Hypersonic aerodynamics is nonintuitive. This is reasonable because our intuition is based upon low subsonic flight. During hypersonic flight, aerodynamic stability is driven by the shockwave. A flat plate at normal incidence to the free stream is actually stable. At perfect normal incidence, the surface pressure is uniform. However if the flat plate is slightly perturbed from normal incident then the edge that was perturbed closer to the shock wave will experience greater surface pressure while the edge that was perturbed away will see less pressure. This will reset the flat plate back to normal incidence. However this mechanism breaks down when the Mach number drops below 2. A cone with an angle of 70 deg. from its axis of symmetry will begin to lose its stability in a carbon dioxide atmosphere (Mars or Venus) at about Mach = 1.8 and will become hopelessly unstable as it approaches Mach = 1.0 (you need to pop the parachute before then) . A 70 deg. cone is too blunt for a nitrogen atmosphere (Earth or Titan) due to shock detachment. For a nitrogen atmosphere, a 60 deg. cone is the best bet. However if there are people on board then the peak decelleration might get too high thus requiring an even further reduction in bluntness. However as you reduce the cone angle, the heating gets worse and the payload volume goes to pot. The complete design involves many tradeoffs.

Gary