Daylight coefficient: direct component dsk -- Algorithm 3.23

These algorithms give the relationship between the luminance of a small finite zone of sky and the illuminance at a point in room, excluding all reflections.

a. General relationship

Input

Angle between surface normal and direction of ray from centre of sky zone, q radians
Overall transmittance of glazing and other obstructions lying on ray, t

Equation

Note

The relationship between internal illuminance, sky luminance, sky zone area and daylighting coefficient is given in algorithm 1.35.

Source

General theory of analytic geometry.

b. Coefficients from small triangular window patch

This algorithm gives the direct components of the daylight coefficients which correspond to the vertices of a window triangle. Each of these is associated with a solid angle equal to one-third of the equivalent spherical triangle area.

Input

Angles between surface normal of receiving plane and directions of vertices qa, qb, qc radians (algorithm 5.13)
Area of spherical triangle, S steradians (algorithm 5.17)
Transmittance of window at incident angle, f tf

Equation

The product of the direct components and the corresponding subtended areas of sky are as follows. There are 3 values, corresponding with the corners of the window triangle:

If two or more sightlines from the receiving point pass through the vertices of the window patch to the same sky zone, the corresponding coefficients are added to give the total coefficient between the point and that sky zone.

Source

General theory of analytic geometry.

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