The tiniest push on the gear on the left causes the gear on the right to fly at thousands of RPM. Of course, there would be a ton of friction in the system to overcome. However, what if the left gear was a pinion connected to a rack that was pushed by an extremely powerful, yet slow-moving source, such as a glacier or tectonic plate? With enough gears in this arrangement, an unstoppable force moving just 1mm/year could spin tons of turbines.
Think about how large the forces will be at the first tooth interface at the left (or in the rack). How strong does that tooth need to be?
Alternatively, you can use it the other way. Connect the gear at left to a tectonic plate. Rest your finger on the gear at right. Voila! You can exert a force great enough to stop the tectonic plate's motion. Plausible?
When Archimedes said, "Give me a lever long enough, and a place to stand, and I'll move the Earth.", he actually meant something more like, "Give me a lever long enough, and a place to stand, and I'll change the momentum of the Earth very very very slowly. Unless that lever is incredibly strong and I have access to a considerable source of energy."
"Alternatively, you can use it the other way. Connect the gear at left to a tectonic plate. Rest your finger on the gear at right. Voila! You can exert a force great enough to stop the tectonic plate's motion. Plausible?"
Nope, the question here would be whether the material used to construct the left gear withstand the force that a tectonic plate exerts given that the gear system will not allow it to move. I don't think the mechanics of the tectonic plate exerting force on our gear system and our gear system exerting force on the tectonic plate are symmetrical.
Good point. And even if the gears were made of unobtanium, the whole gearbox would have to be mounted on the opposite tectonic plate on top of breakable rocks.
So the total gear ratio of that gearchain comes out to something like 1119:1, though that's lower than you intended I suspect because you geared it down with a 9:57-or-so ratio on the end. The penultimate axle is geared at 7089:1 with respect to the first axle.
Now while that implies a rotation of one degree of the first axle is accompanied by a rotation of the penultimate axle through 20 or so revolutions, in practice that's not going to happen, because of that ton of friction you pointed out. The friction force acting to stop the last axle turning gets fed back as resistance to your pushing the first wheel, and it gets multiplied back up through the gearchain by the same factor - so the resistance to your turning the first wheel is 7000-times the resistance of turning the last wheel - plus 2000 times the resistance of turning the wheel before it, plus 918 times the resistance of the wheel before that... in total, assuming all friction forces are equal, you're fighting against a force 12000 times the force you need to turn just one gear - just to beat the friction. Okay, so you posit some frictionless maglev bearings in a vacuum, perhaps. But you still want to get these wheels into motion, so then the same multiplier gets applied to the force you need to accelerate the mass of each gear into (rotational) motion in the first place. Getting all those gears spinning requires 12000-times the acceleration to get one of them turning, so 12000 times the force.
And forget about putting a useful load on the end axle - let's put this thing in a car, say, and use it to drive the rear axle. We'll lift up the rear axle and get the engine up to 5000 RPM. Your engine is going to get that axle spinning 7,000 times for every engine RPM - 35 MILLION revs per minute! But when you drop your 1-ton car to get some traction, the engine's going to act like the car weighed 7000 tons...
You could also think of it in terms of energy. If that last gear spins at thousands of RPM, its got a huge amount of kinetic energy from somewhere. It must have come from your 'tiniest push'. Your tiny push has to transfer all that energy - so it can't be that tiny.
Gears 'distribute' kinetic energy in that they allow you to take a rotational motion on one axis and generate a rotational motion on a different axis. That can be a parallel, offset axis, as in this case, but it can also be at a different angle, using angled or crown gear teeth. So yes, that's one use, certainly. They let you reverse a rotational direction, too - turning clockwise into anti-clockwise.
But the main thing they do is let you trade angular distance of motion against angular force, or torque - same as a lever does, and much like how a pulley system lets you trade off linear distance of motion against linear force. I can make a gear system that multiplies the effective force I can exert by 50, at the expense of my having to rotate a crank on the input shaft fifty times for every time I want the output shaft to rotate. Or I can use it the opposite way around and make an output shaft spin fifty times for every rotation of my input shaft, at the expense that I have to exert fifty-times the force to overcome any load on the output shaft.
There's an art/science experiment piece on display at the Exploratium (unfortunately I can't remember what it's called) that has a similar construction. The gear at one end is turned at a steady pace by an electric motor, and each successive gear attenuates the motion until you get to the last gear, which is set into solid concrete (iirc). If it were free to move, it would take a fantastic span (billions or trillions of years?) to make a full rotation.
Edit: Thanks to bockris for pointing out the name. Turns out the last gear rotates once each 13.7 billion years.
Great arrangement! It will work.
Whether it will be financially feasible to construct such a large system of gears, deploy it in extreme weather, keep it well oiled and maintain it, and then transport the generated power to a usable location are entirely different questions.
Hmm... maybe there are more common sources of strong-but-slow power. The heat expansion of bridges? The weight of vehicles sitting idly at a stoplight? The swaying of skyscrapers?
I wonder if you could make a purely mechanical solar panel that way. Get a giant sheet of metal, put it out in the sun, and attach this gear arrangement to it, braced by opposite sides of the expansion. Hmm... I kinda want to make this now.
What you're describing is a move up the Kardashev scale[1]. The Kardashev scale measures how tech-savvy a society is by how they collect and use energy. A Type I society on the scale is able to harness and store all the energy generated on the planet, which we're moving towards now. Regenerative braking and such are definitely progressions in that area, but presumably bigger gains could be had by harnessing the power of tectonic plate movement, volcanic activity, wind, solar, etc.
The right wheel would spin fast, but anything put there to leverage that momentum into energy, be it simple magnetic generator, would be enough to halt the whole system by equalizing the opposing forces, since whatever minimal force it has, will go trhu the same powers that create the initial speed.
It would work, but it would probably not be practical in terms of materials - any significantly huge gear ratio driven from the low-motion side will run into problems with the strength of the gears and the degree of friction involved (and the steady-state static friction pressure & friction loss per second of the fastest gears being sufficiently large to make it impossible to move the slowest gears at all)- and even if you have an impossibly strong frictionless gearbox, the strength of the contact patches with the objects themselves becomes the weak point - the pressure will impress a hole right through the tectonic plates, rock, or glacier you're dealing with, rather than spinning the gears.
Well you would need an unrealistically long lever for that. With this gear thing, you could conceivably pack an extremely high gear ratio in a tiny area. I guess gears are just levers in a different form. I was just wondering what the limitations would be in this idea. I guess the construction of the gear system would have to be unrealistically high quality and strong.
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The tiniest push on the gear on the left causes the gear on the right to fly at thousands of RPM. Of course, there would be a ton of friction in the system to overcome. However, what if the left gear was a pinion connected to a rack that was pushed by an extremely powerful, yet slow-moving source, such as a glacier or tectonic plate? With enough gears in this arrangement, an unstoppable force moving just 1mm/year could spin tons of turbines.
Would this work?