# Daylight coefficients and subdivision of the sky--Algorithm 1.35

Daylight coefficients embody the geometric relationships that determine daylight illuminance. Each coefficient is the ratio between the luminance of a patch of sky, and the illuminance in the building due to the light from that patch. The sky can be divided into zones of altitude and azimuth, and the daylight coefficient found for each zone. The total daylight illuminance at a point is then the sum of the products of the mean luminance of each sky zone, the subtended area of the zone, and the corresponding daylight coefficient:

a. Sky zones

In general the optimum diameter of a sky zone is about 0.2 radians (11.5 degrees); this enables each zone to be treated, with insignificant error, as a point source. For measurement of sky luminance it is recommended that the scanning pattern is based on 145 zones in 12 degree bands of altitude, centred in azimuth on the solar azimuth. (1) . For daylight coefficient calculations a fixed orientation is required; the grid given below follows the CIE subdivision but is centred on north. The ground is labelled zone 0 but alternatively the different directions of downward view may be allocated zones in a mirror image of the sky, labelled -1 to -145. The solid angle subtended by a sky zone is as follows:

 Altitude of band centre (degrees) Number of zones in band Azimuth increment (degrees) Solid angle subtended by zone (steradians) 6 30 12 0.0435 18 30 12 0.0416 30 24 15 0.0474 42 24 15 0.0407 54 18 20 0.0429 66 12 30 0.0445 78 6 60 0.0455 90 1 360 0.0344

The following procedure gives the zone number from altitude g and azimuth a of a sky point.

 data 8 number of bands in altitude data 30,30,24,24,18,12,6,1 number of subdivisions in each band if g > ¼/2 or a < 0 or a „ 2¼ then (goto error routine) if g < 0 then zone=0 ground else read bands increment g = ¼/(2(bands-0.5)) wg = increment g j = 0 while g > wg select altitude band read subdivisions j = j + subdivisions wg=wg+increment g end while read subdivisions increment a = 2¼/subdivisions wa = incrementa/2 k = 1 while a > wa select azimuth subdivision k = k + 1 wa = wa + increment a end while if k > subdivisions then k = 1 zone = j + k zone number end if

b. The sun

In calculations of global illuminance there are alternative methods of assessing the solar beam:

1. A complete sky zone may be taken as the source of solar illumination. The resulting imprecision is a blurring of shadow edges (due to a change in source diameter from about 0.5 degrees to about 12 degrees) and an error of up to 7 degrees in the position of the source centre. Such a degree of accuracy may be satisfactory in general illuminance calculations.

The sky zone containing the sun is allocated an additional luminance equal to the normal solar illuminance divided by the size (solid angle) of the zone.

2. Solar illuminance (on the appropriate plane) is determined independently, using the methods given in algorithms 1.14, 1.23 & 1.24b, and the result added to calculated values of sky illuminance.

References
1. Commission Internationale de l'Eclairage Guide to recommended practice of daylight measurement. Editor J D Kendrick. (Vienna: to be published by Commission Internationale de l'Eclairage) (1989)

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