Road Fan

My Trek 610 now has a vintage Specialites TA 5 vis chainset, 170 mm, with 46-30. The great thing about this is you can further reduce that as deep as 24 teeth, if you can make sure to set up a front derailleur that can handle that. I also have a few 13-32 of 34 7s freewheels I stashed over the past few years. With such a wide front you don't have to worry too much about gear redundancy. And with remaining availability of TA spindles, it should not be too hard to tune the chainset offset for good chain tracking and stability and some options for chainline with 126 mm rear spacing. And with diligent periodic maintenance, lifetime of the BB bearing set could rival your own!

You won't get close gear spacing, but hey, Velocio lived with it (lol!)! The best you can do is one of two things. Shimano had a series of 6 and 7 speed freewheels whicn spanned 13/34 of 14/34. Those have the first 6 cogs relatively close-spaced, with a big bailout cog on the inside, and one of Shimano's good tooth designs. With the 26 to 32 tooth granny which are possible on a TA 5-vis, you can have a low/close running gear set until you need a stump-puller, perhaps 32/34 or better than 1:1. The high end would be 46/13 or 44/13. With a 27" wheel diameter, that gives you a top gear up to 95 or 96. The bottom would be about 22" with 46 front and 34 rear, rounging the wheel diameter to 27".

Or you can seek or make a freewheel with as close to an even ratiometric step between adjacent cogs, as possible. We can calculate perfect ratios until the cows come home, but real gears have only integer numbers of teeth, and well, the ratios will be the ratios. You can input the freewheel teeth into the common graphical gear calculator, graph it and eyeball the graph for evenness. You can also follow the math and optimize, using a good spreadsheet. I prefer Microsoft Excel because whenever I try this calc on the Google spreadsheet I cause it to crash. Excel can handle this bit of arithmetic and much bigger calculations.

Start by finding the total ratio of the freewheel. For a 13-34, 34/13 = 2.62. Now for example, the ratio between the first pair would be 14/13 = 1.08 if it's 13/14, or 1.155 if it's 13/15. To design we want to find 6 numbers which multiplied together equal 2.62, AND which are the ratios of real gear tooth numbers. In this case the ideal ratio is 1.174 (you can calculate this using logarithms), but obviously we cannot make a freewheel based on this number. We can work out an approximation, which would also result in a good solution for a wide range half-step.

For the first step we can choose 13/14 or 13/15. The ratios respectively have been calculated (above) as 1.08 and 1.174. We choose the second sprocket that gives a ratio closer to the ideal one. I also use a rule of not decreasing steps (monotonicity) - the first gap was 2 teeth so the second one should be at least two. So the next cog would be 17 or 18. For 15 to 17 the ratio is 17/15 = 1.17, and for an increase of three we'll have 20/17 = 1.1765, nearly ideal. So the design so far is 13-15-17-20. Reasoning similarly, the total design is 13-15-17-20-23-27-34. With this a step from the 5th cog to the 6th cog should feel just about hte same as from the first to the second. The big cog, 34 is a bigger step. If that last cog was 32, the step ratios would be about as consistent as possible given the first one is 13-15.

So if it meets your requirements, a slightly better design would be 13, 15, 17, 20, 23, 27, 32. With 46/30 in the front, it still gives you a gear range of 95.5 - 25.3.

If anyone is interested in the spreadsheet, I can send it to you email or maybe on PM here. I don't know if it wilt translate if imported, or remain functional. And you have to be able to open Microsoft Excel files.