Effect of the magnus force and torque on the projectile flight range

Abstract

The paper considers the origin of the Magnus force and torque in the course of the projectile flight; analytical dependencies for their determination are given and justified. The mutual orientation of the Magnus force and angular torque vectors with respect to those of the drag and lift forces, as well as with respect to the stalling, polar quenching and equatorial damping torques acting on the projectile in flight is discussed. The effect of the Magnus force and torque on the firing characteristics of artillery systems is assessed. A mathematical model of the projectile flight is presented, as well as constraints that are imposed on it and that do not considerably affect the accuracy of the description of the spatial motion of the projectile. The mathematical model is implemented programmatically on the basis of a standard subroutine for numerical integration of differential equations written in the Maple software and contains the motion equations for the projectile mass center, the motion equations with respect to the projectile mass center and equations that allow one to determine the coordinates of the projectile fall points in the base reference system. To assess the effect of Magnus force and torque on the projectile flight range, the difference method is employed, which consists in solving the system of differential equations of the spatial motion of the projectile such that changing the magnitude of the Magnus force and torque (at the assumption of the constancy of the aerodynamic forces and torques), one obtains the variation in the projectile flight range. A protocol and a scheme for assessing the effect of deviation of the projectile range on the accuracy of determination of the Magnus force strength and torque, as well as the results of numerical simulation of the deviation of the flight range for the ОФ-462Ж projectile of the 122-mm howitzer Д-30 depending on the accuracy of determination of aerodynamic force coefficients and Magnus torque are presented. It is shown that the largest deviations in the projectile flight range are observed when shooting at large launching angles and full charge (projectile speed 690 m / s); the smallest corresponding values are observed for the fourth charge (projectile speed 276 m / s) at small launching angles.