surly old man
Join Date: Sep 2006
Location: Carlisle, PA
Bikes: IRO Mark V, Karate Monkey half fat, Trek 620 IGH, Cannondale 26/24 MTB, Amp Research B3, and more.
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Its complicated. There are two factors, of course, in determining chainline: where the chainring is in front and where the cog is on the rear. Those two factors break down into several more factors. On the rear, you can flip the cog and sometimes move it in or out, or put a spacer behind the cog. Most importantly, you can move the cog around a lot by choosing how to respace the rear wheel. On the front, you can put the ring on the inside or outside of the spider, or use spacers to push it farther in or out. A different length spindle, or a different crank will also move the chainline around. Lastly, it used to be the custom to have asymmetrical spindles (longer on one side than the other), so you can move the line quite a bit just by flipping it around.
Its complicated, but not hard to mess with most of these factors. Trial and error is maybe the most efficient way to do it.
Do keep in mind that a new single speed wheel will not solve the problem for you by itself. They come set up for a chainline that your spindle/crank cannot achieve without further modification. So, even if you go that route you will have to mess with some of those factors.
My recommendation is to use the current wheel (I presume it is a freewheel?) and try to bring the rear out as much as possible by respacing and redishing. Then hope that you can bring the front in as much as possible by putting the ring on the inside of the ring and maybe using spacers on the bolts. You have a good chance of this working without needing a new BB spindle. You will likely have to do all of this with a purpose-built single speed wheel anyway, so if the current wheel is in decent shape, you might just as well use it.
None of this beyond an interested tinkerer, or none of it is terribly expensive.