# Orientation and Exposure Efficiency of a Solar Tracking Surface in Clear Sky
## 3 Results  
The studies showed that the values calculated by the Equation (10) were significantly underestimated because they were based on low-resolution spectral data. Consequently, the dependency of Rayleigh scattering on the wavelength was overestimated [35]. Thus, the defined optical thickness is additionally marked by the index symbol \(\delta_{b}(m)\) and the \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \(\theta_{z}\) & **0** & **10** & **20** & **30** & **40** & **50** & **60** & **70** & **80** & **85** & **88** & **90** \\ \hline \(AM\) & 1 & 1.015 & 1.064 & 1.155 & 1.305 & 1.556 & 2.000 & 2.924 & 5.759 & 11.474 & 28.65 & \(\infty\) \\ \(m\) **at** & 1 & 1.015 & 1.064 & 1.154 & 1.304 & 1.554 & 1.994 & 2.902 & 5.581 & 10.306 & 19.51 & 37.85 \\ \(z=0\) & & & & & & & & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Values of air and optical masses by Equations (3) and (5) (own study). Figure 1: Optical air mass: 1—by the Equation (5), 2—by the Equation (7); (own study). specified expression for its calculation by a regression equation (exponential function), as for example in the European Solar Radiation Atlas (ESRA) [32; 33] Equations (11) and (12):  
\[\frac{1}{\delta_{R}\left(m\right)}=6.6296+1.7513m-0.1202m^{2}+0.0065m^{3}-0.00013 m^{4} \tag{11}\]  
at \(m<20\) and \(h>1.9^{\circ}\);  
\[\frac{1}{\delta_{R}\left(m\right)}=10.4+0.7518m \tag{12}\]  
at \(m>20\) and \(h<1.9^{\circ}\). Values of the optical thickness obtained by Equations (10)-(12) are the initial parameters for calculation of practically important optical characteristics of a real atmosphere, i.e., visibility, turbidity, dustiness, etc. However, in both cases, they depend on the optical air mass. Thus, their values, calculated at \(m=2\), are considered as standard. Choice of the point for comparison is explained by the fact that, at middle latitudes, the Sun never stays at its zenith. Thus, the closest integer value of air mass is chosen for the sake of convenience (Figure 2). The correlation between them looks like (13):  
\[\frac{\delta_{P}\left(2\right)}{\delta_{R}\left(2\right)}=\frac{0.0893}{0.103 1}=0.8662 \tag{13}\]  
and is used as a ratio of proportionality in the working equations for calculation of a direct flux under fixed transparency or vice versa. Real atmosphere always contains carbon dioxide, water vapor, drops of fog and aerosols. Their total contribution into attenuation of a flux of solar energy is quantitatively assessed by the turbidity factor \(T(m)\), which depends on the optical thickness of air. Quantitatively, it is expressed by a non-dimensional value referring to the contribution of the ideal atmosphere, which is taken as a reference unit. The correlations, proposed in literature for dependency on the optical mass of air, are usually additionally indexed by the last names of the author, i.e., \(T_{L}\)--is the Linke turbidity factor; \(T_{LK}\)--is the Kasten turbidity factor, etc. Thus, considering the described specifications, intensity of the surface flux of solar energy is calculated by Equation (8), which, in the case of \(T_{LK}(AM2)\) use, looks like that presented in the ESRA (14):  
\[G_{b}=G_{sn}\;exp[-0.8662\delta_{R}(m)\cdot T_{LK}(AM2)m] \tag{14}\]  
Figure 2: Correlation between optical thicknesses of air \(\delta_{R}(m)\), and \(\delta_{P}(m)\); (own research). For maximum employment of the energy of controlled flux of solar beams, the angle of their incidence on the tracking surface \(\theta\) should be minimized. During daylight, the permanent value \(\theta\) = 0 is secured only by a double-axis rotating device, which is complicated for production and operation. A simpler design is a feature of uniaxial rotating devices that minimize the irradiation angle and only in some cases is this equal to zero. In both variants for optimization of tracking, it is necessary to set analytical correlations between the space-time parameters of a direct flux of solar energy and the receiving surface.