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Robert-
 
 I think the key word is "theoretically".

AS  I understand it, UTM is based on a perfect cylinder, a Mercator
Projection, for the bulk of the world (outside the polar areas) and given
that distorted projection, your theoretical conversion works perfectly well.
But from the references online it seems that the system is NOT designed to
be converted that way. Rather, the linear mileage (meterage?) is marked off
on each topo quad, and you are supposed to either draw on the quad or use an
overlay on it. The primary purpose is military, i.e. artillery, where maps
will be distributed and the only question is how to tell the big guns
exactly where you are on the map that you were given. UTM works very well
for that, or for anything else where you are using paper quads.

See http://erg.usgs.gov/isb/pubs/factsheets/fs07701.html
and http://ask.usgs.gov/ where the USGS provides PHONE and email contacts
for folks to ask questions.

I know there are conversion utilities for computer use, but I suspect they
are either referencing offset tables, or counting distance and accounting
for the distorted globe. Not something you'd want to do by hand.

I'll let you ask the prime authority directly--I know UTM has become popular
with hikers, but I can work with degrees and have had no need or use for
UTM.

   

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