## 5 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, as follows:  
1. How many heliostats should we model? Simulating the heliostat reflection and target collection through ray tracing requires significant computer time, so the number of heliostats investigated should be kept to a minimum. In this work, however, the research is concentrated on the mechanical rotations of the heliostats, so we only need to orient the heliostats. Therefore, the computer time required is much less than when studying shading/blocking effects. We choose to simulate the layout already used in our previous work [17] to obtain data results that are representative yet simple to analyze and report. This layout is shown in Figure 8, with a total of 66 heliostats in a staggering arrangement. Only the six end heliostats (in green, henceforth named SW, S, SE, NW, N, and NE) are independently oriented, as we identify them as representatives of the whole set. 2. Shall we simulate a horizontal field or a field with a south-north slope angle of \(10^{\circ}\) or \(20^{\circ}\)? Using a slope is more interesting, but choosing a horizontal flat terrain is simpler, closer on average to real land conditions, and better emphasizes the differences between the front and back heliostat rows. In our previous work, we aimed to study shading/blocking effects, so we extensively investigated \(0^{\circ}\) and \(10^{\circ}\) slopes [17]. In  
Figure 7: Pixel-based target rectangle (the collecting detector), perpendicular to the average sun radiation coming from the heliostat field (heliostats are represented in the rest position). The angle, \(\delta\), that the target should rotate depends of the heliostats layout and geometry, the ground slope, and the tower distance and height. this work on mechanical rotations, we want to avoid shading/blocking as much as possible, so we always used the more favorable 10\({}^{\circ}\) slope. 3. Should we use square or rectangular heliostats? Additionally, what dimensions should we use? Larger sizes provide more radiant energy but are less flexible to handle and require stronger mechanical structures to withstand the wind. Rectangular heliostats might handle wind better than square heliostats of the same area due to their lower height. In our previous work, we investigated square 2.0 m \(\times\) 2.0 m and rectangular 2.5 m \(\times\) 1.6 m heliostats, both with an area of 4 m\({}^{2}\) each (typical sizes in tilt-roll heliostat fields). In this work, we used both geometries (see Figure 9); however, for the mechanical rotation studies, the rectangular heliostats were chosen because they seem to be less affected by shading/blocking effects [17]. 4. What should be the distance between the heliostat mirrors in the resting, flat position? Land is expensive, so heliostats should be kept as close as possible (see, for example, [14; 26]) to maximize the collected power, but not closer, to avoid blocking and shading events and mechanical collisions. For square heliostats, we choose 1.0 m for both east-west and north-south separation. For 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 that the same 1.0 m separation is maintained 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 proposed 66-heliostat field, where should the target be positioned to avoid significant blocking/shading effects? We choose to position the target 15 m high and 10 m away from the center of the closer row of heliostats (similar to the target built for the heliostat field at the IMDEA Energy premises in Mestoles, Spain [26]).