# The Googol to 1 gear ratio machine **URL:** \ **Category:** In My Humble Opinion\ **Created:** [July 19, 2022, 1:24am UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182 "2022-07-19T01:24:34Z")\ **Posts on this page:** 19\ **Page:** 2
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [July 19, 2022, 7:48pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/21 "2022-07-19T19:48:37Z")
> [@RitterSport](#): > > OK, I’m not a mechanical engineer, but is it possible to do the ratio in the other direction? I love the idea of barely touching one gear and having the gear at the other end spin and close to the speed of light or something. The person who made this did a one minute video on it answering this question (below). The tl;dw version is he cannot move the last gear at all. [![](https://img.youtube.com/vi/FywIvJ_jIhg/maxresdefault.jpg "Turning a Googol to 1 gearbox from the other side!?") ](https://www.youtube.com/watch?v=FywIvJ_jIhg) ---
**Author:** ![RitterSport](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rittersport/32/6326_2.png) [@RitterSport](https://boards.straightdope.com/u/RitterSport)\ **Post date:** [July 19, 2022, 7:56pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/22 "2022-07-19T19:56:21Z")
Hahaha! That was well done. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [July 19, 2022, 8:07pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/23 "2022-07-19T20:07:02Z")
I was just wondering about that. Not surprising the last gear won’t move. I wonder if the material is strong enough to ever transmit movement to the last gear when driven as intended. ---
**Author:** ![Bonum\_Legatum](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bonum_legatum/32/6183_2.png) [@Bonum\_Legatum](https://boards.straightdope.com/u/Bonum_Legatum)\ **Post date:** [July 19, 2022, 8:25pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/24 "2022-07-19T20:25:41Z")
By the way, the LEGO construction incorporates a “compound planetary gear”, a means of obtaining high ratios because the ratio is the differential of the ring gears. Machinery’s Handbook has the mathematics if you care to look it up. Chrysler used compound planetary gears in radar sets and tank transmissions during WWII The first was to create a high gear reduction with minimal backlash. The second was to create a large reduction in limited space. There are also “split gears” to minimize backlash. ---
**Author:** ![Ponderoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ponderoid/32/19221_2.png) [@Ponderoid](https://boards.straightdope.com/u/Ponderoid)\ **Post date:** [July 19, 2022, 9:18pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/25 "2022-07-19T21:18:46Z")
> [@Chronos](#): > > Based on my experience with Lego gear trains, a 5:1 or 25:1 speed increaser you can drive with ease, a 125:1 gets pretty difficult, and a 625:1, you can usually keep it moving once it’s started, but it’s nearly impossible to start it driving at the slow end, and that only if you’re holding it just right to minimize friction. And thus you demonstrated why it’s necessary for a car to start in a very low gear and shift gears as you gain speed 🙂 ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [July 20, 2022, 12:02am UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/26 "2022-07-20T00:02:29Z")
> [@Riemann](#): > > Obviously you just need two gear trains that work in opposite directions. The first gear train gears down googol-fold to give you enough torque to turn the first wheel on the train that gears up googol-fold. And then if you hook the output of the gear-down train into the input of the gear-up train you’ll have an over-center perpetual motion machine. Wait, _what_??/?!!/!? 😉 😉 ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [July 20, 2022, 6:45pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/27 "2022-07-20T18:45:03Z")
> [@LSLGuy](#): > > hook the output of the gear-down train into the input of the gear-up train Actually, that’s an interesting scenario. Would the end of the gear-up train recover the input torque of the initial drive? Would you see the output shaft of the final drive turning at the speed of the input motor? In a perfect world, it seems like it should. In the real world, I suspect torque losses (lash, rolling resistance, etc.) would eat up the transmitted torque. Just like in abstract mathematics, multiplication and division are perfectly reversible to infinite precision, but in real life you eventually round down to zero. ---
**Author:** ![Whack-a-Mole](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/whack-a-mole/32/141_2.png) [@Whack-a-Mole](https://boards.straightdope.com/u/Whack-a-Mole)\ **Post date:** [July 21, 2022, 12:52pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/28 "2022-07-21T12:52:18Z")
We saw in the video posted above (post 21) that you cannot turn the last gear. It seems the whole thing only works one way. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [July 21, 2022, 1:57pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/29 "2022-07-21T13:57:57Z")
Assuming the whole mechanism is absolutely frictionless, it would work in either direction. However, the drive ratio means that any torque applied to the last gear is reduced by a factor of 10100 on its way to the first gear. Grab that last gear with a firm grip, and maybe you can put 10 lb-ft of torque on it. That means the first gear experiences a torque of just 10/(10100) lb-ft. Most folks are familiar with the basic “force equals mass times acceleration” rule in linear scenarios (like a jet accelerating down a runway), but there’s an analogous equation for rotating systems: “torque equals **[mass moment of inertia](https://en.wikipedia.org/wiki/Moment_of_inertia)** times angular acceleration.” That first gear has some non-zero rotating inertia, and when you apply a very tiny amount of torque to it, it will experience a very tiny amount of angular acceleration. Also, since every intermediate gear has its own inertia, each one will absorb some of the torque applied to it by accelerating, passing on only part of it to the next gear. So the net torque that actually gets applied to the first gear will be extremely small - much, much less than 10/(10100) lb-ft. So if there’s no friction, the mechanism definitely will work - you will be able to get the first gear rotating by applying a torque to the last gear. It’s just that it will take an extremely long time to accelerate that first gear enough to achieve an RPM that you could notice with your unaided eye. ---
**Author:** ![DesertDog](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/desertdog/32/11503_2.png) [@DesertDog](https://boards.straightdope.com/u/DesertDog)\ **Post date:** [July 21, 2022, 4:41pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/30 "2022-07-21T16:41:51Z")
> [@Machine\_Elf](#): > > Most folks are familiar with the basic “force equals mass times acceleration” rule in linear scenarios (like a jet accelerating down a runway) Izzat with or without a treadmill? I’ll let myself out. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [July 21, 2022, 5:15pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/31 "2022-07-21T17:15:08Z")
> [@Machine\_Elf](#): > > Probably this one: > > [video of gear system locked in concrete] I’m curious when this will start to visually break the concrete. ---
**Author:** ![beowulff](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/beowulff/32/542_2.png) [@beowulff](https://boards.straightdope.com/u/beowulff)\ **Post date:** [July 21, 2022, 5:18pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/32 "2022-07-21T17:18:50Z")
Never. The first gear will be worn to a nub before the last gear starts to move. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 21, 2022, 5:35pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/33 "2022-07-21T17:35:22Z")
And of course, “frictionless” is an ideal that’s never realized, either. We can build some devices with really, really low friction, but there’s “really really low”, and then there’s “less than 1/googol”. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [July 21, 2022, 5:37pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/34 "2022-07-21T17:37:42Z")
> [@Whack-a-Mole](#): > > We saw in the video posted above (post 21) that you cannot turn the last gear. It seems the whole thing only works one way. > [@Machine\_Elf](#): > > So the net torque that actually gets applied to the first gear will be extremely small - much, much less than 10/(10100) lb-ft. So if there’s no friction, the mechanism definitely will work - you will be able to get the first gear rotating by applying a torque to the last gear. It’s just that it will take an extremely long time to accelerate that first gear enough to achieve an RPM that you could notice with your unaided eye. So, we build two of these sets out of pure frictionless rigidium. I attach the “ends” of them together, so that both reduced gears are in contact. I then spin the first gear. Does the last gear, after being geared down and back up, spin instantly\* and at the same rate that I’m spinning the first? \*ridgidium has perfect rigidity, which means the speed of sound in it is infinite. ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [July 21, 2022, 5:47pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/35 "2022-07-21T17:47:49Z")
Exactly what I was asking. The reduction should be perfectly reversible by a second set of the geartrain connected in reverse. You should recover the full input torque, at the same rotation speed, on the final output shaft even if the entire middle of the combined geartrain appears completely immobile. Friction, lash, and elasticity should probably prevent this from happening IRL. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [July 21, 2022, 5:56pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/36 "2022-07-21T17:56:33Z")
Yeah, in a problem like this, it’s not just friction. All of the inconvenient real-world factors that we usually pretend are small enough to ignore, are amplified to the point that we can’t ignore them. ---
**Author:** ![Machine\_Elf](https://avatars.discourse-cdn.com/v4/letter/m/82dd89/32.png) [@Machine\_Elf](https://boards.straightdope.com/u/Machine_Elf)\ **Post date:** [July 21, 2022, 8:41pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/37 "2022-07-21T20:41:01Z")
> [@k9bfriender](#): > > So, we build two of these sets out of pure frictionless rigidium. I attach the “ends” of them together, so that both reduced gears are in contact. I then spin the first gear. Does the last gear, after being geared down and back up, spin instantly\* and at the same rate that I’m spinning the first? Should work fine, but reversing the two units - so that the reduced gears are at both ends of the entire assembly - will not. This is because the intermediate gears (particularly the ones at the middle of the entire assembly) will be spinning extremely fast, as described in my earlier post, and will require a lot of mechanical work from your end of the system in order to achieve those speeds. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [July 21, 2022, 9:06pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/38 "2022-07-21T21:06:30Z")
> [@Machine\_Elf](#): > > This is because the intermediate gears (particularly the ones at the middle of the entire assembly) will be spinning extremely fast, as described in my earlier post, and will require a lot of mechanical work from your end of the system in order to achieve those speeds. I am not going to do the math, but I’m pretty sure you are severely understating the case, in that the intermediate gears would probably be breaking lightspeed by a pretty comfortable margin. ---
**Author:** ![Bonum\_Legatum](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bonum_legatum/32/6183_2.png) [@Bonum\_Legatum](https://boards.straightdope.com/u/Bonum_Legatum)\ **Post date:** [July 22, 2022, 4:22pm UTC](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182/39 "2022-07-22T16:22:34Z")
One thought - gears don’t only transmit rotation and torque, they also produce a force that pushes the gears apart. So as the torque approaches - so does the force pushing on the last gear’s axle. [Previous page](https://boards.straightdope.com/t/the-googol-to-1-gear-ratio-machine/968182.md?page=1)