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I got a road bike frame with vertical drops, so can't set the tension up. Tried to remove one link but then the chain becomes too short. My next idea was to change the front sprocket, currently have 46 tooth sprocket.

The question is though: how much will each next tooth affect the chain tension?

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    (It is pointed out by the answer below, but I really want to highlight it once more) Not only you need to set up the chain tension once, you'll have to maintain it throughout the life span of the chain. I found that after a very short while (maybe two weeks of riding), a freshly installed single-speed chain may require its first additional tensioning as it breaks in. – Grigory Rechistov Aug 2 at 20:29
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    You need to get a chain tensioner. – Daniel R Hicks Aug 2 at 20:32
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    @DanielRHicks: 1) please stop answering in comments, 2) chain tensioner is a no-go on a fixie, those are for single speeds only. – whatsisname Aug 2 at 20:40
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    @NazarPasternak "will it at some point stop stretching?" — No, it won't. The stretching is wearing, and it simply is losing the metal on chain rollers which reduces their diameter. There are no known preconditions to completely stop it nor to revert it, lest you replace the chain with a new one (which will require retensioning). – Grigory Rechistov Aug 2 at 22:51
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    @GrigoryRechistov: the reason a chain tensioner is a no-go is because a chain tensioner can't handle the force of backpedaling, or of pedaling in your hypothetical double-tensioner setup. – whatsisname Aug 3 at 1:01
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The short answer, is you generally cannot make a fixie out of a frame with vertical dropouts.

Not only do you need to tension the chain, but the spacing of the axle of the bottom bracket and rear wheel varies, depending on your selection of cog and chainring tooth counts.

Adjusting tooth counts will allow you to try to fine adjust the spacing, but it won't always get you there. The formula for how adding or removing a tooth will change your ideal chainstay length is not simple. You're removing a link from the chain, but you're removing it at an angle, so your reduction in chainstay length will not be the same as the amount of chain you remove.

Online, you can find many magic gear calculators [example] where you can try to pick a ratio that will exactly match your chainstay length.

You can also use a special half-link chain element, to adjust the chain by half as much as an ordinary link.

With all that said, the difference between "slack" and "tight" is a very small amount of chain stretch, and fixies in particular are pretty touchy for the tension. What I describe above I think works well for coaster-brakes and single speeds, but I would not recommend it for fixies.

If you are especially willing to throw caution to the wind, you could file the dropouts to be slightly wider, which might buy you just enough space to make one of the magic gear ratios work. The risks to safety should be obvious but that's up to you.

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    "With all that said, the difference between "slack" and "tight" is a very small amount of chain stretch" — to add some numbers: just merely 1% of relative chain stretch is considered terminal for a drivertrain. 0.1% of stretch is clearly visible on a single speed bicycle without a tensioner as a chain slack. – Grigory Rechistov Aug 2 at 20:35
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    Thank you for your answer, @whatsisname, helped me get more understanding of the whole process. Also, is it an option to redigest the dropouts to the horizontal ones with the aluminium frame? – Nazar Pasternak Aug 2 at 20:55
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    @NazarPasternak even if re-welding the dropouts would have not compromised their strength (which is very likely to happen given it is an aluminum alloy), the cost of such procedure at an experienced welder with Alu-specific skills and equipment will certainly be higher than what a couple of fresh new steel fixie frames would cost. – Grigory Rechistov Aug 2 at 21:13
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If you cannot control the rear cog's position, you can try moving the front chainring to tune the chain tension. That is, get an eccentric bottom bracket:

Eccentric BB in frame

By rotating it in the frame, the distance between rear and front cogs can be tuned.

The same idea is achieved by eccentric rear hubs, e.g. White Ind. Eno:

Eno

The hub choices below offer those of you looking to convert a frame with vertical dropouts, a choice of eccentric hubs.

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    It might be worth mentioning the BB standards where this is reasonably doable. An ordinary 1.27" English bb shell this isn't an option unless you shell out a lot of dough for some exotic parts – whatsisname Aug 2 at 20:44
  • Oh, there are also eccentric rear hubs that will work with vertical dropouts! whiteind.com/eno Yeah, they cost ~200 USD apiece – Grigory Rechistov Aug 2 at 21:18
  • The first option seems appealing, will do a research on that. Thanks! – Nazar Pasternak Aug 2 at 21:29
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    "An ordinary 1.27" English bb shell this isn't an option" — so true. The BB housing on the picture above is huge in diameter, likely to correspond to an Ashtabula-sized system. There is not much space to create eccentricity inside a BSA housing for a BSA spindle (maybe offset external cups? nah, that sounds crazy complicated to align). – Grigory Rechistov Aug 2 at 22:57
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    @GrigoryRechistov There may not be much space in a normal bb shell for eccentricity, but you don't need much eccentricity either. You need exactly one half link's length worth of eccentricity, a quarter link's eccentricity if you are prepared to use a half-link chain lock. I have no clue what eccentricities are available for the normal bb shell, though. With the screw-in system it would be hard to fix the position of the bb anyways. So, I guess, nice idea, but very likely not useful. – cmaster - reinstate monica Aug 3 at 9:43

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