Parachute Terminal Velocity

Parachute terminal velocity: v_t = √(2·m·g/(ρ·C_d·A))

Open a parachute and two things jump at once: the drag area A and the drag coefficient C_d. Both spike, and terminal velocity drops to something a body can survive. A hemispherical canopy sits around C_d ≈ 1.3. Take an 80 kg skydiver under a 30 m² canopy at sea level, where ρ = 1.225 kg/m³: v_t ≈ √(2·80·9.81/(1.225·1.3·30)) ≈ 5.5 m/s, roughly 20 km/h, about what you'd feel stepping off a 1.5 m wall. That same person in free fall hits close to 55 m/s, near 200 km/h. Apollo capsules came down under three main parachutes at splashdown, and SpaceX Crew Dragon does much the same.

Applications

Think military jumps, both paratroopers and cargo airdrops. Recovery of space capsules and reentry vehicles. Fireworks shells, where a small chute delays the fall of spent components. And drag-chute work in athletics, used to add resistance during sprints.

FAQ

Why three parachutes on Apollo and Dragon? Redundancy. Lose one main and the remaining two still bring the craft down within a safe touchdown speed.

Does altitude change v_t? It does. Thinner air means lower ρ, and lower ρ pushes v_t up. At 4 km the density is around 0.82 kg/m³, which raises v_t by roughly 22%.

What is a safe landing speed? Anything under 7 m/s is usually tolerable if you land with proper PLF (parachute landing fall) technique. Military round parachutes are normally tuned for 5–6 m/s.