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So I found the magic gear on one of my bikes and have good chain tension.

Now I want to change the gearing. I know if I keep the total number of teeth the same (cog teeth + chainring teeth), I'm okay with the same chain.

But I also thought there was an easy formula for changing the length of chain, like, one chain link for a 2-teeth difference. I've searched Sheldon and can't find it there. Before I start breaking chains in a trial and error method, does anyone know?
 

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There is 1/2" between two teeth. So if you increse the sprocket size with 2 teeth the cicumference would increase with 1" but since you are only usig (rougly) half the cicumference the chainlength would increase only 1/2". Also because different gearing gives different angles for the chain this will only be approximately true.

An idea is to mount the wheel and put the too long chain on and stretch it and see how much overlap there is and cut it accordingly.
 

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Courtesy of Mr. Brown:

Adding or subtracting a link in the chain will move the axle 1/2". Changing either sprocket size by one tooth is the equivalent of moving the axle 1/8" (4 mm).

So, basically, adding a total of four teeth adds another link.

As an example, if you went from 42x18 (~61 gear inches) to 46x18 (~67 gi) you would add a link. Option B would be to go to a 44x16 (~72 gi) and keep the same length chain, as you are adding two in the front and subtracting two in the back.

The only thing to consider is that the chain angle will be a little different and may affect your magic tension, especially if you do something extreme like go from a 42x18 to a 52x16. So, just because the magic gear works doesn't guarantee that any other similar gears will work. Good chance though.

Regards,
Anthony
 
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