How to calculate sun’s local hour angle: To use this website to find the Line of Position (LOP), you need to be able to calculate the local hour of the sun first.
Hence, on this page, you will find 4 examples of how to calculate The local hour angle of the sun
See first theory of LHA.
Understanding LHA and Polar Angle (P)
Additionally, we convert the local hour angle (L.H.A) from a range of 0° to 360° into the polar angle (P) within the range of 0° to 180° for mathematical purposes.
The detailed condition for this transformation is explained on this page.
Subsequently, we incorporate this converted angle into our mathematical formulas to derive the calculated height and azimuth of the sun.
Introduction:
G is estimated longitude:
add if East
subtract if West
After finding LHA, how to deduce P ?
P (polar angle) simplifies trigonometric formulas when using cosine/sine laws for altitude and azimuth.”
ロ LHA < 180°
sun in the West P = LHA
ロ LHA > 180°
sun in the East P = 360- LHA
P = _ _ ° _ _ ‘, _ NE/SE/NW/SW
How to Interpret Direction: NE / NW / SE / SW
NE → We are in the Northern Hemisphere and the sun is in the East.
NW → We are in the Northern Hemisphere and the sun is in the West.
SE → We are in the Southern Hemisphere and the sun is in the East.
SW → We are in the Southern Hemisphere and the sun is in the West.
For further details, refer to the pages on Sexagesimal System and 360° Formulas.
Calculate LHA and P
4 examples
Worked Examples of LHA and P Calculation
example 1
Observation in northern hemisphere
GHA = 323°23′,5
//////G = 62°52′,3 West
LHA = ? / P = ?
GHA = 323°23′,5
G = 62°52′,3 W
__________________ ⎼
LHA = 260°31′,2
ロ LHA > 180°
sun in the East P = 360- LHA
P = 360 – 260°31′,2 = 99°28′,8 NE
P = NE : North latitude and sun is in the East
How to calculate sun’s Local Hour Angle:
example 2
Observation in southern hemisphere
GHA = 123°23′,5
G = 64°42′,9 East
LHA = ? / P = ?
GHA = 123°23′,5
///////G = 64°42′,9 E
__________________ +
LHA = 188°06′,4
ロ LHA > 180°
sun in the East P = 360- LHA
P = 360° – 188°06′,4 = 171°53′,6 SE
P = SE : South latitude and sun is in the East
How to calculate sun’s Local Hour Angle:
example 3
Observation in southern hemisphere
GHA = 323°23′,5
G = 62°52′,3 East
LHA = ? / P = ?
GHA = 323°23,5
//////G = 62°52′,3 E
__________________ +
LHA = 26° 15′,8
ロ LHA < 180°
sun in the West P = LHA
P = 26° 15′,8 SW
P = SW : South latitude and sun is in the West
How to calculate sun’s Local Hour Angle:
example 4
Observation in northern hemisphere
GHA = 46° 23′,5
G = 62°52′,3 West
LHA = ? / P = ?
GHA = 46° 23′,5
//////G = 62°52′,3 W
__________________ ⎼
LHA = 343° 31′,2
ロ LHA > 180°
sun in the East P = 360- LHA
P = 360° – 343°31′,2 = 16°28′,8 NE
P = NE : North latitude and sun is in the East
