Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Egorov S. F., Vdovin A. Y. Investigation of the need to use the variable value of the ballistic coefficient when modeling the trajectory of the bullet in the shooter simulator. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2023, vol. 23, iss. 2, pp. 253-263. DOI: 10.18500/1816-9791-2023-23-2-253-263, EDN: IXKNHK

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
31.05.2023
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Language: 
Russian
Heading: 
Computer Sciences
Article type: 
Article
UDC: 
004.94
DOI: 
10.18500/1816-9791-2023-23-2-253-263
EDN: 
IXKNHK

Investigation of the need to use the variable value of the ballistic coefficient when modeling the trajectory of the bullet in the shooter simulator

Autors: 
Egorov Stanislav F., Udmurt Federal Research Center of the Ural Branch of the RAS
Vdovin Aleksey Yu., Kalashnikov Izhevsk State Technical University
Abstract: 

When developing electronic shooting simulators for manual automatic weapons that do not use ammunition, it is necessary to achieve the maximum realistic modeling of the bullet flight path for each shot taking into account a set of factors. Traditionally, a system of differential equations of outer ballistics is used in modeling the trajectory. The use of a constant value of the ballistic coefficient in such a mathematical model does not allow to achieve high accuracy of modeling the trajectory for such important for solving the “task of the meeting” parameters as complete flight time and excess of the trajectory for all targeted range of small arms. The initial values in the mathematical model based on the system of differential equations of the outer ballistic are the casting angle (depends on the settings of the sight), the initial speed and the ballistic coefficient of the bullet, and such parameters as the current excess, range, time, speed and direction are calculated. Estimates of the errors of the calculation of the coordinates of the ballistic trajectory at various approaches to the use of the value of the ballistic coefficient are given. It is concluded that at the moment when modeling the flight trajectory of the bullet, simplification based on the use of a constant value of the ballistic coefficient is quite justified but with the relevant requirements of the tactical and technical task the study of ways to increase the accuracy of the trajectory modeling will become relevant. One of these paths is  using the value of the ballistic coefficient, depending on the casting angle proposed in this article.

Key words: 
ballistic coefficient
external ballistics
mathematical model
bullet flight path
shooting simulator
References: 
  1. Munoz J. E., Pope A. T., Velez L. E. Integrating biocybernetic adaptation in virtual reality training concentration and calmness in target shooting. Physiological Computing Systems. Lecture Notes in Computer Science, vol. 10057. Cham, Springer, 2019, pp. 218–237. https://doi.org/10.1007/978-3-030-27950-9_12
  2. Labr M., Hagara L. Using open source on multiparametric measuring system of shooting. 2019 International Conference on Military Technologies (ICMT). Brno, Czech Republic, 2019, pp. 1–6. https://doi.org/10.1109/MILTECHS.2019.8870093 
  3. Bogatinov D., Lameski P., Trajkovik V. Firearms training simulator based on low cost motion tracking sensor. Multimedia Tools and Applications, 2017, vol. 76, iss. 1, pp. 1403–1418. https://doi.org/10.1007/s11042-015-3118-z
  4. Gudzbeler G., Struniawski J. Functional assumptions of “Virtual system to improve shooting training and intervention tactics of services responsible for security” (VirtPol). Conference on Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments (Wilga, Poland), 2017, vol. 10445, Art. 104456M, 6 p. https://doi.org/10.1117/12.2281622
  5. Gudzbeler G., Struniawski J. Methodology of shooting training using modern IT techniques. Conference on Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments (Wilga, Poland), 2017, vol. 10445, Art. 104456L, 6 p. https://doi.org/10.1117/12.2281618
  6. Fan Y. C., Wen C. Y. A virtual reality soldier simulator with body area networks for team training. Sensors, 2019, vol. 19, iss. 3, Art. 451. https://doi.org/10.3390/s19030451
  7. de Armas C., Tori R., Netto A. V. Use of virtual reality simulators for training programs in the areas of security and defense: A systematic review. Multimedia Tools and Applications, 2020, vol. 79, pp. 3495–3515. https://doi.org/10.1007/s11042-019-08141-8
  8. Fedaravicius A., Pilkauskas K., Slizys E., Survila A. Research and development of training pistols for laser shooting simulation system. Defence Technology, 2020, vol. 16, iss. 3, pp. 530–534. https://doi.org/10.1016/j.dt.2019.06.018
  9. Maciejewski M., Piszczek M., Pomianek M., Palka N. Optoelectronic tracking system for shooting simulator — tests in a virtual reality application. Photonics Letters of Poland, 2020, vol. 12, iss. 2, pp. 61–63. https://doi.org/10.4302/plp.v12i2.1025
  10. Taylor P., Piszczek M., Pomianek M., Palka N. Dispatch priming and the police decision to use deadly force. Police Quarterly, 2020, vol. 23, iss. 3, pp. 311–332. https://doi.org/10.1177/1098611119896653
  11. Maciejewski M., Piszczek M., Pomianek M., Palka N. Design and evaluation of a SteamVR tracker for training applications – simulations and measurements. Metrology and Measurement Systems, 2020, vol. 27, iss. 4, pp. 601–614. https://doi.org/10.24425/mms.2020.134841
  12. Egorov S. F. Shooting simulator “Inhibitor”: functional scheme of the software. Intelligent Systems in Manufacturing, 2019, vol. 17, iss. 2, pp. 19–29 (in Russian). https://doi.org/10.22213/2410-9304-2019-2-19-29
  13. Egorov S. F., Vdovin A. Yu., Shelkovnikov Yu. K. Shooting simulator “Inhibitor”: Ballistics software for 5.45 caliber weapons. Intelligent Systems in Manufacturing, 2021, vol. 19, iss. 2, pp. 50–61 (in Russian). https://doi.org/10.22213/2410-9304-2021-2-50-61
  14. Egorov S. F., Vdovin A. Yu., Korobeinikova I. V., Petukhov K. Yu., Siakterev V. N. Shooting simulator “Inhibitor”: Mathematical support for ballistics of 7.62 caliber weapons. Intelligent Systems in Manufacturing, 2021, vol. 19, iss. 3, pp. 121–133 (in Russian). https://doi.org/10.22213/2410-9304-2021-3-121-133
  15. Tablitsy strel’by po nazemnym tselyam iz strelkovogo oruzhiya kalibrov 5.45 i 7.62 mm [Tables of Shooting at Ground Targets with Small Srms of 5.45 and 7.62 mm Calibers]. Moscow, Voenizdat, 1977. 264 p. (in Russian).
  16. Egorov S. F., Kazakov V. S., Korobeinikov V. V. Shooting simulator based on publicly available components. Intelligent Systems in Manufacturing, 2011, iss. 1 (17), pp. 182–185 (in Russian). EDN: NXVFQB
  17. Egorov S. F., Korobeinikov V. V., Kazakov V. S. Information-measuring systems for defense purposes: shooting simulators and electronic targets. Mekhanika i fiziko-khimiia geterogennykh sred, nanosistem i novykh materialov [Mechanics and Physico-chemistry of Heterogeneous Media, Nanosystems and New Materials]: Materials of Scientific Research. Izhevsk, Institute of Mechanics of the Ural Branch of the Russian Academy of Sciences Publ., 2015, pp. 328–349 (in Russian). EDN: ULMFGF
  18. Egorov S. F., Shelkovnikov Yu. K., Osipov N. I., Kiznertsev S. R., Meteleva A. A. Research of optical-electronic recorders of the aiming point of shooting simulators. Problemy mekhaniki i materialovedeniia. Trudy Instituta mekhaniki UrO RAN [Problems of Mechanics and Materials Science. Proceedings of the Institute of Mechanics of the Ural Branch of the Russian Academy of Sciences]. Izhevsk, Institute of Mechanics of the Ural Branch of the Russian Academy of Sciences Publ., 2017, pp. 227–248. EDN: ZFJKKF
  19. Ermolaev S. I., Komarov L. B., Churbanov E. V. Vneshnjaja ballistika [External Ballistic]. Leningrad, 1958. 716 p. (in Russian).
  20. Konovalov A. A., Nikolaev Yu. V. Vneshnjaja ballistika [External Ballistic]. Izhevsk, Institute of Applied Mechanics of the Ural Branch of the Russian Academy of Sciences Publ., 2003. 192 p. (in Russian).
  21. Gudich I. G., Kozlitin I. A. On the calculation of ballistic coefficients of bullets and shells. Elektronnye informatsionnye sistemy [Electronic Information Systems], 2015, iss. 4 (7), pp. 81–88. EDN: VLDHED
  22. Khaikov V. L. Mathematical model of external ballistics of a Dragunov sniper rifle based on the evaluation of ballistic coefficients according to the shooting tables. Voprosy oboronnoy tekhniki. Seriya 16: Tekhnicheskie sredstva protivodeystviya terrorizmu [Issues of Defense Technology. Series 16: Technical Means of Countering Terrorism], 2017, iss. 11–12 (113–114), pp. 16–23 (in Russian). EDN: ZVZGMF
  23. Chepkov I. B., Hurnovych A. V., Lapyts’kyi S. V., Oliiarnyk B. O., Trofymenko V. H., Maistrenko O. A. Method of conversion for the ballistic coefficient of bullets. Strength of Materials, 2020, vol. 52, pp. 419–422. https://doi.org/10.1007/s11223-020-00193-8 
Received: 
12.05.2022
Accepted: 
18.11.2022
Published: 
31.05.2023
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