Compute the stagnation-point heat flux at a reentry capsule's nose using the Sutton-Graves correlation q_dot_s = K sqrt(rho/R_n) V^3 in real time. Linked outputs include local atmospheric density, kinetic energy per unit mass and Mach number, with a capsule-and-shock geometric view.
Parameters
Flight speed V
km/s
Altitude h
km
Nose radius R_n
cm
Vehicle mass m
kg
Defaults represent a LEO return (V = 7.8 km/s, h = 80 km, R_n = 50 cm, m = 5000 kg). Total kinetic energy (1/2) m V^2 of about 152 GJ must be dissipated as heat during reentry.
Results
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Stagnation heat flux q_dot_s
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Atmospheric density rho
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KE per unit mass
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Mach number M
Reentry capsule geometry
Bottom-left = Earth outline and atmosphere bands. Centre = reentry capsule (nose radius R_n). Front arc = detached bow shock. Rear gradient = wake. Nose glow intensity is proportional to heat flux.
Heat flux vs altitude
x-axis = altitude h [km] (40 to 200). y-axis = stagnation heat flux q_dot_s [MW/m^2] (log scale). Speed V and nose radius R_n are held constant. Yellow marker = current altitude.
Theory & Key Formulas
The Sutton-Graves correlation gives the convective heat flux at the stagnation point of a reentry vehicle as a function of density and velocity. For Earth's atmosphere K = 1.7415e-4 in SI units.
$$\dot{q}_s = K\,\sqrt{\frac{\rho}{R_n}}\,V^{3}$$
Local density follows an exponential model (rho_0 = 1.225 kg/m^3, scale height H_s = 8500 m):
Kinetic energy per unit mass and Mach number (c approx 269 m/s at h = 80 km):
$$\frac{KE}{m} = \tfrac{1}{2}V^{2},\quad M = \frac{V}{c},\quad c = \sqrt{\gamma R_{\mathrm{air}} T}$$
$\dot{q}_s$ is in W/m^2, $\rho$ in kg/m^3, $R_n$ in m and $V$ in m/s. Blunter shapes (larger $R_n$) reduce heating as $R_n^{-1/2}$.
What is the atmospheric reentry simulator?
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How hot does a spacecraft coming back from the ISS actually get?
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At the defaults (V = 7.8 km/s, h = 80 km, R_n = 50 cm) the stagnation-point heat flux is about 1.17 MW/m^2. That is roughly the energy density of 1000 household microwave ovens (1 kW each) packed into one square metre. Apollo's lunar-return reentry at V = 11 km/s reaches two or three times that. Sutton-Graves q_dot_s = K sqrt(rho/R_n) V^3 scales as V^3, so a 1.4x increase in speed raises heating by about 2.7x.
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Why does heating peak around 80 km altitude?
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Density rises exponentially as you descend (rho up), but the vehicle is also slowing down (V down). Because q_dot_s scales as sqrt(rho) times V^3, the product peaks at an intermediate altitude where the two competing trends balance. In practice the peak sits at 70-85 km, and the chart in this tool shows the 80 km marker right near the curve maximum. Drop h to 40 km and density is 5x higher, but the vehicle has slowed enough that heating is lower — and the chart shows that non-monotonic shape directly.
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Why does the nose radius R_n matter?
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Sutton-Graves gives q_dot_s proportional to R_n^(-1/2). Physically, a blunt nose (large R_n) pushes the bow shock farther from the body and thickens the boundary layer, smoothing the temperature gradient at the stagnation point. Sweep R_n from 50 cm to 200 cm and heating drops to sqrt(50/200) = 0.5 of the original. Apollo's blunt "bowl-shaped" capsule (R_n about 4 m) is exactly this strategy. Slender ballistic re-entry vehicles, with tiny R_n, instead use intentionally-ablating tips to shed heat as mass.
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Why is vehicle mass m a slider — the formula doesn't contain m?
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Sharp observation. Sutton-Graves is a per-area heating rate, so m does not appear directly. But the total kinetic energy (1/2) m V^2 must all be dissipated as heat during reentry, so larger m drives a larger integrated thermal load. With the defaults (m = 5000 kg, V = 7.8 km/s) the total energy is (1/2)(5000)(7800)^2 = 1.52e11 J = 152 GJ, comparable to the combustion energy of 4000 litres of crude oil. TPS mass allocation depends on total KE and the duration of heating. The tool reports KE per mass = V^2/2 = 30.4 MJ/kg in the stat card.
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Is Mach 29 realistic?
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Very realistic — it is the canonical LEO-return value. At h = 80 km the atmospheric temperature is about 180 K and the speed of sound c = sqrt(gamma R T) is about 269 m/s, so 7800/269 = 29. Apollo's lunar return at V = 11 km/s reaches M about 41. In this hypersonic regime Mach number is actually a weak indicator — dissociation, ionisation and chemistry are driven by stagnation enthalpy (V^2/2)/h_infinity and Reynolds number, not M. Conventionally M > 5 is hypersonic and M > 25 is the "reentry regime".
FAQ
Sutton-Graves is a compact engineering correlation in density, velocity and nose radius alone, used for teaching and early conceptual design. Fay-Riddell (1958) is the full analytical formulation that includes boundary-layer enthalpy difference, viscosity and the Lewis number — more accurate but heavier to evaluate. Both share the R_n^(-1/2) and rho^(1/2) scalings, and Sutton-Graves's constant K is essentially Fay-Riddell evaluated at "average" atmospheric conditions. Detailed TPS design uses DSMC or DPLR-class CFD; this tool is the screening-level baseline.
The model rho(h) = rho_0 exp(-h/H_s) with H_s = 8500 m is within 10% of the real atmosphere across the troposphere and stratosphere (up to about 50 km), but diverges above the mesosphere (h > 80 km) because temperature gradients change. The US Standard Atmosphere 1976 gives rho about 1.8e-5 kg/m^3 at 80 km versus 1.0e-4 for the exponential model — about a 5x-10x discrepancy. The tool's heat flux is correspondingly overestimated at high altitude, but the trends and scaling with R_n and V are still instructive. Detailed analysis uses NRLMSISE-00 or JB2008 table-based models.
Sutton-Graves only gives the convective component; radiative heating from the hot plasma shock layer is not included. For LEO return (V less than about 8 km/s) radiation is under 10% of convection and is usually ignored. For lunar return (V = 11 km/s) radiation matches convection, and for Mars return (V > 12 km/s) radiation dominates. Radiation scales as q_rad proportional to rho^a V^b R_n^c with b approximately 8 to 12, so it explodes at very high speed. The tool supports V up to 15 km/s; keep this extra mechanism in mind above 10 km/s.
This simulator uses Earth's Sutton-Graves constant K = 1.7415e-4 (air, 78% N2 + 21% O2), so it cannot be applied directly to Mars (95% CO2) or Venus (96% CO2). For Mars K is closer to 1.9e-4, the density profile is very different (surface about 0.020 kg/m^3, scale height about 11 km), and densities at any given altitude differ from Earth by a factor of 10^3. JPL uses MarsGRAM or proprietary models for Mars Pathfinder, Curiosity and Perseverance; Sutton-Graves is only a first approximation. Treat this tool as Earth-only.
Real-world applications
TPS design for crewed reentry vehicles: Apollo (V = 11 km/s, lunar return), Soyuz (LEO return), Crew Dragon and Starliner all base their initial thermal-shield design on Sutton-Graves and Fay-Riddell. Apollo used AVCOAT ablator (surface temperature 2700 deg C), Soyuz uses resin-impregnated graphite, and Crew Dragon uses PICA-X (SpaceX's improved PICA). Increase V from 7.8 to 11 km/s in this tool to observe the steep rise in heating.
Reusable heat-protection tiles: Space Shuttle (LEO return at V about 7.8 km/s), Dream Chaser and Starship cannot rely on ablation and use reusable tiles instead (HRSI, LI-900 and similar). The design target is survival until heating drops at lower altitudes (h about 50-70 km), and the heat-flux-vs-altitude curve in this tool is the screening metric. Starship's 2024 reentry tests highlighted an alternative strategy that exploits high-temperature stainless-steel strength.
Planetary entry probes: Mars rovers (Curiosity, Perseverance), Venus probes (Pioneer Venus, Magellan's initial entry) and the Galileo Jupiter probe all face the reentry-heating problem. Galileo's probe experienced about 30000 K radiative heating at Jupiter entry and lost roughly 50% of its heat shield to ablation — an extreme case. This tool is Earth-only, but the Sutton-Graves concept applies to every planet.
Hypersonic weapons and spaceplanes: Hypersonic glide vehicles (Avangard, DF-17), and scramjet test articles X-43A and X-51A spend extended periods (tens of minutes to hours) at hypersonic speeds (M = 5-15). Convective heating is distributed across the entire surface, not just the stagnation point, and Sutton-Graves combined with panel methods and simple boundary-layer codes is the standard early design tool. The simulator is also useful for discussions of hypersonic interception and commercial space tourism (Virgin Galactic is suborbital with M about 3 and mild reentry heating).
Common misconceptions and pitfalls
The first thing to remember is that "heat flux is not the same as wall temperature". Sutton-Graves gives the per-area rate at which energy enters the surface (W/m^2). The actual wall temperature comes from balancing this with radiative cooling epsilon sigma T_w^4. For q_dot = 1 MW/m^2 and epsilon = 0.85, T_w is approximately (1e6/(0.85 x 5.67e-8))^(1/4) = 2050 K. Ablation materials, however, eject heat by vaporising before it conducts inward, which can keep the wall cooler than the radiative-equilibrium prediction. Read the tool's output as the "incoming" rate, not the surface temperature.
Next, "Sutton-Graves assumes continuum flow". The formula is derived from boundary-layer theory and holds where the Knudsen number Kn = lambda / L (mean free path over characteristic length) is small enough (Kn less than 0.01). Above about 90 km the atmosphere becomes rarefied, Kn exceeds 0.1, and Sutton-Graves starts to break down. Real high-altitude analysis uses DSMC simulation with slip effects and incomplete-accommodation coefficients. Treat the tool's predictions above h = 100 km as indicative of the trend, not absolute values.
Finally, "Mach number does not tell the whole story" in hypersonic regimes. In subsonic and supersonic flow M dominates aerodynamic performance, but in reentry molecules dissociate, ionise and react chemically, and the relevant non-dimensional numbers are the enthalpy ratio H_infinity / (c_p T_infinity), Reynolds number, and the Damkohler number (chemistry vs flow time ratio). The tool reports M for context, but TPS designers use the total stagnation enthalpy h_0 = h_infinity + V^2/2 instead. Treat Mach 29 as a "very fast" label, not a complete description.