The Genesis aeroshell had a half angle of 59.8 deg. That's as blunt as possible before shock detachment in a nitrogen atmosphere (70 deg. is the maximum value for carbon dixoide). Maximum bluntness leads to minimum thermal protection mass. Genesis' shape is stable only at supersonic Mach number. The 70 deg. aeroshells on Mars will begin to wobble around Mach=1.8 . The parachute must be deployed between Mach 1 and Mach 2 or the aeroshell will tumble. The important physics driving aerodynamic stabiilty at hypersonic velocity is different from subsonic. At hypersonic velocity the shockwave drives everything. At subsonic velocity, skin friction through gas viscosity drives everything. To achieve aerodynamic stability for all Mach number, the half angle must be 45 deg. or less. Pioneer Venus and Galileo used aeroshells with 45 deg. half angles. Military reentry vehicles have half angles around 11 degrees. They need to come in fast so they have very low drag. However their hypersonic dynamic stability is poor (big angle-of-attack excursions). From a military perspective this is desireable because they tend to fly all over the place at high Mach number and are difficult to hit by an ABM.

Gary