STS-27 was able survive reentry without a tile because the was over a metal component with sufficient thermal inertia to serve as a heat sink without melting.
Would the steel frame of Starship be able to do the same, or is the skin too thin to transmit heat away from the hole quickly enough without melting?
If yes, is there any way it could handle the mechanical strain of what's probably going to be a mess of shocks & turbulent hypersonic airflow?
I think to answer this question, we need to define the term "endure" first. We could define three different failure modes:
If any of these failure modes were to occur, then we could say that the vehicle failed to endure the loss of a heat shield tile. Although, in the third failure mode, it depends on how frequently tiles are lost in practice, and how much inspection and refurbishment work must be done to reduce the tile loss rate.
There is also the question of whether the white padding material between the tile and the skin will be able to protect the steel. It might be Coated Nomex Felt with a temperature rating of 213°C.
Flame-Resistant Felt - Nomex® (also called meta-aramid felt) is a high-temperature felt that protects against extreme heat.
But, without precise knowledge of what this material is, how much of it there is, and what its properties are, it is not possible to determine whether it will remain intact and protect the steel through reentry. However, as your question focuses whether the skin is too thin to transmit heat away from the hole quickly enough without melting, so let's assume for this question that the white material does not hold up long and the steel ends up being directly exposed to the hypersonic airstream after a short while.
Finally, there are lots of tiles and it seems obvious that the answer will depend on which tile. Tiles at the fringes of the protected area are less critical. Let's assume that we are considering only the more important non-fringe tiles.
Let's now examine some of the data that we have on heating during vehicle reentry...
On the third Space Shuttle flight, the Kuiper Airborne Observatory flew under the orbiter as it reentered and captured an image of it's belly.
(ref)
As you can see from the image above, temperatures range from 2000 to 3000 °C.
Stainless steel's melting temperature is between 1,400 to 1,530 °C, depending on the specific consistency of the alloy in question. (ref)
The Space Shuttle endured these temperatures for around 13 minutes.
(ref)
A second source says...
Vehicles zooming through the atmosphere at Mach 20 experience temperatures in excess of 3,500 degrees Fahrenheit (1,927 degrees Celsius), DARPA officials said — hot enough to melt stainless steel.
The size of a thermal protection tile is around the size of a dinner plate, and the thickness of the stainless steel skin is about 4mm.
The 4mm thickness will not provide enough thermal mass to prevent the metal from melting during the 13 minutes of heating that will occur during reentry. However, if there were mass in addition to the skin, such as components of the frame, this may help as it did in the case of STS-27. However, note that STS-27 actually experienced more damage than STS-107 (the Columbia disaster), but just not in as critical a location. Atlantis did not really "endure" the loss of its thermal protection tiles, even though it technically "survived" reentry.
The second question we need to consider is whether the heat would be conducted away from the center of the unprotected region to the edges fast enough to prevent the center melting. Again, anyone who is familiar with heating or welding steel will understand intuitively that stainless steel has insufficient thermal conductivity to conduct heat away fast enough.
Next, there is the question of whether the steel could be kept cool by the fuel or oxidizer that is left in the tanks. If a tile were lost on a surface that did not have a propellant tank behind it, the answer would be, of course, no. If there was a tank behind the lost tile, that tank would be almost empty, and so it is unlikely that the vapor remaining inside the tanks would be able to provide significant convective cooling. But if there did happen to be liquid propellant on the other side of the skin, that propellant would probably prevent the steel from melting.
Finally, it is important to note that well before the skin reaches the melting point of stainless steel, it will reach its ignition point. For a reentry on Earth, oxygen in the air will begin to react with the metal causing it to burn, and this reaction will generate additional heat.
To summarize, the answer to your question as defined above is that, for most of the heat shield tiles, it is unlikely that the stainless steel of Starship will be able to endure the loss of the tile during reentry.
But you don't have to take my word for it. Elon Musk himself said, "...if there's any crack in the armor, it's toast.". (ref)
Update: On May 29th, 2024, Elon Musk tweeted...
Right now, we are not resilient to loss of a single tile in most places, as the secondary containment material will probably not survive. I will explain the problem in more depth with @Erdayastronaut next week. This is a thorny issue indeed, given that vast resources have been applied to solve it, thus far to no avail.
