## 4 Calculation of Monthly Total Energy on an Inclined Surface
Assuming that reflected radiation is diffuse and isotropic, the conversion factor for reflected radiation (\(R_{R}\)) is given by:  
\[R_{R}=(1-\cos(\beta))/2 \tag{58}\]  
The monthly conversion factor (\(R_{M}\)) is the ratio of total solar radiation incident on an inclined/tilted surface to that on a horizontal surface and is given by:  
\[R_{M}=(1-D_{d}/G_{d})*R_{B}+(D_{d}/G_{d})*(1+\cos(\beta))/2+\rho*(1-\cos(\beta ))/2 \tag{59}\]  
Or if we express the ratio of \(D_{d}/G_{d}\) as the fraction of diffuse to global radiation (\(K_{D}\)):  
Figure 29:0After the calculation of mean monthly conversion factor (\(R_{M}\)), the total solar energy received by the inclined surface (\(G_{iM}\)) is given by:  
Figure 29:1  
where \(G_{hM}\) is the total horizontal irradiation in kWh/m\({}^{2}\)/month. The following relations give the total monthly direct energy (\(B_{iM}\)), diffuse energy (\(D_{iM}\)) and reflected energy (\(R_{iM}\)) which is received by an incline panel:  
Figure 29:2  
Figure 29:3  
Figure 29:4  
The results of these calculations are presented in Tables 14 and 15. Table 14 presents the estimated \(R_{B}\) and \(R_{M}\) conversion factors, while Table 15 presents the monthly total energy in kWh/m\({}^{2}\)/month, received by an inclined surface. The highest values for each month and the optimal slope are also highlighted. As it is indicated from the tables the optimum slope angles during the winter-time range between 50 and 60\({}^{\circ}\), while during summer the slopes are close to zero. In spring the optimum slope angle is 15\({}^{\circ}\), in summer is 0\({}^{\circ}\), in autumn is 45\({}^{\circ}\) and in winter is 55\({}^{\circ}\). The annual optimum angle is about 26\({}^{\circ}\) which is about 10\({}^{\circ}\) less than the latitude of the location. Table 16 presents the monthly total energy in kWh/m\({}^{2}\)/month, received by an inclined surface for annual optimum angles ranging from 20\({}^{\circ}\) to 32\({}^{\circ}\). Table 17 compares the annual energy totals for different slopes (\(G_{i}\)) with those measured on a horizontal surface (\(G_{h}\)). For different optimum slopes for each month of the year, we estimate an annual amount of energy equal of 2221 kWh/m\({}^{2}\), while the measured total horizontal energy is 1938 kWh/m\({}^{2}\). Therefore, the percentage increase of energy is 14.6%. For the case of a permanent slope angle of 26\({}^{\circ}\) throughout the year the inclined panel receives 2097 kWh/m\({}^{2}\) with the increase of about 8.2% from the horizontal level. For a slope angle of less than 15\({}^{\circ}\) from the latitude (35\({}^{\circ}\)) we have high production during the summer months. The annual increase is 7.7%. For the case of a slope which is higher by 15\({}^{\circ}\) from the latitude, we have high production in the winter months, but the annual increase is only 1.3%. Finally, for the case the slope \(\beta=\varphi\) (35\({}^{\circ}\)) we have high production during the months of March and September. The annual increase in energy with respect to the horizontal level is 7.3%. Therefore, higher total energy can be obtained if we use two different slopes one for the summer and one for winter period. For instance, if we use a slope of 10\({}^{\circ}\) for the summer period (April-September), then the total energy for this period is 1313 kWh/m\({}^{2}\), while if we use a slope of 50\({}^{\circ}\) for the winter period (October-March), then the total energy for this period is 878 kWh/m\({}^{2}\). Therefore, the annual total by using the two slopes during the year is 2191 kW/m\({}^{2}\), which is higher by about 95 kWh/m\({}^{2}\) from the case of an annual permanent slope of 26\({}^{\circ}\). As a result, the case with two slopes (\(\beta=10^{\circ}\) for summer and \(\beta=50^{\circ}\) for winter) could have an increase of total annual energy by 13% with respect to the horizontal one.