TOTAL DAYTIME ILLUMINATION OF PLANES INCLINED AT AN OBTUDE ANGLE TO THE HORIZON PLANE FROM DIFFERENT FIRMANENT TYPES

Abstract

The article shows graphs of the total daily illumination of planes inclined at an obtuse angle to the horizon plane from different types of firmanents given in DSTU ISO 15469:2008. “Spatial distribution of daylight brightness. Standard cloudy and cloudless sky according to CIE (ISO 15469:2004, IDT)”, created on the basis of the 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 firmanents, which are the initial information for modeling of daylight and other characteristics of the light field.

To calculate the exposure of an obtuse inclined plane to the horizon plane, the 79th day of the year (March 20), the 172nd day of the year (June 21), and the 355th day of the year (December 21) were chosen. The calculations were performed for the latitude of the city of Rivne (50.623° N).

         The orientation of the planes relative to the cardinal points was set in increments of 10 degrees. The angle of inclination of the planes for each location relative to the cardinal points was set in the range from 90⁰ to 170⁰ also in increments of 10 degrees. For each plane, the duration of the solar day from sunrise to sunset for each of the selected days of the year was divided into 30 equal intervals and, accordingly, 31 moments of solar time, on the boundaries of which the illumination was calculated for all 15 mathematical models of the firmament. Thus, discretely presented curves of the dependence of the illumination of a plane inclined at an obtuse angle to the horizon plane on solar time were obtained. Then, the discrete values ​​of illumination were interpolated by cubic splines for the purpose of integration over solar time, which allowed obtaining the total illumination (exposure) for the day.

The article demonstrates results for only three characteristic types of firmanents: the 5th, 8th, and 15th.

Information on illumination of planes inclined at an obtude angle for a given type of firmanent, typical for a certain area, allows you to evaluate daylight resources, determine critical external illumination and rationally use artificial lighting, saving on it. 

Keywords: exposition, critical external illuminance, daylight, lightening, solar time, type of firmanent.