Hmm, I get it. I wonder how much that varies, given the low angles we're dealing with. Is there any good source on the web that has the diameter of sprockets as a function of their number of teeth? I assume, but do not know, that this is constant across sprocket types.

I would be down for trying to hook up a spreadsheet if I got some initial input.

Here's why I'm asking. I'm about to do a ss conversion on an old road bike that has a cassette freehub in back and a 40/52 double up front. I'm building this for one specific ride, a 40 miler in western mass that has a great 10 mile climb and 8 mile descent, so I was going to gear this 40 x 30 (its a big hill). But then I got to thinking how annoying this gearing would be for the rest of the ride (long rolling hills), and so I wondered whether I could put a second sprocket on the freehub that lined up with the 52 tooth chainring. I figured that perhaps there's some chain length conservation law or something, so I might be able to fit an 18 tooth sprocket and not even have to adjust the rear wheel. 52 x 18, btw, would be a perfect gear for the rest of the ride I'm thinking of.

Unfortunately, I haven't yet bought the tools to do the conversion so I can't just test this out.

Anyway, like I said, I'd be happy to pursue this further and try to make some calculations if someone gave me some direction.