DEFINITION ANALYSIS OF THE RATIO OF THE LUMINANCE IN AN ARBITRARY SKY ELEMENTS TO THE ZENITH LUMINANCE GIVEN IN DSTU ISO 15469:2008

Abstract

The article analyzes the definition of the ratio of the luminance in an arbitrary sky elements to the zenith luminance given in DSTU ISO 15469:2008. "The distribution of daylight luminance is spatial. Standard cloudy and cloudless sky according to CIE (ISO 15469:2004, IDT)". This standard was created on the basis of a foreign analogue CIE S 011/E:2003 (ISO 15469:2004(E). «Spatial distribution of daylight – CIE standard general sky». The standards consider 15 mathematical models of types of skies, which are the source information for modeling natural illumination and other characteristics of the light field.. Since these documents are still relatively new, they require additional analysis.

In the article it was shown that in the case of the location of the element of the sky at the zenith, the formula for determining the ratio of the luminance of an arbitrary element of the sky to the luminance at the zenith is significantly simplified.

The authors set themselves specific initial data and substituted them in the considered formulas. The obtained results were illustrated in the form of sky luminance surfaces in spherical coordinates.

The latitude was equal to 50.6230 (the latitude of the city of Rivne), the solar time was equal to noon, the day of the year was set to the 81st (March 22). These raw data were used for all 15 mathematical models of sky types. The results were shown for three characteristic types of skies: the first, fourth and fifteenth.

The results showed that the luminance surface for the first type of sky is a rotation surface and the value equal to the value at the zenith does not oscillate. For the other two surfaces, this point oscillates on the contrary. The luminance surfaces for the third and fifth types of sky were also surfaces of rotations without oscillations. Therefore, for the remaining twelve types of skies, it was suggested to approximate this point.

The conducted analysis will allow correct calculation of luminance for all mathematical models of sky types. This will help solve various problems related to lighting technology. For example, when modeling the amount of day lighting for light openings of various configurations.

Keywords: angular height, luminance, luminance gradation, oscillation, scattering indicatrix, Sun, zenith.