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The formulas to convert between lat/lon and UTM in the Explanatory
Supplement to the Astronomical Almanac (1992, first printing) seem to
work well after the mistake on p. 210 is corrected. I got a C language
implementation running. A lat/lon -> UTM -> lat/lon set of conversions
on the Clarke 1866 spheroid yields

40N 90W -> X=756106.3785 Y=4431859.1322 -> 40.000000001N 89.999999996W

The error in the final longitude is equivalent to about .3 mm. The UTM
values duplicate the NGS online calculator within less than 1 mm as
well.

As presented in the book, the equations are ill-suited to direct
translation to source code because they use many integral powers.
E.g., 2 + 3D + 4D^2 + 5D^3. To avoid writing inelegant code you have
to factor out D: 2 + D(3 + 4D + 5D^2). Then D can be factored out one
more time inside the parentheses.

It's just high-school algebra, but the grid equations are much more
complex than my simple example, so I had to work carefully to avoid
making a mistake.

After failing many years ago, it's pleasant to have finally gotten
these equations working.

   

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