The Mathematical Model of the Study of Free Movement of Weapons on the Example of Kalashnikov Assault Rifles

Abstract

The reason for the dispersion of shots in automatic shooting is the heterogeneity of the interaction of weapons, deviating from the point of sight under the influence of force factors, and the shooter compensating these deviations, if possible. A mathematical model of the study of free (without the shooter) spatial movement of weapons, taking into account the gas-dynamic processes in weapons, emerging power factors, strikes at automation at their location outside the center of mass of the shooter. In the calculation scheme of the mathematical model, the location of the center of rotation of the weapon, pressed to the shoulder and fixed relative to it, on the axis of symmetry of the shooter in the center of its mass when removing the shoulder thrust at objective distances along the side and height, characteristic for the average shooter. The location of power factors typical for the operation of automation is determined by the layout of the mechanisms of weapons. The force factors acting in the weapon and influencing its movement in space, creating tipping or stabilizing moments relative to the center of mass of the shooter, are indicated. The equations are made up for rotational motion of the weapon according to the shock interactions in the extreme positions of the bolt and when the bolt is unlocked, and kinematic equations defining the rotation angles of the weapon, and also deviation of hitting points falling from the aiming point. These elements are taken into account in the block diagram of the system of equations that determine the movement of the machine with the removal of powder gases. The output data are the values of the tipping moments and deviations from the point of sight of the weapon, allowing us to consider the stability of the weapon in shooting as a background scattering when the shooter is present. The developed model is used to assess the effectiveness of measures to stabilize the AK-47 in space: reducing the caliber to decrease the impact pulse and the use of muzzle gas devices.