# Orientation and Exposure Efficiency of a Solar Tracking Surface in Clear Sky
## 3 Results
For instance, at the latitude close to \(50^{\circ}\) there are such stations as \"Boryspil\": \(50.35^{\circ}\) northern latitude and \(30.97^{\circ}\) eastern longitude and \"Kovel\": \(51.22^{\circ}\) northern latitude and \(24.68^{\circ}\) eastern longitude, placed at the altitude \(z=124\) and \(172\) m above sea level, respectively. Actinometrical observations at the stations are consolidated in two meteorological reference books of 1966 [25] and 1990 [26]. The corresponding orientation values and parameters of a direct surface flux of solar energy at the latitude \(50^{\circ}\) in clear sky are presented in Tables 2 and 3, respectively. Table 3 additionally measures daily energy exposure of the surface, standard to the direction of solar beams. Numerical integration of hourly values is performed by the trapezoidal method with application of the modified equation, for consideration of a symmetric set of data and a time interval for the threshold values less than \(1\) h.  
Figure 1:2  
where \(\Delta\tau=1\) h, \(\Delta_{n}\tau=0.075\) h during the summer solstice; \(\Delta_{n}\tau=0.92\) winter solstice. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & & & & & & & \\ \hline \(\tau_{s}\) & \(\mid\omega\tau\mid\), & \(\theta_{z}\), & & & & & & & & \\ hour & grad & grad & & & & & & & & \\  
92 & 58.87 & 90.000 & 0 & 1.0000 & 0 & 0 & 51.75 & 0.6190 & 0.7854 \\ \hline \end{tabular}
\end{table} 
Table 2: Angular dimensions of a direct flux of solar energy for the latitude \(\varphi=50^{\circ}\); (own research). \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \(\tau\)**, Hour** & **0** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **8.075** & \(\Sigma\)** \\ \hline \(G_{b}(T_{LK})\) & & & & & & & & & & & \\ \(\theta_{z}\) & 26.56 & 29.03 & 36.36 & 43.80 & 53.15 & 62.78 & 72.25 & 81.25 & 89.93 & 90 & – \\ \(cos\theta_{z}\) & 0.8945 & 0.8744 & 0.8155 & 0.7218 & 0.5997 & 0.4574 & 0.3048 & 0.1522 & 0.0100 & 0 & – \\ \(z=124\) m & 1.1008 & 1.1126 & 1.2072 & 1.3732 & 1.6399 & 2.1463 & 3.2024 & 6.2218 & 27.420 & 37.291 & – \\ \(\delta_{R}\) (\(m\)) & & & & & & & & & \\ \(z=124\) m & 0.1188 & 0.1185 & 0.1165 & 0.1133 & 0.1086 & 0.1010 & 0.0892 & 0.0702 & 0.0332 & 0.0269 & – \\ \(G_{b}\) (\(T_{LK}=2\)) & 1056 & 1054 & 1038 & 1012 & 973 & 910 & 809 & 623 & 275 & 233 & 15,244 \\ \(G_{bFigure 4 demonstrates hourly data of the energy, registered at the meteorological station \"Kovel\" in clear sky in June, and presented in watt-hours per square meter. They are depicted by a column diagram and numerically equal values of the flux intensity, in watts per meter square in the form of a continuous dependency, are represented by a thin bypass line. The heavy curve refers to a modeled flux under air turbidity \(T_{LK}\) = 4. The same comparison of modeled hourly dependencies and those registered at the meteorological station \"Boryspil\" are demonstrated in Figure 5.  
In both cases, results of the modeling satisfactory demonstrate real hourly dependencies, which are average values of the intensity of many years of measurements. It is obvious  
Figure 4: Hourly data of energy \(I\) (columns) and intensity of the flux \(G_{b}\) (own research): natural—a thin bypass line; the modeled one at \(T_{LK}\) = 4—a line of standard width (the meteorological station “Kovel”); time by the Sunbelt. Figure 5: Correlation of the natural flow intensity at the meteorological station “Boryspil” (a heavy line) and that modeled under two values of air turbidity (thin lines)—(own research).