Mathematical Model of the Uncontrolled Bullet’s Motion in the Air with the Resistance Forces Assigned as Approximating Functions

Abstract

The paper is devoted to the actual problem of increasing the accuracy of automatic short shooting bursts. Particular attention is paid to the description of a new method of increasing the accuracy of short shooting bursts, in which bullets with constructional features move along an altering trajectory in a given direction. The method described assumes that at a certain distance all of three bullets can hit one point or provide an effective dispersion law that allows to improve the effectiveness of target hitting and its defeat. This makes possible to significantly increase the fire accuracy from Kalashnikov conventional assault rifles of usual calibers or advanced small arms using even more powerful cartridges. The main content of the research is the development of a mathematical model of the bullet’s motion in the air in a three-dimensional space with resistance forces given in the approximating functions form. Considerable attention is paid to determining the resistance forces acting on the bullet in the air flow without calculating the ballistic coefficients and the method they are represented in the mathematical model for calculating the motion’s trajectory. Based on the system of differential equations of motion complied in this paper, the bullet’s external ballistics of the 7N6 cartridge is calculated and the relative errors of the main parameters of trajectory are analyzed. In conclusion, the main results of the performed work are presented and the necessity of expanding the system of differential equations for studying external ballistics of a wider range of bullets with different constructional features is substantiated.