## 8 Conclusions  
1. The heliostats' orientation must be updated at least once a minute to adequately follow the sun's trajectory. 2. The daily rotation curves are quite symmetrical for both the primary and secondary axes, as well as for the azimuth-elevation and tilt-roll models. 3. In azimuth-elevation models, the primary axis controls azimuth, and the secondary axis controls altitude. In tilt-roll models, the primary axis controls altitude, and the secondary axis controls azimuth. 4. The daily rotation curves are strikingly similar in both the azimuth-elevation and tilt-roll models, for the axes controlling azimuth and the axes controlling altitude. 5. Tilt-roll models are more efficient than azimuth-elevation models, requiring smaller angular ranges and smaller angular rotations throughout a full working year, every day from 08:00 to 16:00 LCT. 6. When the daily working period is defined without taking into account the local longitude, westerly and easterly heliostats require different rotations, even when symmetrically located in the heliostat field. 7. Front and back row heliostats have significantly different mechanical requirements. Front heliostats are notoriously more difficult to orient in TA/AE models, particularly at low sun altitudes (in the morning, during winter, at high latitudes). 8. The yearly rotation curves indicate that to achieve orientation, azimuth-elevation heliostats rotate more in summer, while tilt-roll heliostats rotate more in winter. 9. Axial-based azimuth-elevation and tilt-roll models exhibit similar performance to that of the (more complex) equivalent radial-based models. 10. Target-aligned models with tilt-roll rotations work better than the tilt-roll model. Target-aligned models with azimuth-elevation rotations perform worse than the azimuth-elevation model. In the limit, target-aligned models with azimuth-elevation rotations might be vulnerable to numerical inaccuracies. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Location**} & \multirow{2}{*}{**Angle**} & \multicolumn{6}{c}{**Heliostat**} \\ \cline{3-8}  & & **SW** & **S** & **SE** & **NW** & **N** & **NE** \\ \hline \multirow{2}{*}{Jülich} & \(\alpha\) Min (\({}^{\circ}\)) & \(-15.96\) & \(-16.71\) & \(-16.89\) & \(-5.75\) & \(-5.90\) & \(-6.66\) \\  & \(\alpha\) Max (\({}^{\circ}\)) & \(42.77\) & \(13.98\) & \(36.93\) & \(32.93\) & \(23.37\) & \(31.00\) \\ \hline \multirow{2}{*}{Protaras} & \(\alpha\) Min (\({}^{\circ}\)) & \(-11.52\) & \(-12.23\) & \(-14.33\) & \(-0.84\) & \(-2.23\) & \(-3.69\) \\  & \(\alpha\) Max (\({}^{\circ}\)) & \(46.79\) & \(18.82\) & \(43.62\) & \(38.51\) & \(31.26\) & \(38.01\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Minimum and maximum \(\alpha\) angles for the TA/TR model, for Julich and Protaras, and for the six representative heliostats: SW, S, SE, NW, N, and NE (see Figure 8). \(\alpha\) Min is more negative for the front row and for Julich. 11. Parking heliostats at the end of each working day significantly increases the total mechanical rotations for the axis controlling altitude in both azimuth-elevation and tilt-roll models. The wide range of significant conclusions achieved in this work shows that accurate computer modeling of large solar facilities is essential for improving our knowledge of the mechanical (and optical) aspects involved, decreasing costs, and maximizing economic efficiency. J.C.G.P., conceptualization, methodology, software, data curation, validation, and writing--original draft preparation. L.G.R., formal analysis, validation, writing--review and editing, project administration, and funding acquisition. All authors have read and agreed to the published version of the manuscript. This work benefited from financial support from the European Union through the SFERA-III project, Grant Agreement No. 823802 (proposal SURPF2101310018-CAHO \"Development of Computer Algorithms to Optimize Heliostat Orientation\").