Reentry Heating Calculator Formula

Understand the math behind the reentry heating calculator. Each variable explained with a worked example.

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Formulas Used

Heat Flux

heat_flux = 1.83e-4 * sqrt(air_density / nose_radius) * pow(velocity, 3)

Heat Flux (kW/m2)

heat_flux_kw = 1.83e-4 * sqrt(air_density / nose_radius) * pow(velocity, 3) / 1000

Variables

VariableDescriptionDefault
velocityEntry Velocity(m/s)7800
air_densityAir Density(kg/m3)0.001
nose_radiusNose Radius(m)1

How It Works

Stagnation-Point Reentry Heating

The heat flux at the stagnation point of a blunt body during reentry is governed by the Sutton-Graves correlation.

Formula

q = k * sqrt(rho / r_n) * v cubed

where k = 1.83 x 10 to the -4 (for Earth atmosphere in SI units).

A larger nose radius spreads the heat over a wider area, reducing the peak flux. This is why reentry capsules are blunt.

Worked Example

LEO reentry at 7800 m/s, rho = 0.001 kg/m3, r_n = 1.0 m.

velocity = 7800air_density = 0.001nose_radius = 1
  1. 01q = 1.83e-4 * sqrt(0.001 / 1.0) * 7800^3
  2. 02sqrt(0.001) = 0.03162
  3. 037800^3 = 4.746e11
  4. 04q = 1.83e-4 * 0.03162 * 4.746e11
  5. 05q = 2 746 000 W/m2 = 2746 kW/m2

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