Luminance of external obstructions--Algorithm 1.42

The luminance of a distant object depends on the viewing distance and on the effects of atmospheric scattering. For the majority of daylight calculations, external obstructions may be assumed to be diffuse reflectors and sufficiently close for atmospheric effects to be negligible.

a. Nearby luminance of diffusely-reflecting surfaces, Lg

Input
Illuminance on the surface, Evk, lx
Reflectance, rk

Equation

Source
General photometric theory
Note
Reflectance values for some common building materials may be found in BS 8206(1)

b. Luminance of distant diffuse surface under CIE Overcast sky, Lx

The following expression gives the luminance of a distant surface as a proportion of the luminance of the overcast sky at the horizon.

Input
Luminance of horizon sky, Ls cd/m2
Tilt of surface from the horizontal (or zenith angle from surface normal), q radians
Reflectance of surface, r
Reflectance of ground, rg
Distance, x km
Mean atmospheric attenuation coefficient, s km-1
(For normal calculations under an overcast sky it is recommended that the value of s be taken as 0.3)

Equation

Note
In the expression for kq the part within brackets, {}, gives the ratio between the luminance of an inclined surface and a horizontal surface of the same reflectance. It is based on algorithms 1.33b and 1.41b

Source
Tregenza(2)

References
  1. British Standards Institution BS 8206: Part 2: 1992 Code of practice for daylighting (London: BSI) (1992)
  2. Tregenza P R Luminance of distant objects under overcast skies Lighting Research and Technology 24 (3) 155-159 (1992)


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