## 7 Results and Discussion
### Mechanical Rotation Angles
This is expected since the sun's altitude changes significantly more in Protaras than in Julich throughout the day, both in summer and winter (see [25]). Figure 14: Total daily rotation (in degrees), adding the two angles for primary and secondary axes, for the six representative heliostats (SW, S, SE, NW, N, and NE), calculated for the azimuth-elevation mechanical model at Julich, for the whole year of 2024. Figure 16: Total daily rotation (in degrees), adding the two angles for primary and secondary axes, for the six representative heliostats (SW, S, SE, NW, N, and NE), calculated for the tilt-roll mechanical model at Jülich, for the whole year of 2024. Figure 15: Total daily rotation (in degrees), adding the two angles for primary and secondary axes, for the six representative heliostats (SW, S, SE, NW, N, and NE), calculated for the azimuth-elevation mechanical model at Protaras, for the whole year of 2024. For the AE model, both Julich and Protaras show that the westerly-oriented heliostats (SW, NW) rotate more, and the easterly-oriented heliostats (SE, NE) rotate less than the central heliostats (Figures 14 and 15). As discussed above, these significant differences occur because throughout the whole year, the sun's altitude is always lower at 16:00 LCT than at 08:00 LCT in Julich and Protaras, due to their eastern location in the time zone [25]. Therefore, the closer westerly-oriented heliostats at 16:00 LCT require more daily rotations than the farther easterly-oriented heliostats. It is important to note that in winter, it is night at 16:00 LCT in Julich (the sun's altitude is negative) (see [25] for more details), so the mechanical rotations needed slightly decrease. Daily rotations in the AE models are larger in summer, when the sun's trajectory reaches greater ranges of altitude and azimuth (Figures 14 and 15). Interestingly, the opposite occurs in the TR models because the smaller rotations needed in TR models are more affected by low Sun trajectories in winter, making orientation more difficult (Figures 16 and 17). In the TR model, both in Julich and Protaras, the southern heliostats (SW, S, and SE), which are closer to the target, rotate less than the northern heliostats (NW, N, and NE). However, this trend is not observed in the azimuth-elevation model, where the heliostat that rotates more is the SW, and the heliostat that rotates less is the SE. Figures 16 and 17 show that in spring and autumn, the three southern heliostats (SW, S, and SE) in the TR model experience a sudden slight increase in total rotation (\(\alpha+\beta\)) toward the winter direction, which is almost discontinuous. This increase is only due to the primary angle \(\alpha\) (which controls altitude) and occurs around 4 March and 5 October in Julich and around 8 April and 5 September in Protaras. These dates are not associated with any notable astronomical dates for Julich or Protaras [25]. Figure 17: Total daily rotation (in degrees), adding the two angles for primary and secondary axes, for the six representative heliostats (SW, S, SE, NW, N, and NE), calculated for the tilt-roll mechanical model at Protaras, for the whole year of 2024.