Hypervelocity Drag

Based on Trajectory Optimization for an Apollo-type Vehicle under Entry Conditions Encountered During Lunar Returm by John W. Young (famous astronaut) and Robert E. Smith Jr., May 1967, NASA TR-R-258, Langley Research Center.

Equations on Page 5 in Foot-second-slug-BTU :

• 1a convective power: ~ ~ \dot Q_c = 20 \rho^{1/2} \left( V \over 1000 \right)^3 Btu/ft²-s

• 1b radiative power: ~ ~ \dot Q_r = 6.1 \rho^{3/2} \left( V \over { 10 000 } \right)^{20} Btu/ft²-s

• Equations assume an effective nose radius of 1 foot

• Equations from Shock Layer Radiation During Hypervelocity Re-Entry by Robert M. Nerem and George H. Stickford, AIAA Entry Technology Conference, CP-9, American Institute of Aeronautics and Astronautics, Oct. 1964, pp 158-169.

Density in slugs/ft³: multiply kg/m³ by 1.9403203e-3

Power in Btu/ft²-s: multiply by 11350.54 to get W/m²

Velocity in ft/s: divide m/s by 0.3048

Metric equations:

• Metric 1a convective power: ~ ~ \dot Q_c = 3.53e-4 \rho^{1/2} V^3

• Metric 1b radiative power: ~ ~ \dot Q_r = 1.24e-69 \rho^{3/2} V^{20}

These are for a 1 foot diameter nose, and scale by r_n^0.5 according to equation 4B-4 on page 520 of Part 4B (Entry Heat Transfer) of the SAE Aerospace Applied Thermodynamics Manual. That sites reference 1, A study of the motion and aerodynamic heating of missiles entering the earth's atmosphere at high supersonic speeds, H. Julian Allen and A. J. Eggers, Jr, NACA TN 4047, 1957.