Mythbuster museum exhibit takes off March 15, 2012 6:55 AM Subscribe
Still not convinced about that plane on a conveyor belt thing? (See also here here and here.) Well, now you can try it for yourself at the new Mythbusters exhibit at the Museum of Science and Industry.
Make it a meetup EC. I'd come.
posted by IndigoRain at 7:58 AM on March 15, 2012
posted by IndigoRain at 7:58 AM on March 15, 2012
*starts considering a quick weekend trip to Chicago this summer*
Make sure the runway doesn't move or you'll stay at home.
posted by Namlit at 8:44 AM on March 15, 2012
Make sure the runway doesn't move or you'll stay at home.
posted by Namlit at 8:44 AM on March 15, 2012
ohh, are there cannons involved in any of the exhibits ? /off to read article..
posted by k5.user at 9:13 AM on March 15, 2012
posted by k5.user at 9:13 AM on March 15, 2012
Mythbuster museum exhibit takes off
Ugh, NO IT DOESN'T I thought this was settled.
posted by Hoopo at 9:36 AM on March 15, 2012 [3 favorites]
Ugh, NO IT DOESN'T I thought this was settled.
posted by Hoopo at 9:36 AM on March 15, 2012 [3 favorites]
Come to Chicago for the Mythbusters exhibit, but stay for shakespeherian's fairly large doorway.
posted by SpiffyRob at 10:35 AM on March 15, 2012 [3 favorites]
posted by SpiffyRob at 10:35 AM on March 15, 2012 [3 favorites]
Should this not be a straight up FPP?
posted by Artw at 11:38 AM on March 15, 2012 [1 favorite]
posted by Artw at 11:38 AM on March 15, 2012 [1 favorite]
I never understood what was so tough about understanding that the plane takes off. If it were a glider with motorized wheels it wouldn't, but propellors/jets pull the plane through the air, not roll it over a surface. The wheels are just friction reducers.
posted by cmoj at 12:25 PM on March 15, 2012 [2 favorites]
posted by cmoj at 12:25 PM on March 15, 2012 [2 favorites]
Oh boy, Chicago! That's where I'm a viking!
posted by chinston at 12:45 PM on March 15, 2012 [1 favorite]
posted by chinston at 12:45 PM on March 15, 2012 [1 favorite]
"I never understood what was so tough about understanding that the plane takes off."
People are weird about how they misunderstand things. God, paulsc drove me nuts in that first thread.
posted by Ivan Fyodorovich at 1:02 PM on March 15, 2012
People are weird about how they misunderstand things. God, paulsc drove me nuts in that first thread.
posted by Ivan Fyodorovich at 1:02 PM on March 15, 2012
Okay, here's the secret of the thought experiment: It's a really, really poorly-constructed thought experiment. So:
If the plane is powered on the ground by the wheels, then no, it can't take off because there's no air going over the foil, so it can't lift.
HOWEVER, if the wheels are NOT what is powering the plane (which is how modern aircraft actually work) then they and the conveyer belt are both meaningless. The plane moves forward as normal but the wheels spin at double speed, until it takes off.
Does everyone understand now? It's a shitty thought experiment which was either 1) made by someone who doesn't understand how landing gear functions, or else 2) made by someone who was being a dick about the fact that most people don't know how landing gear functions.
Either way, it is stupid. We may let it drop now.
posted by Navelgazer at 1:21 PM on March 15, 2012 [1 favorite]
If the plane is powered on the ground by the wheels, then no, it can't take off because there's no air going over the foil, so it can't lift.
HOWEVER, if the wheels are NOT what is powering the plane (which is how modern aircraft actually work) then they and the conveyer belt are both meaningless. The plane moves forward as normal but the wheels spin at double speed, until it takes off.
Does everyone understand now? It's a shitty thought experiment which was either 1) made by someone who doesn't understand how landing gear functions, or else 2) made by someone who was being a dick about the fact that most people don't know how landing gear functions.
Either way, it is stupid. We may let it drop now.
posted by Navelgazer at 1:21 PM on March 15, 2012 [1 favorite]
Unless you work in the science field, chances are your days of conducting cool experiments are over.
As someone who once worked in "the science field," I have some very disappointing news for you....
posted by schmod at 1:22 PM on March 15, 2012 [1 favorite]
As someone who once worked in "the science field," I have some very disappointing news for you....
posted by schmod at 1:22 PM on March 15, 2012 [1 favorite]
Aeronautical engineer here! Here's the reason the airplane can fly:
Elves.
posted by backseatpilot at 1:29 PM on March 15, 2012 [9 favorites]
Elves.
posted by backseatpilot at 1:29 PM on March 15, 2012 [9 favorites]
"Does everyone understand now? It's a shitty thought experiment which was either 1) made by someone who doesn't understand how landing gear functions, or else 2) made by someone who was being a dick about the fact that most people don't know how landing gear functions."
I don't think that's true because a lot of the people who got the problem wrong are pilots, who certainly know how their landing gear work.
posted by Ivan Fyodorovich at 1:57 PM on March 15, 2012
I don't think that's true because a lot of the people who got the problem wrong are pilots, who certainly know how their landing gear work.
posted by Ivan Fyodorovich at 1:57 PM on March 15, 2012
The problem is that if you say that the treadmill's speed ALWAYS EXACTLY matches the rotation of the wheels, then things break. A real plane can take off from a real treadmill because a real treadmill reaches its max speed before the plane's wheels (this totally reputable site claims the world's fastest treadmill is only 32mph). But if you had a hypothetical treadmill that could reach arbitrary velocities, then it and the wheels would keep on accelerating in tandem until the plane's wheels exploded from heat. If both the treadmill and the plane's wheel are indestructible and capable of arbitrarily high velocities, then you're asking what happens when an unopposable force meets an immovable object.
posted by Pyry at 3:08 PM on March 15, 2012
posted by Pyry at 3:08 PM on March 15, 2012
Pyry: In that set of rules, you don't have to extrapolate or have infinitely strong anything. The only state that meets that description is that neither the plane nor the treadmill are moving at all. Unless you are willing to "cheat" and let the wheels slip or something. (Without slippage, the wheels are turning at the speed of the plane plus the speed of the treadmill, and the treadmill is defined as moving at the speed of the wheels. This is inconsistent unless the speed of plane = 0)
posted by aubilenon at 3:27 PM on March 15, 2012
posted by aubilenon at 3:27 PM on March 15, 2012
I saw their touring show in Dallas this week, and they mentioned this exhibit. I went to Chicago a few times as a kid, and I always begged to go to this museum. This would have made it even better.
On a side, the Behind the Myths show was pretty fun. They had some obvious technical difficulties (among them: jammed paintball machine gun, broken stationary bike pedal, and a Buster that refused to fall), but Adam kept the audience laughing despite the mishaps. Definitely go see it of you get the chance - it's nothing novel, if you're a fan of the show, but they're great to see live.
posted by SNWidget at 3:39 PM on March 15, 2012
On a side, the Behind the Myths show was pretty fun. They had some obvious technical difficulties (among them: jammed paintball machine gun, broken stationary bike pedal, and a Buster that refused to fall), but Adam kept the audience laughing despite the mishaps. Definitely go see it of you get the chance - it's nothing novel, if you're a fan of the show, but they're great to see live.
posted by SNWidget at 3:39 PM on March 15, 2012
"It's a really, really poorly-constructed thought experiment"
I like it - it makes you realise that just because something has wheels, those wheels aren't the thing that pushes to vehicle along.
Given that 99.9% of the time this is what happens (e.g. cars), people assume it's what always happens.
Another aeronautical engineer here and I'm sure it took me 30 seconds of thinking to work it out the first time I heard it - it's not like you'd have a reason to consider this situation in reality.
Although I still don't understand the physics behind the "directly downwind faster than the wind" :-)
posted by trialex at 3:52 PM on March 15, 2012
I like it - it makes you realise that just because something has wheels, those wheels aren't the thing that pushes to vehicle along.
Given that 99.9% of the time this is what happens (e.g. cars), people assume it's what always happens.
Another aeronautical engineer here and I'm sure it took me 30 seconds of thinking to work it out the first time I heard it - it's not like you'd have a reason to consider this situation in reality.
Although I still don't understand the physics behind the "directly downwind faster than the wind" :-)
posted by trialex at 3:52 PM on March 15, 2012
Hey so how is this metafilter related anyway? Because we had a post about something related to this thing at the science museum, or is it because we own asavage?
posted by crunchland at 4:23 PM on March 15, 2012
posted by crunchland at 4:23 PM on March 15, 2012
Hey so how is this metafilter related anyway? Because we had a post about something related to this thing at the science museum, or is it because we own asavage?
This is MetaFilter related purely because it annoys crunchland.
posted by loquacious at 5:00 PM on March 15, 2012 [1 favorite]
This is MetaFilter related purely because it annoys crunchland.
posted by loquacious at 5:00 PM on March 15, 2012 [1 favorite]
The problem is that if you say that the treadmill's speed ALWAYS EXACTLY matches the rotation of the wheels, then things break.
No, because no matter the speed of the wheels, the plane is moving forward through the air. So, the wheels would move faster and faster without significantly affecting the plane's forward motion until the plane takes off.
The wheels are a red harring. They spin freely. Say you have a near vertical treadmill that's running uphill and you set a hotwheels car on it. It'll still roll down hill (at plausible speeds).
posted by cmoj at 5:12 PM on March 15, 2012
No, because no matter the speed of the wheels, the plane is moving forward through the air. So, the wheels would move faster and faster without significantly affecting the plane's forward motion until the plane takes off.
The wheels are a red harring. They spin freely. Say you have a near vertical treadmill that's running uphill and you set a hotwheels car on it. It'll still roll down hill (at plausible speeds).
posted by cmoj at 5:12 PM on March 15, 2012
I think the non-intuitive element is that the movement of conveyer belt translates completely into movement of the wheels and none of it gets transferred to the body of the plane.
posted by Artw at 5:21 PM on March 15, 2012
posted by Artw at 5:21 PM on March 15, 2012
"The wheels are a red harring. They spin freely."
They are a red herring and they do spin freely. The difficulty is that the problem can't actually occur in the real world as stated. The treadmill would always be chasing the speed indicated by the wheels and would escalate quickly to infinity.
So, yes, the problem is simple if you already understand it. That is, if you know that the rotation of the wheels and the treadmill don't have anything to do with the plane's ability to fly. But if you don't already understand that, then you'll try to parse the problem by accepting its premise: that the treadmill moves equal and opposite to whatever the wheels are doing. If that were possible, the plane wouldn't move. But it's not possible because the treadmill can't possibly counteract the forward motion caused by the propeller, assuming that the wheels function as ideal wheels (i.e., frictionless rotation).
As stated, the problem assumes something impossible. In the most obvious sense, this impossibility is revealed by the fact that a plan will, in fact, take-off. But the impossibility of the premise is a bit more subtle, really.
Bottom line: like many problems that people are widely confused about (such as the Monty Hall Problem), this one confuses people because it's a kind of misdirection. It's hiding something in its premise that means that unless you're predisposed to noticing that flaw in its premise, it's hard to figure what's going on. If you do see the flaw in the premise, it's hard to understand how anyone can get the answer wrong.
posted by Ivan Fyodorovich at 5:38 PM on March 15, 2012
They are a red herring and they do spin freely. The difficulty is that the problem can't actually occur in the real world as stated. The treadmill would always be chasing the speed indicated by the wheels and would escalate quickly to infinity.
So, yes, the problem is simple if you already understand it. That is, if you know that the rotation of the wheels and the treadmill don't have anything to do with the plane's ability to fly. But if you don't already understand that, then you'll try to parse the problem by accepting its premise: that the treadmill moves equal and opposite to whatever the wheels are doing. If that were possible, the plane wouldn't move. But it's not possible because the treadmill can't possibly counteract the forward motion caused by the propeller, assuming that the wheels function as ideal wheels (i.e., frictionless rotation).
As stated, the problem assumes something impossible. In the most obvious sense, this impossibility is revealed by the fact that a plan will, in fact, take-off. But the impossibility of the premise is a bit more subtle, really.
Bottom line: like many problems that people are widely confused about (such as the Monty Hall Problem), this one confuses people because it's a kind of misdirection. It's hiding something in its premise that means that unless you're predisposed to noticing that flaw in its premise, it's hard to figure what's going on. If you do see the flaw in the premise, it's hard to understand how anyone can get the answer wrong.
posted by Ivan Fyodorovich at 5:38 PM on March 15, 2012
It's a really, really poorly-constructed thought experiment.
Actually, the thought experiment as posed - with a treadmill whose backward speed is made to track the plane's forward speed - is perfectly well constructed.
What's often terribly badly constructed is the thought experiment as understood. Many people seem to fall into the trap of pegging the plane's forward speed to the speed of its wheels, missing the point that unlike a car, a taxiing plane doesn't use its wheels to generate drive; then they focus on the speed of the wheels, conclude that the treadmill speed matches the wheel speed and that the plane's forward speed is therefore zero.
The point is that these are not the conditions described in the original question. The original question says nothing at all about wheels, only about planes and treadmills.
And the point of the original question, it seems to me, is not to raise a poser about airplanes taking off, but to apply the same kind of gentle misdirection that illusionists use and cause similar amounts of bafflement and wonder.
if you don't already understand that, then you'll try to parse the problem by accepting its premise: that the treadmill moves equal and opposite to whatever the wheels are doing.
Again, that's not the premise of the question as posed, which speaks only of airplanes and treadmills and doesn't mention wheels at all.
It's incredibly tempting to think about wheels first and plane speed second. Many people apparently make that error, which is the only reason this question is interesting. But it's an error all the same.
posted by flabdablet at 5:54 PM on March 15, 2012
Actually, the thought experiment as posed - with a treadmill whose backward speed is made to track the plane's forward speed - is perfectly well constructed.
What's often terribly badly constructed is the thought experiment as understood. Many people seem to fall into the trap of pegging the plane's forward speed to the speed of its wheels, missing the point that unlike a car, a taxiing plane doesn't use its wheels to generate drive; then they focus on the speed of the wheels, conclude that the treadmill speed matches the wheel speed and that the plane's forward speed is therefore zero.
The point is that these are not the conditions described in the original question. The original question says nothing at all about wheels, only about planes and treadmills.
And the point of the original question, it seems to me, is not to raise a poser about airplanes taking off, but to apply the same kind of gentle misdirection that illusionists use and cause similar amounts of bafflement and wonder.
if you don't already understand that, then you'll try to parse the problem by accepting its premise: that the treadmill moves equal and opposite to whatever the wheels are doing.
Again, that's not the premise of the question as posed, which speaks only of airplanes and treadmills and doesn't mention wheels at all.
It's incredibly tempting to think about wheels first and plane speed second. Many people apparently make that error, which is the only reason this question is interesting. But it's an error all the same.
posted by flabdablet at 5:54 PM on March 15, 2012
Either way, it is stupid. We may let it drop now.
We may, but we probably won't. We got it on us again. I expect that once again it will take several hundred comments to get it off.
posted by flabdablet at 5:57 PM on March 15, 2012
We may, but we probably won't. We got it on us again. I expect that once again it will take several hundred comments to get it off.
posted by flabdablet at 5:57 PM on March 15, 2012
Oh, and you should totally switch doors.
posted by flabdablet at 5:57 PM on March 15, 2012 [2 favorites]
posted by flabdablet at 5:57 PM on March 15, 2012 [2 favorites]
They are a red herring and they do spin freely.
As a thought experiment, imagine an ideal cart (just four wheels affixed to a block) on a treadmill, where the cart's wheels spin without friction.
Now, supposing the treadmill starts at rest and accelerates up to some constant velocity. What happens to the cart? Summon all your high-school knowledge of rigid body dynamics before answering-- imagine you're taking the AP physics test.
a) the cart remains perfectly motionless as the treadmill spins just the wheels; the treadmill exerts no linear force on the wheels, only an angular force (torque)
b) the cart is accelerated backwards and the wheels spin; the treadmill exerts both torque and a linear force on the wheels
c) the cart is accelerated backwards, but the wheels do not spin; the treadmill exerts only a linear force on the wheels
Ok, you probably have an answer, but before committing to it, imagine just a wheel on the treadmill; as the treadmill accelerates, what happens to this free wheel? If your answer is different for the free wheel and the cart, what force is causing this difference?
-------
-------
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Answer time: the correct answer is (b), for both the cart and the free wheel. The treadmill exerts a force at the point of contact with the wheel (through friction), and this force applies both a torque to the wheel, and a linear force at the wheel's center of mass, translating into both angular and linear acceleration. This is because both linear and angular momentum are conserved. Imagine an idealized sphere on a treadmill (a free wheel); as the treadmill accelerates, the sphere does not simply rotate in place, but is also accelerated linearly in the direction of the treadmill.
In other words, the wheels cannot 'spin freely', but must transmit linear force to the plane proportional to the acceleration of the treadmill.
If the treadmill has unlimited power, it can simply continue accelerating at a rate such that the backwards force it applies to the plane through this acceleration equals the plane's thrust. In reality, neither the plane's wheels nor the treadmill can continue to accelerate indefinitely, and so whether the plane is able to take off depends on which one wins in this battle of acceleration; in the real world, this is the wheels.
posted by Pyry at 6:52 PM on March 15, 2012
As a thought experiment, imagine an ideal cart (just four wheels affixed to a block) on a treadmill, where the cart's wheels spin without friction.
Now, supposing the treadmill starts at rest and accelerates up to some constant velocity. What happens to the cart? Summon all your high-school knowledge of rigid body dynamics before answering-- imagine you're taking the AP physics test.
a) the cart remains perfectly motionless as the treadmill spins just the wheels; the treadmill exerts no linear force on the wheels, only an angular force (torque)
b) the cart is accelerated backwards and the wheels spin; the treadmill exerts both torque and a linear force on the wheels
c) the cart is accelerated backwards, but the wheels do not spin; the treadmill exerts only a linear force on the wheels
Ok, you probably have an answer, but before committing to it, imagine just a wheel on the treadmill; as the treadmill accelerates, what happens to this free wheel? If your answer is different for the free wheel and the cart, what force is causing this difference?
-------
-------
-------
Answer time: the correct answer is (b), for both the cart and the free wheel. The treadmill exerts a force at the point of contact with the wheel (through friction), and this force applies both a torque to the wheel, and a linear force at the wheel's center of mass, translating into both angular and linear acceleration. This is because both linear and angular momentum are conserved. Imagine an idealized sphere on a treadmill (a free wheel); as the treadmill accelerates, the sphere does not simply rotate in place, but is also accelerated linearly in the direction of the treadmill.
In other words, the wheels cannot 'spin freely', but must transmit linear force to the plane proportional to the acceleration of the treadmill.
If the treadmill has unlimited power, it can simply continue accelerating at a rate such that the backwards force it applies to the plane through this acceleration equals the plane's thrust. In reality, neither the plane's wheels nor the treadmill can continue to accelerate indefinitely, and so whether the plane is able to take off depends on which one wins in this battle of acceleration; in the real world, this is the wheels.
posted by Pyry at 6:52 PM on March 15, 2012
By the way, I got the following expression for the backwards linear force applied by the treadmill to the plane:
F_plane = (m a_tread) / (2 pi m r^2 / I + 1)
m is the plane's mass, r is the radius of the wheels, a_tread is the acceleration of the treadmill, and I is the total angular momentum of the wheels.
This force is linearly proportional to the treadmill's acceleration, but the constant will be very small since the plane has a huge mass and the wheels have very little angular momentum. Nonetheless, an unlimited treadmill would be able to counteract the plane's forward thrust with an appropriately huge acceleration.
posted by Pyry at 7:43 PM on March 15, 2012
F_plane = (m a_tread) / (2 pi m r^2 / I + 1)
m is the plane's mass, r is the radius of the wheels, a_tread is the acceleration of the treadmill, and I is the total angular momentum of the wheels.
This force is linearly proportional to the treadmill's acceleration, but the constant will be very small since the plane has a huge mass and the wheels have very little angular momentum. Nonetheless, an unlimited treadmill would be able to counteract the plane's forward thrust with an appropriately huge acceleration.
posted by Pyry at 7:43 PM on March 15, 2012
Sorry, I is the total rotational inertia of the wheels; I don't know why I wrote angular momentum twice instead of rotational inertia.
posted by Pyry at 7:55 PM on March 15, 2012
posted by Pyry at 7:55 PM on March 15, 2012
They spin freely
Nearly freely, right? There's some friction there, so you need an (imperceptible) extra space on the runway, correct?
posted by spaltavian at 7:59 PM on March 15, 2012
Nearly freely, right? There's some friction there, so you need an (imperceptible) extra space on the runway, correct?
posted by spaltavian at 7:59 PM on March 15, 2012
It's a shitty thought experiment which was either 1) made by someone who doesn't understand how landing gear functions, or else 2) made by someone who was being a dick about the fact that most people don't know how landing gear functions.But how could anyone think that a 747 is accelerated to 180-odd miles per hour through torque applied to its wheels? I mean look at it.
posted by planet at 8:49 PM on March 15, 2012
The point of my earlier comment was that this whole "thought experiment," if it means any damn thing at all, is "do you know that landing gear spins freely?" It's silly and insulting and pointless.
posted by Navelgazer at 9:12 PM on March 15, 2012
posted by Navelgazer at 9:12 PM on March 15, 2012
And the point of my comment is that it doesn't matter if the landing gear spins freely; as long as the landing gear has non-zero rotational inertia, some fraction of the treadmill's acceleration will be transferred to the plane. Even with ideal wheels with zero friction against the axle, the treadmill exerts a backwards force on the plane. Hiding behind a dumb trick question is actually a more interesting physics problem than you're giving it credit.
posted by Pyry at 9:59 PM on March 15, 2012
posted by Pyry at 9:59 PM on March 15, 2012
OK, Pyry, does your thesis apply if the treadmill derives its acceleration from the plane's engines and also benefits from frictionless rollers (as do the wheels, apparently)? In this scenario the only energy source should be the engines.
In order to create rolling interaction between the wheels and the treadmill, I permit friction at the join of tire to belt.
There is air resistance as well.
I have a mental model answer, but do tell!
posted by mwhybark at 11:48 PM on March 15, 2012
In order to create rolling interaction between the wheels and the treadmill, I permit friction at the join of tire to belt.
There is air resistance as well.
I have a mental model answer, but do tell!
posted by mwhybark at 11:48 PM on March 15, 2012
Oh, and the MSI is one of my favorite places in the whole world. Sliced humans!
posted by mwhybark at 11:51 PM on March 15, 2012 [2 favorites]
posted by mwhybark at 11:51 PM on March 15, 2012 [2 favorites]
Pyry and Ivan: I think you're over-complicating this a bit. Here's the problem wording as reported by the Straight Dope:
And we generally don't use wheel RPM in talking about the speed of baseballs, bicycles, baby buggies, budgies, beagles, or bombers, on or off a treadmill. So the only question here is whether we're talking airspeed (estimated by gas pressure against the nose of the plane) or ground speed (using GPS or other navigational features).
If the treadmill has unlimited power, it can simply continue accelerating at a rate such that the backwards force it applies to the plane through this acceleration equals the plane's thrust.
Well, power and force are beyond the scope of the question. What the question defines is:
Plane velocity: +X m/s along a horizontal axis.
Conveyor velocity: -X m/s along a horizontal axis.
We can calculate a finite force exerted by the conveyor on the plane roughly equivalent to wheel drag at 2X m/s. There's no reason to invoke infinities in this problem.
posted by CBrachyrhynchos at 11:53 PM on March 15, 2012
A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off? (emphasis added)The linear speed of any kind of object is defined as change in position over time, not RPM. In cars, trucks, and motorcycles, you use the RPM of the wheels to estimate change in position over time under normal operating conditions. The rotation of the wheels doesn't define vehicle speed. The speed of a car running on a test stand is zero, no matter what the speedometer says. The speed of a car in a locked-wheel skid is often a painful and scary greater than zero.
And we generally don't use wheel RPM in talking about the speed of baseballs, bicycles, baby buggies, budgies, beagles, or bombers, on or off a treadmill. So the only question here is whether we're talking airspeed (estimated by gas pressure against the nose of the plane) or ground speed (using GPS or other navigational features).
If the treadmill has unlimited power, it can simply continue accelerating at a rate such that the backwards force it applies to the plane through this acceleration equals the plane's thrust.
Well, power and force are beyond the scope of the question. What the question defines is:
Plane velocity: +X m/s along a horizontal axis.
Conveyor velocity: -X m/s along a horizontal axis.
We can calculate a finite force exerted by the conveyor on the plane roughly equivalent to wheel drag at 2X m/s. There's no reason to invoke infinities in this problem.
posted by CBrachyrhynchos at 11:53 PM on March 15, 2012
I was so bummed I had to be out of town today; I would have taken time off in the morning to go see the grand opening. I'll have to drive right by tomorrow on the way to a project site, and the temptation to go bust myths instead will be nigh-overwhelming.
This should definitely be a meetup.
posted by BevosAngryGhost at 11:58 PM on March 15, 2012
This should definitely be a meetup.
posted by BevosAngryGhost at 11:58 PM on March 15, 2012
LOL.
Here's a new paradox for you:
Start with a bottle compressed air, puncture one end, and it will clearly rocket away in the other direction right?
Now, what if you start with a new bottle of the same parameters., but instead pump out all the air, then puncture it in the same place in the saw way as before.
Which way does the evacuated bottle move once its been punctured?
posted by Chekhovian at 12:00 AM on March 16, 2012
Here's a new paradox for you:
Start with a bottle compressed air, puncture one end, and it will clearly rocket away in the other direction right?
Now, what if you start with a new bottle of the same parameters., but instead pump out all the air, then puncture it in the same place in the saw way as before.
Which way does the evacuated bottle move once its been punctured?
posted by Chekhovian at 12:00 AM on March 16, 2012
Apparently there's a third option to my original comment: THIS WHOLE THING IS NERD TROLLING.
Beyond the issue of the wheels propelling the plane as it taxis, we have to ask whether we can assume the wheels as frictionless, whether the treadmill can track the speed of the plane, and from what component of the plane, and how, whether the acceleration of the treadmill matches that of the appropriate component of the plane, and so on.
Y'all are right, I was wrong. This is all a very well-designed question.
Just kidding. Fuck this question, which people are spending too much time debating because it is ludicrously stupid.
Wheels taxi the plane? Plane doesn't take off. Wheels spin freely? Plane takes off.
Question stupid? Argue ad infinitum, apparently.
And yeah, pick the other door. You double your chances.
posted by Navelgazer at 12:08 AM on March 16, 2012 [2 favorites]
Beyond the issue of the wheels propelling the plane as it taxis, we have to ask whether we can assume the wheels as frictionless, whether the treadmill can track the speed of the plane, and from what component of the plane, and how, whether the acceleration of the treadmill matches that of the appropriate component of the plane, and so on.
Y'all are right, I was wrong. This is all a very well-designed question.
Just kidding. Fuck this question, which people are spending too much time debating because it is ludicrously stupid.
Wheels taxi the plane? Plane doesn't take off. Wheels spin freely? Plane takes off.
Question stupid? Argue ad infinitum, apparently.
And yeah, pick the other door. You double your chances.
posted by Navelgazer at 12:08 AM on March 16, 2012 [2 favorites]
Okay, here's the secret of the thought experiment: It's a really, really poorly-constructed thought experiment. So:
If the plane is powered on the ground by the wheels, then no, it can't take off because there's no air going over the foil, so it can't lift.
HOWEVER, if the wheels are NOT what is powering the plane (which is how modern aircraft actually work) then they and the conveyer belt are both meaningless. The plane moves forward as normal but the wheels spin at double speed, until it takes off.
Or, in other words:
Only try to realize the truth -- there is no conveyor belt.
posted by Anything at 1:22 AM on March 16, 2012
If the plane is powered on the ground by the wheels, then no, it can't take off because there's no air going over the foil, so it can't lift.
HOWEVER, if the wheels are NOT what is powering the plane (which is how modern aircraft actually work) then they and the conveyer belt are both meaningless. The plane moves forward as normal but the wheels spin at double speed, until it takes off.
Or, in other words:
Only try to realize the truth -- there is no conveyor belt.
posted by Anything at 1:22 AM on March 16, 2012
OK, Pyry, does your thesis apply if the treadmill derives its acceleration from the plane's engines and also benefits from frictionless rollers (as do the wheels, apparently)? In this scenario the only energy source should be the engines.
Well, an unpowered treadmill (which I will model as basically a large log spinning on a fixed axis, so the whole thing looks approximately like this) won't be able to track the plane's acceleration, because it just passively reacts to the plane and can't be directly driven.
Note that since the system starts at rest the total angular momentum (which must by conserved) is zero.
I haven't bothered to set up the equations, but my gut feeling is that if the plane is driven by its wheels (wheels spinning clockwise), the log will absorb some fraction of the plane's acceleration by spinning counter-clockwise. The clockwise angular momentum of the wheels and plane's center of mass are counterbalanced by the counter-clockwise angular momentum of the log, so angular momentum is conserved.
If the plane is driven by an engine (a linear force on its center of mass, pointing right), then the log will be driven clockwise, in the same direction as the plane, at some fraction of the plane's acceleration. This would seem to be a violation of conservation of angular momentum, since the plane's wheels, the plane's center of mass about the system's center, and the log are all rotating clockwise. However, the trick here is that there is no free lunch in terms of forces: the engine can't just apply a magic force, but must react against something, namely its exhaust. The engine's exhaust travels to the left and thus has counter-clockwise angular momentum, balancing the system.
Well, power and force are beyond the scope of the question.
These types of rigid body dynamics problems are fundamentally about forces and power, with velocities and positions being produced almost as byproducts; if force and power are out of scope, then we aren't talking about physics, but rather geometry.
We can calculate a finite force exerted by the conveyor on the plane roughly equivalent to wheel drag at 2X m/s. There's no reason to invoke infinities in this problem.
I have not invoked any 'infinities', and in fact I gave an expression for exactly this force, an expression, which you will note, evaluates to a finite number. What I pointed out is that to maintain this force, the treadmill must continue to accelerate, and that this acceleration is unsustainable by a real world treadmill. A hypothetically powerful treadmill which could accelerate indefinitely (I said 'unlimited', but at no point in time would it require literally 'infinite' power) would be able to exert enough force on the plane to cancel out the forward thrust from the engines.
posted by Pyry at 8:08 AM on March 16, 2012
Well, an unpowered treadmill (which I will model as basically a large log spinning on a fixed axis, so the whole thing looks approximately like this) won't be able to track the plane's acceleration, because it just passively reacts to the plane and can't be directly driven.
Note that since the system starts at rest the total angular momentum (which must by conserved) is zero.
I haven't bothered to set up the equations, but my gut feeling is that if the plane is driven by its wheels (wheels spinning clockwise), the log will absorb some fraction of the plane's acceleration by spinning counter-clockwise. The clockwise angular momentum of the wheels and plane's center of mass are counterbalanced by the counter-clockwise angular momentum of the log, so angular momentum is conserved.
If the plane is driven by an engine (a linear force on its center of mass, pointing right), then the log will be driven clockwise, in the same direction as the plane, at some fraction of the plane's acceleration. This would seem to be a violation of conservation of angular momentum, since the plane's wheels, the plane's center of mass about the system's center, and the log are all rotating clockwise. However, the trick here is that there is no free lunch in terms of forces: the engine can't just apply a magic force, but must react against something, namely its exhaust. The engine's exhaust travels to the left and thus has counter-clockwise angular momentum, balancing the system.
Well, power and force are beyond the scope of the question.
These types of rigid body dynamics problems are fundamentally about forces and power, with velocities and positions being produced almost as byproducts; if force and power are out of scope, then we aren't talking about physics, but rather geometry.
We can calculate a finite force exerted by the conveyor on the plane roughly equivalent to wheel drag at 2X m/s. There's no reason to invoke infinities in this problem.
I have not invoked any 'infinities', and in fact I gave an expression for exactly this force, an expression, which you will note, evaluates to a finite number. What I pointed out is that to maintain this force, the treadmill must continue to accelerate, and that this acceleration is unsustainable by a real world treadmill. A hypothetically powerful treadmill which could accelerate indefinitely (I said 'unlimited', but at no point in time would it require literally 'infinite' power) would be able to exert enough force on the plane to cancel out the forward thrust from the engines.
posted by Pyry at 8:08 AM on March 16, 2012
Pyry: These types of rigid body dynamics problems are fundamentally about forces and power, with velocities and positions being produced almost as byproducts; if force and power are out of scope, then we aren't talking about physics, but rather geometry.
You're putting the question backwards. Velocity and positions are the knowns in this problem. What is the velocity of the plane? X. What is the velocity of the treadmill -X. If the plane moved 10 meters in a second, the treadmill moved 10 meters in the same second. It's the same kind of problem as determining the forces on a car moving against a headwind, or a boat moving against the current.
We can estimate the forces involved here from the velocities of the objects. But the problem depends on the premise that airplanes minimize resistance forces with the ground and maximize propulsive forces with the air.
What I pointed out is that to maintain this force...
The question does not specify that the treadmill maintains force, only speed. "Maintaining" that force is relatively easy if you have a large enough chock.
posted by CBrachyrhynchos at 10:06 AM on March 16, 2012
You're putting the question backwards. Velocity and positions are the knowns in this problem. What is the velocity of the plane? X. What is the velocity of the treadmill -X. If the plane moved 10 meters in a second, the treadmill moved 10 meters in the same second. It's the same kind of problem as determining the forces on a car moving against a headwind, or a boat moving against the current.
We can estimate the forces involved here from the velocities of the objects. But the problem depends on the premise that airplanes minimize resistance forces with the ground and maximize propulsive forces with the air.
What I pointed out is that to maintain this force...
The question does not specify that the treadmill maintains force, only speed. "Maintaining" that force is relatively easy if you have a large enough chock.
posted by CBrachyrhynchos at 10:06 AM on March 16, 2012
CBrachyrhynchos, you're right. But that's sort of the point: the way the problem is set up, the reader is strongly encouraged to think of the plane being kept motionless relative to the ground. Which is the impossibility that I was ultimately talking about. Put another way, the reader isn't explicitly encouraged to think the plane would be motionless, because that would obviously tell them the answer (though for many people the problem may in fact be this tautological), but, rather, it encourages them to assume some mechanism which retards the forward motion of the plane without necessarily stating explicitly that this occurs. Which puts the reader in a weird, ambiguous place.
"The point of my earlier comment was that this whole 'thought experiment,' if it means any damn thing at all, is 'do you know that landing gear spins freely?' It's silly and insulting and pointless."
No, you're wrong. Many pilots get the answer wrong—paulsc is a pilot and even the pilot Mythbusters used predicted wrongly—and I'm certain that pilots are well-aware that wheels rotate freely.
If you look at the arguments in that old thread by paulsc, you'll see that he ended up, later, asserting that the relative doubled speed of the treadmill would cause handling problems for the pilot at take-off, preventing it...but that was clearly a fall-back position from where he began the argument.
What is actually happening is that the way the problem is described encouraged people to start their thought process assuming some mechanism that is counteracting the forward motion of the plane. Even when people know that the plane's props provide the forward motive, they still get the problem wrong because they are confused.
When you actually do understand something like this (or, really, anything) it can be very difficult to understand other people's misunderstanding because you discount the possibility of misunderstandings that, to you, seem improbable or impossible because you actually understand the thing.
posted by Ivan Fyodorovich at 5:14 PM on March 16, 2012
"The point of my earlier comment was that this whole 'thought experiment,' if it means any damn thing at all, is 'do you know that landing gear spins freely?' It's silly and insulting and pointless."
No, you're wrong. Many pilots get the answer wrong—paulsc is a pilot and even the pilot Mythbusters used predicted wrongly—and I'm certain that pilots are well-aware that wheels rotate freely.
If you look at the arguments in that old thread by paulsc, you'll see that he ended up, later, asserting that the relative doubled speed of the treadmill would cause handling problems for the pilot at take-off, preventing it...but that was clearly a fall-back position from where he began the argument.
What is actually happening is that the way the problem is described encouraged people to start their thought process assuming some mechanism that is counteracting the forward motion of the plane. Even when people know that the plane's props provide the forward motive, they still get the problem wrong because they are confused.
When you actually do understand something like this (or, really, anything) it can be very difficult to understand other people's misunderstanding because you discount the possibility of misunderstandings that, to you, seem improbable or impossible because you actually understand the thing.
posted by Ivan Fyodorovich at 5:14 PM on March 16, 2012
the way the problem is set up, the reader is strongly encouraged to think of the plane being kept motionless relative to the ground.
What's interesting to me is the way that as soon as that thought takes root, it really takes root, even though it is directly contradictory to one of the stated premises of the question.
If the plane ends up motionless by whatever means, its speed is zero; yet the question explicitly talks about the plane moving on one direction and the conveyor moving in the other.
The only ambiguity is that the question doesn't explicitly state what the speeds it refers to should be measured with respect to. But in fact there is only one interpretation that makes sense, so that ambiguity is illusory.
It does no good to argue that the speeds should be taken relative to the surface of the conveyor, because the conveyor's speed relative to itself is obviously always zero. In other words, interpreting speeds as relative to the conveyor makes the conveyor's stated motion impossible; therefore, this interpretation is wrong.
It also does no good to argue that the plane's speed should be taken as relative to the conveyor and the conveyor's as relative to the plane. With that interpretation, the stated relationship between plane and conveyor speeds exists regardless of either's speed relative to the ground; the conveyor's backward speed wrt the plane wouldn't need controlling in order to make it match the plane's forward speed wrt the conveyor, which contradicts the question's explicit statement that it is so controlled. So that interpretation is wrong too.
The only plausible interpretation is that both speeds are measured with respect to the ground or (equivalently, assuming windless conditions) surrounding air. Which means that the conveyor's speed is not increasing at whatever ridiculous rate is required to make inertial effects on the plane's wheels matter. The conveyor's backward speed is controlled so as to match the plane's forward speed, exactly as in the Mythbusters setup, and apart from some second-order effects on steering, the plane scarcely notices it's there.
This also means that the whole rope on roller skates model is still, to a large degree, a redundant response to skilful trolling. Even if taxiing were in fact wheel-driven then the plane and conveyor could be made to move as described. Achieving takeoff under these conditions might require modifications to the gear train driving the wheels, because these would need to be made to spin at twice the usual rate to produce any given ground speed, but would not need extra engine power.
posted by flabdablet at 4:32 AM on March 17, 2012
What's interesting to me is the way that as soon as that thought takes root, it really takes root, even though it is directly contradictory to one of the stated premises of the question.
If the plane ends up motionless by whatever means, its speed is zero; yet the question explicitly talks about the plane moving on one direction and the conveyor moving in the other.
The only ambiguity is that the question doesn't explicitly state what the speeds it refers to should be measured with respect to. But in fact there is only one interpretation that makes sense, so that ambiguity is illusory.
It does no good to argue that the speeds should be taken relative to the surface of the conveyor, because the conveyor's speed relative to itself is obviously always zero. In other words, interpreting speeds as relative to the conveyor makes the conveyor's stated motion impossible; therefore, this interpretation is wrong.
It also does no good to argue that the plane's speed should be taken as relative to the conveyor and the conveyor's as relative to the plane. With that interpretation, the stated relationship between plane and conveyor speeds exists regardless of either's speed relative to the ground; the conveyor's backward speed wrt the plane wouldn't need controlling in order to make it match the plane's forward speed wrt the conveyor, which contradicts the question's explicit statement that it is so controlled. So that interpretation is wrong too.
The only plausible interpretation is that both speeds are measured with respect to the ground or (equivalently, assuming windless conditions) surrounding air. Which means that the conveyor's speed is not increasing at whatever ridiculous rate is required to make inertial effects on the plane's wheels matter. The conveyor's backward speed is controlled so as to match the plane's forward speed, exactly as in the Mythbusters setup, and apart from some second-order effects on steering, the plane scarcely notices it's there.
This also means that the whole rope on roller skates model is still, to a large degree, a redundant response to skilful trolling. Even if taxiing were in fact wheel-driven then the plane and conveyor could be made to move as described. Achieving takeoff under these conditions might require modifications to the gear train driving the wheels, because these would need to be made to spin at twice the usual rate to produce any given ground speed, but would not need extra engine power.
posted by flabdablet at 4:32 AM on March 17, 2012
SNWidget: "Definitely go see it of you get the chance "
I can't! Much to my dismay, they're NOT COMING to Chicago!
posted by IndigoRain at 6:53 AM on March 17, 2012
I can't! Much to my dismay, they're NOT COMING to Chicago!
posted by IndigoRain at 6:53 AM on March 17, 2012
* gets to end of all the plane-on-a-runway comments*
....So, who wants to talk about the exhibit itself? Anyone?
posted by EmpressCallipygos at 11:47 AM on March 17, 2012
....So, who wants to talk about the exhibit itself? Anyone?
posted by EmpressCallipygos at 11:47 AM on March 17, 2012
Which way does the evacuated bottle move once its been punctured?
No takers?
Metafilter, I am disappoint.
I'll even give you a hint.
posted by Chekhovian at 4:46 PM on March 17, 2012
No takers?
Metafilter, I am disappoint.
I'll even give you a hint.
posted by Chekhovian at 4:46 PM on March 17, 2012
This whole thing somehow reminds me of our confused physics teacher, when we were learning about curves of Things Thrown. Imagine you're standing on a turning platform and have a ball in your hand which you throw outward at some point. Ball will fall down. Seen from above: in a straight line; relative to the earth surface: in some type of curve.
So some witty person asked what happens when you're spinning around on a large circle and throw the ball toward the center of that the circle instead of outward.
It took our poor teacher one wrong answer (hmm. Then the ball should go down in a spiral, I guess) and a whole lesson full of practical tests (teacher on a turning platform, throwing balls. I'm not kidding), to get him to understand that he'd shifted relativity. Relative to the person still spinning, the ball goes down in a spiral. Relative to the earth, just as above.
(I'm predicting some bearings getting really warm and perhaps a landing gear collapsing, no idea what the max. speed-margins are in these things. Also steering errors would have a greater effect until takeoff. Other than that, happy flight)
posted by Namlit at 12:15 PM on March 19, 2012
So some witty person asked what happens when you're spinning around on a large circle and throw the ball toward the center of that the circle instead of outward.
It took our poor teacher one wrong answer (hmm. Then the ball should go down in a spiral, I guess) and a whole lesson full of practical tests (teacher on a turning platform, throwing balls. I'm not kidding), to get him to understand that he'd shifted relativity. Relative to the person still spinning, the ball goes down in a spiral. Relative to the earth, just as above.
(I'm predicting some bearings getting really warm and perhaps a landing gear collapsing, no idea what the max. speed-margins are in these things. Also steering errors would have a greater effect until takeoff. Other than that, happy flight)
posted by Namlit at 12:15 PM on March 19, 2012
People are quirky. Years ago, my friends who were high school physics textbook editors encountered at work the "shoot blowgun dart at monkey falling out of tree" problem. They mentioned it to me and I was pleased with myself that I immediately thought of just putting the problem in the accelerated frame of gravity and answered that you just aim directly at the monkey and you'll hit it.
Well, I was so pleased with myself, that I emailed my newly ex-girlfriend, the astrophysicist, that night. And she said I was wrong. After some back-and-forth, she explained that I was wrong because "the monkey might hit the ground before the dart hits the monkey".
Which is of course true, but I though it was a very odd practical consideration for an astrophysicist. Except she's an experimentalist, so maybe that explains a lot. (Well, you know by "experimentalist" I mean not a theorist.)
Anyway, the point is that people get hung up on weird things, especially toy problems which are designed, really, to cause people to get hung up on one thing or another. Or maybe not "designed", but those that become popular are culturally selected for being "interesting", which mostly involves being counterintuitive or troublesome in some respect.
posted by Ivan Fyodorovich at 2:07 PM on March 19, 2012
Well, I was so pleased with myself, that I emailed my newly ex-girlfriend, the astrophysicist, that night. And she said I was wrong. After some back-and-forth, she explained that I was wrong because "the monkey might hit the ground before the dart hits the monkey".
Which is of course true, but I though it was a very odd practical consideration for an astrophysicist. Except she's an experimentalist, so maybe that explains a lot. (Well, you know by "experimentalist" I mean not a theorist.)
Anyway, the point is that people get hung up on weird things, especially toy problems which are designed, really, to cause people to get hung up on one thing or another. Or maybe not "designed", but those that become popular are culturally selected for being "interesting", which mostly involves being counterintuitive or troublesome in some respect.
posted by Ivan Fyodorovich at 2:07 PM on March 19, 2012
"No takers?
Metafilter, I am disappoint.
I'll even give you a hint."
I sort of hate that the social context gets involved in these kinds of questions. I assume that the obvious answer is "towards the direction of the puncture", so you'd only ask the question if the answer weren't obvious, especially since you explicitly specified the normal behavior. But I think I'd guess the non-obvious answer (away from the direction of the puncture) anyway because the air isn't being pulled in by the bottle, it's being pushed in by the atmosphere.
posted by Ivan Fyodorovich at 2:19 PM on March 19, 2012
Metafilter, I am disappoint.
I'll even give you a hint."
I sort of hate that the social context gets involved in these kinds of questions. I assume that the obvious answer is "towards the direction of the puncture", so you'd only ask the question if the answer weren't obvious, especially since you explicitly specified the normal behavior. But I think I'd guess the non-obvious answer (away from the direction of the puncture) anyway because the air isn't being pulled in by the bottle, it's being pushed in by the atmosphere.
posted by Ivan Fyodorovich at 2:19 PM on March 19, 2012
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posted by EmpressCallipygos at 7:39 AM on March 15, 2012