Overcast sky luminance and illuminance Lvoc, Evoc--Algorithm 1.33

a. Luminance distribution

Input

Altitude of sky point, g radians

Equation

The luminance at altitude g, Lvoc(g), is, as a fraction of the zenith luminance, Lvocz ,

Source

CIE(1)

b. Relative illuminance

Input

Tilt of surface from the horizontal (or zenith angle of surface normal), q radians

Equation

Note

If the sky luminance is given in cd/m2, the units of illuminance are lux.

Illuminance from ground-reflected light is given in algorithm 1.41

Source

Wilkinson(2)

c. Absolute illuminance

The actual illuminance under an overcast sky can vary greatly. The following empirical equation gives an indication of the average horizontal illuminance, but it should be noted that there is a very large scatter of measured values at every solar altitude.

Input

Solar altitude, gs radians

Equation

Source

Krochmann(3)

1. Commission Internationale de lÕEclairage 3.2 Natural daylight: official recommendations 13th Session (1955 ) Commission Internationale de lÕEclairage, Paris
2. Wilkinson M A Natural lighting under translucent domes Lighting Research and Technology 24 (3) 117-126 (1992)
3. Krochmann J and Seidl M Quantitative data on daylight for illuminating engineering Lighting Research and Technology 6 (3) 165-171 (1974)