## 3 Heat Load Estimation for an Electric Bus
### Solar Heat Loads
#### 3.2.4 Solar Heat Gain Estimation for Romania  
Romania is situated in the Central to East European continent area, between 43\({}^{\circ}\)37\({}^{\prime}\) and 48\({}^{\circ}\)15\({}^{\prime}\) latitude North, and 20\({}^{\circ}\)45\({}^{\prime}\) and 29\({}^{\circ}\)41\({}^{\prime}\) longitude East, having a temperate continental weather, with about 6 months of cold weather (from October to March). January and December are the coldest months of the year, with average temperatures of about \(-\)6 \({}^{\circ}\)C at midday, with lower temperatures (down to \(-\)10 \({}^{\circ}\)C) during mornings and evenings, and with minimum temperatures of down to \(-\)24 \({}^{\circ}\)C (based on the official data from the National Meteorological Administration from Romania [26]). During this 6-month period, the solar irradiation to be considered is usually between 9.00 and 15.00 h of the day (direct radiation load decreases due to the decrease in the sun elevation angle for the simulation period, which happens after midday [24]), having clear sky for about 40% of the day [27]. The solar heat gain for a bus varies permanently because it depends on a multitude of factors: time of day, clear or covered sky, the angle of incidence of solar radiation, the variable position of the vehicle, the possibility of shading it depending on the route (especially in the urban areas, with boulevards sheltered by high buildings), varying surfaces, and the transparency of the windows, etc. Therefore, the estimation of heat gain from solar radiation can only be carried out roughly, considering several simplifying hypotheses. Existent data about the solar irradiation in Bucharest, the Romanian capital, during December and January are summarized in Table 1--global irradiation includes measurements for both direct and diffused solar radiation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Hourly Average of Sun’s** & **Hour** & **9** & **12** & **15** & **Daily Irradiation** \\  & **Brightness, around 12** & & & **Global Solar Irradiation,** & & **Average,** \\  & **O’Clock** & & & **[W/m\({}^{2}\)]** & & **[W/m\({}^{2}\)]** \\ \hline \multirow{2}{*}{December} & \multirow{2}{*}{0.36} & Clear sky & 89 & 145 & 85 & 106.3 \\  & & Overcast sky & 25 & 68 & 24 & 39.0 \\ \hline \multirow{2}{*}{January} & \multirow{2}{*}{0.39} & Clear sky & 130 & 280 & 132 & 180.7 \\  & & Overcast sky & 65 & 145 & 68 & 92.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Global irradiation includes measurements for both direct and diffused solar radiation. If \(HA_{12}\) is the \"Hourly average of Sun's brightness, around 12 o'clock\", and \(I_{gIC}\) and \(I_{gIC}\) are the global solar irradiation for the clear sky, respectively, for the overcast sky, then the maximum solar irradiation of the bus happens at noon and can be calculated with the following relation:  
\[I_{Max}=HA_{12}\cdot I_{gIC}+(1-HA_{12})\cdot I_{gIO}\ \ \ [\text{W}/\text{m}^{2}], \tag{7}\]  
With the data in Table 1, the above relation shows \(I_{Max}\) = 197.7 W/m\({}^{2}\). However, the solar irradiation of the bus during these two winter months manifests for maximum of 6 h per day and not all is transformed into the heat. Factors that reduce solar heat inputs, such as the transmissivity of windows, exterior shading, and reflective surfaces, etc., must be taken into account. The 12 m bus has a transparent window area of 29 m\({}^{2}\), and for a double pane window the transmissivity is \(\tau\) = 0.75 [18]. Keeping the same hourly average of Sun's brightness and applying Relation (7) for the daily average of solar irradiations, the average heat gain is given in Table 2 for both of the winter months considered. The presented calculation is a rough estimation of the heat gain and daily heat input. Contributions of the shading factor or reflected radiation, due to the ground, are neglected. Results showed that the most demanding month for the heating installation is December.