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At 06:10 AM 6/7/2006, George Huxtable wrote:

>I have written a program in bastard-Basic which runs on my 1980s Casio
>programmable calculator (FX 730P or FX 795P), and if anyone is
>interested would be happy to send it or post it up. It would be simple
>to adapt it to another machine. It takes the 6 quantities, dec, GHA,
>and altitude for each of two bodies, and returns two possible
>positions in terms of lat and long, for the user to choose the
>appropriate one. It does not require a DR or AP, and provides an exact
>result without going through an iteration process.
>
>It's not original, in that versions of the method have been described
>previously beforehand. For example, in an article by George Bennett in
>the journal "Navigation"  (which is, I think, the American one) Issue
>no. 4, vol 26, winter 1979/80, titled " General conventions and
>solutions- their use in celestial navigation", and to the book
>"Practical navigation with your calculator", by Gerry Keys, (Stanford
>maritime, 1984), section 11.12. The method has also been described in
>"The K-Z position solution for the double sight", in European Journal
>of Navigation, vol.1 no, 3, December 2003, pages 43-49, but that
>article was bedevilled by printing errors that render it more-or-less
>unintelligible, which were corrected in a later issue. Not to mention
>several serious errors and misunderstandings by the author, which have
>never been acknowldged or corrected in that journal.

George:

Do any of these sources spell out the math in detail?  I've searched in
vain for a complete algorithm so a long time ago, I sat down and worked out
the math.  One of the tricky things is determining what quadrant angles lie
in when doing a inverse trig function.  I have a c++ windows application
which will find all the equal altitude circle intersections for a set of
observations.  It also can plot the equal altitude circles on a world map.

Mike

   

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