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| . 1a: $ \dot Q_c = 20 \sqrt{ \rho } ( V / 1000 )^3^ $ Btu/ft^2^-s | . 1a convective power: $ ~ ~ \dot Q_c = 20 \rho^{1/2} \left( V \over 1000 \right)^3$ Btu/ft^2^-s . 1b radiative power: $ ~ ~ \dot Q_r = 6.1 \rho^{3/2} \left( V \over { 10 000 } \right)^{20} $ Btu/ft^2^-s . Equations assume an effective nose radius of 1 foot |
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| . 1b: $ \dot Q_r = 6.1 \rho^{3/2} ( V / 10 000 )^20^ $ Btu/ft^2^-s | . 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. |
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| Density in slugs/ft^3^: multiply kg/m^3^ by ...... | Density in slugs/ft^3^: multiply kg/m^3^ by 1.9403203e-3 |
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| Power in Btu/ft^2^-s: multiply by ..... to get W/m^2^ | Power in Btu/ft^2^-s: multiply by 11350.54 to get W/m^2^ |
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. 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, [[ http://hdl.handle.net/2060/19930084817 | 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. |
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.