[HN Gopher] Very Wrong Math
___________________________________________________________________
Very Wrong Math
Author : breadbox
Score : 179 points
Date : 2025-01-10 23:10 UTC (23 hours ago)
(HTM) web link (www.charlespetzold.com)
(TXT) w3m dump (www.charlespetzold.com)
| BalinKing wrote:
| Related Wikipedia article:
| https://en.wikipedia.org/wiki/String_girdling_Earth#Implicat....
|
| The takeaway is that the extra length of the arc is likely _much_
| smaller than one would intuitively expect. The problem is usually
| framed like so: If you wrapped a rope around the earth, how much
| more rope would you need to add so that it would be 1 meter above
| the ground at all points? The answer is only 2p meters!
| shortrounddev2 wrote:
| (2pi * (n + 1)) - (2pi * n)
|
| -> 2pi * (n + 1 - n)
|
| -> 2pi * 1
|
| -> 2pi
|
| If I remember my algebra correctly. Someone else check my work
| I'm a dropout
| freeopinion wrote:
| For convenience, we set t=2pi. :-)
|
| x = t(r+1) - tr = t(r+1-r) = t(1) = t
| shortrounddev2 wrote:
| How do you pronounce that symbol?
| Tistron wrote:
| Tau. cf vihart:
| https://www.youtube.com/watch?v=jG7vhMMXagQ&t=0s
| freeopinion wrote:
| https://doc.rust-
| lang.org/stable/std/f64/consts/constant.TAU...
|
| https://docs.python.org/3/library/math.html#math.tau
|
| https://www.google.com/search?q=tau*1
|
| https://docs.oracle.com/en/java/javase/21/docs/api/java.b
| ase...
|
| https://learn.microsoft.com/en-
| us/dotnet/api/system.math.tau...
| layer8 wrote:
| https://tauday.com/tau-manifesto
|
| https://en.wikipedia.org/wiki/Tau
| kurthr wrote:
| The only issue I see with this is that as a classic physics
| trope, we've approximated the earth as a sphere.
|
| If, instead we approximate it as a fractal... then the distance
| is infinite, or at least highly dependent on the thickness of
| the rope!
|
| The error in the original is assuming that the radius is
| proportional to the height above the earth (Earthradius=0?).
| Dylan16807 wrote:
| > infinite, or at least highly dependent on the thickness of
| the rope
|
| The latter. But that's only if it's not somewhat taut. Some
| tension brings it closer to a circle and makes the actual
| thickness pretty unimportant.
|
| But I like the idea overall. It means that lifting up the
| string makes it smoother and it actually needs _less_ length.
| How 's that for being unintuitive?
| kurthr wrote:
| Exactly, if you're only 1cm off the surface you follow
| every nook and cranny. If you're 10km off the surface only
| Everest is a blip.
| seanhunter wrote:
| We actually model the earth as a very large _spherical cow_.
| This is approximately the same for most purposes but ends up
| being more convenient.
|
| P.S. Not a physicist, but my child is studying maths and
| physics at Uni at present, so I have it on good authority
| that this is still going on. They told me in their first week
| one of their classes had a worked example where the lecturer
| used the phrase "Assume the penguin's beak is a cone".
| davrosthedalek wrote:
| A spherical cow /in vacuum/
| kergonath wrote:
| > I have it on good authority that this is still going on
|
| Do you mean making simplifying assumptions to make a
| problem tractable? Of course it's still going on. It _has
| to be_ , otherwise you just cannot do anything.
|
| > Assume the penguin's beak is a cone
|
| It is _impossible_ to consider the true shape of a
| penguin's beak for several reasons:
|
| - you'd need to go all the way down to the electron clouds
| of the atoms of the beak, at which point the very concept
| of shape is shaky
|
| - every penguin has a different beak so even if you
| describe perfectly one of them, it does not necessarily
| make your calculation more realistic in general.
|
| There is a spectrum of approximations one can make, but a
| cone is a sensible shape at a first order. It's also simple
| enough that students can actually do it without years of
| experience and very advanced tools.
|
| What do you think they should do instead?
| seanhunter wrote:
| Bet you're fun at parties as they say.
|
| I totally understand why simplifying assumptions are
| helpful in modelling and definitely don't need you to
| explain that. It also is a bit ridiculous if you think
| literally about it which makes it something that is fun
| to laugh about as here.
| kergonath wrote:
| Yes, sure, I get the jokes. I just found it puzzling that
| someone would think it stopped.
|
| And I don't talk about work at parties anyway :)
| eminent101 wrote:
| But nobody in this thread thought it (simplifying
| assumptions) stopped. You seem to be making an assumption
| that someone thought that and then posting long
| explanations that nobody asked for. I read the "P.S." of
| grand-grand-parent comment as good humor. Nothing there
| implied that they really thought that simplifying
| assumptions would/should stop.
|
| Imagine a world where every bit of humor is interpreted
| literally and then refuted pedantically! What kind of a
| world would that be?
| aardvark179 wrote:
| Just because your initial fractal path is infinite does not
| imply that a line offset from it is also infinite (even for
| an infinitely thin rope), at least if the offset version is
| not self intersecting.
| gsf_emergency wrote:
| This could be why dimensional analysis is one of the few things
| from physics class that can't be drilled enough..
|
| Without forcefully dumping the geometric "intuition", this
| would still feel counterintuitive to me!
| nayuki wrote:
| And the text about the airplane problem was added on
| 2024-11-26:
| https://en.wikipedia.org/w/index.php?title=String_girdling_E...
| travisjungroth wrote:
| > The takeaway is that the extra length of the arc is likely
| much smaller than one would intuitively expect.
|
| Maybe it's because I'm a pilot and we never account for
| altitude when measuring distance, my intuition puts the
| difference at "effectively zero". I also have it internalized
| that the earth's atmosphere is _very_ thin.
| nejsjsjsbsb wrote:
| Are we talking spacetime?
| kubb wrote:
| Curious, does the air being thinner affect flight time?
| Waterluvian wrote:
| I think in a way that's why planes fly so much further up than
| you'd think they'd need to. They want more consistent and
| minimal atmospheric conditions. Less air means less energy
| means less turbulence, I think?
|
| If you're talking about friction... oooh that's an interesting
| one. Intuitively yes. But is it also negligible?
| seanhunter wrote:
| Presumably this would affect drag significantly. Here are the
| equations of motion of an aircraft
| https://eaglepubs.erau.edu/introductiontoaerospaceflightvehi...
|
| ...and indeed it does. Here is a discussion
| https://aviation.stackexchange.com/questions/24641/what-is-t...
| jhanschoo wrote:
| There's no straightforward answer because there are many
| factors that affect flight time and fuel economy, including the
| aerodynamics of the plane and the engine technology. I hazard a
| guess that for commercial airplanes these are chosen primarily
| for reasons of fuel economy per seat and then that determines
| the model's designated cruising altitude.
|
| For a particular model, flying above the model's cruising
| altitude should lead to lower fuel efficiency.
| aja12 wrote:
| From what I've learned reading AdmiralCloudberg's plane crashes
| analysis [1]: altitude heavily matters in fuel consumption. Jet
| planes use a lot less fuel at a higher altitude, up to the
| point that a plane on the verge of running out of fuel at a
| medium altitude might manage to squeeze in 50 or 100 more miles
| of flight by climbing 5000 feet, even accounting for the
| increased fuel consumption during climb. I guess that
| correlates with speed as well. Turbofan engines, on the other
| hand, are more fuel efficient than jet engines at lower
| altitudes, hence they remain common for interstate transit. The
| difference seems to be directly caused by the effect of air
| "thickness" on the engines.
|
| [1] https://admiralcloudberg.medium.com/
| danieldk wrote:
| I'm confused, isn't turbofan a type of jet engine?
|
| https://en.m.wikipedia.org/wiki/Turbofan
|
| Did you mean turboprop?
| kergonath wrote:
| Yes, because friction depends on the air density. You can think
| of this as the molecules in the air colliding with a moving
| object and pushing it backwards, thus slowing it. If there are
| fewer molecules, there is less friction and the object can move
| faster with the same thrust.
|
| Thrust itself decreases because there are also fewer molecules
| to push against, so it can get quite complicated if you want to
| account for everything. But overall it is easier to fly faster
| higher up in the atmosphere. Also, atmospheric currents are
| important.
|
| There is a useful discussion here:
| https://aviation.stackexchange.com/questions/57209/how-does-...
| seanhunter wrote:
| I have seen a very similar (incorrect) argument used to justify
| the idea of a flat earth. A builder on youtube made the argument
| (with a similar out of scale drawing of the earth) that if he
| drops a plumb bob and makes a right angle so he has a straight
| horizontal line and then goes across that line for a bit and
| drops another plumb bob, the two lines he has dropped are
| parallel, "proving" that the surface of the earth must be
| parallel to the horizontal line and therefore flat and not
| curved. If the earth's surface was actually curved he argued then
| the two lines he has dropped should tilt slightly inward towards
| each other. Which of course they do. The earth is just much much
| much bigger than in the diagram so the effect is within the
| margin of error for the measurement he was taking.
|
| As a meta point, our intuition often fails us hilariously when we
| are dealing with stuff that is out of the scale we have commonly
| seen in our lives. We joke about LLMs hallucinating but I'm not
| convinced we are so superior when we are outside our personal
| "training data".
| munch117 wrote:
| Ah, but would they actually be parallel on a flat earth?
|
| Say the earth is disc-shaped. Then the center of gravity is
| only directly beneath you if you're standing at the exact
| center. You get ever-so-slightly not parallel lines, just like
| on a round earth.
|
| The fun part of a disc-shaped earth comes as you move towards
| the sides, and gravity, still pointing towards the center,
| makes you stand at an increasingly acute angle to the surface.
| The ground beneath you will then appear like one big endless
| mountainside, with an increasingly steep slope the further away
| from the center that you get.
| jimmaswell wrote:
| I'm considering what flat-surfaced shape you could construct
| with equal gravitational pull at all points. Maybe something
| where the center is thin as a point, the edges have a lot of
| depth, and they curve towards the center either convex or
| concave. Might run some calculus to figure it out.
| t_mann wrote:
| That way you should be able design a disc-shaped earth with
| constant strength of the gravitational force on the whole
| surface. But it would still have a center of mass (likely
| lying outside the shape you're describing, in the void
| beneath the center point), and the _direction_ of the force
| should still be pointing towards that center, no? So the
| problem the GP has described, that you 're starting to tilt
| as you move towards the edge, should remain in principle.
| benterris wrote:
| I believe the strength of gravitational force would not
| be constant either, as your center of mass would still
| have a fixed location, so every point on the disc have
| different distances to that center of mass (in addition
| to not being orthogonal to the surface). But maybe it
| might be approximated with an infinitely long cylinder,
| so the center of mass is infinitely far away below the
| surface ?
| t_mann wrote:
| The thinking in the other post, that the mass increases
| as you move away from the center, in a manner that the
| two effects cancel out, intuitively seems like it should
| be feasible. Remember that the center of mass is just an
| abstraction, you need to take the full integral over all
| mass to get the force vector at each point. And if you're
| closer to more mass further away from the center, which a
| shape like the one described above should give you, it
| might work. But one would have to do the math to be sure.
|
| Edit: come to think of it, maybe that effect would let
| you adjust the direction of the force, too. Thinking
| about center of mass can be treacherous with more complex
| shapes...
| somat wrote:
| yes, we call it a sphere.
|
| I am just joking with you, I know what you mean, however
| the fruit was hanging too low not to pick.
| t_mann wrote:
| A sphere is only locally approximable by flat surfaces,
| but it's nowhere actually flat, which was a requirement
| in the previous post.
| somat wrote:
| Eh, the original post wanted a convex disk that would
| have a uniform gravitational pull, flatness was already
| thrown out as a design requirement. Once convex disks are
| allowed, a specific category of convex disk that provides
| a uniform perpendicular gravitational field comes to
| mind. The sphere. The very object we were trying to
| avoid. It is one of those it's funny because of the irony
| things.
| jimmaswell wrote:
| You misunderstood, I mean for the top to be flat but the
| "underground" to have some kind of shape to compensate
| for the gravitational pull at all points on the flat
| surface. For a 2Dish example in the ballpark, you could
| think of one of these wooden toy bridge blocks:
| https://thumbs.dreamstime.com/b/natural-wood-
| blocks-364582.j...
|
| I think you could construct a curve such that the mass's
| gravitational pull on the right cancels out the pull on
| the left, for any point on the surface.
| thombat wrote:
| Standard flat-earther response is to scornfully deny the
| existence of gravity. It's all density/buoyancy you see...
| Gravity is a hoax promulgated by the notorious cabalist
| Newton, in service to his Illuminati/Papal masters, etc, etc.
| mp05 wrote:
| Why do we still talk about these people? The more we stand
| in awe of their calculated ignorance, the more satisfied
| they are.
|
| I feel like there are better things to do with my time than
| be as fascinated by it as some people.
| tempestn wrote:
| Depends what causes things to stick to the flat Earth. IIRC
| flat earthers have various explanations for gravity,
| including the disc continuously accelerating upward; in that
| case you'd experience the same force everywhere on it.
| munch117 wrote:
| If this mysterious disc-accelerating force also accelerated
| the people and things on the surface, we'd all be
| weightless.
|
| I guess it must be a pushing force from below.
|
| So, who's doing the pushing? I'm thinking a big turtle.
| nkrisc wrote:
| They mean it is actually accelerating constantly.
|
| My math might be wrong, but if we were accelerating at
| 9.8m/s/s for at least 4000 years (roughly as long as we
| have continuously recorded history and the minimum time
| "gravity" has been observed) then we ought to currently
| be traveling through space at over 1,000,000,000,000m/s.
|
| Now I'm no physicist, but I reckon that might end up
| violating causality.
| jbeninger wrote:
| Nah, when you move that fast, further acceleration stops
| increasing speed and starts squishing time instead, so
| you asymptotically approach C.
|
| So I guess what I'm saying is I see absolutely no problem
| with the flat earth arguments?
| bryanrasmussen wrote:
| wait, is the flat earth theory going to make me immortal?
| lukan wrote:
| Only if you truly believe in it. Then you create a belive
| field, shaping your reality in any form you desire.
| nkrisc wrote:
| Can't argue with that, I guess.
| plagiarist wrote:
| We should see this as all the celestial bodies traveling
| "down" at relativistic speeds by now. Unless maybe they
| are also experiencing 1 G in the same direction as us in
| addition to whatever other accelerations.
| empath75 wrote:
| Some of them think that.
|
| The problem with trying to "explain" this is that
| fundamentally, flat-earthers, to the extent that they
| could be said to have a coherent world view at all, are
| usually a kind of occasionalist[1]. They don't _believe_
| in natural laws or cause and effect. For the most part,
| they believe that god is in complete control of all
| events, and things go down because god wants them to go
| down. There's no required explanation for _anything_. The
| sun moves across the sky because god wants it to, and he
| could stop it or make it go backwards if he wanted it to,
| etc.
|
| Indeed, that a flat earth is incompatible with physics is
| part of the appeal of believing in it to begin with. They
| _want_ to overthrow Newton, because a clockwork universe
| is incompatible with their belief system.
|
| It's also sort of immune to any kind of argumentation.
| The result of any experiment is simply that god wants it
| that way, that they're predictable and testable doesn't
| _prove_ anything, because you can do an experiment a
| million times, and god could still cause it to fail any
| time he wants to. God just doesn't want to argue with
| Netwon right now, for his own reasons, you see.
|
| 1: https://en.wikipedia.org/wiki/Occasionalism
| mlyle wrote:
| https://www.xkcd.com/2440/
| f1shy wrote:
| We can give them points for creativity.
| lukan wrote:
| The theological argument I recently heard is, the creator
| just made up and down. And things move down. But it is not
| gravity.
| cratermoon wrote:
| "A wizard did it"
| mlyle wrote:
| > And things move down.
|
| It's not a bad way to look at it for a start. Things move
| down because it is their nature to move downwards. And
| this kind of empirical law is what we rely upon for
| _most_ thought.
|
| It takes a lot of work to get to a theory that makes more
| general predictions.
|
| And even after having that, 98% of the time my thought is
| effectively just "things move down." Another 1.5% it's
| "things move down at 9.8 m/s/s". It's an extreme
| edge/special case when I'm thinking "massive things are
| attracted to each other, with a force proportional to
| their masses and inversely proportional to the square of
| their distances".
|
| And even with "massive things are attracted to each
| other, with a force proportional to their masses and
| inversely proportional to the square of their distances"
| ... if you ask me why, it's because "uh, they just do
| that?"
| lukan wrote:
| "with a force proportional to their masses and inversely
| proportional to the square of their distances" ... if you
| ask me why, it's because "uh, they just do that?""
|
| To be fair, that is somewhat the current scientific
| consensus on gravity. It just is. We can meassure it and
| determine a general constant and calculate with it (and
| even though some people claim to have understood way
| more, it is highly debated terrain as far as I know)
|
| And in general, I was actually arguing with flat earthers
| recently a lot, I even met a flat earther in real life.
| It is an interesting intellectual challenge debating
| them. Basically rebasing all the physical theory I have.
| (Main summary is, they have a high ego, but lack
| understanding of everything and make up for it with make
| believe.)
|
| If I found a school one day, one of the lessons will be
| the teacher telling the students: "The earth is flat!
| Proof me otherwise." Or more advanced, model a flat earth
| on a computer. Flat earthers try that for real - it gets
| weird very quickly, so much that I could not believe
| anyone taking it serious and it all is just satire. But
| they are for real (but with a very different concept of
| reality).
| mlyle wrote:
| > To be fair, that is somewhat the current scientific
| consensus on gravity. It just is. We can meassure it and
| determine a general constant and calculate with it (and
| even though some people claim to have understood way
| more, it is highly debated terrain as far as I know)
|
| Sure, and if we come up with some fancy unified theory,
| and ask "why" once more, the answer will still be "uh,
| because they do?."
|
| > But they are for real (but with a very different
| concept of reality).
|
| We think ourselves so advanced. I wonder what big
| counterfactual scientists believed in the 1900s and 2000s
| will be laughed at a few hundred years from now.
|
| And, of course, some of that will be libel; e.g. that we
| thought the world was flat "just like Christopher
| Columbus's compatriots" [who didn't].
| rendaw wrote:
| Doesn't the flat earth extend infinitely in all directions?
| phkahler wrote:
| Even physicists have a hard time with disks and gravity. I
| can't tell you how many times I've seen them use the shell
| theorem on galaxies (does not apply). The only dark matter is
| in their head ;-)
| Someone wrote:
| > and gravity, still pointing towards the center, makes you
| stand at an increasingly acute angle to the surface. The
| ground beneath you will then appear like one big endless
| mountainside
|
| That's why you never hear of people who went to the edge of
| that dis: they slid down that mountainside, and dropped off
| :-)
|
| Alternatively, you can postulate that disc to be arbitrarily
| thick.
|
| That will decrease the deviations. If that's not enough to
| make them immeasurable, postulate that the stuff "deeper
| down" has higher density.
|
| In the limit, just postulate that there's an enormous black
| hole millions of light years below the center of the earth.
|
| Flat-earthers probably won't accept Newton's theory of
| gravity, however, so you can make up anything.
| userbinator wrote:
| _The earth is just much much much bigger than in the diagram so
| the effect is within the margin of error for the measurement he
| was taking._
|
| It's actually measurable on a human scale:
|
| https://www.mathscinotes.com/2017/01/effect-of-earths-curvat...
|
| 1 5/8" difference over 693', or slightly less than 1 part in 5
| thousand --- definitely measurable on a smaller scale with
| accurate machinists' tools.
| pvillano wrote:
| One can also watch a boat leaving shore descend "under" the
| horizon with a telescope
| sigmoid10 wrote:
| You don't even need a boat or a telescope. Just watch the
| sun set on the ocean while lying down at the beach just in
| front of the water. The moment it disappears completely,
| stand up. You'll see part of it again. If you measure the
| time it takes disappear completely again and know your own
| height, you can even get a rough estimate of earth's
| radius.
| yen223 wrote:
| Unless I'm picturing it wrong, wouldn't this still happen
| even if the world were flat?
| ben_w wrote:
| > We joke about LLMs hallucinating but I'm not convinced we are
| so superior when we are outside our personal "training data".
|
| Every time I see the phrase "common sense", I expect to see an
| example of the human failing you describe.
| jerf wrote:
| "We joke about LLMs hallucinating but I'm not convinced we are
| so superior when we are outside our personal "training data"."
|
| In all seriousness one of the things about LLMs that most
| impress me is how close they get to human-style hallucination
| of facts. Previous generations of things were often egregiously
| and obviously wrong. Modern LLMs are much more plausible.
|
| It's also why they are correspondingly more dangerous in a lot
| of ways, but it really is a legitimate advance in the field.
|
| I observe that when humans fix this problem, we do not fix it
| by massive hypertrophy of our language centers, which is the
| rough equivalent of "just make the LLM bigger and hope it
| becomes accurate". We do other things. I await some AI
| equivalent of those "other things" with interest; I think that
| generation of AI will actually be capable of most of the things
| we are foolishly trying to press hypertrophied language centers
| into doing today.
| teo_zero wrote:
| And of course pi = 22/7! ;)
| necovek wrote:
| That's actually a lot closer to the actual value of pi than the
| implied difference in the article vs the 0.15% actual
| difference in path length.
|
| As in, the illustration would be less wrong if it only used
| 22/7 for Pi and correctly portrayed dimensions of Earth and
| flight heights.
| bruce511 wrote:
| Even if the math of the arc length was correct (and you don't
| need to be a math professor to figure out it isn't) there's
| another logic misstep.
|
| Implied in the caption is that the speed is the same at all
| heights (given that an increase in distance is implied as an
| increase in time.)
|
| This is again obvious nonsense - speed is a function of thrust
| versus drag, and it's safe to say that both of those are affected
| by air density.
|
| It becomes even less true once one gets to space. There height is
| a function of speed which means that to "catch up" something in
| front of you, you need to slow down.
| mastermedo wrote:
| > It becomes even less true once one gets to space. There
| height is a function of speed which means that to "catch up"
| something in front of you, you need to slow down.
|
| Can you expand on this? My brain is not connecting the dots.
| db48x wrote:
| He is talking about orbital mechanics, rather than free
| space. When you are in an orbit, the shape of the orbit is
| determined by your speed. At every distance from the center
| of the object you are orbiting (such as the Earth), there is
| a speed that makes your orbit a circle. If you are going at
| any other speed then your orbit will be an ellipse instead.
| Too fast and your orbit rises higher above the Earth. Too
| slow and it dips back down closer to it. If you try to "catch
| up" with an object ahead of you in your orbit by speeding up
| you will only turn your orbit into an ellipse that gets
| further away from the Earth, and thus further away from the
| object you were trying to catch. Instead of catching it
| you'll go up and over it. As Niven wrote, "forward is up, up
| is back, back is down, and down is forward". It's rather
| counterintuitive at first. Playing KSP can help you get a
| feel for it, especially once you start docking multiple craft
| together.
| davrosthedalek wrote:
| Just to point out here what's different between "space" and
| "not space": "Space" assumes no "height control",i.e. ways
| to exert force "down or up" along the earth-object
| direction. That's obviously not true for a plane. If you
| can exert force in that direction, you can change speed and
| keep the shape of the trajectory around earth constant.
| falcor84 wrote:
| Wait, why wouldn't an orbiting satellite not be able to
| apply its thrusters "down"?
| Sharlin wrote:
| It's even worse than that. By speeding up you end up
| actually getting _further behind_ your target because in
| your new higher orbit you actually move _slower_ on
| average, _and_ as your average orbital radius gets longer,
| so does the circumference, so you end up on a "detour"
| trajectory compared to your target!
|
| Whereas if you slow down, you drop to a lower, shorter,
| higher-speed orbit.
| nyc111 wrote:
| This is called Kepler's Third Law, right? Radius^1.5 ::
| Period
| f1shy wrote:
| You are literally going way and beyond what the target audience
| of that post (the original with bad math) was for.
| syntex wrote:
| just 2piR and then extra h change the result very little
| fraction. How is that counter-intuitive :)
| chrismorgan wrote:
| I think the funny thing about this article is this numeric error
| (though not so egregious as the one that caused the article!):
|
| > _The mean radius of the earth is actually 3,459 miles or over
| 18 million feet._
|
| That's off by 500 miles; the correct figure is 3,959 miles. That
| makes it almost 21 million feet, and yields a ratio of about
| 1.0013378, even smaller than the quoted 1.0015.
| prmph wrote:
| One question I've always had with this: How does the rotation of
| the earth affect an airplane's flight time, if any? And how does
| this change with altitude?
| kergonath wrote:
| It does not really, at least not directly. What matters is
| relative velocity compared to the starting and final locations,
| and relative to the air around the aircraft. It just happens
| that there are very powerful atmospheric currents that go west
| to east (those are due to the earth's rotation, among others
| phenomena).
|
| So, when flying towards the east, catching these currents can
| significantly reduce flying time. When flying towards the west,
| we want to avoid them by flying below or elsewhere.
| prmph wrote:
| Thanks for this explanation; quite interesting.
|
| But it still seems to me that there might be a
| gravitational/inertial effects at play as well. At a
| (hypothetical) infinite altitude, it can no longer be said
| the the plane is moving perfectly in lock-step with the
| gravity/rotational acceleration of the earth. This implies
| the inertia of the plane relative to the rotation of the
| earth still has an effect at lower altitudes.
|
| The effect might be tiny, but would be interesting to learn
| more about it nonetheless.
| BlueTemplar wrote:
| What gravity/rotational acceleration ?
|
| Something like this does exist under general relativity :
|
| https://en.m.wikipedia.org/wiki/Frame-dragging
|
| However,
|
| > This does not happen in Newtonian mechanics for which the
| gravitational field of a body depends only on its mass, not
| on its rotation.
| prmph wrote:
| Yes frame-dragging seems to be the name of the concept I
| was thinking of. Cool.
| f1shy wrote:
| Simple answer: Zero. Because the planes move inside the
| atmosphere, which moves with the earth.
|
| A more nuisance would be that earth rotating generate all sorts
| of things in the atmosphere, including winds and Coriolis
| effect on the winds, and you can account for that considering
| the winds. Btw a flight from Chile to France and back, will
| have a leg significantly shorter (up to 2 hs in a 13hs flight)
| and which leg it is, depends on the time of the year.
| prmph wrote:
| Interesting to know about the Coriolis effect.
|
| I get that what really matters is the relative motion, but it
| still seems to me that there might be a
| gravitational/inertial effects at play, even if tiny.
|
| Consider this thought experiment: Planes cannot really fly
| into space, but assume they can. At a certain altitude, it
| cannot be said the the plane is moving perfectly in step with
| the gravity of the earth. At infinite altitude, that
| certainly cannot be the case.
|
| So that tells me there is some deviation due to the inertia
| of the plane, even at low altitudes. Like I said, the effect
| might be tiny, but would be interesting to learn more about
| it nonetheless.
| f1shy wrote:
| I meant coriolis effect on the wind. Not sure if noticeable
| in a plane.
| Derbasti wrote:
| In general, the air moves with the ground, so the earth's
| rotation does not affect airplanes.
|
| However, rotation of the earth imparts a coriolis force on the
| air, which results in jetstream winds. Aircraft routes are
| optimized to use/avoid jetstreams for shorter travel times.
| n4r9 wrote:
| Don't know if anyone mentioned this yet, but presumably the
| flight path does not follow a normal vector to gain height, but
| generally something more diagonal in the direction of travel.
| pessimizer wrote:
| Does _" Remember the high you go the further it'll have to
| travel"_ really need to be debunked? Did the "design and
| construction firm" spell "drill" with one "l"?
| simplicio wrote:
| Seems intuitively obvious. On a flat Earth the two distances
| would be the same, and while the Earth isn't flat, its close
| enough to approximate a flat surface for most purposes, so you'd
| expect the differences in the two arcs to be ~0
| lynguist wrote:
| I would do it like this:
|
| Approximate Earth as a flat line. (The 5000ft path is close
| enough that it is also represented by the flat line. This is the
| 5000ft path.)
|
| Then make the 33000ft path which is a slightly looser line on top
| of this line.
|
| This new path is not 4 times longer. Just a little bit raised,
| because 33000 ft is "nothing" compared to Earth. (To become 4x
| longer we would go deep into outer space and back.)
| wittjeff wrote:
| "the high you go" reinforces my initial assumption that this is
| self-filtering clickbait.
| mppm wrote:
| xkcd.com/386
| svilen_dobrev wrote:
| Charles Petzold.. His c++ book stood on the shelf behind me. 30y
| ago. heh :)
| 1970-01-01 wrote:
| All models are wrong, but some are useful. = Some models are
| wrong and useless.
| fargle wrote:
| i've seen that exact image posted semi-regularly on various
| reddit and facebook groups. (it's one of 500 things i hate about
| those sites. but for some communities that's where the
| information lives, that's where marketplace lives, etc., so i'm
| stuck with it)
|
| these kind of things are intentionally wrong "puzzles" that are
| designed to get hundreds of people mad and post rebuttals to
| "drive engagement" or whatever. the pictures of a wheel with
| sledgehammers and chains and jacks with lugnuts plainly still in
| place and a post "how can i get this off it's stuck and i've
| tried everything". sigh... it's just another form of trolling.
|
| sure enough, notice the sibling comments here. how many nice
| people took the time to patiently explain the fallacy(ies) for
| the 1000th time. then the pedants who correct the
| grammar/math/etc. in the 98% correct explanations. then the "true
| believers"/trolls who don't get it and argue back. and so on.
|
| https://xkcd.com/386/
| juresotosek wrote:
| haha crazy
| csours wrote:
| Reminds me of this classic:
|
| https://www.politifact.com/factchecks/2020/mar/06/msnbc/bad-...
|
| "Bloomberg spent $500 million on ads. The U.S. population is 327
| million. He could have given each American $1 million and still
| have money left over."
|
| https://www.youtube.com/watch?v=6egeUxIEQnM
| jodrellblank wrote:
| Earth in the picture is scaled to roughly 300,000 feet per pixel;
| Earth's surface and both flying altitudes would be the same pixel
| if drawn to scale.
|
| (~42M feet diameter shown in ~134 pixels).
| quantified wrote:
| Holy crap is one drop of stupid consuming a lot of mental energy.
| This is after the drop of stupid that was Terence Howard's "1 x 1
| = 2" physics rant fell on everyone's head. Individual drops
| quickening into rain would drown us all, apparently. Do serious
| people like Charles Petzold (here) and in other venues address
| this stupid out of fear that the stupid spreads, or because they
| just can't stand someone being wrong somewhere like a cognitive
| itch that must be scratched? If one troll flooded the zone with
| 30 of these over a month, mayhem would ensue. Absent knowing the
| true origin for this diagram, we don't even know if was stupid or
| malicious.
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