8 ms·
A googol-to-one gear ratio [video]
- Valgrim 7y agoWhat happens to the energy used to rotate the device? Is it dissipated as heat before it reaches too far?
- wrkronmiller 7y agoProbably, but I think even in a frictionless system you could still get the same effect. I suspect even if slip between teeth, slack in system, etc... was eliminated you could still get the same effect. The amount of energy in the system isn't the same thing as the amount of movement, so in a perfectly efficient system (I think) the initial gear would spin faster than the final gear but the final gear would turn with more force (same amount of energy).
- deleted 7y ago[deleted]
- cwillu 7y agoThe energy not lost to friction is being loaded into the system as the gears and axles start to strain from the stresses applied. Some energy is potential energy like a compressed spring. The balance is spent making the material yield; this will be lost as heat.
- Khoth 7y agoFriction basically. In a perfectly idealised version of the system with no friction/slack/materials being deformed/etc, if you started it off then let go then everything would keep spinning forever. You don't need to pump a whole lot of energy into the device to make it go.
- kangnkodos 7y ago"...if you started..." That's a big if. I haven't done the math yet, but I'll bet that the outside rim of at least one of the gears would have to be started moving faster than the speed of light. I'm not sure how you would do that. The gear just before the first gear at light speed would have the outside rim moving at about 100th of the speed of light. It would take quite a bit of energy to do that. (Others have pointed out that at speeds well before the speed of light, some of the gears would melt. I'm ignoring that.)
- Thorentis 7y agoWhy can't it spin faster?
- chrisseaton 7y agoI'm sure it can spin a bit faster. Why can't it spin so fast that the final wheel visibly turns? Well the first wheels would melt from friction or be torn apart before then, and where are you going to get that much energy to turn them so fast? At some point there's the speed of light as a limit as well.
- owenmarshall 7y agoThere are 10^80 electrons in the universe, Eddington thinks. Even if you managed to make a contraption that turned one electron into one rotation of the first wheel, and you fed the entire universe to your contraption... you’re coming up a few dozens order of magnitude short to make that full turn :^)
- chrisseaton 7y agoThat's what I already said > where are you going to get that much energy to turn them so fast?
- owenmarshall 7y agoI guess you just have to make a machine that manages two turns per electron. (I know you did - but any chance to introduce Eddington’s number is fun)
- chrisseaton 7y ago> I guess you just have to make a machine that manages two turns per electron. But that just isn't going to be tractable.
- klyrs 7y agoWhat's 80 orders of magnitude between friends? https://en.wikipedia.org/wiki/One-electron_universe https://en.wikipedia.org/wiki/One-electron_universe
- robertfw 7y agoIn the same vein, check out "Machine with Concrete" https://www.youtube.com/watch?v=5q-BH-tvxEg https://www.youtube.com/watch?v=5q-BH-tvxEg
- aj7 7y agoI bet the zero point fluctuation motion of the last gear dwarfs the deterministic motion.
- autonoshitbox 7y agoThe word you're looking for is "thermal." The bulk of the gear behaves completely classically at this temperature.
- aj7 7y agoI think you are right in the sense that at room temperature, thermal fluctuations dominate. Better stated, my point is that if the entire assembly is at absolute zero, the quantum fluctuations in the final gear are much greater than the deterministic motion associated with one revolution of the first gear.
- autonoshitbox 7y agoIf this entire assembly is at absolute zero, something is very wrong in the universe.
- _underfl0w_ 7y agoPart of me likes to thing something crazy would happen if you turned it from the other end. Turn one gear once and the gear at the far other end turns a googol times but melts somewhere around a trillion rotations. Almost doesn't feel too outlandish given a scope that already includes "more energy than the entire known universe has" (per the article) for a measurement.
- warent 7y agoAll this time we've been fussing about clean energy and perpetual motion machines when all we needed was this machine to apply essentially infinite leverage and generate a universe of energy at the flick of the wrist
- peteradio 7y agoWoops accidentally solved fermi's paradox and the mystery of what created the big bang, in one shot.
- tuco86 7y agoAt first there was God. Then Adam and Eve. Then one of their descendants built this machine and prayed for god to turn the last wheel. Bang! (a big one)
- taneq 7y agoStep 1 is have a universe's worth of energy in your wrist. ;)
- hnuser123456 7y agoIn the hour-long video, from the start to the end, only the first seven gears move visibly, and the 8th moves maybe a pixel. You probably couldn't move anything past the 3rd or 4th gear with your hand, depending on how low-friction the bearings are, how strong you are, and how little you care about hurting your hand. You could attach a long lever to one, but that'll only get you one, maybe two gears further.
- Benjammer 7y agoThe original mentioned, Arthur Ganson's Machine with Concrete, is quite a bit more artistic. The end is cast in concrete. The idea is that there is a certain amount of energy lost as friction in each gear, per turn. If you calculate the gear ratios and how many turns of the earlier gears would be required to make the final gear move, even infinitesimally, the amount of energy lost becomes more than all the energy in the known universe. It's not really about RPMs.
- noncoml 7y agoImpressive but imho he could take it one step further and instead of concrete on the other end, he could rotate the gear in the opposite way.
- jagged-chisel 7y agoWhen all the slack has been rotated out, it would require a tremendous amount of force to rotate that last gear in reverse. After all, the system wants to amplify the gear speed from that end.
- NegativeLatency 7y agoI think parent’s idea would work if the system was mirrored and duplicated. Then you could attach the two the them together with the stationary gears in the middle
- rtkwe 7y agoSo 10^100:1:10^100? I think the slack, friction losses, flex, material strength would all take out so much of the energy you'd get a tiny fraction of movement at the far end if any.
- Benjammer 7y agoWow I like this idea, instead of concrete you really emphasize the point with another motor the opposite direction and the other end.
- lacker 7y agoIf every electron in the universe came over and cranked that first gear around a hundred times, it still wouldn't be enough to make the last gear visibly move.
- deleted 7y ago[deleted]
- deleted 7y ago[deleted]
- ehsankia 7y agoStupid question, but realistically what would happen if you tried to manually turn that last gear? Would nothing move? What if you put a lot of force, what would happened / which part would break?
- inimino 7y agoAn interesting question! As a guess, there should be some slack and elasticity in the last two gears or so, which you could get out if you used enough force. Beyond that, the effective torque is reduced by 100x or 1000x already, which means moving any further gear even by the width of an atom would probably require more torque than the final gear can bear, and either the teeth or some other weak point would fail on the last gear. Of course, even what motion there is (up to failure) would be hard to observe. Moreover, putting this much torque on the end of the structure would also likely torque the entire machine end to end (like twisting a rope) and generally mess things up in uninteresting ways. Putting all that together, I think an observer would probably say nothing is moving, right until the last gear and/or entire structure fails spectacularly.
- high_pathetic 7y agoJust for fun, I would connect the first gear to an electric motor and let it run for an hour or so.
- tempestn 7y agoHere you go: https://www.youtube.com/watch?v=ApqfqiFTO4E https://www.youtube.com/watch?v=ApqfqiFTO4E
- pbhjpbhj 7y agoFlip it around .. what's the fastest rotational speed achieved via a hand powered machine?
- dTal 7y agoI imagine you could get several thousand RPM at least with a hand pump and a dentist's drill, if mechanical gearing is not a requirement.
- praptak 7y agoI think ~100k RPM is achievable with a shirt button on a bunch of twisted strings, pulled on both ends. This was actually used to construct a cheap mechanism that needed the high g to separate some chemicals to analyse samples. I can't remember the details though.
- astatine 7y ago125k RPM. For malaria detection using a whirling paper centrifuge, powered entirely by hand. https://news.stanford.edu/2017/01/10/whirligig-toy-bioengineers-develop-20-cent-hand-powered-blood-centrifuge/ https://news.stanford.edu/2017/01/10/whirligig-toy-bioengine...
- praptak 7y agoThank you! I was not able to dig this up.
- xwdv 7y agoIf you made this in a physics engine could you get the last gear to spin in a reasonable time and not break the simulation?
- banana_giraffe 7y agoNope. Even if your physics engine could deal with the rotation of the first gear in one "unit", and batch the rotation of that gear a million times in a "super unit", then calculate a million "super units" each second, it would still take longer than the universe has been around, by 10^70 times, to complete one rotation of the final gear.
- kibwen 7y agoOnly if you're okay with some sort of extreme fast-forward mechanism (which seems like cheating), since even if you turned the first gear once per CPU cycle you'd still be spending about 10^90 seconds to turn the last gear once. There's otherwise no problem with representing the state of the simulation itself; a googol only takes 333 bits to represent.
- autonoshitbox 7y agoSure, just do something with Fourier transforms. Okay, it's not completely accurate, but most simulations aren't anyway. In fact, I can simulate this in text form with no floating-point or number theory issues at all. Here's the simulation: > For every 10^100 turns of the first gear, the last gear will move about one full turn.
- bilekas 7y agoThis is insane. My OCD is tempered and my love for all things mechanical has been re-ignited. I am curious how this ratio is calculated though, I didn't drill into the relative ratios.. If anyone has a link I would love to see!
- elihu 7y agoIt's pretty simple: for each pair of gears that mesh with each other, one has ten times as many teeth as the other, which gives a ten to one reduction. If you chain 100 such reductions, you get 10^100 to one reduction.
- bilekas 7y agoBut the construction of it ??! It's one thing to put the numbers down, we know they round out nicely, but in my head this needs a very minute level of construct engineering.. For example: If 1 gear(cog?) is 1/1000 of a cm out, would that not effect the ratio over this 'distance' ? Edit: I might just sound like an idiot right now, but when we get down (or up) to these numbers, i can't help but feel manufacturing numbers play a bigger role
- jxcole 7y agoNow if on the slow end you connected an exactly reversed series of gears you could configure it such that the final gear moves at exactly the same speed as the first gear, but the middle gear moves at 1/googol the speed. Of course this is likely to break down at some point but it would be interesting to see exactly what the maximum recoverable ratio is for gear movement and what the limiting factors are.
- rtkwe 7y agoCan't imagine how long it'll take to get the slack out of that gear train.
- kjaku 7y agoSo after rotating enough to reduce clearance between teeth, you can move last gear lets say tooth to the distance 10^65 smaller then Planck Length -- smallest known length, wchich is 1.6 x10^35 m and where all strange things like quantum foam, or micro wormholes are supposed to happen ...?
- gizmo686 7y agoI ran the numbers for going in the other direction. Suppose that: * The 99 slower gears are massless. * the fastest gear weighs 10 grams * The fastest gear is a cylinder of radius of 2cm * The slowest gear completes 1 rotation every 3 days. * Relativity only applies when I want it to. We have: * The fastest gear has an angular velocity of: w=10^95 radians/second = 10^95 s^-1 //Since radians are unitless * The fastest gear has a moment of intertia given by: I=mr^2 / 2 = 10^-2 * 4*10^-4 / 2 kg*m^2 * The fastest gear has a rotational energy of: E=Iw^2 / 2= 10^-2 * 4*10^-4 / 2 kg*m^2 * 10^190 s^-2 / 2 E = 10^184 kg*m^2*s^-2 * Ignoring all of relativity except E=mc^2, we have m = E/c^2 m ~ 10^184 kg*m^2*s^-2 / 10 ^ 17 m^2*s^2 m ~ 10^167 kg * Acknowledging more of relativity now, we have: Schwarzschild radius = 2Gm / c^2 Schwarzschild radius ~ 10^-12 m^3*kg^-1*s^-2 * 10^167 kg * 10^-17 m^-2*s^2 Schwarzschild radius ~ 10^138 m Giving us a black hole large enough to fit about 112 googol observable universes. I'm sure that I'm missing some relativistic effects here, but I don't even know how to begin to approach that.
- spectramax 7y agoWhat would be the torque required to spin the slowest gear 1/3 rotation per day? Let's assume the same radius: 2cm.
- hnuser123456 7y agoI would say you could ballpark it as something north of 10^100 Nm or ft-lb If you want to make these figures a little more reasonable, we could try to spin the slow gear only once in 100 years, in which case you can take about 5 whole powers of 10 off these numbers
- hnuser123456 7y ago>Giving us a black hole large enough to fit about 112 googol observable universes. *Giving us a black hole with a radius large enough to fit about 112 googol observable universes stacked end-to-end in a line. ~Triple the number of zeros for the number of universes to fit in its 3D volume. 112 x (4/3) x pi followed by 336 zeroes, more or less.
- forkexec 7y agoNice! I'm surprised Oskar van Deventer (YT: OskarPuzzle, https://oskarvandeventer.nl/ https://oskarvandeventer.nl/ ) hasn't done more than 10^9:1 reduction. https://youtu.be/b_pbOCIg_nI https://youtu.be/b_pbOCIg_nI I think this calls for 10^10^2 reduction using a series of cycloidal drives (34x 1000:1 should do it just fine)
- SamReidHughes 7y agoNow put a shaft connecting the last gear to the first.
- profmonocle 7y agoI would love for someone who knows more about physics to explain what effect a single rotation of the front gear actually has on the last one. Naively you would assume that every rotation of the first gear rotates the last by one googolth. But (I assume) that can't be true in the real world, since that distance is significantly smaller than a planck length. I have some educated guesses as to how the rotation is actually being "stored" if it's not physically moving the final gear, but I'm probably more ignorant than I think - for example I'm not totally sure I understand what a "planck length" is.
- deleted 7y ago[deleted]
- baddox 7y agoThere’s nothing particularly strange about it. There would be probably be some measurable heat that would eventually make it to the final gear if you had an ideal setup for measurement. I haven’t done the order of magnitude estimation, but it’s probably not significantly different than snapping your fingers in your bedroom and asking precisely what effect it has on a specific air molecule in your kitchen.
- hnuser123456 7y agoThere's slop in between the teeth of the gears, they aren't perfectly tightly meshed. All of the gears can wiggle back and fourth that amount, but the "wiggle room" of the last gear gets shifted one googlth of a rotation per one rotation of the first gear. If all of the gears were pre-loaded, such that the slop was "behind" the contacting teeth, then the last gear would turn one googlth of a rotation, with an incomprehensible capacity for torque if it were to encounter any resistance in that very small distance. Being less than a planck length, you might say that the probability of finding the gear's atoms one planck length behind, and one forward, shifts continuously. Of course the atoms are vibrating far greater distances due to ambient heat, but still bonded together. The frequencies are typically of the order of 10^13 Hz, and the amplitudes are typically of the order of 10^−11 m. A Planck length is about 10^-35. https://en.wikipedia.org/wiki/Atom_vibrations https://en.wikipedia.org/wiki/Atom_vibrations Maybe you could say that the gear that shifts approximately one atom vibration (#11) or one planck length (#35) applies as much torque as needed to shift the slower gears behind it, once the force applied becomes greater than the friction resistance, which will happen quite often (about as fast as the atoms are vibrating, if the gears are perfectly tightly meshed) because of the tremendous capacity for torque. There will be higher pressure from the source of the force than from the resistance of the further gears.
- raverbashing 7y agoOk what if instead of gears we use belts to connect? I think some of the slack will be taken out (as long as you tension the belt accordingly) and transmission of power should be more uniform.
- nkrisc 7y agoAre there any science museums that have something like this? When you look at this, you think that surely you can make that last gear spin. After all we've all spun gears, we know how they work. But it would be so counter intuitive to spin one of those gears by hand and basically see nothing happen no matter how much you spin it. I know that would blow the minds of some kids (and adults).