Yeah, yeah, I know there is a different forum for this. Hipsters scare me though. I think it is the ironic facial hair. It could be the lack of bathing too. Either way, I'll stop before i offend most every one.

Anyhow, my commuter is a fixed conversion with vertical dropouts. 46/18 is too slack. 48/17 is too tight, although maybe in 3-6 months the chain wear will make it acceptable.

So my question is does adding a tooth to the cog pick up more chain slack than adding a tooth to the front ring? Or visa versa? Or is it the same? I figure there is an easy answer instead of pulling out my protractor and compass to do some serious geometry. That nightmare ended in 9th grade. I choose not to do any more.

The reason is it will be $50 to buy a 47. So will a 47/18 have more slack than the 48/17? Will a 47/17 be tighter than the 46/18? But if all things are equal, the $50 will go for beer. Or something.

Play with this?

https://eehouse.org/fixin/formfmu.php

Great question and I have no idea. Sheldon might answer Biopace? Or something.

Have you tried using a half link with the 48x17 setup?

Diameter change is a greater % of a smaller circle adding a 1/2" of circumference, than a larger .

+1) have you already tried a half link in the chain?

Yes, half link is the answer.

+1 on the half-link.

Failing that, there's always the White Industries eccentric hub:

The difference is basically the same since tooth spacing is 1/2inch on both front and rear. You will be better off buying a couple of half links to get you spacing right 3-4$ apiece and you will still have money left for beer.

True, but irrelevant. Circumference is the main thing we're after here. There is a secondary effect of the angularity due to the difference sizes of the cog & chainring, but for a 1 tooth difference on a real world combination, it isn't significant.

Thank you gentlemen and ladies.

LBS is closed but I will try tomorrow on my ride home.

If one half link doesn't work for you, two won't help either since that would be the same as adding a whole link.

Neat page btw.

According to that, the 47/18 will have a bit more slack than the 48/17 and a 47/17 will be a touch tighter than a 46/18.

I think you'd be happier buying a frame with horizontal dropouts.....not that there's anything wrong with your existing frame....but who doesn't more bikes?

I agree with John above that you never need to use more than one half link. "Magic gears" are cool, but it's not exactly cheap unless you already have a bunch of parts; I've never needed to find one.

A lot of guys in my local club ride road frames with vertical dropouts using the White Industries ENO hub and a few have eccentric BBs.

Hopefully you can get good enough tension with a half link.