Hello

[c_davidson]

Mike,

We are all trying to master this skill and make it as easy as possible and it does get confusing.

Firstly, Chris Nolan is very good at explaining celestial navigation.  But sometime there's complexity we miss.

The following formulas are found in the Almanacs at TheNauticalAlmanac.com and also here;
https://thenauticalalmanac.com/Formulas.html

Arriving at Hc is very simple and I can get it in about 10 seconds using a calculator, of course (and I'm no math whiz-bang).

To get Hc

Here's the proper formula;

Hc = sin-1[sin(declination) x sin(Latitude) + (cos(Latitude) x cos(declination) x cos(LHA)]

Here's the formula when using the easy Natural Math calculators;

Hc= Sin-1(Sin(Latitude) x Sin(declination) + Cos(Latitude) x Cos(declination) x Cos(LHA)

To get Z and then Zn;

Z proper formula;

Z  = cos-1[(sin(declination) – sin(Latitude) x sin(Hc)) / (cos(Latitude) x cos(Hc))]

Z formula when using the easy Natural Math calculators;

Cos-1((Sin(declination) – Sin(AP Latitude) x Sin(Hc)) / (Cos(AP Latitude) x Cos(Hc)

Once you obtain Z you got to get Zn using the following Rules;

To obtain Zn apply the following rules for Northern and Southern latitudes;.

In Northern Latitudes

LHA greater than 180°....Zn=Z
LHA less than 180°...........Zn=360° – Z

In Southern Latitudes

LHA greater than 180°....Zn= 180° – Z
LHA less than 180°...........Zn= 180° + Z

Please let us know if that solves your problem.

Welcome aboard.....

Clen