Originally Posted by
MEversbergII
I have a Shimano 3 speed hub I am looking to do a modification to. It currently has a 19t cog, which gives me 3.93, 5.24 and 6.97 meters development (49.28, 65.68 and 87.36 gear inches). In the terrain it gets used in and the purpose I have in mind for the bike, this isn't going to work too well. What I'd like is for the third gear to give me somewhere around 5m development (~60-63 gear inches), so that it's the ideal for flat ground (which, in theory, is the height of the rider).
Unfortunately, this appears to math out to a 26t cog, which does not appear to exist according to Google searches. What's the largest cog that's made for these kind of hubs? New territory, unfortunately.
M.
EDIT: Here's my spreadsheet o' reasoning.
You have to link the spreadsheet,
But without seeing it, I suggest you consider reducing the chainring size, instead of, or in addition to, increasing the sprocket size. What matters is the ratio of input to output sizes, so it's workable at either end.
However before you start shopping rings, be aware that many IGH hubs have ceilings on the primary drive (chainring/sprocket) ratio. That's because a low primary drive ratio make it possible for you to deliver more torque to the hub than it's designed to handle.
There's always some wiggle room, especially because not all humans deliver the same power to the pedals, so a small rider with a spinning type pedaling style can probably cheat, but a heavier rider riding in hilly terrain has to take these limits very seriously, or risk internal failure of the hub.