Revolutionary Nano Gears: The Potential of Megaten Speed Bicycles

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The discussion explores the theoretical potential of constructing nano gears for bicycles, suggesting that if the last gear's radius is 10,000 times smaller than the first, it could significantly increase speed. The feasibility of such gears hinges on the ability of the chain or belt to handle friction and the structural integrity of the materials used. Current technology has already achieved smaller gears, as seen in Swiss watches, though nano-gears lack immediate commercial applications. Theoretical limits include friction heat and inertia affecting gear durability. Overall, while the concept is intriguing, practical implementation faces significant challenges.
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Suppose that it was possible to construct gears smaller than ones of modern ten speed bicycles(nano gears) and suppose your chain or belt could turn them and withstand the friction. First gear of course would be the same as a modern ten speed in order to get it moving. If the last gear's radius was 10,000 times smaller than the first gear how fast could this megaten speed bicycle travel
 
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How big are the wheels, how much force can the person push down on the pedals?

You can find it if you know the angular acceleration at the pedals.
 
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It's certainly already possible to make gears way smaller than those in a bicycle; try dissecting a Swiss watch sometime. (And they have made nano-gears, but there's no immediate commercial use for them.)
The only theoretical limits that I can think of when it comes to a gear train show up when either the friction heat or the inertia overcome the structural integrity of the gears and cause them to fail.
As for the practical limits, Cyrus has it covered.
 

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