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Principles of daylighting calculations. Stanislav Darula Institute of Construction and Architecture SAS Bratislava, Slovakia. Daylighting in exterior. Daylighting (sunlight and skylight). Pv – parallel beam illuminance Dv – diffuse illuminance Gv – global illuminance Gv = Dv + Pv.
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Principles of daylighting calculations Stanislav Darula Institute of Construction and Architecture SAS Bratislava, Slovakia
Daylighting in exterior Daylighting (sunlight and skylight) Pv – parallelbeam illuminance Dv – diffuse illuminance Gv – global illuminance Gv = Dv + Pv Luminous solar constant 133.8 klx Top of the atmosphere Sky radiation Pv, Dv, Gv Ground level Brno 24.07.07_3
Luminance distribution under real skies Nikon Coolpix 990 Nikon Fisheye Converter FC-E8 Program LumDISP Brno 3.12.07_11
Interior illuminance Daylight Factor, DF e = eo + ei + ee eo - sky komponent ei - interreflextion component ee - exterior reflextion component 3 CIE overcast sky ( Moon-Spencer, 1942) Lz E L g eo Interior daylighting ei Ei e 1 ee
1.2 2.8 1.6 21.1° 0.9 0.85 Section Plan 2 wR 2 lR Example of Daylight Factor caclulation Daylight Factor izolines Obstruction Room 5 m x 5 m
Exterior sky illuminance Lv- luminance of the sky element in cd.m2
Example Luminancecalculation of sky element L Inputs: For Sky IV.4 is (a, b, c, d, e parametes, taken from ISO 15469:2004) Position of Sun: s = 38.02, As= 147.67 Pozítion of sky element: = 10, A = 130 Calculation procedure: Sun zenith angle: Zs = 90 - s =90 - 38.02 = 51.98 = 0.907 rad Azimuth of sky element measured from sun meridian Az = s - = 147.67 -130= 17.67 Angular distance between position of Sun and sky element cos = cos Zs cos Z + sin Zs sin Z cos Az cos = cos 51.98 cos 80 + sin 51.98 sin 80 cos 17.67 = 0.8462 = 32.20 = 0.562 rad
Input data in radians Example Calculation of luminance of sky element L Calculation of gradation and indicatrix functions: Gradation function for the sky element: (Z) = 1 + a exp (b/cos Z) (Z) = 1 - 1 exp(-0.55 / cos 80) = 0.9579 Gradation function for zenith: (0) = 1 + a exp (b/cos 0) (0) = 1 + a exp b = 1 - 1 exp(-0.55) = 0.4231 Indikatrix function for the sky element : f () = 1 + c[exp(d) - exp(d/2)] + e cos2 f () = 1 + 10[exp(-3 * 0.562) - exp(-3 /2)] + 0.45*0.84622 = 3.0847 Indikatrix function for zenith: f (Zs) = 1 + c[exp(dZs) - exp(d/2)] + e cos2Zs f (Zs) = 1 + 10 [exp(-3*0.907) - exp(-3 /2)]+ 0.45 cos2 51.98 = 1.7385
Example Calculation of luminance of sky element L Relative luminance predetermination L / Lz = (Z) f () / (((0) f (Zs)) L / Lz = 0.9579* 3.0847/(0.4231* 1.7385) = 4.0175 Relative sky luminace distribution for IV.4 standard when solar altitudes = 38,02 ifthe measuredLvz = 4404 cd/m2 then absolute luminance is L=Lvz (L / Lz)=4404* 4.0175=17693 cd/m2 DARULA, S. - KITTLER, R. CIE General Sky standard defining luminance distributions. The bi-annual conference of IBPSA Canada eSim 2002. http://www.esim.ca/2002/documents/Proceedings/other2.pdf
P P Overast sky conditions
P P Clear sky conditions
Conclusions • For precise calculation we need a computer and information: • plan and section drawings of the building design • be careful to check the inputs: • - - room and window dimensions, glass transmittance • - - interior reflectances • - - exterior obstructions and their reflectances • apply an appropriate algorithms • - - check the results Today the laptop will do ...
What was the vision of scientists in 1954 how will look like a „home computer“ after 50 years later, i.e. in 2004?