# Passive Solar Solutions for Buildings: Criteria and Guidelines for a Synergistic Design
## 2 Passive Solar Systems
### Standard Modelling  
As clearly evidenced in the models of Figure 1, the sizing of a distinct passive solar system with a defined objective appears to be a quite difficult task due to the synergistic effects of different parameters that act together in defining the effectiveness of a passive solar system. Therefore, energy performance can only be determined by considering this synergy. As Table 2 shows, parameters can be classified into extrinsic factors, external to the passive system, such as latitude or building shape, and intrinsic, such as collector inclination and orientation. These factors have a different impact on final performance: they act directly on the incident solar radiation or influence the operativity of the passive system and its integrability in building design. All these parameters contribute to the performance of passive solar systems at different stages of a project: while building orientation, shape, and position should be adapted to maximize the potential performance of passive solar systems, building use and latitude are usually given parameters, so they must be considered for a preliminary screening to limit the choice to the most suitable strategies. Then, another set of parameters allows to identify the most appropriate system for a specific building. The selection process is strictly country-dependent, as microclimatic conditions, architectural details, and related costs widely differ from place to place. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Kind** & **Affected Element** &
\begin{tabular}{c} **Influence on** \\ **Design Process** \\ \end{tabular} \\ \hline Orientation & Intrinsic & Solar radiation & Design adaptation to \\ Building shape & Extrinsic & Integrability & maximize \\ Building positioning & Extrinsic & Solar radiation & performance \\ \hline Latitude & Extrinsic & Solar radiation & Primary selection \\ Building use & Extrinsic & Operativity & parameters \\ Surface area to volume ratio & Extrinsic & Integrability & \\ \hline N\({}^{\circ}\) of services involved & Intrinsic & Operativity & \\ Overheating sensitivity & Intrinsic & Operativity & \\ Adaptability & Intrinsic & Integrability & Secondary selection \\ Range of the effect & Intrinsic & Operativity & parameters \\ Cost of construction and maintenance & Intrinsic & Integrability & \\ \hline Cost/performance ratio per & Intrinsic & Integrability & Sizing parameters \\ unit area & & Integrability & Sizing parameters \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Influence of design parameters. The performance of each solar system is related to incident solar irradiance G (W/m\({}^{2}\)), that depends on the different position of the site, latitude and longitude, on the different seasons, on the hour of the day, and on the position of the surface exposed to solar radiation. Solar irradiance can be evaluated with the following law [27]:  
\[G_{T}=G_{on}\times\tau\times\cos\theta \tag{1}\]  
with  
\[G_{on}=\ G_{sc}\bigg{(}1+0.033\ \cos\bigg{(}\frac{360n}{365}\bigg{)}\bigg{)} \tag{2}\]  
\[cosT=\ sin\delta sin\delta cos\beta-sin\delta cos\delta sin\beta cos\gamma+cos \delta cos\delta cos\delta cos\delta cos\omega+ \tag{3}\]  
\[+cos\delta sin\delta sin\delta cos\gamma cos\omega+cos\delta sin\beta sin\gamma sin\omega\]  
\[\tau=e^{-b\lambda^{-a}mu} \tag{4}\]  
where \(G_{T}\) is global irradiance on a tilted surface, \(G_{sc}\) is the solar constant, \(\theta\) is angle between surface normal and incident radiation (Figure 4a) and \(\tau\) represents atmospheric attenuation of solar radiation. Figure 4b reports the maximum daily solar irradiance per month at different latitudes. As Equation (3) states, latitude and surface inclination are the most impactful parameters to determine solar irradiance on a surface. Latitude affects the number of hours of sunlight on the surface.