Sailaranta Timo, Pankkonen Antti, Siltavuori Ari. Upwards Fired Bullet Turning at the Trajectory Apex

Applied Mathematical Sciences, Vol. 5, 2011, no. 25, 1245 – 1261.A six-degree of freedom simulation model is used to investigate a bullet turning at the trajectory apex, particularly when fired about vertically. The bullet model includes an aerodynamic model covering angles of attack up to 180 degrees. The bullet attitude is computed based on the quaternion in order to avoid equation singularity problems. Two separate codes with different body-fixed coordinate systems are used to verify the results obtained. The role of Magnus-phenomena in turning is particularly studied at around the apex. Also some disturbance effects, like atmospheric turbulence on the bullet response, were analyzed. The objective of the study is to find out the terminal velocity of the conceptual 7.62 mm bullet. Based on the results it seems that carelessly upwards fired projectile can be, at least, dangerous to the crowd in the vicinity of the shooter.