How to calculate sun’s Local Hour Angle

image of how to calculate the LHA and P

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 on spherical sphere. LHA = GHA +/- G

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:
Synopsis of how to calculate the line of position with the calculator
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)

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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Calculate LHA and P

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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 W

      __________________ ⎼

LHA = 260°31′,2

How to calculate sun's Local Hour Angle, image from GHA to LHA example 1

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 example 1

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

How to calculate sun's Local Hour Angle, image from GHA to LHA example 2

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, image of how to deduce polar angle from LHA example 2

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

How to calculate sun's Local Hour Angle, image from GHA to LHA example 3

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, image of how to deduce polar angle from LHA example 3

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

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