Reentry Heating Calculator

It's a widely used engineering correlation for stagnation-point convective heating during atmospheric entry, q = k × √(ρ/Rn) × V³, published by NASA's Kenneth Sutton and Randolph Graves Jr. in 1971 (NASA TR R-376) from stagnation-point heat-transfer theory and used as a standard first-order estimate in aerospace reentry analysis since the 1970s. This calculator uses the standard Earth constant (k ≈ 1.7415×10⁻⁴ in SI units). It's a well-established estimate for the convective heating component, but real mission design also accounts for radiative heating at very high velocities and detailed flowfield effects a single correlation can't capture.

Atmospheric density falls off exponentially as altitude increases, and this calculator's Altitude input spans a wide 0-150 km range, so that exponential swing in density ends up outweighing the cubic velocity term across the more modest Entry Velocity range offered. Physically, both matter -- heating scales with velocity cubed -- but for the specific input ranges this calculator allows, Altitude is the input that moves Stagnation Heating Rate the most.

Because heating rate scales with 1/√(Nose Radius) in the Sutton-Graves correlation -- a larger, blunter radius spreads the same heat flux over more surface area and reduces the peak heating rate at the stagnation point. This is precisely why capsules like Apollo, Dragon, and Orion use large rounded heat shields rather than a sharp, pointed nose, even though a sharp nose would be more aerodynamically efficient at other flight regimes.

The Sutton-Graves correlation for stagnation-point heat flux depends only on local atmospheric density, Nose Radius, and Entry Velocity -- it describes a purely local heat-transfer phenomenon at the nose's stagnation point, not the vehicle's overall deceleration. Vehicle Mass, Drag Coefficient, and Vehicle Diameter do matter for this calculator's Total Heat Load and Peak Deceleration outputs, which model how quickly the vehicle slows down, but they have no path into the heating-rate formula itself.

It's the radiative-equilibrium temperature a surface would reach if it re-radiated 100% of the incoming stagnation heat flux, using the Stefan-Boltzmann law with an assumed 0.85 emissivity typical of many high-temperature ablative and ceramic thermal protection materials. A real heat shield doesn't operate in pure radiative equilibrium -- ablative materials also carry heat away by charring and shedding mass -- so treat this as an illustrative upper-bound estimate for surface temperature, not a precise material response prediction.