# Orientation and Exposure Efficiency of a Solar Tracking Surface in Clear Sky
## 4 Discussion
Percentage efficiency is calculated referring to maximum data of the energy in clear sky, presented in Table 3. In line with the above, it is convenient to estimate the hourly or seasonal efficiency of each period and, if necessary, compare them with the energy efficiency of a stationary space. A vertical-axis rotating tracker secures compensation of the azimuth constituent of a daily path of the Sun in the sky. Its path is demonstrated at Figure 11 and is marked by continuous lines of a standard width. In contrast, normal of the tracking surface of the permanent inclination outlines the path of the same height over the horizon. On the scheme, they are demonstrated by dash lines and meet the condition of the maximum irradiation at the sunny midday with the inclination angles:  
* in summer: \[\cos\theta=\frac{DC}{R}=DC \tag{25}\]0 (32)
* in winter: \[\cos\theta=\frac{DC}{R}=DC \tag{25}\]1 (33)  
\[\cos\theta=\frac{DC}{R}=DC \tag{25}\]2 Pathway of the Sun (continuous lines) and end of the normal (dash lines) of the tracking surface of a vertical-axis tracker)—designed based on [21, 23, 35, 36]: 1-in winter; 2-in the period of equinox; 3-in summer. \[\cos\theta=\frac{DC}{R}=DC \tag{25}\]3 Orientation (**a**) and exposure (**b**) efficiency of the tracking surface of a horizontal-axis “north–south” tracker in the periods (own research): 1—summer solstice; 2—spring equinox; 3—winter solstice. at equinox:  
\[\cos\theta=\frac{DC}{R}=DC \tag{25}\]4  
The rest of the day, the minimum angle of irradiation is marked under conditions of equal azimuth angles of the Sun and the rotating surface \(\gamma=\gamma_{s}\). Making its substitution in the Equation (8), one can obtain the following equation for the initial angle of irradiation:  
\[\cos\theta=\frac{DC}{R}=DC \tag{25}\]5  
Current values for the above-presented angles of inclination are demonstrated in Table 6, which have the appropriate graphical dependencies 1, 2, and 3 in \[\cos\theta=\frac{DC}{R}=DC \tag{25}\]6  
At less angles of inclination, the full sun is characterized by a local minimum of irradiation with two symmetric maximums aside (curve 1b) and increased values \(cos\theta\) in the rest of the daylight. For instance, at the angle of inclination of the tracking surface \(\beta=\varphi=50^{\circ}\) during summer solstice, trajectory of the \"spring\" normal \(n_{2}\) crosses the solar one at 3.67 h: in Figure 12, the point of intersection is marked by a symbol of the Sun. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\tau_{r}\) & \multicolumn{3}{c}{**Summer Solstice**} & \multicolumn{3}{c}{**Spring Equinox**} & \multicolumn{3}{c}{**Winter solstice**} \\ \cline{2-9} \multicolumn{1}{c}{**Hour**} & \multicolumn{2}{c}{\(\beta=\varphi-\delta\)} & \multicolumn{2}{c}{\(\beta=50^{\circ}\)} & \multicolumn{2}{c}{\(\beta=50^{\circ}\)} & \multicolumn{2}{c}{\(\beta=\varphi\)} \\ \cline{2-9}  & \(cos\theta\) & \(E,W\cdot m^{2}\) & \(cos\theta\) & \(E,W\cdot m^{2}\) & \(cos\theta\) & \(E,W\cdot m^{2}\) & \(cos\theta\) & \(E,W\cdot m^{2}\) \\ \hline
0 & 1.0000 & 1056 & 0.9175 & 969 & 1.0000 & 1026 & 1.0000 & 842 \\
1 & 0.9991 & 1053 & 0.9338 & 983 & 0.9996 & 1017 & 0.9998 & 822 \\
2 & 0.9854 & 1023 & 0.9718 & 1009 & 0.9942 & 988 & 0.9967 & 748 \\
3 & 0.9551 & 966 & 0.9942 & 1006 & 0.9745 & 919 & 0.9845 & 576 \\
3.67 & – & – & 1.0000 & 987 & – & – & – & – \\
3.92 & – & – & – & – & – & 0.9588 & 342 \\
4 & 0.8942 & 870 & 0.9985 & 972 & 0.9320 & 795 & – & – \\
5 & 0.8068 & 734 & 0.9752 & 887 & 0.8623 & 547 & – & – \\
6 & 0.6985 & 565 & 0.9255 & 749 & 0.7660 & 267 & – & – \\
7 & 0.5780 & 360 & 0.8549 & 533 & – & – & – & – \\
8 & 0.4482 & 123 & 0.7668 & 211 & – & – & – & – \\
8.075 & 0.4471 & 104 & 0.7660 & 178 & – & – & – & – \\ \hline \(H\), & & 13,384 & – & 14,440 & – & 10,851 & – & 5715 \\ W\(\cdot\)hours & – & 87.8\% & – & 94.7\% & – & 96.2\% & – & 97.8\% \\ \hline \end{tabular}
\end{table} 
Table 6: Orientation and exposure efficiency of the tracking surface while rotating around the vertical axis (own research).