# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: UTM to lat/lon formulas**

**From:**Paul Hirose

**Date:**2003 Dec 12, 13:30 -0800

George Huxtable wrote: > > Basic on a pocket calculator, ready to test. I have taken heed of Paul's > warning about a misprint. If he can recall anything about that misprint, or > in what way the problem showed up, it would be good to learn more. I have more on this. Following the link Herbert Prinz provided to this page http://www.posc.org/Epicentre.2_2/DataModel/ExamplesofUsage/eu_cs34h.html , I think I've found the typo in the Explanatory Supplement to the Astronomical Almanac (1992 edition). The book and Web page both appear to use the same formulas, with slight differences in the variable names. Look at the variable the Web page denotes with Greek letter nu (resembles v) in the Easting and Northing formulas. There's a little problem with the page layout, in that it doesn't include the formula for nu with the other auxiliary quantities such as T and C. However, if you read on a bit, it's there. (Just delete the "1" subscript from nu and phi.) Now turn to the Explanatory Supplement. It uses N sub phi rather than nu. The formula for N sub phi is on page 210. But this formula is quite different from the one for nu on the Web page. In fact, it's identical to the formula for rho sub 1, immediately below! Thankfully, we can clear this up because the Web page includes a fully worked example, including values for auxiliary quantities. (Those who would post math online, take note.) I was able to confirm that the formula for nu does yield the stated value. Also, the wrong formula in the book yields a value fairly close but definitely not right. That matches my recollection of what I saw several years ago when trying to code the Explanatory Supplement formulas. By the way, I used Geotrans to check that Web page's example, which converts lat/lon to British National Grid. The page is correct.