🔥 Re-entry Heating & Ballistic Coefficient Calculator
🔥 Re-entry Heating & Ballistic Coefficient Calculator
Estimate ballistic coefficient, stagnation-point heat flux, peak heating, peak deceleration and total heat load along a constant-angle entry — the numbers that set a heat shield's size and shape.
Stagnation-point convective heat flux against altitude along the entry path. The marker is the peak.
Entry and heating detail
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The Sutton–Graves estimate, ballistic coefficient, and the assumptions that make this a screening tool
Stagnation-point heating. For a blunt body in high-speed flight, the cold-wall convective heat flux at the stagnation point is approximated by the Sutton–Graves correlation q̇ = 1.7415×10⁻⁴ √(ρ/Rn) V³ in SI units, with ρ in kg/m³, nose radius Rn in metres, V in m/s and q̇ in W/m². It rises with the cube of speed and with the square root of density, and falls with the square root of nose radius — a sharper nose concentrates the same energy into a smaller area. The constant assumes air and a cold wall; it is an engineering estimate, not a solution of the shock layer.
Radiative equilibrium temperature. The surface temperature shown is the temperature at which a grey body of the entered emissivity radiates away the incoming flux: T = (q̇/(σ ε))1/4. A real ablative heat shield never reaches that temperature because material pyrolyses and blows away, carrying energy with it; a reusable tile surface does approach it. The number is a useful upper bound for a non-ablating surface, not a material limit.
Ballistic coefficient. β = m/(CdA) is the mass per unit drag area, in kg/m². A high-β vehicle (dense, small, streamlined) punches deeper into the atmosphere, spends longer at high speed, and generally sees higher peak heating and a longer heat pulse. A low-β vehicle (large, light, blunt) decelerates high and fast, with a shorter, more intense pulse lower in the atmosphere. The same mass with a bigger aeroshell lands differently.
The trajectory model. The path is assumed to be a straight line at a constant flight-path angle below the horizon, with gravity and lift neglected, and the atmosphere is a tabulated standard-atmosphere density profile. Velocity falls through drag: dV/ds = −ρV/(2β). Heat load is ∫q̇ dt along that path. It captures the first-order trade between entry angle, ballistic coefficient, nose radius and peak heating, but it cannot model pull-up, skip-out, lift-to-drag steering, a changing angle of attack, or the shock-layer chemistry of a real entry.
What is missing. Radiative heating becomes important above roughly 9 km/s and can dominate for lunar or Mars return; the Sutton–Graves term is convective only. Ablation, pyrolysis-gas injection, surface roughness, turbulence, boundary-layer transition and shape change all move the answer. Use this for intuition and preliminary sizing, then a validated entry simulation (such as NASA's DPLR/LAURA class tools or a verified 3-DOF model) for hardware.
Sutton & Graves, A general stagnation-point convective-heating equation for arbitrary gas mixtures (NASA TR R-376, 1971); US Standard Atmosphere 1976. Last reviewed: 2026-10-19. A teaching and screening aid, not a TPS design tool.