be on the conveyor. If you grant that the conveyor can keep up with Cessna, the Cessna never develops any velocity with respect to the air under it's wings, (except for the small area in the prop wash). It can't fly, without developed lift. That's the way Cessnas and all other general aviation aircraft are built.

And yes, out in the real world, off conveyors, Cessna's fly every day, because, with about 1000 feet of take-off roll:

Lift + thrust > Drag + weight

Anytime it isn't, the pilot and airplane wind up in the weeds, and the FAA calls the NTSC, and we have an accident investigation.
posted by paulsc at 12:33 AM on September 30, 2007


If you drive your DeLorean on a treadmill at 88mph but the treadmill is keeping your position stable, can the flux capacitor activate?
posted by furiousxgeorge at 12:34 AM on September 30, 2007 [6 favorites]


“I don't mean to be condescending, but like I said, one has to read the problem correctly before answering it and be able to justify all of the assumptions. Otherwise you're answering a different question.”

I explained this earlier. The reason this matters is because what's important here isn't just the correct answer to the question. The reason we're discussing it is because people don't understand the question at least as often as they don't understand how to answer the question when they understand it.

In order to help people understand stuff like this, you need to try to understand how they misunderstand things.

And not only that, but the way the problem is phrased is either intentionally misleading or the person who originally wrote it misunderstood what is involved and intended something slightly different. In either case, the difference between those things and the actual question and its answer is that is happening with the wheels and the conveyor belt.

My argument with paulsc is a good example. He's not going to arrive at the correct answer until he understands what's really happening with those wheels and the conveyor belt and how that affects the plane's relative motion. You can keep pounding on him that the correct answer is that the plane will take off pretty much as normal, but he's not going to get it.

Similarly, with the Monty Hall Problem, the misunderstanding of the problem occurs with regard to how Monty is or isn't constrained in his decision to open a door and how that relates to what has changed between the contestant's first selection of a door and his later opportunity to switch. If you just keep telling people the correct answer to the problem, they won't believe you because they're still coming up with what happens to be the right answer to a different problem. (Which is also the case of paulsc here.)

And what is of value for people thinking about and discussing this problem is not merely the problem properly parsed and reduced to its relevant elements and then solved. It's developing some intuitive feel for how all these things interelate. Why is that important? Because getting a problem right in terms of its reduction and formalization is both a matter of skill and luck. Because the latter is always involved, you can't count of always being lucky enough to immediately see the reduced problem and answer it without considering it in more complexity. You need some facility for thinking around problems. And developing this also means that you'll develop that skill of reduction. But I suspect that when this is the case, those people don't freak out at weird misinterpretations of problems, they anticipate them.
posted by Ethereal Bligh at 12:36 AM on September 30, 2007 [2 favorites]


But no amount of right rudder applied to a Cessna on a conveyor belt would work, because there is no developed airstream, other than pure prop wash, for the rudder to apply.

You're really missing this one, paulsc, so very unusual for you. Time to back off and think about this again.

For the conveyor to stop the plane, it needs to exert a force on the plane at least as great as the engine. But it has only two forces it can impart; acceleration, as it speeds up, and the friction of the wheels turning on the axles. It has no other method to retard the Cessna's forward motion.

So, the Cessna pilot applies full throttle. Initially, the conveyor accelerates, applying some backward pressure on the plane, but that abates as soon as it comes up to speed. As the plane continues to accelerate forward, the conveyor would need to accelerate backward to counteract the force, and would very, very rapidly exceed the ability of any conveyor belt to move. The Cessna can keep accelerating until its tanks are empty, but the belt can only accelerate for a brief time before it, or the wheels of the plane, disintegrate(s).

If the conveyor was just matching SPEEDS, rather than ACCELERATIONS, then the Cessna wheels would spin twice as fast, but the plane would otherwise take off normally.

If we somehow built an incredibly fast conveyor, we could probably destroy the Cessna's wheels before it took off, but we couldn't otherwise stop it with any conveyor buildable by humans.

(note that I added in the acceleration argument from the second link: I didn't consider this before, but it is true.)

Let me rephrase it another way so that you might get it: the Cessna will take off because it's pushing against the air, not against the conveyor belt. In your formula of lift + drag, the extra drag from the conveyor doesn't really matter. Ground friction is for steering, but is otherwise almost unimportant, compared to the other forces involved.
posted by Malor at 12:39 AM on September 30, 2007 [1 favorite]


I think we need a beanplate tag now.
posted by BeerFilter at 12:43 AM on September 30, 2007 [1 favorite]


paulsc: here's the question you need to ask yourself: just how, exactly, does the conveyor oppose the forward roll? How can it push back against the plane to keep it from moving in a forward direction?

On preview: what Malor said.
posted by zsazsa at 12:45 AM on September 30, 2007


Note that, as mentioned in Straight Dope and then again above, you can experiment with this yourself, with the treadmill/roller skates/rope approach. It's the exact same thing.

Stand on a treadmill wearing roller skates, holding a rope attached to a wall. Turn on the treadmill. As the treadmill accelerates, you feel a force on the rope; you have to pull to hold your position. As it reaches its speed, the pull abates to a very tiny amount, the friction of your wheels.

If you then turn the dial to a faster speed (start the treadmill accelerating), then you will have to exert more force to hold your position; you have to counteract the acceleration. When it's done accelerating, you again have to exert very little force to hold yourself in place.

So could you make a treadmill fast enough to keep you from pulling yourself up the rope? Yes, briefly; you could make a treadmill that accelerated exactly fast enough to match the strength of your arms. But you can keep pulling and pulling and pulling, and the treadmill has to go faster and faster and faster to stop you. Eventually, it's going to reach its physical limits, and you can keep pulling.

Eventually, you will pull yourself to the wall, assuming your skates hold up.
posted by Malor at 12:48 AM on September 30, 2007


“Because, if the conveyor couldn't, the Cessna would no longer be on the conveyor.”

Sure. That's the aircraft carrier version. It just falls off the conveyor belt first thing.

“If you grant that the conveyor can keep up with Cessna”

What do you mean by “keep up”? This is where I think you're stumbling.

If by this you mean “somehow keep the Cessna motionless relative to the ground and air, regardless of how fast the belt has to move backward”, then, yes, the Cessna wouldn't be able to fly. Neither would a jet without some downward directed force from its engines (which makes it more than a plane).

But the problem says precisely how fast the belt moves backward. It implies that it would make the plane motionless. But it wouldn't.

It wouldn't because we already know that the friction of wheels against their axles is relatively small compared to what a plane needs to do to take off. The conveyor belt, as specified in the problem, would be regulated not such that it created zero forward motion, but rather merely that whatever speed the plane would be going on a normal runway as it took-off, the conveyor belt would be going exactly the opposite backwards. That implies that the plane would be motionless with regard to the ground and air—but, in fact, it wouldn't be. Wheels turn easily. In the real world, they'd just spin twice as fast, the plane's airspeed would pretty much increase as normal, and the plane would take off.

Providing the conveyor belt was long enough, of course. But the only people who visualize a short conveyor belt are those who are visualizing a motionless plane, which is wrong.

If you've followed me so far, then I'll repeat the rest of it. The alternative here is to assume that, contrary to the statement of the problem, the belt's speed isn't specified, but that it goes however fast backward it needs to go to actually push hard enough on the plane to keep the plane's airspeed at zero. What happens then? The plane doesn't take off. Which is trivial because that just like asking whether a tethered plane will rise up into the air if you gun the engines hard enough. Nope.
posted by Ethereal Bligh at 12:49 AM on September 30, 2007


"1) What matters for lift is forward motion."

Wrong. Men couldn't have walked on the Moon, if this assumption were correct. More importantly, the Wright Brothers would never have flown.

"2) The engines act to push the plane forward, not push the plane up into the air."

Wrong. NO airplane cares about its airspeed. It flies if the lift + the thrust is greater than the drag + weight. In the case of certain ultralight powered aircraft, that airspeed can be around 4 MPH, in stable flight. In the case of vectored thrust aircraft, such as the Harrier, the minimum airspeed can be 0. The wings, literally, don't have to work, at all, if the engine is working right. Thus, Neil Armstrong is in the history books.

"Which means that since the problem specifies exactly a backward speed of the conveyor belt, then the plane will appear to take off normally, excepting that it might move backward a little bit right at first and the wheels will be turning twice as fast."

Really, really wrong. Frame of reference issue. A normal plane (such as a Cessna) will never take off from the conveyor, period, because it will never achieve flight conditions in the still air (relative to the rest of world) in which its wings exist.

"And if the plane isn't moving forward, it won't take off because of points 1 and 2."

Finally!!! Congratulations! I think you're ready to begin ground school, EB!

"... I think that covers everything."
posted by Ethereal Bligh at 3:17 AM on September 30

I really, really wish it did, EB. The aircraft carrier thing? Hugely out in left field, but I'm not gonna start with that...
posted by paulsc at 12:52 AM on September 30, 2007


Looks like I picked the wrong week to quit sniffing glue.
posted by Poolio at 12:52 AM on September 30, 2007 [2 favorites]


He's not going to arrive at the correct answer until he understands what's really happening with those wheels and the conveyor belt and how that affects the plane's relative motion.

He's not going to arrive at the correct answer because he keeps making up conditions that were not in the original problem. Like the 15 foot belts and ground speed indicators.
posted by c13 at 12:53 AM on September 30, 2007


“Eventually, you will pull yourself to the wall, assuming your skates hold up.”

Yeah, but I think it's really simpler than that. If the friction of the wheels on the skates on their axles is zero—perfect wheels—then the speed of the treadmill doesn't matter whatsoever. You are essentially on a frictionless surface, you can pull yourself on the rope with perfect efficiency.

If the wheels aren't perfect, as real world wheels aren't perfect, then it's a matter of how imperfect they are. If they wheels don't work at all, they're locked up, then, well, you'll tumble. :) But, imagining that it could push on you directly against how you're pulling on the rope, then you'd move one way or the other depending upon which is stronger, you or the treadmill.

As we think of less and less amounts of friction, then we're just talking about less and less efficiency of the treadmill in its transmission of force from its motion to you. The less friction—that is, the better the skates—the faster the treadmill would have to go to manage to push you back hard enough to keep you from pulling yourself forward.
posted by Ethereal Bligh at 12:57 AM on September 30, 2007


"For the conveyor to stop the plane, it needs to exert a force on the plane at least as great as the engine. But it has only two forces it can impart; acceleration, as it speeds up, and the friction of the wheels turning on the axles. It has no other method to retard the Cessna's forward motion"

Wrong, malor. Real Cessnas respond a lot more to aerodynamic drag, than the friction in their wheel bearing. That's why, in the flight equation, we talk about drag as opposed to friction. There are several kinds of drag, actually, only one of which, a minor one, is wheel bearing friction.

And "acceleration" isn't a "force," it's a product of force over time. "Thrust" is the force.
posted by paulsc at 12:58 AM on September 30, 2007


“Wrong. Men couldn't have walked on the Moon, if this assumption were correct. More importantly, the Wright Brothers would never have flown.”

Okay. I need to ask you if you understand the Bernoulli Effect and how that is different than thrust.

I'm baffled as to how you're confused. You are definitely confused and this should be clear to you as you are the only one arguing against a number of people. I can't figure out what you think is the relevance of your comment to malor. Aerodynamic drag only matters if the plane is moving through the air (or air is moving over the plane). How do you think this will come about in this problem? Please explain that part to me.

“A normal plane (such as a Cessna) will never take off from the conveyor, period...”

It will if the conveyor is about as long as the normal runway a Cecssna needs to take off. The conveyor belt won't push back against the plane as much as the engines push forward.
posted by Ethereal Bligh at 1:08 AM on September 30, 2007


Real Cessnas respond a lot more to aerodynamic drag, than the friction in their wheel bearing.

You just said exactly why the plane will fly: the friction in the wheel bearings won't keep the plane from moving forward through the air, generating enough lift to get it aloft. The plane's forward thrust generated from the prop is greater than the backwards force generated from the wheel bearings (which is small) and aerodynamic drag (which is not).
posted by zsazsa at 1:14 AM on September 30, 2007


And "acceleration" isn't a "force," it's a product of force over time.

Dude, you really need to stop talking out of your ass. The more you post, the more you demonstrate that you have no fucking clue what you're talking about.

EB, Bernoulli Effect is only a minor contribution to the total lift of the wing. That's why planes can fly up side down perfectly fine.
Here is a link that explains why planes fly.
posted by c13 at 1:16 AM on September 30, 2007 [1 favorite]


"paulsc: here's the question you need to ask yourself: just how, exactly, does the conveyor oppose the forward roll? How can it push back against the plane to keep it from moving in a forward direction?"

As soon as the Cessna pilot releases his brakes, and shoves his throttle to full takeoff power, the plane will try to move forward on the conveyor. Instantly, the conveyor must start moving in the opposite direction, by an exact like amount, at an exact same rate, if we're to have anything to consider. If the conveyor and the Cessna exactly cancel each other's motion in the first second, the experiment continues. Otherwise, either the conveyor throws the Cessna back into the weeds behind it, or the Cessna pulls forward, off the conveyor, and slowly starts its normal takeoff roll.

That situation continues, in every instant, irrespective of any situations with wheel bearings or tires or forces they generate on the conveyor, until the Cessna pilot either does something aerodynamically to change the static conditions, or the experiment ends tragically, with an FAA investigation. Probably, at full power, about 70 seconds after the experiment starts, the Cessna pilot will be indicating 62 MPH ground speed, but 0 air speed, and will have about 400 pounds of developed lift, from prop wash over his wing sections nearest the fuselage, causing his tires to slip, ever so slightly, against the speeding conveyor.

The conveyor, because of the wheel slip due to reduced wheel friction caused by the Cessna's prop induced lift, will perhaps go up to 68 or even 70 MPH, but the Cessna's pilot will only observe 62 MPH on his ground speed indicator, because his wheels are skidding, due to minor prop induced lift. And then, the Cessna pilot, in order to fly, will have to rotate, to create the lift needed to break gravity's hoary embrace.

As soon as he does that, the nose wheel will come up, and no longer be in contact with the conveyor. There will be no induced lift from the wing tips, which are not feeling any pressure from the still air, in which they live, if the conveyor is doing its job, because prop induced lift only occurs around a small area just above and to a few feet next to the cockpit; the majority of the wing area never feels any prop wash; for most of the wing of our Cessna, no air is moving over it, at any point, no matter what the conveyor or the plane's engine is doing. In this condition, in less than a second, the Cessna shifts left, and is thrown by the conveyor, backwards into the weeds, because of residual friction with its back two landing gear wheels, having failed to lift off, when the thrust vector of it's engine abrupt pitched up, in reponse to pilot input.

The NTSC concludes "Pilot error." and goes home, and the FAA closes the investigation.
posted by paulsc at 1:24 AM on September 30, 2007


If you know that no real-world conveyor belt would prevent a plane from taking off, congratulations: you have thought about this problem for three seconds more than 90% of the people on the internet.
posted by Optimus Chyme at 1:25 AM on September 30, 2007 [1 favorite]


"Okay. I need to ask you if you understand the Bernoulli Effect and how that is different than thrust."

If Bernoulli Effect were sufficient to cause planes to take off, planes wouldn't need to rotate at V1. They'd just, I guess, lift smoothly away from their runways.

But, generally they don't. They rotate. Why do think pilots go to all that trouble, to lift the nose, at a specific speed, EB?
posted by paulsc at 1:28 AM on September 30, 2007


"You just said exactly why the plane will fly: the friction in the wheel bearings won't keep the plane from moving forward through the air, generating enough lift to get it aloft. ..."

My whole point is that the parts of the Cessna's wing which would normally provide the lift at V1 to allow it to fly, provide nothing, if the conveyor is matching the aircraft's ground speeds. No drag, but no precious lift, either.

For that reason, the Cessna cannot fly, and is dragged by the conveyor into a horrible, crumpled mess of twisted metal, which the insurance company will try to avoid paying on, citing "Pilot error."
posted by paulsc at 1:33 AM on September 30, 2007


I suspect the problem is more that the question has been mangled over time. It's like the "words ending in -gry" riddle, where in the re-telling, the important points have been lost.

Since this is a physics question, I'd suspect it lost some numbers (one of the links above still has some) to be re-told to the layman. And then the speed issue becomes confused, and the matching the speed of the wheels absurdity got included.
posted by Auz at 1:36 AM on September 30, 2007


paulsc: first of all, the experiment specifies a conveyor as long and wide as any runway you'd expect to be taking off from in a Cessna. But that doesn't really matter.

You're also assuming that somehow the conveyor is keeping the plane from moving forwards relative to the ground and the air around it. But it can't. That does matter.

The pilot releases his brakes and starts to inch forward relative to the ground ever so slightly. The conveyor underneath his plane's wheels then begins moving backwards just as slightly. The plane experiences a teeny bit more drag from the wheel bearings, but, hey, that's no problem as the prop is still generating enough thrust to accelerate forward. At the next instant, the plane is moving forward just a little bit faster. The conveyor speeds up to match. This generates a little bit more drag, but it's still really small. This keeps going on and on until the plane takes off, with an indicated ground speed of 144 MPH and air speed of 62 MPH. Everything's cool, nothing goes into the weeds, and the FAA begins an investigation to find out who replaced a runway with a giant conveyor belt.
posted by zsazsa at 1:40 AM on September 30, 2007 [5 favorites]


Correction: ground speed of 124 MPH.
posted by zsazsa at 1:41 AM on September 30, 2007


But also, please note, that if you give me the JATO equipped, 1950's vintage F-100 fighter, in every case, I'll fly it, however inelegantly, off your conveyor. So long as the JATO bottle works, the F-100 will never wind up in the weeds, no matter what the conveyor does.

For the JATO equipped F-100, Lift + thrust will always be greater than Drag + weight.
posted by paulsc at 1:42 AM on September 30, 2007


“EB, Bernoulli Effect is only a minor contribution to the total lift of the wing. That's why planes can fly up side down perfectly fine.

Here is a link that explains why planes fly.”


Yeah, I'm aware that it's more complicated. The BE is taught to physics students and aeronautical engineers as a first approximation. That this is the case tells me that it's probably not merely a “minor” contribution. Or, alternatively, there's a shifting of thought on this question.

I suspect that the BE is more efficient because it causes less turbulence. Thus, modern wings are designed to maximize the BE. However, some planes can fly upside-down because the flaps can manage enough lift, too.

The point, though, is that the degree to which this matters in this argument is that planes don't generate lift via the engine pushing air over the wings. They generate lift by the forward motion of the plane through the air, which, in turn, is caused by the engines pushing the air backward.

“But, generally they don't. They rotate. Why do think pilots go to all that trouble, to lift the nose, at a specific speed, EB?”

Because at that speed they are able to and translating some of the backward thrust into upward thrust is a big gain in lift until the airfoil reaches a speed at which it manages that lift itself optimally?

If planes and jet engines were, or needed to be, powerful enough to provide most of the upward thrust themselves, then we'd launch planes by pointing them straight up—especially the military would do this. But because the airfoil provides most of the lift, once aloft the engine doesn't have to do nearly as much work, which is especially nice because a forward motion is most of what you want, anyway. Weight and thus efficiency are key, thus engines are only as powerful as they need to be.

One of the things they need to be able to do is get the plane in the air, which takes considerably more energy than it does to keep the plane in the air. Thus, they have enough power to do as you describe: rotate slightly upward and generate some extra lift that way.

But that's just not that large a force compared to the lift generated on the wing. Again, if it were, planes wouldn't need the forward motion they need to take-off.

A backwards-moving conveyor belt just won't push against a plane enough to keep it from moving forward. The prop(s) or turbines are pushing air directly backward, which gives you a direct Newtonian counterforce forward. In contrast, the conveyor belt only has the mechanism of the wheels and their axles with which to convey any force against the plane's forward motion. And because the whole point of the design of the wheel is to minimize this force as much as possible, the relative force we're talking about here is very, very small. The belt would need to be moving extremely fast—impossibly fast, probably—in order to manage to counteract the force of the engines.

And so the plane will move forward anyway, assuming the speed of the belt is limited. If it isn't, then you're really just talking about locking the plane in place, and we can readily see that it won't take off if it's locked into place if it wouldn't do so from a standstill under normal conditions, anyway.

If the plane moves forward, then either the length of the belt is sufficient for the plane to take off like it would from a normal runway, or it's not. If it is, it takes off, and the whole scenario is pretty much exactly like the plane taking off regularly, excepting that the engines will have to work slightly harder (though probably so slightly that it won't be noticeable to anyone). If the length is insufficient, then the plane rolls off the end. I don't know what happens then, that's beyond the scope of the problem.
posted by Ethereal Bligh at 1:47 AM on September 30, 2007


Paulsc, you can't have rotation without forward motion through the air. Rotation is achieved not by rotating the props or engines, but via the flight surfaces. For the flight surfaces to cause the plane to rotate around the axis of wingtip-to-wingtip, they need to have an airspeed. Your example of a Cessna that manages to be kept still by the belt (which it wouldn't) is misconceived because rotation wouldn't even happen at all.
posted by Ethereal Bligh at 1:52 AM on September 30, 2007


"This keeps going on and on until the plane takes off, with an indicated ground speed of 144 MPH and air speed of 62 MPH."

Wrong. The Cessna can't take off at 62 MPH indicated air speed, unless it rotates. If it rotates at 62 MPH indicated ground speed, it loses nose wheel steering before it gains aerodynamic lift, or full rudder control. It's in the weeds, at V1 indicated ground speed, every time. But even worse, since the wings never generated any lift, because they never gained relative motion against the air, the plane never even tries to lift, even if it responds sluggishly to pilot input, on prop wash against the elevators.

Let's suppose our intrepid pilot keeps the nose down, by applying nose down full elevator, until simple Bernoulli lift could cause the plane to rise, around 80 mph, indicated air speed. That'll be an infinite amount of time, on the conveyor, and the ground speed will be way past 144 MPH, since as long as the plane is on the conveyor, the wing end airspeed is zero, relative to ambient air. The plane never develops Bernoulli lift, and can't fly.
posted by paulsc at 1:54 AM on September 30, 2007


“But also, please note, that if you give me the JATO equipped, 1950's vintage F-100 fighter, in every case, I'll fly it, however inelegantly, off your conveyor.”

If this were true, we wouldn't need aircraft carriers or VTOLs.

“Wrong. The Cessna can't take off at 62 MPH indicated air speed, unless it rotates. If it rotates at 62 MPH indicated ground speed, it loses nose wheel steering before it gains aerodynamic lift, or full rudder control.”

He didn't say it would take off at 62MPH indicated ground speed. He said it would be able to take off at 124MPH indicated ground speed, which would actually be 62MPH ground speed as measured by GPS, and which would also be 62MPH air speed on a calm day. The plane would rotate and take off. Just like it always does. The movement of the belt doesn't matter.

And, again, if somehow the movement of the belt were made to actually do what you think it will do, then we're just talking about the equivalent of a tethered airplane. It'll achieve an airspeed of zero, won't be able to rotate, and pretty much nothing will happen except a lot of noise and turbulent air.
posted by Ethereal Bligh at 2:00 AM on September 30, 2007


Given the number of posts here that end with "and that's the end of it" (or some variation), may I humbly suggest that many of us may not have read the Pedantry post earlier today, nor taken it to heart?
posted by rokusan at 2:02 AM on September 30, 2007


I think you're not even listening to us, paulsc. Get it into your head that either

a) the belt cannot keep the plane from moving forward (which is what will happen both in the real world and as the problem is stated), or

b) if it could keep the plane from moving forward, we're just talking about whether a stationary plane can take off without moving forward.

It's not complicated.
posted by Ethereal Bligh at 2:02 AM on September 30, 2007 [2 favorites]


paulsc: ""Wrong, malor. Real Cessnas respond a lot more to aerodynamic drag, than the friction in their wheel bearing. That's why, in the flight equation, we talk about drag as opposed to friction. There are several kinds of drag, actually, only one of which, a minor one, is wheel bearing friction."

Paulsc, you just proved my point and you're not seeing it. You just said: the friction is irrelevant. That means that the conveyor belt is irrelevant.
posted by Malor at 2:06 AM on September 30, 2007


For the JATO equipped F-100, Lift + thrust will always be greater than Drag + weight.

For the Cessna on a conveyor, lift + thrust will also be greater than drag + weight, because friction is irrelevant. You said so yourself.
posted by Malor at 2:09 AM on September 30, 2007


"paulsc: first of all, the experiment specifies a conveyor as long and wide as any runway you'd expect to be taking off from in a Cessna. But that doesn't really matter. ...

Wrong. It matters, a lot.

If the conveyor is longer than 1200 feet, and moving at less than 5 MPH, peak, during the whole experiment, the Cessna will make it every time. Raise the peak speed, or shorten the conveyor's length, and the Cessna's chances drop accordingly. At 1000 feet, and a conveyor speed of 15 mph, the Cessna winds up in the weeds, every time.

The F-100 fighter, of course, flies away, clumsily, every time.
posted by paulsc at 2:09 AM on September 30, 2007


Note: If we accept the premise that the conveyor moves backwards at exactly the rate that the Cessna moves forward, you take off at 124mph indicated ground speed. You're not actually going that fast, but your wheel sensors think you are. You, as the pilot, have to adjust your reading of that particular instrument, but the takeoff will be almost identical to a normal one.
posted by Malor at 2:11 AM on September 30, 2007


At 1000 feet, and a conveyor speed of 15 mph, the Cessna winds up in the weeds, every time.

NO IT WILL NOT. The conveyor is irrelevant because friction is irrelevant. The wheel friction doesn't matter. It's not a signficant force.

If the wheels could take it, you could take off in a little more than 1000 feet if the conveyor was moving at 100mph against you. Your wheels would spin like mad, and you'd lose some forward momentum from that frictional loss, but you would still take off.
posted by Malor at 2:14 AM on September 30, 2007


What I like about paulsc's misunderstanding is that he's not being able to keep all the parts of the problem in his head at the same time. He can say that that the friction in the wheel bearings doesn't really matter, yet at the same time retain the assumption that the backward-moving belt will keep the plane motionless.

So now he's thinking about a plane that thinks, via it's groundspeed indicator connected to the wheels, that it's accelerating to 62MPH while, in fact, it's not moving through the air at 62MPH, thus has an airspeed of zero because, you know, it's not moving.

Then he starts talking about how a plane rotates to generate lift and take off.

Not understanding that the plane rotates because it uses the flight surfaces to create a twisting force on the wings (relative to their lengths) via the air moving across them, he thinks a Cessna, rolling its wheels at 62MPH but not actually moving either through the air or relative to the terrain around it, will start to rotate upward, generating some amount of upward thrust. Which it wouldn't because the plane isn't moving through the air.

But assuming it would, he says it will start then to go upward, but because that isn't enough to get the plane off the ground really, it will stall and fall back down.

In contrast, and continuing to wrongly assume that it will rotate when it's standing still (assuming we're not talking about engines that actually rotate), he thinks that a more powerful aircraft, like the F-100, will rotate while it is standing still and then will continue upward, taking off.

This isn't actually true, either, because that upward thrust of the supposedly rotated jet (which wouldn't actually rotate) is still only a portion of the total amount of lift required to get that jet into the air. How do I know this? Because if this weren't true, then the F-100 and other jets would take off into the air from a standstill. How do I know they don't do this? Because the amount a jet rotates is not insignificant. If you do the math, you'll see that a mere, say, ten degrees of rotation would push that plane upward pretty damn fast if it were actually pushing the plane in exactly that direction. Jets could take off and be over 40 feet within only a small multiple of that horizontally. Which would be great for aircraft carriers. There's a reason jets aren't propped up, already rotated at 10 degrees upwards and just fly into the air, never touching a runway. It's because the airfoils are still doing most of the work.

So what we've got in paulsc's argument is an interesting series of misunderstandings chained together. The belt wouldn't prevent forward motion, but he assumes it would. Assuming the plane was standing still, he assumes it would rotate. But it wouldn't. If it rotated, he assumes that the thrust of the engines moves the plane in the direction of the rotation, accounting for the majority of the upward lift. Which it doesn't, or every plane and jet which rotates pretty much wouldn't need any runway to take off.

What does this teach us? Well, my sense is that we're not making headway with paulsc for two separate reasons which are working in a vicious synergy. First, he is using his competence as a pilot and his familiarity with planes as a measurement of his relative competence in discussing this problem. This allows him to disregard the fact that everyone disagrees with him. The error here is that flying a plane isn't necessarily the same thing as understanding the physics involved. And you need to understand the physics involved if you are to evaluate a physics problem that is superficially about planes, but is really about basic physics.

Second, something both in his discursive style and our interaction with him is making it so that he's jumping around between different aspects of the problem, in each case involving what's going on in the previous point, and not seeing that his whole understanding of the problem isn't actually internally consistent.

My guess is that the proper way to resolve this is to somehow create a fresh and unsullied discursive context. That might be with someone else, or at a different time, or similar. Second, each part of the problem has to be dealt with separately while resisting the temptation to move along to a different part. A step-by-step working through of it needs to be done methodically, with cooperation between paulsc and someone else each step of the way. That's very hard to do in a medium like this one.
posted by Ethereal Bligh at 2:27 AM on September 30, 2007 [4 favorites]


"... That means that the conveyor belt is irrelevant."
posted by Malor at 5:06 AM on September 30 [+] [!]

Agreed, in the case that the conveyor can't keep up with the plane's developed ground speed, and the plane rolls off the forward end of the conveyor, and thereafter, performs a more or less normal takeoff. Or that the conveyor overspeeds, and tosses the plane into the weeds, behind it. In both those cases, the conveyor's speed is completely irrelevant, although the result to the Cessna is entirely different.

But as long as the plane is a Cessna, and stays on the specified conveyor, it's not flying anywhere, unless the conveyor is so long, and the relative speed differences between the Cessna and the conveyor are essentially those of the Cessna and a concrete runway in some operational envelope, in which case, the conveyor isn't keeping up with plane, violating the specified condition of the problem, but allowing the Cessna to fly away. Maybe.

Shudders. Doesn't want to think what that would feel like.
posted by paulsc at 2:34 AM on September 30, 2007


*reads entire thread, begins screaming and waving hands overhead*

*still screaming, walks to kitchen, obtains pickle-fork*

*stops screaming, calmly plucks out eyeballs with pickle-fork*

*resumes screaming*
posted by loquacious at 2:36 AM on September 30, 2007 [5 favorites]


Paul, you're not thinking this through. Assume the conveyor belt is a mile long, just for the purposes of the argument.

As you apply power in your Cessna, the plane starts moving forward. The conveyor starts moving backward at precisely the same speed. The Cessna does not sit still...it continues moving forward at the same speed, the conveyor moves backward at that speed, and the wheels spin twice as fast. That's why you HAVE wheels; they decouple you from the ground!

The conveyor can't stop the plane because it has no way to exert force on the plane body. The Cessna isn't pushing against the conveyor, it's pushing against the AIR. The conveyor is pushing on the WHEELS, which just spin faster. They don't transmit the power to the plane body. That's the whole purpose of wheels.

The Cessna will need a tiny bit more runway than usual, because of the double friction loss, but that's all the conveyor will do. Well, that, and the and the pilot can't trust his groundspeed readout; he has to wait for double indicated groundspeed to pull back on the stick.

Just like indicated airspeed changes at altitude, because the air itself changes, indicated groundspeed changes on moving ground. You could put it in the weeds if you're not aware that your groundspeed indicator is screwy, but if you know to make the adjustment, your takeoff proceeds normally.
posted by Malor at 2:49 AM on September 30, 2007 [2 favorites]


Do they have conveyor belts in wind tunnels?
posted by seanyboy at 2:53 AM on September 30, 2007


And note.... in a very real way, you can argue that planes don't have groundspeed. All they really have, for purposes of flying, is airspeed. That's why you need less runway into a headwind, because you get some airspeed 'for free'.

Groundspeed, for a plane, is just a measure of 'how fast my wheels are spinning.' For purposes of actually flying, it's entirely irrelevant... what matters is how fast the air is moving over the wings. And because the plane is pushing on the air, not on the ground, all a conveyor will do is make the wheels spin faster.

If you turned it around, and made the conveyor HELP the plane, instead of FIGHT it.... it would also make almost no difference. The wheels would be stationary while the plane accelerated to 62mph entirely normally.
posted by Malor at 2:57 AM on September 30, 2007


paulsc, planes rotate at Vr to set the angle of attack of the wing, trading drag for lift, not to vector their thrust upwards; if the latter were true, then with constant thrust the plane would take off immediately on rotation which is not in general the case, rather, the plane continues to accelerate with its nose up until the wings are generating more lift than the plane's weight and it takes off.

And, you're confused (or at any rate confusing other people) about V1, which is the takeoff decision speed (the speed below which you could scrub the takeoff without running off the end of the runway, and at which you could climb at a high enough angle with one engine out to clear any obstructions) not the speed at which you rotate or take off - and which doesn't apply to single-engine aircraft. Unless you're trying to sound like an expert, just say "takeoff speed".

More generally, you still haven't said what force the conveyor is exerting on the body of the plane (not its wheels) that counteracts the thrust of its engine. Or what you mean by "keep up with"; everywhere the question has been posed, the conveyor moves backward at the same speed as the plane - not "fast enough to stop the plane". Or why you think the conveyor is just as long as the plane - obviously, its at least as long as a runway, or the answer is trivial.
posted by nicwolff at 2:57 AM on September 30, 2007


"You just said: the friction is irrelevant. ..."
posted by Malor at 5:06 AM on September 30

Actually, I didn't say that. What I said was:

"Real Cessnas respond a lot more to aerodynamic drag, than the friction in their wheel bearing. That's why, in the flight equation, we talk about drag as opposed to friction. There are several kinds of drag, actually, only one of which, a minor one, is wheel bearing friction."

V1 is a very important point in takeoff, for any pilot, in any airplane. At V1, in normal aircraft, lift had better damn well exceed weight, and thrust had better damn well exceed drag, or you're dead, or bent, at best. But the laws of flight are plastic enough, that if you have a Saturn V, you can, for a very short time, fly, even if lift is zero, and drag is very large. You just substitute thousands of pounds of thrust for lift, and vector it, to overcome the complete lack of induced drag that normal control surfaces create.

In normal planes, like Cessnas, at V1, what I'm saying is that, for some moment, every force must necessarily be in rough balance, with a real world trend toward a positive result, if a takeoff is to occur. And in the real world, if you put a Cessna on a conveyor moving 124 mph in the wrong direction, even if the velocity of that conveyor were smoothly ramped otherwise, at the moment of rotation, it doesn't take much to catastrophically unbalance the flight equation. In the instant the rotation of the plane is trying to create take off lift, there is enough loss of steering friction, and enough resultant slew, to put the hypothetical plane needing such an unfortunate take-off roll in the weeds.

The usual way of accomplishing re-balance of the flight equation for unusual take-off conditions is to consult the manufacturer's data sheets for those conditions. All I can tell you, is that for 62 MPH tail winds (equivalent to your double speed conveyor example of 124 MPH), Cessna says to tie the plane down, stay in your hotel, and contact your insurance company. They expect the plane to be ripped apart on its tie downs.

NOBODY, not even Charles Frickin' Lindbergh, takes off in a 62 MPH tail wind.
posted by paulsc at 2:59 AM on September 30, 2007


Oh, and Ethereal Bligh said: There's a reason jets aren't propped up, already rotated at 10 degrees upwards and just fly into the air, never touching a runway. It's because the airfoils are still doing most of the work.

You're a little bit wrong about this. The FA/18 actually developed more thrust, with full afterburners, than its total weight; it was literally capable of taking off like a rocket. But they still put it on a short runway, because it still needs airflow for control. It lit up, went to full thrust, and they'd catapult it... and as soon as it had enough forward speed to use its control surfaces, it could climb straight up.

They didn't launch it vertically because A) that's inconvenient for storage and getting into and out of, and B) if something goes wrong at launch, there's no chance of recovery, you've got a dead pilot. By flinging it forward, if the engine flamed out, you still had a small chance of survival.
posted by Malor at 3:06 AM on September 30, 2007


"Then he starts talking about how a plane rotates to generate lift and take off.

Not understanding that the plane rotates because it uses the flight surfaces to create a twisting force on the wings (relative to their lengths) via the air moving across them, he thinks a Cessna, rolling its wheels at 62MPH but not actually moving either through the air or relative to the terrain around it, will start to rotate upward, generating some amount of upward thrust. Which it wouldn't because the plane isn't moving through the air."


Anybody who has ever sat in a 172 can tell you that you can lock the brakes, and bounce the plane on prop wash. Just because you can bounce the front wheel on run up, doesn't mean you can take off with no roll, EB.
posted by paulsc at 3:06 AM on September 30, 2007


Yeah, he might be confusing me about rotation. I assumed from his adamant comments that the direct thrust matters. Obviously, given that I already know that it's the airfoil which mostly matters, I should have been entirely aware that changing the attack angle of it matters far more than any amount of direct thrust from the engines. Dammit.

“Groundspeed, for a plane, is just a measure of 'how fast my wheels are spinning.' For purposes of actually flying, it's entirely irrelevant...”

Well, it does matter with regard from getting from one place to another on the ground. :)

“If you turned it around, and made the conveyor HELP the plane, instead of FIGHT it.... it would also make almost no difference.”

I really like this.

I've maintained that Monty Hall Problem page for eleven years now and argued about it often with people just for the purpose of accumulating things like that comment of yours there.

I'm really fascinated with prowling around the perimeters of a problem and how it can be viewed—because, of course, we all see things differently. Partly I enjoy this because I have the intuitive sense that this is how the closest approximation to truth is achieved; and partly I enjoy this because it helps me understand both other people and how people, including me, think in general.
posted by Ethereal Bligh at 3:07 AM on September 30, 2007 [1 favorite]


The usual way of accomplishing re-balance of the flight equation for unusual take-off conditions is to consult the manufacturer's data sheets for those conditions. All I can tell you, is that for 62 MPH tail winds (equivalent to your double speed conveyor example of 124 MPH), Cessna says to tie the plane down, stay in your hotel, and contact your insurance company. They expect the plane to be ripped apart on its tie downs.

That's not the same thing at all. Ground speed and air speed are different. Ground speed, to an airplane, is IRRELEVANT. It's just a measure of how fast the wheels are spinning. All that matters is airspeed.

A 62mph tailwind is death. A 62mph conveyor, whether helping or hindering you, is irrelevant.
posted by Malor at 3:08 AM on September 30, 2007


The conveyor is moving at 64 MPH backwards, not 124 MPH - that's the apparent ground speed. The only part of the plane that is taking more stress than normal is the wheel assembly; the rest of the plane is in a 64 MPH apparent headwind just like a normal takeoff. If your argument has now been whittled down to insisting that a good Cessna pilot couldn't possibly rotate and stay on the runway at 124 MPH, then it's time to cede the field.
posted by nicwolff at 3:10 AM on September 30, 2007 [1 favorite]


“You're a little bit wrong about this. The FA/18 actually developed more thrust, with full afterburners, than its total weight”

Thanks for the correction. I knew that some jet had that much thrust but I had forgotten it.

Are you sure there aren't other reasons for not launching it this way? Because the benefits otherwise would be huge in some applications. We go to great lengths already to fly jets on and off carriers. Shooting them straight up? Especially at sea? Wouldn't that be a real boon?

My guess is that when it's all said and done, it's not worth the fuel and you have to have a horizontal surface to land, anyway.
posted by Ethereal Bligh at 3:12 AM on September 30, 2007


"paulsc, planes rotate at Vr to set the angle of attack of the wing, trading drag for lift, not to vector their thrust upwards;..."
posted by nicwolff at 5:57 AM on September 30

Technically, you're right, nicwolff. But for our hypothetical Cessna, V1 is so near Vr, most weekend warriors treat it as the same thing.

As for the rest of your comment, I'm not sure to whom you are directing your remarks. If to me, previously addressed.
posted by paulsc at 3:13 AM on September 30, 2007


"... A 62mph conveyor, whether helping or hindering you, is irrelevant."
posted by Malor at 6:08 AM on September 30

Not at the moment of rotation. Except, perhaps, in thought experiments.
posted by paulsc at 3:17 AM on September 30, 2007


Oh, and in regard to this:

In the instant the rotation of the plane is trying to create take off lift, there is enough loss of steering friction, and enough resultant slew, to put the hypothetical plane needing such an unfortunate take-off roll in the weeds.

You're still misunderstanding. On the mile-long conveyor, somewhere around the normal takeoff range, your indicated groundspeed will be 124 miles per hour. Your actual airspeed will be 62mph like normal. As you pull back and lift the front nose wheel, the only difference between this and a normal takeoff is that your rear wheels are spinning twice as fast. Everything else is exactly the same as normal.

Why? Because your prop is pushing on the air. Your plane is swimming through the air, and is barely connected to the ground at all.

And, reversing it, so the conveyor is helping you -- the indicated groundspeed is 0, your real airspeed is 62mph, and you pull back exactly the same way as normal. Your rear wheels are sitting there motionless, and you can still take off and fly normally.

On preview:

Shooting them straight up? Especially at sea? Wouldn't that be a real boon?

Not really. It didn't take long at all for them to develop enough speed to go vertical, certainly no more than 2 or 3 carrier lengths. In the Amiga's FA/18 Hornet game, you could actually go vertical by the end of the carrier, though such an early computer game probably shouldn't be taken as proof of anything. :)

With the relative sizes of the ocean, carrier, and plane, I don't see that true vertical takeoff is all that valuable. Vertical now or five seconds from now wouldn't seem very important.

If the game was any indicator, though, vertical landings would be really nice. Landings were hard.
posted by Malor at 3:21 AM on September 30, 2007


Oh, I should say... you might get some turbulence from the air at takeoff off a moving conveyor, but that hasn't been what we've been arguing; you've been insisting that the plane wouldn't move and would have no airspeed.

No fair changing the argument midstream. :)
posted by Malor at 3:22 AM on September 30, 2007


"... If your argument has now been whittled down to insisting that a good Cessna pilot couldn't possibly rotate and stay on the runway at 124 MPH, then it's time to cede the field."
posted by nicwolff at 6:10 AM on September 30

Huh?

I don't know any Cessna 172 pilot who would even try this. I think 124 MPH is up around Vmax, in flight for many 172s. On the ground? No freakin' way.
posted by paulsc at 3:26 AM on September 30, 2007


This question was previously flown into the ground in AskMe.
posted by Kirth Gerson at 3:28 AM on September 30, 2007


I have this vision of the plane spinning its wheels kinda like a cartoon character running on the spot and then suddenly sprinting off down the runway.
posted by L.P. Hatecraft at 4:01 AM on September 30, 2007


paulsc, the plane isn't traveling at 124 MPH. Vno - the "normal operation" speed sometimes called Vmax - is the speed for which the airframe is rated in turbulent conditions, it's got nothing to do with how fast the wheels can turn! In this case, the apparent wind is a nice easy 62 MPH, and we have normal rudder control for steering; the wheels are being turned at twice that, and uncorrected deviations from the center line will move us off the runway at twice the usual speed, so we'll have to be extra careful and real light on the rudder, but other than that everything's completely normal.
posted by nicwolff at 4:03 AM on September 30, 2007 [1 favorite]


"You're still misunderstanding. ...
posted by Malor at 6:22 AM on September 30

No, I'm not. And I'm not being obtuse, just to make my point.

A lot of things change, at rotation, particularly in a single engine prop plane. And you need to be aware of them, and be putting in compensatory control inputs, or things can go wrong quickly.

For one thing, rotation does change the angle of thrust applied to the plane. The engine force that was accelerating you down the runway, is suddenly diminished, just at the time the induced drag created by your wings being suddenly upturned is greatly increased. The result is that you should get a momentary increase in lift, powered mostly by momentum developed during your takeoff roll, sufficient to get you off the ground, but while this is occurring, there is an obvious penalty to be paid, in flight forces, which the pilot needs to smoothly countermand.

The plane wants to bank right, in part because of differential torque forces created on the prop, due to the takeoff rotation movement nosing the right side of the prop "up" (greater "bite" into the air, as seen by the prop, and reflected in reverse torques to the airframe), and left side of the prop "down" (lesser "bite" into the air, which adds to the reflected torque to the airframe), which must be countermanded by a control input of right aileron. And that precessing of torque, also creates a moment about the vertical axis, which would turn the plane left, if not countermanded by right rudder, which should be applied smoothly, in concert with the commanded aileron correction. Do it right, and it looks like you did nothing. Do it wrong, and your climb rate suffers, as you slew air speed and altitude into additional corrections.

In point of fact, nobody does it perfectly, all of the time. Aircraft performance points are chosen so that a pilot can generally screw up quite a bit on takeoff, and still get airborne, and climb away to safety, if his engine is still working normally, and his airplane is intact.

But to say that the case of a plane taking off normally from a runway is equivalent to that of a plane taking off from a conveyor moving either with or against the plane at a significant fraction of that plane's normal takeoff speed, minimizes the balance needed for conversion to flight, in practical terms. Maybe this is acceptable in the simplicity of a thought experiment, but it will not be acceptable in real life. If it were, every general aviation airport would be launching Cessnas and LearJets from big slingshots.

I've said that for low values of velocity, on conveyors of length greater than the normal takeoff roll of a normal plane, a takeoff might be possible. But I would equally expect that for X number of such trials, even within the performance specs of the plane, Y number of accidents would occur, simply because the conversion of a relatively low powered plane (like a Cessna) from a rolling ground object, to a flying machine, is not all that instantaneous, or perfectly predictable, except perhaps in thought experiments.

And at critical moments in flight profiles, it doesn't take much to break bad.
posted by paulsc at 4:05 AM on September 30, 2007


I couldn't make it through the whole thread, but I don't think anyone has accounted for the fact that the conveyor belt could have two positive effects on the ability of the plane to take off:

- the movement of the conveyor would create turbulence in the air above its surface, which being beneath the wing of the plane, subtly helps to generate lift
- the drag of the conveyor on the air molecules above it encourages the air to move in the direction of the conveyor belt, requiring the plane to generate less thrust
posted by SNACKeR at 4:06 AM on September 30, 2007


Isn't the rotation of the earth is, in effect, a giant conveyer?
posted by moonbiter at 4:13 AM on September 30, 2007


I didn't even notice until reading that thread that the question specifies a backward conveyor speed equal to the wheel speed. Which, as someone mentioned and I didn't understand at the time, is paradoxical and, if attempted, would ramp up to infinity quickly.

It's interesting that several of us tried to make sense of this by assuming the conveyor speed was calibrated against the actual groundspeed (not from the wheels, from GPS). That gives us a relatively tidy version of the question with the answer that it makes almost no difference, though probably a tiny bit of added thrust (and thus runway) is needed as a result of the friction of the wheels on their axles.

People say this question isn't fair.

But it does teach us something. A big problem for anyone studying elementary physics is that the abstractions required to solve problems are, in the real world, relatively arbitrary and often quite unrealistic. This means that when you are doing real world physics, you actually have to think about what problem you're actually trying to solve. Not the problem you want to solve, not the problem that is the most obvious abstraction, but the problem that actually describes the behavior you're interested in.

I mean, I don't do any real-world physics, but I'm sure this is true. You've got to actually understand a real system from numerous perspectives before you can formulate an abstraction which will be useful to investigate and use.

When this question is asked, because it contains misdirection, it forces people to argue about what the question really is. And that's a good thing.

For example, as someone says more concisely in the AskMe thread than I say here, interpreting the question to mean that the belt keeps the plane still is another way of framing the question to ask whether keeping the plane from taking off will keep it from taking off.

Well, not exactly, depending upon someone's attempt to make sense of the question. Someone might wonder what happens if a plane is kept from moving forward but its engines can go really fast? Does that make the plane go up at all? And that's a good question, too, because it teaches people that lift is generated by the forward motion of the plane through the air, not by the propeller or jet engine itself.

If someone takes the question literally with the wheel speed versus conveyor speed phrasing, then they are forced to confront the paradox of two things interdependently pushing the other faster. Whoops, that doesn't make sense because, as stated, if the belt could keep up with the wheels, responding instantly (thus “equaling” the speed as stated) then instant infinite motion. If there's a lag, that's not the question, but you'd ramp up to infinity pretty quickly, depending upon lag. So, again, whoops, that taught me something but it's not really a sensible question.

So if not that, then what? Well, maybe the question meant that the plane would move forward, but the belt would move backward the same speed. Um, but why? The plane is still moving forward. Does the belt moving backward matter? Why does the question mention this? Okay, if it does matter, then it must be pushing back on the plane somehow. How could it? Well, maybe there's friction in the wheels. This would slow it down.

How much would it slow it down? Enough to stop the plane? Well, that doesn't make sense because or else the plane wouldn't have been able to start moving forward in the first place. So maybe it slows it down a little?

Does that matter? Well, yeah, because the plane needs forward motion through the air to get airborne. If the belt somehow slows the plane down, the engines will need to work harder to get it going fast enough to get airborne.

Hey, maybe the question intended that the belt just somehow goes fast enough to keep the plane from moving forward at all! Okay, I've already figured out that this would be hard to do because wheels turn pretty easily, but it's possible. So what then? Well, now this person has come around to what the first person started with: does a plane that's not moving forward through the air have any upward lift? And they learn about how airfoils work and they answer "no".

But hold on. Someone says that the plane takes off with no problem. How can this be? Wait, “I” forgot that there was another possibility: that the belt moving backward doesn't really matter. Like I realized, if the plane is moving forward through the air, that's all that matters. Wheels spin pretty easily, that's the point of wheels, so maybe the question was intentionally giving me a red herring in the form of the conveyor belt, intending to say that it goes backward in some fixes ratio to something or other, and yet I eventually am supposed to realize that the wheel speed doesn't matter. What makes a plane fly into the air is its motion through the air (or the motion of the air past it). So, in that sense, the answer is that it takes off pretty normally!

I don't think this is a useless exercise and that this phrasing is a mistake or a prank. I think that it's designed to make people think carefully about the question which, in turn, forces them to think pretty carefully about all the various things involved in trying to answer a version of the question that makes sense. In the process, you learn some things you wouldn't have learned with a “better” phrased question.
posted by Ethereal Bligh at 4:20 AM on September 30, 2007 [1 favorite]


"paulsc, the plane isn't traveling at 124 MPH. ..."
posted by nicwolff at 7:03 AM on September 30

You've either just described the case of taking off in a 62 MPH tailwind, assuming you could survive the first part of the takeoff roll, or you've got the mythical conveyor moving 62 MPH in a direction opposite the plane. If you can fly the first case, my hat is off to you; I can't. No one I know can.

If you can fly the second, please advise your tire and wheel supplier, and how you got clearance on the Space Shuttle's very flat, very smooth runway, as at 124 MPH, any 172 I've ever commanded on a real runway would lose its nose wheel, entirely, prior to making it to rotation, if it's engine could even supply the energy necessary to achieve that ground speed.

At some point, nicwolff, we aren't really talking about airplanes, are we?
posted by paulsc at 4:31 AM on September 30, 2007


“But to say that the case of a plane taking off normally from a runway is equivalent to that of a plane taking off from a conveyor moving either with or against the plane at a significant fraction of that plane's normal takeoff speed, minimizes the balance needed for conversion to flight, in practical terms.”

At this point you just seem to be saying that at rotation, the rear wheels are still on the ground and thus the movement of the belt will alter any lateral forces applied to the plane if the wheels are aimed away, for any reason, from the belt's parallel, which would be weird for the pilot. Well, yeah. I'd bet, though, that if it was predictable, pilots would get used to it. After all, that's exactly what is happening when you compare the moment of rotation for a slow moving Cessna with its rear wheels on the ground and a fast moving jet with its rear wheels on the ground. The jet pilot has to contend with strong lateral forces if the plane's wheels become out-of-parallel with the runway in the least. They still manage to fly.

On Preview: you seem to be finally understanding the question. Almost. Yeah, the truth is that the belt moving backward would never manage to actually push the plane backward. It just wouldn't—the whole point of wheels is that they spin easily. So, yeah, the plane would be moving forward at 62MPH, the belt backward at 62MPH, and the wheels turning at 124. The plane would take off as normal, assuming the tires don't fly apart. Someone said at the very beginning of the thread that this was a practical consideration.

The alternative you list is that the plane has a 62MPH tailwind. But that could only happen if the conveyor belt could actually manage to push the plane backward to 62MPH. It wouldn't. And, anyway, nothing in the statement of the problem postulated backward motion of the plane in the first place. The problem, as stated, doesn't even manage to provide for no motion, much less backward motion. But if the plane wasn't moving at all, it wouldn't have lift. If it was moving backward at 62MPH, for whatever damn reason, it'd have fallen apart long before.
posted by Ethereal Bligh at 4:41 AM on September 30, 2007


Because the conveyor belt determines how fast the freely turning airplane wheels spin but does not determine the speed of the air or the propellers churning through them, the conveyor belt doesn't matter.

The wheels would turn faster and faster in response to the matching speed of the conveyor belt, but the plane, pulled through the relatively motionless air by its propellers, would move forward in relation to the rest of the world. It would do so at its normal rate, regardless of how fast its wheels were spinning..

The plane would rise and fly away to a land that doesn't have silly giant conveyor belts instead of normal runways. The pilot will warn others and no one would land at Conveyor Belt Airport ever again. Airport staff would have to find an alternative means of income, perhaps by moving the conveyor into a hangar and hosting aerobics classes that combine normal aerobics with constantly having to chase the beautiful instructor or fall into a trough of burning jet fuel. Or something like that.
posted by pracowity at 4:43 AM on September 30, 2007 [2 favorites]


"... A 62mph conveyor, whether helping or hindering you, is irrelevant."
posted by Malor at 6:08 AM on September 30

A 62 MPH conveyor helping you might not be all that great, either.

You really couldn't afford to put much power on the plane, with that kind of external forward thrust, or you'd quickly exceed normal takeoff parameters. Essentially, the conveyor would throw you ahead, like the catapults on an aircraft carrier, and, perhaps, like the jets thrown off carriers, you'd be able to start flying on your own power, just after the momentum imparted to you died off in aerodynamic friction, without stalling.

It's a first rate trick, really. Best tried when you have a couple of 30,000 pound thrust engines behind you, rather than the 160/180 horsepower of an O-360 Lycoming, coupled through a fixed pitch, two blade prop.

Hence my personal preference, above, for military fighters, and JATO bottles.
posted by paulsc at 4:48 AM on September 30, 2007


"... After all, that's exactly what is happening when you compare the moment of rotation for a slow moving Cessna with its rear wheels on the ground and a fast moving jet with its rear wheels on the ground. ..."

Huh?

There's a big difference, intentionally, in the directional control characteristics during takeoff of jetliners (or business jets) and single engine puddle jumpers. The bigger the jetliner, the bigger, intentionally, the difference.

And moreover, jetliners are not single engine planes, and have considerably different control characteristics than single engine planes do, for that reason alone, among others.

But hey, whatever assumptions you need to make to feel you've got this down. Go ahead. Don't mind me, EB.
posted by paulsc at 5:04 AM on September 30, 2007


Dammit, paulsc, you are just not getting this. Read pracowity's comment for another short take.

The plane is being pulled forward THROUGH THE AIR by the PROPELLER. The conveyor belt DOES NOT MATTER. Helping or hindering, it DOES NOTHING. Well, no, that's not completely true.

If the conveyor is 'helping' the plane, matching the speed of the plane exactly, then you have a problem: your wheels aren't spinning anymore, so you can't make wheel corrections. So you'd have to be lined up well enough to get enough airspeed to use rudder corrections instead of wheel steering.

But the conveyor belt does not push the plane.

Let me repeat that a few times so maybe you'll get it.

The belt does not push the plane.

The belt does not push the plane.

The belt does not push the plane.

Do you get it yet? The conveyor belt does not push the plane. It spins the wheels.
posted by Malor at 5:25 AM on September 30, 2007 [4 favorites]


Hmm, and you'd probably have a hell of a time making corrections at all, now that I think about it, because your wheels wouldn't be spinning at all..... even with rudder controls, without any wheelspin, the plane is going to act really, really wonky, and be very hard to turn at all.

If the conveyor helped at, say, half speed instead, then you could still steer and would still see that it wasn't helping you take off any faster.
posted by Malor at 5:30 AM on September 30, 2007


Will someone build the damn conveyor already?!
posted by horsemuth at 5:53 AM on September 30, 2007


Stop saying "conveyor"!!!
posted by horsemuth at 5:54 AM on September 30, 2007


Insert aw jeeze not this shit again guy here.

(Malor is exactly correct, btw.)
posted by eriko at 6:00 AM on September 30, 2007


“But hey, whatever assumptions you need to make to feel you've got this down. Go ahead. Don't mind me, EB.”

I do have this down. My point was just what nicwolf had said earlier (which I didn't notice 'till I reread the entire thread just now). The only difference the wheels turning faster on the belt underneath them will make is that any slew of the plane while the wheels are still on the ground will cause left or right motion on the belt corresponding to the wheel rotational speed, not the actual groundspeed/airspeed. And my point in comparing a craft that takes off slow and one that takes off fast is that pilots deal with those difference all the time. It would be weird when the Cessna moved to the right because of slew twice as fast as you expect (given your airspeed), but it's not that big a deal. Which is exactly what nicwolf said.

What would be weirder is what Malor just wrote: in the opposite formulation with zero wheelspeed, slew wouldn't make the plane move left or right at all because the wheels wouldn't be acting against anything. I don't fly planes so I don't know how weird this would really be. You seem to be describing something at take-off where you're controlling some lateral motions of the plane with the friction of your real wheels. If so, then this opposite formulation with the conveyor belt moving forward and the wheels unturning would be problematic.

The bottom line, though, is this: you can't make the plane not move forward through the air with the conveyor belt and wheels. So the plane moves forward and the belt affects nothing with regard to lift and all that. It does however change how the plane moves on the runway with regard to its direction and the wheels' (sideways) friction if they are not parallel to the runway. To the degree to which this matters for real pilots in the real world, this somewhat complicates things. It's not going to prevent most pilots from figuring out how to take-off, providing they understand what's going on. Like nicwolf says, you just need be easy on the rudder because a change in orientation will move you across the runway faster than you expect. The only other thing which might matter is how fast the tires are rated for. If they need to be spinning at 124MPH and they aren't rated for that, this is a problem.

But those few complications are really trivial relative to what the problem is aiming for. Either the belt, as long as a normal runway, doesn't keep the plane from moving forward relative to the ground and air and the plane takes off mostly normally; or the belt manages to keep the plane at a standstill, and the plane doesn't take off because planes don't fly up into the sky from standstill. In theory, either is possible depending upon how the belt behaves and how much, if any, there's friction on the wheels' axles.

The remaining complication is that the problem as stated couples the wheel speed and belt speed in what is either a paradoxical or extremely impractical fashion, depending upon how you look at it.
posted by Ethereal Bligh at 6:04 AM on September 30, 2007


I think a more interesting question would be the opposite.

Can a plane placed on a conveyor belt be accelerated by a forward motion of the conveyor belt to fly without engine thrust?

Assume:
The plane is on wheels
The wheels are free-spinning (no drive train)
The conveyor belt is infinitely long
Standard air pressure at sea level
"Fly" just means get off the ground--since there's no engine thrust, it's unlikely the plane would stay aloft for long...

I have a feeling a lot would depend on the type of plane because the biggest determinate would be the forward movement of air canceling out or even overcoming the friction of the wheels on the conveyor belt. Even if you accelerated the conveyor belt slowly, at some point in time the air pushing against the plane is going to roll the plane back, negating the forward lift. So, a glider might get airborne, but a heavy, small-winged plane like a jet won't ever get off the ground.

I admit to not completely thinking this one through.
posted by Civil_Disobedient at 6:25 AM on September 30, 2007


I'm so glad i talked myself out of going into grad school for physics education.
posted by roguewraith at 6:43 AM on September 30, 2007


"... Do you get it yet? The conveyor belt does not push the plane. It spins the wheels."
posted by Malor at 8:25 AM on September 30

I get it. I'm not sure you do. There are lots of possible cases for conveyor, and this is part of the frustration in talking about this problem.

When you pull on to a controlled runway, you usually put on the brakes at the hold point, and wait for ATC clearance. Usually, when you get that, you add power, and release the brakes. Your takeoff roll starts immediately thereafter.

But what of the mythical conveyor? Have we pulled on to it, and then locked our brakes? If so, and it's running at a constant 62 MPH in the takeoff direction, we're definitely going that way at 62 MPH pretty shortly, until we release the brakes. Then, we may slow up, or speed up, ground speedwise, depending on our engine power settings and aerodynamic drag. Unless we're damned careful to be adding power at the right moment, we may take off, but we won't fly far.

Or, maybe the conveyor doesn't move when we pull on to it, and just keeps pace with our airplane's normal acceleration at half our airspeed rate once we start our takeoff roll, giving us a 1/2 rate of acceleration down the runway, in terms of ground speed. That would be nice, as it would cut our frictional losses a bit, and might shorten our take off roll, ever so slightly. We'd still need our engine to get us to an airspeed of 62 MPH, and if the conveyor or plane had any real world mass, at rotation, we might get a little push this way or that, but basically, it's not much help and a hindrance mainly during the first couple hundred feet of our takeoff roll, when frictional directional tire slip is minimized, making steering slushy, until rudder command air speed is achieved.

But, suppose the conveyor is entirely unpowered, but pretty low in friction both ways, and we pull on to it, lock our brakes, and run up the engine as soon as ATC says go. We'll accelerate to some airspeed, with our brakes on and our wheels not turning, thanks to the low friction of the conveyor. As soon as we release brakes, we may indicate even negative ground speed for a moment, if the conveyor belt has enough inertia, as our wheels might roll slightly "backward," as the conveyor continues forward. But we could still be gaining air speed, even as that occurred. Takeoffs might not be materially affected, but woe to the airmen trying to make a landing on such a contraption, depending on braking forces, which would be reduced to nil. And woe to the airmen aborting a takeoff, before rotation, for the same reason.

Next suppose the conveyor runs at a speed of less than our plane, in a direction against the plane's progress. This is kind of what I was talking about when I threw out figures of 1200 feet of roll, for a 15 MPH conveyor speed. Obviously, there is going to have to be a greater achieved ground speed for the necessary air speed to fly. At some point, the engine has to supply some part of that additional power, even if the bearing friction is low, and tire losses are small, and that accounts for the longer needed roll. Is that clear?

Next, suppose the conveyor runs at exactly the acceleration needed to match our plane, in the direction our plane needs to go to take off, so that, the wheels never move, yet the plane achieves normal airspeed in the normal takeoff run. There's no particular upside other than lower tire wear, and obviously, the downside is that if your wheels don't ever turn, you can't steer, until you can do so entirely aerodynamically, as you point out. Very weird for the pilot, much like being flung off a carrier deck. You'd have to hope you were flying on your own power when your conveyor momentum was finally expended.

Next, suppose the conveyor works against the plane, at airspeed. I contend that the plane is hindered by this to the extent that wheel and tire friction is a hinderance, and is touchy at rotation, in proportion to the speed of the conveyor as a proportion of airspeed. That's simply a matter of how tires work, and the flight physics I've previously explained. At the point where the conveyor's relative motion is causing the plane's wheels to operate at double airspeed, practical limits appear, and I think the plane is uncontrollable before it reaches flight airspeed. But it's really responsive to nose wheel steering at 10 MPH indicated air speed, if that happens to be important to anyone. However, just as in the case above where the plane needed 1200 feet to create the velocity needed, after supplying the minor losses of wheels and tires, it needs that, or more, now. Probably proportionately more. But it's twitchy enough before you ever get to sufficient airspeed to fly, that I think it's going to be thrown in the weeds regularly by the speeding conveyor. Professionals have a slightly different view of the outcome, but it is still dim, as covered in Salon's Ask The Pilot column of Jan. 5, 2007:
"According to Paul J. Camp, a professor in the department of physics at Spelman College, it's all pretty simple. "At first, the conveyor will hold the plane still. But only to a certain point, after which, driven by thrust from its engines, the craft will accelerate."

But the problem clearly states: The conveyer belt is designed to exactly match the speed of the wheels, moving in the opposite direction.

"The key is in the behavior of friction," Camp says. "Friction is a peculiar force in that it has an upper limit. For instance, push an object on your desk, but not hard enough to move it. Why doesn't it move? Because the friction force exactly balances the force of your push. At some point you push hard enough to set the object in motion. This is the point where friction has topped out and is not capable of growing any larger."

With the airplane and treadmill, there is, at the outset, friction force capable of rotating the tires at the proper speed to keep the plane stationary. However, as the thrust is increased, that force eventually maxes out. (Two separate frictions are at play here, actually, one between the tires and belt, the other between the plane's axles/bearings and its wheels. The first will max out before the second.)

"And at that point the wheels no longer roll, they slide," says Camp. "Or rather, they roll and slide at the same time. Tire motion is now decoupled from the belt motion. No matter how much you whiz up the treadmill, you won't add any more rotational velocity to the wheels because friction is already doing everything it is capable of. The plane skids toward takeoff -- likely accompanied by much smoke and a powerful rubbery stink."

And there you have it, at least on paper. Bear in mind that for a plane to reach that point of decoupling would require two things above and beyond the pale of normal engineering. First, a remarkable amount of power -- far more than any jetliner, and probably any military plane, is capable of developing. The illustration on Pogue's blog is of an Airbus A320; some sort of rocket plane would be more appropriate. Second, no existing aircraft tires could take such abuse. The rotational velocity required before reaching the friction limit would have them bursting within seconds, causing the plane to be flung backward. Believe it or not, landing gear isn't engineered with giant treadmills in mind, and pilots need to adhere to maximum groundspeed limits, lest their tires wind up like this. These limits occasionally present problems during tailwind operations or in the case of flap and slat malfunctions -- scenarios dictating the need for unusually high takeoff or landing speeds.

For good measure, the treadmill itself, as described, could never be built. It can't "exactly match the speed of the wheels," because the wheels will turn at the speed of the treadmill plus the speed of the plane relative to the ground. When the speed of the plane is greater than zero (which it is the moment its wheels start to spin; otherwise they would never move), then the problem becomes impossible. By definition, the wheels have to be turning faster than the treadmill. "
Have I covered all the cases? If not, what have I missed?

If I have, what case improves the aircraft's performance at rotation, making a takeoff easier, or more likely? If any case robs the plane of power, or control, wouldn't you say that successful takeoffs are less likely? Some of these clearly do.

Thus, I contend that over all, the introduction of conveyors makes takeoff a less likely proposition, at normal distances and power, for normal planes. But if we're going to keep discussing this, it would help a lot to pick a conveyor type and case...
posted by paulsc at 6:51 AM on September 30, 2007


Metafilter: over analyzing a plate of beans simple high school physics problem. (bhnyc said it best all the way up thread)
posted by caddis at 6:54 AM on September 30, 2007


Ok, I'm assuming it works like this. You pull up to the end of your runway, which is a conveyor belt a couple miles long. You release your brakes and apply power, just like on a normal runway. There's a laser rangefinder that measures how fast your plane is moving, and it moves the conveyor belt against you at exactly your present forward air velocity.

The net effect on your plane? Almost nothing. You have double wheel friction, and your control inputs are doubly sensitive, so you have to be a little careful. And your ground speed indicator reads double, so you can't take off as soon as you think you can. But other than that, your plane will take off normally.

And there you have it, at least on paper. Bear in mind that for a plane to reach that point of decoupling would require two things above and beyond the pale of normal engineering. First, a remarkable amount of power -- far more than any jetliner, and probably any military plane, is capable of developing.

That's just silly. As I've said above, even if you ran the conveyor at a very high speed, all it's doing is spinning your wheels, and the only real effect on the plane is the wheel friction. As I said in my very first post here, yes, you COULD stop the plane this way, but you would need to run the conveyor at incredible speed... hundreds of miles an hour. This would destroy the wheels long before it provided enough frictional force to prevent the plane from taking off.

Overall, you're changing your argument around: you have stated above that you'd never reach enough airspeed to fly, and now you're trying to say, "well, it wouldn't take off because it would be uncontrollable".

I can't argue about that, because I'm not a pilot. But I can argue with your previous statements about not developing airspeed. You will develop airspeed normally and you will take off normally, assuming you can control the plane properly with double-speed tires.
posted by Malor at 7:09 AM on September 30, 2007


YUO ARE ALL EDACUTED STIPUD
posted by Henry C. Mabuse at 7:11 AM on September 30, 2007


(well, you'll develop airspeed a tiny bit slower, but probably barely enough to notice.)
posted by Malor at 7:12 AM on September 30, 2007


But what of the mythical conveyor? Have we pulled on to it, and then locked our brakes? If so, and it's running at a constant 62 MPH ...

Your mythical conveyor is not the one in the question. Here:
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 the opposite direction).

If you have the brakes locked, neither the plane nor the conveyor is moving. When you release the brakes and start moving, the conveyor moves at the same speed in the other direction. Please note that both motions and speeds are relative to the surface of the Earth.

Also please note that there's nothing in the question to justify your very short conveyor, or your Cessna 172, or any other specific plane. It's a theoretical question (duh), and putting in all sorts of limiting parameters that are not in the original question is going to generate answers to different questions, which is what you're doing.
posted by Kirth Gerson at 7:22 AM on September 30, 2007


No such unit can exist. If I put power into the model, in a short time the conveyor belt is running faster than the speed of light. In order to set up the very conditions of the problem, you have to break the rules of physics.

This is well covered in the very first link of the OP.

As mentioned there, the airplane/conveyor belt problem has been posed in different, confusing ways, but the only one that actually makes sense is the one where the speed of the backwards-moving conveyor belt exactly matches the forward movement of the plane.

Meaning that if the plane is moving 1 MPH forward relative to the ground, the conveyor belt moves 1 MPH backwards relative to the ground. The plane's wheels are now spinning at 2 MPH.

Plane 2 MPH forward, conveyor belt 2 MPH backward; wheels spinning at 4 MPH.

Plane 3 MPH forward, conveyor belt 3 MPH backward; wheels spinning at 6 MPH.

Plane 4 MPH forward, conveyor belt 4 MPH backward; wheels spinning at 8 MPH.

etc. . . . until, for example, we have the plane going 62 MPH forward while the conveyor belt moves 62 MPH backward; wheels spinning at 124 MPH.

At that point, if the plane is the Cessna (as discussed above), it can take off.

As others, including Cecil, have mentioned, much of the confusion about this problem lies in how it is written down.

If written down as "the conveyor belt exactly matches the speed of the WHEELS, but going backwards", presumably meaning the speed as shown by a speedometer type apparatus that measures the rotational speed of the wheels, there is only one speed where this is theoretically or physically possible--ZERO MPH.

If written down as "the conveyor belt exactly matches the speed of the PLANE, but going backwards" then it is a reasonable and mildly interesting little thought problem--and has the solution I've outlined above.
posted by flug at 7:29 AM on September 30, 2007


The problem is just really, really stupid. Here are the conditions required for the plane to take off:

i) Frictionless, indestructible wheels
ii) Infinite thrust

and here are the requirements for the plane -not- to take off:

i) Infinitely fast, indestructible conveyor belt
ii) Mysterious ghost drag that happens out of nowhere

If you actually set this up, either the plane's wheels or engines would fail, and the plane would be dragged backward, or the conveyor belt would fail, thus allowing the engines to overcome the frictional force of the wheels spinning at a million times a second, and take off. There is no way it would come to anything resembling an ideal conclusion.
posted by tehloki at 7:30 AM on September 30, 2007


OH MY GOD

Everyone took physics in high school, right? Problems like this which are worded confusingly should always be worked as a free-body problem. But you don't need to. The free-body approach just helps to cut through your assumptions or sloppy hand-waving.

Speed = change in distance over time. If the plane has positive speed EVER, such that the conveyor belt spins then the plane is moving, which will move air over the wings, which will generate lift and the plane will get airbourne.

F=ma, right? The acceleration is relative to the air, not the belt. The wheels transmit no force - they aren't like car wheels that are mechanically linked to the motor and generate force. The plane engines pull the plane through the medium of the air. The wheels are to reduce friction between the body and the ground. You could just as easily cover the underside of the plane with butter, but wheels are less silly, so that's what we use.

The conveyor belt matches the plane's speed (i.e. velocity). Let's say at time t=t1 the planes velocity v1 = 200km/hr. The conveyor moves 200km/hr the other way. Fine. The wheels are spinning at 400km/hr. Wheeeee. No one cares.

BUT THE PLANE IS STILL MOVING AT 200km/hr. If the plane stopped moving, the conveyor belt would stop moving because it matches the plane's speed. See the paradox that arises if the plane can't take off? If the conveyor belt matching the speed meant that the belt would cancel the plane's speed, then the plane would have no speed, and the belt wouldn't turn. Huh, what? Exactly.

The fact that the conveyor belt turns means that the plane must be moving forward through the air.

Which means that at a certain speed there will be enough lift to get the plane airborne.

If a problem seems paradoxical, work it out on paper with a good old free body diagram. Start with the engines.
posted by Pastabagel at 7:30 AM on September 30, 2007


Have I covered all the cases? If not, what have I missed?

Please include in your calculations: posted by sfenders at 7:37 AM on September 30, 2007 [2 favorites]


This question is easy, bordering on trivial.

A better question: if a bird in a cage is hovering, and you put the cage on a scale, how much does it weigh?
posted by neuron at 8:08 AM on September 30, 2007


IT'S ALL ABOUT THE WHEELS.

If you change the problem so that it's no longer a conventional plane then it's all very simple. Getting rid of the wheels and covering the belly in butter (or better yet, postulating a maglev system) makes it clear that you can simply factor the belt out of the equation entirely and watch the plane take off unheeded.

But I think that you have to follow some conventions when you solve problems like this. You're allowed to assume that conditions are "ideal". Bearings are zero friction and things don't fall apart when they go too fast. But you have to obey the basic mechanical structure of the system.

In this case, I make the assumptions:
- The airplane is on wheels
- The wheel bearings have zero friction
- The wheel surfaces have infinite friction on the conveyor belt surface

That's the way "ideal" wheels work in real life, and I think we are obligated to include that behaviour in our thought experiment.

When these hold true, the airplane cannot take off.

When the plane applies thrust, the conveyor system will sense the forward motion and start accelerating backwards. This will apply a backwards force on the airplane due to the angular acceleration of the wheels. The conveyor system will apply as much force as required in this manner until the plane halts, thus achieving its objective. If the system doesn't do this, then it's not doing its job as described in the problem.

The longer the airplane applies thrust (even constant thrust, it doesn't need to accelerate), the faster the wheels will go. All that energy produced by the jet engines will be turned into kinetic energy in the angular motion of the wheel.

The wheels would have relativistic speeds after a while, and I'm not qualified to comment and what would happen then.

(I think I might have just broken some kind of lurking record. I think I've been here since year 1.)
posted by CaseyB at 8:11 AM on September 30, 2007 [1 favorite]


The model is incomplete. No one has mentioned how fast the conveyor belt is moving. And what if the plane is using maglev bearing in the wheels...?

...if only we could harness all the brain power spent on this thread for something truly useful.
posted by rmmcclay at 8:15 AM on September 30, 2007


I think I have to add just one more assumption:
- The wheels have mass.
posted by CaseyB at 8:17 AM on September 30, 2007


Casey, that's true only if the conveyor goes much, much faster than the plane, and only if you assume infinitely strong materials that we couldn't possibly make. The problem as originally stated is generally that the belt moves at the airspeed of the plane, which means that it spins the wheels at double speed. Assuming they're rated for double the takeoff speed, and the pilot can maintain control with wheels that are spinning twice as fast, the plane will fly.

In real life, with real materials, we couldn't possibly build a conveyor fast enough to stop a plane from friction or angular momentum alone. The only way to prevent the plane from taking off is to spin the wheels fast enough to destroy them before it gets up to speed. THAT we could do.

The question, as originally posed, is 'will this stop the plane?' The answer is 'no'. Your version assumes things that we could never possibly make, so your 'yes' answer may be true theoretically, but will never be actually true in any world inhabited by humans.
posted by Malor at 8:44 AM on September 30, 2007


I saw this exact same problem on an episode of I Love Lucy, only it was chocolates on the conveyor belt, and they definitely didn't generate enough lift. So I think you'd probably end up having to eat the plane to keep it from falling off the belt.
posted by FelliniBlank at 8:51 AM on September 30, 2007


But, if we attach rollerskates to some of the people posting in this relatively simple thread, and position them in front of the wing, facing backward, the airflow across the foil generated by their bloviations will most definitely produce enough lift for the plane to fly.

Some of you should consider a career as legislators. You missed your true calling. :)
posted by BeerFilter at 9:27 AM on September 30, 2007


OK, so what happens if the hold of the plane is full of like ten tons of hummingbirds, and then they all start hovering in mid-air inside the plane? Huh?
posted by Phanx at 9:34 AM on September 30, 2007 [1 favorite]


“One of my favorites is if you shot and drop identical bullets at the same time, which hits the ground first?”

What, shot one bullet parallel to the ground? They'd hit the ground at the same time. That's just high school physics. More interesting is what happens if you shoot something that is higher than you that begins to fall just as you shoot at it. What do you aim for?

posted by Ethereal Bligh at 1:31 AM on September 30 [1 favorite +] [!]

So, when did the Earth become flat? There is no parallel to the ground, only tangent to the location of where the bullet was shot. The shot bullet will have to fall slightly further than the dropped bullet due to the curvature of the Earth and so the dropped bullet will hit the ground first.
posted by Green With You at 9:58 AM on September 30, 2007


Oh for god's sake! *grins* The question is, in terms of reality and physics, clearly inexcusably simply phrased. No doubt the person who phrased it knew that it could and would readily be bastardised by people who needed to overcomplicate its terms and therefore turn it into a new question! I've grinned many times during this thread and been fascinated by all the physics and so on. But to the question, and keeping ONLY to its terms:

"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 the opposite direction). Can the plane take off?"

In terms of the question as posed, what you really end up with is a plane with no wheels, with its engines going at max thrust. You might as well imagine empty air instead of wheels, or marshmallows, or pixies.

There's no way, therefore, for the engines' thrust to translate to forward movement of the nose of the plane relative to a building or marker alongside. The plane isn't moving through the air, and since wind isn't mentioned in the question, there is no wind either.

(To remind you, takeoff requires air moving over and under the entire length of a plane's wings. For any given model of plane, you need the wing length and width properly matched to the plane, and you need air moving under and over every part of the wing.)

But all you have here is a stationary plane with a normal pair of jet engines moving *some* air over *part* of the wings. So no, of course it bloody well doesn't take off! :oD
posted by paperpete at 10:00 AM on September 30, 2007


Not the damn airplane on a conveyor belt problem again!

I've ploughed through this thread hoping to find the point at which paulsc has his eureka moment and is able to understand that the problem is far simpler than he believes it is and that of course the belt has little to no effect on the motion of the plane through the air.

Still it's only been about half as frustrating as when I tried the problem out on a couple of writer friends of mine who'd forgotten what little physics they'd learnt in school.
posted by electricinca at 10:19 AM on September 30, 2007


Wow, pete, all that reading and you missed it too.

There's no way, therefore, for the engines' thrust to translate to forward movement of the nose of the plane relative to a building or marker alongside. The plane isn't moving through the air, and since wind isn't mentioned in the question, there is no wind either.

This is wrong. The propeller pushes on the AIR, and the plane moves forward IN THE AIR no matter what the ground does underneath it. If the ground 'moves' against the plane, the wheels spin twice as fast, but the plane still takes off.
posted by Malor at 10:34 AM on September 30, 2007


Thus, I contend that over all, the introduction of conveyors makes takeoff a less likely proposition, at normal distances and power, for normal planes. But if we're going to keep discussing this, it would help a lot to pick a conveyor type and case...
posted by paulsc at 6:51 AM on September 30 [+] [!]


Here's your problem. Takeoff is not a "less likely proposition" when being discussed in a (classical) physics problem. The plane takes off, or it does not take off. We are not interested in the possible mistakes of the pilot, and assume he is completely perfect. We also assume that the wind is perfect, and the wheels are perfect, and the plane is perfect, and the conveyor belt is perfect. "The plane runs out of gas" is not a correct answer, nor is "the pilot has a stroke and dies and the plane never takes off." What the problem really asks is only clouded by these technical details of reality.

This confusion leads to our other disagreements. For example, 62mph airspeed is exactly equivalent to a 62mph tailwind from the plane's perspective (GIVEN OUR PERFECT WORLD). They mean the same thing, the speed of wind relative to the plane. In reality, a 62mph tailwind is very bad, because wind is not perfect: it's not all moving in one direction at once but lashing in many different directions, making takeoff difficult or impossible.

One can completely cheat this question by noting, as people have in this thread, that the rotation of the earth is a type of conveyor belt. It's a very large conveyor belt with an enormous surface area, which has been rotating so long that it has transferred significant kinetic energy to the air, but it still qualifies as a conveyor belt, as it's conveying us through space right now (at 1000mph at the equator), unless you're at the pole of course.

It's immediately clear that this conveyor belt is not relevant to the plane; or at least that its relevance shrinks into insignificance relative to wind conditions. (Wind and planetary rotation are of course related...)

Perhaps you could explain the differences in taking off going east vs. going west, and the importance of latitude, paulsc?
posted by mek at 10:34 AM on September 30, 2007


“This confusion leads to our other disagreements. For example, 62mph airspeed is exactly equivalent to a 62mph tailwind from the plane's perspective...”

No, it's equivalent to a 62mph headwind.

People who think that the problem, as stated, can result in a motionless plane are misunderstanding what will happen.

The conveyor belt cannot match the speed of the wheels in the reverse direction. Why? Because as soon as the plane's props/jets start pushing the plane forward, the wheels have exactly that much more motion than the belt. Since any motion the belt produces adds exactly that much to the wheels, a control mechanism that tries to equalize the backward motion of the belt to the rotational motion of the wheels will always be chasing the wheels, never to catch up. The system will quickly escalate and, as people say, the backward motion of the belt approaches the speed of light. So the problem, as stated, cannot equalize the plane's indicated groundspeed (from the rotation of the wheels) with the belt's backward motion relative to the earth nearby.

People rightly imagine that a car, instead of a plane, will work in this problem. How come there's a difference? Because the engine working through the car's wheels can be acted directly and equally against by the backward motion of the belt, causing it to be stationary relative to the ground, the speedometer eventually showing 64mph and the belt's indicator showing -65mph. This won't happen with a plane because the plane's engine push back via the air, pushing the plane forward, pretty much completely independently of the wheels. The belt's attempt to counteract the forward motion of the plane won't work—the plane will keep accelerating forward, the wheels and the belt spinning faster and faster in a futile effort to hold the plane still.

That's with perfect wheels which is, as many have pointed out, the correct assumption to make with this kind of physics problem.

So the exact answer to the problem as stated is that the plane will take off normally and the belt will be moving backwards approaching the speed of light with a corresponding angular rotation of the wheels. If there's no lag in the control mechanism, which is the correct assumption in this idealization, this will happen effectively immediately. Everything else we can assume to function perfectly, as well. So the plane takes off normally, the belt moves backward near the speed of light, and the wheels are spinning at the correspondingly high rate.

The only other possible interpretation of the problem is if, rather than how the problem states it, the plane is somehow prevented by the belt mechanism from moving forward. For this to be possible, you'd have to have imperfect wheels which transmit some of the belt's backward motion into force against the plane's forward motion. In this variation, we don't at all know how fast the belt would move and the wheels rotate because that is dependent upon the inefficiency of the wheels. But, however fast the belt moves backwards, the point is that the plane doesn't move forward. In this version, the plane doesn't take off because planes don't suddenly take off into the air no matter how much you gun the engine...in theory. In practice, the backward wash from the prop(s) or engine will generate some small lift and a sufficiently powerful engine could make the plane airborne. But that's not very interesting because there really aren't such sufficiently powerful engines and, anyway, this isn't the only real-world effect we'd have to consider to try to answer this problem with a combination of ideal elements and real-world elements. What's the point?
posted by Ethereal Bligh at 10:58 AM on September 30, 2007


No, it's equivalent to a 62mph headwind.

Oops, that's what I get for cutting and pasting from paulsc. Why was he comparing airspeed and tailwind to begin with?
posted by mek at 11:03 AM on September 30, 2007


“Oops, that's what I get for cutting and pasting from paulsc. Why was he comparing airspeed and tailwind to begin with?”

Because for some reason he also (sometimes) thinks the plane is moving backwards through the air. Or something. When I re-read his comments in this thread earlier (at about 6AM), I was struck by how he occasionally made sense and occasionally did not make sense. In particular, there's one comment (I can't be bothered to find it) where he pretty much gets everything right. But he before that and after that contradicts the assumptions he made about what happens in that comment. Er, that's not articulate of me. In other words, in one comment he says, well, if it did X, Y, and Z, then the plane would act thusly. And he's right that X, Y, and Z would happen and the plan would act as he predicts. Weirdly, though, he otherwise, before and after, argues that one, two, or all of X, Y, and Z wouldn't happen, says something else would happen, and then tries to predict the action of the plane as a result.

We can't get him to start over and look at those initial assumptions and recognize the correct ones, so we're pretty stuck. However, I get the strong sense that somehow or the other he's beginning to understand the correct X, Y, and Zs, but he doesn't really want to because then he'd have to admit (mostly to himself, probably) that he's been wrong. So he flirts with the correct understanding of the problem, then jumps onto another tangent to argue against people, usually misconceiving something while doing so. And sometimes those misconceptions are things he has earlier gotten correct.

It's weird, but I've seen this patter before. Hell, I know I've displayed this pattern before. It's not being dumb, exactly, though not quite understanding something, for whatever reason, is part of it. It's also a product of circumstance, involving things like peculiar and contingent preconceptions that one has difficulty abandoning, being besieged by other people, the compounding complications of being confused by one thing which makes you confused about another, and finally how discursive argument can often solidify a misconception because our rhetoric begins to have a life of its own causing its own attraction to a misconception.

That said, I've thought all along that his bringing up a tailwind was particularly weird.
posted by Ethereal Bligh at 11:26 AM on September 30, 2007


For crying out loud... The wheels do not generate the forward thrust. It's the jet at the back or the propellor at the front.

Of course the friction of the conveyer against the wheels could provide enough backward thrust to counteract the forward thrust of the plane but if you start going down that road I suspect that you're overcomplicating things.

Why? BECAUSE NOBODY IS REALLY GOING TO DO THIS!!! Vn Thrust to power ratios with minimal head winds and a gravitational constant within current physical parameters is not going to change the point of the question.

The point of the question is to trick you into thinking that the initial forward movement comes from the wheels. Once you get that aha moment where you realise the plane drags itself through the air, you've got the point of it. You've won. Congratulations.
posted by seanyboy at 11:30 AM on September 30, 2007


For the sake of completeness, I'd like everyone to know that I had trouble getting to the answer too. I believed the opposite point of view for a while. In fact, iI may change my mind again.

I got stuck in my "The plane can't take off because it can't move forward" train of thought for a while. And because other people were saying it could take off I spent a while shaking my head slowly whilst thinking.. "The plane needs forward speed to produce lift... Don't these stupid people realise this."

I think that's the point of the question. To highlight our arrogance, and to show our inability to see other peoples world views.

Now - can anybody please explain to me why things look smaller when they're further away...
*There's a story here. I actually believe that over 50% of the population are incapable of answering this question. From time to time, I ask random people why it is so. You'd be suprised at who struggles with it*
posted by seanyboy at 11:40 AM on September 30, 2007


At 1000 feet, and a conveyor speed of 15 mph, the Cessna winds up in the weeds, every time.

See, I thought paulsc was just doggedly defending the (highly questionable) interpretation of the question where the conveyor cancels out the thrust of the engines through friction with the (non-ideal wheels), however crazy fast it needs to run to do that.

But this quote makes it pretty clear that no, he just doesn't understand. AAARGH.
posted by flashboy at 11:51 AM on September 30, 2007


Ethereal Bligh writes "There's a reason jets aren't propped up, already rotated at 10 degrees upwards and just fly into the air, never touching a runway. It's because the airfoils are still doing most of the work."

Planes like the Mig-29 generate more thrust than the plane masses. These planes (in theory anyways) could be stood on their tails on specially prepared launch towers and takeoff (abet fairly slowly, the Mig-29's thrust ratio is only 1.05). And in theory you could land the same way. The reason we don't do this is
  1. it would be extremely wasteful of fuel,
  2. the planes would need a second control system that would allow maneuvering at extremely low air speeds,
  3. doesn't leave much margin for error,
  4. special training would be required.
As mentioned planes like the Harrier essential do this now but instead of standing the whole plane on end we just stand the output of the engine on end. This neatly takes care of 2 and much of 3.

On preview, ya mostly what Malor said.
posted by Mitheral at 12:11 PM on September 30, 2007


I've ploughed through this thread hoping to find the point at which paulsc has his eureka moment and is able to understand that the problem is far simpler than he believes it is and that of course the belt has little to no effect on the motion of the plane through the air.

Me too.

Paulsc, please post the exact definition of the problem you're debating. As has been stated a million times, the only reason people should disagree on this problem is that they're trying to solve differently stated questions.

Many people have performed this experiment and posted the results on YouTube.

Owing to the way the camera moves it's not immediately obvious that the runway just behind the one closest to the camera is moving back with equal thrust to the little car.
posted by 6am at 12:17 PM on September 30, 2007 [1 favorite]


seanyboy writes "can anybody please explain to me why things look smaller when they're further away..."

Because as distance increases angular length decreases and we don't perceive actual length but instead angular length.
posted by Mitheral at 12:25 PM on September 30, 2007


“You'd be suprised at who struggles with it”

Doesn't seem trivial to me unless you count facile answers which, I suspect, don't actually mean much to many people but are technically correct.

There's a number of seemingly simple things that are actually difficult to really understand. Irrational numbers. Atmospheric pressure and hydraulics (combined: what happens when you sip through a straw). A bit more subtle though so common as to interfere with comprehension is the apparent “reversal” in mirror images. The Gambler's Fallacy. The Monkey and the Blowgun (which I think I mentioned earlier). The Monty Hall Problem. Newton's Bucket and Mach's Principle.

Some of these are things commonly argued about just as this plane problem is. Others are things that most people who think they understand them really only understand them more superficially than they realize. And perhaps in all these cases, the vast majority of all people fail to understand them at all.

Pretty much everyone but St. John's College and most of we alumni believe that teaching science via its history is wrong-headed. But, for some purposes (emphatically not for the purposes of educating a large portion of eventually practicing scientists), the historical progressive-from-blank-slate pedagogy is very helpful because it makes correct but facile comprehension much less likely. I really feel like a lot of what most of us know (including me, but I'm obviously emphasizing this for the more conventionally educated) are really very narrowly “correct” answers to specific and abstracted problems. That works, and is efficient, when we stay within that restricted problem domain.

And you can't say that doing so is “artificial” and exceptional. It really isn't.

In contemporary education, we learn to solve a progressive set of quite artificial and narrow problems as a means of building a toolkit for solving specific, later, messier ones where the artificiality of the tools (in terms of the abstracted problems they each specifically address) doesn't matter so much. There's a whole lot of elementary physics that actual physicists would struggle mightily with if they were to attempt to do genuine research in that area. A nice example is how Feynman in his later years went back to the problem of the nature of friction. What is friction, really? Mostly, for doing most physics, we don't really need to know. We only need a sufficient approximation of it.

For every purpose, there's an appropriate level of description.

You don't need “true” comprehension of every single detail in order to have “true” comprehension of some specific behavior at some specific level of description. I'm not sure what “true” comprehension could be, but the point is that you can not really understand a bunch of details and still get the answer right. And the point is that this is usually the case for all of us, all the time.

However, in my opinion the one big problem with this is when people don't realize that they mostly don't understand anything. If they (we) don't realize this, then whenever anything moves outside of the usual narrowly-defined problem our handy toolkit is designed to solve, they don't realize this. Perhaps being instantly aware of this is asking too much, but asking that people suspect this might be the case isn't.

In my opinion, problems like this one and others that people argue about are all examples where people are presented with a problem that appears to be of the kind they are familiar with and their toolkits are designed for, when, actually, they're not. Of course this varies by person. Most of us here understand this plane problem easily. That's because our toolkit is pretty big. It's not just high school physics or a bright person's intuitive physics. We've developed a bit more awareness and skills than that. This doesn't mean we won't all be confounded by a problem designed to fool us into thinking we're competent to solve it with the usual tools when we're really not.

However, a reason I believe that the historical pedagogy is useful, and useful in a way that is relevant to this discussion, is that the actual historical progression of science is that all the problems are things which appear to be one thing, but are another, and which everyone initially thinks they can competently solve with the tools and simplifications they've always used. And when you learn science as a progression of corrected misunderstandings, or refined understandings (depending upon how charitable or epistemologically relativistic you want to be), then you're much more sensitive to the limitations of the usual tools and much more likely to be aware that you misunderstand something. “More likely” in comparison to basically having been giving all the correct answers to a whole bunch of coherently simplified problems in sequence of increasing difficulty. That disguises how tenuous this whole “comprehension” thing really is.
posted by Ethereal Bligh at 12:26 PM on September 30, 2007


“Because as distance increases angular length decreases and we don't perceive actual length but instead angular length.”

That's a nice articulation and I stand corrected that making it isn't trivial. There's a whole bunch of ways we could quibble with it, but fixing the quibbles would force language and phrasing that anyone who doesn't immediately know the answer to the problem wouldn't understand, anyway. I'm not sure that your phrasing would immediately enlighten anyone who doesn't understand the answer, but I think it gives them a strong push in the right direction.
posted by Ethereal Bligh at 12:32 PM on September 30, 2007


My brother almost hated me once because of this question. I understood immediately that it was poorly worded, but that if I understand what the question is supposed to be saying, then the plane takes off. (If this were a car, OTOH, which pushes against the ground to go forward, it would be a different story.)

Planes don't need traction to move forward. The plane would move just as if it were on ice. The wheels would spin madly and the bearings possibly melt, but that plane will take off.

No sense trying to explain it to someone who can't see that because, like my brother, they never will.
posted by Camofrog at 1:47 PM on September 30, 2007


The system will quickly escalate and, as people say, the backward motion of the belt approaches the speed of light.

...but as the speed of the belt approached C, it would acquire staggeringly huge relativistic mass, which might be strong enough to hold the airplane down.
posted by ROU_Xenophobe at 2:34 PM on September 30, 2007 [1 favorite]


I contend that any solution that allows the plane to take off is ignoring the rules of the original problem. You can argue implementation details, but it's a simple problem:

Airspeed is equal to the difference between the wheel speed and the belt speed. Any solution involving nonzero airspeed must allow the wheels to turn faster than the counter-velocity of the belt, which is specifically disallowed. QED.

You're not being beaten by physics here, you're being beaten by logic.
posted by CaseyB at 2:36 PM on September 30, 2007


“...but as the speed of the belt approached C, it would acquire staggeringly huge relativistic mass, which might be strong enough to hold the airplane down.”

Heh. Which illustrates why there's problems picking and choosing what to be realistic and what not.

“You're not being beaten by physics here, you're being beaten by logic.”

Not quite, because interpreting the problem literally, exactly as stated, (which is the basis upon which you disallow a non-zero airspeed) creates an impossibility. Which means that logic cannot answer the question as stated. So in this regard I think it's you who is logic's bitch.

You can't have the wheel speed be the same as belt speed because the problem also says that the planes engines work and are turned on. That means the plane is pushed forward. The wheels will always turn faster than the belt if the engine is creating forward thrust. The question presupposes a normally working engine. Two premises of the question are contradictory. You know what that means, don't you?

I contend that the solution that allows the plane to take off is ignoring the most implausible of the two contradictory premises. We can't answer the question with both, so we have to modify one. Which one? Well, I'm pretty sure that a question involving a plane with a non-functional engine on a conveyor built isn't really interesting and not what was intended. That leaves modifying the premise about what the belt and wheels do to something that might happen in the real world. We're still going with an ideal problem, so we assume frictionless bearings on the wheels.

The plane takes off as usual.
posted by Ethereal Bligh at 3:24 PM on September 30, 2007


Well, this thread certainly took off.
posted by Mikey-San at 3:39 PM on September 30, 2007


Forgot to mention that I emailed this question to Richard Muller, who teaches the Physics for Future Presidents class mentioned here months ago.

He says the plane takes off, too.
posted by Camofrog at 3:53 PM on September 30, 2007


Planes? Conveyor belts?

I'm still worried about the blue eyes puzzle. How can any blue-eyed islander ever believe that any other blue-eyed islander is unaware of the existence of blue-eyed fellow islanders? And why could it not be a brown-eyed person who sets the logic chain in motion?

This keeps me awake.
posted by goodnewsfortheinsane at 4:15 PM on September 30, 2007


GNFTI, I haven't looked at the answer. I want to figure this out. I haven't even re-read your comment and I've forgotten what is said. (A good trick while I'm writing this one.)

But I'm having a problem with the instant deduction part. If it's actually instant, then the sequence where you learn something because someone hasn't acted, which causes you to act, which then causes them to act, isn't possible. Is this the intent of the question? I want to collapse it to accommodate instantaneous deduction to the correct conclusion given the information present, but I'm not seeing how to do so.

Okay, maybe it works this way: instants are infinitesimals. In the first instance, no one is able to deduce anything. Instantly, someone is able to deduce something from nonaction and instantly acts, which allows for a subsequent instantaneous deduction. And so forth. This allows a sequence of an indeterminately small duration with all possible deduced information the result. Is this the intention? Oh, hell, don't tell me.
posted by Ethereal Bligh at 4:49 PM on September 30, 2007


First pass, then: I'm thinking that all the blue-eyed people realize they are blue-eyed and leave the island.
posted by Ethereal Bligh at 4:52 PM on September 30, 2007


One more scenario to imagine to help understand this (I hope it hasn't been said already):

Imagine the plane has a cable attached to its nose that connects to a winch off the conveyor belt. Turn the conveyor belt's speed to 8 million mph or so. The plane doesn't move. Its wheels would start smoking, but let's assume frictionless bearings. Now turn on the winch and see the plane creep forward. Turn the winch to takeoff speed and the plane takes off.

The cable and winch (or propellor) pulling the plane from the front are no different than an engine's thrust from behind. All a plane's wheels do is keep it off the ground.
posted by Camofrog at 4:54 PM on September 30, 2007


And this, and then I hope I'm done: Say you are flying. You hit a switch that makes your wheels spin really fast backward. Do you think your plane will instantly stop and drop from the sky?

The answer is of course not, for the exact same reasons that the plane takes off no problem.
posted by Camofrog at 5:00 PM on September 30, 2007


EB, I don't thinking it's been posted here yet, feel free to FPP it.
posted by goodnewsfortheinsane at 5:17 PM on September 30, 2007


Oh, I see that ferry spec. Man, I hate this instantaneous crap. It's the only thing which is confusing me. If the amount of time it takes to make the deduction is merely small and not zero, then the weirdness goes away. That's why I like thinking of “instantly” in this problem as an infinitesimal of time.

So, if you can have sequence with instanaeity, then I think all the blue-eyed people will realize immediately after midnight that they are blue-eyed. They leave that night.

My reasoning is that if there's only one blue-eyed person, he'd know he was blue-eyed when the oracle speaks. This doesn't happen.

With two blue-eyed people, they would each notice that the one blue-eyed person they see does not meet that ferry at midnight, and thus they both realize immediately afterward that they are both blue-eyed. This doesn't happen.

With three blue-eyed people, they'd each see two blue-eyed people and expect those other two to meet the ferry immediately after midnight when those two others each realize the other one isn't the only blue-eyed person. When this doesn't happen, each realizes that he, too, is blue-eyed, in addition to the two he sees. However, this doesn't happen.

The previous three cases don't happen because, of course, there's one-hundred blue-eyed people on the island, not one or two or three.

So, in this case with one hundred blue-eyed people, they each look at the other ninety-nine blue-eyed people and one-hundred brown-eyed people at midnight, figure out why those ninety-nine blue-eyed people don't immediately march off the island (because what would have been true for one, two, or three would be true for ninety-nine) and leave he/she and the rest alone and instantly realize that he/she must be a blue-eyed person, too. The brown-eyed people and the guru stay put as all the blue-eyed people get on the boat.

The guru moves into that big double cabin she wanted and rues that fact that she's not allowed to speak again.

You can get confused if you ask why any given brown-eyed person doesn't conclude he/she is blue-eyed when the blue-eyed people don't move. The answer is that the blue-eyed people do move.

What keeps them from moving and then moving when they do? Magic. Dammit, I don't know. If the answer isn't that no one gets on the boat, then I can't see how it's not that all the blue-eyes get on the boat. If so, then somehow the sequence just collapses. I can't shake the feeling that this weirdness is the whole point and I'm making a mistake.
posted by Ethereal Bligh at 5:55 PM on September 30, 2007


Okay, I Googled and my worries about the instantaneous thing bedeviled me. I wanted to go with “on the hundredth night”, because that was neat, but I resisted it because I wanted the logic sequence to collapse all at once to the final deduction. My narrative pretty much points right at a stepwise deduction culminating in the mass action on the hundredth night and obliviates the “how to know when to finally go” problem.

Ah, well. I'm always about half as smart as I wish I were in any given situation. The real point of the problem is making my head spin. The solution is no big deal relative to what the problem teaches us. I really, really want to grok common knowledge the way I grok, for example, this plane problem. But, nope, I've got to worry at it, nibble around it, digest, start over, think some more, get confused, get unconfused. Which is fun and being omniscient would be boring, but being ignorant and confused is also a bit annoying and frustrating.
posted by Ethereal Bligh at 6:17 PM on September 30, 2007


The conveyor belt would not affect a planes ability to take off, that would take a mammoth wind tunnel . Even getting off the ground the plane would be trapped in the stream of air inside the tunnel.
posted by hortense at 7:44 PM on September 30, 2007


Zach's possible responses to this thread. Please pick the one that's right for you:

*) That's why ah never kiss'em on the mouth!

*) How many of you are under the impression that people actually read down this far?

*) "...and so junior, that's where baby's come from." "Wow."

*) I like peanut butter and jelly sammiches.

*) Are you suggestin' that coconuts migrate??

*) Which came first? The chicken or the egg macguffin?

*) Why, no stewardess. I'm not yet a member of the Mile High Club. Why do you ask?

*) Pete and Repeat were on a bridge Pete fell off who's left?

*) NERRRRRRRRRRRRRRRDSS!

*) Oh. My. Gawd. You guys have taken several cans of beans and duct taped them into an airplane that's not going anywhere. Congratulations. What are you using for propellant? No wait. Don't tell me. Let me guess. Beans?
posted by ZachsMind at 8:22 PM on September 30, 2007


The logic sequence is dependent on the passing nights as proof that each theorem is false. If there was only one blue-eyed person, then they would leave immediately; if there was two, they need the passing of the first night to prove there isn't only one. If there are three, they need the passing of the second night to prove there isn't only two. And so on until the ninety-ninth night passes, and only one (correct) possibility remains.
posted by mek at 8:55 PM on September 30, 2007



As far as I'm concerned, there are only two correct answers that the original proposer of this question could have been expecting:

1. Hah! Planes aren't cars and their wheels don't drive them! It takes off!

2. Hah! You haven't defined the scenario well enough so it could go either way!

Taking the time to construct a longer answer is wasting your time unless we can actually find the author of the original question, or unless you've made up your own specific question you like better.


Also, this thread proves beyond a shadow of a doubt that man was not meant to fly.
posted by mmoncur at 8:56 PM on September 30, 2007


The whole thing depends on how you read the wording of the question. What does "speed" of the conveyor belt mean? And does it match the plane's airspeed, ground speed (by GPS), or wheel speed?

If it's supposed to match wheel speed, in RPM, then friction of the wheels can't be ignored. Otherwise, the treadmill has no way of reaching that given. As the treadmill speeds up, the wheel speeds up ahead of it.

But, if it has to match wheel RPM, and friction is a factor, then the problem's given becomes the case where paulsc believes that the treadmill holds the plane stationary. It has to match RPM by speeding up until friction holds the plane back. Obviously, with real wheel bearings, that would be unrealistically fast.

If treadmill speed only has to match ground speed (or, to disambiguate that from wheel speed, call it geographical speed,) in mph, then the problem is as simple as taking off normally with wheels spinning twice as fast.

The vagueness of what exactly is meant by speed is what causes all the confusion. Furthermore, if it's wheel rpm, then the problem makes you assume some things are ideal, but not others, in kind of a bogus way.
posted by ctmf at 9:41 PM on September 30, 2007


I take part of that back. The treadmill speed won't match the wheel speed in RPM unless they're the same radius.

I guess this is further complicated by WTF does "wheel speed" really mean, if not in RPM? And how can a treadmill linear speed match an RPM?

Anyway, it still turns out that if wheel speed is the reference, friction has to be included to satisfy the conditions. You would still need either a ridiculously fast treadmill or ridiculously terrible wheel bearings, and the plane still wouldn't fly.
posted by ctmf at 10:05 PM on September 30, 2007


ctmf: except at speed 0, it's not possible for the treadmill speed to match the wheel speed, because the treadmill speed contributes TO the wheel speed. The wheel will always be faster than the treadmill, because its speed is a combination of treadmill speed and plane speed. No matter how much the treadmill speeds up, the wheel will always be faster.
posted by Malor at 10:10 PM on September 30, 2007


It's probably not meant to be answered at all. It's probably meant to be a very frustrating group exercise to impress upon students what kind of confusion happens when you allow yourself to use non-technical, imprecise terminology. If so, it's a good one, but only if the point is explained at the end.
posted by ctmf at 10:14 PM on September 30, 2007


Malor: That's what I said. It only works if you allow frictional forces, so that speeding up the treadmill slows the plane (however little) until the plane is again at speed zero.
posted by ctmf at 10:16 PM on September 30, 2007


So, you'd need both ideal and non ideal wheel bearings at the same time. Wheel bearings that had friction, but also can go infinitely fast without eating themselves.
posted by ctmf at 10:22 PM on September 30, 2007


I refer you back to my first comment in the thread.

Obviously, we've gotten to the point of silly repetition at this point, so I will stop posting any further. :)
posted by Malor at 10:47 PM on September 30, 2007


this question is yet more proof homo sapiens are actually two separate species, homo sapiens (clue) and homo sapiens (no-clue) with an intertwining reproductive strategy.

anyway, clearly the most important factor in whether the plane can take off or not is whether jesus says it can.
posted by lastobelus at 1:56 AM on October 1, 2007


SOMEONE on Metafilter must be a R/C model airplane hobbyist -- get a running treadmill, saw off the arms, and put the damned model plane on it and tinker.

Put it on YouTube. I'm getting tired of reading.
posted by Extopalopaketle at 2:22 AM on October 1, 2007


http://www.metafilter.com/65155/Physics-101-stumper#1856453 !!!
posted by 6am at 2:43 AM on October 1, 2007


http://www.metafilter.com/65155/Physics-101-stumper#1855985 !!!
posted by Kirth Gerson at 3:37 AM on October 1, 2007


The level of ineptitude in this thread is stunning, especially when the answer can be found in the first two links of the post.
posted by caddis at 4:44 AM on October 1, 2007


http://www.faiththedog.net/video.asp !!!
posted by 6am at 5:08 AM on October 1, 2007


I propose a new problem: If you drop or shoot identical Cessna's which will hit the ground first?
posted by spock at 5:37 AM on October 1, 2007


If there was only one blue-eyed person, then they would leave immediately; if there was two, they need the passing of the first night to prove there isn't only one. If there are three, they need the passing of the second night to prove there isn't only two. And so on until the ninety-ninth night passes, and only one (correct) possibility remains.

Common knowledge or not, formal logic or not; I don't see how this chain could not fall apart after n iterations, where n is probably 3, in my mind.

If you disagree with my objection, please explain your answer to the following question - I'm serious - as if I were a six-year old:

How can a given BLue-Eyed Islander (BLEI) *ever* consider the possibility of another BLEI considering the possibility of only *one* BLEI existing when it is clear that every BLEI is acutely aware of the existence of at least 99 BLEIs?
posted by goodnewsfortheinsane at 5:44 AM on October 1, 2007


I didn't take the time to read the whole blog but putting it simple:

Yes the plane will take off due to the fact that:

The wheels don't "drive" the plane, the engines do. The wheels will spin at the speed of the jet engines. Once the engines get the plane going faster than 100 mph? (not too sure on that speed) the airplane will take off. It will no longer be on the treadmill but up in the air.
posted by Mastercheddaar at 5:53 AM on October 1, 2007


What if the treadmill speed is 0.999... of the airplane speed?
posted by the number 17 at 7:33 AM on October 1, 2007 [1 favorite]


“The level of ineptitude in this thread is stunning, especially when the answer can be found in the first two links of the post.”

Right, because competency in answering a physics question is looking up the answer.

Which is actually pretty true in most cases. As I said earlier, for the most part people don't really need to understand every little damn thing. However, problems like this one and others are built around exposing the flaw in that—they reveal false understanding.

In the case of the Monty Hall Problem, I know many people who think they understand the problem and answer because they read or someone simply told them the answer. You can read/hear a sequence of plausible logical steps and it will seem like you understand what's going on. But, often, if you do, it's tenuous at best.

I think this is also very clearly true with the blue-eyed problem. Really, the core of the reasoning involved in merely solving the problem isn't that hard. Within fifteen seconds of reading the problem I reduced it to three people, then added another, etc. And that basically gave me the answer. But almost everything surrounding that answer I either don't quite understand or is mysterious to me. I vaguely understand what is wrong with gnfti's objection, but not even remotely well enough to answer it. And the core idea of first order knowledge and common knowledge is deeply mysterious to me. Basically, this isn't comprehension at all. It's just knowing the right answer, perhaps the sequence of steps to arrive at it, and a slightly developed intuition for some of the key ideas involved.

Sometimes I wonder if there's not a subset of people for whom knowing rote answers isn't actually the limits of their comprehension. I can't help but feel that's inferior; however, I've worked all my life to learn to appreciate (in others) the simple pragmatic utility of not really having to deeply understand every goddam thing, as well as continuing to refine my realization that none of us really understands anything. To make an arbitrary quantification, so I'm six times more facile at working through and around the Monty Hall Problem than some other person. So what? That's not necessarily even approaching the complete truth of the problem. I mean, really, I don't know what that would be other than some inborn complete and unfailing grasp of every facet of probability mathematics. Who has that? Nobody.

To some degree I think I understand your criticism, especially if it's really a frustration. God knows, I've felt this way about a million times with regard to correspondents on the MHP. I'll say, look, quit telling me you know it's 50-50 when you can look up the damn problem in math textbooks and elsewhere in the citations I've given you. Do you really think all these authoritative sources are wrong? And an amazingly large portion of people will say either “yes”, or, even more weirdly, “not really, but I don't care enough to look them up, and they still could be wrong, and I'm sure that I'm right”. The latter is incoherent, but it really represents a particular class of viewpoints/reactions. It's pretty close to knowing self-delusion which, seemingly an oxymoron, might be a common aspect of human nature.
posted by Ethereal Bligh at 7:47 AM on October 1, 2007


GNFTI, the way I've been worrying at the problem is thinking in terms of distributed uncertainty. The logical sequence (which isn't merely deductive, it requires communication of information via observation of others' actions) is necessary for the isolation and elimination of that uncertainty.

That's the intuition I'm using (which might be false) to try to resolve the issue raised in your objection. For me, its formulation is wondering why all the blue-eyed people don't just jump to step 99 at the announcement, which would mean all 100 would all get on the boat on the second night.

I have a gut sense that if you and I really and truly understood what was happening in this problem, we'd understand why our objections are non sequitors. I mean, really, the objection is just another way of asking, “don't they already know this?” But the exact same thing can be asked of the guru's announcement.
posted by Ethereal Bligh at 7:59 AM on October 1, 2007


So, what would happen if a new baby was born during those 100 days? (Born with perfect reasoning abilities, of course.)
posted by sfenders at 8:33 AM on October 1, 2007


Right, so a hypothetical single bluey (who cannot directly observe his own eye colour, remember) sets the logic chain in motion, leading to the shared conclusion and action. Hypothetical, because all bluey come to this realization simultaneously, making all blueys the chain's "initiator" in their own right.

This I understand. But given the fact that one's own eye colour cannot be directly observed, what exactly prevents a browney from initiating the logic chain?
posted by goodnewsfortheinsane at 8:36 AM on October 1, 2007


A browneye needs 101 days to falsely deduce he is blue eyed. By day 100 the blue eyed people have already left.

( According to the answer that is, it still smells fishy to me )
posted by the number 17 at 8:49 AM on October 1, 2007


This Wikipedia page says that what sets things in motion is that the existence of one blue eyed person becomes common knowledge, i.e. everybody realises that everybody knows there is one blue eyed person.

I fail to see how this is not true before the guru speaks:

Every person can see two blue eyed people. Therefore, everybody knows that everyone can see a blue eyed person.

Can we talk about Leonard Cohen? I understand Leonard Cohen.
posted by the number 17 at 8:59 AM on October 1, 2007


Ethereal Bligh writes "In the case of the Monty Hall Problem, I know many people who think they understand the problem and answer because they read or someone simply told them the answer. "

Your explanation of the Monty Hall problem is very good. I admit the 50/50 answer I've heard never made much sense but I figured it was because I wasn't understanding the dynamics of the game show (having never seen it) and I never gave it much thought past that.
posted by Mitheral at 9:08 AM on October 1, 2007


From here:

N individuals enjoy a picnic supper together which includes barbecued spareribs. At the end of the meal, k ≥ 1 of these diners have barbecue sauce on their faces. No one wants to continue the evening with a messy face. No one wants to wipe her face if it's not messy, for this would make her appear neurotic. And no one wants to take the risk of being thought rude by telling anyone else that he has barbecue sauce on his face. Since no one can see her own face, none of the messy diners makes a move to clean her face. Then the cook who served the spareribs returns with a carton of ice cream. Amused by what he sees, the cook rings the dinner bell and makes the following announcement: "At least one of you has barbecue sauce on her face. I will ring the dinner bell over and over, until anyone who is messy has wiped her face. Then I will serve dessert." For the first k − 1 rings, no one does anything. Then, at the kth ring, each of the messy individuals suddenly reaches for a napkin, and soon afterwards, the diners are all enjoying their ice cream.

For some reason, this variant melts my (irrational or no) objections. I feel I've come closer to understanding, and I'm now going to try to reconcile that fact with the still annoying blue eyes problem. :)
posted by goodnewsfortheinsane at 9:35 AM on October 1, 2007


*opens thread, begins screaming again*

Thanks a lot, guys. I'll just have you all know that my therapist is putting me on electroshock therapy so I can forget all of this.

*runs away, waving arms overhead, screaming and gibbering, tearing out fistfuls of hair*

The plane fucking takes off, ok? For the purposes of this argument, you can replace "wheels" with "skiis" and "conveyor" with "ice and/or snow". Does that make it easier, for you?

THE GODDAMN HYPOTHETICAL, THEORETICAL PLANE TAKES THE FUCKING FUCK OFF, OK? YOU DON'T EVEN NEED MATH TO FIGURE THAT SHIT OUT. FUCK YOUR CESSNA. FUCK YOUR V1 ROTATION-MOMENT. WE'RE TALKING ABOUT A HYPOTHETICAL MOTHERFUCKING PLANE WITH A HYPOTHETICAL THRUST-TO-WEIGHT RATIO OF SUFFICIENT QUALITY TO FLY "NORMALLY". GET THE FUCK OUT OF THE FUCKING BOX OR I'LL TAPE IT SHUT WITH YOU INSIDE OF IT AND MAIL IT TO FUCKING BURMA. AIRMAIL. ON A PLANE, ON A CONVEYOR-BELT FUCKING RUNWAY.

Fuck this shit. I got your V1 right here.

*grabs JATO bottle, climbs on and lights the fucker*

posted by loquacious at 2:11 PM on October 1, 2007 [2 favorites]


.99999... = 1
posted by king walnut at 5:55 PM on October 1, 2007


One of the things that occurred to me after my last comment in this thread, is that there might be a real world equivalent of the conveyor problem, in the world of seaplanes on rivers. But I'm not seaplane endorsed, so I stepped away from the thread for a bit to look into what's involved with taking off and landing a seaplane on a river.

Turns out, in the real world, it's not for the faint hearted, if the river is moving very fast, for a lot of nasty practical reasons, which our arm chair bound, theory bedazzled friends can safely ignore. Here's a 15 page introduction to the operation of seaplanes, for those interested, but, for me, the take away from this little investigation, and this thread, is that armchair pilots should fasten their seat belts, and continue building hours in their Barcaloungers, where crosswinds will never trouble them, and imaginary conveyors don't bother imaginary airplanes at all, except for the imaginary tire wear :-)
posted by paulsc at 6:48 PM on October 1, 2007


That's because pontoons don't decouple the plane as well as wheels do.

A river will indeed push directly on pontoons, and would make landing really tricky. Plus, you get cross-currents as well, which would be even trickier.

A conveyor belt barely pushes on wheels at all... it just spins them.

So, no, the two situations aren't at all analogous.
posted by Malor at 8:48 PM on October 1, 2007


"... A conveyor belt barely pushes on wheels at all... it just spins them. ..."
posted by Malor at 11:48 PM on October 1

In the imaginary world, I'm sure you're right, Malor. After all, it's your imagination, my friend...

And I'll never have to take off from a conveyor, whether 15 foot or 1200 foot in length, even though you've said:

"... That means that the conveyor belt is irrelevant.
posted by Malor at 5:06 AM on September 30

We're both happy, so long as you stay in your Barcalounger, and I don't face a conveyor equipped runway, or a river in a seaplane, in the real world.
posted by paulsc at 9:19 PM on October 1, 2007


paulsc, you have no business sneering at people when you're that wrong.
posted by Malor at 10:18 PM on October 1, 2007


"paulsc, you have no business sneering at people when you're that wrong."
posted by Malor at 1:18 AM on October 2

I'm not sneering. I'm chicken, when it comes to 1200 foot long conveyor equipped runways that I might have to tackle with my puny 160 horsepower 1977 Cessna 172, with a fixed pitch 2 blade prop, high hour tires, and no ground speed indicator.

You'll pardon me, please, if I'm not as confident as you, in the absolute invincibility of your logic, and your imagination.
posted by paulsc at 10:33 PM on October 1, 2007


paulsc: you're just making an ass of yourself now.
posted by Pendragon at 2:13 AM on October 2, 2007


"paulsc: you're just making an ass of yourself now."
posted by Pendragon at 5:13 AM on October 2

No more than I do, on any negative weather report, on a cross country flight.

As my first instructor was happy to say, often and loudly:

"There are old pilots, and bold pilots, but there are no old, bold pilots."

I feel sure he'd been offered the chance to take off from a conveyor equipped runway. Fortunately, he's still flying, down at Jekyll Island, Georgia. Where are the Barcalounger instructors flying, these days?

I'll shut up, when those who argue for the physics of thing, show me a single engine plane taking off from a conveyor, of less than 1200 feet length, running in a direction opposite the plane's engine thrust, in the next 12 hours.

Put up, or shut up, theoreticians...
posted by paulsc at 2:44 AM on October 2, 2007


In other words, "I'll shut up if and only if you fulfull the following impossible conditions."

Yeah, right. Whatever. I've lost a lot of respect for you in this thread.
posted by Malor at 3:43 AM on October 2, 2007


"... Yeah, right. Whatever. I've lost a lot of respect for you in this thread."
posted by Malor at 6:43 AM on October 2

I'll try to be heartbroken, Real Soon Now.

While I'm trying, do you want to show me that 1200 foot conveyor, and that single engine plane, and the successful pilot you'd like to promote, above Charles Lindbergh? I can apologize, very sincerely, if you can show me I'm mistaken.

You've still got, nearly, 11 hours...
posted by paulsc at 4:11 AM on October 2, 2007


Come on, girls, you both have lovely bottoms.
posted by Wolof at 4:19 AM on October 2, 2007


I think, paulsc, that you need to prove yourself right, by demonstrating that a plane cannot take off on a conveyor.

You have 10 hours.
posted by Malor at 4:35 AM on October 2, 2007


"Come on, girls, you both have lovely bottoms."
posted by Wolof at 7:19 AM on October 2

I think you'd have to grant, however, Wolof, that Malor's bottom fits a Barcalounger better. Whilst mine could be reasonably envisioned twirling into the seat of a real plane.
posted by paulsc at 4:37 AM on October 2, 2007


"I think, paulsc, that you need to prove yourself right, by demonstrating that a plane cannot take off on a conveyor."

You're right. No single engine plane or pilot I know of can take off, on a 1200 foot conveyor. I know, without trying, because of flight training and previous experience that I can't.

QED, I win, unless you can show me I'm lying.

Thanks for playing.
posted by paulsc at 4:41 AM on October 2, 2007


PAULSC !!!
posted by 6am at 6:20 AM on October 2, 2007


Paul, you're not just disagreeing with me and Ethereal, you realize, all your snide comments about Barcaloungers notwithstanding. Every physicist that has registered an opinion says the plane takes off.

In general, I find disagreeing with physicists about physical effects to be a low-probability bet.

Given two possibilities, that:

A) Physicists don't understand how planes interact with the ground and propel themselves through the air, or;
B) paulsc is confused about how wheels work.

I'll go for B every time.
posted by Malor at 7:33 AM on October 2, 2007


And note that in those videos that 6am linked, that tiny little engine with relatively huge wheels, on a CARPET (thus, in a very, very high-friction environment compared to the one we're talking about) is still able to move forward while the rug is being pulled like crazy out from underneath.
posted by Malor at 7:36 AM on October 2, 2007


Also: http://www.youtube.com/watch?v=mAA_WbgyD8I

Also:
http://www.youtube.com/watch?v=Tmbsd_o5whI

And again, the purest test:
http://www.youtube.com/watch?v=eSxUHHcfsro
posted by 6am at 8:00 AM on October 2, 2007


The fundamental misunderstanding here is the assumption that the contact patch of the tires conforms to the movement of the belt surface.

With the brakes on, they will. But with ideal frictionless bearings, the shear force of the moving surface on the tires will result in forward wheel rotation without (any/much?) backward movement of the plane.

Amateurs talk about speed, pros analyze momentum.

With real-world bearings, and a moving runway surface, there will be some small force transmitted from the wheel hub via the landing gear to the plane itself.

This is the force that must counter-act the thrust of the engine(s) for the plane to remain stationary.

It is theoretically possible for this force to keep the plane from accelerating, but as mentioned above would require quite large belt speeds not attainable in reality.

This book is the bible of road-wheel interaction. Highly recommended.

OK, back to retirement
posted by Heywood Mogroot at 10:30 AM on October 2, 2007


Holy 237 comments physicsfilter! Answering a question that the links of the post answered.

That is awesome.
posted by Jeremy at 1:43 PM on October 2, 2007


This Wikipedia page says that what sets things in motion is that the existence of one blue eyed person becomes common knowledge, i.e. everybody realises that everybody knows there is one blue eyed person.

I fail to see how this is not true before the guru speaks:

Every person can see two blue eyed people. Therefore, everybody knows that everyone can see a blue eyed person.


Being perfectly logical people, they have worked out both these facts long before the day the guru spoke:

1. I know that there is at least one blue-eyed person on the island (1st order)

2. Everyone else on the island knows that there is at least one blue-eyed person on the island (2nd order)

3. Since everyone else is a perfect logician, everyone else knows that everyone else knows that there is at least one blue-eyed person on the island (3rd order)

etc.

So there is a flaw in the setup of these problems.

Why?

The essential issue is that all these type of puzzles work via an inductive argument, and to make an inductive argument work, you need two things:

1. A definite starting point
2. Discrete (rather than continuous) steps of time

One reason reason these examples (blue-eyed islanders, people with dirty faces) seem paradoxical or contrary to our normal, real-life experience is that in real life the definite starting point and discrete time-steps needed for the inductive magic to happen, just are not there.

To make the inductive logic of the puzzles work, you must have these two elements present. And if you are not really careful, the attempt to introduce these two elements is going to come across as strained and artificial.

In the "dirty faces" example, why is is so important that the waiter start to ring a bell repeatedly?

In the blue-eyed islander example, why is it so important that the people who have come to a realization leave at some certain pre-established time of day?

These devices are only introduced so that the puzzle-poser can have some artifice (discrete time steps) on which to hang the inductive argument.

Why does the waiter make an announcement about faces, and the guru make an announcement about eye color?

That is simply to give the necessary starting point for the inductive argument.

If the problem setup could make these two devices more convincing, the puzzles themselves would be more convincing and less confusing.
posted by flug at 6:54 PM on October 2, 2007


But given the fact that one's own eye colour cannot be directly observed, what exactly prevents a browney from initiating the logic chain?

The blueys are debating whether there are 99 or 100 blueys (they can see 99 blueys but don't know about themselves).

The brownies are debating whether there are 100 or 101 blueys (they can see 100 blueys but don't know about themselves).

According to the logic of the solution, after day 99 no one leaves, and at that point each bluey realizes* that there must be 100 blueys--because they know from direct observation there must be 99 or 100, and if the answer was 99 then those 99 would have left on day 99. So know they know there are 100 blueys and that they themselves are bluey #100. Now they know their own eye-color and must leave.

When the brownies see everyone leave at day 100, they realize from that fact alone* that there are 100 blueys in total. They have already counted 100 blueys that they could see, and therefore they know that they themselves are not blue.

They still don't know what color they are--just narrowed it down to "not blue".

*Because the islanders are not just perfect logicians, but more specifically perfectly versed in this kind of inductive logic about what other people think, and make all their decisions on that basis.
posted by flug at 8:06 PM on October 2, 2007


No single engine plane or pilot I know of can take off, on a 1200 foot conveyor. I know, without trying, because of flight training and previous experience that I can't.

QED, I win, unless you can show me I'm lying.


You have previous experience of taking off in still air with your wheels being overspun by a conveyor belt below you? Post that shit to YouTube!

You're lying, and losing. Wow, you can't even correctly answer a question you made up yourself in a desperate attempt to avoid the question you'd already answered incorrectly. That's a very high level of wrong!
posted by nicwolff at 10:30 PM on October 2, 2007


For some reason, this variant melts my (irrational or no) objections. I feel I've come closer to understanding, and I'm now going to try to reconcile that fact with the still annoying blue eyes problem. :)
posted by goodnewsfortheinsane at 9:35 AM on October 1 [+] [!]


I have similar objections to the problem. The problem is only resolved because every agent is assumed to be perfectly rational, which is a completely absurd premise. The solution has to be independently arrived at by absolutely everyone for the solution to in fact BE the solution. Without every agent conceiving of it, it's utterly wrong. Every agent must be perfectly rational for the perfectly rational answer to be perfectly rational... its a bizarre circularity. So while this teaches you something about logic, it's not a very useful lesson.
posted by mek at 12:51 AM on October 3, 2007


flug: Why does the waiter make an announcement about faces, and the guru make an announcement about eye color?

That is simply to give the necessary starting point for the inductive argument.


So the guru is not really necessary - the islanders should come to the same conclusion even without the guru speaking?
Can you formulate the solution without a guru ? Let's say the islanders where living in different caves, and they come together at a specified day.

mek: I have similar objections to the problem. The problem is only resolved because every agent is assumed to be perfectly rational, which is a completely absurd premise. The solution has to be independently arrived at by absolutely everyone for the solution to in fact BE the solution.

That's not my problem at all - maybe it will be if i'm convinced the solution as given is correct. In fact I'd like the problem to be formulated in some abstract manner, so we can get all the islanders out of the way. Does anyone have a good starting point for this kind of approach?

This thread is somewaht bloated already - maybe we take this somewhere else?
posted by the number 17 at 1:52 AM on October 3, 2007


The traditional way to put the blue-eyes problem, which I remember from many years ago, and which I also looked up on google, is to say that one day the King decrees that from now on, if anyone realizes they have blue eyes, they must on the following morning leave the Kingdom never to return. I find it quite a bit easier to understand, that way. The way it's put by xkcd, I don't see anything that'd prevent the brown-eyed people from doing the same thing, assuming it's logical for anyone to start the logical chain there.
posted by sfenders at 2:39 AM on October 3, 2007


I think posing this question a different way might help people understand. Take the lift aspect off the table. Imagine one of those rocket cars like the Blue Flame. If you placed that car on a conveyor belt would the conveyor belt stop it from moving? No. The rocket cars' wheels move freely and do not push off on the ground to make the car move. Instead the rocket works because the thrust generated moves by creating an equal and opposite reaction.

In a car, the wheels themselves are the actual method of creating the equal and opposite force--the friction of the tires against the road allows the engine which spins the tires to move the car forward. In that case, an opposite force against the tires equally will hold the car in position.

The reason that people get this confused is because of personal experience which the great majority of people will trust instinctively over any amount of physics. People walk on those airport movers all of the time. If you just stand there, they will push you back. The same principle applies to a treadmill. What people don't realize is that when applying friction to a surface is how they move, moving that surface will counteract that motion. But when something moves via straight mechanical thrust, it isn't using friction against the ground to move.

The thing that needs to be remembered to get this problem right is that a plane is not gaining speed by pushing off against the ground by imparting force from an engine to the ground via the tires. A plane's engines push against air. If they didn't it would never fly in the air.
posted by Ironmouth at 8:23 PM on October 3, 2007


I don't know about you but there is no way in hell I'm getting in an airplane that will be taking off (or attempting to) from a conveyor belt. That just seems silly and dangerous!
posted by CuJoe at 11:42 PM on October 3, 2007


The guru's announcement is required. There is a crucial difference between everyone knowing something and everyone knowing that everyone knows something.

Also, the omniscient approach is confusing. The right approach to the problem is to pare it down to only four people, one of them being yourself, and that you see three blue-eyed people. Ask yourself what you know; what you can be certain other people know; and, most importantly, what you can be certain all other people can be certain all other people know.

The crux of the matter is that one's own uncertainty about one's own eye-color “taints” what one can know about what other people can know with certainty. But the guru's announcement creates a single certainty that everyone shares and which everyone knows that they share.
posted by Ethereal Bligh at 8:58 AM on October 4, 2007


"I know, without trying, because of flight training and previous experience that I can't." - posted by paulsc

You're lying, and losing. Wow, you can't even correctly answer a question you made up yourself in a desperate attempt to avoid the question you'd already answered incorrectly. That's a very high level of wrong!"

posted by nicwolff at 1:30 AM on October 3

I'm not lying, and I think I've let enough time go for further arguments and "proofs" to come in for this thread, if there were any. As I've said, I've never tried this, and the reason I wouldn't is because, through flight training, and crosswind takeoffs in gusty winds, I know that at the moment of rotation, for an instant, a plane is neither truly flying, or truly rolling. On a good day, a near ideal day, that moment of transition is mercifully short, perhaps a second or so, and you push a bit more right rudder, and, maybe, a touch of aileron, and keep pulling back smoothly, and she flies. Off a freakin' concrete runway. Immediately thereafter, you pull back to maintain 72 knots airspeed, or whatever the maximum rate of climb speed is for the particular airplane you're flying, and start checking your alternate landing and emergency sites. It's a lot touchier in a 10 knot, 45 degree to head-on crosswind, and still worse if the crosswind is faster, or farther off beam, or even a tail wind. Which is pretty much the same result that would be generated, during rotation, by the slightest mis-alignment of real wheels to a real conveyor.

So, do I think a conveyor running 60+ MPH under my wheels might make as much difference as maximum allowable crosswind, or worse? Yep. Call me crazy. Do I think any conveyor of minimum takeoff length, whatever that might be, might not be perfectly flat, and that my plane might careen crazily off it, during the takeoff roll, when hitting bumps, on a conveyor doing 60+ MPH in the opposite direction? Yep. Call me short sighted, and chicken. Do I think that a ground loop is a real possibility? Hells yeah! Boys, it's just the pragmatist in me, from my mother's side, speaking.

I've watched all the YouTube links, and read all the BarcaLounger experts' posts, and you know what? On the immense strength of the certainty y'all have expressed, and on the incredible load bearing capacity of all the hot air in this thread, I've concluded I might be wrong! But pardon me if I'm not willing to be the test pilot for the certainty of others, who really risk nothing, in their enviable, comfortable, padded chair certainty.

Put up, or shut up time: $1,000 total, out of my own pocket, for any person or group from this thread, that shows me, in person, an actual factory standard Cessna 172 taking off from a conveyor belt of less than 1200 feet length, from an agreed location (no wild goose chases to Tierra del Fuego, folks), while the conveyor belt is doing at least 60+ mph in a direction opposite flight, with the plane rolling on it unrotated before takeoff, before Thanksgiving, 2007, against a total similar wager from all you physics fans and BarcaLounger pilots. I'll want a look at the pilot's logbook, a look at the aircraft logs, and a very good technical look at that conveyor. I may bring as many additional observers as I want, at my expense, to verify data and flight. We'll probably film the heck out of it. If your pilot doesn't make it, you bear the travel expenses for me and my crew, and all costs of failure, that you can't insure, and I'll pay for filming, and a nice flower arrangement, if required, to the funereal home. Payment by me, to the winner(s), based on my agreement of performance, within 24 hours of takeoff, via cash or Paypal. Payment to me, by any/all of you, expected within 48 hours following 12:01 A.M. of November 23, 2007, if you can't show me. Arrangements via MeFiMail!

When I get the first dollar in my hand for failure, or notification that my PayPal account has been credited even $1, I'll post back to this thread, with thanks. Anybody want a piece of that happening, as a side bet? If you're not giving me odds on the side bet, I'll have a hard time taking you seriously...

And if the damned thing flies, I'll be the first to post back with the real, once and for all, YouTube link.
posted by paulsc at 1:02 AM on October 24, 2007


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