Ballistic Coefficient: Why Every Reentry Capsule Falls Differently

Defining the ballistic coefficient

Two objects of identical shape entering the atmosphere at the same speed can decelerate at wildly different altitudes, reach wildly different peak temperatures, and land with wildly different precision — all because of a single ratio: the ballistic coefficient.

BC = m / (Cd · A)
m  = vehicle mass (kg)
Cd = drag coefficient (shape-dependent)
A  = frontal area (m²)         Units: kg/m²
High BC — Apollo capsule ≈ 400 kg/m²
Low BC  — flat parachute ≈ 5-20 kg/m²

BC measures inertia per unit of drag force available. A high-BC vehicle needs denser air — meaning lower altitude — before drag can meaningfully slow it down, so it punches deep before decelerating. A low-BC vehicle, like a parachute, presents so much drag area relative to its mass that it decelerates high up, gently.

Deceleration altitude

The equation of motion along the entry path balances gravity against drag, which itself depends on the exponentially increasing atmospheric density as altitude drops.

Drag force:      F_d = ½ρ(h)v²Cd·A
Deceleration:    a = F_d / m = ½ρ(h)v² / BC
Atmosphere:      ρ(h) = ρ₀·exp(−h / H)   (H ≈ 7-8.5 km on Earth)

BC = 400 kg/m² decelerates near 40-60 km altitude
BC = 15 kg/m² (Mars parachute) decelerates near 8-12 km on Mars

Mars air density is only about 1% of Earth's, which makes the landing problem far harder there: a given ballistic coefficient decelerates much less effectively before reaching the ground, which is why heavy rovers like Curiosity needed a supersonic parachute plus a powered sky-crane rather than a parachute alone.

Peak heating and heat pulse shape

Convective heat flux to the vehicle's stagnation point scales with the cube of velocity and the square root of atmospheric density — a combination first analysed rigorously by H. Julian Allen and Alfred Eggers in 1953, giving rise to the entire blunt-body reentry concept.

Stagnation-point heat flux (Sutton-Graves):
q̇ ≈ k·√(ρ/R_n)·v³   (R_n = nose radius)

Because high-BC vehicles decelerate lower, at higher density, they experience higher peak heat flux but over a shorter duration. Low-BC vehicles decelerate higher up, at lower density and lower peak heat flux, but the pulse lasts longer — so total heat load can end up comparable, and engineers must trade peak flux against total load when sizing a heat shield.

G-load and real vehicles across the BC spectrum

The Apollo Command Module (BC ≈ 400-500 kg/m²) decelerated near 60-70 km altitude with peak g-loads around 6-7 g for lunar-return entries — deliberately tuned to be survivable for a crew. SpaceX Crew Dragon sits in a similar blunt-body BC class, using a PICA-X ablative heat shield to survive the intense but brief pulse. High-BC military reentry vehicles, by contrast, decelerate fast and low, producing sharp peak decelerations that can exceed 10-15 g. The Space Shuttle Orbiter, with a low BC and large lifting wing area, spread its deceleration over a long, shallow entry corridor — trading peak heating for a much longer total heat-soak duration.

Frequently asked questions

Try it live

Everything above runs in your browser — open Atmospheric Re-entry and tune entry angle, lift-to-drag ratio and ballistic coefficient to see whether the capsule skips out, lands safely, or burns up. Nothing is installed, nothing is uploaded.