Forensic Ballistics Trajectory Simulator: Bullet Path Reconstruction

simulator advanced ~12 min
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Drop = 35 cm at 100 m — 9mm at 370 m/s

A 9mm bullet (8 g, 370 m/s muzzle velocity) drops approximately 35 cm over 100 m and arrives with about 290 m/s, retaining 61% of its original kinetic energy.

Formula

Δy = ½g(d/v₀)² (simplified drop, flat fire)
v(d) = v₀ × exp(-Cd·ρ·A·d / (2m))
E_kinetic = ½ × m × v²

The Science of Projectiles

Forensic ballistics applies the physics of projectile motion to criminal investigation. When a bullet is fired, it follows a trajectory governed by its initial velocity and angle, modified by gravity, air resistance, and environmental conditions. By analyzing bullet holes, impact craters, and recovered projectiles, forensic examiners can reconstruct the shooter's position, the weapon type, and the sequence of events at a crime scene.

External Ballistics

Once a bullet leaves the barrel, it is subject to gravity (pulling it down), aerodynamic drag (slowing it), and spin from rifling (stabilizing it gyroscopically). The trajectory is a curved path — not a straight line — that drops increasingly with distance. A 9mm pistol bullet drops about 35 cm at 100 m; a rifle bullet at 800 m/s drops only 8 cm at the same distance but over 3 m at 500 m. These differences are critical for crime scene reconstruction.

Terminal Ballistics

The bullet's condition at impact — its velocity, energy, and deformation — provides forensic evidence. Kinetic energy determines penetration depth and wound characteristics. Hollow-point bullets expand on impact, transferring energy rapidly; full-metal-jacket rounds may pass through, creating both entry and exit wounds. The bullet mass and impact velocity together determine the energy available, following E = mv²/2.

Reconstruction in Practice

This simulation models a bullet's flight from muzzle to impact, accounting for gravity and aerodynamic drag. By adjusting muzzle velocity, launch angle, bullet mass, and drag coefficient, you can match real-world scenarios: from a 9mm pistol shot across a room to a rifle engagement at hundreds of meters. The computed drop, velocity retention, and energy help forensic analysts verify or refute witness accounts and suspect statements.

FAQ

How do forensic examiners reconstruct bullet trajectories?

Examiners use bullet holes, impact marks, and recovered projectiles to establish the bullet's path. By inserting trajectory rods into holes in walls or objects, they trace the line of flight. The angle and direction, combined with ballistic calculations accounting for gravity and drag, reveal the shooter's approximate position.

What is bullet drop?

Bullet drop is the downward displacement caused by gravity during flight. A bullet fired horizontally at 370 m/s falls about 35 cm over 100 m and over 1.5 m at 200 m. Forensic analysts must account for drop when reconstructing firing positions from impact points.

How does rifling help forensic identification?

Rifle barrels impart spiral grooves (lands and grooves) onto the bullet, creating unique striations. These marks are compared microscopically to test-fired bullets from a suspect weapon. Like fingerprints, no two barrels produce identical marks, enabling positive weapon identification.

What factors affect bullet trajectory?

Gravity, air resistance (drag), wind, air density, bullet spin (gyroscopic stability), and the Coriolis effect all influence trajectory. For forensic distances (typically under 100 m), gravity and drag dominate; wind and Coriolis become significant only for long-range rifle shots.

Sources

Embed

<iframe src="https://homo-deus.com/lab/forensic-analysis/ballistics-trajectory/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub