## 6 Computational Details
In rectangular heliostats, we choose the same 1.0 m for east-west separation and 1.9 m (2.5 + 1.0 \(-\) 1.6) for north-south separation (so the same 1.0 m separation is obtained if the heliostats are rotated 90\({}^{\circ}\)). In our simulations, we also check if the four mirror vertices are touching the ground or neighboring mirrors. (5) For the 66-heliostat field just proposed, where shall the target be positioned to avoid significant blocking/shading effects? We choose to initially position the target 15 m high, 10 m away from the center of the closer row of heliostats, similar to the target built for the IMDEA Energy heliostat field at the Technology Park of Mostoles, Spain [26]. Simulating afterwards the radiation received throughout the year (particularly in winter), we can acquire insightful information and make adjustments to the target position accordingly. (6) Assuming that we choose a spherical curvature for the heliostats, what should the deflection be (2 cm, 1 cm, or 0.5 cm)? The actual choice depends on the average distance from the heliostats to the target, which in our case ranges from 21.3 m (square heliostats, 10\({}^{\circ}\) slope) to 24.3 m (rectangular heliostats, no slope). For example, in the 169-heliostat field of IMDEA, Madrid, two different curvatures were used, for heliostats closer to and farther from the target [12]. In our case, for the 2.0 m \(\times\) 2.0 m square heliostats, the focal distance is 24.8 m for 2.0 cm and 49.7 m for 1.0 cm, while for the 2.5 m \(\times\) 1.6 m rectangular heliostats, the focal distance is 27.4 m for 2.0 cm and 54.8 m for 1.0 cm. For the sake of simplicity, we choose to use the same deflection for all heliostats (so closer heliostats produce larger, less concentrated target images). We choose 1.0 cm for deflection, as we do not want to focus the radiation at the target, only to slightly concentrate the radiation. (We do not want to melt the target!) (7) Finally, we need to set the location of the heliostat field, as the latitude plays a significant role in determining the sun's trajectory over the local site throughout the year. For this work, we selected the two locations with higher and lower latitude from the list reported by SFERA-III [27] for European Union CSP research infrastructures with heliostat fields: Julich, Germany (latitude = 50.9133\({}^{\circ}\), longitude = 6.3878\({}^{\circ}\)), and Protaras, Cyprus (latitude = 35.0125\({}^{\circ}\), longitude = 34.0583\({}^{\circ}\)). This 15\({}^{\circ}\) difference in latitude between the two locations is enough to produce insightful changes between the two sets of results. A second group of choices must also be considered regarding working conditions:  
(i) It seems logical to scan a full year, from 1 st January to 31 st December, for instance 2024. But what should the scanning frequency be? Every hour seems a good compromise, to detect blocking and shading events, as the danger of losing significant events seems small, and the needed computing time is not impossibly high (for this particular task, using 10\({}^{6}\) rays is acceptable, as we are not attempting to create a very accurate image of the radiation on the target; we are only checking for interception events). To obtain an accurate measurement of the total mechanical rotations made and the maximum mechanical angles achieved, every minute or every 5 min is probably needed (no time-consuming ray tracing is involved, as we only need to orientate the heliostats). (ii) What is the daily working range? We choose the range of 08:00 to 16:00 LCT time (i.e., local time). This depends on the date and latitude, but for most common places, it seems a reasonable choice. We note that throughout this work, we ignore daylight saving time (DST) and other purely administrative or political changes to standard local time. (iii) The heliostats should start every day from the flat resting position and come back to this position at the end of the day (mostly to protect the heliostats from strong winds during the night).