Airplane/Conveyer Belt Question

[Marcus]

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?

Now I don't have any aerospace/aero-dynamics training, but this is the logical deduction I have made. I say Yes, the plane although moving relatively at speed will remain static due to the coveyer belt matching its speed, and therefore would create the lift needed to create sustainable flight.

Thoughts?

[Squirrel Killer]

So the plane is going in reverse with no additional thrust? It might take off, but it's going to be a bumpy, and short, ride.

[Bill Dungsroman]

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?

Now I don't have any aerospace/aero-dynamics training, but this is the logical deduction I have made. I say no, the plane although moving relatively at speed will remain static due to the coveyer belt matching its speed, and therefore would not create the lift needed to create sustainable flight. We also have the guys who feel that it would get up to flight speed and take off.

Thoughts?

Assuming windless conditions, you'd be correct. Lift requires wind resistance. If your plane is not moving forward through the air, it isn't pushing through an air mass.

The cross-section of a plane's wing is such that when it flows through air, the relative air pressure above the wing is less than the relative air pressure below it, thus lift. It's why the top of a wing, from front to back, has more of a curve than the bottom. Since the wing is moving through the air, adjacent air pockets that the wing touches will move over and under the wing at differing rates in order to be left by the wing still adjacent (airstream observations support this), and the air pocket above the wing must travel faster in order to traverse the larger curve of the top of the wing and still arrive at the back of the wing at the same time the bottom air pocket does. I'd drop Bernoulli's Equation on you at this point if I wanted your head to explode, but suffice it to say that pressure and velocity are inversely proportional per B's Equation, so if you increase velocity, you gots to decrease pressure. So, your wing pulls upwards and takes the fuselage with it.

Another example is a truck bed with a tarp over it: the tarp pops up because the faster moving air over the tarp is inducing a pressure drop.

[Phil_Stein]

Yes, because taking flight is not primarily a measure of the friction between the plane's wheels and the ground, but rather, between the plane's wings and the air. And when the plane is going 200+ mph (or whatever it's takeoff speed is), the wings will generate sufficient lift to take off. The effect of wheels on ground is fairly neglible.

[JMR]

Yeah because it's a Harrier.

[MikeSofaer]

Phil has pretty much said it, the fact that the conveyor belt is clocking along real fast backwards under the wheels isn't going to make any difference to the actual acceleration of the plane, which is being pushed by the turbines on the wings. The wheels will spin twice as fast, though.

[Case]

If no air is actually passing over and under the wings, there's no lift. So the plane won't take off.

Think about the opposite situation. If you have an enormous wind tunnel blowing air at the plane, it will lift off the ground. It might not go anywhere, but it will certainly be "flying."

[Union Carbide]

http://www.straightdope.com/columns/060203.html

Short summary: The plane takes off.

[XPav]

And the thread saying why Cecil is wrong...

http://boards.straightdope.com/sdmb/showthread.php?t=361386

[Lunch of Kong]

Having heard both arguments, this thread is now closed.

[XPav]

Seriously though, planes need air over the wings to take off. If the plane isn't moving relative to the air, it won't take off. The treadmill is irrelevant.

[Ben]

XPav- What makes you think the plane won't move relative to the air?

Here's a freehand drawing shamelessly stolen from some dude on another forum:


http://img210.imageshack.us/img210/1011/plane8oz1cl.jpg

[russellmz00]

why isn't jesus in the copilot seat?

[Lunch of Kong]

Respect mah authoritay!

[XPav]

Because the wings aren't moving relative to the air! Groundspeed != Airspeed. Sure, the wheels are turning like mad, but unless there's an external source of wind, airspeed is going to measure 0!

That diagram is dumb. Anyone who has ever read a flight-sim manual from Janes or Microprose knows that there are 4 forces for a plane (going clockwise from top), Lift, Thrust, Gravity, and Drag.

There is no lift in the diagram! Sure, you've got a shitpile of thrust going on, but that doesn't help you.

It all gets back to (as referenced in the straight dope message board link) that it's really a question of what the conveyer does. My interpretation is that the aircraft is stationary on the treadmill, no matter the thrust applied.

[Lunch of Kong]

The question posed was this:

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

The belt matches the speed and acceleration of the plane. So if the plane is moving FORWARDS at 10mph, the belt is moving at 10mph, making the wheels spin at 20mph minus some small fraction for friction. Let's say 20%. So if the belt is cranked up to 10mph, the plane will only "feel" 2mph of that. The rest will be the wheels spinning freely.

Or think of it this way. Lets put YOU in an office chair with wheels on it, and lets put the chair on a conveyer belt. We'll give you a steel bar that you can hold on to for support that is not connected in any way to the conveyer belt.

Lucy cranks up the conveyer belt to 50mph and it moves underneath you. But, to stay still, you just have to hold on to the steel bar. Indeed, you can actually push off the steel bar and move in whatever direction you want, because your wheels are just spinning under you.

The aircraft engines are like that steel bar that you're pushing yourself against. Pushing against the steel bar generates thrust, just like an aircraft engine pushing against air. Your arms only have a reach of about three feet, though, and that's the extent of your thrust. A plane can generate thrust for as long as it needs to.

So you see, what the conveyer belt is doing is only imparting a little bit of extra drag at the wheels. The plane will not be held in place, but will move forward at 80% of it's normal acceleration for a given throttle setting.

[Ben]

XPav- The arrow with the V is what direction the plane moves. The conveyor spins and the plane moves along it, eventually reaching takeoff speed.

Here: What is stopping the plane from moving forward? The engines are pushing the plane in one direction. What possible force is pushing the plane backwards?

[Lunch of Kong]

Actually, reading the question again, it's rather mudane.

The conveyor matches the speed and acceleration of the plane. If the plane is not actually moving, then the conveyor belt wouldn't be moving either. But if the plane starts to accelerate at 1G, that indicates forward motion. At that point, the speed of the conveyor belt is not relevant: the plane is in motion and air is passing over the wings.

[Case]

The question posed was this:

Lucy cranks up the conveyer belt to 50mph and it moves underneath you. But, to stay still, you just have to hold on to the steel bar. Indeed, you can actually push off the steel bar and move in whatever direction you want, because your wheels are just spinning under you.


Except that the problem states that the belt "perfectly matches" the speed of the airplane, except in reverse.

[Ben]

Case- Planes don't derive their forward energy from their wheels.

[Lunch of Kong]

see above.

actually, picture this.

Two identical planes, with big velcro rollers on the bottom of each instead of wheels, are belly to belly, but facing opposite directions. Assume no gravity.

If you pushed both of their engines into full throttle at the same time, would they move, or would they stay stationery?

They would move. The rollers would not pose any impediment to their forwards movement, even though there is a roller under them with the exact opposite speed and acceleration.

[russellmz00]

i'm confused by the wheels going forward making it impossible to stay still on a treadmill part. the treadmill goes backwards, so the wheel goes...forwards? the treadmill goes forwards, so the wheel goes...forwards? whah?

in my mind the question is, if i were pedaling on a bicycle on a treadmill, would it be 100% impossible to be stationary even if the treadmill was perfectly operated by a computer to speed/slow/go backwards? wouldn't this be the equivalent of a treadmill being made out of perfectly smooth ice, resulting in the wheel going nowhere? but the engines make it go forward, so the treadmill has to go backwards but then i'm back to, is it impossible for the treadmill to make it go backwards/stay still..

[Lunch of Kong]

in my mind the question is, if i were pedaling on a bicycle on a treadmill

That's the wrong question. You're not pedaling a bicycle on a treadmill. You are not fighting the motion of the treadmill. Rather, you are COASTING on a bicycle with a ROCKET strapped to your back. You may as well not be attached to the bicycle at all, and the only reason why you are is because we have gravity and you have to have something under you lest you leave a big red skid mark on the ground.

[russellmz00]

see above.

actually, picture this.

Two identical planes, with a big roller on the bottom of each instead of wheels, are belly to belly, but facing opposite directions. Assume no gravity.

If you pushed both of their engines into full throttle at the same time, would they move, or would they stay stationery?

They would move. The rollers would not pose any impediment to their forwards movement, even though there is a roller under them with the exact opposite speed and acceleration.

but to sim a treadmill the plane on the bottom would be facing the same horizontal direction as the one on top wouldn't it? if the top part of the roller was going the opposite direction of the top plane to make it stand still the bottom plane would have to be heading in the same direction as the top plane.

[Lunch of Kong]

but to sim a treadmill the plane on the bottom would be facing the same horizontal direction as the one on top wouldn't it? if the top part of the roller was going the opposite direction of the top plane to make it stand still the bottom plane would have to be heading in the same direction as the top plane.

if that were the case, they'd launch off together in unison, attached at the hip with their velcro rollers. :)

[russellmz00]

That's the wrong question. You're not pedaling a bicycle on a treadmill. You are not fighting the motion of the treadmill. Rather, you are COASTING on a bicycle with a ROCKET strapped to your back.

this makes more sense.

but assuming gravity, wouldn't there be a magic point where the rocket going at full blast and the treadmill going backwards at x fraction of lightspeed make me stand still?

still trying to think this one out...

[shift6]

Thoughts?
On the face of it, I'd say no. Because we've all seen a commercial with some new car driving on a conveyer belt, and it doesn't go anywhere.

However, cars get their forward motion by friction between the ground and tires. Planes do not. The jets would push the plane forward at speed X. With the conveyer belt were moving backwards at speed X, you'd have the tires spinning at speed 2X but neither hindering nor contributing (significantly) to takeoff.

Think of a vertical analogy: put a conveyeyer belt under the space shuttle and have its wheels on it: wouldn't matter because it's the rocket moving the shuttle upwards, not the wheels. It "sounds" better in the vertical analogy, IMHO.

[Wholly Schmidt]

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction...
This is the crux of the question, how you interpret this line. If you're measuring the speed of the plane by how fast the wheels are rotating (like how your speedometer tells you how fast your car is going) then the plane will not take off. Arguably, that's the wrong way to measure the speed of the plane though, it should be measured by its movement relative to a separate location in space. You can get all stupid about how the whole planet is spinning and flying through space and what the heck is speed relative to anyway, but for common sense purposes, the speed of the plane, conveyor or not, is how fast it "looks like" it's going to someone standing next to the runway, not how fast its wheels are actuallly revolving. When there's no conveyor, the speed of the plane and what the wheels' revolutions are reading for distance travelled happens to match up, but that's just lucky for us (and cars).

[DennyA]

The plane will fly.

It's time to call the Mythbusters.

[magnet]

And the thread saying why Cecil is wrong...

http://boards.straightdope.com/sdmb/showthread.php?t=361386

And Cecil's definitive reply (http://www.straightdope.com/columns/060303.html).

Here's how I look at it: suppose an F/A-18 were making a carrier landing at 120 kts, but something goes wrong and the trap didn't engage. No problem: as we all learned from the Jane's sim, the pilot just applies more thrust, climbs away for a bit, and comes around again.

Now suppose the jet fighter were making the same approach, but for some reason the carrier crew replaced the trap with a conveyer belt running 120 kts in the opposite direction. Heck, run the belt at 300 kts even! The landing gear makes contact, and what happens? I think it's pretty obvious the jet would roar past the tower as before, again apply thrust, and fly away.

There's just no way a conveyer belt would apply any substantial braking force to the landing jet - which means there's no way it can impede a plane that wants to accelerate.

[Bill Dungsroman]

Wait, I know what the problem is: the scenario ranvarian's friends posited is possible only in theory, which is how all physics riddles get away with this type of bullshit. Until motherfuckers start popping out giant conveyor belts that magically match forward thrust for jet engine aircraft, at any rate.

Also, if Roger is right and it's all due to friction, I'm taking a big dump in ranvarian's friend's mouth the first chance I get. A big, steaming, post Baja Fresh dump. With green sauce.

[Wholly Schmidt]

The plane will not fly.

It's time to call the Mythbusters.
You're not going to even pretend to back that up?

[Wholly Schmidt]

Until motherfuckers start popping out giant conveyor belts that magically match forward thrust for jet engine aircraft, at any rate.
See, this way of interpreting it leads to the plane taking off. Engines thrust x mph left, conveyor pushes x mph right, wheels spin at 2x mph, (give or take negligble friction) and away the plane goes. Most people who think it doesn't take off don't think of the conveyor in terms of matching forward thrust of the engines (which is basically the actual velocity of the plane, give or take more negligble stuff like wind and air resistance), they think of it in matching rotational speed of the wheels.

[Bill Dungsroman]

See, this way of interpreting it leads to the plane taking off. Engines thrust x mph left, conveyor pushes x mph right, wheels spin at 2x mph, (give or take negligble friction) and away the plane goes. Most people who think it doesn't take off don't think of the conveyor in terms of matching forward thrust of the engines (which is basically the actual velocity of the plane, give or take more negligble stuff like wind and air resistance), they think of it in matching rotational speed of the wheels.

Let me say again: air resistance is not negligible, it is how planes fly.

[Nellie]

The plane will remain stationary on the conveyor belt until the engine generates sufficient thrust to overcome the friction holding the wheels to the conveyor belt. After which point it will move forwards regardless of the conveyor belt and take off.

[TriggerHappy]

Apparently the real reason it *would* fly is that the source of the plane's acceleration is not the wheels, but the engine. So the plane wouldn't stand still, and would eventually move forward in relation to the air, generating the required lift.

Or something.

[Rywill]

Let me say again: air resistance is not negligible, it is how planes fly.
Yeah, but his point is that there will be air resistance, because the plane will move foward through the air despite the conveyor turning under its wheels. A car would not, because its only source of forward power is friction between the wheels and the road: take that away (by moving the road backwards in tandem with the wheels), and the car goes nowhere. A plane, on the other hand, gets forward power by pushing back on the air behind it (via its engines), not by pushing against the road underneath it. So to the plane, it doesn't matter how fast the conveyor is moving, the plane will still move foward and take off.

Here's another way of thinking about it: instead of a conveyor, imagine a frictionless road (like the ultimate oil-coated ice skating rink). The car can't move forward, obviously -- the wheels will just spin in place. But the plane still can, and if you could keep it pointed straight, you could take off.

[Hawkeye Fierce]

What an incredibly badly worded physics problem. There are two ways to interpret it - first, the conveyor belt spins to match the groundspeed. That is, wheels are moving forward at 10mph, belt moves backwards at 10mph. The net force that gets applied to the actual body of the airplane is a small amount of drag generated by the friction from the wheels. Thus, the conveyor belt in this configuration isn't gonna keep the plane from moving forward and generating lift under its wings, so it takes off.

The scenario I guess the problem is trying to make you think about is, if the plane is generating thrust like crazy, but somehow this magic conveyor belt is keeping it from moving forward, will it take off? I suspect, though I'm sure as hell not going to do the force vector calculations to figure it out, that you could prove that such a situation is actually physically impossible, and thus such a gedanken experiment is meaningless. But yeah, if the plane doesn't move forward, it doesn't take off. (Edit - barring obvious exceptions like VTOL planes)

[Ben]

Hawkeye- It's not that badly worded. Ranvarian can't be held responsible for people assuming that it's a magic conveyor belt that keeps the plane still for no reason. It isn't even a physics question, it's a "How planes work" question. They don't go fast because their wheels spin, their wheels spin because the giant honking enginges on the wings make the plane go fast.

[Hawkeye Fierce]

Hawkeye- It's not that badly worded. Ranvarian can't be held responsible for people assuming that it's a magic conveyor belt that keeps the plane still for no reason. It isn't even a physics question, it's a "How planes work" question.

Well, my answer to "how do planes work?" would probably be along the lines of "Physics!" But I used to be a science nerd, so maybe it's just me.

[Ben]

My point is that it's just a little "gotcha" where the questioner asks someone, the person thinks about car commercials and says "no", and then the questioner reveals the truth. You don't need to know the actual physics, you just need to know what part of the plane provides thrust.

[Wholly Schmidt]

Let me say again: air resistance is not negligible, it is how planes fly.
I'm sorry, you're right, I figured if I kept responding to this I'd screw my own wording up. I realize air resistance is what gives it the lift, what I meant was that if the engine is providing X thrust in one direction, the plane moves in that direction at a little less than X because some of that thrust is being lost to the wind resistance on the whole plane moving through space in any direction. I didn't mean for us to get bogged down in my hasty explanation there, but you're right about my wording being wrong. What I meant in my post is still right though.

[Hawkeye Fierce]

Ben - Aren't we agreeing about the answer to this question? Why are we arguing about this? :-)

[MarchHare]

I'm going to preface my response by saying that I'm a pilot and for two years I instructed groundschool classes at a flight school. Furthermore, I consulted my best friend who has a master's degree in aerospace engineering about this answer.

The plane will not take off.

The problem, though, is that the question is worded poorly. I think what it really means to ask is to assume that there is some force (a conveyor belt in this case, but it doesn't matter what) that is preventing the aircraft from moving forward relative to a particular point on the ground. Let's say there's a line painted on the runway 5 feet in front of the plane. No matter how much thrust the engines produce, our magical force will never allow the plane to cross that line. Instead of using a conveyor belt, you can imagine the landing gear is bolted to the runway and you get the same effect. If we further assume the windspeed is 0 Kts, you won't get any airflow over the wings, and therefore the plane will not produce lift. Lift is determined by the airspeed of the plane, which is measured by a pitot tube which detects the force of air pressure moving against the aircraft. Groundspeed is absolutely irrelevent for generating lift. Suppose you have a plane flying at 100 Kts (airspeed) with a 15 Kts tailwind. The groundspeed will be 115 kts, but no additional lift will be generated. In fact, just the opposite is true, which is why aircraft always takeoff and land into the wind, not with it.

Incidentally, you can get the reverse effect for a plane in flight. Suppose you have a plane travelling into a really strong headwind that matches the airspeed perfectly. To an observer on the ground, the plane will appear motionless in the air, but the airspeed indicator will tell the pilot that he's flying at sufficient speed to maintain lift and not stall. I've actually seen something very close to this situation with a glider flying into heavy wind. The groundspeed of the glider was only maybe 10 or 15 Kts, but the airspeed was above 50 Kts.

[Hawkeye Fierce]

I'm going to preface my response by saying that I'm a pilot and for two years I instructed groundschool classes at a flight school. Furthermore, I consulted my best friend who has a master's degree in aerospace engineering about this answer.

The plane will not take off.

The problem, though, is that the question is worded poorly. I think what it really means to ask is to assume that there is some force (a conveyor belt in this case, but it doesn't matter what) that is preventing the aircraft from moving forward relative to a particular point on the ground.

Right, it's all a question of interpretation, which is why people can't agree. And this interpretation is equivalent to saying "What if a plane were bolted to the ground? Would it take off?"

[MikeSofaer]

MarchHare just gave another explanation of why the plain will take off. Airspeed is what matters, not groundspeed, so any crazy stuff you make the ground do is not relevant. The logical leap from there to a realization that because a conveyor belt would do nothing the questioner must have meant to specify an immobilizing force eludes me, though.

[Lunch of Kong]

I think what it really means to ask is to assume that there is some force (a conveyor belt in this case, but it doesn't matter what) that is preventing the aircraft from moving forward relative to a particular point on the ground.

It's all in the wording.

Your interpretation where there is some conveyor belt that spins at ridiculously high speeds to counteract the thrust of the engines based merely on the small friction forces between the spinning wheel and the landing gear strut: NO.

My interpretation where there is some conveyor belt that spins at slightly less ridiculously high speeds and that merely matches the speed of the wheels: YES

This thread is closed! :)

[Rob Beschizza]

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?

Now I don't have any aerospace/aero-dynamics training, but this is the logical deduction I have made. I say no, the plane although moving relatively at speed will remain static due to the coveyer belt matching its speed, and therefore would not create the lift needed to create sustainable flight. We also have the guys who feel that it would get up to flight speed and take off.

Thoughts?

The plane will take off. Its obvious when you consider that the thrust is not applied to the equal but opposite conveyor, but to air.

This question always results in writhing and screaming. I got it wrong at first, because I thought the car/bycicle rules applied, and the energy goes through the wheels, the plane never moves relative to the air, never generates lift, and so never takes off. But in fact the thrust from the plane pushes against air, while the opposite thrust from the conveyor never gets to the plane to balance it out -- it just makes the wheels spin.

Right! Right? :)

[Marcus]

This question always results in writhing and screaming.

Thats why I love it.

[ElGuapo]

My take on the way it would work is thus:

The plane applies thrust out of its engines, which is supposed to accelerate it. But the conveyor belt is trying to counteract this forward thrust by spinning backwards. On a runway, when this plane reaches a certain air speed on the runway, there is enough lift on the wings and the plane takes off. But on the conveyor belt, if it really can match the forward thrust, the plane should not take off.

What might happen is that the thrust of the plane would be so powerful as to make it start going forward anyway. Kind of creeping along towards to end of the conveyor belt. At that point though, the realized forward momentum would be so little that no lift would be generated and the plane would stall off the end of the conveyor belt and crash.

The plane needs wind resistance and lift in order to take off. If the belt can counteract this, it doesn't matter if the thing strapped to the jets is a fuselage and wings or a steel cube, the thing won't take off.

That's how I'd imagine it'd work out on Mythbusters. The thing would creep along toward the endge as it's power thrust overcame the real-world-not-able-to-keep-up conveyor belt.

If the thrust is so great coming from the engines, the conveyor belt is meaningless anyway. But if you have a truly theoretical belt that can counteract 30,000 lbs of thrust, the plane shouldn't go anyhere.

Put it another way: Imagine the conveyor belt is only say 20 feet long, enough to put all sets of wheels on. Now imagine it's 10,000 feet long. In both cases it moves equally quickly backwards, so if you were observing the plane, it's not moving forward. In neither of these cases will the plane generate lift and take off.

[MarchHare]

MarchHare just gave another explanation of why the plain will take off. Airspeed is what matters, not groundspeed, so any crazy stuff you make the ground do is not relevant. The logical leap from there to a realization that because a conveyor belt would do nothing the questioner must have meant to specify an immobilizing force eludes me, though.

Airspeed is measured as the speed the airflow is moving over the wings. If the conveyor belt is preventing the plane from moving forward (relative to a fixed point on the ground), there will be no airflow over the wings; therefore, your airspeed is zero and no lift is produced regardless of how much thrust your engines are producing.

Again, I think the problem arises because the question is worded so poorly. Those of you who say the plane will takeoff are assuming that the conveyor belt will just cause the wheels to spin really quickly but the airplane will still move forward (causing airflow over the wings), produce lift, and become airborne. My intrepretation of the question is that they just want some force that is preventing the aircraft from gaining forward momentum relative to a fixed position adjacent to the runway, and they used the example of a conveyor belt.

[Lunch of Kong]

http://www.slylockfox.com/images/dinosaur.gif

[MarchHare]

I think a better question would be this:

You have a seaplane on floats trying to takeoff against the current. The current changes dynamically and always matches the forward thrust generated by the plane's engine. Windspeed is zero. Does the seaplane take off?

IMO, that's what the conveyor belt question is really trying to ask, but they introduced an awkward system when they described the scenario.

[Rob Beschizza]

Thats why I love it.

I first saw it in a chain-spam email list titled along the lines of "10 questions that intelligent people will get wrong and have tantrums about."

One of the others, I remember, was a thermodynamics trick something like so, and it illustrates better why the airplane-conveyor questions is so ANNOYING:

"A young man is playing with a radio controlled car. To get up a hill, the car would require 1.9 watts of electrical power. The boy puts a battery in the car that provides 2 watts of power. Does it go uphill?"

And the answer was no.

The question makes it appear as if the entire physical logic is present in the question. But the question, while not actually a riddle, requires further information to solve: the impossibility of perfect energy exchanges. Like the airplane's wheels, if the question is poorly phrased, you won't know they are there.

[Enidigm]

I first saw it in a chain-spam email list titled something like "10 questions that intelligent people will get wrong and have tantrums about."

I got a chain-mail thing that asked whether you could rotate your left foot clockwise and draw the number 6 in the air counterclockwise. They declared IT CAN'T BE DONE! But, yea, i did it.

[mouselock]

but assuming gravity, wouldn't there be a magic point where the rocket going at full blast and the treadmill going backwards at x fraction of lightspeed make me stand still?

Yes, because your tires will have a coefficient of rolling friction.

The end result of whether or not the plane takes off comes down to:

Does the linear negative velocity of the treadmill match the applied positive velocity due to thrust before or after the coefficient of friction
for the plane's wheels is taken into account? If it's before, then the plane will take off because the wheels have a less than unity coefficient of friction, meaning that only a small percentage of the treadmill's linear velocity is being imparted to the plane. If it's after, then the forward velocity of the plane is exactly matched by the negative velocity of the treadmill, the net effective velocity is zero, and the only thrust generated is that of whatever the wind velocity of the day is.

There's not a disagreement on the science anywhere; there's a disagreement as to what the poorly worded "riddle" is trying to convey in terms of the actual problem system.

[mouselock]

If you pushed both of their engines into full throttle at the same time, would they move, or would they stay stationery?

They would move. The rollers would not pose any impediment to their forwards movement, even though there is a roller under them with the exact opposite speed and acceleration.

Err.. no.. it depends on how sticky the velcro is. The rollers would roll around and the resultant force from the rollers would become more aligned with the direction of thrust (rather than normal to it, as they start out). If the thrust is sufficient to overcome the parallel component of the exerted force the velcro connection will rupture and the system will decouple at which point it's obvious the planes will fly. If the thrust is not sufficient to seperate the planes, the planes will actually start spinning around the point of contact because the planes are basically in "orbit" at this point. (They'll also start to recede or advance perpendicular (rather than normal) to the direction of thrust due to the imposed torque response of these large massive bodies rotating at a set angular momentum around a central point.)

At the scale we're talking about, physics is deterministic. Someone can make a little java applet to describe the situation more or less accurately. (Though if you're actually modelling the lift instead of just using empirical formulas it'll take a bit more effort.)

[mouselock]

Apparently the real reason it *would* fly is that the source of the plane's acceleration is not the wheels, but the engine. So the plane wouldn't stand still, and would eventually move forward in relation to the air, generating the required lift.

Or something.

There's always a theoretically possible speed for the conveyor belt to go to impose an exactly counterbalancing force to the thrust, unless someone's come up with magic, frictionless wheels. (Which would be great for gas mileage on cars, if you could just get the things going in the first place! Turning would suck, though.)

[SpoofyChop]

This is a classic scenario in which the conservation of energy should be used to prove that the plan will/won't take off. Trying to draw force diagrams and stuff is only going to confuse people. Figuring out how the plane taking off/not taking off would violate conservation of energy would probably be a lot easier.

[MikeSofaer]

I don't think consevation of energy can be easily applied in a situation with friction, engines and a magical conveyor belt.

I think MarchHare's rewrite of the question makes no sense, he seems to be aware that a conveyor belt won't impede an aircraft very much, but feels the questioner intended to specify a mechanism that would, so we should answer that question instead.

But perhaps we have too many variables, let's strip one out. We don't need the engines for now:

Let's say you know the standard acceleration profile of a plane that's taking off and you program that into a conveyor belt. Then you put a plane on the belt and run the program without turning on the engines, and with the brakes off. What will the plane do?

[Enidigm]

I must have missed the brain boat because this one seems diabolically easy. The conveyor belt moves at the same speed as the plane would if the wheels could roll; therefore, it never takes off.

I agree with Mouselock it seem too easy to read into the question some deeper context.

I guess if you really wanted to throw a wrench into the equation; is the speed of the conveyor belt matching the planes' "true" speed, before the friction of parts is taken in account, or its "apparent" speed to the conveyor belt; ie, does the conveyor belt just go 10% faster to make up for the 10% of friction? After all, the conveyor belt isn't (i'm assuming) powered by the plane. If it's just a passive "unpowered treadmill" sort of thing, yea the plane would eventually start to move.

Of course, and here's another little fun problem if you're trying to account for friction; the plane's maximum thrust. At some point the engines can't move air any faster. So does the plane reach a takeoff speed by eeking out a 10% (or whatever) advantage due to friction before it reaches maximum thrust. Ect.

Honestly these are all too complicated :). The plane, she ain't going nowhere.

[edit: BTW what the question is "asking" is whether people understand the difference between airspeed and groundspeed. The wheels might be rolling at 500/mph, but the airspeed is still 0.]

[Bill Dungsroman]

Let's look at ranvarian's OP:

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?

"Special system." "Perfectly match speed and acceleration." I don't see nothin' bout no "land vs. air speed," or "of course, it's not a magical conveyor belt that perfectly matches speed and acceleration, even though I just said that" or any of the other bullshit qualifiers you dudes are throwing down to make your argument work. The post as written implies an hypothetical situation. I have inferred nothing beyond what was stated. A lot of you have. The way you guys are making it sound, I could put on a scarf and it would flap behind me as I ran on a treadmill at top speed. Per ranvarian's OP, the speed and acceleration of the plane, not just its landing gear, is matched by the conveyor belt. Everyone pulling that condition out of their bag is disqualified, ran's post never makes that distinction, a distinction that is IMO so mother effing critical to answering this fruity Bugs Bunny riddle correctly, assuming the riddle "meant" "land speed as measured by the landing gear tires" instead of what was was actually stated, "speed and acceleration of the plane," would be to assume ranvarian meant black when he said white.

I'm sure that's at least part of the critical point of this riddle, the "I am a liar, I lie all the time" point of contention. There's a sweet spot of knowledge base for figuring this out. People who know nothing about aerodynamics and physics mavens who take the vague offered text and run widdit are ass-out; dudes who don't overthink what little ranvarian gave us and like people who actually fly planes may fare better, is all I'm sayin'.

And not to single anyone out, but MikeSofear: we're arguing ranvarian's riddle, not yours. You keep adding and removing stuff to make your case, which automatically invalidates it every time you do it.

[Bill Dungsroman]

[edit: BTW what the question is "asking" is whether people understand the difference between airspeed and groundspeed. The wheels might be rolling at 500/mph, but the airspeed is still 0.]

I agree. Airspeed is a seperate measurement becuase, as the term implies, it is movement through the air. NO DUHHHH but the key word here is "through." An airplane on a giant magic gay conveyor belt is not moving through any air mass; all of its movement is confined to its wheels. Air is a fluid in regards to its physical dynamics. Imagine turning a convertible car upside-down (pretending that it could float that way) in water and dropping it into gear and doing 120MPH with its wheels spinning in the air. Are you going to get water plowing into your face? No, because all you've got is spinning effing wheels; you aren't moving through the water mass, because all the movement is in the wheels. In order to take flight, you have to have the wings move through an air mass. If your plane is on a big conveyor belt, it's not moving through an air mass, so it cannot take flight - as TSG points out, it has zero airspeed, because a plane's airspeed indicator requires air to be moving through/past it.

[MarchHare]

[edit: BTW what the question is "asking" is whether people understand the difference between airspeed and groundspeed. The wheels might be rolling at 500/mph, but the airspeed is still 0.]


Actually, the groundspeed of the plane in this case is also 0 (since the plane itself isn't moving relative to any fixed position on the ground) regardless of how fast the wheels are spinning.

[playingwithknives]

You could test this with a microlight and one of those rolling roads in mechanic shops they test a cars BHP on.

Its alot easier to imagine than a jumbo on a conveyor belt.

I'm on the side that says it sits there with its wheels spinning madly on the rollers and the engine at full throttle.

[Rywill]

Imagine turning a convertible car upside-down (pretending that it could float that way) in water and dropping it into gear and doing 120MPH with its wheels spinning in the air. Are you going to get water plowing into your face? No, because all you've got is spinning effing wheels; you aren't moving through the water mass, because all the movement is in the wheels.
But imagine if, instead of trying to get movement by spinning your upside-down wheels in the air, the car instead had a couple of propellers attached to the roof. In that case, the car would move forward through the water -- even though the car's wheels were unable to get any friction against the air. Planes are the same way: they get their forward thrust by pushing on the fluid (in their case, pushing on the air behind them), not by pushing on the surface beneath their wheels.

[MikeSofaer]

All right, not to act singled out, but I believe I only removed anything once, and it was in my very last post because I was trying to point out that a plane's speed through the air is not defined by the rotational velocity of its wheels over the ground, especially if the ground is moving.

The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

Previous posters have pointed out that this is not fully fleshed out and that the answer depends on how you flesh it out. I contend that the "no" answer depends on fleshing it out wrong.

The sentence mentions both speed and acceleration. Speed is a scalar quantity, acceleration is a vector quantity. Speed (and its vector buddy velocity) are frame dependent, acceleration is frame-independent in an inertial frame, which we may or may not have. The meaning of the sentence in physical terms varies depending on the frames chosen. Acceleration is the derivative of speed, so matching speed implies matching acceleration, although the converse is not true. I will only talk about speed, and all speeds will be in the direction of the nose of the plane.

What does it mean to have the conveyor belt match speed with the plane? What is the "speed of the plane" here? What is the frame of reference?

1) It could be interpreted to mean the speed of the plane relative to the moving conveyor surface, so that if the plane is moving 10 MPH forward over the conveyor, the conveyor would be moving backward at 10 MPH. In this case the frame of reference is the surface of the conveyor, so let's rewrite the second speed. The earth is moving forward at 10 MPH under the conveyor. You now have a plane that is motionless relative to the ground because you have created a frame of reference that defines the speed of the earth as equal to the speed of the plane. So you have defined the speed of the plane relative to the earth to be 0. This is blatant wankery and a wrong interpretation of "speed of the plane". Note that in this case there is no reason for the wheels ever to turn. They would turn if you started the conveyor, because they would have to in order to keep the plane motionless and thus satisfy your asinine interpretation of the assumption, but basically the plane just sits there, parked. Yay.

2) It could mean the speed of the wheels over the conveyor, no skidding. This reduces to 1) and is still wankery. Note that in this case the wankery becomes clear if you imagine the plane moving. You suddenly realize that you have defined the speed of the conveyor to be greater than itself.

3) It could mean the speed of the plane relative to the ground. This would mean that from the point of view of the ground the plane is moving forward at 10 MPH, and the conveyor backward at 10 MPH. From the point of view of the conveyor the earth is moving forward at 10 MPH and the plane is moving forward at 20MPH. The wheels on the plane turn at 20 MPH. This is the only interpretation that makes any sense because a) it uses a definition of "speed" that is sane and b) it does not start by defining everything to be motionless. In this case the plane takes off, but with the wheels spinning at double speed.

This interpretation, known colloquially as "the right one", is analagous to running a toy car along a table the normal way, i.e. by grabbing it, moving it with your hand and saying "vroom vroom". The car's speed is defined by your hand's speed pushing it. If someone pulls out the tablecloth at the same speed as you move the car it will make the car's wheels spin faster but he can't stop your car from moving by matching speed with you.

What if he pulls the tablecloth at a speed such that the rate at which the car moves over the tablecloth is the same at which the table moves under the tablecloth? Then you aren't moving the car, probably because you are punching him in the head.

[Wholly Schmidt]

The plane will not take off.

The problem, though, is that the question is worded poorly. I think what it really means to ask is to assume that there is some force (a conveyor belt in this case, but it doesn't matter what) that is preventing the aircraft from moving forward relative to a particular point on the ground.
This is my favorite part of this thread, where MarchHare proves to us that the plane will take off, by showing us how he would change the question to prevent the plane from taking off.

Here is all you need to know about planes to understand this problem:

1. The wings and air crap. We all know this. The planes (Harriers and whatnot aside) get their upward thrust from all that airflow over the wings stuff that plenty of you explained earlier in the thread. I don't think any of us have debated that, no point to spend any more time here.

2. The wheels are just there to prevent things from exploding. They don't move the plane down the runway to achieve the speed to take off. I think maybe they're used at ridiculously slow speeds for something like backing into a hanger, or for steering at those ridiculously slow speeds to manuever on to the runway, but they have nothing to do with getting the plane into the air other than their role to reduce, to the extent possible, the friction between the plane and the ground. You could replace them with skiis, pontoons, huge sticks of butter, whatever. You just need something to allow the plane to move along the ground until part 1 takes over with enough air moving past the wings for lift-off and elimination of that friciton with the ground; something better suited than the underside of the plane (that would be the explosion route).

If I'm wrong on that, let me know, because I haven't seen anything to the contrary in any discussion of airplanes, or this problem in particular (I saw it launch a zillion comments when it was posted on kottke.org (http://www.kottke.org/06/02/plane-conveyor-belt) a month or so ago). Does anyone disagree up to this point?

The problem isn't supposed to be a physics question (though physics are obviously involved), it's supposed to be a psyche-out brain teaser. It expects the audience is anticipating a trick, so it tries to make you think you've got the "trick" figured out. Your thought process is supposed to go something like this:

1. Duh, the engines are still working, of course it would take off!
2. Oh wait! It's a trick question! The plane has to be moving forward for the wings to work! I'm so smart! It won't take off.

And the person asking it smiles smugly because you never made it to

3. But the question never says it wasn't moving forward, just that the conveyor was moving backward.

Of course it's a "poorly worded" physics problem, it's not supposed to show up on your AP exam, it's supposed to make your friends look dumb when you ask them.

[Enidigm]

*boggle* /slaps head

I'll get back to this post in a couple hours if someone hasn't cleared up all this befuddlement before my return.

[Wholly Schmidt]

I must have missed the brain boat because this one seems diabolically easy. The conveyor belt moves at the same speed as the plane would if the wheels could roll; therefore, it never takes off.
Emphasis mine, what do you mean by that? The problem doesn't say anything at all about the wheels. This question invents a hypothetical conveyor belt and describes its function; nowhere does it say the wheels of the plane have been modified to work any differently than the wheels on any other plane. The wheels can roll. So the conveyor belt moves at the same speed as the plane, but in the opposite direction. The wheels, free to roll, provide a disconnect, eliminating more than enough friction for the plane to move forward and eventually take off.

[Rob Beschizza]

Jesus, people. This question is as old as drakes and THE PLANE TAKES OFF. It could only be different if Ranvarian fucked the question up, and if he did, then dissecting the implications of the fuckup as regards the canned, well-established outcome is kinda pointless, no?

I've got one for y'all:

Which is the third commonplace English word, other than angry and hungry, that ends with the letters -GRY?

[Bill Dungsroman]

Actually, the groundspeed of the plane in this case is also 0 (since the plane itself isn't moving relative to any fixed position on the ground) regardless of how fast the wheels are spinning.

It hardly matters, but you're sort of wrong. It is moving at whatever velocity on the conveyor belt, just like you can run 6 or 7 MPH on a treadmill. The treadmill is the "unfixed" position on the ground you are moving relative to, otherwise - in the plane's instance - you would be inferring that the engines aren't providing any thrust, which is not the case. That's really the point of this riddle IMO, the engines provide thrust, but not through an air mass.

Mike: sorry, I confused you a little with MarchHare. My apologies for that, but:

3) It could mean the speed of the plane relative to the ground. This would mean that from the point of view of the ground the plane is moving forward at 10 MPH, and the conveyor backward at 10 MPH. From the point of view of the conveyor the earth is moving forward at 10 MPH and the plane is moving forward at 20MPH. The wheels on the plane turn at 20 MPH. This is the only interpretation that makes any sense because a) it uses a definition of "speed" that is sane and b) it does not start by defining everything to be motionless. In this case the plane takes off, but with the wheels spinning at double speed.

According to your calculations there, when I set a treadmill to spin at 7 MPH, I'm actually running 14MPH? That doesn't make any sense, your colloquialisms be danged. If the plane is attempting to move forward at 20mph, per the riddle, the conveyor belt would match perfectly that 20mph in the opposite direction. You're telling me that the only sane definition of speed you can come up with is one where things move twice as fast in one direction relative to what is meant to be equal, opposing speed in the other direction? Are you telling me dynamic equilibrium of motion is impossible? Because that's what this riddle's scenario is a model of - dynamic equilibrium of forward velocity. You bust out this:

The sentence mentions both speed and acceleration. Speed is a scalar quantity, acceleration is a vector quantity. Speed (and its vector buddy velocity) are frame dependent, acceleration is frame-independent in an inertial frame, which we may or may not have. The meaning of the sentence in physical terms varies depending on the frames chosen. Acceleration is the derivative of speed, so matching speed implies matching acceleration, although the converse is not true. I will only talk about speed, and all speeds will be in the direction of the nose of the plane.
That's great, because it helps me make my point, although your verbiage is a little clunky. Velocity is a vector quantity alright, and in the case of an airplane attempting to take flight, it has a horizontal and vertical component.

Flight occurs when forward horizontal thrust allows the plane's wings to be pushed through the air, whereupon Bernoulli's Equation as compared between the top and bottom surfaces of the wing indicates that as a wing slices through a (relatively) stationary air pocket, that imaginary vertical slice of air remains intact - that is, air that travels over the wing will remain in space in the same place relative to the adjacent air that traveled under the wing. In order for this to happen (as the top of a plane's wing has a larger curvature than the underside), the velocity of the air traveling over the wing must be greater, for it to cross the longer cross-sectional length of the wing's top to meet the air traveling from the underside at the same time at the back of the wing. Per B's Equation, you get a proportional decrease in pressure relative to the increase in velocity of the air traveling over the wing. Then you get flight. You get a vertical component of the velocity vector.

The point? You must have air traveling over and under the wings in order to obtain the vertical velocity component. The jet's engines remain fixed in the horizontal plane - there is no way (on a hypothetical perfectly flat surface) those engines alone can produce a vertical velocity vector component. That's fundamental physics. Fixed horizontal velocity cannot produce vertical velocity.

Now, the idea of the conveyor belt is meant to remove the plane's ability to physically move forward through a volume of air. The wings have no way of providing the vertical lift component. They are not moving through air. Your model has the plane immediately moving at twice the speed of the conveyor velt, which invalidates the only thing stated about it, that it matches forward velocity perfectly. Your saying the plane would take off because it would double the conveyor belt's reverse velocity. Sure would - but that's not what the riddle states.

If a car is on a similar conveyor belt with the top down, would your face be blasted with rushing air? Would your Jack Ball flap in the headwind? There wouldn't be any headwind. Headwind isn't moving air, it's you moving through it. If you aren't moving through the air (on a conveyor belt), you aren't getting air rushing past you. If an airplane isn't getting air rushing past it, it does not take off.

But the question never says it wasn't moving forward, just that the conveyor was moving backward.

No offense WS, but what part of "The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction" leads you to believe that the plane could possibly be moving forward? As in, "moving forward through the air?"

Sorry about the bolds and shit, but this is getting a little ponderous. I'm just trying to make it easier to follow.

[XPav]

3. But the question never says it wasn't moving forward, just that the conveyor was moving backward.

Of course it's a "poorly worded" physics problem, it's not supposed to show up on your AP exam, it's supposed to make your friends look dumb when you ask them.

<raises hand>

[DeepT]

How can people be stuck on this question. Jeasus christ!

Look its really simple:

I am on a lawn chair, under an umbrella sipping on a sasperilla. In front of me is this plane / conveyor belt contraption.

Now you max out the planes engies and you have the conveyor belt at full force...

Then look at your watch for a few seconds, then look at the plane. Has it moved? Is it still infront of my lawn chair? If the answer is YES then the plane does NOT take off.

If the answer is NO, then it DOES take off.

The only thing that matters here is the air speed of the plane. Jet engines can not lift a noraml commerical jet off the ground (I am assuming this thing is not a harrier jet, because if it was, this whole question would be moot).

The real question is, will the plane move forward.

A car uses friction with the ground to move forward. So if a car was on this conveyor belt, it would not go anywhere.

However, a plane does not use this to move forward. It uses friction with air, not the ground.

Now lets eliminate the minor fiction of the wheels with the bearings and all that. We only want big friction here. Now lets say the wheels are frictionless, and for all intensive purposes, the ground is frictionless, right? Now the speed of the conveyor belt doesn't matter does it? If its stopped or going a million miles per hour, it has no frictional equivilent here.

Checking back with our car however, if the ground was frictionless, or the conveyor matched it speed prefectly, the car would not move.

Now think about the plane who does not NEED friction with the ground. Infact friction is its enemy, where it is the friend of the car. The engines provide forward thrust against the air, and the ground speed is irrelvent. If the conveyor was matching the speed of the plane in the direction is was going (which starts stopped) it would still make no difference.

At this point you should realise the plane will indeed move forward, the 'ground speed' is completly irrelevent, and since the plane will move forward, it will gain air speed, which will eventually lift the plane off the ground.

Now in real life, there is some friction, so the conveyor would hinder the plane a little, but not enough to matter really.

[Rob Beschizza]

I think I've found a really good illustration of why the plane moves, assuming that the question is properly phrased, etc. etc.

Imagine you are on a skateboard. Your arm is out, placed against a wall. The skateboard is stationary beneath you. You push against the wall, the skateboard moves away from the wall. Easy, OK?

Now, imagine the skateboard is on a treadmill running toward the wall. Your arm is out, holding against a wall. so the skateboard is stationary beneath you, but the wheels are of course running as fast as the treadmill. If you push against the wall, the skateboard moves away from the wall, even if the treadmill is moving much faster than the skateboard.

Yes, the friction still has an effect, and the skateboard soon exhausts the energy from your push, stops, and starts to move back toward the wall. But in the the airplane version of the scenario, the engines provide consistent forward thrust!

Most bolded thread eva!

[Wholly Schmidt]

Now, the idea of the conveyor belt is meant to remove the plane's ability to physically move forward through a volume of air.
Let me stop you there. Where do you see that stated specifically in the question? This, right here, nothing else, is the whole "trick" of the question. A conveyor belt could do that, sure. It's never stated that this conveyor belt is meant to do anything. It proceeds merrily in reverse, oblivious to our expectations. It doesn't intend to do anything, it just does one thing. Moves backward at the rate the plane moves forward.

The wings have no way of providing the vertical lift component. They are not moving through air. Your model has the plane immediately moving at twice the speed of the conveyor velt, which invalidates the only thing stated about it, that it matches forward velocity perfectly. Your saying the plane would take off because it would double the conveyor belt's reverse velocity. Sure would - but that's not what the riddle states.
Here you're getting back into debating specifically Mike or March's points or something, so moving on...

If a car is on a similar conveyor belt with the top down, would your face be blasted with rushing air? Would your Jack Ball flap in the headwind? There wouldn't be any headwind. Headwind isn't moving air, it's you moving through it. If you aren't moving through the air (on a conveyor belt), you aren't getting air rushing past you. If an airplane isn't getting air rushing past it, it does not take off.
Here I've gotta step in again. You are correct, a car in this scenario would not leave you with anything at all flapping in the wind. A car derives its forward thrust from the rotation of its tires. A plane does not. The wheels on a plane rotate as necessary to eliminate friction between the plane and the ground. If that means rotating at speed X against the ground, or speed Y against a conveyor, it doesn't affect forward thrust of the plane one bit because that's being generated by the engines of the plane. Arguably, some versions of the Batmobile would leave something flapping in the wind, but that's neither here nor there.

But the question never says it wasn't moving forward, just that the conveyor was moving backward.
No offense WS, but what part of "The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction" leads you to believe that the plane could possibly be moving forward? As in, "moving forward through the air?"

Sorry about the bolds and shit, but this is getting a little ponderous. I'm just trying to make it easier to follow.
No offense taken at all, and please don't think I'm talking down to you or anyone else in this thread when I respond. Let's try to look at the question in parts without rewording any of it, that way lies madness.

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?
Let me focus on this part:

The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

Ok, so there's a conveyor that's going to match the speed of a plane, plane in one direction, conveyor in the other. This sentence, in isolation, does not imply any relationship between the two (plane and conveyor) other than the hypothetical connection this question is based on. It does not establish the plane is on the conveyor. Bear with me, but would the plane take off it was sitting on a runway next to a conveyer? Of course. The wheels rotate as freely as necessary on the stationary runway to allow the engines, and more importantly, the body of the plane, to not have to worry about friction with the runway.

So how does the situation change if we put back the first sentence? The wheels just have to spin a little faster. That's all. That's the only connection, literal or figurative, between the plane and the runway, the wheels. Which are not responsible for thrust. At all.

[Wholly Schmidt]

This thread is responsible for like an hour and a half of lost productivity at work. This will definitely be the first and last time I do this at work :)

[Enidigm]

God almighty damn. This is going to take all night.

I'm going to respond to each post with it's own individual post so i don't confuse myself.

Whether the plane moves or not, my post count sure is going to go up!

[Wholly Schmidt]

No offense WS, but what part of "The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction" leads you to believe that the plane could possibly be moving forward? As in, "moving forward through the air?"
Saying what I already said a second ago, but dissatisfied with the way I said it, I'll try responding to this better.

What part of that leads me to believe that the plane could possibly be moving forward? None of it leads me to believe that, just like none of that leads me to believe otherwise. No part of the conveyor is acting on the plane's source of forward thrust. The only thing connecting the plane to the conveyer are free spinning wheels, oblivious to who's thrusting who and what's dangling in the wind.

[DeepT]

Ok I logged off and went to bed, and then thought of something else for you poeple who think the plane will not take off..

Its a basic problem with this whole stupid argument, a big ass red flag.

Forget the flying part.

Ok, we got a plane, on a conveyor blet. Its stopped, the belt is stopped.

Now this 'magic' belt perfectly matches the speed of the plane, right?

Lets assume what would have to happen if the belt somehow was able to prevent the plane from moving forward (which is the foundation of it not being able to take off)

So you fire up the engines of the plane to full thrust. Then what?

A paradox...
If the plane moves forward the belt is supposed to match is speed and keep it from moving. There is no lag here, the belt PERFECTLY matches the speed.

If the plane moves forward, then for an instant the belt was not moving at the same speed to counter it. The given is that it does. So this can not happen.

The other choice is the belt does match the speed, and counters the planes movement. But since the planes movement is zero, the belt wouldnt actually move. The end result here, is a plane, at full thrust totally stationary on a non-moving conveyor belt. The brakes are not on, the plane is not super gluded down. Its totally free to roll forward, yet it doesn't. There no physics in the world that will explain that.

So just from logic and basic physics, the scenerio where the plane does not move is impossible.

Since the two possibilites under the condition of 'the plane does not move' are impossible by either "Givens" (in the first case) or "The laws of Physics" (in the second case), we must conclude that the original premis must be wrong.

[Enidigm]

But imagine if, instead of trying to get movement by spinning your upside-down wheels in the air, the car instead had a couple of propellers attached to the roof. In that case, the car would move forward through the water -- even though the car's wheels were unable to get any friction against the air. Planes are the same way: they get their forward thrust by pushing on the fluid (in their case, pushing on the air behind them), not by pushing on the surface beneath their wheels.

MikeSofaer was right about the problem with the frame of reference, and there is an unspoken part of the question. It is the airmass. The only thing that matters, the only point of reference that matters to the plane is it's relative position to the airmass.

And the airmass is related to the earth. So the ultimate frame of reference, the only one that matters, is that we are observing this from the earth, because THAT is the frame of reference to the airmass.

So here, Rywll, you'r wrong. For the exact same reason. Unless the car is floating, the car has settled onto the bottom. Just like a plane sitting on a runway in a lake of air. The propellers won't move the car ANYWHERE because it doesn't have wheels to overcome the friction of GRAVITY. Unless it has enough propulsion to, literally, pick the car up and cause it to fly in the water, without touching the ground. And that is not how a plane flies even by analogy (unless it's a Buck Rogers plane!).

[Enidigm]

Mike, you're pretty confused so let me try and help you out...
3) It could mean the speed of the plane relative to the ground. This would mean that from the point of view of the ground the plane is moving forward at 10 MPH, and the conveyor backward at 10 MPH. From the point of view of the conveyor the earth is moving forward at 10 MPH and the plane is moving forward at 20MPH. The wheels on the plane turn at 20 MPH. This is the only interpretation that makes any sense because a) it uses a definition of "speed" that is sane and b) it does not start by defining everything to be motionless. In this case the plane takes off, but with the wheels spinning at double speed.

Let me ask - how fast is the body of air moving to an observer that is ON the conveyor? Assuming that it is stationary. -10 mph.

Let me ask again, if a car passes a cop heading the opposite direction, both going 70 mph, does he get a ticket for going 140?

Your flaw is in the wheels. The wheels AREN'T turning at 20 mph; their turning at 10 mph. They only APPEAR to be MOVING at 20 mph FROM and observer ON the conveyor.

You've somehow got general relativity mixed and confused with everyday common sense.

[Wholly Schmidt]

The best analogy I've seen is Rob Beschizza's skateboard and the wall, but even then, if the analogy doesn't make it clear to you, starting to argue about the points of an analogy will only end in tears.

[MikeSofaer]

According to your calculations there, when I set a treadmill to spin at 7 MPH, I'm actually running 14MPH? That doesn't make any sense, your colloquialisms be danged.
Your treadmill analogies screw you up because they take as an assumption that there is no forward motion relative to the ground. If you are on a treadmill that's moving at 7mph and you are making progress along it at 7mph relative to the ground then you are going 14 mph relative to the treadmill surface.

If the plane is attempting to move forward at 20mph, per the riddle, the conveyor belt would match perfectly that 20mph in the opposite direction.
Well, the riddle involves the plane's actual speed, not its attempted speed. So it can move forward at 20mph and the conveyor can move at 20mph in the opposite direction.
You're telling me that the only sane definition of speed you can come up with is one where things move twice as fast in one direction relative to what is meant to be equal, opposing speed in the other direction?
I can't parse that. I think you are upset at my use of the (non-inertial, but it doesn't matter, I don't think) frame of reference of the conveyor belt. One way to know whether you have a physics problem right is see if it still makes sense in a different frame of reference.

Are you telling me dynamic equilibrium of motion is impossible? Because that's what this riddle's scenario is a model of - dynamic equilibrium of forward velocity.

I don't know what that means. Is Fnet still zero in dynamic equilibrium of forward velocity?

Now, the idea of the conveyor belt is meant to remove the plane's ability to physically move forward through a volume of air. The wings have no way of providing the vertical lift component. They are not moving through air.
Why would a conveyor belt remove a plane's ability to move forward? The riddle doesn't say it can do that, and in real life it couldn't do that. If you walk along the street at 2 mph a 2 mph headwind doesn't prevent you from making any forward motion.
Your model has the plane immediately moving at twice the speed of the conveyor velt, which invalidates the only thing stated about it, that it matches forward velocity perfectly.
Well, in the FoR of the control tower the speeds are matched, one forward, one back. In the FoR of the belt itself the plane is moving twice as fast as the ground. From the point of view of the air in my walking example, the above guy is moving at 4 mph and the ground is moving at 2mph the other way

If a car is on a similar conveyor belt ...
Well, if it's a ROCKET car with free-spinning wheels ..... These treadmill analogies aren't valid because planes don't accelerate relative to the ground by applying force to the ground, they accelerate relative to the air by applying force to the air. Just like a walker isn't seriously hindered by an equal and opposite head-wind, a plane isn't seriously hindered by an equal and opposite ground-slip.

[Enidigm]

2. The wheels are just there to prevent things from exploding. They don't move the plane down the runway to achieve the speed to take off. I think maybe they're used at ridiculously slow speeds for something like backing into a hanger, or for steering at those ridiculously slow speeds to manuever on to the runway, but they have nothing to do with getting the plane into the air other than their role to reduce, to the extent possible, the friction between the plane and the ground. You could replace them with skiis, pontoons, huge sticks of butter, whatever. You just need something to allow the plane to move along the ground until part 1 takes over with enough air moving past the wings for lift-off and elimination of that friciton with the ground; something better suited than the underside of the plane (that would be the explosion route).

Ok, Wholly Schmidt, you're the closest to getting the plane off the ground. It really depends upon how convoluted you make the question, and our frame of reference.

Wheels don't make the plane move at all. But without wheels, the plane isn't going anywhere.

So what happens is this becomes a question of friction which is not at all what the original question was about. You're reading into this into it.

The problem is that we know nothing of the conveyor. THIS IS ESSENTIAL. So, you say, the conveyor is moving -50, the plane has an IMPULSE of +50. The wheels, now, it doesn't matter how fast they move. The movement of the ground below doesn't effect the speed of air moving through the propellors THEREFORE the plane moves foward and takes off.

The problem is that WE CAN'T ASSUME that the wheels reduce friction. We can't assume that the conveyor doesn't increase friction.

All of these additional factors were assumtions that you've brought into the question incorrectly.

The original question is that saying, essentially, that RELATIVE TO THE GROUND the plane remains stationary. Therefore, it can't fly. You say "wait!" and bring all sorts of frictional cooefficients into it that AREN'T DESRCIBED. So by making these assumtions, we've left the boundaries of the original question.

[Wholly Schmidt]

Just like a walker isn't seriously hindered by an equal and opposite head-wind, a plane isn't seriously hindered by an equal and opposite ground-slip.
I like that. Succinct.

[Enidigm]

I think I've found a really good illustration of why the plane moves, assuming that the question is properly phrased, etc. etc.

Imagine you are on a skateboard. Your arm is out, placed against a wall. The skateboard is stationary beneath you. You push against the wall, the skateboard moves away from the wall. Easy, OK?

Now, imagine the skateboard is on a treadmill running toward the wall. Your arm is out, holding against a wall. so the skateboard is stationary beneath you, but the wheels are of course running as fast as the treadmill. If you push against the wall, the skateboard moves away from the wall, even if the treadmill is moving much faster than the skateboard.

Yes, the friction still has an effect, and the skateboard soon exhausts the energy from your push, stops, and starts to move back toward the wall. But in the the airplane version of the scenario, the engines provide consistent forward thrust!

Most bolded thread eva!

Bad analogy though. Because the treadmill isn't a "giant magic gay conveyor belt". As soon as you pushed foward, the treadmill GOT FASTER. That is the magic conveyor belt.

[MikeSofaer]

How fast is the body of air moving to an observer that is ON the conveyor? Assuming that it is stationary. -10 mph.
Yes, that's right.

If a car passes a cop heading the opposite direction, both going 70 mph, does he get a ticket for going 140?
Not if the cop is honest.

Your flaw is in the wheels. The wheels AREN'T turning at 20 mph; their turning at 10 mph. They only APPEAR to be MOVING at 20 mph FROM and observer ON the conveyor.
I think I confused you. Fundamentally wheels don't turn at a speed, they turn at an angular velocity. Any observer in an inertial frame will observe the same angular velocity and wheel radius(Since you brought it up, only true before Relativity). Thus all observers must agree on the "speed" at which tire moves across conveyor.

You've somehow got general relativity mixed and confused with everyday common sense.
Changing reference frames is Newton. GR doesn't enter into it. SR, maybe, if things start going fast enough.

I can't figure out where you were going with this, but I hope I've adressed your individual points.

[MikeSofaer]

Wheels don't make the plane move at all. But without wheels, the plane isn't going anywhere.
Seaplanes? Can't take off.

[MikeSofaer]

I like that. Succinct.
Thank you! OK, Oblivion is done installing. With luck I won't post for a while.

[Wholly Schmidt]

Ok, Wholly Schmidt, you're the closest to getting the plane off the ground. It really depends upon how convoluted you make the question, and our frame of reference.

Wheels don't make the plane move at all. But without wheels, the plane isn't going anywhere.

Ok, I'm with you, basically. I mean, the plane would go somewhere, but it wouldn't make it off the ground before scraping along the runway sets it on fire.

So what happens is this becomes a question of friction which is not at all what the original question was about. You're reading into this into it.

I don't think I'm reading anything into it. Friction is always there. The wheels reduce most of the friction with the runway to allow the plane to leave the ground in normal circumstances. All we're asking of them with the conveyor in the mix is that they spin a little faster, which will mean a little more friction in the bearings and whatnot. We could split hairs and point out that it would therefore take a little more thrust from the engines than normal circumstances, but I'd hardly think that would stop it from taking off. I hope you'd agree that's trivial and nitpicking, we might as well start asking if the plane has enough gas for the trip down the runway, if it has a pilot, whatever. Friction with the air itself is unchanged, runway or conveyer, so that doesn't need to enter into things, which again, I think you'll agree. So I don't see how I'm reading anything into it.


The problem is that we know nothing of the conveyor. THIS IS ESSENTIAL. So, you say, the conveyor is moving -50, the plane has an IMPULSE of +50. The wheels, now, it doesn't matter how fast they move. The movement of the ground below doesn't effect the speed of air moving through the propellors THEREFORE the plane moves foward and takes off.

Right, though I'm not sure what you mean by impulse I think from context you're correctly representing my argument.

The problem is that WE CAN'T ASSUME that the wheels reduce friction. We can't assume that the conveyor doesn't increase friction.

If we can't assume the wheels reduce friction, than I can't assume the next flight I get on will leave the ground. Like I said above, the wheels are only there to reduce friction (as this all relates to the takeoff scenario), it's what they always do, and there's no reason they wouldn't do the same on a conveyor.

All of these additional factors were assumtions that you've brought into the question incorrectly.

Like I said, I don't think I'm bringing anything to the question that isn't already there and relevant.

The original question is that saying, essentially, that RELATIVE TO THE GROUND the plane remains stationary. Therefore, it can't fly. You say "wait!" and bring all sorts of frictional cooefficients into it that AREN'T DESRCIBED. So by making these assumtions, we've left the boundaries of the original question.
The original question is if, relative to the ground, the plane remains stationary. That's what we're here to figure out, you can't start with the belief that the question has ruled that out and get to where I am. That's your problem. Read the question as many times as you need until you realize that.

[Enidigm]

But here you're confused. Lets say angular velocity instead?

You've said, essentially, that by changing the frame of reference we've changed the angular velocity of the wheels. Which is exactly the opposite of what you've just purported to desire.

[Enidigm]

The original question is if, relative to the ground, the plane remains stationary. That's what we're here to figure out, you can't start with the belief that the question has ruled that out and get to where I am. That's your problem. Read the question as many times as you need until you realize that.

It's important because what does it mean by speed, and to what frame of reference?

Here we're at a loggerheads; but i'd contend that the only important frame of reference is the AIRBODY. Because it is airspeed that gets a plane to fly, right?

So, from the perspective of the air: "The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction."

It doesn't matter how much the wheels reduce friction. They might be spinning at 20x their normal speed. If it's "perfectly matching" it doesn't mean it's going the same speed! That is, the actual conveyor belt. It just MATCHES the acceleration of the plane, it doesn't equal it. It goes as fast as it has to, (in your view) to keep up with the wheels. To keep it stationary.

[Wholly Schmidt]

I just deleted my last post, hopefully you weren't in the middle of quoting it and responding, because after rereading I saw the point you were trying to make, I just don't have time to respond at the moment.

[Wholly Schmidt]

If it's "perfectly matching" it doesn't mean it's going the same speed! That is, the actual conveyor belt. It just MATCHES the acceleration of the plane, it doesn't equal it. It goes as fast as it has to, (in your view) to keep up with the wheels. To keep it stationary.

The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

That's how it's originally stated. If you decide matching means the conveyer will do what it takes to keep the plane in the same place, that's you bringing that into the equation, and you starting from a different point from me, which we agree leaves us at loggerheads. In the original statement, I don't think you can safely interpret matching to mean anything other than equaling.
Just to humor you, if we take your interpretation of the question, the conveyer is going to do everything it can to match--to stop movement of the plane, not just equal its speed, we're going to end in explosions again. The wheels will still in no way act to stop the plane from moving forward other than that negligible bearing friction. Your conveyer's going to quickly go from zero to ludicrous speed, and we're probably going to blow the tires or melt the bearings as it tries to keep up with a force (the engines) that it has no direct means to affect.

[Wholly Schmidt]

Or, sort of as I put it earlier, could this part of the question:

The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

Be true of a conveyer and a plane if the plane was on the runway and the conveyer was just nearby for observation? Of course it could. Your interpretation of matching speed is implying intent on the part of the conveyer that's never stated.

[Rob Beschizza]

Bad analogy though. Because the treadmill isn't a "giant magic gay conveyor belt". As soon as you pushed foward, the treadmill GOT FASTER. That is the magic conveyor belt.

It doesn't matter much how fast the treadmill goes, because the treadmill CAN'T EXERT FORCE ON THE PLANE through the wheels, except for friction. The only force that matters is the engines vs. the air: the wheels exist insulate the plane from the treadmill/ground, as far as is possible (there has to be some friction, yes, but it's not enough). So the treadmill moves faster in response to the thrust? It doesn't matter: the wheels press rubber against and move 1-to-1 with the treadmill/conveyor, so they move faster. But the wheels are oiled slick ball bearing near-frictionless to the plane, so the plane doesn't feel much of it at all.

You could have a stationary airplane on a treadmill: even with no thrust at all, if you fire that treadmill up fast enough, the plain will just stay still for a while until friction builds enough momentum to start moving it backwards.

Here's another analogy, maybe closer to the original.

Imagine Luke Sywalker in his hovercar, hovering over a conveyor . If he turns his forward thrust on, the conveyor starts to move in the opposite direction at the same speed. Does the hovercar stay still? Of course not! It's not even attached to the conveyor.

The airplane analogy is in principle the same, because even though there are wheels instead of a hover-field, the wheels have little role in conducting energy between the treadmill and the plane. The engines' forward thrust is not transmitted to the ground through the wheels, but against the air, just like the hovercar. And while friction ensures some iof the conveyor's movement is transmitted back to the plane (unlike the hovercar, which suffers no friction), that friction is no-where near equal to the force of the thrust, even if the conveyor is moving as fast as the plane. In fact, the conveyor could move twice as fast as the plane: the plane can still push itself forward against the air, given enough thrust pushing against the air.

The plane always has the air to push itself against, and wheels that let it slide over the ground, albeit with a friction penalty. The conveyor however, even blasting along, can't get a grip on the plane to slow the bastard down. All it can do it turn the plane's wheels, which just don't rub hard enough on the plane to slow it enough.

Now, here's how you stop the plane: Let the conveyor move fast enough to generate enough friction in the wheels to equal the THRUST of the plane, regardless of whatever speed it's attained. Such a speed would be many times the plane's forward speed.

See how that subtly changes the equation and reveals how the original pulls the wool over our eyes by neatly equalizing relative speeds, instead of equalizing the actual force the conveyor and the plane are exerting on one another?

The best thing about this thread is being able to say thrust. Unh!

We need a thread that likewise permits the legitimate use of girth.

[MikeJ]

Nearly a hundred posts later... wow. I think Wholly Schmidt is a lot more patient that I would be. Maybe this will all be more clear after the holdouts have a good night's sleep.

[Squirrel Killer]

...the answer is a whole lot easier.

The plane's engine's are providing thrust. The plane's wheels are freewheeling. The wheels are simply spinning at roughly twice the speed they normally would. The plane lifts off.

[Wholly Schmidt]

The airplane analogy is in principle the same, because even though there are wheels instead of a hover-field, the wheels have no role in conducting energy between the treadmill and the plane. The engines' thrust is not transmitted to the ground through the wheels, but against the air, just like the hovercar. And while friction ensures some iof the conveyor's movement is transmitted back to the plane (unlike the hovercar, which suffers no friction), that friction is no-where near equal to the force of the thrust, even if the conveyor is moving as fast as the plane.
Let me step in and see how well I understand what Gene is saying. I believe Gene's point is that the wheels aren't the same as hovering, because there is that little bit of friction, and that the conveyer will spin as fast as it has to to get that little bit of friction high enough to stop the plane from moving forward. Which I think is wrong, but that's what he's saying. That's what we need to address to win Gene over, he's not answering the same question we are (or in my opinion, the one that was asked).

[Ben]

No offense, Bill, but downside of your overthetop patronizing writing style is shown right about a-here:

Now, the idea of the conveyor belt is meant to remove the plane's ability to physically move forward through a volume of air.

No, the point of the conveyor belt is to trick people who don't think things through all the way into being wrong.


"The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction" leads you to believe that the plane could possibly be moving forward?

Uh, what part about it leads to you to believe the plane wouldn't move?

Plane goes->, wheels go-->, belt goes<-. Don't try to read into the motivations of the conveyor belt(???), what it does is spin. It's all it does. If the plane goes 10mph east, the belt spins 10 mph west. The plane still goes 10mph east, mind you, because wheels spin. They spin at 20mph in this example.

The only legitimate reason the plane wouldn't take off is mechanical limitations of the landing gear. Maybe spinning at 2x takeoff speed would break them. As noted, by, oh, 3 or 4 people by now, that's not the point of the question.

[Ben]

Alright, I have an even sweeter and definitive example:
Say the plane is off. It has the usual fantastic frictionless neverbreaking landing gears and there are no brakes. I turn the conveyor belt on going 10mph east.

How fast does the plane go?

[Enidigm]

Let me step in and see how well I understand what Gene is saying. I believe Gene's point is that the wheels aren't the same as hovering, because there is that little bit of friction, and that the conveyer will spin as fast as it has to to get that little bit of friction high enough to stop the plane from moving forward. Which I think is wrong, but that's what he's saying. That's what we need to address to win Gene over, he's not answering the same question we are (or in my opinion, the one that was asked).

Well, i say this because i think the question isn't asking about the wheels, it's just about airspeed. If you ask about the wheels, then you ask about things like slippage, ect. To me it's a cheap question that allows you to assume certain unknown variables.

If that's the trick - that the wheels reduce friction because they aren't force of motion, and that the treadmill only matches the groundspeed of the tires - then i submit and say the plane takes off. I didn't think that was the question being asked. I'm not trying to argue the physics of it, only the question itself. Athough, to be fair, you could say that the treadmill matched the speed/rotation of the tires...

In fact, if you're measuing groundspeed by the tires, well, then the plane doesn't move at all. In other words, if the plane is "moving" at 50 mph because the tires are rotating at 50mph, then the treadmill would move at -50mph. In fact, isn't this the right answer? How else would you measure groundspeed except by the rotation of the tires? Because the tires aren't 'slipping' in normal use. Again! You see, the question is poorly worded unless you assume certain conditions that let your explanation be the right one.

It's like in Junior High school (many years ago, but i still remember it) we had a question that said "plane flying in a 40 mph headwind, and a 40 mph tailwind. It's flying at X mph for 2 hours to it's destination and back. How long did it take?
No one gets it right. The teacher then smarmily replies "Oh, it's ___! Because the FAA won't let planes travel faster then ___ miles per hour".

[Rob Beschizza]

Let me step in and see how well I understand what Gene is saying. I believe Gene's point is that the wheels aren't the same as hovering, because there is that little bit of friction, and that the conveyer will spin as fast as it has to to get that little bit of friction high enough to stop the plane from moving forward. Which I think is wrong, but that's what he's saying. That's what we need to address to win Gene over, he's not answering the same question we are (or in my opinion, the one that was asked).

To prove how insignificant the friction is, think of the skateboard again. You're on the skateboard, on the treadmill, your arm held out against the wall so you stay still while the treadmill runs.

Thge treadmill has complete control of the wheels. The treadmill and the wheels are 1 to-1 in lockstep. But how much friction is there between the wheels and the rest of the skateboard, and you?

Find out. Turn up the treadmill. Make the bastard go 5 MPH, then 10, then 15. By God you'll be scared, but your arm holding you in place against the will feel little extra force from the treadmill, so long as the wheel bearings are in shape and oiled up.

The airplane is the same. To stop it, the conveyor must produce enough friction to match the thrust. It could be done, yes, but the convoyer would have to move DAMN fast, many times faster than the plane, for the same reason that your treadmill would have to go stupendously fast to make life difficult for the arm holding the skateboard in place on it.

In fact, anyone with a skateboard and a treadmill could try this. Just sit by the treadmill and put your hand behind the skateboard. Turn the treadmill on. Even at fast speeds, even with the wheels spinning like crazy, it's not hard to hold the skateboard in place. You don't need to be pushing the skateboard forward as fast as the treadmill is moving back. There's so little friction coming up through the wheels, you could push the skateboard forward with your pinkie.

[Rob Beschizza]

To me it's a cheap question that allows you to assume certain unknown variables.

Bingo. The question doesn't clue you into the wheels. It distracts you into thinking that it's a tautology, that the treadmill is moving however fast it takes to keep the plane motionless (see Bill's perfect physical expositions on this very interpretation), when it sneakily really only said the treadmill was moving as fast as the plane, regadless of its thrust. That's the gay magic: the wheels. We know they are there, and the question tricks us by:

1) Letting us assume the wheels are not freewheeling. We think wheels, we think axles and gears and brakes and a powertrain intimately controlling the movement of the wheels. But with planes taking off, the wheels are kept as frictionless and freewheeling as possible.

2) Telling us it's an airplane, which is something so big and heavy we assume massive weight and thus massive friction. But the friction is still insignificant, because in this case, it's fighting 30,000 pounds of thrust and the very best in well-oiled bearings.


Hmm. Friction. Well-oiled bearings. The thread that just keeps giving.

[Enidigm]

Well again though - if we're talking about the plane's speed, what is it's groundspeed?

As fast as the body of the plane is moving, or as fast as it's wheels are turning?

[MikeSofaer]

Well again though - if we're talking about the plane's speed, what is it's groundspeed?

As fast as the body of the plane is moving, or as fast as it's wheels are turning?
Like I said last page, if you measure speed by the wheels then you are measuring the plane's speed relative to the conveyor, and thereby defining the plane to be motionless relative to the ground. That's idiotic.

The plane's speed is the speed of the center of mass relative to the ground, which is approximately equal to the speed of the center of mass relative to the air.

So the plane moves at x relative to the ground, and the conveyor moves at -x relative to the ground. That satisfies the initial assumption about speed matching. This means the plane moves at speed 2x relative to the conveyor, which isn't a big deal because the wheels aren't geared.

[Bill Dungsroman]

Would all of you deciding that for whatever unknown reason you think it's a good idea to add a related question to the one already making us sodomize housepets and do our rendition of Stellan Skarsgaard's wearily nihilistic Saxon Warrior King from King Arthur ("Burn it all.") mind waiting until we at least half-settle the fucking one in front of us? Thanks!

Okay, would someone from the "She'll fly!" camp mind telling me how air ends up moving past the plane's wings to let it gain lift? Because no matter how many times I read

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

I don't see shit about its wheels.

And I'm not being condescending, you fucking dimwitted asshats (kidding!). Not everyone took, nor taught, physics.

[Nick Walter]

I guess one could assume that the plane's body is just sitting on the conveyer belt directly, but that's rather silly. Pretty much all planes have wheels, so it's a reasonable assumption to make.

If we want to assume that the plane is in direct contact with the belt without wheels being in between then no, the plane won't take off. It will instead be shredded by friction with the belt.

[MikeSofaer]

Bill, the conveyor is matching the speed of the plane. It seems like you are reading it as saying that the conveyor matches the speed of the wheels, which would mean the plane can't be moving relative to the ground.

But if the speed of the plane means, well, the speed of the plane, then the conveyor zips along backwards under it just fine.

Since you like treadmills:

If a child is running at 4 mph relative to a moving walkway, and the walkway is moving him backward at 2 mph, what is the "speed of the child"? You might say 4 mph, but really 2 mph makes the most sense, as that is how fast his dad needs to stroll along next to the walkway with the bags.

[Squirrel Killer]

Okay, would someone from the "She'll fly!" camp mind telling me how air ends up moving past the plane's wings to let it gain lift? Because no matter how many times I read

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

I don't see shit about its wheels.

And I'm not being condescending, you fucking dimwitted asshats (kidding!). Not everyone took, nor taught, physics.
Well, first off, if no air moves past the wings, wouldn't that mean the plane is stationary, and thus the speed and acceleration of the plane, and consequently the conveyer belt, be 0 mph?

But really here's what it comes down to, and why the shit about the wheels come in to play: the thrust from the plane generates forward force on the airframe, the wheels are only acting as support. They're ball bearings. Spin them as fast as you want, unless they're braking, they don't have shit to do with the speed of the aircraft.

So the plane winds up its engines which starts the plane moving, which in turn starts the conveyer belt. That cancels out the forward motion of the plane, right? Nope, remember those foot loose and fancy freewheeling wheels? Unless their spin rate is locked to the speed of the plane (which they're not in a real plane), the effort for them to match the difference between the speed of the plane and the speed of the conveyer by simply spinning faster is significantly less them trying to cancel out x thousands of pounds of thrust. If the plane is traveling at 10 mph, the conveyer belt also at 10 mph, the wheels are spinning at a rate that would equal to 20 mph if it was for this crazy contraption we've thought up. Ramp this up until you reach take-off speed. I hope the conveyer belt is long enough.

[fire]

At the air show where I volunteer I saw a plane both take off and land on the roof of a Winnebago that was driving fast down the runway.

[Squirrel Killer]

It must not have had a treadmill on top.

[Wholly Schmidt]

Would all of you deciding that for whatever unknown reason you think it's a good idea to add a related question to the one already making us sodomize housepets and do our rendition of Stellan Skarsgaard's wearily nihilistic Saxon Warrior King from King Arthur ("Burn it all.") mind waiting until we at least half-settle the fucking one in front of us? Thanks!

Okay, would someone from the "She'll fly!" camp mind telling me how air ends up moving past the plane's wings to let it gain lift? Because no matter how many times I read

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

I don't see shit about its wheels.

And I'm not being condescending, you fucking dimwitted asshats (kidding!). Not everyone took, nor taught, physics.
Bill, I've read the question over and over, and I don't see shit about its wings.

Bah, I can't let myself leave this with just my snarky comment. You're not seriously proposing the plane has no kind of landing gear, are you? You don't have to know much about physics to get the question, but you do have to know a little bit about planes. You have to know that air must be moving over the wings to provide lift, which all of us seem aware of. You also have to know the role the wheels (or any landing gear for a plane for whatever its specialty is, pontoons for water, and maybe they really have skiis for arctic planes or something, I don't know. Probably no butter anywhere) have in takeoff. Neither of those is mentioned in the question, we're not pulling this wheels stuff out of thin air any more than you're making up this stuff about the wings.

I'm not sure I'm answering your question, but that's my best stab at what you were asking.

[Rob Beschizza]

Would all of you deciding that for whatever unknown reason you think it's a good idea to add a related question to the one already making us sodomize housepets and do our rendition of Stellan Skarsgaard's wearily nihilistic Saxon Warrior King from King Arthur ("Burn it all.") mind waiting until we at least half-settle the fucking one in front of us? Thanks!

Okay, would someone from the "She'll fly!" camp mind telling me how air ends up moving past the plane's wings to let it gain lift? Because no matter how many times I read

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

I don't see shit about its wheels.

Sure, if we don't assume the freewheeling nearly friction-free wheels, the plane doesn't get air, doesn't get lift. Taking the question literally, the plane just sits like a beached whale on the conveyor, and assuming it is an indestructible airplane, the friction of it against the conveyor might well mean that however fast it grinds forward, the equal and opposite speed of the conveyor keeps it motionless.

However, allowing that the plane has wheels, it gets movement because the thrust against the air propels it forward. In this case, the movement of the conveyor is not sufficient to slow it down, because the wheels spin freely underneath the plane without transmitting the full energy of the conveyor to the plane where it might counteract the forward thrust.

There is some frictive drag, however, because the plane is heavy, and the wheels are, after all, touching and moving against the plane, no matter how well oiled the bearings. So a conveyor moving much faster than the plane might slow it down. But a conveyor only moving at the same speed as the plane is doomed to failure. So long as there are wheels that are freewheeling relative to the plane.

[mouselock]

Now, imagine the skateboard is on a treadmill running toward the wall. Your arm is out, holding against a wall. so the skateboard is stationary beneath you, but the wheels are of course running as fast as the treadmill. If you push against the wall, the skateboard moves away from the wall, even if the treadmill is moving much faster than the skateboard.

Yes, the friction still has an effect, and the skateboard soon exhausts the energy from your push, stops, and starts to move back toward the wall. But in the the airplane version of the scenario, the engines provide consistent forward thrust!


In the airplane example, the treadmill also instantaneously speeds up to counter the increase in velocity, as opposed to the treadmill which runs at constant velocity (0 acceleration). Clearly if you're force balanced to begin with and you impart a force (pushing against the wall) you're going to generate an acceleration. However, if you get an opposing instantaneous acceleration, you're going to be met by a proportional (with the constant of proportionality relative to the frictional transfer coefficient) force in the opposite direction.

Nice way to try to think about it, but not actually the same system at all.

[Wholly Schmidt]

In the airplane example, the treadmill also instantaneously speeds up to counter the increase in velocity, as opposed to the treadmill which runs at constant velocity (0 acceleration). Clearly if you're force balanced to begin with and you impart a force (pushing against the wall) you're going to generate an acceleration. However, if you get an opposing instantaneous acceleration, you're going to be met by a proportional (with the constant of proportionality relative to the frictional transfer coefficient) force in the opposite direction.

Nice way to try to think about it, but not actually the same system at all.
I'd contend that it is the same system where it counts, but that's neither here nor there. Are you in the no-fly camp? Can you explain it in terms of the question originally stated? That's the only thing that's going to help either of us understand each other.

[Rob Beschizza]

In the airplane example, the treadmill also instantaneously speeds up to counter the increase in velocity, as opposed to the treadmill which runs at constant velocity (0 acceleration). Clearly if you're force balanced to begin with and you impart a force (pushing against the wall) you're going to generate an acceleration. However, if you get an opposing instantaneous acceleration, you're going to be met by a proportional (with the constant of proportionality relative to the frictional transfer coefficient) force in the opposite direction.



But it illustrates why the equal instantanous acceleration from the treadmill doesn't get to the plane, where it could oppose the plane's acceleration: lack of friction between the wheels and the plane.

The proportional force that meets the conveyor's acceleration exists, but in the wheels, not in the plane. Though it's not really "force," it's just reciprocal movement caused by the wheels' strong friction against the conveyor, as compared to the wheels' very weak friction against the plane.

The frictional transfer coefficient, as you put it, sucks so bad you'd have to have the conveyor blasting along much faster than the plane to counteract its forward movement.

(Bear in mind that the question rather sneakily suggets a direct connection between the plane and the ground, by telling you that the conveyor reacts exactly to its speed and acceleration. Because it seems like the plane has a causal, phyisical effect on the conveyor, one naturally assumes the same going in the other direction. We don't know what causes the conveyor to speed up in tandem with the plane: it's a situational deus ex, arbitrary and without recourse to the physics actually in play. But isn't it slyly implied the plane's own thrust is being transmitted down through the wheels into the conveyor and pushing it back?)

[mouselock]

I'd contend that it is the same system where it counts, but that's neither here nor there. Are you in the no-fly camp? Can you explain it in terms of the question originally stated? That's the only thing that's going to help either of us understand each other.

I'm in the "It's a fucking vague question and you have to assume something odd about what it means when it says 'The treadmill exactly matches the speed of the plane in an opposite direction.' camp." If you read that to mean that the plane is stationary despite throwing tons of thrust, then it won't fly. If you read that to mean that the linear velocity of the treadmill at the contact of the wheels is the same as the net forward velocity of the plane, then obviously only a tiny fraction of that is being imparted to holding the plane back.

As for the folks saying "Well, if the plane isn't moving forward, then the treadmill doesn't have any speed now does it." I think you're forgetting your basic calculus and the idea of instantaneous impulses. Look at it like this.. at time 0 the plane is trying to move forward and the treadmill exactly counters this. The net velocity is zero. At time x, the plane is trying to move forward and the treadmill has a net velocity of zero (just established) so the plain moves forward y amount at some speed. At time 2x, the treadmill kicks up again because the plane has a speed and offsets the plane's motion again.

Now, let the distance x go to zero, and the plane is permanently and instantaneously stopped from moving. As soon as it starts to gain some forward velocity, that velocity is instanteneously countered. As soon as the this happens, the treadmill stops.. so the plane goes forward again.. and is countered.. and the treadmill stops. It's a steady state system. And this, btw, is why Bill is having issues with all your "common sense" approaches, because the idea of this instantaneous response treadmill is already so ludicrous that there's no real reason to carry over the rest of "real world" physics necessary to make the plane take off. If this treadmill can enforce this instantaneous, no net-impulse response, it can sure as fuck zip around at something clost to the speed of light necessary to impart friction on the wheels sufficient to hold the plane in place.

The problem is just poorly specified.

[mouselock]

But it illustrates why the equal instantanous acceleration from the treadmill doesn't get to the plane, where it could oppose the plane's acceleration: lack of friction between the wheels and the plane.

No, not lack of friction. Diminished friction. If you want to posit some frictionless wheels, have at. I think everyone involved will happily acquiesce that in a world with frictionless wheels, only the sheer will of God himself could keep the plane from lifting off.


The proportional force that meets the conveyor's acceleration exists, but in the wheels, not in the plane. Though it's not really "force," it's just reciprocal movement caused by the wheels' strong friction against the conveyor, as compared to the wheels' very weak friction against the plane.


Dude, the wheels are attached to the plane. Pretty damn firmly too! If you apply 20k newtons to the wheels in the backward direction, you're applying it to the whole plane. They're not an isolated system. If you apply 20k newtons to the very outer edge of the tire of a wheel, you're still applying some fraction of that force to the plane. Yes.. a truckload of that force gets burned up in making the wheel spin (and since force through a distance is energy, and we have to conserve energy, that spinning wheel creates a torque, which is also proportional to the energy). But some of it still transfers to the plane because of the fact that we don't have magical frictionless bearings, wheels, or anything else. Maybe we should assume such magical things from the same place that the magical gay conveyor belt comes from. But it seemed like the problem wanted us only to assume some magical gay conveyor belt. (Which works in one of two ways, each of which have very different implications for the airworthiness of the plane.)


The frictional transfer coefficient, as you put it, sucks so bad you'd have to have the conveyor blasting along much faster than the plane to counteract its forward movement.


Well, that depends entirely on what you mean by "the conveyor goes backwards in proportion to the plane going forward" or whatever the hell stupid way it was vaguely phrased. Which is why you and Mr. D. are at loggerheads here.

But isn't it slyly implied the plane's own thrust is being transmitted down through the wheels into the conveyor and pushing it back?

Not to me. That question is stupid; it's essentially asking "Would a plane take off with frictionless wheels." Yeah, it would, next question. (If it were the wheels driving the conveyor belt backwards, in fact, as the plane lifts off you'll have poorer and poorer transfer, making the condition of the problem in the first place, that the conveyor go backwards at the same "speed", whatever the hell that means, fail continuously the closer the plane got to taking off. There'd have to be some external source driving the conveyor.)

If they'd simply asked "If you put a plane on an infinitely long, frictionless conveyor belt would it be able to take off" it'd be a much simpler question. But I fully suspect at this point they didn't because there's some stupid gotcha trick that they like pulling out at parties.

[Wholly Schmidt]

I'm in the "It's a fucking vague question and you have to assume something odd about what it means when it says 'The treadmill exactly matches the speed of the plane in an opposite direction.' camp." If you read that to mean that the plane is stationary despite throwing tons of thrust, then it won't fly. If you read that to mean that the linear velocity of the treadmill at the contact of the wheels is the same as the net forward velocity of the plane, then obviously only a tiny fraction of that is being imparted to holding the plane back

....(a bunch of stuff here that wasn't in response to anything I'd said, snipped for clarity)...

The problem is just poorly specified.
Yes, it is poorly specified, but that's sort of the point of the trick question, and poorly specified does not mean there's not still a correct way of interpreting it. It just means it's (potentially) harder to figure out.

Again I fall back to breaking the stated problem into parts.

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

The only part of the question that explains the actions of the conveyer belt is the second sentence.

The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.

Anything other than that sentence that you bring into your understanding of the question has no basis outside of your presuppositions. Based on that sentence alone, it doesn't matter if the plane is on the ground, on the conveyer, on the runway, it could actually already be flying for all this part of the problem cares. Wherever that plane is, its speed and acceleration are matched by the runway's speed and acceleration in the opposite direction. So right now, the plane takes off, keeps flying, whatever, the conveyer doesn't do anything to the plane at all.

A plane is on a conveyer belt.

Oh, well now things change, right? Nope. Wheels. As we've agreed, they'd add a little friction to things (as they always do, conveyer or not), but would reduce enough friction to make the conveyers impact on the plane almost exactly as insignificant as the runway's impact on the plane during normal takeoff. She flies.

[Rob Beschizza]

The problem is just poorly specified.

I think it's very well specified to confuse us. The intended answer, is the one you outlined second: "the linear velocity of the treadmill at the contact of the wheels is the same as the net forward velocity of the plane, and obviously only a tiny fraction of that is being imparted to holding the plane back" so the plane can still move forward and take off.

However, it's airplanes, which are big and heavy and apt to make us overestimate frictive drag and the effects of gravity. And its buried in a weird scenario of giant conveyor belts that react magically to the plane's movement, as opposed to simpler, more real-world examples like the skateboard. It's easily phrased so that the intended meaning, "treadmill velocity = plane velocity" can be misinterpreted a dozen different ways as a kind of tautologous "treadmill velocity = whatever it takes to stop the plane." And finally a lot of stuff is missing, so that you have to actally assume necessary mechanical components not even mentioned in the question, like freewheeling wheels -- allowing us the mistake of assuming fixed wheels (as on a car's axle), or no wheels (Bill understands this entire problem better than anyone and is toying with us!).

[Wholly Schmidt]

Did everyone go to sleep? I'm going to dream of conveyers.

[Rob Beschizza]

Did everyone go to sleep? I'm going to dream of conveyers.

I actually just nodded off in front of the TV for a few minutes, and dreamt of my huge longhaired german sherpherd/eurasian dog, who looks rather like a giant 80 lb hamster, running in a huge hamster wheel that for some reason was set up in the lounge.

That's one bird that won't fly, I guess.

[Wholly Schmidt]

I actually just nodded off in front of the TV for a few minutes, and dreamt of my huge longhaired german sherpherd/eurasian dog, who looks rather like a giant 80 lb hamster, running in a huge hamster wheel that for some reason was set up in the lounge.

That's one bird that won't fly, I guess.
Give me another 15 posts, I'll have it in the air.

[nutsak]

http://www.deadbored.net/qt3/conveyorwing.jpg

So long as the airflow over the wing is greater than the drag then it'll fly. (You can see this effect in radio controlled aircraft that can take off from a standing start). I'll be happy to make an animated gif to explain it better if my shitty diagram doesn't help.

[Rob Beschizza]

I just don't see how it could work, sorry! Maybe Schmidt can get her off the ground.

http://www.celestialmechanics.com/avatar/con2.jpg

[TriggerHappy]

If Ben and SquirrelKiller's explanations don't convince anyone in the no-fly camp, I don't think anything will.

[Houngan]

Good grief, let's settle this:

Original question + assumption: Plane on conveyor, not moving. No flight.

Original question, erroneous assumption removed: Plane on a conveyor, somebody hits the throttle, plane moves forward on conveyor relative to ground because wheels are free spinning, gains airspeed, plane takes off.

Original question +/- assumption, + experimental fagdancing: pointless.


The crux of it is this: speed of wind over wings generates lift. All the conveyor crap just degrades into arguing about how to set up the thought experiment so it works/doesn't work. To make a plane fly, there has to be relatively speedy wind hitting the wings, regardless of if the plane is moving, the wind is moving, or a combination.


H.

[MarchHare]

I think we're arguing five pages worth of semantics over an interpretation of a question which most of us agree is poorly worded to begin with. When it says "The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction," what does it mean by "plane"?

Those in the "no fly" camp assume it means the wings, and that the conveyor will move in such a fashion as to prevent the aircraft from gaining any airspeed (airflow relative to the wings); therefore, no lift is generated and the plane doesn't takeoff.

Those in the "fly" camp, assume that by "plane" the question means "the plane's landing gear", in which case the aircraft does indeed gain forward momentum, has airflow over its wings, and takes off.

So it turns out that both answers can be equally valid depending on your interpretation of the question, and we don't know what the author's original intention was. I've asked a few other friends about this since yesterday. One was a pilot, one was an engineer, and two were science geeks. The engineer and pilot both chose the first interpretation and said "no fly" whereas the two physics geeks chose the latter and said "fly". I'm not sure if that means anything, but I thought it was kind of interesting.

[MikeJ]

When it says "The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction," what does it mean by "plane"?

Those in the "no fly" camp assume it means the wings, and that the conveyor will move in such a fashion as to prevent the aircraft from gaining any airspeed (airflow relative to the wings); therefore, no lift is generated and the plane doesn't takeoff.

Those in the "fly" camp, assume that by "plane" the question means "the plane's landing gear", in which case the aircraft does indeed gain forward momentum, has airflow over its wings, and takes off.


As far as I can see, the argument isn't about what 'the plane' means, but what 'match the speed and acceleration' means.

If you assume that the plane moving to the right at x mph means the conveyor moves to the left at x mph (all relative to a stationary observer and the still air), then of course the plane takes off. That seems like the most natural interpretation to me.

If you assume 'match the speed and acceleration' means the conveyor moves in whatever fashion is needed to keep the plane from moving (relative to the stationary observer and the still air) then of course the plane can't take off. This interpretation seems like quite a stretch of the original phrasing to me.

[TriggerHappy]

As far as I can see, the argument isn't about what 'the plane' means, but what 'match the speed and acceleration' means.

If you assume that the plane moving to the right at x mph means the conveyor moves to the left at x mph (all relative to a stationary observer and the still air), then of course the plane takes off. That seems like the most natural interpretation to me.

If you assume 'match the speed and acceleration' means the conveyor moves in whatever fashion is needed to keep the plane from moving (relative to the stationary observer and the still air) then of course the plane can't take off. This interpretation seems like quite a stretch of the original phrasing to me.

Exactly. Especially since the conveyor belt would have to accelerate, what? 10? 100 times faster than the plane in order for the wheel friction to counteract the engine thrust.

[Wholly Schmidt]

I think we're arguing five pages worth of semantics over an interpretation of a question which most of us agree is poorly worded to begin with. When it says "The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction," what does it mean by "plane"?

Those in the "no fly" camp assume it means the wings, and that the conveyor will move in such a fashion as to prevent the aircraft from gaining any airspeed (airflow relative to the wings); therefore, no lift is generated and the plane doesn't takeoff.

Those in the "fly" camp, assume that by "plane" the question means "the plane's landing gear", in which case the aircraft does indeed gain forward momentum, has airflow over its wings, and takes off.

So it turns out that both answers can be equally valid depending on your interpretation of the question, and we don't know what the author's original intention was. I've asked a few other friends about this since yesterday. One was a pilot, one was an engineer, and two were science geeks. The engineer and pilot both chose the first interpretation and said "no fly" whereas the two physics geeks chose the latter and said "fly". I'm not sure if that means anything, but I thought it was kind of interesting.
I've agreed it's poorly worded, but ultimately I don't think that lends validity to the no-fly camp, as I stated. I just think it confuses things until you understand the question. I don't know any better way to explain the question than by breaking it down like I did in my last post before this, so if you can't understand or agree with that, we're stuck.

[MikeSofaer]

In order for the plane to not fly you need to read "speed of the plane" as meaning the plane's speed relative to the conveyor belt. I don't think that's valid, so the right answer is that the plane flies.

[Squirrel Killer]

Those in the "no fly" camp assume it means the wings, and that the conveyor will move in such a fashion as to prevent the aircraft from gaining any airspeed (airflow relative to the wings); therefore, no lift is generated and the plane doesn't takeoff. (my emp.)
Why would they think that when the question clearly states that the conveyor simply matches the plane's speed. Match speed != Run at a speed that prevents plane from gaining any airspeed.

Maybe this will make things more clear...
http://img130.imageshack.us/img130/7324/conveyerbelt0yt.gif (http://imageshack.us)

[Wholly Schmidt]

Is Rob's Shaggy-hamster-dog powering the magical gay treadmill with his wheel?

[Rob Beschizza]

This lunchtime I am going to win the thread, and I'm going to do it by getting hamster dog onto a real life treadmill and taking a photo of her.

[Squirrel Killer]

Is Rob's Shaggy-hamster-dog powering the magical gay treadmill with his wheel?
Well, what do you know, it is.
http://img66.imageshack.us/img66/2737/conveyerbeltzoom3xw.gif (http://imageshack.us)

[Chris Nahr]

Does the amount of snakes on the plane make any difference regarding its take-off speed?

[Squirrel Killer]

Does the amount of snakes on the plane make any difference regarding its take-off speed?
Only if they twist themselves into a Mobius strip.

[Rob Beschizza]

Does the amount of snakes on the plane make any difference regarding its take-off speed?

They merely constrict its movement.

[Enidigm]

Ah, but the game's not over, just yet. I have one last dart to throw before i concede.

I just can't elaborate right now at work. But i'll give you all a hint: acceleration.

[MarchHare]

The magical gay conveyor belt "has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction". Speed, of course, is relative, so in order to properly answer the question we need to know what speed the conveyor belt is matching and in relation to what. Therein lies the ambiguity in this question.

Pilots naturally concern themselves only with airspeed, thus it was logical to assume the conveyor belt was matching the rate at which the airflow was moving over the wings, thus there was a net effect of zero airflow, and we get no lift.

It's not necessary to make up some scenario with a magical gay conveyor belt, though. We already have a similar case with seaplanes and water currents. Suppose you have a seaplane revving its engine at full throttle, which on still water would give it a maximum speed of 100 knots. Rather than still water, though, we have a 100 knot current going the opposite direction of the plane. Assume no wind. Relative to the water, the plane is moving at a speed of 200 knots. Relative to an observer on the shore, the plane is not moving at all. Relative to the air, the plane isn't moving either, therefore there's no net airflow over the wings and no lift.

So how is that scenario different from the magical gay conveyor belt?

[Wholly Schmidt]

The magical gay conveyor belt "has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction". Speed, of course, is relative, so in order to properly answer the question we need to know what speed the conveyor belt is matching and in relation to what. Therein lies the ambiguity in this question.

Pilots naturally concern themselves only with airspeed, thus it was logical to assume the conveyor belt was matching the rate at which the airflow was moving over the wings, thus there was a net effect of zero airflow, and we get no lift.

No no no NO nO NO nononono-no.

Assume the conveyor belt matches the rate at which the airflow was moving over the wings? Ok, I'm with you. But the conveyer belt, no matter how fast it is moving, is having almost no EFFECT on the airflow over the wings, even if it's MATCHING it. The conveyer matching the rate of airflow over the wings does not create net zero airflow, because the conveyer is ONLY ACTING ON THE WHEELS.

It's not necessary to make up some scenario with a magical gay conveyor belt, though. We already have a similar case with seaplanes and water currents. Suppose you have a seaplane revving its engine at full throttle, which on still water would give it a maximum speed of 100 knots. Rather than still water, though, we have a 100 knot current going the opposite direction of the plane. Assume no wind. Relative to the water, the plane is moving at a speed of 200 knots. Relative to an observer on the shore, the plane is not moving at all. Relative to the air, the plane isn't moving either, therefore there's no net airflow over the wings and no lift.

So how is that scenario different from the magical gay conveyor belt?
And we're back to answering other questions. Lovely. It's different only because I think the river acting on the pontoons creates more friction than wheels on a runway. The pontoons, like any boat or something, are going to be designed to have the least resistance possible with the water, so even with engines cut, if the river starts kicking along at 100 knots, the plane's going to take a while to reach 100 knots because a lot of that water will be sliding past the pontoons. It's only the gradual transfer of that friction into inertia that would cause it to gain speed to eventually almost match the river speed (air resistance would keep it from ever moving at the same exact speed of the river). So fire up the engines at that still-water-100-knots speed, and it's not going to reach 100 knots, but it's not going to be at a standstill either. It will be moving forward. Maybe not fast enough to launch the plane, but it might.

Wrong question anyway though.

[Squirrel Killer]

The magical gay conveyor belt "has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction". Speed, of course, is relative, so in order to properly answer the question we need to know what speed the conveyor belt is matching and in relation to what. Therein lies the ambiguity in this question.
There is no reasonable reading of "special system that will perfectly match the speed and acceleration of the plane in the opposite direction" that means "special system that ensures the plane stays motionless." Why? Because in order to do so, it would have to exceed the speed of the plane, not just match it. It would have to exceed it so much that the conveyor belt transmits, through the landing gear, as much force as the engines develop. Think of it this way, the plane develops 80 hojillion newtons of force, the most force the conveyor belt can transfer to the plane is equal to maybe twice what the plane receives, as transmitted through the landing gear, from a normal runway right before it takes off.

It's not necessary to make up some scenario with a magical gay conveyor belt, though. We already have a similar case with seaplanes and water currents. Suppose you have a seaplane revving its engine at full throttle, which on still water would give it a maximum speed of 100 knots. Rather than still water, though, we have a 100 knot current going the opposite direction of the plane. Assume no wind. Relative to the water, the plane is moving at a speed of 200 knots. Relative to an observer on the shore, the plane is not moving at all. Relative to the air, the plane isn't moving either, therefore there's no net airflow over the wings and no lift.

So how is that scenario different from the magical gay conveyor belt?
Because friction from water on pontoons > friction from conveyer transmitted through landing gear. Sea planes are designed to take off despite that friction, landing gear is designed to eliminate enough of it.

[Houngan]

Ah, but the game's not over, just yet. I have one last dart to throw before i concede.

I just can't elaborate right now at work. But i'll give you all a hint: acceleration.

Let me jump in front of that: acceleration doesn't matter, only wind speed across the wing. It can take you a year to get up to 200mph, or whatever takeoff velocity is, but you ain't moving 'til you (meaning the plane, wing, and wind) get there.

H.

[MikeSofaer]

Pilots naturally concern themselves only with airspeed, thus it was logical to assume the conveyor belt was matching the rate at which the airflow was moving over the wings, thus there was a net effect of zero airflow, and we get no lift.
That's some pretty tortured logic. The conveyor matches the airspeed, ok. But that doesn't mean net 0 airspeed. In fact the only time those two statements are compatible is if the conveyor belt isn't moving and the plane is off. You are assuming that the conveyor belt moves the plane backwards, but there is no reason that it should.

[dannimal]

This may well be the stupidest thread on the entire intarweb.

[MarchHare]

This may well be the stupidest thread on the entire intarweb.

Sadly, it's not alone.

If you google for the topic, you'll find a few other forums that have a similar thread on this subject just as stupid as this one.

[Bill Dungsroman]

So, after all this exhaustive research, we've agreed that we're all going to find where ranvarian lives and collectively kick his ass?

...brilliant.

[Saxman_72]

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?

Yes, because a conveyor belt moving at an equal velocity but opposite direction beneath the plane won't prevent it from moving. The conveyor belt could likely even surpass the velocity of the plane and it wouldn't make a difference. It's not acting in direct opposition to the plane itself, but on components of the plane which are specifically designed to reduce friction and are largely irrelevant to the motion of the plane.

For those of you thinking that the plane will remain absolutely stationary, are you nuts? Do this simple test - put two skateboards on top of one another. Push the top one in one direction and the bottom one in the opposite direction at the exact same time (or rig up little booster rockets on them, who the fuck cares). In any event, that top skateboard (the plane) certainly isn't going to remain motionless. The only way it could would be if the bottom one (the conveyor belt) was moving significantly faster than it. But it can't, it can only match it (according to the posed question). Therefore, they both move.

[magnet]

Pilots naturally concern themselves only with airspeed, thus it was logical to assume the conveyor belt was matching the rate at which the airflow was moving over the wings
Right.

Relative to the water, the plane is moving at a speed of 200 knots.
Wrong. In your example, it's moving at a speed of 100 knots relative to the water. But that's neither here nor there.

Relative to the air, the plane isn't moving either, therefore there's no net airflow over the wings and no lift.

So how is that scenario different from the magical gay conveyor belt?
For one thing, the river isn't matching the airspeed, which as you pointed out is zero. Rather, it's matching a force that will counteract the maximum thrust the plane can produce.

If the question were, "Can a plane take off if it's sitting on a conveyer belt that will always spin fast enough to prevent it from taking off", then the answer is easy. But that wasn't the original question.

[playingwithknives]

Sadly, it's not alone.

If you google for the topic, you'll find a few other forums that have a similar thread on this subject just as stupid as this one.

Yeh this is my third plane on a conveyer belt thread now.

I'm actually moving to the take off side of things. The Parliament/Camaro diagram made things all the more clearer.

[Nick Walter]

Yeh this is my third plane on a conveyer belt thread now.

I'm actually moving to the take off side of things. The Parliament/Camaro diagram made things all the more clearer.

Ahem. That was a "Parliment/Bitchin Camero" diagram.

[Bill Dungsroman]

However, allowing that the plane has wheels, it gets movement because the thrust against the air propels it forward. In this case, the movement of the conveyor is not sufficient to slow it down, because the wheels spin freely underneath the plane without transmitting the full energy of the conveyor to the plane where it might counteract the forward thrust.

There is some frictive drag, however, because the plane is heavy, and the wheels are, after all, touching and moving against the plane, no matter how well oiled the bearings. So a conveyor moving much faster than the plane might slow it down. But a conveyor only moving at the same speed as the plane is doomed to failure. So long as there are wheels that are freewheeling relative to the plane.
See Rob, you keep busting out explanations that need qualifiers like "But what the question secretly asks is..." and I'm just not down with going there. I guess what it is is, if this question appeared on a physics exam (but it didn't, it appeared on Qt3 put through a ranvarian filter, which IMO automatically makes dissecting the wording of it a futile exercise - sorry ran, but you aren't always the most lucid of motherfuckers), you would have to be told what forces you were allowed to assume and/or ignore. I mean, otherwise some homo could say "Well, eventually it would hit imperfections in the conveyor belt's surface and attain lift SCREEEEEEEEEEEEEEEE" so the bottom line is, EXECUTIONER FIVE, WHICH FORCES?

I go with the only forces mentioned and the only ones that can automatically be implied. Speed and acceleration are mentioned, and it is a plane, so wings are included. Who the fuck said wings can't be assumed? The question said airplane, and an airplane without wings is a bus. Friction forces? The question stem makes friction irrelevant, which many basic physics questions will do to make it easier to solve the question. My train of thought goes straight to the hypothetical similarly, becuse of, I dunno, I guess maybe THE BIG MAGIC GAY CONVEYOR BELT the question mentions. Maybe I've read too many doofy physics questions just like this one, I guess.

Because the nigh-impossible conveyor belt is introduced, automatically this question becomes academic, hypothetical. Does anyone argue that point? I'm not being condescending - if we can't agree on that point, I'm just going to shoot this stray cat I found last night, eat it raw and beat off all over its drying bones instead of wasting one more word on this queertastic riddle. I'm effing tired of arguing with all these dudes who I'm totally down with. IT HURTS ME TO DISAGREE WITH MIKE, SCHMIDT AND ROB SOB.

So, this riddle is practically impossible to test IRL as written, yes? Now, once you make a physics riddle hypothetical, if you don't flesh out the hypothetical physical conditions, you may as well be jacking off into a wood chipper; oh, you'll get some distance, but is it ultimately worth it? Which, of course, is what we've all essentially realized. Nobody's wrong!

Rob, Mike and the Fly Be Free Gang are right because IRL you can't effing ignore forces that are like, there, man. You bet your tits there's friction blah blah de blah and that fucker takes off like VROOOOM.

And yet!

I'm right because if there ever existed a big magic gay conveyor belt (BMGCB) that perfectly matched an airplane's speed in the opposite direction, de plane, de plane would not pass through a body of air and allow the wings to provide lift because in my hypothetical interpretation, there are no other forces implicit or mentioned to lead to me to believe otherwise.

See, IMO the question stem asks you to ignore the fac tthat the object in question is even an airplane at all, hence the ridiculous BMGCB qualifier. IMO, the point of that is to make you consider the airplane first as simply an object. Ignore its wings, wheels, Jesus, etc. initially; it's just an object in motion - rather, in dynamic forward velocity equilibrium. The force diagram for this problem would initially be a box representing the airplane with 4 force vectors in 2 opposing pairs: forward velocity of the planebox, reverse velocity of the BMGCB, and the obligatory stupid force due to gravity downwards on the plane and what is termed the "normal" force in the opposite direction (that must exist, or the plane would smash flat due to gravity). Equilibirum. I'm not trying to be right at all costs, but I am telling you that that sort of assumption per the original question is so commonplace in physics, it's odd to think otherwise. You say big magic gay conveyor belt to Dr. Patel, he's going to go straight to Hypothesisville and then he's going to pelt you with force qualifiers ARE DERE FRICTIONAL FORCES UND IF SO WHAT ARE DEY? and whatnot. Oh, you'll have pissed him off. What fun!

So, the real question is, Rob's Late-Night-Sneaky-Uncle ones aside, are you gonna roll on this bad boy as pure hypotheticals, where all unmentioned frictive and assorted forces are assumed to be canceled out by the BMGCB's efforts, or NAWT. Because mang, it don't effing matter if it is an airplane or a Hummer or Liberace's grand piano or Liberace's gay bones on that belt. See, if we go there, we can say a car on that conveyor belt will eventually go flying forward off it, won't we? Anyone who thinks otherwise is not grasping the problem well enough, no offense. I took physics from the department chair and Dr. Kwong (or The Kwonger as I called him affectionately) literally made students go AAAAAAGHGHH during tests, they were so tough, and the curve in his class was so high a D- was not just a passing grade, it was a good one. Not getting physics is the same as not getting sticking your head into a ceiling fan and stopping the blades with your face - no shame if you don't or can't.

I say the BGMCB makes this riddle purely hypothetical, so assuming the belt induces a state of dynamic forward velocity with a net value of 0 m/s isn't crazy talk. It is actually the most reasonable assumption to make in this instance. And going off that, if the plane is sitting still in space relative to the air around it, the wings cannot provide lift. You dudes bringing up horizontal engine thrust magically translating to vertical lift without wings being involved are just dead wrong, sorry. You are assuming/inferring way, wayyyy too much.

[Squirrel Killer]

http://img505.imageshack.us/img505/1897/lance0ay.gif (http://imageshack.us)

[MikeSofaer]

Bill, your hypothetical diagram makes no sense. You can't cancel velocities like forces. You can't say something is moving one way, also moving another way, and therefore is Dynamically static.

If the plane isn't going anywhere then it has no speed and the conveyor is stopped.

Trying to move a plane with a conveyor is like pulling the rug out from under a bird.

[bago]

I can't believe that this has gone on for 6 pages.

Car on a treadmill will drive, but not move anywhere relatively.
Plane in a windtunnel will fly, but not move anywhere relatively.

Mixing up the metaphors is just stupid.

[Rob Beschizza]

I'm right because if there ever existed a big magic gay conveyor belt (BMGCB) that perfectly matched an airplane's speed in the opposite direction, de plane, de plane would not pass through a body of air and allow the wings to provide lift because in my hypothetical interpretation, there are no other forces implicit or mentioned to lead to me to believe otherwise.

If the plane is thrusting against the air (unh!), how does the conveyor belt, perfectly matched an airplane's speed in the opposite direction, slow the plane down? How does the kinetic energy it generates reach the plane?

But ahah, I see where you are at now: I'm falling into the trap of assuming some Real World situation of an airplane, etc., while you take the question as an abstract physical model with no such assumptions of wheels or friction or whatever. The plane is just a cipher for an arbitrary physical entity resting on the conveyor, and they start to move against one another. It pushes, but the conveyor pulls.


IMO, the point of that is to make you consider the airplane first as simply an object. Ignore its wings, wheels, Jesus, etc. initially; it's just an object in motion

My guess is that this hypothetical interpretation is rare. Most folks will "render" the scenario in their mind as a real world physical problem, including a giant pink conveyor belt, wheels acting as airplane wheels do, and maybe some screaming passengers. Turning it into a straightforward mechanical model of an sole arbitrary object moving against a conveyor in a world of perfect hypothetical abstraction is, however sexually inviting, likely to be the first port of call only for physics buffs.

IMO, the whole point of the question is social engineering, to force the viewer (by identifying the object as an airplane) to make further assumptions to complete a "reality-compliant" model. The puzzle is in identifying what assumptions should be correct, and the madness is in how the attendant physics go all over the map depending on which assumptions are chosen.


So, the real question is, Rob's Late-Night-Sneaky-Uncle ones aside, are you gonna roll on this bad boy as pure hypotheticals, where all unmentioned frictive and assorted forces are assumed to be canceled out by the BMGCB's efforts, or NAWT.

Nawt. :-) If only because it just seems to turn the whole thing into a physics problem disguising a tautology, "Does the plane move if the conveyor stops it from moving."


I say the BGMCB makes this riddle purely hypothetical, so assuming the belt induces a state of dynamic forward velocity with a net value of 0 m/s isn't crazy talk.

Sure, the fact that the conveyor reacts instantly to plane velocity is magic, but I still don't move from that to a purely hypothetical physics problem involving only "entity with mass," "conveyor" and the second law, at least not as comfortably as you do.

So then the plane never moves. But where's the visceral, interesting, compelling, next-gen fun in that?

[Squirrel Killer]

I can't believe that this has gone on for 6 pages.

Car on a treadmill will drive, but not move anywhere relatively.
Plane in a windtunnel will fly, but not move anywhere relatively.

Mixing up the metaphors is just stupid.
If you're talking about my bitchin' Camero, then this idiocy is exactly why it's gone on for six pages.

[playingwithknives]

If the conveyor belt moves at the same speed as the plane, the plane takes off. If the belt moves at the same speed as the planes wheels, the plane doesnt take off? Is that it?

[Rob Beschizza]

http://img505.imageshack.us/img505/1897/lance0ay.gif (http://imageshack.us)

Fantastic! $LOL++;

[Squirrel Killer]

If the conveyor belt moves at the same speed as the plane, the plane takes off. If the belt moves at the same speed as the planes wheels, the plane doesnt take off? Is that it?
No. The only way the plane doesn't take off is if the MGCB runs at a speed where the force it imparts to the plane (after being transmitted through the wheels) is greater than the force the plane's engines provide. Given that the wheels are very efficient at reducing precisely that very force, the conveyor belt is going to have to move incredibly fast. Far faster than the take-off speed of the plane in question.

[Wholly Schmidt]

Part the first:
See Rob, you keep busting out explanations that need qualifiers like "But what the question secretly asks is..." and I'm just not down with going there. I guess what it is is, if this question appeared on a physics exam (but it didn't, it appeared on Qt3 put through a ranvarian filter, which IMO automatically makes dissecting the wording of it a futile exercise - sorry ran, but you aren't always the most lucid of motherfuckers)
Bill, given what you just said, would you agree that the specific wording and question ranv posed results in in the plane flying? You seem determined to answer the question you think ranv meant to ask. No one has yet responded with any kind of refuting of my logic when I break the question down sentence by sentence. Does that mean you all agree that the specific question ranv asked, that started this thread, would end with the plane in flight, but that all of you are still trying to start with your presupposition of what the question was supposed to ask and work from there?

(if this question appeared on a physics exam) you would have to be told what forces you were allowed to assume and/or ignore. I mean, otherwise some homo could say "Well, eventually it would hit imperfections in the conveyor belt's surface and attain lift SCREEEEEEEEEEEEEEEE" so the bottom line is, EXECUTIONER FIVE, WHICH FORCES?

I go with the only forces mentioned and the only ones that can automatically be implied. Speed and acceleration are mentioned, and it is a plane, so wings are included. Who the fuck said wings can't be assumed? The question said airplane, and an airplane without wings is a bus.
Ok, with you so far.
Friction forces? The question stem makes friction irrelevant, which many basic physics questions will do to make it easier to solve the question.
Ok, I'll bite. No friction. Carry on.
My train of thought goes straight to the hypothetical similarly, becuse of, I dunno, I guess maybe THE BIG MAGIC GAY CONVEYOR BELT the question mentions. Maybe I've read too many doofy physics questions just like this one, I guess.
Now why do we go for the BMGCB here? Too many doofy physics questions is a cop out, because if that's really your answer then you should follow this up with "In light of that and setting aside my predilection for the magical and gay, I realize that this question is not asking that, and blah blah blah, the plane will fly."

Because the nigh-impossible conveyor belt is introduced, automatically this question becomes academic, hypothetical. Does anyone argue that point?
Grab the cat, I'll argue it. What has to be magical and hypothetical about this conveyer, other than the prohibitive cost associated with trying this out? Find a way to control the throttle of the plane remotely. Control the speed of the conveyor remotely. Make one go faster, make the other go faster. Ta-da! I really need more to work with to understand why you think this exists in some kind of hypothetical scenario that allows us to play fast and loose with how planes work.

I'm not being condescending - if we can't agree on that point, I'm just going to shoot this stray cat I found last night, eat it raw and beat off all over its drying bones instead of wasting one more word on this queertastic riddle. I'm effing tired of arguing with all these dudes who I'm totally down with. IT HURTS ME TO DISAGREE WITH MIKE, SCHMIDT AND ROB SOB.
Flattering, but after that paragraph, I'm not sure I want to be down with you. I'm a dog person.

So, this riddle is practically impossible to test IRL as written, yes?
No! Why do you think that? When you say "as written", do you still mean "as I imagine it was meant to be written before ranv got his hands on it"? Because if that's still your hangup, go read the straight dope (http://www.straightdope.com/columns/060203.html) link for another version. Written slightly differently, but no less possible to test, and it also ends with the plane in flight.
Now, once you make a physcis riddle hypothetical, if you don't flesh out the hypothetical physical conditions, you may as well be jacking off into a wood chipper; oh, you'll get some distance, but is it ultimately worth it? Which, of course, is what we've all eseentialyl realized. Nobody's wrong!
That's where you're wrong. Get it? Haha!
Rob, Mike and the Fly Be Free Gang are right because IRL you can't effing ignore forces that are like, there, man. You bet your tits there's friction blah blah de blah and that fucker takes off like VROOOOM.
Right, we're right. Got it.

And yet!

I'm right because if there ever existed a big magic gay conveyor belt (BMGCB) that perfectly matched an airplane's speed in the opposite direction, de plane, de plane would not pass through a body of air and allow the wings to provide lift because in my hypothetical interpretation, there are no other forces implicit or mentioned to lead to me to believe otherwise. The forces of the planes engines are pretty implicit, at least as implicit as the wings you love to harp on. So fire up the engines, crank up the conveyer belt, and we're going to get two things at least trying to push each other in opposite directions. What happens on some level depends on whether you believe this is a big gay magical airplane that they forgot to add wheels to, but on some level, even that doesn't matter. The plane's going to go forward.

ROLLING OR SCRAPING, THE CONVEYER WON'T DO CRAP TO THE ENGINES, NEVER WILL, NEVER IMPLIED IN THE QUESTION THAT IT WOULD.

So at this point your big magical gay plane you magically gayly imagined on its maybe real maybe hypothetical coneyer with no wheels but definitely wings would STILL GO FORWARD, which you've argued wouldn't happen. Your BMBGMGMBMMGMMORPG scenario would probably not end in flight without wheels. But you've twisted the question so far from reality as to be absurd.

Stay tuned...

[Wholly Schmidt]

See, IMO the question stem asks you to ignore the fac tthat the object in question is even an airplane at all, hence the ridiculous BMGCB qualifier. IMO, the point of that is to make you consider the airplane first as simply an object. Ignore its wings, wheels, Jesus, etc.

What what what? Where's the Bill that just wrote:

I go with the only forces mentioned and the only ones that can automatically be implied. Speed and acceleration are mentioned, and it is a plane, so wings are included. Who the fuck said wings can't be assumed? The question said airplane, and an airplane without wings is a bus.

Because your whole point there was that you consider that it is a plane, not just an object, or bus.

And Jesus doesn't come into play till we get to bumble bees anyway.

initially; it's just an object in motion - rather, in dynamic forward velocity equilibrium. The force diagram for this problem would initially be a box representing the airplane with 4 force vectors in 2 opposing pairs: forward velocity of the planebox, reverse velocity of the BMGCB, and the obligatory stupid force due to gravity downwards on the plane and what is termed the "normal" force in the opposite direction (that must exist, or the plane would smash flat due to gravity). Equilibirum. I'm not trying to be right at all costs, but I am telling you that that sort of assumption per the original question is so commonplace in physics, it's odd to think otherwise. You say big magic gay conveyor belt to Dr. Patel, he's going to go straight to Hypothesisville and then he's going to pelt you with force qualifiers ARE DERE FRICTIONAL FORCES UND IF SO WHAT ARE DEY? and whatnot. Oh, you'll have pissed him off. What fun!

As far as I remember the D I got in physics (which was in a class where a D was not good, granted), your two opposing pairs of vectors are fine. No argument with how you start to set this bad boy up, except for the equilibrium part, because...

So, the real question is, Rob's Late-Night-Sneaky-Uncle ones aside, are you gonna roll on this bad boy as pure hypotheticals, where all unmentioned frictive and assorted forces are assumed to be canceled out by the BMGCB's efforts, or NAWT.

NAWT, I guess. Because your hypothetical way of answering this is so far just an incomplete setup. Because the question, "will it fly" means we can't just stop with your two opposing vectors, or else the answer is no whether it moves or not, cause your vectors ain't got no wings. And every bit as important to a plane as wings are those engines we left out, and it does matter that the force pushing the plane down the conveyer is generated from the engines acting on the air, and not from tires acting on the conveyer.
Because mang, it don't effing matter if it is an airplane or a Hummer or Liberace's grand piano or Liberace's gay bones on that belt. See, if we go there, we can say a car on that conveyor belt will eventually go flying forward off it, won't we?

Back to the "answer a different question game", yeah, if your car had engines generating thrust through something other than friction with the ground, it would go flying forward too. Like my Batmobile from a dozen posts ago. Maybe like V's Bitchin' Camero, I'm not positive on that though.

Anyone who thinks otherwise is not grasping the problem well enough, no offense.

I think I just demonstrated otherwise. You're the one who's either not grasping it well, or at least not setting up your hypothetical box o'vectors well enough to demonstrate that you do.
I took physics from the department chair and Dr. Kwong (or The Kwonger as I called him affectionately) literally made students go AAAAAAGHGHH during tests, they were so tough, and the curve in his class was so high a D- was not just a passing grade, it was a good one. Not getting physics is the same as not getting sticking your head into a celing fan and stopping the blades with your face - no shame if you don't or can't.

That's great, but nothing in this is really getting into physics much past high school, and still has a great deal more to do with the presuppositions you bring into the question and a few basic facts about aviation than the physics that you may or may not need to describe the situation to someone.

I say the BGMCB makes this riddle purely hypothetical, so assuming the belt induces a state of dynamic forward velocity with a net value of 0 m/s isn't crazy talk. It is actually the most reasonable assumption to make in this instance. And going off that, if the plane is sitting still in space relative to the air around it, the wings cannot provide lift. You dudes bringing up horizontal engine thrust magically translating to vertical lift without wings being involved are just dead wrong, sorry. You are assuming/inferring way, wayyyy too much.
So you summarize what I broke down elsewhere, nothing new for me to rebutt here, except to point out that I've never personally discounted the wings seriously, only in joking response to your trying to discount things like engines and wheels.

[Saxman_72]

No. The only way the plane doesn't take off is if the MGCB runs at a speed where the force it imparts to the plane (after being transmitted through the wheels) is greater than the force the plane's engines provide. Given that the wheels are very efficient at reducing precisely that very force, the conveyor belt is going to have to move incredibly fast. Far faster than the take-off speed of the plane in question.

Bingo.

[Marcus]

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?


You know I went back and reread the above and seriously it seems pretty simple to me.

I also still think the plane takes off.

[Rob Beschizza]

Also, I've never found anything Bill's written condescending. I don't get it when people have tantrums when Bill argues with them. Just because someone has a distinctive jibber jabber when they flame you, it doesn't mean that they are always flaming you when the jibber jabber is on.

I find Bill's intelligent jibber jabber very much to my liking, to the point where I want to be flamed by one of his apparently inexaustible supply of enemies, just so I can have the pleasure of telling them I like Bill and not them and it pleases me to see them upset about it.

[Squirrel Killer]

I also still dont think the plane takes off.
What force is acting to counter the 80 hojillion newtons of force the engines are generating?

[Marcus]

What force is acting to counter the 80 hojillion newtons of force the engines are generating?

I have no idea what you are talking about.

[Ben]

The "Doesn't fly gang"-
A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. The plane goes 10mph east. Therefore, the belt goes 10mph west.

Have I lost anyone? The belt matches the speed perfectly in the opposite direction. So plane goes 10 east, belt goes 10 west. Do any of you disagree with me this far?

[Squirrel Killer]

Nothing because the plane isnt moving.
So all those newtons just, what, evaporate?

[Wholly Schmidt]

Nothing because the plane isnt moving.
What? The engines aren't generating force because the plane isn't moving? The whole damn question comes down to if the plane is moving (for the wings to work Bill, I know, I know!).

[Marcus]

So all those newtons just, what, evaporate?

They help the plane fly as I said already!

[Ben]

So you think the question is "Are stationary things moving?"

[Marcus]

No I thought the question was will the plane go back in time?

So you think the question is "Are stationary things moving?"

But yeah stationary things are always moving.

[MikeJ]

A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?


You know, I think I'm having a slight change of heart here. It all comes down to what 'perfectly match the speed and accleration of the plane' means, exactly. In words, what is the control system on the conveyor belt measuring?

Say the conveyor measures the speed of the plane relative to rest and the still air. Call that the Mark I control system. In that case, it's clear that the plane can end up going say 100 mph to the right (+100 mph), the belt moves 100 mph to the left (-100 mph), the speed of the plane relative to the belt is +200 mph. The plane takes off.

So far, so good. But wait. The counter-example in everyone's head is that a car on the same conveyor belt, with the same control system, WOULDN'T be able to move.

Yet that's not true. Say the car is moving 50 mph to the right (+50 mph), the belt moves 50 mph to the left (-50 mph), the speed of the car relative to the belt is +100 mph. This is a stable speed. The speedometer on the car reads 100 mph, and engine is having to work to overcome friction in the wheel, loss in the transmission, etc, etc, but it could do it.

Also worth noting that it has the air resistance of it's real speed (half the speedometer speed), so it then engine doesn't have to transmit as much force as it would if it was 'really' driving the speed indicated on the speedometer. If the car sped up so the speedometer read 120 mph, then it would be going 60 mph, relative to rest, with the belt going 60 mph in the other direction.

Well, what kind of control system would be needed to keep the car in place? The belt has to move back at the speed of the car, *relative to the belt*. Call this the Mark II control system. So if the car speedometer reads 100 mph, the speed of the car, relative to the belt is +100 mph, and the belt moves at 100 mph to the left (-100 mph). Speed of the car, relative to rest, is zero. In this situation, the car can crank the speedometer up to whatever speed it likes, it still won't move.

What happens if we take that same, Mark II control system, and apply it to the plane example? Bad things. If the airplane wheels are frictionless, then as soon as the plane fires off it's thrusters, the belt goes to lightspeed and the whole universe collapses. Or whatever.

If plane wheels have some friction, then there is some conveyor speed where the engine thrust is balanced by the force transmitted through the wheels, and the plane doesn't move, relative to rest. The Mark II control system achieves this speed. Probably at this speed, the tires will explode and the plane will go up in a big ball of fire, killing all onboard. But at least the universe didn't collapse. Whew.

The question is, which is a more reasonable control system, judging from the question? You can have a system where the plane can take off and car can move, or you can have a system where neither the plane or car can move (but it has work harder to keep the plane in place). Intuitively, you want a system where the plane takes off and the car can't move, but I don't see how to get that.

[MikeSofaer]

If the conveyor belt moves at the same speed as the plane, the plane takes off. If the belt moves at the same speed as the planes wheels, the plane doesnt take off? Is that it?
Yes, that's it. If the conveyor is moving as the same speed as the wheels, then you have defined the plane stopped.

[Wholly Schmidt]

Yes, that's it. If the conveyor is moving as the same speed as the wheels, then you have defined the plane stopped.
And to be clear, you've defined it with no thrust from the engines. Because the conveyer can't go the same speed of the wheels with another force acting in the opposite direction of the conveyer (the engines). The wheels are being acted on by the thrust from the plane and the movement of the conveyer, so for both engines and conveyer to be applying opposite thrusts, the wheels cannot be moving the same speed as the conveyer.

[MikeSofaer]

Intuitively, you want a system where the plane takes off and the car can't move, but I don't see how to get that.
I think what confuses people is the habit of referring to the speed of a treadmill as your speed. As in "I ran 3 miles at 6 mph at the gym today" when in fact the treadmill went 3 miles at 6 mph and you went nowhere at 0 mph and moved your legs a lot.

[Hanzii]

I posted this riddle at work today. Watched my coworkers mirror this very thread at the coffee stand and at dinner, then was very smug when I gave the answer (the plane takes off). I even offered a Logitech laser mouse to the first with the right answer (only two out of 18).
Now 16 people including my boss hates me.

We even have one guy perfectly mirroring Bill "I will rephrase the riddle in many gay ways untill I'm magically right" Dungsroman... unfortunately he's a the deski opposite mine and not as fun or with quite as colourful a vocabulary as our Bill.

Fun stuff.

[Wholly Schmidt]

I think what confuses people is the habit of referring to the speed of a treadmill as your speed. As in "I ran 3 miles at 6 mph at the gym today" when in fact the treadmill went 3 miles at 6 mph and you went nowhere at 0 mph and moved your legs a lot.
Yes, which is what the car would be doing. Going nowhere at no speed, but moving its wheels a lot. While the plane would actually be acting on something other than the treadmill (the engines on the air) to actually move it x distance at x mph.

[MikeSofaer]

It's not much of a physics problem if you start by assuming that the plane isn't moving.

It's like asking "You have a rock that is always 6" off the ground and you cut the string suspending it. What happens?"

[Ben]

MikeSofaer- But the question doesn't say anything about the conveyor rotating as fast as the wheels are, so that whole line of discussion is moot.

The conveyor is going the same speed as the wheels. The wheels are moving 10 mph east when the conveyor is going 10mph west, it's just they are spinning at 20mph. How fast the wheels spin is not a part of the initial question.

[MikeSofaer]

Yes, which is what the car would be doing. Going nowhere at no speed, but moving its wheels a lot. While the plane would actually be acting on something other than the treadmill (the engines on the air) to actually move it x distance at x mph.
Actually, I was agreeing with the other Mike that a car would reach 88 mph and leave the conveyor, just like a plane, if you use a consistent definition of speed.

In other words, in normal use a treadmill doesn't match your speed, it matches the speed of your legs. Your speed is 0. If you had a non-zero speed to match you would be moving along the treadmill relative to the ground.

[MikeSofaer]

MikeSofaer- But the question doesn't say anything about the conveyor rotating as fast as the wheels are, so that whole line of discussion is moot.

The conveyor is going the same speed as the wheels. The wheels are moving 10 mph east when the conveyor is going 10mph west, it's just they are spinning at 20mph. How fast the wheels spin is not a part of the initial question.
If you got through this thread believing that I think the wheelspeed interpretation is the correct one then you haven't been reading the author fields.

[Ben]

I disagree that there are multiple legitimate interpretations of the question, and I think you're helping our sworn "No Fly" enemies with that line of debate. I'm calling you out as a terrorist.

[Wholly Schmidt]

Actually, I was agreeing with the other Mike that a car would reach 88 mph and leave the conveyor, just like a plane, if you use a consistent definition of speed.

In other words, in normal use a treadmill doesn't match your speed, it matches the speed of your legs. Your speed is 0. If you had a non-zero speed to match you would be moving along the treadmill relative to the ground.
Sorry, I need to go back and reread that post, I was getting a little distracted. Good thing cars have nothing to do with this thread. :)

[Wholly Schmidt]

I disagree that there are multiple legitimate interpretations of the question, and I think you're helping our sworn "No Fly" enemies with that line of debate. I'm calling you out as a terrorist.
When the revolution comes, he'll be first against the conveyer.

[MikeSofaer]

When the revolution comes, he'll be first against the conveyer.
The revolution will not be motorized.

[Wholly Schmidt]

The revolution will not be motorized.
Obviously. It will apparently be big, gay, and magical.

[bago]

With a saturn rocket strapped to its back.

[Linoleum]

I'm still waiting for the google video link of this happening in real life to the tune of Yakkity Sax.

[Bill Dungsroman]

Bill, given what you just said, would you agree that the specific wording and question ranv posed results in in the plane flying?
No. *ducks*


You seem determined to answer the question you think ranv meant to ask. No one has yet responded with any kind of refuting of my logic when I break the question down sentence by sentence. Does that mean you all agree that the specific question ranv asked, that started this thread, would end with the plane in flight, but that all of you are still trying to start with your presupposition of what the question was supposed to ask and work from there?
Well, ranvarian just said it wouldn't, so there goes that thought. And seriously, I don't even understand WTF you're talking about at this point. I said we are both correct, but you seem unable to admit the question can be interpreted more than one way.


Now why do we go for the BMGCB here? Too many doofy physics questions is a cop out, because if that's really your answer then you should follow this up with "In light of that and setting aside my predilection for the magical and gay, I realize that this question is not asking that, and blah blah blah, the plane will fly."
Until whoever wrote this cunt-punching riddle comes along as tells us definitively what the question is asking, nobody gets to put the rubber stamp on that account; not me, not you, nobody. I've given up on that tip, I think maybe you ought to as well.

And I went for the BMGCB because, I dunno, the question stem does, too.


Grab the cat, I'll argue it. What has to be magical and hypothetical about this conveyer, other than the prohibitive cost associated with trying this out? Find a way to control the throttle of the plane remotely. Control the speed of the conveyor remotely. Make one go faster, make the other go faster. Ta-da! I really need more to work with to understand why you think this exists in some kind of hypothetical scenario that allows us to play fast and loose with how planes work.
Because that's how most physics questions work, WS. Blame the Germans, they invented physics. <Han>It's not my fault!</Han>

Can you answer this: if I'm on a car driving in place on a conveyor belt, is there wind in my face? I'm not sure why you dudes can't imagine an object moving on a conveyor belt in place relative to everything but the surface of the conveyor belt.


No! Why do you think that? When you say "as written", do you still mean "as I imagine it was meant to be written before ranv got his hands on it"? Because if that's still your hangup, go read the straight dope (http://www.straightdope.com/columns/060203.html) link for another version. Written slightly differently, but no less possible to test, and it also ends with the plane in flight.
That link doesn't illustrate what ranvarian's question asked, it illustrates a real-life approximation of it, and you're trying to reconcile the two, IMO.

The forces of the planes engines are pretty implicit, at least as implicit as the wings you love to harp on.
Dude WHAT THE FUCK. Seriously. Read out loud what you just typed there to yourself. "The wings (I) love to harp on?" WTF?

And those forces: horizontally-vectored. YOU CANNOT PRODUCE A VERTICAL VECTOR FROM A DYNAMICALLY STATIC HORIZONTAL VECTOR, VICTOR.


So fire up the engines, crank up the conveyer belt, and we're going to get two things at least trying to push each other in opposite directions. What happens on some level depends on whether you believe this is a big gay magical airplane that they forgot to add wheels to, but on some level, even that doesn't matter. The plane's going to go forward.
Why? If the belt matches the plane's speed, it will have to match whichever speed, ground or air, is greatest. Otherwise, the question stem's scenario invalidates itself. If the plane moves forward, it has attained a speed faster than the conveyor belt. This, according to the question, cannot happen. You are answering this question every single time by invalidating it.

So at this point your big magical gay plane you magically gayly imagined on its maybe real maybe hypothetical coneyer with no wheels but definitely wings would STILL GO FORWARD, which you've argued wouldn't happen. Your BMBGMGMBMMGMMORPG scenario would probably not end in flight without wheels. But you've twisted the question so far from reality as to be absurd.
No, not really. The question stem itself did that; you're trying to make two ends meet, I'm telling you what end we get going off what the question gave us. Without insulting big fonts, either.


Stay tuned...
No fucking thanks, Big Guy. The plane takes off. Be on it.

[Bill Dungsroman]

MikeSofaer- But the question doesn't say anything about the conveyor rotating as fast as the wheels are, so that whole line of discussion is moot.

The conveyor is going the same speed as the wheels. The wheels are moving 10 mph east when the conveyor is going 10mph west, it's just they are spinning at 20mph. How fast the wheels spin is not a part of the initial question.

Really? The question stem said "plane" in terms of matched speed, not wheels. Where are you silly motherfuckers getting wheels from?

[Ben]

Bill- You're missing context there, but you do know what a wheel is, yes? And we are assuming that this plane has wheels, right? Wheels that are attached to the plane?


If the plane moves forward, it has attained a speed faster than the conveyor belt.

That's not correct at all. Again, Bill, what part of this do you disagree with:
A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. The plane goes 10mph east. Therefore, the belt goes 10mph west.

[Bill Dungsroman]

Because your whole point there was that you consider that it is a plane, not just an object, or bus.
"Initially," WS. Initially, the wings don't matter, do they? They must not, since you were like making fun of me for mentioning them at all, or whatever.

NAWT, I guess. Because your hypothetical way of answering this is so far just an incomplete setup. Because the question, "will it fly" means we can't just stop with your two opposing vectors, or else the answer is no whether it moves or not, cause your vectors ain't got no wings. And every bit as important to a plane as wings are those engines we left out, and it does matter that the force pushing the plane down the conveyer is generated from the engines acting on the air, and not from tires acting on the conveyer.
Why? The engine's thrust/force is in a purely horizontal plane, it cannot be imparted into vertical thrust unless the plane moves forward through an air mass, and I maintain that the question is worded such that it never does.


Back to the "answer a different question game", yeah, if your car had engines generating thrust through something other than friction with the ground, it would go flying forward too. Like my Batmobile from a dozen posts ago. Maybe like V's Bitchin' Camero, I'm not positive on that though.
So, like, treadmills are unable to keep objects in motion upon them? What?


I think I just demonstrated otherwise. You're the one who's either not grasping it well, or at least not setting up your hypothetical box o'vectors well enough to demonstrate that you do.
All I've seen you do is, as I have said, completely invalidate the question in order to attempt to answer it. I like how you're getting digs in on me mentioning wings when you dudes are going on about fucking wheels.


That's great, but nothing in this is really getting into physics much past high school, and still has a great deal more to do with the presuppositions you bring into the question and a few basic facts about aviation than the physics that you may or may not need to describe the situation to someone.

So you summarize what I broke down elsewhere, nothing new for me to rebutt here, except to point out that I've never personally discounted the wings seriously, only in joking response to your trying to discount things like engines and wheels.
Now you show me where I discounted the plane's engines, Boss. I'm waiting. And the question discounts the plane's wheels, because of the operation of the conveyor belt, which all you seem to account for in regards to it is to tell me I'm altering the question to make it work for me. You silly motherfuckers are trying to tell me the plane's wheels move at a different rate than the rest of the plane, which is more impossible than a giant fucking conveyor built. You dudes are repeatedly telling me dynamic equilibrium of velocity is so impossible it will freeze objects in space should it ever occur.

[Squirrel Killer]

I'm not sure why you dudes can't imagine an object moving on a conveyor belt in place relative to everything but the surface of the conveyor belt.
We can. It's just that we realize that for that to happen the conveyor needs to be moving at a speed far greater than perfectly matched to the speed and acceleration of the plane.

I'll ask again, the jet engines/propellers are generating 80 hojillion newtons of force. What force is countering that?

[jeffd]

fyi I hear sea-tac installed a giant fucking conveyer belt on their runway. I'm going to be flying out of there tomorrow; I'll let you guys know what happened. WIll that end this thread?

[MikeSofaer]

If the plane moves forward, it has attained a speed faster than the conveyor belt
Only if you measure the plane's speed against the conveyor belt, but that's silly. What matters is the plane's speed relative to the air.

Really? The question stem said "plane" in terms of matched speed, not wheels. Where are you silly motherfuckers getting wheels from?
The question says the plane is on a conveyor belt but it doesn't say the conveyor belt moving also moves the plane. Why should it? If you hold a toy car in the air and spin its wheels it doesn't go anywhere. That's where wheels come in, they are the reason you can't conclude that the conveyor belt moves the plane.

So, like, treadmills are unable to keep objects in motion upon them?
That is correct. What they do is allow wheels/legs to move at a different speed than the object. So you can move your legs or spin your wheels on a treadmill and not move. But if you are moving then you are not going to stay on the treadmill.

[Bill Dungsroman]

So, like, treadmills are unable to keep objects in motion upon them?

That is correct.

I surrender!

[XPav]

Bill, I surrendered 4 pages ago. The plane moves forward on the belt, the wings get lift, the plane takes off.

The question is stupid. I'm considering asking at work, but I'm afraid:
1) I'll bring the entire engineering department with 85 engineers including some ridiculous eggheads to a standstill.
2) People will treat me as a smug bastard when I play know-it-all and tell them the answer.

I think I'll do it anyway.

[Nick Walter]

Bill, I surrendered 4 pages ago. The plane moves forward on the belt, the wings get lift, the plane takes off.

The question is stupid. I'm considering asking at work, but I'm afraid:
1) I'll bring the entire engineering department with 85 engineers including some ridiculous eggheads to a standstill.
2) People will treat me as a smug bastard when I play know-it-all and tell them the answer.

I think I'll do it anyway.

Heh. I'm contemplating something similar but I'm waiting for a techhead at work to annoy me, then I can paralyze them with this argument and leave them frustrated all day.

[bago]

Of course. Think about it in reverse.

If a car is driving through a wind tunnel at 30 mph, and the wind tunnel is blowing at 30 mph, does the car come to a complete stop? No. You just double the effect of the drag co-efficient of the vehicle. (windspeed against skin of car is 60 mph) The car still goes forward, just not quite as fast because of the of the extra drag from the air. Same with the plane, just with extra drag from the tires.

Any half-way decent egghead will tell you the plane takes off. It's simple algebra.

[Peter Frazier]

I still don't get it.

[Wholly Schmidt]

This is just going to get messier and messier without the cascading quotes, so I apologize for that, as well as for my font size in that previous post. I only meant for that one line to be big.

I don't even understand WTF you're talking about at this point. I said we are both correct... We are both correct about the systems we're describing. The difference is that my system was also described by the question. Yours wasn't.
...but you seem unable to admit the question can be interpreted more than one way. Well you've nailed that part, congratulations. I mean, you can interpret the question differently, but not correctly. There is one correct interpretation of the question, and it's not yours. That's been my point to you (and others) for most of this argument, that your interpretation of the question is wrong, and if that was muddied by my indulging your every whim with counter-points, I'm sorry.
Until whoever wrote this cunt-punching riddle comes along as tells us definitively what the question is asking, nobody gets to put the rubber stamp on that account; not me, not you, nobody. I've given up on that tip, I think maybe you ought to as well.
Why Bill? Why? The question is in plain english. There is absolutely nothing to suggest it has a meaning other than what we can all read, without calling up the Big Magic Gay Conveyer Belt Inventor. Why can't we all just hammer out the finer points of the question as it was very specifically worded here? Maybe somewhere, someone really did have some sinister secret meaning for the question. Who cares?! If it's not evident from the question they presented us (hint: it's not), how is it our fault for answering correctly the question posed at the begining of the thread? Ranv, or Cecil, or whoever, isn't going to jump out and say "Gotcha!" if you decide the plane would fly as worded. "Haha, you fell for the oldest trick in the book, answering the question I asked instead of the one I was thinking of! Sucker!"

There is absolutely one correct way to interpret this question, and it leads to a plane in the air every single time.


Can you answer this: if I'm on a car driving in place on a conveyor belt, is there wind in my face? I'm not sure why you dudes can't imagine an object moving on a conveyor belt in place relative to everything but the surface of the conveyor belt.
I know I shouldn't even induldge this because it will just distract from the actual question you still won't acknowledge, but sure, I can absolutely imagine what you just described. I hoped we'd been communicating clearly enough that you would realize I never made any claim to the contrary, but you still apparently don't understand the difference between a car and a plane.

What gives a plane forward thrust? No trick to that question, I'm not asking what gets it into the air (air moving over the wings), free yourself completely from the context of the actual question (since we're already doing that by bringing in cars), and answer, what gives a plane forward thrust? Jet or propellor engines. They act on the air to push/pull the plane forward through it.

What gives a car forward thrust? No trick here either. The rotation of tires against the ground.

So if we drop them both on any moving conveyer, it doesn't have to match speed or exceed speed or whatever, different things happen for the car and the plane.

If the conveyer happens to be moving backward at X and the tires happen to be doing what would normally, on solid ground, push the car forward at X, then I will sit there next to you in the car and smile as my hair fails to go anywhere right along with yours. It will be beautiful, and nothing can take that away from us, because on this point almost totally unrelated to the question at hand, you and I (and everyone else but what we have is special) see eye to eye. But if we keep that same value of X, conveyer moving backward at X, plane's engines generating X in the other direction, something different will happen. If the plane doesn't have normal landing gear and wheels, since you don't seem to like it when I suggest that this plane is at all plane-ish other than the wings, the plane will slide forward despite the conveyer belt. It will scrape and sound awful, but it will move. If we drop a normal plane on the belt, away it goes. The wheels aren't there to generate any foward thrust, the engines are. So the wheels just pick a speed that lets the engines push one way, the conveyer push the other, and the wheels keep the conveyer and plane from tearing each other apart. By allowing the plane to move forward.

If you don't address my assertion that there's only one way to skin this cat, (no, not that cat), then please show me where you disagree with that part of my response, if nothing else.

....(other stuff that's just pointless to respond to through no fault of our own but the quoting system because it gets further from context with each rebuttal)...
If the belt matches the plane's speed, it will have to match whichever speed, ground or air, is greatest. Otherwise, the question stem's scenario invalidates itself.
I totally agree.
If the plane moves forward, it has attained a speed faster than the conveyor belt.
No. No it absolutely has not. Why does the plane moving forward mean it somehow has achieved a faster speed than the conveyer? Does not compute, no comrendo amigo, sell crazy somewhere else.

All it means is the wheels of the plane will have to rotate faster. That's not the plane achieving a speed faster than the conveyer, that's the wheels of the plane rotating faster than the conveyer. That's no more relevant to the speed of the plane than the rotational speed of a pinwheel you hold out the window of your car as you cruise down the highway. It's an indication that stuff's moving, but it's not creating the thrust in either scenario, only responding to forces it has no control over.[/quote]

[Wholly Schmidt]

Just a few more choice responses

So, like, treadmills are unable to keep objects in motion upon them? What?

Sometimes, sure. If the object, whatever it is, is getting its forward thrust from any source other than thrust normally generated by the bottom of the object acting on the ground, the treadmill can't interefere with that directly. The treadmill can't stop the engines from pushing the plane forward. They can't stop me from standing next to a small treadmill and pushing an object that's on the treadmill. They can't stop Colm Meany's Porsche from rolling along the treadmill as it's pulled from above by Con Air. I don't know where that came from, I'm sorry.
You silly motherfuckers are trying to tell me the plane's wheels move at a different rate than the rest of the plane, which is more impossible than a giant fucking conveyor built.
We're trying to tell you the speed of the rotation of the plane's wheels can be whatever it damn well pleases, and it can sure be way different from the rate the rest of the plane is moving. Even in your car, the rotation of your tires isn't, strictly speaking, the speed you're moving at. It's just the best way in a car you can get a measurement of that. Most of the time it's right, but if you hit some ice and your wheels suddenly start spinning really really fast, your speedometer goes up, but your car isn't actually moving any faster till they grip again. At that point, the car's wheels move at a different rate than the rest of the car, which sounds eerily similar to your impossibility above. Planes don't grip, ever.

[Bill Dungsroman]

Yeah. I get it now. I'm a complete moron. Good night America!

[Wholly Schmidt]

B-b-b-b-but...now what do we talk about?

[MikeJ]

What gives a plane forward thrust? No trick to that question, I'm not asking what gets it into the air (air moving over the wings), free yourself completely from the context of the actual question (since we're already doing that by bringing in cars), and answer, what gives a plane forward thrust? Jet or propellor engines. They act on the air to push/pull the plane forward through it.

What gives a car forward thrust? No trick here either. The rotation of tires against the ground.

So if we drop them both on any moving conveyer, it doesn't have to match speed or exceed speed or whatever, different things happen for the car and the plane.


You know, I've come to realize that the difference between car and plane really isn't critical to this example. The way the control system on the conveyor belt is being interpreted, both car and plane would make headway (see my previous post).

Rywill made the analogy a few (dozen?) pages back, saying you could replace the conveyor belt with slick ice or something. In that case, the difference between sources of thrust WOULD be critical. But that's not true. The conveyor belt isn't acting like slick ice, or free-spinning rollers.

Back to your example above of a car and plane placed on a conveyor that moves at a fixed speed. Say the plane's thrust is such that it's speed would normally top out at 50 mph. The conveyor moves back at 50 mph. The plane's forward velocity would top out at, say, 47 mph, due to rolling friction of the wheels.

Place the car on the same conveyor that is moving back at 50 mph. If you specify the car's speed as say 50 mph by wheel-rotation, then of course it's not going to move. But we didn't specify the *plane's* speed by wheel rotation, why the car? The more correct analogy engine thrust would be like engine output, or how far you've depressed the accelerator.

So say the acclerator is depressed such that the car would normally top out at 50 mph. In normal driving at 50 mph, there's two forces holding the car back: friction in the form of losses in the transmission and rolling friction on the wheels, and air resistance. At 50 mph, the air resistance is dominant. But the car on the conveyor, when it's wheels are spinning at 50 mph, isn't subject to air resistance, so it will continue accelerating until those two combined forces are enough to prevent acceleration. Since it has more sources of friction that scale with wheel speed than the plane, it won't end up as fast as the plane. But it might end up at 30 or 35 mph, with the speedometer reading 80 or 85.

[Rob Beschizza]

Hamster dog declined to participate, BTW. She will sit by the treadmill but has no interest in getting on it. Now we will never know if Puck the Hamster Dog will fly.

Also, someone should actually set up a conveyor big enough to accomodate, say, a single-engine WWII fighter plane or something similarly tiny. Mythbusters need to get ON it.

[TriggerHappy]

I can totally see the Mythbusters doing this with an R/C plane.

[instant0]

Conveyor belt moves in direction x
Wheels move in direction y
If x = y then the result is 0

You may want to add Friction, Bearings on the Whells, Gravity, Air Density, wind, thrust from engines as modifiers.

But in the problem stated, the Wheels and the Belt are ALWAYS moving at the same speed, so the other factors do not matter as they can not influence the forward momentum of the plane.

For the plane to take off, it needs forward momentum to gain lift for its wings.


Example:
Plane is at 0
Thrust set to 10 km/h
Wheels begin moving from 0-10 km/h
Ground begins to move in the opposite direction from 0-10 km/h
Wheels will be spinning at 20 km/h but the plane will stand still.

At around 700 km/h the wheels will explode, the plane will get a lot more friction with the ground and begin to loose speed rapidly and will explode in a fiery inferno killing everyone inside and those who are waiting at the end of the conveyor belt as a burning wreck traveling at 350 km/h hits them.

[Phil_Stein]

>>
A plane is on a conveyer belt. The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction. Will this plane take flight?
<<

As I read this question, if the plane is moving 10 mph, the belt is moving 10 mph in the opposite direction. No problem - implicitly, the wheels spin a little faster, but that doesn't stop the plane from going the 10 mph that it's going (relative to a stable observer not on the belt).

[mouselock]

Also, someone should actually set up a conveyor big enough to accomodate, say, a single-engine WWII fighter plane or something similarly tiny. Mythbusters need to get ON it.

Why? So Mythbusters can then argue about which interpretation of "match the speed" to use and come to the same conclusions depending on which interpretation is used that we have?

(Or more likely find that in one interpretation the plane takes off, and in the other the treadmill/conveyor breaks because it's not a magical gay treadmill.)

[Squirrel Killer]

Example:
Plane is at 0
Thrust set to 10 km/h
Wheels begin moving from 0-10 km/h
Ground begins to move in the opposite direction from 0-10 km/h
Wheels will be spinning at 20 km/h but the plane will stand still.
Where are the 80 hojillion newtons of force the engines are generating going?

[Squirrel Killer]

I can totally see the Mythbusters doing this with an R/C plane.
This is a great idea, but they probably don't have access to a Magical Gay Conveyor Belt. How would just using a regular conveyor belt that was simply set to go faster than the anticipated speed of the R/C plane change the experiment?

[Rob Beschizza]

Where are the 80 hojillion newtons of force the engines are generating going?

AREN'T YOU LISTENING? THE LANGOLIERS ATE THEM! AND WHEN THE DREAMING GODS AWAKEN YOU WILL BE EATEN FIRST!

[Dave Markell]

Where are the 80 hojillion newtons of force the engines are generating going?

Friction, of course. Friction between the wheels and the conveyor belt, internal bearings, etc. I'm firmly in the "the plane won't fly camp," btw. I'll admit the question is poorly written, but I feel the intent is to state that the plane will have no forward motion relative to an observer standing beside the belt and therefore no lift on its air-stationary wings.

[Houngan]

Friction, of course. Friction between the wheels and the conveyor belt, internal bearings, etc. I'm firmly in the "the plane won't fly camp," btw. I'll admit the question is poorly written, but I feel the intent is to state that the plane will have no forward motion relative to an observer standing beside the belt and therefore no lift on its air-stationary wings.


Oh good grief. You're suggesting that you can spin the wheels fast enough that the torque generated across the ball bearings is sufficient to counteract a jet's engines? If it were that significant, they'd grease the runways.

H.

[Squirrel Killer]

Friction, of course. Friction between the wheels and the conveyor belt, internal bearings, etc. I'm firmly in the "the plane won't fly camp," btw. I'll admit the question is poorly written, but I feel the intent is to state that the plane will have no forward motion relative to an observer standing beside the belt and therefore no lift on its air-stationary wings.
So the wheels, designed specifically to reduce friction between the plane and a stationary runway, are going to magically sense that the runway is moving in the opposite direction and start creating enough friction to suck up those 80 hojillion newtons of force?

Of course, taking the question as you've interpreted it ("no forward motion relative to an observer standing beside the belt"), the plane doesn't fly. The problem is that for the conveyor belt to generate enough backwards force to offset, through the friction-reducing wheels, the forward force of the engines that it's speed doesn't match (as specified by the question) the speed of anything else, it greatly exceeds it.

Furthermore, I highly doubt the original intent of the question was to specify that the plane had no forward motion relative to an observer standing beside the belt. The answer to that question is trival. The hard thing to figure out, what makes this question interesting, is whether or not there is forward motion relative to an observer standing beside the belt.

[MikeSofaer]

Dave, like essentially everyone getting this problem wrong, isn't concerned with the engines. He intereprets "speed of the plane" as speed relative to the conveyor belt. This defines the real speed of the plane to be 0 and makes all other factors irrelevant. It's a silly definition of speed, though.

[shift6]

I'm right because if there ever existed a big magic gay conveyor belt (BMGCB) that perfectly matched an airplane's speed in the opposite direction, de plane, de plane would not pass through a body of air and allow the wings to provide lift because in my hypothetical interpretation, there are no other forces implicit or mentioned to lead to me to believe otherwise.
Think of it this way dude: let's say a plane is in flight and it has its landing gear out. If the BMGCB were to suddenly appear under it and contact the wheels, would the plane stop flying?

They key is what Houngan (I believe) mentioned earlier, and which I neglected in my original post. The wheels on a plane are (effectively) free spinning. They aren't axeled to each other, nor are they driven by the engines. They are only there to give it an easy time of landing and taking off. Some planes, like water planes, don't even have wheels. Not the same for cars.

[Marcus]

Think of it this way dude: let's say a plane is in flight and it has its landing gear out. If the BMGCB were to suddenly appear under it and contact the wheels, would the plane stop flying?

What the fuck dude. You are kidding right?

[shift6]

But in the problem stated, the Wheels and the Belt are ALWAYS moving at the same speed, so the other factors do not matter as they can not influence the forward momentum of the plane.
Engines are influencing forward motion. They are shooting out like a hundred thousand pounds of force. The wheels have nothing to do with the motion of a plane.

[shift6]

What the fuck dude. You are kidding right?
No, not at all. I'm working backwards. Let's say it's an RC airplane to remove some of the bizarre magic-ness. So you've got an RC plane going at say 20 mph through the air, ten feet above the ground. You have pre-installed a conveyor belt moving at 20 mph in the opposite direction in front of it. The plane flies directly forward to the belt such that the wheels "land on" the conveyer which is perfectly matching the plane's speed (we'll assuming no acceleration to make it easier).

Does the plane stop? If not, why would it be different at half that speed: 10 mph? Or half that speed: 5 mph? And so forth.

[Marcus]

The wheels have nothing to do with the motion of a plane.

Well except you know when its like well trying to take off or something.

And dude I 100% get what you are saying but you cant use that arguement because the plane is already in the air.

[shift6]

Well except you know when its like well trying to take off or something.

And dude I 100% get what you are saying but you cant use that arguement because the plane is already in the air.
The plane is always in the air. Only unpowered wheels touch the ground.

[MarchHare]

The plane is always in the air. Only unpowered wheels touch the ground.

Unpowered wheels which create friction (how much?) which may be enough to slow the plane below its stalling speed and prevent it from flying.

And now we're back to where we started...

[Squirrel Killer]

Unpowered wheels which create friction (how much?) which may be enough to slow the plane below its stalling speed and prevent it from flying.
Certainly they do create friction. If they create so much friction that they slow the plane below the stall speed, however, how do planes take off in the first place?

[Saxman_72]

Unpowered wheels which create friction (how much?) which may be enough to slow the plane below its stalling speed and prevent it from flying.

No, it won't be slowed down enough by something which is only causing the wheels to turn twice as fast as normal as they would be were they in contact with the ground. This is what the question implies.

[Dave Markell]

Oh good grief. You're suggesting that you can spin the wheels fast enough that the torque generated across the ball bearings is sufficient to counteract a jet's engines? If it were that significant, they'd grease the runways.

H.

Certainly. Friction is capable of infinite force. The faster the wheels spin, the more friction they generate. In this setting, their rate of rotation would reach a truly enormous level, and so would the friction they generated.

Admittedly, I'm a biochemist by training, but I had seven years of undergraduate and graduate science courses, including physics. I understand how thought experiments are supposed to work, and this conveyor belt clearly is such an experiment. Though badly written, as I mentioned before, its intent is clear.

[instant0]

Are'nt there some 3d Physics Magic Software out there where this can be simulated... :-)

We need answers!

[Dave Markell]

Dave, like essentially everyone getting this problem wrong, isn't concerned with the engines. He intereprets "speed of the plane" as speed relative to the conveyor belt. This defines the real speed of the plane to be 0 and makes all other factors irrelevant. It's a silly definition of speed, though.

Not at all. I interpret "speed of the plane" as speed relative to the ground, not the conveyor belt. It could achieve infinite speed relative to the conveyor belt and still not take off so long as there was no speed relative to the ground. No air flow over the wings = no lift = no flight.

[Saxman_72]

Though badly written, as I mentioned before, its intent is clear.
Clear like mud.
The belt has a special system that will perfectly match the speed and acceleration of the plane in the opposite direction.
When I read this, it implied to me (quite clearly) that speed and velocity (with regards to both the conveyor belt and the plane) was relative to the ground - in which case, the plane will take off.

[Houngan]

Certainly. Friction is capable of infinite force. The faster the wheels spin, the more friction they generate. In this setting, their rate of rotation would reach a truly enormous level, and so would the friction they generated.

Admittedly, I'm a biochemist by training, but I had seven years of undergraduate and graduate science courses, including physics. I understand how thought experiments are supposed to work, and this conveyor belt clearly is such an experiment. Though badly written, as I mentioned before, its intent is clear.

I don't think anyone is arguing whether or not, if you increase factors in the equation to infinity, that you can't get certain results. However, to infer that "conveyor belt moves backwards as fast as wheels move forwards" means that "conveyor belt moves backwards fast enough to generate torque via friction to counteract forward thrust of engines" is begging the question quite a bit.

As we began, the ultimate information is that airspeed over wings = lift. When we add the fact that airplanes do not transfer or use any power to/from the wheels, the answer is clear. Conveyor belts make the wheels spin faster, but have no effect on the plane, which has no relationship thrust-wise with the wheels, other than relatively infintesimal torque generated by friction inside the bearings.

Were that a valid way to motivate a vehicle, axles would just freespin inside the bearings to make cars go, rather than be attached directly to the wheels.

H.

[MikeSofaer]

Not at all. I interpret "speed of the plane" as speed relative to the ground, not the conveyor belt. It could achieve infinite speed relative to the conveyor belt and still not take off so long as there was no speed relative to the ground. No air flow over the wings = no lift = no flight.
But you think it isn't moving relative to the ground. So you think the conveyor is stopped?

[Dave Markell]

As we began, the ultimate information is that airspeed over wings = lift. When we add the fact that airplanes do not transfer or use any power to/from the wheels, the answer is clear. Conveyor belts make the wheels spin faster, but have no effect on the plane, which has no relationship thrust-wise with the wheels, other than relatively infintesimal torque generated by friction inside the bearings.

And this is where we disagree, and your side wanders down an erroneous path :-). To move a plane on the ground, the engine thrust must overcome initial inertia, wind resistance, and the frictional force generated by the wheels. As wheel rotation speed increases, so does said force, to potentially infinite levels. It can and will consume every erg of power a jet can provide in this scenario for the very reason you mentioned: "conveyor belts make the wheels spin faster." This magic conveyor belt can make them spin so fast that the plane is stationary relative to the ground.

It's really a case of reductio ad absurdum. You have to consider the extreme and infinite cases in thought experiments such as this.

[Dave Markell]

But you think it isn't moving relative to the ground. So you think the conveyor is stopped?

Sigh. Look Mike, let's break it down:

Speed = distance traveled per unit time. Since I argue that the plane will remain stationary relative to the ground, its speed by definition is therefore zero.

However, the conveyor belt is moving at potentially infinite speed relative to the ground, in the opposite direction of engine thrust. And the plane's wheels are rotating at a potentially infinite rate to match the conveyor. But wheel rotation does not equate to "speed" for the plane as a whole.

Clear?

[MikeSofaer]

Sigh. Look Mike, let's break it down:

Speed = distance traveled per unit time. Since I argue that the plane will remain stationary relative to the ground, its speed by definition is therefore zero.

However, the conveyor belt is moving at potentially infinite speed relative to the ground, in the opposite direction of engine thrust. And the plane's wheels are rotating at a potentially infinite rate to match the conveyor. But wheel rotation does not equate to "speed" for the plane as a whole.

Clear?
Sure, clear. That situation is theoretically consistent.

Just completely in contradiction to the actual question, which states that the conveyor belt matches the speed of the plane. In your situation the plane has 0 speed at the conveyor has a huge speed. This is not matched speed.

Clear?

[Dave Markell]

Sure, clear. That situation is theoretically consistent.

Just completely in contradiction to the actual question, which states that the conveyor belt matches the speed of the plane. In your situation the plane has 0 speed at the conveyor has a huge speed. This is not matched speed.

Clear?

As I said before, the thought experiment is badly written. I assure you, no one with serious science training would put it in such terms.

[MikeSofaer]

As I said before, the thought experiment is badly written. I assure you, no one with serious science training would put it in such terms.
Well, the written problem isn't the one you think it is, you have that much right.

[MikeJ]

I am amazed that after so long, we can't even seem to agree on what we are talking about.

Not at all. I interpret "speed of the plane" as speed relative to the ground, not the conveyor belt. It could achieve infinite speed relative to the conveyor belt and still not take off so long as there was no speed relative to the ground. No air flow over the wings = no lift = no flight.

Dave, tell me which 'control system' best describes the action of the conveyor (or propose a third):

Mk I Control System: If the center of mass of the plane has an instantaneous velocity (relative to rest) of +x mph at time t, then the conveyor belt has an instantaneous velocity (relative to rest) of -x mph at time t.

If v_plane and v_belt represent the horizontal component of velocity, relative to rest, of the plane and the (top surface of the) belt, respectively, under the Mk I system, at all times,
v_plane + v_belt = 0


Mk II Control System: If the center of mass of the plane has an instantaneous velocity (relative to the *belt*) of +x mph at time t, then the conveyor belt has an instantaneous velocity (relative to rest) of -x mph at time t.

If r_plane represents the velocity of the plane relative to the belt, then the rule for control system Mk II is:

r_plane + v_belt = 0

But r_plane = v_plane - v_belt, so...

(v_plane - v_belt) + v_belt = 0
v_plane = 0



So there are 3 questions:

Q1: Does the belt operate under control system Mk I or Mk II?
Q2: If under Mk I, does the plane take off?
Q3: If under Mk II, does the plane take off?

The answer to Q3 is no. The plan can't take off, because it can't achieve any horizontal velocity. Note that under this scenario, the belt would be moving really fast (many times faster than take-off speed) to counteract the engine thrust.

The answer to Q2 is yes.

The answer to Q1 is debatable.

Note that the distinction of whether the plane is powered through it's wheels or by jet engines isn't critical to the above.

[Dave Markell]

Well, the written problem isn't the one you think it is, you have that much right.

And more. Much more.

[MikeSofaer]

And more. Much more.
You have built yourself a logically unassaible position, in which you view any disagreement between your interpretation of the question and the actual text to be bad writing. The questioner must have meant to specify the system you envision, rather than the system he specified. That's silly, but at least it's consistent.

[Dave Markell]

I am amazed that after so long, we can't even seem to agree on what we are talking about.

The reason is the poor wording of the original question. GIGO for sure.

As for your question, I feel that the author's intent is that this magic (literally) conveyor belt operates instantaneously. This is the key, a true lapse of no time. Were there even a pico-picosecond's worth of lag between changes in plane and belt speed, the plane would take off, period. However, via magic, the belt responds with true simultaneity. As a result, the v_plane component in the Mark I system is always 0, since the plane can never achieve any motion relative to the ground. The r_plane variable in the Mark II system is a better expression of the magic nature of the experiment.

And yes, I think the belt would achieve near-relativistic velocities pretty quickly :-)

[Dave Markell]

You have built yourself a logically unassaible position, in which you view any disagreement between your interpretation of the question and the actual text to be bad writing. The questioner must have meant to specify the system you envision, rather than the system he specified. That's silly, but at least it's consistent.

Clearly, I'm talking past you here and cannot reach you. Toss around all the insults you want, Mike--not planning to answer you again.

[MikeSofaer]

Clearly, I'm talking past you here and cannot reach you. Toss around all the insults you want, Mike--not planning to answer you again.
I didn't intend to insult you, and I think I only addressed your arguments, although more colorfully than I might have.

There are several logically consistent positions one can take.

1) The plane's speed is measured relative to the ground, and "matching speed in the opposite direction" means that the conveyor moves relative to the ground and the same rate that the plane moves relative to the ground. I think this is the least silly interpretation.

2) The plane's speed is measured relative to the conveyor, and "matching speed" means the conveyor moves relative to the plane at the same rate it moves relative to the ground. This defines the plane as motionless mathematically. I think this is silly, but it's consistent.

3) The plane's speed is measured relative to the ground and "matching speed in the opposite direction" means "moves at whatever speed is necessary to keep the plane from moving". I think this is a stretch based on the wording, but it is consistent.

If you think 3) is the correct interpretation, and that 1) agrees with the text better due to an accident of bad writing, that's also a consistent position, and can't be refuted.

[Saxman_72]

There are several logically consistent positions one can take.

1) The plane's speed is measured relative to the ground, and "matching speed in the opposite direction" means that the conveyor moves relative to the ground and the same rate that the plane moves relative to the ground. I think this is the least silly interpretation.
This is the position that I took when I read the question as it seemed to make the most common sense - the plane will take flight in this scenario.

[DeepT]

Will somebody just build a god-dammed conveyor belt and launch a plane from it so we can be done with this discussion? To bad those mythbuster guys dont read this fourm, they could proabbly McGyver one together and put an end to this debate.