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We have a completely uniform, hollow sphere made of high-strength steel. Inside this sphere a Tsar Bomba (RDS-220) is detonated. How thick (ballpark figure) would the sphere need to be to withstand the detonation without the outer surface being breached?

Some key values that may or may not be relevant:

  • Blast yield: 210 PJ (50 megatons of TNT, from the wikipedia page)
  • Diameter of the hollow space inside the sphere: 8m (just enough to fit the length of the bomb, from the wikipedia page)
  • Steel: I'm not sure which parameters are neccessary, but as a start I'm gonna post the data sheet of Strenx 1300. Any other high-strength steel is fine too, in case some important data is missing on this specific one.

Strenx 1300 data sheet

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How big a sphere could the bomb melt completely?

Just a first attempt, probably hasn't a lot to do with the actual question, but at least we get a number in the end, so here it goes.

According to this paper, the energy for melting steel from room temperature is about $1247 \frac{\text{MJ}}{\text{t}} = 1247 \frac{\text{kJ}}{\text{kg}}$. This means with our blast yield of $210 \text{PJ}$, we can melt $\frac{210 \cdot 10̂^{15}}{1247 \cdot 10^3}=168\cdot10^9 \text{kg}$ of steel. With a density of $7850 \frac{\text{kg}}{\text{m}^3}$, the meltable volume is $\frac{168\cdot10^9}{7850}=21.4\cdot10^6 \text{m}^3$. Neglecting the hollow inner space, this gives us a radius (which equals the thickness) of $\sqrt[3]\frac{3\cdot21.4\cdot10^6}{4\cdot\pi}=172\text{m}.$

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  • $\begingroup$ Let's take a step back.... The thermal radiation from this bomb would have caused 3rd degree burns 100 km away. The shock wave still broke windows 900 km away. It detonated 4.2 km above the ground and the shock wave caused a 5-5.25 earthquake. The fireball was 8 km high. You are talking in the neighborhood of several thousand kPA of pressure per square inch on the inside radiating in all directions. Your calculation may be correct.... but I would not bet on it... $\endgroup$ – Rick Dec 28 '20 at 3:47
  • $\begingroup$ @Rick A 400m diameter massive steel sphere isn't exactly small either. I can't find a mistake in my calculation, but if you find one I'd love to see it. $\endgroup$ – MaxD Dec 28 '20 at 4:04
  • $\begingroup$ I am not doubting the calculations. I am wondering if if it can truly take into account of everything that happens in an event of this magnitude. Does the 200 PJ take into account the radiant X-ray pressures that force the initial fusion reaction, the 100M C heat of the fusion that cannot be released into the atmosphere. Since it cannot be released, I would expect the fusion reaction would be extended increasing the temperature that is being maintained within the steel sphere. $\endgroup$ – Rick Dec 28 '20 at 14:14
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    $\begingroup$ your back of the envelope is not that bad, just imagine an underground explosion $\endgroup$ – Wolphram jonny Dec 29 '20 at 3:32
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I used to watch science shows. They were showing an explosion trapped in various medium and its effects. They detonated an explosion in water, then in corn starch, then in the open air.
The explosion was causing destruction in every medium.
They finally put an explosion in a box with no medium (i.e Vacuum).

Guess what happened next?

The explosion just filled the vacuum space and not causing any destruction. I was very much surprised and excited about watching that happen.

As much I can guess that a Spherical Container having Large diameter for vacuum space with strong Vacuum that is coated with Radiation absorbing material, which can sustain that strong vacuum force is required.
This will definitely nullify the shock wave formed due to the Thermonuclear Detonation.
Thus Vacuum acts as an invisible Blast Shield and filling that Container immediately with Cryogenic Nitrogen will definitely help in lowering the extreme detonation temperature.

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