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The AM Sturmey is an excellent hub, but only for the right circumstances. It gives differences of (about) 12% down and 13% up from direct drive. So if you have, for example, 46 x 18 with 26" wheels you have 66.4" direct, and approx. 58" bottom with 75" top.
Those gears would be fairly good for a club run somewhere without very steep climbs, but for touring or child carrying the low gear wouldn't be enough for most people.
I think you would do better with an AW (25% down,33% up) As mentioned elsewhere these are plentiful and cheap or free (in skips). The ratios aren't ideal, but in my experience the hubs are super reliable.
If you can't find one, let me know.
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https://www.ebay.co.uk/itm/234935374415?mkcid=16&mkevt=1&mkrid=711-127632-2357-0&ssspo=Uk1zsGtHRHu&sssrc=2349624&ssuid=zb3kpnpgQlG&var=&widget_ver=artemis&media=COPY
Its not really old enough to be in this thread i know but it looks like it has a kids seat on the back and it would be great fun and it has gears.
Talking of Sturmey Archer, does anybody happen to have a decent but cheap AM or similar hub built into a 700c wheel They might consider selling? MY daughter is coming up to bike seat age, I've been given one that attaches to the stem/seatpost over the top tube, that I was going I to fit to my JRJ as it's comfortable and has decent MAFAC brakes, but I don't really fancy riding fixed up the (admittedly fairly short, but steepish) hills around North East London/Epping forest way with an excitable 1 year old sending my balance off, so thought a Sturmey might suit whilst keeping the look of the bike.