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Heat shields used for Earth reentry are usually curved but heat shields used for Mars’ entry are coned shaped. Why is this?

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The following paragraph, in section IIIF of Prabhu and Saunders On Heatshield Shapes for Mars Entry Capsules, is the only direct comparison between 70-degree cones (Mars Viking heritage) and spherical sections (Earth human capsule heritage) I've found so far. Emphasis mine.

In all of the preceding discussion, the focus has been on the 70° sphere-cone shape. However, results for the alternate baseline shape – the spherical section heatshield – have been shown as well. The spherical section shape clearly has much superior aerothermal performance compared to the 70° sphere-cone at the same angle of attack. Firstly, there are no inflections in surface pressure because there are no curvature discontinuities over the acreage except at the junction of the dish section and the shoulder. Secondly, the streamwise pressure gradient is always favorable, which means transition to turbulence is less likely. Thirdly, even if transition does occur on the acreage, the turbulent heating levels are much lower than those of the 70° sphere-cone. Therefore, it would appear that the spherical section heatshield is a natural choice to replace the 70° sphere-cone heatshield for a Mars entry capsule. However, the technology readiness level of the spherical section heatshield for flight through Mars atmosphere is low, even though it has flight heritage in Earth atmosphere. Furthermore, the aerodynamic trim characteristics for the spherical section heatshield are likely to require more ballast mass than the 70° sphere-cone for a lifting entry (Viking and MSL), and compared to a 70° sphere-cone, there is significant loss of packing volume for the spherical section heatshield. With the development of systems analysis frameworks such as COBRA (Co-Optimization of Blunt-body Re-entry Analysis), it is possible that the spherical section heatshield parameters ($R_n$ and $R_s$ ) can be optimized to meet multiple objectives such as maximizing the drag area while keeping maximum heat flux to a minimum and reducing the amount of ballast required. However, the problem of elevating the technology readiness level of a spherical section heatshield will remain, and investments will have to be made to characterize its aerodynamics and aerothermodynamics. Since this is true of any shape, regardless of its non-Mars flight heritage, the present study explores several other options.

I'd prefer to dig up some earlier papers on how the 70-degree sphere-cone was arrived at for Viking in the first place, but a lower ballast mass requirement could easily be a clincher for an engineering trade study between two heatshields. That could also be a greater factor in a Mars mission than an Earth-orbit mission.

The packing volume statement isn't completely clear to me.

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    $\begingroup$ I think the "packing volume" refers to the space on the inside of the heatshield which can be used by the spacecraft. Spherical section heatshields are typically much flatter than the 70° cones, so there's little room in them for useful equipment (for the same diameter of the shield). $\endgroup$
    – TooTea
    Aug 15, 2022 at 8:41
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    $\begingroup$ This is key! I looked into it a little; most of what I found just sounded like flight heritage reasons + no compelling reason to change, but this gives a rationale. $\endgroup$ Aug 15, 2022 at 12:02

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