Mathematical model of external ballistics of projectiles

Abstract

The paper presents mathematical model of external ballistics of projectile, fired from cannon. The drag force has a decisive influence on the dynamics of the projectile. Direct calculation of the functional dependence of the drag force on the set of parameters is quite controversial and has not been utilized so far. Therefore, the author calculus the functional relativity, approximately, solving the inverse problem of mechanics. The flight range of a projectile at certain aiming angles, noted in the firing tables, determine the drag force according to the effect on a projectile of its weight and Coriolis force. Its functional dependence is described separately at the stages of projectile’s motion with supersonic, transonic and subsonic velocities. Due to the functional dependence of the drag force of a projectile, the influence of a charge projectile, initial velocity, atmospheric pressure, air temperatures and projectile’s mass effect on kinematic parameters of its motion can be calculated. Knowledge of this dependence of the drag force of the projectile’s movement allows to automate, using appropriate software, the determination of the elevation angle depending on the location of the target and the values of deterministic and nondeterministic factors.