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I have an 11 speed cassette 11-32 teeth. I am running a 52 teeth chainring on the front. What would be a good recommended smaller chainring for the front? It needs to be big enough to take up the slack of the chain when i am on the smallest cog at the back.

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    The job of taking up the slack is the rear derailleur. Note that your choices are limited by what the front derailleur can shift and what the rear derailleur has capacity for. Also, running in small/small is usually not a good idea except for maintenance. – Batman Apr 23 '18 at 2:44
  • I understand that you have a single 52 ring or a double in the front? – Carel Apr 23 '18 at 7:55
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    Could you clarify your question? What do you want to use the bike for? Are you running only a 52-tooth at the moment? Are you asking about a single chainring that's smaller than your current 52-tooth, or for a double chainring that would be 52-and-something? – David Richerby Apr 23 '18 at 13:50
  • If you're asking for an additional ring to your 52, it would be a 36. Or you could change both to a 50/34 which would both work together with an 11-32 and a medium cage RD possibly without removing a link from your chain. – Carel Apr 23 '18 at 20:32
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As was mentioned in the comments, this question will depend on what derailleur you are using both front and rear (since they have a rated capacity). Too large a difference and the front derailleur will not shift well, but you also have to make sure the the total difference between large-large and small-small is within the range of the rear derailleur so that it takes up the slack and does not overextend. The specifications for your derailleur should have these numbers listed and then you can pick an appropriate sized ring to fit your crank from there.

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You'll generally want to get the smallest inner chainring possible, in order to maximize the spread of gears. The actual size of that chainring will be determined by your crank's BCD (bolt-circle diameter). It's impossible to say what size your BCD is, although with a stock 52t big ring I would guess that it's a road standard size, 130mm. This means your smallest available inner ring is 39-tooth. 52/39 is a modern standard combination, and 52/42 is an older standard; either will work.

I wouldn't worry too much about your derailer capacity and chain slack. If your rear derailer can accommodate a 32 tooth cog, it must have a medium or long cage, both of which are capable of "wrapping" plenty of chain. The only instance in which chain slack becomes an issue is when combining the inner small chainring with a small cog on the cassette. This combination is horrid for your drivetrain, and ought to be avoided at all times.

If you are worried about chain slack because of dropping a chain, that is a separate issue, largely unrelated to derailer/chainring compatability. 1) dropped chains are a fact of life. get used to "picking up" a chain using the front shifter to avoid having to get off the bike. 2) if it's a mechanical problem, your limit screws may be improperly set. 3) don't shift under heavy load. if you shift into a low gear while you're already climbing the hill, you're doing it wrong and you're breaking your parts. shift BEFORE you need the gear you want to be in.

sorry for the pithy attitude, i've had a few beers and am striving for clarity.

edit: if your cranks end up being 110bcd (compact BCD), you can go pretty low on your inner ring. You could even do a 52/34 (I do!), but you must accept tricky front shifting.

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    Re: 'dropped chains are a fact of life'. Maybe for you. No rider with a modern drivetrain should have to put up with that. – Argenti Apparatus Apr 23 '18 at 10:23
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    @ArgentiApparatus A dropped chain is my bike's way of telling me, "Erhum, could you adjust me please?" – David Richerby Apr 23 '18 at 13:52
  • Dropped chains are a fact of life, especially when racing. You can have a perfectly adjusted group and if you happen to hit that bump in the road at the right moment that you down shift, your chain's going to hop off the crank. Instead of complaining about your expensive parts not working, learn to deal with that situation when it occurs. Also, there are a lot of lower end groups with shoddy tolerances that require a trade-off between tight limit screws and constant chain rub. If the customer complains about the noise, I tell them what I can do to fix it and the risk that incurs. – Nathaniel Hoyt Apr 24 '18 at 15:35

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