Approaches of international standards

3.4.1. ISO 9050 and EN 410 for glazing systems

The standards ISO 9050 (2003) and EN 410 (2011) provide almost identical information on how to calculate the optical and energetic properties of glazings. In particular, they both provide equations and boundary conditions for the calculation of light transmittance and reflectance coefficients, as well as for the total solar energy transmittance gtot. Apart from the calculation instructions, both standards include a set of tables that provides the relevant spectral distributions necessary to model the spectral power distribution of the global radiation spectrum and visible light. EN 410 additionally contains spectral distributions relevant to colour rendering, colour perception and a standard illuminant light source. ISO 9050 does not explicitly contain this information but refers to the applicable CIE standards for that purpose. Instead, the supplemental spectral distributions provided in ISO 9050 can be used to evaluate the damaging properties of light for artwork or general purposes as well as for human skin.
To determine the optical and energetic behaviour of a glazing system consisting of one or multiple layers, the shortwave radiation and heat balance of the system is modelled and solved. The shortwave radiation balance considers reflection, absorption and transmission in all relevant components. Consequently, interreflections between the individual interfaces are also considered in the model. All calculations are performed taking into account the relevant spectral distributions. For calculation of the total solar energy transmittance, the global radiation spectrum ranging from 300 nm to 2500 nm is considered, whereas, for the visual light properties, the appropriate spectral distribution between 380 nm and 780 nm is applied. The detailed consideration of the spectral distributions is essential for the accurate modelling of solar radiation.
However, concerning the angular profile of the incident solar radiation, both standards show a severe limitation as the scope of the model provided is restricted to ‘quasi-parallel, near normal radiation incidence’ (ISO 9050, 2003, p.2; EN 410, 2011, p.8). This poses a significant restriction as it reflects an idealised case that does provide benefits regarding calculation, spectral measurement or lab testing but has little relevance for the modelling of real-world applications.
Based on the proposed shortwave radiation model for normal incidence, a heat balance model is solved to determine the secondary internal heat gains caused by solar radiation. While the underlying equation systems can be solved for any number of layers, only the solutions for the cases of singleglazing, double-glazing and triple-glazing are provided in an explicit analytic form in both standards.

3.4.2. ISO 15099 approach for fenestration systems with a shading layer

The international standard ISO 15099 (2003) provides a methodology to calculate the thermal performance of fenestration systems. In order to consider the entire heat balance, the standard provides models for thermal transmission (i.e. conduction, convection and thermal radiation exchange), as well as for energy flows caused by solar irradiation. The models are based on the assumption of a layered quasi-parallel structure covering glass panes, air or gas gaps and shading layers. The thermal performance of the glazing is determined by setting up and solving the energy balance of the layered system. The standard provides many details regarding suitable calculation methods for modelling heat exchange via radiation (longwave), conduction and convection. However, regarding the solar (shortwave) irradiance components, it refers to ISO standard 9050 (2003) or applies its methods. As mentioned in the previous section, ISO 9050 and EN 410 do consider the spectral distribution of the State-of-the-art analysis RadiCal, D. Rüdisser 26 incident radiation but are restricted to the case of near-normal incidence, which poses a significant restriction for accurate calculations relevant to real-world applications.
While the ISO standard 15099 does not provide additional information regarding the shortwave model of the glazed layers, it does contain specific information regarding the modelling of shading devices. The model is, however, restricted to shading devices ‘which are or which may, by proper approximation, be treated as a layer parallel to the pane(s) of the window’ (ISO 15099, 2003, p.31).

In order to integrate such a shading layer into the fenestration system, a separation into a disturbed and undisturbed component of the incident radiation is introduced. The disturbed part represents any radiation diffusely reflected or transmitted by the surfaces of a shading device (see Figure 9). This component is assumed to be perfectly diffusing (Lambertian). According to the model, both components, the direct (undisturbed) as well as the diffuse (disturbed), propagate through the fenestration systems independently. It is, therefore, necessary to provide diffuse transmittance and reflectance values for all layers contained in the system. The standard notes this fact; however, it does not state how these values should be calculated for glass panes or coatings, as the underlying standard ISO 9050, which it refers to, is restricted to ‘quasi-parallel, almost normal radiation’ (ISO 9050, 2003).
The standard ISO 15099 does, however, provide a detailed calculation method for the necessary coefficients for the case of idealised Venetian blinds. The model assumes an infinite array of tilted, parallel, infinitely extended, perfectly flat and ideally diffuse reflecting slats. Based on these assumptions, it is possible to derive the necessary reflectance, transmittance and absorption values for the shading layer for the three components direct→direct, direct→diffuse and diffuse→diffuse. The view-factor-based calculation relies on a model defined by the input parameters slat angle 𝛾, front-and back-side slat reflectance (𝜌𝑓(), 𝜌𝑏()), slat width and slat distance. By introducing a shading layer, characterised by these reflectance, transmittance and absorption coefficients, into the energy balance of the entire fenestration system, it is possible to approximate the energetic effect of the shading layer.
Apart from the substantial simplifications necessary for the idealized Venetian blind model, several other significant issues have to be considered in the approach:

• unspecified determination of glass or film properties for diffuse radiation component
• assumption of perfectly diffused radiation caused by the shading layer
• assumption of normal incidence for the direct radiation component for the involved glass layers

Despite these issues and the potentially significant errors associated with them, the ISO 15099 approach is widely used, even in modern building performance simulation tools.

3.4.3. Standard approach ISO 52022 series for fenestration systems with a shading layer

While ISO 15099 is widely used in the US, most European countries refer to the similar ISO 52022 (2018) standard series. The first part of the three-part series contains a method to estimate total solar transmittance, direct energy transmittance and light transmittance based on a simplified approach for various configurations. This simplified approach will not be discussed here.
Similar to ISO 15099, the third part of the standard series contains a section which specifies how to implement a shading layer into the energy balance of a fenestration system. Instead of referring only to ISO 9050 for modelling the shortwave radiation exchange, the standard primarily refers to the EN 410 (2011) standard. The information contained in EN 410 is very similar to ISO 9050, and, in particular, the severe restriction to ‘quasi-parallel, near-normal radiation incidence’ is explicitly included again.
Regarding the reflective and transmissive properties of shading layers, the standard refers to EN 14500 (2018). This standard covers measurement methods for ‘curtain elements of solar protection devices’. The definition of curtain elements includes metallic or glass slats as well as fabrics. The standard is mainly intended for measuring the optical properties of the materials that form the device but can also be applied to the ‘whole product’ if the ‘equipment is sufficiently large’ (EN 14500, 2018, p.12). The testing methods distinguish between diffuse and direct reflectance and transmittance; however, for calculating the product properties, several references to methods covered by the ISO 52022 series or unspecified, ‘more accurate methods’ are included. The proposed calculation method for Venetian blinds, as detailed in ISO 52022-3, however, uses the provided information for the diffuse and direct optical properties in a very limited manner.
In analogy to ISO 15099, Annex D of ISO 52022-3 provides a geometrical calculation model to calculate the transmittance, reflectance and absorption properties of a shading layer formed by Venetian blinds. Again, the slats are assumed to be ideally flat, infinitely extended and to show no specular reflection (i.e. perfectly diffuse reflecting Lambertian surfaces).
The first significant deviation from the approach provided in ISO 15099 is that ISO 52022 restricts the calculation of shading layers to cases where no direct transmittance of solar radiation is possible. Consequently, only the direct→diffuse transmittance and reflectance are provided in section D.3 Direct radiation (ISO 52022 part 3, 2018, p.24) and the diffuse→diffuse transmittance and reflectance formulae are provided in section D.4 Diffuse radiation, whereas the direct→direct component is excluded from the calculation method. The calculation is again based on the diffuse reflectance values for the front- (𝜌) and back-side (𝜌′) of the blinds. The calculation method for the determination of the view-factors is not specified. Only view-factors for the specific case of slats adjusted perpendicular to the solar beam with a spacing ratio of slat distance to slat distance of 𝑑/𝑙 = 1.0 are provided in tabular form (ISO 52022 part 3, 2018, p.25).
Somewhat confusing, part two of the ISO 52022 standard series contains an ‘informative’ annex G (ISO 52022 part 2, 2018, p.23), that does consider direct→direct radiation and provides calculation adaption methods for pitched and vertical elements and additional view-factor tables. However, the Annex is not referred to in the standard and is denoted as ‘informative’ (instead of normative). While the model based on these additional equations extends the applicability of the method in a reasonable way, it is still based on the same model as presented in the actual standard method and, therefore, shares most of its limitations.
The calculation of view factors for any configurations, as it is implied in the standard, is a task that can be solved rather easily, best by using simple 2D raytracing algorithms. The significant issues of State-of-the-art analysis RadiCal, D. Rüdisser 28 the ISO 52022-3 method are, however, again related to the general assumption of normal incidence and the consideration of diffuse radiation. Nevertheless, there is a different approach regarding handling the diffuse component, representing the second significant difference between the two standards. Unlike ISO 15099, ISO 52022 does not suggest modelling the propagation of separate direct and diffuse components through the entire fenestration system. The additional diffuse component is solely considered for the radiation incident to the shading layer. Two individual calculation models are presented to model the effect of the diffuse and direct incidence radiation. A share of 85% direct and 15% diffuse radiation or other values ‘suitable for the local climatic conditions’ (ISO 52022 part 3, 2018, p.25)are then recommended as a ratio to calculate weighted averages of the two results. The finally generated “mixed” transmittance and reflectance values of the shading layer are then used in the radiation exchange model for direct normal incidence, as the general Scope section of the standard explicitly specifies: ‘Diffuse irradiation or radiation diffused by solar protection devices is treated as if it were direct’ (ISO 52022 part 3, 2018, p.1).