A lot of discussions of SSTOs and the potential for making upper stages re-usable hinge on the fact that thermal protection systems for reentry from full orbital velocity are pretty heavy (and historically either expendable or so expensive to maintain to make one wish that they were expendable).

Is there a reasonably simple rule of thumb to estimate a minimum mass for a thermal protection system?

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    $\begingroup$ I think it's more complicated than just having a simple rule of thumb that suits most cases. It seems to be that historically the majority of expendable atmospheric entry heat shields were ablative. The shield mass would heavily depend on ablative properties, shape of the vehicle (blunt objects give best ablation results), entry profile (high angle->more peak heat, but the heat is gone quicker, low angle- less peak heat but for longer period), entry velocity (earth orbit or returning from Moon/Mars) etc. $\endgroup$ – Sergiy Lenzion Jan 29 '20 at 11:00
  • $\begingroup$ Yep, it's complicated. If the original plan for the Space Shuttle heat protection had worked - i.e. 8 or 10 large thermal pads instead of a few thousand, the cost would have been quite reasonable. (and very low mass) . But reentry from orbital will require careful control of the upper stage's attitude too. $\endgroup$ – Carl Witthoft Jan 29 '20 at 15:44
  • $\begingroup$ @LeoS definitely I would imagine so. Part of why I thought this might be tractable is that the vehicle is here shaped like a booster, has mass/density like a booster, and is coming along whatever is optimal from LEO. $\endgroup$ – ikrase Jan 30 '20 at 10:54

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