Daylight Methods and Tools to Design Glazed Windows and Skylights

Abstract

The general trend in recent building has been to use glass much more than in the past because of its lower price and modern technology enabling larger windows in durable frames. Historically, these technology advancements of the Industrial Revolution were demonstrated by the cast iron and glass building of the Crystal Palace in London housing the 1851 Great Exhibition. This represented the starting era of glass architecture including the novel modular design, panel prefabricated construction and also documenting problems of sunshine overheating and of thermal insulation and water vapor condensation as well as questions of visual privacy.

Appendix 9

9.1.1 Comparison of Calculation Tables and Tools for the Sky Components from Vertical or Sloped Glazed Windows

With the mass production of relatively cheap glass during the Industrial Revolution in the second half of the nineteenth century, larger glazed windows became the main features of house fronts as well as in long-span buildings (e.g., exhibition halls and railway stations). The small light losses of roughly 10% of the light flux falling perpendicularly on the glazed surface were an advertisement slogan. Even in renowned books on building materials (e.g., Handisyde 1950, p. 284) the daylight transmission of glass was introduced by two sentences: “Ordinary polished plate or drawn sheet glass, when clean, transmits about 90% of daylight which falls upon it. In passing through the glass the light is slightly refracted, but this factor can usually be ignored.” However, as shown in Fig. A9.1, only a few glazed window elements are penetrated by sky luminance normally, so the reduction of transmittance caused by arbitrary rays of nonnormal direction has to be considered.

The directional angle $\psi$ is defined as the angle between the arbitrary directional ray and the normal to the glass plane. Thus, the maximum transmittance ${\tau_{\rm{n}}}$ of the glazing is when $\psi = 0^\circ$, i.e., for the shortest pass of the ray through the least glass thickness. So, the most effective element of any vertical, sloped, or horizontal aperture is that which is facing the illuminated place with the largest solid angle as well as the normal transmittance (Fig. A9.1). Furthermore, such normal glass elements (in red) are even more effective when momentarily facing the sun position or very high sky luminance patches owing to window orientation and time on a particular day. Every extended oblong aperture due to the pair of parallel frames has a solid angle gradually decreasing toward the lune vanishing points. Thus, together with the solid angle, also the directional transmittance ${\tau_{{\rm{\psi }}}}$ toward the possible four vanishing points is decreased, so finally ${\tau_{{\rm{\psi }}}} = 0$ as $\psi = 90^\circ$, as indicated in Fig. A9.1.

Although the directional or oblique transmittance of glazing was differently taken into account, several tables were published for the sky factor or sky component either for vertical rectangular windows or for sloped apertures illuminating the element of the horizontal illuminated plane. For the different tables or diagrams two different ratios of window dimensions were used for the simplest position of the window with its lowest corner at its zero point of the coordinate system, i.e.:

• The window width is only one side to the normal taken as the width coordinate $W$, or $L$, or the coordinate axis direction $y$.

• The height of the window head above the horizontal plane of the illuminated element as $H$ or the direction of the vertical axis $z$, or even arbitrarily as $a$.

• The distance of the illuminated element is $D$, or it can be taken as the prolongation of the axis $x$.

Various authors used different ratios in their formulae or tables, e.g.:

• In the comprehensive series of daylight tables published by Rivero (1958), ratios $H/D = z/x$ and $L/D = y/x$ are preferred.

• In Building Research Station simplified daylight tables by Hopkinson et al. (1958, 1966) the ratios $H/D = z/x$ and $W/D = L/D = y/x$ determine the window dimensions.

  Fig. A9.1

  

  Differently tilted apertures have also the glazing with different normal and directional transmission

• Kittler and Ondrejička (1964, 1966) used both $L = a/x = z/x$ and $N = y/x$ as well as the width parameter ${\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}} {S}} = y/a = y/z$ and the point distance parameter $D = x/a = x/z$ (Kittler and Kittlerova 1968, 1975).

• Puškaš (1979) denoted vertical window ratios as $d = L = a/x$ and $s = N = y/x$.

There are also several possibilities for how to derive the dependence of the sky component on the above parametric ratios. The renowned sky component tables published by the Building Research Station (Hopkinson et al. 1958) and reproduced also in the seminal book by Hopkinson et al. (1966) as Table 5.1 was deduced from summated values of the sky component for a uniform sky, then corrected for the CIE overcast sky (1:3) and glazing losses obtained from a large-scale Waldram (1929) diagram. To demonstrate the differences in the sky component values, the same ratios $H/D = z/x = L$ and $W/D = L/D = y/x = N$ were applied by Kittler and Ondrejička (1964, 1966).

To determine sky component results in the case of vertical windows, one can use either tables or the graphical tools mentioned in the appendix in Chap. 8, but in the twenty-first century more sophisticated computer programs are favored. These can simulate besides overcast sky conditions also the whole range of ISO/CIE sky types and instead of relative sky component values can respect the local sun paths and sky luminance patterns at any time in absolute luminance or illuminance values either outdoors and indoors (Darula and Kittler 2005). Such a program is based on the possibility to calculate absolute sky luminance along the window meridian using the Method for Aperture Meridians (MAM) (Kittler and Darula 2006) by applying the sophisticated software modeling of the hour and date sun position in an arbitrary geographical location, then simulating any of the 15 ISO/CIE sky patterns with absolute luminance and illuminance levels and with their representation within the window solid angle as well as interior sky illuminance in lux on the chosen element of the horizontal working plane (Roy et al. 2007). Such a user-friendly program called MAMmodeller is freely available in an online form at http://www.cadplan.com.au.