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I am new to the list and have just recently started using a programmable 
calculator for sight reductions.  I have found several useful formulae on 
this list and in other references, however the one shown in the Nautical 
Almanac for azimuth puzzles me.
Can anyone explain the formula for azimuth from the Almanac?

Summarizing from page 279 - 2002 Nautical Almanac

6. The calculated altitude and azimuth.
Step 1.  Calculate the local hour angle.
        LHA = GHA + Long.

Step 2.  Calculate S, C and the altitude Hc from
        S = sin Dec
        C = cos Dec cos LHA
Sin Hc = (S sin LAT + C cos LAT)

(This appears to be analogous to the fundamental cosine formula of spherical 
trigonometry and to be the classic formula for computing altitude.   Most 
references however seem to use [+ or abs. difference]) i.e. sin Hc = sin LAT 
* sin Dec [+ or absolute diff.] cos LAT * cos Dec * cos LHA.

The trouble, for me, starts in using the formula for azimuth from the almanac, 
which seems to be quite different from those most commonly shown in other 
references, such as one that seems fairly standard

        Cos Z = (sin Dec  [+ or abs. diff.] sin Hc) / (cos Hc * cos Lat)

The Almanac formula for azimuth show in Step 3 is as follows;

Step 3. Calculate X and A from
        X= (S cos Lat - C sin LAT)/cos Hc
        Cos A = X

Determine the azimuth Z
If HA > 180 degrees than Z= A
Otherwise Z = 360 degrees - A

The formula than seems to be
Cos A = [(sin Dec * cos LAT) - (cos Dec *cos LHA * sin LAT)]/cos Hc

As I said, I have not seen this formula anywhere else and also I have had 
trouble with it when Dec and Lat are opposite signs. Please understand that I 
am not much of a mathimatician.

Ralph Clampitt

   

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