## 7 Results and Discussion
### Shading/Blocking Effects on the Efficiency Loss of the Heliostats  
To clarify the role played by shading and blocking in the efficiency loss of the heliostats, the daily amount of shading, blocking, and night events for the same four configurations (Julich and Protaras, square and rectangular heliostats) and for the three back heliostats (NW, N, and NE) is plotted in Figures 14-17, which is considered a better description of the whole heliostat field. Essentially, the shading and blocking fractions for each hour are obtained, and then the shading and blocking averages for the 08:00-16:00 sampled range are calculated. At 16:00 LCT in Julich in winter, when altitude \(<0\), the daily average loss amounts to 0.5/8.0 = 0.0625, as reported in Figures 14 and 15.  
The results for all four configurations show that shading is negligible from March to October, as the sun's altitude is high enough, even at 16:00 and 08:00 LCT, to prevent these effects. However, in the winter, shading increases rapidly, particularly at Julich but also at Protaras. Even in the best case, rectangular heliostats at Protaras, shading loss amounts to 10% around the winter solstice (21 st December). Shading decreases sharply on 3 rd November and 21 st January in Julich, going in the winter direction, because it becomes night at 16:00 (no shading), and the shading daily average drops.  
Unlike shading, blocking is significant, almost constant, from March to October for all four configurations studied here. Blocking is smaller for the central N heliostat, as the reflected rays must point higher to get the target, making them less prone to be intercepted by neighboring heliostats.  
As before, the NE heliostat is less efficient than the NW for the four configurations, probably due to the same reasons presented above: the NE heliostat has more difficulty reflecting the rays at 16 than the NW at 8 h. These four graphics seem to suggest that blocking decreases in winter, but this is just a technical effect: when shading occurs, the ray does not reach the mirror, so it is not tested anymore whether the ray could reach the target, and then blocking is not considered. Theoretically, blocking in winter would be significant; however, it is ignored simply because shading occurs first.  
An example can be seen in Figures 14 and 15, at Julich, where the NW heliostat blocking curve suddenly drops when the sun's altitude becomes negative at 16:00, signaling that blocking was occurring at 16:00 at this heliostat when the sun's altitude was still positive. This drop does not occur in the N and NE heliostats, signaling that blocking did not occur at these heliostats. The reason is that the N and NE heliostats were shaded at 16:00, so no blocking was possible, while the NW heliostat cannot be shaded at 16:00, given its westerly position in the field, so blocking can indeed occur.  
Finally, it is noted that a heliostat can be shaded and blocked simultaneously: rays in some regions are intercepted before reaching the mirror, and rays in other regions are intercepted after reflection in the mirror. These events are often observed in our simulations.  
The graphic representations of the average daily results are very useful to understand the optical phenomena occurring but are inefficient to numerically characterize the whole efficiency of a heliostat field. To produce a quantitative rating for a given heliostat field that can be ranked and compared with other layouts, representative averages for the whole year need to be calculated.