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  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
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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

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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.