TRAJECTORY SIMULATIONS BY THE NUMERICAL SOLUTION OF THE POINT-MASS EQUATIONS OF MOTION FOR 7.62MM/.308” RIFLE BULLETS

Abstract

Abstract Simulations of free-flight trajectories of seven different 7.62mm/.308 rifle bullets (designated B0-B6) have been carried out by the numerical solution of the equations of motion. The average drag force coefficients (CD) for B0-B6 have been calculated by scaling the variation of CD with the Mach number of flight with reference to the G7 standard projectile. The Point-Mass trajectory model and its Flat-Fire approximation have been studied with and without the effect of range winds. The solutions of the systems of equations have been carried out by writing scripts in the Python programming language. It is observed that an increase in the bullet weight and consequently the sectional density lowers the CD. Furthermore, a hollow-point adds to the drag, while a plastic tip on the bullet reduces the drag, when compared to a FMJ or Spitzer bullet. As expected, it is seen that the bullet with the highest drag (B0) has the shortest range and lowest apogee, while lower drag bullets fly further and higher. The crossover of trajectories is observed at ~30 angle of gun elevation, which implies that the maximum range is not achieved when fired at 45, as is the case with vacuum trajectories. Flat-fire approximation of the point-mass model was also solved to observe trajectories and crosswind deflections of the bullets when fired at 5 angles of elevation. The simulated trajectories exhibit rigid trajectory behaviour about the origin/gun muzzle.