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Derivation of the solar geometric relationships using vector analysis

Author

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  • Sproul, Alistair B.

Abstract

The standard mathematical approach used in deriving equations to describe the apparent motion and position of the Sun is spherical trigonometry. Additionally, the derivation of the equations for the intensity of the direct beam radiation, incident on the surface of a solar collector or architectural surface, also generally relies on the same approach. An alternative approach utilizing vector analysis is used to derive all of these equations. The technique greatly simplifies the derivation of equations for quantities such as the declination, altitude and azimuth of the Sun, and the intensity of the direct beam radiation on a tilted panel with an arbitrary orientation. Additionally, it allows a simple derivation of the equations needed to accurately describe the Equation of Time and the right ascension.

Suggested Citation

  • Sproul, Alistair B., 2007. "Derivation of the solar geometric relationships using vector analysis," Renewable Energy, Elsevier, vol. 32(7), pages 1187-1205.
    • Handle: RePEc:eee:renene:v:32:y:2007:i:7:p:1187-1205
    DOI: 10.1016/j.renene.2006.05.001
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    Cited by:

    1. Mendoza Castellanos, Luis Sebastian & Carrillo Caballero, Gaylord Enrique & Melian Cobas, Vladimir Rafael & Silva Lora, Electo Eduardo & Martinez Reyes, Arnaldo Martin, 2017. "Mathematical modeling of the geometrical sizing and thermal performance of a Dish/Stirling system for power generation," Renewable Energy, Elsevier, vol. 107(C), pages 23-35.
    2. Rapp-Arrarás, Ígor & Domingo-Santos, Juan M., 2009. "Algorithm for the calculation of the horizontal coordinates of the Sun via spatial rotation matrices," Renewable Energy, Elsevier, vol. 34(3), pages 876-882.
    3. Luo, Yongqiang & Zhang, Ling & Wu, Jing & Wang, Xiliang & Liu, Zhongbing & Wu, Zhenghong, 2017. "Modeling of solar transmission through multilayer glazing facade using shading blinds with arbitrary geometrical and surface optical properties," Energy, Elsevier, vol. 128(C), pages 163-182.
    4. Nsengiyumva, Walter & Chen, Shi Guo & Hu, Lihua & Chen, Xueyong, 2018. "Recent advancements and challenges in Solar Tracking Systems (STS): A review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 250-279.
    5. Copper, J.K. & Sproul, A.B. & Bruce, A.G., 2016. "A method to calculate array spacing and potential system size of photovoltaic arrays in the urban environment using vector analysis," Applied Energy, Elsevier, vol. 161(C), pages 11-23.
    6. Chandra Mouli, G.R. & Bauer, P. & Zeman, M., 2016. "System design for a solar powered electric vehicle charging station for workplaces," Applied Energy, Elsevier, vol. 168(C), pages 434-443.
    7. Zhu, Yongqiang & Liu, Jiahao & Yang, Xiaohua, 2020. "Design and performance analysis of a solar tracking system with a novel single-axis tracking structure to maximize energy collection," Applied Energy, Elsevier, vol. 264(C).
    8. Shapiro, Finley R., 2022. "The position of the sun based on a simplified model," Renewable Energy, Elsevier, vol. 184(C), pages 176-181.
    9. Soulayman, S., 2018. "Comments on solar azimuth angle," Renewable Energy, Elsevier, vol. 123(C), pages 294-300.
    10. Zech, Matthias & von Bremen, Lueder, 2024. "End-to-end learning of representative PV capacity factors from aggregated PV feed-ins," Applied Energy, Elsevier, vol. 361(C).
    11. Zhang, Taiping & Stackhouse, Paul W. & Macpherson, Bradley & Mikovitz, J. Colleen, 2021. "A solar azimuth formula that renders circumstantial treatment unnecessary without compromising mathematical rigor: Mathematical setup, application and extension of a formula based on the subsolar poin," Renewable Energy, Elsevier, vol. 172(C), pages 1333-1340.

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