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

S. F. Egorov ; A. Yu. Vdovin

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 23 (2023) no. 2, pp. 253-263.

Résumé

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.

Bibliographie

[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, 10057, Springer, Cham, 2019, 218–237 | DOI

[2] Labr M., Hagara L., “Using open source on multiparametric measuring system of shooting”, International Conference on Military Technologies (ICMT) (Brno, Czech Republic, 2019), 2019, 1–6 | DOI

[3] Bogatinov D., Lameski P., Trajkovik V., “Firearms training simulator based on low cost motion tracking sensor”, Multimedia Tools and Applications, 76:1 (2017), 1403–1418 | DOI

[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), Proc. SPIE, 10445, 2017, 104456M, 6 pp. | DOI

[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), Proc. SPIE, 10445, 2017, 104456L, 6 pp. | DOI

[6] Fan Y. C., Wen C. Y., “A virtual reality soldier simulator with body area networks for team training”, Sensors, 19:3 (2019), 451 | DOI

[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, 79 (2020), 3495–3515 | DOI

[8] Fedaravicius A., Pilkauskas K., Slizys E., Survila A., “Research and development of training pistols for laser shooting simulation system”, Defence Technology, 16:3 (2020), 530–534 | DOI

[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, 12:2 (2020), 61–63 | DOI

[10] Taylor P., Piszczek M., Pomianek M., Palka N., “Dispatch priming and the police decision to use deadly force”, Police Quarterly, 23:3 (2020), 311–332 | DOI

[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, 27:4 (2020), 601–614 | DOI | MR

[12] Egorov S. F., “Shooting simulator “Inhibitor”: functional scheme of the software”, Intelligent Systems in Manufacturing, 17:2 (2019), 19–29 (in Russian) | DOI

[13] Egorov S. F., Vdovin A. Yu., Shelkovnikov Yu. K., “Shooting simulator “Inhibitor”: Ballistics software for 5.45 caliber weapons”, Intelligent Systems in Manufacturing, 19:2 (2021), 50–61 (in Russian) | DOI

[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, 19:3 (2021), 121–133 (in Russian) | DOI

[15] Tables of Shooting at Ground Targets with Small Srms of 5.45 and 7.62 mm Calibers, Voenizdat, M., 1977, 264 pp. (in Russian)

[16] Egorov S. F., Kazakov V. S., Korobeinikov V. V., “Shooting simulator based on publicly available components”, Intelligent Systems in Manufacturing, 2011, no. 1(17), 182–185 (in Russian)

[17] Egorov S. F., Korobeinikov V. V., Kazakov V. S., “Information-measuring systems for defense purposes: shooting simulators and electronic targets”, Mechanics and Physico-chemistry of Heterogeneous Media, Nanosystems and New Materials, Materials of Scientific Research, Institute of Mechanics of the Ural Branch of the Russian Academy of Sciences Publ, Izhevsk, 2015, 328–349 (in Russian)

[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”, Problems of Mechanics and Materials Science, Proceedings of the Institute of Mechanics of the Ural Branch of the Russian Academy of Sciences, Institute of Mechanics of the Ural Branch of the Russian Academy of Sciences Publ, Izhevsk, 2017, 227–248

[19] Ermolaev S. I., Komarov L. B., Churbanov E. V., External Ballistic, L., 1958, 716 pp. (in Russian)

[20] Konovalov A. A., Nikolaev Yu. V., External Ballistic, Institute of Applied Mechanics of the Ural Branch of the Russian Academy of Sciences Publ, Izhevsk, 2003, 192 pp. (in Russian)

[21] Gudich I. G., Kozlitin I. A., “On the calculation of ballistic coefficients of bullets and shells”, Electronic Information Systems, 2015, no. 4(7), 81–88

[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”, Issues of Defense Technology. Series 16: Technical Means of Countering Terrorism, 2017, no. 11–12(113–114), 16–23 (in Russian)

[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, 52 (2020), 419–422 | DOI