The Effect of Gravitational, Drag, Magnus, and Coriolis Forces on a Roundball Bullet

The trajectory of a bullet is influenced by numerous factors including the gravitational, drag, Magnus, and Coriolis forces. These forces complicate the ability for precise accuracy and effectiveness in shooting scenarios across various applications, from military sniping to competitive marksmanship. This work presents a simulation of the trajectory of a 50-caliber roundball bullet fired from a Pendersoli 1853 Enfield Musket Rifle. An ordinary differential equation (ODE) solver was utilized to solve the coupled differential equations of projectile motion including the effects of gravity, drag, Magnus, and Coriolis forces. Using the real-life scenario of a bullet fired in the northern hemisphere at 1.3 meters above level ground at a 30-degree angle while facing East, the bullet will travel 13 km and drift 1.5 km to the left. The results of this project display that external forces significantly impact the flight path of a 50-caliber bullet with the Coriolis force having the largest effect on the final distance, with a 40.6% decrease in distance. This research could lead to future work on modern muzzleloaders, rifles, shotguns, and long-range ballistics, such as rockets and missiles.