# Computer Modelling of Heliostat Fields by Ray-Tracing Techniques: Simulating the Sun
## 6 Conclusions  
1. Writing robust software, accurate, as simple as possible, to calculate the Sun's position is crucial to simulate solar-concentrating facilities such as heliostat fields, solar furnaces, linear Fresnel and cylinder-parabolic concentrators. The software described here, including the ray-tracing techniques to generate randomized solar vectors, can be used to simulate heliostat fields, for a variety of layout and mechanical conditions, as will be reported in future publications.
2. A simplified description of a well-known step-by-step algorithm developed by the astronomy community to calculate the Sun's position is first reported. According to the community, the output coordinates have an average accuracy of 1 arch minute, which should be enough for most thermal applications.
3. Our C computer language implementation of this algorithm was successfully validated against official astronomy sources, for all 366 days and nine sampling moments (from 08:00 up to 16:00 LCT time) involved in our study of heliostat fields, for Julich and Protaras, the two locations chosen from the SFERA-III list of EU solar facilities with heliostat fields.
4. To simulate solar facilities all that is needed is to calculate a vector pointing to the Sun, as a function of latitude, longitude, time, and date. In general, this software allows the calculation of altitude and azimuth data, sunrise and sunset data, analemma curves, and angular speed data, as exemplified here. The results obtained for solar trajectories along the year for Julich and Protaras show that altitude and azimuth change in a complex way, producing two maxima and minima for azimuth and one maximum and minimum for altitude, as shown by the analemma curves.
5. The ideal time schedule for an optimized solar-concentrating facility depends on the local longitude, as this affects Sun's altitude at working hours.
6. The Sun's angular speed measured from the observer's position is continuously changing, because the plane defined by the Sun's circular daily trajectory around the Earth is continuously moving, only including the observer's position at the spring and autumn equinoxes.  
Figure 14: Sun’s trajectory throughout the year of 2024, calculated at true midday, for Julich (11 h 34 min 26.93 s LCT time) and Protaras (11 h 43 min 46.01 s LCT time). Each dot represents one of the 366 days of 2024 (leap year). The two images are represented at the same scale so they can be easily compared.  
**Author Contributions:** J.C.G.P. conceptualization, methodology, software, data curation, validation, writing--original draft preparation. G.D. original draft preparation, formal analysis, data curation, visualization. L.G.R. validation, writing--review and editing; project administration and funding acquisition. All authors have read and agreed to the published version of the manuscript.  
**Funding:** 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\"). The authors would like to thank the Fundacao para a Ciencia e a Tecnologia (FCT) for its financial support through the LAETA Base Funding (DOI: 10.54499/UIDB/50022/2020).  
**Data Availability Statement:** The software source code and data supporting the conclusions of this article will be made available by the authors on request.  
**Acknowledgments:** The authors would like to thank The Cyprus Institute for providing access to its installations and the support of its scientific and technical staff in 2022, in the frame of the European Union SFERA-III project (Grant Agreement No 823802).  
**Conflicts of Interest:** The authors declare no conflicts of interest.