About 10 years back, when I stopped track racing, I built up a single speed 
coaster brake wheel for my track bike (using a ca. 1938 Bendix hub that I found 
in a box in my basement and have no recollection of buying; it was smooth as 
silk after rebuilding it).  That worked great except the bike wasn't very 
comfortable to ride on city streets.  So I sold that and then I built a single 
speed frame a few years back around that wheel, with no accommodation for a rim 
brake on the back.  My friend Mike Pofahl, who builds frames in Faribault MN, 
walked me through it; it was a lot of fun, very interesting and made it clear 
that I would not want to try to build frames for a living.  To do it right is a 
*lot* of fiddly detail work with files and grinders and test fittings, etc.  If 
I had been paid the US median wage I'd have had about $800 in labor alone into 
that frame.  Building that frame really made me appreciate 
Waterford/Joe/Curt/Match/etc.  It also put me in awe of Tom Ritchey, who has 
said that he can start with a set of tubes first thing in the morning and have 
a frame ready for painting by lunchtime (the result of personally building 
thousands of frames- a lot of my time was spent learning how to miter and align 
and then doing the mitering and alignment, plus filing lugs.  Hours filing 
lugs).

That was fun for a year or so but I decided gears would be nice.  Jim Thill set 
me up with a Sachs/SRAM 3 speed coaster brake wheel about 4 1/2 years ago and 
it has worked great.  Like many 3 speeds, though, the jump between gears is 
really wide.  Too wide, really, as it mimics the Sturmey Archer AW gearing 
pattern.  I think an AM style spread would be better.  The difficulty becomes 
choosing the gearing.  Do you gear it so that 2nd or 3rd is about 70"?  If you 
choose 2nd, then 3rd is going to be about 90" and 1st is going to be about 42".

After puttering around with different options, my current setup is a 42 x 21 
resulting in gearing of 34", 53" and 72".  I find this works fairly well 
although top practical speed is about 20 mph.  Steep hills aren't a problem.  
This isn't a bike I tend to ride in a hurry, though, as I mainly use it for 
commuting and pottering about.

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