THE SPECULAR REFLECTION COEFFICIENT INFLUENCE OF THE CYLINDRICAL LIGHT SHAFT INNER SURFACE ON THE EFFICIENCY FOR DIFFERENT TYPES OF FIRMAMENTS

Abstract

Article is devoted to determination of the specular reflection coefficient influence of the cylindrical light shaft inner surface on the efficiency for different types of firmaments standardized by CIE (International Commission on Illumination). Efficiency of the light shaft was calculated as the relation of the output luminous flux (exiting through the lower base of the shaft) to the entering luminous flux (entering through the upper base of the shaft). The output luminous flux consists of the luminous flux created by direct light (gets on base of the shaft directly from the sky) and the luminous flux created by light which is repeatedly reflected from its inner side surface.

Calculation was carried out for the 173rd day of year (summer solstice: On June 22). Calculations were carried out for latitude 50^o N. For the fifteenth type of firmament (white-blue turbid sky with broad solar corona), graphs of the dependence of the total efficiency of the light shaft on the shaft index for different values ​​of the specular reflection coefficient of the inner surface of the shaft are presented. For the fifteenth types of firmament the maximum values ​​correspond to solar noon (from 67.14% to 96.9% for reflection coefficient – 0.96; from 33.72% to 95.84% for reflection coefficient – 0.8; from 17.97% to 93.43% for reflection coefficient – 0.6), and the minimum values ​​are at sunrise and sunset (from 46.28% to 96.18% for reflection coefficient – 0.96; from 14.11% to 91.23% for reflection coefficient – 0.8; from 5.59% to 87.46% for reflection coefficient – 0.6).

It can be argued that solar time has little effect on the efficiency, which allows us to generalize the results obtained in a certain way. For example, we can calculate the arithmetic mean value during the day, but ignore the value at noon, which is significantly different from other values, and the value for a certain interval at the beginning and end of the solar day, since these are insignificant time intervals compared to the entire solar day.

As the light shaft index increases, that is, as the ratio of the radius to the shaft height increases, the efficiency value asymptotically approaches one hundred percent, which is physically correct. Knowing the radius, height, index of the shaft and the specular reflection coefficient of its inner surface, it is possible to predict natural lighting under the shaft and use energy resources more rationally.