1. Science
2. Publications
3. Systems of Arms and Military Equipment
4. 1(57)'2019
5. Mathematical model definition the functional dependence of the force of air drag on the movement of the projectile

#### Mathematical model definition the functional dependence of the force of air drag on the movement of the projectile

L. Velychko, M. Voytovych, M. Sorokatiy
Annotations languages:

Description: Theoretical studies of determining the components of the air resistance forces of the projectiles are quite complex and do not always give the desired accuracy of calculations. Consequently, the main methods of their definition are experimental research. The most common is the carrying out of special firing at landfills. This method allows the best estimate of the strength of the air resistance, but this is not enough. Therefore, when firing on land targets artillery projectiles use firing tables, which are based on experimental research. In case of firing at different from normal meteorological conditions, it is necessary to make corrections. Formulas for determining their quantities are obtained, mainly, by the decomposition of the corresponding dependences in the Taylor series, taking into account its first members. If the values of the parameters change slightly, then the value of the corrections give a small difference with the practice of their application. However, in opposite cases, the differences become significant. The article deals with the mathematical model of the determination of the functional dependence of the magnitude of the frontal air resistance force on its velocity, mass and caliber, temperature and air density, atmospheric pressure, air velocity. Functional dependence, although it has the same form of recording when the projectiles move with supersonic or subsonic velocities, however, the values of their coefficients are different. To determine their values, the inverse problem of dynamics is solved, that is, knowing the results of experimental studies for a given type of projectiles by the iteration method, their values are selected. Based on the proposed mathematical model, the kinematic parameters of the motion of the fragmentation-explosive projectiles ОФ45 caliber of 152 mm the fourth charge released from the howitzers 2А65 were determined. The differences between the kinematic parameters of the projectiles motion which are determined theoretically, using the proposed mathematical model, and experimentally are within 1% when shooting at a horizontal distance of less than 9200 meters. When shooting at a distance of 9400 - 10609 meters, the error exceeds 1%. The proposed mathematical model for determining the functional dependence of the value of the frontal air resistance force of the projectiles movement allows us to investigate the influence of deterministic and non-deterministic factors on the kinematic parameters of the projectile movement, that is, to determine the magnitudes of corrections, and to create of appropriate software.

Keywords: artillery, external ballistics of projectiles, air resistance force, temperature of the air and of the charge

#### References

1. Chernozubov, A.D., Kyrychenko, A.D., Razin, I.I. and Mykhajlov, K.V. (1954), “Vneschnaya balistica. Chast 1” [External
ballistics. Part I], Printing house of the Artillery Engineering Academy, Moscow, 467 p.
2. Chernozubov, A.D., Kyrychenko, A.D., Razin, I.I. and Mykhajlov, K.V. (1954), “Vneschnaya balistica. Chast ІI” [External
ballistics. Part II], Printing house of the Artillery Engineering Academy, Moscow, 501 p.
3. Grabchak, V.I. and Bondarenko, S.V. (2013), “Analiz isnuyuchyh ta perspektyvnyh metodiv vyznachennya syly oporu
povitrya ruchu snaryadiv” [Analysis of existing and perspective methods for determining the air resistance force of the projectiles
movement], Military Technical Collection, No. 2(9), pp. 13-19.
4. Tkachuk, P.P., Velychko, L.D. and Horchynskiy, I.V. (2018), “Vplyv vitru na zovnishnu balistyku kuli vypeshchenoi z
SVD” [Wind influence on the exterior ballistics of the bullet movement released from SVD], Military Technical Collection,
No. 19, pp. 43-49.
5. Velychko, L.D. and Horchynskyj, I.V. (2018), “Vyznachennya velychyny syly lobovogo oporu povitrya kuli vypushhenoyi
z kulemetiv PK, PKB, PKS i PKT” [Determination of the air resistance force of the bullets released from PK, PKB, PKS
and PKT], Military Technical Collection, No. 18, pp. 26-30.
6. Zygmunt, B., Motyl, K., Machowski, B., Makowski, M., Olejniczak, E. and Rasztabiga, T. (2015), Theoretical and experimental
research of supersonic missile ballistics, Bulletin of the Polish Academy Of Sciences Technical Sciences, No. 63(1),
pp. 229-233. https://doi.org/10.1515/bpasts-2015-0027.
7. Stepanov, E. and Vavilov S. (1997), The main problem of external ballistics, Computers Math. Application, No. 33(5),
pp. 95-101. https://doi.org/10.1016/S0898-1221(97)00022-9.
8. Cech, V., Jedlicka, L. and Jevicky, J. (2014), Problem of the reference height of the projectile trajectory as a reduced
meteo-ballistic weighting factor, Defence Technology, No. 10, pp. 131-140. https://doi.org/10.1016/j.dt.2014.06.002.
9. Ke Liang, Zheng Huang and Jing-min Zhang (2017), Optimal design of the aerodynamic parameters for a supersonic
two-dimensional guided artillery projectile, Defence Technology, No. 13, pp. 206-211. https://doi.org/10.1016/j.dt.2017.05.003.
10. Albertas Pincevičius, Vaclovas Jonevičius and Romualdas Baušys (2011), External ballistics task modeling features,
Aviation, No. 15(4), pp. 112-116. https://doi.org/10.3846/16487788.2011.648311.
11. Surdu, George and Slămnoiu, Georgică (2015), Considerations on efficiency in experimental tests specific for projectiles
of low caliber, Procedia Economics and Finance, No. 32, pp. 899-905. https://doi.org/10.1016/S2212-5671(15)01541-5.
12. Tutorial (2017), “Tablyczy strelby 152-mm prychipnoi gaubytsi 2F65, 152-mm samochidnoi gaubytsi 2С19, TS № U
00001” [The firing tables 152 mm trailer sofa 2F65, 152 mm, self-propelled howitzers 2С19], Lviv, 760 p.

Reference:
﻿ Velychko, L.D., Voitovych, M.I. and Sorokatyi, M.I. (2019), “Matematychna model vyznachennia funktsionalnoi zalezhnosti velychyny syly lobovoho oporu povitria rukhovi snariadu” [Mathematical model definition the functional dependence of the force of air drag on the movement of the projectile], Systems of Arms and Military Equipment, No. 1(57), pp. 62-68. https://doi.org/10.30748/soivt.2019.57.09.