How to calculate sun’s Local Hour Angle

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.

How to calculate sun's Local Hour Angle, image spherical position triangle
spherical position triangle

The understanding of this position triangle and the formulas generated from it is complex and not necessary for our main goal, which is to calculate the sun’s line of position.

Furthermore, the formulas are integrated into our calculation grid.

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.

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.

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Introduction:
How to calculate sun's local hour angle, image  part of the worksheet( from GHA to LHA and to Polar angle)
Please refer to the page: GHA + pp = GHA (for the exact hour of the observation)

G is estimated longitude:

add if East

subtract if West

After finding LHA, how to deduce P ?

ロ     LHA <   180°        

sun in the West       P = LHA

ロ     LHA >   180°        

sun in the East          P = 360- LHA 

 

P = _ _ ° _ _ ‘, _ NE/SE/NW/SW

sexagesimal system

360°formulas


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let's start with sextant-sun-sight-observations and exercises

Calculate LHA and P

4 examples

How to calculate sun’s Local Hour Angle: 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

      __________________ –

LHA = 260°31′,2

How to calculate sun's Local Hour Angle, image from GHA to LHA

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, image of how to deduce polar angle from LHA

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

__________________ +

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

      __________________ +

 LHA = 26° 15′,8

ロ     LHA <   180°  

sun in the West       P = LHA

P = 26° 15′,8 SW

P = SE : 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

      __________________ –

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