Design schemes’ universalization in calculation of daylight factor under side and roof lighting system in buildings

The article describes the methods of contemporary daylight factor’ (D.F.) design either with top or side natural lighting systems in buildings. The different methods of design, with different design formulas are based on preliminary determination of the type of lighting system used. But this division is rather conditional and not accurate. Sometimes the source of natural light (say, a window in a wall), which traditionally is judged as a source of a side light, is placed higher, than a monitor or skylight on a roof, which usually are determined as a sources of a top light. The same situation can be seen in determination of an angle of observation of a sky vault portion, observed from a design point within the premise considered. Thus, taking into account the above mentioned statements, one can assume, that with no strict division of external natural illumination under the overcast sky conditions, adopted as a basic theory in contemporary domestic «Codes and Regulations on Natural Lighting of Interiors», it is necessary to offer an universal design formula. This one should be based on standard formulas with respect to specific points, typical either to elements of window, monitor or skylight structures.


Introduction
The daylight factor (D.F.) values under any system of outdoor natural illumination (side or top ones) are being calculated in accordance with main laws of lighting research and technology theory and with use of modern domestic and foreign «Codes and Regulations» on Natural lighting of interiors. The basic law used is the «Moon and spencer law», which determines the luminance' condition of a sky vault as cloudy. The sky is in this case called an «overcast» and natural outdoor illuminator is evaluated as «diffuse». Such a conditions and requirements are adopted in majority of the leading countries, as a result of «Internal Commission on Illumination» (C.I.E.). recommendations. [1][2][3][4][5][6][13][14][15][16][17][18][19][20].
In this case, the determination of the type of lighting system simultaneously leads, to the design' method needed. This problem in latest years is being discussed on the «Design of Buildings and Structures» Chair of Moscow State University of Civil Engineering [7][8][9][10][11][12].

Theoretical background
Under constant size of a lighting opening (a window, a monitor or a skylight), the D.F. values changes in relation with the height of an opening' central point over a working plane' level.
The angle of the observation a sky vault «» from a design point changes and leads to change of a «q» factor, which takes into consideration the non-uniform brightness of a sky vault. Moreover, the changes in «» value leads to the change in value of «Geometric daylight factor»' values (G.D.F.) «», due to non-uniform brightness of the standard overcast sky. All this proves the Moon-Spencer law' approving about the higher efficiency of upper parts of the sky vault in question, as compared with its low parts, but should not affect the physical sense of the design formulas 1 and 2. For side-lit premises the design formula looks like [1,2,3,4]: Where:  D. F. D s − designed daylight factor for side system of natural illumination of premises;   S − geometric daylight factor, which takes into account the direct light from an overcast sky vault;  q − a factor, which takes into account the non-uniform brightness of an overcast sky;  K B − a factor, which takes into account a geometry of opposite-standing buildings;   B − geometric daylight factor, which takes into account the reflected light from opposite-standing buildings;  b F − a factor, which takes into account the facade' brightness of the opposite-standing buildings'.  K S − the spare factor;   T − a total factor of light transmission through an element of side lighting system;  r T − a total factor of light reflection from a premise' surfaces. for top-lit premises the design formula looks like: Where:  D. F. D s − designed daylight factor for top system of natural illumination of interiors;   T − geometric daylight factor, which takes into account the direct light from an overcast sky vault for top system of illumination;  q and K S − see note to formula (1);   AV − an average geometric daylight factor;  r 2 − a factor of light reflection from a premise' surfaces;  K M,S − a factor, which takes into account a structural type of a roof' lighting element (monitor, skylight or shed);   T − a total factor of light transmission through an elements of roof lighting system.

Desk studies
The above mentioned points are illustrated with Figures 1 and 2 and data in Table 1. According to these, it is possible to state, that one has no strict border between side and roof natural lighting of interiors. The only serious difference is that Formula 1 takes into account the lighting effect of nearby surrounding buildings, which in its pure form' is absent in Formula 2, but the physical sense of this effect is somehow replaced with account of «K M,S » factor. For the time being, the authors of this article are trying to bridge such a gup and to elaborate the universal formula to calculate a D.F. values with respect to any system of natural lighting of interiors adopted [7,8,9,10,11,12].  Key: M, C. L. , WPL, φ 1 , φ 2 , φ 3 -see figure 1; t, K S , r -see formulas 1 and 2; B -the depth of a premise; h -the height of a window' top over the working plane' level; L Z , L H , L φ -the luminance of the sky vault in zenith, horizon and angles of sky vault' observation φ respectively.
Note Under system of side natural lighting the quotients «q» and «» (see Formulas 1 and 2) have the minimum values; with system of side-top lighting they have the medium values and with system of top lighting they have the maximum values. This conclusion is evident in accordance to «Moon and Spencer» Law. Table 1. The analysis of specific design factors (quotients) universality (according formulas 1 and 2).

Design factors
The degree of design factors' universality Specific factor «q» Possesses an absolute universality. Used in a daylight factor' design under systems of side and top natural lighting of interiors Specific factor « G » Specific factor «K S » Specific factor «r G and r 2 » These factor are analogues in physical sense, but used in daylight factor' calculations either under side or top systems of natural lighting of interiors Specific factor «K M,S » These factors is used only for daylight factor' calculations with top system of lighting. It is partially similar to quotient «r 2 » and therefor may be associated with quotient «r G », used for side lighting design. The role of the ground' reflection in «r G » is replaced with the roofing' reflection in «r 2 » Specific factor «b F and K B » These factors is use, according to the contemporary «Codes and Regulations» only for design of a daylight factor with side lighting system of premises. However, the proves universality of lighting environment makes it possible to use them with system of top lighting in the case of implementation of skylights or monitors in deepened buildings, surrounded with high-rise buildings Authors of the studies in question offered the new design hypothesis, which said, that under the universal spread of light in outdoor environment, the spread of light flows in interiors of buildings must be an universal, too. Such a spread does not depend on lighting system adopted in a building, since the physical character of it remains the same and is only taken into account by the number of design factors, which characterize the specific features of a premise (present of monitors, skylights, windows or oppositestandings. Buildings, etc.). 2. It was shown, that the most important specific factor, which highly influenced the D.F. ' values in a premise, was the «q» factor, which depended on angle of observation of a standard overcast sky from a design point. In this case the terms «side» or «roof» lighting systems had no sense, as far the lighting system in a building became universal. Hence, the offering of a new universal formula for all the cases of lighting system became essential and this must affected the main concepts of «Codes and Regulation» on Natural Lighting.