## 6 Computational Details  
Unless we are studying an already-existing heliostat field, many choices and compromises must be taken into account before designing the new model:  
(1) How many heliostats shall we model? In a computer with an i5 processor, each heliostat ray-tracing simulation takes 1 min of CPU time for \(10^{8}\) rays. Therefore, the number of heliostats should be kept to a minimum. To simulate a heliostat field close to reality, we used the layout shown in Figure 9, with a total of 66 heliostats in a staggered arrangement. However, only the six end heliostats (in green) are fully simulated as we identify them as representatives of the whole set. The 20 first neighbors (in red) and the 8 s neighbors (in pink) must also be orientated to catch possible blocking and shading events (but this task does not involve ray tracing, so it is not time-consuming). We assume that only these first and second neighbor heliostats can effectively contribute to shading or blocking events. This is possible because blocking events are due to close heliostats only (the reflected rays must travel upwards to the target) and shading events can be seen as resulting from close  
Figure 8: Pixel-based target rectangle, perpendicular to average sun radiation coming from the heliostat field (heliostats are represented in the rest position). heliostats only (even when the received rays are almost horizontal, close heliostats will stop most rays stopped by farther heliostats). During this work, we will be independently simulating each of these six groups of heliostats (henceforth named N, NW, NE, S, SW, and SE, as shown in Figure 9), formed by one green heliostat, three or four red heliostats, and one or two pink heliostats. (2) Shall we simulate a horizontal field or a field making some south-north slope angle? If so, should it be 10\({}^{\circ}\) or 20\({}^{\circ}\)? Using a slope is more interesting, but choosing a horizontal flat terrain is simpler, on average closer to real land conditions, and better emphasizes the differences between the front and the back heliostat rows. In this work, we simulate and compare the 0\({}^{\circ}\) and 10\({}^{\circ}\) slopes. (3) Shall we use square or rectangular heliostats? And which dimensions shall we use? Larger sizes provide larger radiant energy but are less flexible to handle and require stronger mechanical structures to cope with the wind. Rectangular heliostats might handle wind better than square heliostats with the same area, due to their lower height. In this work, we use heliostats with an area of 4 m\({}^{2}\) each. We compare square 2.0 m \(\times\) 2.0 m with rectangular (5/2) \(\times\) (2/5 \(\times\) 4) = 2.5 m \(\times\) 1.6 m heliostats (typical sizes in tilt-roll heliostat fields). Therefore, the total power of our heliostat model (assuming an average DNI = 800 W/m\({}^{2}\)) becomes 66 \(\times\) 4 \(\times\) 800 = 0.21 MW. (4) What should the distance between the heliostat mirrors be in the resting, flat position? Land is expensive, so heliostats should be kept as close as possible, to maximize  
Figure 9: Layout for the simulated heliostat field, with 66 heliostats in a staggered arrangement. The target (T) points north (N), to collect the sun rays (S) reflected. Only the 6 green heliostats are fully simulated. The 20 closer (red) and 8 farther (pink) heliostats must be orientated, to test for possible blocking and shading events. The heliostat mirrors are 2.0 m \(\times\) 2.0 m, separated by 1.0 m in both the north–south and east–west directions. The two central heliostats are rotated 45\({}^{\circ}\) to emphasize that they cannot touch. We also simulated this heliostat field with mirrors 2.5 m (east-west) \(\times\) 1.6 m (north–south), with 1.0 m separation east–west and 1.9 m north-south. the collected power, but not closer, to avoid blocking and shading events and mechanical collisions [25]. In square heliostats, we choose 1.0 m for both east-west and north-south separation.