# What shape most efficiently disperses an overpressure wave from a nuclear weapon?

One rule of architectural design in one of my settings is the prime number rule: a building that abides by this rule can survive a 2-kiloton nuclear surface burst 300 meters away 5 times in a row while keeping the occupants safe. It's called the prime number rule because 2,3, and 5 are the first prime numbers. Don't laugh, weirder things have been come up with IRL.

In practice, no nuclear weapons in my setting reach the level of 2 kilotons, as nuclear detonations above 1 kiloton are forbidden by treaty, and generally result in the offender getting scrubbed off the map by everyone else's megaton-level missile forces, but corporate and the public both decided that the prime number rule was a snazzy quality-assurance kind of thing, and so it stuck.

One part of surviving a 2-kiloton surface burst at 300 meters is withstanding, according to NUKEMAP-2:

• 65,000 rem of radiation (neutron/gamma; alpha/beta radiation is nonexistent for the purposes of this).

• 17 psi of overpressure.

The 65,000 rem of radiation can be resolved, and I already have done that. However, my problem is the overpressure. I cannot find as many reliable sources regarding defense against overpressure.

What shape of construction most efficiently dissipates the energy from a 24-psi overpressure/shock wave?

Undergrounding the structure is not a viable option here; the area in question has a rather high water table, and the soil is heavily contaminated with perchlorates that would seep in and be detrimental to the structure's occupants, among other consideration. I need an above-ground structure, and I need to know its shape.

• @ARogueAnt. I will. Commented Oct 15, 2021 at 0:35
• Do you assume the blast is always coming from the same direction and altitude (ie the same exact target)? Otherwise, you need a shape like a sphere or cylinder that can resist forces from multiple directions equally. Commented Oct 15, 2021 at 0:40
• @DWKraus Not necessarily the same direction. Commented Oct 15, 2021 at 0:41
• BTW, if the perchlorates are those on a not terraformed Mars, the low atmospheric pressure makes the atmospheric nuke blasts way less effective - there's not enough of it to create 17psi of overpressure. (pedantic note: you forgot to specify the Earth-conditions for your setup). Commented Oct 15, 2021 at 2:24
• Maybe some topics on se/physics would help find answers ? physics.stackexchange.com/questions/187272/… and physics.stackexchange.com/questions/109888/… Commented Oct 15, 2021 at 9:41

# Cylinders or domes:

With explosions coming from potentially multiple different directions, you need the advantages a circle can give you. Maximize internal space per unit of surface with a sphere, although this isn't always the most living-space friendly option. A sphere, like an egg, is strong against external force disproportionate to the thickness of the wall.

The classic example of a blast-resistant above-ground structure is the German Flak tower. A number of these structures still exist simply because they are so hard to demolish that people repurpose them or even bury them rather than demolish them. These are, admittedly not quite circular due to construction limitations. But the closer you get to a sphere or circle, the more resistant your structure will be.

• FlaK does NOT HAVE A C IN THERE! Flug Abwehr Kanone Fl A K. That being said, you don't want a tower, those irl were like 6 stories high, you want more like 3 Stories max Commented Oct 15, 2021 at 8:56
• @Hobbamok Fair enough. If you've been following this line of questions, the OP wants above-ground buildings as normal as possible, but I agree a hemispheric dome as short as possible (or better yet, underground) is better. I'd make an artificial hill covering my building, personally, if the water table were really that high. Commented Oct 15, 2021 at 16:40

Lenticular shape, with rotation catenoid up-down faces (dome+inverted dome), placed on stilts.

The lateral cross-section will break a lateral shockwave, the catenoid shapes will distributed the load with a minimal surface.

The space underneath (between the stilts) will determine reflections of the shockwave on the ground, weakening it fast. If way too much overpressure in top, the stilts underneath will absorb a lot of the energy by crumbling - rebuilding them is way easier than rebuilding the lenticular shell.

Alternatively - just the upper catenoid shell should do just fine. A low elevation at the peak will offer a low profile on lateral hits by experiencing the blast on a tangential direction.

Disclaimer I'm not a building engineer, doing my best to suggest a plausible solution.

Glossary:

• catenary - the shape an uniform chain takes under uniform gravity. Invert it and that's the optimal shape an arch takes to support the weight of the wall on top of it

• catenoid dome - rotate a catenary around the vertical axis. Examples of such structure - igloos, musgum earth architecture. You will need it flattened, like the recently 3D printed bridge in Venice

• other refs of the compression bridge in Venice here, here. This one includes cross-sections of the blocks - they are not monolithic, but hollowed - yet no steel reinforcement was needed.

• Yes, but can crumbling supports resist five consecutive blasts? Commented Oct 15, 2021 at 0:41
• Are there things IRL with that shape that you could cite as an example? I have no idea what that looks like - not because you somehow failed in your answer, but just because I can't parse fancy people-what-knows-things words. Commented Oct 15, 2021 at 0:42
• @DWKraus a matter of engineering. If you ask if the problem admits a solution: yes, I believe so (but see the disclaimer). Can you demonstrate the impossibility of a solution? Commented Oct 15, 2021 at 1:01
• @KEY_ABRADE these are example of lenticular shape (think lentils): pinterest.fr/pin/376121006358207161 this one is flatter in the lower part than the upper part, but it doesn't have to. Commented Oct 15, 2021 at 8:05

## Concrete Domes

I know you say the radiation is taken care of, but I just want to point out that 65,000 Rem is 10,000 times the OSHA lifetime safety limit. That's a stupid dangerous amount of Rem. Roughly 500 Rem is considered fatal exposure.

If you built your shielding out of concrete, it would take 2 feet to get the radiation levels into low single digit Rem values.

Which is good, because a 20 psi over pressure wave is generally understood to damage or destroy heavily built concrete structures.

So you're going to need something that exceeds "heavily built" if you want to survive the 17 or 24 psi over pressure you site in your question. So probably a dome, since its a naturally strong shape that will evenly distribute energy from every direction.

Basically, these structures are going to be 3-4 foot thick concrete domes without any windows. Doors and other penetrations (eg ventilation) will be at ground level, and protected by short concrete tunnels.

• I did the math, it's more like 28 inches if you count the half-value thickness of concrete as 44.5 millimeters, and take into account that it needs to survive this five times in a row, meaning that each 65,000 rem dose needs to be reduced to less than 1 rem. Commented Oct 15, 2021 at 15:38
• @KEY_ABRADE - updated to better reflect your numbers Commented Oct 15, 2021 at 15:48

### Underground bunkers.

When the United States and Soviet Union governments were designing structures that were required to survive nuclear explosions, they universally went to designing underground bunker complexes. Most famously you have things like Cheyenne Mountain in the United States or the launch bunkers used by the US nuclear arsenal, there were a number of other underground complexes constructed by both sides of the Cold War.

If building above-ground structures was a viable means of resisting a nuclear assault, then the United States or USSR would have done so, because it would have been much cheaper than building underground structures. The fact that they never did suggests that it isn't.

If building an actual underground structure isn't viable due to poisons in the ground that can somehow penetrate solid rock and concrete, then they'd have to simulate building an underground structure with a sufficiently large amount of concrete.

• There's a difference between hundred megatons strategical nukes and tactical nukes. See Davy Crockett, MGR-3 Little John, Pluton. See also Five Men at Atomic Ground Zero Commented Oct 15, 2021 at 9:46
• The way against underground bunker is to drop one bomb after another on the same spot, using ground burst instead of airburst Commented Oct 15, 2021 at 14:11
• At the low kiloton level, above-ground structures work just fine at resisting nuclear explosions. See, for example, "Jumbo" at the Trinity test, or the Bank of Hiroshima vault.
– Mark
Commented Oct 15, 2021 at 20:34