## 4 Conclusions and Discussion  
The present study investigated solar availability across Saudi Arabia on flat-plate solar panels that track the Sun along its daily path in the sky. The main objective was to find the optimum tilt angles of solar panels that produce maximum annual energy in this configuration under all-sky conditions. This was achieved by calculating the annual energy sum on flat-plate surfaces with tilt angles tracking the Sun in the range 5\({}^{\circ}\)-55\({}^{\circ}\) with an increment of 5\({}^{\circ}\) at 82 sites across Saudi Arabia; the solar availability on a horizontal plane was also included for reference purposes. The calculations of the energy received on the tilted surfaces were performed for a ground albedo equal to 0.2 (as a reference value) and also for a near-real ground albedo. The first outcome of the work was that the optimum tilt angles for flat-plate solar collectors mounted on a vertical axis that track the Sun over Saudi Arabia are 40\({}^{\circ}\), 45\({}^{\circ}\), and 50\({}^{\circ}\). The second finding of the study was that these three optimum tilt angles can group the 82 sites into the three (solar energy) zones (SEZ) defined in [1], i.e., SEZ-A with 40\({}^{\circ}\), SEZ-B with 45\({}^{\circ}\), and SEZ-C with 50\({}^{\circ}\). The third conclusion was related to the variation of the annual maximum solar energy in each SEZ, i.e., 2767-3314 kWhm\({}^{-2}\)year\({}^{-1}\) (average 3044.9 kWhm\({}^{-2}\)year\({}^{-1}\) in SEZ-A), 2159-4078 kWhm\({}^{-2}\)year\({}^{-1}\) (average 2975.6 kWhm\({}^{-2}\)year\({}^{-1}\) in SEZ-B), 2324-3692 kWhm\({}^{-2}\)year\({}^{-1}\) (average 2932.5 kWhm\({}^{-2}\)year\({}^{-1}\) in SEZ-C), and 2159-4078 kWhm\({}^{-2}\)year\({}^{-1}\) (average 2991.9 kWhm\({}^{-2}\)year\({}^{-1}\) in all SEZs). In relation to fixed-tilt solar systems reported in [1], the one-vertical axis solar systems in Saudi Arabia show an average increase in the maximum annual solar energy yield of +21.8% for SEZ-A, +22.6% for SEZ-B, +31.2% for SEZ-C, and +23.5% for all SEZs. Beside the annual energy sums, monthly solar energy values averaged over all locations belonging to the same SEZ as well as to all SEZs were estimated under all-sky conditions. Regression equations were provided as best-fit curves to the monthly mean energy sums that estimate the solar energy potential per SEZ (and all SEZs) with great accuracy (R\({}^{2}\geq\) 0.82). These expressions may prove very useful to architects, civil engineers, solar energy engineers, and solar-energy-system investors in order to assess the solar energy availability in Saudi Arabia for Sun-tracking flat-plate solar collectors throughout the year. Seasonal solar energy sums were also calculated. They were averaged over all sites in the same SEZ as well as over all sites (all SEZs), under all-sky conditions. For every case, regression curves that best fit the mean values were estimated with absolute accuracy (R\({}^{2}\) = 1). Maximum sums were found in the summer (836.6 kWm\({}^{-2}\)), and minimum ones in the winter (664.1 kWm\({}^{-2}\)), as expected. The corresponding figures for the maximum energy received on a flat-plate solar collector in Saudi Arabia having an optimum tilt angle towards south are 659.9 kWm\({}^{-2}\) and 532.3 kWm\({}^{-2}\), respectively for summer and winter [1]. Therefore, the single-axis solar systems provide a high increase in the maximum seasonal energy yield in comparison to the static ones of +26.8% and +24.8%, respectively. The correction factor, CF, introduced in [1], was used in this work, too. A graph of CF as a function of the tilt angle (in the range 5\({}^{\circ}\)-55\({}^{\circ}\)) showed exponential growth for sites having ratios \(\rho_{\rm r}=\rho_{\rm g}/\rho_{0}>1\), or exponential decay in the cases of \(\rho_{\rm r}<1\). Such curves are assumed to be universal (i.e., representable as nomograms), since similar graphs in [1] had the same shape.