# Orientation and Exposure Efficiency of a Solar Tracking Surface in Clear Sky
## 4 Discussion
The current maximum of irradiation is achieved under the evident condition that the receiving surface is perpendicular to the plane, drawn across the rotation axis, the Sun normal and the surface. The appropriate scheme of irradiation and construction for measuring of the dependency of the angle of inclination and orientation efficiency of the receiving surface for the first half of a day is presented in Figure 9.  
Figure 8: Orientation (**a**) and energy (**b**) efficiency of the tracking surface of horizontal-axis “east-west” tracker in the periods (own research): 1-summer solstice; 2-spring equinox; 3-winter solstice. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Summer Solstice**} & \multicolumn{3}{c}{**Spring Equinox**} & \multicolumn{3}{c}{**Winter Solstice**} \\ \cline{2-13} \(\tau_{\tau}\) & \multicolumn{3}{c}{**H\({}_{max}\) = 15,244 W/d**} & \multicolumn{3}{c}{**H\({}_{max}\) = 11,282 W/d**} & \multicolumn{3}{c}{**H\({}_{max}\) = 5846 W/d**} \\ \cline{2-13}
**Hour** & \multicolumn{3}{c}{**HWE**} & \multicolumn{3}{c}{**H\({}_{\text{HNS}}\)**} & \multicolumn{3}{c}{**HWE**} & \multicolumn{3}{c}{**H\({}_{\text{HNS}}\)**} \\ \cline{2-13}  & \(cos\theta\) & \(E_{\tau}\) & \(cos\theta\) & \(E_{\tau}\) & \(W/\text{m}^{2}\) & \(cos\theta\) & \(E_{\tau}\) & \(W/\text{m}^{2}\) & \(cos\theta\) & \(E_{\tau}\) & \(W/\text{m}^{2}\) & \(N/\text{m}^{2}\) \\ \hline
0 & 1 & 1056 & 0.8945 & 945 & 1 & 1026 & 0.6428 & 660 & 1 & 842 & 0.2849 & 240 \\
1 & 0.9714 & 1024 & 0.9061 & 955 & 0.9659 & 982 & 0.6727 & 684 & 0.9714 & 818 & 0.3557 & 292 \\
2 & 0.8886 & 922 & 0.9356 & 971 & 0.8660 & 861 & 0.7483 & 744 & 0.8886 & 666 & 0.5027 & 377 \\
3 & 0.7611 & 770 & 0.9705 & 982 & 0.7071 & 667 & 0.8406 & 793 & 0.7071 & 414 & 0.6583 & 385 \\
3.92 & – & – & – & – & – & – & – & – & – & 0.5170 & 185 & 0.7847 & 280 \\
4 & 0.6073 & 591 & 0.9954 & 968 & 0.5000 & 427 & 0.9237 & 788 & – & – & – & – \\
4.58 & 0.5190 & 487 & 1.0000 & 939 & – & – & – & – & – & – & – \\
5 & 0.4634 & 422 & 0.9972 & 908 & 0.2588 & 164 & 0.9802 & 621 & – & – & – & – \\
6 & 0.3980 & 322 & 0.9667 & 782 & 0 & 0 & 1.0000 & 348 & – & – & – \\
7 & 0.4634 & 289 & 0.8991 & 560 & – & – & – & – & – & – & – \\
8 & 0.6073 & 167 & 0.7945 & 218 & – & – & – & – & – & – & – \\
8.075 & 0.6191 & 144 & 0.5170 & 120 & – & – & 1.0000 & – & – & – & – \\ \(H\), & & 10,971 & – & 14,373 & – & 8254 & – & 8928 & – & 5441 & – & 2509 \\ W-hours & – & 72.0\% & – & 94.3\% & – & 73.2\% & – & 79.1\% & – & 93.1\% & – & 42.9\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Orientation and exposure efficiency of the tracking surface of horizontal axis trackers (own research). According to the construction, the following correlations are performed; particularly a parallel shift of the normal of the tracking surface--the vector \(\overrightarrow{n}\)--does not change the angular correlations. The current angle of irradiation is determined from the following equations for a right triangle \(ODC\), where \(D\) is a right angle:  
\[\cos\theta=\frac{DC}{R}=DC \tag{25}\]  
\[DC^{2}=BD^{2}+BC^{2} \tag{26}\]  
\[\frac{BC}{R}=sin\ h=\cos\theta_{z} \tag{27}\]  
\[\frac{OB}{R}=cosh=sin\theta_{z} \tag{28}\]  
\[BD=OB\ sin\gamma_{s}=sin\ \theta_{2}sin\gamma_{s} \tag{29}\]  
hence:  
\[\cos q=\sqrt{cos^{2}q_{z}+sin^{2}q_{z}\cdot sin^{2}\gamma_{S}} \tag{30}\]  
or:  
\[\cos q=\sqrt{cos^{2}q_{z}+cos^{2}q_{z}\cdot\delta sin^{2}\omega\tau} \tag{31}\]  
The calculated values \(cos\theta\) are presented in the column \(HNS\) of Table 5 and the corresponding graphical dependencies are demonstrated in Figure 10a. Figure 9: Scheme for measuring of the parameters of irradiation of the surface while it rotates around the horizontal axis “north–south” \(HNS\) axis tracker—designed based on [21, 23, 35, 36]. In the bottom line of Table 5, there are absolute values of daily energy exposures of the tracking surface of both types of horizontal-axis trackers.