Adam said:

>Final question - of Gary, if he's around - is the stagnation
>temperature of Apollo's shock-wave at its re-entry peak.
>I'm fuzzy on the details - I estimated ~ 9,500 K, for a 9 gee
>peak at ~ 11 km/s re-entry speed. No wonder it was an
>ablation shield. Apollo's CM massed ~ 5,800 kg and its base
>was ~ 12 sqm in area.

The Apollo case that I like to study is AS-501 (Apollo 4). There
were two Apollo unmanned test flights that were launched from Saturn-Vs, i.e. AS-501 and AS-502. AS-502 was unsuccessful because the Saturn-V second stage malfunctioned, placing the vehicle into a junk orbit. There were two earlier Apollo test flights launched from Saturn-1Bs but they are less interesting because their entry velocities were not that high.

The inertial frame entry vector that I use for AS-501 is:

velocity 11.2 km/sec
entry velocity angle -7.2 deg.
heading angle 68.14 deg.
entry altitude 121.920 km (400 kft)
latitude 21.55 deg.
longtude 151.6 deg.

entry mass 5424.51 kg.
heat shield radius 4.66 m

This entry vector is not "dead nuts" because I had to pull some values off of graphs. AS-501 flew a "pile driver" trajectory, i.e. the Saturn S-IVb stage hammered the Apollo CM and SM back into the atmosphere from Earth orbit to achieve a lunar return trajectory velocity.

Simulating an Apollo CM entry is not easy because it flew a lifting
entry (angle-of-attack -26.0 deg. at L/D = 0.37) with roll modulation. The roll modulation is what makes simulation difficult. The Apollo CM autopilot would spin the vehicle multiple times from a lift-up to a lift-down trajectory in order to minimize the G-loading. The autopilot algorithm was actually broken for the earlier AS-202 test flight and had the CM doing a semi-random jitter back and forth (had it been manned, the flight crew would have pitched biscuits).

I found the single bank angle of 47.96 deg. makes a very crude trajectory fit for AS-501 (decelleration is too high).

For my simulation (which is inaccuate):

peak deceleration was 11 G.
peak convective stagnation point heat flux was 185 Watts/cm^2
peak radiative stagnation point heat flux was 333 Watts/cm^2
peak stagnation point wall temperature was 3237 deg.K
peak shock layer temperature was 10591 deg.K

Another reason why my simulation was inaccurate beyond the roll modulation was in assuming a straight Fay-Riddell catalytic equilibrium convective heating approximation. Because the CM was flying at -26 deg. angle-of-attack, the peak heating location gets shifted over to near the CM's edge. Consequently there is a combined stagnation point and expansion effect with nonequilibrium chemisty mixed in. The CFD guys say that engineering heating approximations don't work for Apollo when doing a lifting lunar return.

Finally, forget about using an Apollo shape for a Mars return, e.g. 12.5 km/sec. The G loading is unacceptable and the entry corridor requires impossible accuracy. The L/D ratio needs to be higher than what an Apollo CM can do. A better vehicle shape is either a raked conic or a biconic.

Gary

p.s. The peak inner wall temperature of the Apollo CM got so hot that an astronaut standing in the CM would have burned his feet if he didn't wear boots. Good thing they landed in water. The Apollo astronauts were very brave men and true heros.