СИЛА ТА МОМЕНТ СИЛИ МАГНУСА. ЇХ ВПЛИВ НА ДАЛЬНІСТЬ СТРІЛЬБИ 155-ММ СНАРЯДІВ

Abstract

An important component of the main vector of aerodynamic forces and moments of the projectile is the force and moment from the Magnus force, which significantly affect the dynamics of the projectile flight. At the same time, the influence of the Magnus force and moment on the flight of projectiles has been studied relatively little, in addition, the leading scientists of Ballistic Research Laboratories (USA) published quantitative indicators achieved during its calculations, which do not fully meet the requirements for the accuracy of their determination. It is shown that the Magnus force and moment depend on the density of the air, the angular velocity of rotation and the velocity of the projectile, the lateral surface and diameter of the projectile, as well as the angle of its nutation. To evaluate the influence of the Magnus force and moment (their aerodynamic coefficients) on the range of the projectile, a difference method is used, which consists in solving the system of differential equations of spatial motion of a projectile so that changing the value of the aerodynamic coefficient results in a change in the value of the flight range. Numerical modeling of the dependence of the flight range of the 155-mm PF Assegai M2000 projectile and the 155-mm PF ERFB/BB projectile on the change in the magnitude of aerodynamic force and Magnus moment coefficients by 1 % was carried out. It is shown that the aerodynamic force coefficient of Magnus creates the largest errors in the range at the minimum charge, the deviation reaches – 0,005 %, the smallest at the maximum charge – 0,003 %. The largest error in the flight range of the projectile from the aerodynamic coefficient of the Magnus moment is observed at the minimum charge, the deviation reaches 0,6 % D; the effect on other charges leads to much smaller deviations, which are 1-3 orders of magnitude smaller compared to the minimum charge. The obtained results provide an opportunity to assess the required accuracy of determining the aerodynamic coefficients of the Magnus force and the moment of the Magnus force under different conditions of firing by artillery systems.