IDEAS home Printed from https://ideas.repec.org/a/eee/renene/v172y2021icp1333-1340.html
   My bibliography  Save this article

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 point and atan2 function

Author

Listed:
  • Zhang, Taiping
  • Stackhouse, Paul W.
  • Macpherson, Bradley
  • Mikovitz, J. Colleen

Abstract

A conceptually and mathematically concise formula for computing the solar azimuth angle has been used by a subgroup of scientists, but for lack of documentation and publication, it has not been well circulated. This paper introduces this formula which is based on the idea of a unit vector, S, originating from the observer’s location and pointing toward the center of the Sun. The vector is completely determined by the coordinates of the subsolar point and of the observer. The x- and y-components of the vector determine the solar azimuth angle, and their use along with the function atan2, which is available in a number of programming/scripting languages, including Fortran and Python, renders any circumstantial treatment absolutely unnecessary. The z-component of the vector, at the same time, determines the solar zenith angle. The use of the unit vector also facilitates a figure that can be used as a full 3D graphic depiction of the daily and annual cycles of the Sun’s position for any given location, and this figure can be called “wreath of analemmas”.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:renene:v:172:y:2021:i:c:p:1333-1340
    DOI: 10.1016/j.renene.2021.03.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960148121004031
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.renene.2021.03.047?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Soulayman, S., 2018. "Comments on solar azimuth angle," Renewable Energy, Elsevier, vol. 123(C), pages 294-300.
    2. Sproul, Alistair B., 2007. "Derivation of the solar geometric relationships using vector analysis," Renewable Energy, Elsevier, vol. 32(7), pages 1187-1205.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. João R. B. Paiva & Alana S. Magalhães & Pedro H. F. Moraes & Júnio S. Bulhões & Wesley P. Calixto, 2021. "Stability Metric Based on Sensitivity Analysis Applied to Electrical Repowering System," Energies, MDPI, vol. 14(22), pages 1-21, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Soulayman, S., 2018. "Comments on solar azimuth angle," Renewable Energy, Elsevier, vol. 123(C), pages 294-300.
    2. 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.
    3. Soulayman, S. & Hammoud, M., 2018. "Performance of the east–west oriented single-axis tracked collector," Energy, Elsevier, vol. 155(C), pages 1090-1092.
    4. 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).
    5. Shapiro, Finley R., 2022. "The position of the sun based on a simplified model," Renewable Energy, Elsevier, vol. 184(C), pages 176-181.
    6. 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).
    7. Maria Nunez Munoz & Erica E. F. Ballantyne & David A. Stone, 2023. "Assessing the Economic Impact of Introducing Localised PV Solar Energy Generation and Energy Storage for Fleet Electrification," Energies, MDPI, vol. 16(8), pages 1-27, April.
    8. 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.
    9. Ali Saleh Aziz & Mohammad Faridun Naim Tajuddin & Mohd Rafi Adzman & Makbul A. M. Ramli, 2021. "Impacts of albedo and atmospheric conditions on the efficiency of solar energy: a case study in temperate climate of Choman, Iraq," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(1), pages 989-1018, January.
    10. 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.
    11. 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.
    12. 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.
    13. Wu, Jing & Zhang, Ling & Liu, Zhongbing & Luo, Yongqiang & Wu, Zhenghong & Wang, Pengcheng, 2020. "Experimental and theoretical study on the performance of semi-transparent photovoltaic glazing façade under shaded conditions," Energy, Elsevier, vol. 207(C).
    14. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:renene:v:172:y:2021:i:c:p:1333-1340. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/renewable-energy .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.