Vehicle Nose Heating
I'm still learning about the heating of nosecones. Launch loops will supply very inexpensive kinetic energy to one-time-use cargo vehicles. However, the heat resistant nose cones needed to exit the atmosphere tangentially, from 80 km loop altitude to space vacuum, could be far more expensive. What is needed?
Symbol Table |
|||
Pr |
Prandtl number |
|
|
Re |
Reynolds number |
|
|
H |
Power/area |
W/m² (watt/m², kg/s³ ) |
0.0685218 slug / s³ |
ρ |
air density |
kg/m³ |
1.94032e-3 slugs / ft³ |
m |
mass |
kg |
0.0685218 slug |
σ |
nosecap radius |
m (meter) |
3.28084 ft |
V, u |
freestream velocity |
m/s |
3.28084 ft/s |
T |
Absolute temperature |
K (kelvin) |
1.8 °R (rankine) |
Q |
Heat transferred |
J (joule) |
0.737562 ft-lb |
μ |
viscosity |
kg/m/s |
0.0208854 slugs/ft/s |
subscripts |
|||
r |
recovery conditions |
||
s |
stagnation conditions |
||
w |
wall conditions |
||
According to the standard atmosphere model, the atmosphere at 80 km is 1.8458e-5 kg/m³, 1.5e-5 as dense as that at the surface (I expect it to be denser at the equator than at the 45.5425 degree latitude of the standard model). For a 10 km/s exit, the enthalpy (thermal and chemical power, more or less) of the flow impinging on the nose cone is ½ ρ V³ = 9.23 MW/m².
A seminal paper in space history is "A Study of the Motion and Aerodynamic Heating of Missiles Entering the Earth's Atmosphere at High Supersonic Speeds" by H. Julian Allen and A. J. Eggers, Jr. The revised October 1957 version is NACA (National Advisory Committee for Aeronautics) Technical Note 4047, available from the NASA NTRS Technical Reports Server.