Estimating a nuclear blast with bits of paper
dannen.com
dannen.com
Of course Taylor got an estimate within 2 as well, using photographs published in Life magazine.
So my theory is ten miles out the difference in volume between 10 miles and 10 miles+2.5 meters is half a billion cu ft. Now it doesn't expand the dirt so the sphere result is 1.25 meters or 4 feet or assuming about 5000 feet per mile we're talking a thousandth of a mile.
So my adjusted "done in my head" is at 10 miles, half a billion cu ft is the difference between 10 miles and 10.001 miles. At 5000 feet per mile 10 miles is about 50000 feet.
So if V = 4/3 pi r cubed, the derivative is 4 pi r squared, huh where have I seen that before, so at ten miles worth of feet radius, the volume slope is about 4 pi 50k squared or what twelve times 2.5 million? Or 25 million cubic feet of air slope at 10 miles per foot of blast front expansion?
So my blast front of 10 kilotons or 50 Zeppelins worth of gas should result in a shift of a good 20 feet but the dude reports 2.5 meters which is about 10 feet.
That would imply to me that he measured a good 5 kilotons of air displacement.
There's a heck of a lot of "round to one sig fig" and "spherical cows" and room temperature TNT explosions and foolishness like that so he probably gave himself a factor of two to handle that and I think that's a realistic way to do in your head what he did.
The atmosphere is not a perfectly linear gas, its not constant pressure with height, blah blah.
Of course what he probably actually did, since this project was kinda his day job, he likely calculated this stuff out on a blackboard without any rounding or spherical cows to "prove" it should be about 1 meter of displacement for every 4 kilotons then his real "in the head math" was 2.5 times 4.
Are any of these numbers reasonable? Well sure. At 10 miles the blast wave of a 10Kt simple nuke is a couple feet and virtually everyone survives it plus or minus building collapses. Good luck with the fallout and the fire, but the blast won't kill you, just knock you over probably. At 1 megaton that would be 100 times worse or like 250 meters instead of 2.5 meters and yes the survival rate at 10 miles of a 1 megaton fusion bomb is in fact roughly zero as you'd expect.
https://nuclearsecrecy.com/nukemap/
That gives 2.5km as the lethal radius for radiation, 3km as the 100% lethal radius for blast, 7km as the radius for "injuries are universal, fatalities are widespread" and 12.6km as the radius for 3rd degree burns from thermal radiation. At 16 km you'd still get badly burned if you were exposed to the flash and you could get killed by a collapsing building if you weren in something sturdy, but you'd have a decent chance of surviving.
On another note, did you account for the fact that it's only a half sphere since the bomb explodes near the ground? I might have just missed it.
(Incidentally, this is why they used to teach "duck and cover." At this sort of distance, your chances of surviving are much better if you're on the ground and under something sturdy when the shockwave hits. I never understood why "duck and cover" ended up with such a bad reputation.)
Because in the the probability of being in a location where it would make a difference to even short-term survival was minimal, and, in the event of a major superpower exchange (the main plausible scenario when those drills were common for anything that would include attacks on US population centers) short-survival was widely perceived (with some good reasons) to most likely buy you a long, painful death from a combination of the effects of fallout and those of the effects of the collapse of organized society.
Duck and cover dates from the 1950s, where the US's end of nuclear war would have looked much closer to a strangelovian "hair mussed" than the total apocalypse you describe. The Soviet Union didn't have the capability to cause that level of damage to the US until the mid 1960s or so.
The bad reputation of duck and cover does not, however.
> The Soviet Union didn't have the capability to cause that level of damage to the US until the mid 1960s or so.
The bad reputation dates from later than the 60s, AFAICT. It's not like duck and cover went away then: we were doing duck and cover drills in my elementary school in the 1980s, and classrooms in community colleges I saw had duck and cover instructions posted prominetly in the 1990s.
the relatively small bombs of hiroshima and nagsaki exploded about a mile above ground. the goal here is to make the shockwaves double up near the ground, causing more destruction.
i'd assume that bigger bombs would detonate at higher altitudes to achieve the same effect further out.
A commander might attempt to destroy some types of hardened bunkers by penetrating the ground before detonating, or completely destroy a fleet of armored vehicles or a single specific building with a direct strike on the fleet itself, or upon the building's roof. Destroying population centers, or industrial zones is another matter, where an airburst maximizes above ground damage distributed across an area.
The blast wave doesn't precisely "double up" as much as it smashes downward, and plows outward, with a reflection of the sphere bouncing back upward. This effect does result in two waves, above a certain height, closer in, near ground zero, with harsher effects on tall buildings, if there are any. But the angle of the reflection grows more acute, as distance from the center of the sphere increases, and the equator of the blast sphere widens. So, once you get out past a few miles from ground zero, unless your in a building taller than 200 feet (66 meters), it's still really just going to be a single front that slams the structure you're occupying.
Furthermore, while airbursts do take advantage of the principle of reflected force, peculiarities of the target terrain also play a role, in terms of both ground texture (stone vs. soil) and topography (hills and valleys). A city center with lots of concrete and asphalt will be highly reflective, but rural targets surrounded by agricultural soil will be absorbent and inelastic, and produce a distorted, lower fidelity reflection.
Topography, meanwhile, will produce additional distortion and blurred shadows, behind and around corners, so targets, set back, behind the crests of hills, or behind many layers of tall buildings, might enjoy a lateral shadows from both flash heat and blast forces, but not ambient heat after the wave passes.
Hiroshima: 1900 ft [1] Nagasaki: 1650 ft [2]
[1] https://en.wikipedia.org/wiki/Little_Boy [2] https://en.wikipedia.org/wiki/Fat_Man
- thermal radiation is, in fact, light, which travels at the speed of light - but you should not imagine the entirety of the thermal energy to be released by a nuclear weapon to be released instantaneously in a radially travelling sphere. that being said, youre not going to outrun such an explosion. where you are at the time of detonation pretty much determines your odds of survival.
Maybe not. Richard Feynman claimed to have watched a nuclear explosion with nothing but regular glass between him and the blast. He assumed the glass would block any ultraviolet light and he was not blinded.
http://calteches.library.caltech.edu/34/3/FeynmanLosAlamos.h...
What kills the most people depends on the size of the bomb. For really small ones (like the US Army's nuclear bazooka from the 50s) the prompt radiation has the greatest lethal radius. For medium sized ones like Hiroshima, blast is the major one. For really big ones, thermal effects reach the farthest.