# Orientation and Exposure Efficiency of a Solar Tracking Surface in Clear Sky
## 2 Materials and Method  
The performance of solar trackers is judged against criteria that are difficult to compare. The difficulty arises from the variability of the parameters of the solar surface flux, which depend on the weather, season and territorial specificity. The assessment, presented in the literature [20; 21; 22; 23], usually makes a comparison of the obtained energy, relating to the stationary surface or efficiency of active solar energy installations. Besides weather conditions, the results are additionally influenced by constructive peculiarities and exploitation characteristics of energy installations. Trackers are devices necessary to optimize the use of direct solar flux. Hence, it is more objective to compare initial figures, particularly angle of illumination, irradiation and energy exposure, i.e., the amount of energy arriving at the surface per time unit. The monograph [23] presents hourly dependencies of irradiation of tracking surfaces, separately for each season of a year--summer and winter solstice and equinox. They are calculated for surface flux of standard intensity at latitude 35\({}^{\circ}\) and without specification of standard parameters. In contrast, [24] estimates energy irradiation of the surface of discrete orientation in a flux assumption. Its intensity \(G_{b}\) is described by the convenient equation of Kastrov. Equation (1) is as follows:  
\[G_{b}=\frac{G_{sn}}{1+cm} \tag{1}\]  
Constant \(c\) agrees with the results of many years' pf experiments on the intensity of solar beams in a clear sky. Hence, a daily distribution of intensity, adopted for calculation, in both cases is based on statistical average characteristics of natural fluxes of solar energy. This causes dependency of the results of comparison on applied databases. Results of immediate measuring of energy efficiency of a flat surface under illumination by a natural flux of solar energy always have diffusion and reflection components. Contribution of these components are hardly considered because of the impact of weather-dependent factors on the space distribution of the diffusion flux intensity and elements of relief and cloudiness on a reflected flux. Thus, current irradiation of the tracking surface is reasonably assessed by a modeled flux, with parameters which are close to the natural direct one, according to the maximum transparent atmosphere. At the entrance of the atmosphere, density (intensity) of the flux of solar energy during a year variates from the maximum 1415 to minimum 1321 W/m\({}^{2}\) due to ellipticity of the earth's orbit. Its average value, which is equal to \(G_{sc}=1367\) W/m\({}^{2}\), is called a solar constant and current values for \(G_{sn}\) for any day in a year have a sequence number \(n\); accuracy, appropriate for comparison, can be calculated by the known Equation [21] (2):  
\[G_{sn}=G_{sc}\bigg{(}1+0.033\ cos\frac{360n}{365}\bigg{)} \tag{2}\]  
On 21 June (the day of summer solstice), \(G_{sn}=\)1323 W/m\({}^{2}\); on 21 March (equinox), it is equal to 1376 watts per square meter; and on 21 December (the day of winter solstice) it is 1412 W/m\({}^{2}\). The presented values are very close to the average in the same month and, thus, the accordingly calculated parameters of modeled fluxes can be convenient verified with the appropriate results of actinometrical measuring, first by hourly data of direct solar radiation on the surfaces, which are normal to the beams in a clear sky. The corresponding values are presented in meteorological databases, particularly in [25; 26], in Ukraine. In the CI system of optical energy values, the beam energy, received by the surface, is called energy exposure, marked by the letter \(H\) and is measured in watts per hour or joules. This value is an integral characteristic of a flux of solar energy, which is practically divided into hour exposure, marked by letter \(I\), and daily exposure, which is marked by \(H\)[23].