## 7 Results and Discussion
### Improved Configurations  
Comparing simulations with different parameters help us understand how the various aspects are subtlety related, giving us a precious insight to optimize a heliostat field. As an example, we study here the effect of three improvements: (i) increasing the distance between heliostats to 2 m, (ii) increasing the tower height to 20 m, and (iii) increasing the slope to 20\({}^{\circ}\). First, we apply these improvements separately to the worst (Jalich, square, flat) configuration (JSF \(\rightarrow\) JSF\({}_{1}\), JSF\({}_{2}\), JSF\({}_{3}\)) to compare their efficacy. Finally, the three improvements are combined and applied to the best (Protaras, rectangle, slope) configuration (PRS \(\rightarrow\) PRS\({}_{123}\)) to get a glimpse of the maximum achievable efficiency. AHE and ATE results for these four new configurations are reported in Table 4.  
These JSF\({}_{1}\), JSF\({}_{2}\), and JSF\({}_{3}\) results show that AHE improves slightly more when the heliostat distance increases to 2 m, then when the slope rises to 20\({}^{\circ}\), and finally when the tower becomes 20 m high. However, when ATE results are considered, the best result is obtained for the tower improvement, which is better than for the distance improvement and in turn better than the slope improvement. This is because the tower improvement mostly reduces blocking in the 10:00-14:00 period of the most productive hours, while the distance and slope mainly reduce shading in the less productive 08:00-10:00 and 14:00-16:00 intervals. While AHE considers only the geometric efficiency of the heliostat layout, ATE takes into account the sun height at each measuring moment (in our work, hourly from 08:00 to 16:00 LCT), thus providing a better figure of merit to rank the efficiency of the heliostat field to grab energy.  
It is interesting to see that AHE for JSF\({}_{1}\) (0.8052), where square heliostats are 2.0 m apart, horizontally and vertically, is still lower than for JRF (0.8213), where rectangular heliostats are separated by 1.0 m horizontally and 1.9 m vertically, reinforcing the conclusion that tall square heliostats block more of the reflected radiation than rectangular heliostats.  
The PRS\({}_{123}\) result is important because it shows approximately the maximum efficiency that can be achieved for this type of heliostat field in the northern hemisphere. AHE is almost equal to 1 (0.9989), so the ATE value measured (0.5498) is about the maximum that can be achieved in Protaras. This is the heliostat field listed in the European Union SFERA-III project [27] with the lowest latitude (+35.0125\({}^{\circ}\)), so to obtain better results, it will be necessary to investigate heliostat fields closer to the equator. Assuming a maximum DNI flux of 1000 W/m\({}^{2}\), the value reached for PRS\({}_{123}\) corresponds to an average flux of 550W/m\({}^{2}\) reaching the target, from 08:00 to 16:00 LCT, from 1 st January to 31 st December, in 2024 (leap year).  
Again, assuming that half of the 366 days in 2024 were cloudy, an average of 275 W/m\({}^{2}\) can be expected for the whole year from 08:00 to 16:00 LCT, an enormous total amount of energy: 275 \(\times\) 8 \(\times\) 366 = 805,200 J/m\({}^{2}\). As our simulated heliostat field has 66 mirrors, each of 4 m\({}^{2}\), the total amount of energy collected becomes 805,200 \(\times\) 4 \(\times\) 66 = 212,572,800 J, the maximum estimated energy collected during the full year of 2024. Results for future years should be very similar, as sun trajectories change very little. For example, on the summer solstice, on 20 th June 2025, in Julich at 08:00 LCT, the altitude and the azimuth are 26\" and 46\" (seconds) larger, respectively, when compared with 2024.