Calculating Local Hour Angle (LHA)

When trying to solve the PZX triangle, we need to know the LHA. This is simply the angle between our Longitude (by EP) and the Sun’s Longitude (called its Greenwich Hour Angle, GHA).

In this example our Longitude is 10° W. The GHA of the sun is 60°. The diagram shows that the angle between us and the sun must be the GHA – our Longitude.

 LHA = GHA – Longitude (if Long is West)

 e.g.

 LHA = 60° - 10° = 50°

In this example our Longitude is 10° E. The GHA of the sun is 60°. The diagram shows that the angle between us and the sun must be the GHA + our Longitude.

LHA = GHA + Longitude (if Long is East)

e.g.

LHA = 60° + 10° = 70°

Here’s an example; 

GHA                 154°  23’.4
Long (EP)         27°  52’.3 W
LHA                 126° 31’.1

If we were solving the PZX triangle using a scientific calculator and trigonometry, this would work just fine, however, most of us use Sight Reduction tables to solve the problem. This leads to a problem in that the tables only work in whole degrees.

Changing your EP longitude to make the maths easier
The LHA need to be a whole number (no minutes or decimals). To achieve this, you will need to manipulate your E.P Longitude to make the sums work out. We are able to do this because by its nature, the E.P is an estimated position, so moving it a little makes no difference.

Example 1

GHA                                                                       325° 12’.4
EP Longitude 7° 15’.3 W change EP to              7° 12.4W
Because we are west we subtract        LHA 318° 00’.0

Example 2

GHA                                                                 225° 45’.7
EP Longitude 15° 22’.1E change EP to     15° 14’.3 E
Because we are east we add         LHA  241° 00’.0