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 as 19930084817.pdf from NTRS, the NASA Technical Reports Server.

This paper teaches that a hypersonic reentry body nose should be rounded, not pointy. A pointed nose will endure higher heating at the point, and cannot conduct heat fast enough to the body behind, so it will burn away. The thermal stresses may shatter the nose cone. A rounded nose will move the shock wave farther in front of the vehicle, and deflecting more of the entry heat into the air, and less to the stagnation point (the center of a symmetric flow) on the nose itself.

The Allen/Eggers paper concerns warhead entry; the idea is to deliver the warhead near the surface without damaging it, before it does it's job and destroys a city. As my late friend Jordin Kare, formerly a laser physicist at Lawrence Livermore National Labs, said:

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