07.03 Sunlight calculations

Categories: Lighting

Definitions

Symbol	Variable	Definition
D	Declination	The angle of the sun's rays to the equatorial plane, positive in summer.
L	Latitude	The angle from the equator to a position on Earth's surface.
H	Hour angle	The angle the Earth needs to rotate to bring the meridian to noon. Each hour of time is equivalent to 15 deg.
g	Altitude	The angle of the sun above the horizon plane.
z	Azimuth	The compass direction of the sun. May be measured in degrees clockwise from North, or degrees East or West of South.
N	Day Number	The day number, January 1st is 1.

Formulae

sin g = cos D x cos L x cos H + sin D x sin L

cos z = ( cos D x cos H x sin L - sin D x cos L ) / cos g

sin z = ( sin H x cos D ) / cos g

tan z = sin H / ( sin L x cos H - cos L x tan D )

cos H_g=0 = - tan D x tan L

Number of daylight hours = cos^-1 ( - tan D x tan L ) x 2 /15 hours

Declination = 23.4 x sin [ 360 (284 + N ) / 365]

Using the convention, declination is positive in summer,

cos z_g=0 = - sin D / cos L

g_noon = 90^o - L + D

(see also this image)

g_midnight = L + D - 90^o

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