# Orientation and Exposure Efficiency of a Solar Tracking Surface in Clear Sky
## 4 Discussion  
Daily distribution of the intensity of a modeled flux and its integral amount at minimum turbidity of the air should be taken as a theoretically maximum for a double-axis tracker. One-axis rotating trackers, which are less effective, but simpler in production and operation, are classified by orientation of the rotation axis, signified by the name and the short title [23]: \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Databases**} & \multicolumn{3}{c}{**Daily Exposure \(H\), W/m\({}^{2}\)**} \\ \cline{2-4}  & **Summer Solstice** & **Spring Equinox** & **Winter Solstice** & **Note** \\ \hline Extra-atmospheric flow \(G_{sin}\) & 21,366 & 16,512 & 11,070 & (21) \\ “Kovel” Registered & 10,161 & 8001 & 4312 & \\ “Boryspil” Registered Calculated at: & 10,572 & 8223 & 3987 & \\ \(T_{LK}=2\) & 15,244 & 11,282 & 5846 & \\ \(T_{LK}=3\) & 12,778 & 9153 & 4281 & \\ \(T_{LK}=3.5\) & 11,751 & 8414 & 3667 & \\ \(T_{LK}=4\) & 10,829 & 7494 & - & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Daily energy exposure of a direct flux on the surface, normal to solar beams (own research). Figure 6: Seasonal changes of the intensity of a direct flux in very clear sky (\(T_{L}=2\))—(own research): 1—summer solstice; 2—spring equinox; 3—winter solstice. a device with a horizontal rotation axis, oriented in the direction \"east-west\" (horizontal \(E\)-\(W\) axis tracker--\(HEW\) axis tracker);
* a device with a horizontal rotation axis, oriented in the direction \"north-south\" (horizontal \(N\)-\(S\) axis tracker--\(HNS\) axis tracker);
* a device with a vertical rotation axis (vertical axis tracker)--\(VAT\);
* a device with a polar rotation axis (polar axis tracker)--\(PAT\). The last two devices expect seasonal optimization of the angle of irradiation by deflection of the tracking surface from the rotation axis, which should be considered while quantitatively assessing their efficiency. A horizontal rotating device with the rotation axis in the direction \"east-west\" (\(HEW\)) only follows the change in the Sun's height over the horizon by the scheme presented in Figure 7. The rotating axis is in line with the parallel of the horizontal latitude. Thus, the device should be titled as latitude-rotating. 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 and the Sun, and which contains the triangle \(BOC\). According to the structure:  
\[AB=\cos h=\cos\theta_{z} \tag{21}\]  
\[OB=AB\cdot sin\ \gamma_{s}=sin\ \theta_{s}\cdot sin\ \gamma_{s} \tag{22}\]  
\[sin\theta=OB/R=sin\ \theta_{z}\cdot sin\ \gamma_{s} \tag{23}\]  
\[cos\theta=\left(1-sin^{2}\theta\right)^{0.5}=\left(1-sin^{2}\theta_{z}\cdot sin ^{2}\gamma_{z}\right)^{0.5} \tag{24}\]  
The hourly values \(cos\theta\), calculated for the tracking surface by the equation, are presented in Table 5 (column \(HWE\)) and the corresponding graphical dependencies for \(cos\theta\) of summer and winter solstice and periods of equinox are demonstrated by Figure 8a. In the period between the spring and autumn equinox, the Sun stays in the northern part of the semi-sphere after the sunrise and before the sunset. To employ the flux of morning and evening periods, it is necessary to change orientation of the receiving surface from southern to northern. Theoretically, this means that twice a day from the moment of transition of the Sun azimuth across the line \"east-west\", the azimuth of the tracking surface changes to the opposite one, and on the graphical dependency the decay \(cos\theta\) is changed into growth. Figure 7: Scheme for measuring the parameters of irradiation of the surface while it rotates around the horizontal axis “east-west” (\(HEW\) axis tracker)—designed based on [21; 23; 35; 36]. A tracker with a horizontal axis of rotation in the direction \"north-south\" (_HNS_ axis tracker) follows a daily azimuth path of the Sun from the east to west.