Steel may not remain solid within meters of a nuclear explosion
- The safe is not “extremely strong” at all. The model is likely Liberty Safe Co.'s Freedom 30. According to the specs, the save is constructed from 14 gauge steel sheet, which is slightly under 2mm of thickness. There is a layer of thermal insulation rated for 40 minutes in a 1200°F, or 650°C fire. The mass of the safe is 200kg. This is rather an entry-level safe, satisfying most U.S. states minimum requirements for a gun safe.
Evidence from the Trinity test
- For comparison, the steel tower of the Trinity test was 30m tall, mounted on a rebar-reinforced concrete foundation. I could not find the construction documentation, but it was obviously constructed from very much not 2mm-thick steel. The photograph below shows that each of the four main weight-bearing columns were square extrusions with a cross-section somewhat larger than an adult man's thigh, about 500mm. Extrusion profile is unknown, but we can safely put the thickness of the extrusion wall at 75mm. This yields the estimate of steel cross-section at 1300 cm², and each column's mass, assuming steel density of 7.9 g/cm³, 1300×3000×7.9=31 metric ton. Adding the cross-tie members of the tower, we can estimate the total mass of the steel construction to in the 200‒300 ton range (1,000 to 1,500 of “extremely strong” safes).
Trinity tower foundation close-up
Trinity tower, full view
- The Gadget was detonated on top of the tower, with the yield later estimated at 21 kt TNT equivalent. The tower has evaporated completely, according to the U.S. DoE. The annotated image of the fireball at 25ms after detonation shows the scale of the fireball. Note that the heating front had not yet been overcome by the shock wave adiabatic expansion front, which means that at this point the thermal radiation from the compressed air fireball core was still ongoing (v. infra), and the temperature and pressure at the fireball periphery had been increasing.
Annotated fireball profile at 25 ms. The scale bar size equals 100m.
- While most of the concrete foundation also either evaporated or remelted with the surrounding sand, a few rebar ties of one of the concrete pillows have partially survived. Molten and recrystallized sand surface is clearly visible.
Surviving foundation rebar ties
Rough theoretical analysis of fireball conditions
Dynamics of a nuclear explosion is analyzed in (Glasstone), while (Brode) additionally elaborates on the thermodynamics of the early internal fireball conditions.
After the energy is released by the nuclear device on the order of fractions of a microsecond, its X-ray part of the spectrum radiatively heats surrounding air. Cold air is opaque to X-rays, and is radiatively heated up to the temperature of about 1,000,000 K, at which point it becomes transparent to this part of the spectrum. The hot ionized gas at this temperature is itself a source of X-rays; this mechanism forms an expanding heating front of the fireball, isothermically propagating outwards, until the temperature drops to 800,000K, when the plasma loses thermal equilibrium with the X-ray radiation, and becomes confined to the outer opaque shell of air. This process is significantly faster than the adiabatic propagation of the shock front of expanding gas, due to the gas inertia, and dominates the fireball up to 75 μs since the explosion, reaching the radius of about 30 m from the explosion. From this point onward, the heat front propagation races against the adiabatic expansion of the hot gas. In the Trinity case, the last frame showing the expansion of the heat front is timed at 25 ms from the explosion. At this time the adiabatically expanding and cooling ball of gas overcame the radiative heat front, and temperature and pressure began to drop significantly.
The steel construction readily absorbs the thermal X-ray radiation, and, partially, γ-radiation: HVL=2.2 cm in pure iron for Co-60 γ-source (Johnson), which puts the absorption figure at about 50%, pre-heating if not melting the bulk of material from the initial intense γ-pulse. This combined radiative heating causes quick ablation of material, with the entire tower material undergoing more likely a supercritical phase transition than evaporation, on the time scale of 100-1000 μs, well within the intense thermal radiation-dominated, high-pressure fireball state, persisting for about half the time of the observed shift to adiabatic regime at 25 ms since the detonation, i.e. ~10 ms. The wide estimate range reflects a multitude of unknown and hard to account factors in this test, but still, even conservatively, is under an order of magnitude of the timespan of the required environment conditions.
Brode H. L. A Review of Nuclear Explosion Phenomena Pertinent to Protective Construction. R-425-PR. RAND Corp., May 1964.
Glasstone S. (ed.) The Effects of Nuclear Weapons, rev. ed. U.S. DoD, U.S. AEC. April 1962.
Johnson T. E., Birky K. B. Health Physics and Radiological Health, 4th ed., Wolters Kluwer, 2012