Tracing the Invisible Path
A bullet travels too fast to see, but the physics of its flight are well understood. From the moment it leaves the muzzle, a bullet follows a parabolic arc — rising slightly if angled upward, then falling under gravity — while air resistance continuously decelerates it. Forensic ballistics uses these physical laws to work backward from impact evidence to determine where a shot originated.
The Physics of Drag
Air resistance is the dominant force shaping bullet trajectories beyond a few meters. Drag force increases with the square of velocity, so a bullet at 800 m/s experiences four times the drag of one at 400 m/s. Most handgun bullets begin supersonic and transition to subsonic flight, crossing a turbulent transonic region that complicates precise trajectory calculation. The drag coefficient captures the bullet's aerodynamic efficiency — streamlined rifle bullets have Cd around 0.15, while flat-nosed pistol rounds may reach 0.45.
Crime Scene Reconstruction
At a shooting scene, investigators identify bullet holes, ricochet marks, embedded projectiles, and shell casings. By inserting trajectory rods through aligned holes and projecting the path backward, they establish the flight line. Combined with ballistic calculations accounting for gravity drop at the estimated range, this geometry identifies the shooter's position to within a few degrees of accuracy.
Simulation: From Muzzle to Impact
This simulation integrates the equations of motion for a bullet with aerodynamic drag, step by step through time. Watch how muzzle velocity, launch angle, bullet mass, and drag coefficient interact to determine range, flight time, and impact velocity. The trajectory visualization shows why even small angle changes at the muzzle translate to large positional differences downrange.