## 2 Materials and Methods
### Simplified Methodology for the Calculation of the Solar Heat Gain Factor  
When considering glazing systems, one of the most important parameters for building energy performance calculation is the g-value, the total solar transmittance of the glazing which is also called solar heat gain coefficient (SHGC). Measurements of g-value need complex and expensive experimental set-ups; therefore, only a few estimated data are available in the literature and they refer to samples with a granular aerogel [22]. In this study, the solar factor was estimated following the procedure suggested by the EN 410 and ISO 9050 standards [23; 24], in which it is calculated as the sum of direct solar transmittance \(\tau_{\text{e}}\) (calculated from spectral transmittance measured data) and the secondary heat transfer factor (q\({}_{\text{i}}\)). It takes into account the heat transfer due to the radiation absorbed by the glazing and re-emitted at infrared long waves to the inside. The standards apply for multiple glazing units, in which each pane is bordered by a gas layers, thus, it is not directly applicable to this case. It is, therefore, necessary to add a hypothetical thin layer of air between each glass and the aerogel pane. The glazing unit is modelled as a three-layer system consisting of an external layer of glass (the same as the original), a hypothetical thin air layer, aerogel layer, hypothetical thin air layer and an internal layer of glass. This theoretical sample is considered to have: (i) the same thermal resistance as the real sample; (ii) the same optical properties as a real glazing unit [17]. According to this procedure, the optical properties of the aerogel layer were calculated starting from the relevant formulae for transmittance and reflectance of triple glazing unit found in [23; 24]:  
\[\tau(\lambda)=\frac{\tau_{1}(\lambda)\tau_{2}\text{ (}\lambda)\tau_{3}(\lambda)}{ \left[1-\rho_{1}^{\prime}(\lambda)\rho_{2}(\lambda)\right]\left[1-\rho_{2}^{ \prime}(\lambda)\rho_{3}(\lambda)\right]-\tau_{2}^{2}(\lambda)\rho_{1}^{ \prime}(\lambda)\rho_{3}(\lambda)} \tag{5}\]  
\[\rho(\lambda)=\rho_{1}(\lambda)+\frac{\tau_{1}^{2}(\lambda)\rho_{2}(\lambda) \left[1-\rho_{2}^{\prime}(\lambda)\rho_{3}(\lambda)\right]+\tau_{1}^{2}( \lambda)\tau_{2}^{2}(\lambda)\rho_{3}(\lambda)}{\left[1-\rho_{1}^{\prime}( \lambda)\rho_{2}^{\prime}(\lambda)\right]\left[1-\rho_{2}^{\prime}(\lambda) \rho_{3}(\lambda)\right]-\tau_{2}^{2}(\lambda)\rho_{1}^{\prime}(\lambda)\rho_ {3}(\lambda)} \tag{6}\]  
where:  
\(\bullet\)\(\tau\) (\(\lambda\)) = spectral transmittance of the whole sample;  
\(\bullet\)\(\rho\) (\(\lambda\)) = spectral reflectance of the whole sample measured in the direction of incident radiation;  
\(\bullet\)\(\tau_{1}\) (\(\lambda\)) = spectral transmittance of the outer (first) pane within the triple layer model (glass layer);  
\(\bullet\)\(\tau_{2}\) (\(\lambda\)) = spectral transmittance of the second pane within the triple layer model (aerogel layer);\(\tau_{3}\) (\(\lambda\)) = spectral transmittance of the inner pane within the triple layer model (glass layer), equal to \(\tau_{1}\) (\(\lambda\));
* \(\rho_{1}\) (\(\lambda\)) = spectral reflectance of the outer (first) pane within the triple layer model (glass layer) measured in the direction of incident radiation;
* \(\rho^{{}^{\prime}}_{1}\) (\(\lambda\)) = spectral reflectance of the outer (first) pane within the triple layer model (glass layer) measured in the opposite direction of incident radiation (\(\rho_{1}\) (\(\lambda\)) = \(\rho^{{}^{\prime}}_{1}\)(\(\lambda\)));
* \(\rho_{2}\) (\(\lambda\)) = spectral reflectance of the second pane within the triple layer model (aerogel layer) measured in the direction of incident radiation;
* \(\rho^{{}^{\prime}}_{2}\) (\(\lambda\)) = spectral reflectance of the second pane within the triple layer model (aerogel layer) measured in the opposite direction of incident radiation.