# Orientation and Exposure Efficiency of a Solar Tracking Surface in Clear Sky
## 4 Discussion
Since that moment and until the set (rise) of the Sun, a polar-rotating tracker is switched to passive tracking, with irradiation changes similar to the stationary, focused on the east (west) of the vertical surface, according to Equation (7) at:  
Figure 12:3  
Figure 12:4  
Figure 12:5 Scheme for measuring of the parameters of irradiation of the tracking surface of a polar-rotating tracker—designed based on [21; 23; 35; 36]. Duration of the passive regime on the day of a summer solstice can be measured by the evident equation:  
Figure 12:6  
where 6 is hours, constituting 2.075 h for the latitude 50\({}^{\circ}\). Hour values of the orientation and exposure efficiency are presented in Table 7 in the columns for the angle of initial (at full sun) inclination:  
Figure 12:7  
A polar-rotating tracker also secures performance of seasonal optimization of the tracking surface efficiency by its deflection from the axis of rotation at the value of a current inclination:  
- in summer:  
Figure 12:8  
- in winter:  
Figure 12:9  
Figure 15 demonstrates this as a combination of the trajectories of the normal \(\overrightarrow{n}\) with direction to the Sun. Moreover, due to deflection towards the polar axis, the normal touches the line of the horizon, not six hours after the full sun, but earlier and simultaneously with the Sun. Thus, the one-axis polar-rotating tracker secures the same regime of irradiation as the double-axis one at the angle of deflection of the tracking surface from the axis of rotation, which is equal to the sun's inclination. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\tau\), & & & \multicolumn{3}{c}{**Summer Solstice**} & \multicolumn{3}{c}{**Spring Equinox**} & \multicolumn{2}{c}{**Winter Solstice**} \\ \cline{2-10} \multirow{2}{*}{**Hour**} & \(\gamma_{s}\) & \(\gamma\) & \(\delta_{0}=\varphi\) & \(\beta_{0}=\varphi\) & \(\beta_{0}=\varphi-\delta\) & \(\beta_{0}=\varphi\) & \(\beta_{0}=\varphi\) & \(\beta_{0}=\varphi\) \\ \cline{3-10}  & & \(\beta_{0}=\varphi\) & \(cos\theta\) & \(E\), \(W/\text{m}^{2}\) & \(cos\theta\) & \(E_{\
u}\) & \(E_{\
u}\) \\ \hline
0 & 0 & 0 & 0.9174 & 969 & 1.0 & 1056 & 1.0 & 1026 & 0.9174 & 772 \\
1 & 29.29 & 19.27 & 0.9174 & 967 & 1.0 & 1054 & 1.0 & 1017 & 0.9174 & 754 \\
2 & 52.42 & 37.01 & 0.9174 & 952 & 1.0 & 1038 & 1.0 & 994 & 0.9174 & 688 \\
3 & 69.60 & 52.55 & 0.9174 & 928 & 1.0 & 1012 & 1.0 & 943 & 0.9174 & 537 \\
3.92 & – & – & – & – & – & – & – & – & 0.9174 & 328 \\
4 & 83.12 & 66.14 & 0.9174 & 893 & 1.0 & 973 & 1.0 & 853 & – & – \\
5 & 94.77 & 78.40 & 0.9174 & 835 & 1.0 & 910 & 1.0 & 634 & – & – \\
6 & 105.6 & 90.00 & 0.9174 & 742 & 1.0 & 809 & 1.0 & 348 & – & – \\
7 & 116.4 & 101.9 & 0.8861 & 552 & 1.0 & 623 & – & – & – & – \\
8 & 128.1 & 114.2 & 0.7944 & 218 & 1.0 & 275 & – & – & – & – \\
8.075 & 128.2 & 114.9 & 0.7852 & 183 & 1.0 & 233 & – & – & – & – \\ \hline H, & & & & & 13,907 & – & 15,242 & – & 11,282 & – & 5267 \\ W\(\cdot\)hours & – & – & – & 91.2\% & – & 100\% & – & 100\% & – & 90.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Orientation efficiency of the tracking surface while rotating around the polar axis, \(cos\theta\) (own, research). The energy-saving double-axis tracker is constructively reasonable to be made in the structure of polar and horizontal axes. A drive unit of the polar axis can operate continuously in the mode of permanent angle speed 15 grad/hour, or be switched at equal time periods, e.g., hourly. In contrast, rotation around the horizontal axis is done much more seldom, with the average speed \(2\delta_{0}/183=46.9^{\circ}/183\approx 0.26\) grad/day. Correcting the inclination twice a month, the average deflection from the optimal direction to the Sun does not exceed \(4^{\circ}\). In the majority of practical installations, such deflections are neglected, because they reduce irradiation of the tracking surface only by 0.23%. Hence, a double-axis tracker with the polar and horizontal axes can efficiently track the Sun according to the simplest synchronic algorithm of control.