NavList:

Now that calculators (in my opinion) are rapidly becoming "old technology" --

I thought it would be good to highlight a formula for sight reduction that calculates the altitude and azimuth of a body, given its declination and local hour angle.

   < r, A> = POL( tan dec cos lat - sin lat cos lha, -sin lha)

   Hc = acos(r * cos dec)

   Zn = A  (add 360 if A is negative)

After using this formula for some time, I think it should be more familiar, and possibly more popular, as it has some advantages:

   1) Only one complicated formula to memorize/type in

   2) The altitude Hc and azimuth Zn are (almost) found in one step

   3) No complicated sign rules to remember to find the azimuth

I first became aware of this approach from a post by Robin Stuart.  After digging through the archives, I found that people have pieced together the idea, but never made much comment on it:

   https://NavList.net/m2.aspx/Sight-Reduction-Formula-Question-Huxtable-jan-2005-w21338

   https://NavList.net/m2.aspx/POL-arctan2-Bergman-nov-2005-w26304

   https://NavList.net/m2.aspx/Which-calculator-use-for-arctantan269-Stuart-feb-2017-g38110

Enclosed is:

1) A short "how to use it" write-up, "Polar Reduction"

2) A derivation, based on coordinate transformations (using rotation matrices)

3) Some math background on rotation matrices that explain some of the details (for those who like such stuff).