Hypersonic Reentry Heat Shield Calculator — Sutton-Graves Heating & TPS
Estimate stagnation-point reentry heating with the Sutton-Graves correlation and solve 1D transient conduction through a thermal-protection stack to check temperature margins.
Stagnation-envelope visualization
Through-thickness temperature field
- T(x)
Benchmark / runtime summary
Heat flux and temperature evolution
- Convective
- Net into TPS
- Surface T
- Backface T
Altitude and velocity history
- Altitude
- Velocity
Thermal performance summary
Current through-thickness node temperatures
- Current node T
Thermal performance report
• ρ cp ∂T/∂t = ∂/∂x(k ∂T/∂x)
• Surface reradiation: εσ(Ts⁴ − Tspace⁴)
{
"peakHeatFlux_W_m2": 3824144.243,
"peakSurfaceTemp_K": 3007.701,
"peakBackfaceTemp_K": 300.751,
"integratedHeatLoad_J_m2": 8118166.219,
"minMargin_K": -2557.701,
"timeAboveAllowable_s": 541,
"finalSurfaceTemp_K": 1675.4,
"finalBackfaceTemp_K": 300.751,
"finalAltitude_km": 20,
"finalVelocity_m_s": 1600
}A clear path from inputs to results.
Size a reentry heat shield by estimating the fierce stagnation-point heating a capsule meets on its way down and tracking how that heat soaks through the thermal-protection layers. It uses the Sutton-Graves correlation for convective heating along a flight trajectory and a 1D transient conduction solver to show whether each material layer stays below its allowable temperature.
How to use
- Choose a trajectory preset (Earth return, lunar return, or Mars entry) or paste your own time/altitude/density/velocity table; the engine interpolates density and velocity at each time step.
- Set the nose radius Rₙ of the heat-shield stagnation region — a smaller nose concentrates heating and raises the flux.
- Keep or adjust the Sutton-Graves coefficient C (default 1.83×10⁻⁴ SI for Earth air) that scales the convective heating correlation.
- Build the layer stack from outside in — for each layer give thickness, density, specific heat cₚ, conductivity k, and allowable temperature. Defaults model an ablator over insulation over an aluminium structure.
- Set the surface emissivity for reradiative cooling, the back-face boundary (adiabatic or fixed temperature), and the initial temperature, then choose the time step and node count for the implicit solver.
- Read the peak convective heat flux, peak surface and back-face temperatures, integrated heat load, and the minimum temperature margin to each layer’s limit.
The formula
Reference: Sutton & Graves, “A General Stagnation-Point Convective-Heating Equation for Arbitrary Gas Mixtures,” NASA TR R-376 (1971); 1D transient conduction solved by implicit finite-volume marching as in NASA NTRS TPS thermal-response analyses. Earth-air coefficient C ≈ 1.83×10⁻⁴ (SI).
Worked example
Peak stagnation heating on an Earth-return corridor
- Earth-return trajectory; nose radius Rₙ = 0.65 m; Sutton-Graves coefficient C = 1.83×10⁻⁴ (SI). Evaluated at the t = 300 s point of the preset, where free-stream density ρ∞ = 7.0×10⁻³ kg/m³ and velocity V∞ = 5800 m/s.
- 1
The convective stagnation flux is q̇_c = C·√(ρ∞/Rₙ)·V∞³. Here √(ρ∞/Rₙ) = √(7.0×10⁻³ / 0.65) = √(0.0107692) = 0.103775, and V∞³ = 5800³ = 1.95112×10¹¹ m³/s³. So q̇_c = 1.83×10⁻⁴ × 0.103775 × 1.95112×10¹¹ = 3.7055×10⁶ W/m² = 3.705 MW/m². Because the correlation scales as √ρ·V³, the true peak falls slightly later, between the 300 s and 360 s points: as density keeps climbing while velocity bleeds off, the product √ρ·V³ maximises near t ≈ 314 s (ρ ≈ 9.98×10⁻³ kg/m³, V ≈ 5525 m/s), giving q̇_c ≈ 3.824 MW/m².
Convective stagnation-point flux ≈ 3.705 MW/m² at the 300 s point, with the trajectory peak ≈ 3.82 MW/m² — the value the solver carries into the layer-conduction balance to check surface temperature against the ablator limit.
Interpreting the result
The flux scales as the cube of velocity and the square root of density, so the heating pulse peaks where their product √ρ·V³ is largest — typically well into the descent, after the vehicle has slowed but while the air is still thickening. A smaller nose radius sharply raises the flux (it goes as 1/√Rₙ), which is why reentry capsules use blunt noses. What ultimately protects the structure is the balance between incoming flux, reradiation from the hot surface, and conduction inward: the minimum margin tells you whether any layer breaches its allowable temperature during the run.
Assumptions & limitations
- Sutton-Graves gives the stagnation-point convective flux only; radiative gas heating (significant above ~9-10 km/s) is not added separately, and ablation/pyrolysis mass loss is not modeled — this is a design-screening tool, not a CFD or ablation solver.
- The coefficient C is a single constant (default 1.83×10⁻⁴ SI for Earth air); other atmospheres or gas mixtures require a different C.
- Heat conduction is treated as strictly 1D through the thickness; the 3D capsule view is a visualization of the stagnation envelope, not the solver domain.
- The surface energy balance reradiates against a reference temperature with the entered emissivity, linearized each time step and solved implicitly, so results are unconditionally stable but depend on the chosen time step and node count.
- Material properties (ρ, cₚ, k, allowable T) are constant per layer and do not vary with temperature; real TPS materials change properties and may char.
Frequently asked questions
What is the Sutton-Graves equation and why use it here?
It is the standard engineering correlation for convective heating at the stagnation point: q̇_c = C·√(ρ∞/Rₙ)·V∞³. With Earth-air C = 1.83×10⁻⁴ (SI), a 0.65 m nose at ρ∞ = 7.0×10⁻³ kg/m³ and 5800 m/s gives 3.705 MW/m². It is widely used for EDL first-cut sizing because it captures the dominant velocity-cubed and nose-radius dependence with a single coefficient.
When during descent does the heating peak?
Because q̇_c goes as √ρ·V³, the peak occurs where that product is largest — not at entry interface (thin air) nor at the bottom (slow speed), but in between. On the Earth-return preset it lands near t ≈ 314 s at roughly 3.82 MW/m², after the vehicle has decelerated but while density is still rising steeply.
What does the minimum margin tell me?
It is the smallest gap, in kelvin, between the hottest node in each layer and that layer’s allowable temperature over the whole trajectory. A positive margin means every layer stayed within limits; a negative margin (and non-zero time-above-allowable) means the stack overheated and you need more thickness, a better insulator, or lower peak heating.
Why does a smaller nose radius make heating worse?
The flux scales as 1/√Rₙ, so halving the nose radius multiplies the stagnation flux by √2 ≈ 1.41. A blunt (large Rₙ) nose spreads the shock stand-off and lowers peak heating, which is exactly why reentry capsules are blunt rather than pointed. Pointed noses are reserved for low-heating or actively cooled applications.
Does the tool account for the heat shield radiating heat away?
Yes. The surface boundary balances incoming convective flux against reradiation εσ(T_s⁴ − T_ref⁴) and conduction into the stack. A hot surface sheds a large fraction of the incoming heat by radiation (it scales as T⁴), which is a primary cooling mechanism for reusable, high-emissivity TPS; low emissivity reduces this and drives wall temperature up.
Can I model a lunar return or Mars entry?
Yes — pick the lunar-return preset for a steeper, higher-speed Earth corridor (hotter pulse) or the Mars-entry preset for a thin, high-speed atmosphere. You can also paste a custom time/altitude/density/velocity table. Keep in mind the convective correlation uses an Earth-air coefficient by default, so change C for other gas mixtures.
Methodology last reviewed 2026-10-06. Results are informational and not financial or engineering advice — see our disclaimer.