The ballistic coefficient measures how well a projectile resists air drag: the ratio of its mass to the product of its drag coefficient and cross-sectional area.
C = m / (Cₓ·A), A = π·d²/4
m·dv/dt = m·g − ½·ρ·Cₓ·A·|v|·v
ρ(h) = ρ₀·(1 − 2.25577e-5·h)^5.25588
- Higher C (heavy, slim, streamlined) → drag decelerates it less → flatter trajectory, longer range.
- Lower C (light, wide, blunt) → drag dominates quickly → the shot drops short, like the grey reference shell.
- Both shells share the same muzzle velocity (200 m/s) and launch angle, so any difference in their paths comes purely from C.
- Firing altitude thins the air the projectile pushes through: at 4000 m the air is roughly 60% as dense as at sea level, so drag drops and both shots carry noticeably farther — the same reason long-range shooters re-dope their scope for a high-altitude match.
Real-world relevance: fire-control computers and long-range shooters use the ballistic coefficient — corrected for local air density at altitude — to predict how far a specific bullet or shell will carry before it drops out of the target zone.