Computer Study of the Mathematical Model of the Artillery Shot Process

Abstract

The article deals with the issue of computer research of the mathematical model of the artillery fire process. Russia’s war against Ukraine showed that the success of the Armed Forces of Ukraine (AFU) largely depends on artillery units. The effectiveness of the actions of the artillery units depends on the normal functioning of artillery weapons. 
 The phenomenon of the shot is characterized by short duration, high pressure and high temperature. The duration of the shot phenomenon is determined by tenths and even hundredths of a second. A pressure of up to 400 MPa and a temperature of more than 2000 С develop in the bore of the weapon.
 It should be noted that the processes of gunpowder combustion are very complex. They depend on the manufactures, namely, on the type of gunpowder, chemical composition, its type (geometry) and pressure. So, the process of gunpowder combustion is described by equations that were obtained experimentally. Such experiments were carried out a long time ago, so most of the constants currently used in the calculation of the combustion process are expressed in the old ICGSS system of units. Therefore, it should be taken into account in the calculations when determining, for example, the pressure in MPA.
 The mathematical model of the artillery shot process takes into account all the factors that affect the processes occurring in the barrel. The mathematical model of an artillery shot consists mainly of the gunpowder combustion equation, the energy conversion equation, the projectile motion equation, the initial and boundary conditions. The numerical solution of the given systems of equations was carried out by numerical methods and the differential equations were solved by the Runge-Kutta method. The obtained values of the maximum pressures of powder gases and their comparison with the experimental ones showed that the error does not exceed 3 % which confirms the adequacy of the mathematical model of the artillery shot. Thus, the proposed mathematical model of an artillery shot and the method of its solution can be used to study the influence of various parameters (gunpowder parameters, design parameter of the guns, mass of the projectile and others) on the processes occurring during a shot.