Originally Posted by Road Fan

Grim,

Let me try to add clearer mud, if I can. Your 6-speed freehub is a pretty good basis for a half-step. It has an average incremental ratio of 14.9%. The chainring ratio it needs is 7.5%. A 52-48 is a pretty good match to that, since it comes out to about 8.3%. If you want to go to 7-speeds and keep the same chainwheels, you pretty much need to keep the 14-16-18-21-24-28, and add a bigger 7th cog with the same ratio. Mathematically it would have to be 32 teeth, so you'd need to find a 14-16-18-21-24-28-32.

The 7-speed you are getting ready to use, 14-16-18-20-22-24-28 is also a pretty even spread, with an average incremental ratio of 12.2%. It wants a chainring ratio of 6.1%. If you want to keep your 52 tooth big ring, you'd want 52/1.061 = 49 teeth. With this cassette and a 50T big ring, you need a 47 tooth to replace your 45 T. So I think you figured out correctly.

If you went to a 52/47, the chainring ratio would be 52/47 = 1.106. The incremental ratio for the cassette needs to be 1.212. Starting with a 14 small gear, the 7th would have to be 41 teeth, which is very hard to buy, and a derailleur that will handle it is also pretty tough. Taking 6 speeds and a 34 tooth, you get an average increment of 19.4%. Going to a 13 small gear, the incremental ratio is right at 1.212. So you could do a 52/47 with 13/34 (with the right spacing), and have a pretty good half-step. Other chainwheel combos will work with this cassette: 51/46, 50/45, 49/44, and 48/43.

So if you found a suitable 13/34 6-speed, you can get pretty well-matched to your Fuji's 50/45.

Again, I hope I've added some clarity. I think you are on the right track. The hard part in all this hardware-wise is to find a suitable cassette. If you already have the 14/28 7-speed as defined, search out a 47 tooth middle chainwheel. It will be a lot easier to find than the 13-16-19-23-28-34, if you don't have one.