ABSTRACT
Clear Skies The equation for a clear sky as standardized by
the CIE (1), takes into account mean real conditions and fundamental solar light diffusion and refraction effects in a perfectly clear and cloudless atmosphere. The distribution of the luminance is expressed in terms of three angles (Figure 1): • al: angular distance between the point P of the
sky and the sun • angular distance between the sun and the
zenith - zenithal distance from the sun • 71/2 - 0: zenithal distance of the point P
Lp(m/2 - 0,a) / Lz = f(rl) . 4)(n12 - 0) / f() .4)(0)
Lp =11 Lpe (I -11) Lpo
where: Lpe is the luminance of the clear sky Lp0 is the luminance of the overcast sky 11 = [i + cos (CR .70]/2
A similar formula is proposed by Winkelman and Selkowitz (4) for calculations of natural lighting in the DOE 2 software. • Nakamura and Old (5): A mathematical formula (that can only be used with y < 80°) of the intermediate average sky is proposed from measurements made over a long period:
Lp / Lz = L(y, 7c/2 - 0) / L(y, 0/2, where: f(x) = 0.91 + 10 exp(-3x) + diffusion) 4)(x) = 1 - exp(-0.32 / cos(x)) tl = arccos [cos(4).cos(n/2 - 0).cos(a) a is the azimuth angle
0.45 cos(x) (standard
0) + sin().sin(Tc/2 -
• Pierpoint (6): An expression identical to that of the CIE clear sky, but with different f and 4) functions :
f (x) = 0.526 + 5 exp(-1.5x) (x) = 1 - exp[-0.80 / cos(x)]
Figure 1 - Definition of sky dome angles.
