Estimating a nuclear blast with bits of paper(dannen.com)
dannen.com
Estimating a nuclear blast with bits of paper
http://www.dannen.com/decision/fermi.html
31 comments
Lets see if I can replicate his mental math. Assuming a lot of spherical cows. A Zeppelin weighs like 200 tons and is about 10 million cubic feet of gas. I did cheat and look that up, everything else, including all the following mistakes, was messed up in my own head. 10 KT of TNT is 10e3/0.2e3 or 50 Zeppelins of gas when it goes boom aka 50 * 10 M cu ft = 500 million cu feet of gas.
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.
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.
According to the NUKEMAP, the survival rate at 10 miles of a 1 megaton bomb should be pretty good:
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.)
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.)
> 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.
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.
The probability of being in a location where it would make a difference was high. Huge parts of major cities would be in that zone.
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.
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.
> Duck and cover dates from the 1950s
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 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 bad reputation applied retroactively, though. People think it's stupid it was ever taught.
the bomb does not explode "near" the ground.
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.
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.
I do believe that the altitude of detonation is a tactical decision, based on target selection.
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.
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.
Much less than a mile altitude at detonation for both bombs.
Hiroshima: 1900 ft [1] Nagasaki: 1650 ft [2]
[1] https://en.wikipedia.org/wiki/Little_Boy [2] https://en.wikipedia.org/wiki/Fat_Man
Hiroshima: 1900 ft [1] Nagasaki: 1650 ft [2]
[1] https://en.wikipedia.org/wiki/Little_Boy [2] https://en.wikipedia.org/wiki/Fat_Man
about 1/3rd of a mile? weird units are weird :P
Trinity was on top of a tower, and Fermi was 10 miles away. A half sphere is much closer to that situation than a full sphere.
Per thermal radiation, does that mean essentially light? So if you see the explosion, no time to get out of the way, already burned?
- if you "see" the flash, thats the last thing youre ever going to see. will blind you.
- 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.
- 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.
> - if you "see" the flash, thats the last thing youre ever going to see. will blind you.
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...
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...
glass does block ultraviolet light, which makes it effective protection.
Trying to figure out the most rational thing to do at each distance. In fireball, say goodbye. Sounds like shock wave isn't that big of a deal on its own far beyond the fireball region, beyond eardrums, but obviously shrapnel and collapses will get you indirectly. But thermal radiation seems to extend much farther per the website and there's no escape. So is that what actually kills the most people? (Though it's 2017, who ever goes outside anymore?) And then of course fallout, but I guess you can flee or shelter from that.
The thermal pulse lasts several seconds for a large bomb. If you can immediately throw yourself into a ditch or behind a wall or otherwise shelter from it, you may greatly reduce the burns you receive.
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.
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.
In the latter, do you mean thermal radiation or thermal conduction? I guess it doesn't make a huge difference because radiation hits you before you cam do anything about it, and conduction is impossible to get away from. But curious anyway.
Radiation. I assume you men conduction through the air? That's basically what the fireball is, and it covers a much smaller area.
The shock wave is a serious hazard to personnel far beyond the fireball. Just a few pounds of dynamic overpressure presents a hurricane-force wind hazard, and five will result in catastrophic damage to non-hardened structures and a near complete loss of life. The shock front detaches quite early from the fireball. The classic scary videos of residential structures annihilated during nuclear testing were sampled from beyond the maximum fireball radii.
Yeah those videos make me wonder. But my understanding from https://en.wikipedia.org/wiki/Effects_of_nuclear_explosions
is that humans are quite a bit more resilient than structures. So a shock wave that utterly destroys an otherwise strong structure may not kill a human. However that seems related purely to the atmospheric shock wave itself. I guess shrapnel (even dirt), building collapse, maybe even "throwing the person" (so the ground, rather than atmospheric effects, kills) would greatly add to the indirect ways of dying. But is it most likely thermal radiation that actually does you in?
The thermal radiation and resulting firestorm would be the cause of most deaths from an attack on a city.
I'm reminded of Ender's Game playing with this.
One can only imagine what this moment must have been like for Fermi.
I believe he was often very silent about political or ethical matters of the "The Gadget". In contrast to other physicists at the time, like Oppenheimer and Szilard.
This anecdote is described in greater detail in "The Pope of Physics", by Gino Segrè & Bettina Hoerlin (Enrico Fermi's biography told by a nephew of a close collaborator of the famous physicist). This fascinating episode is told in the first chapter, if I rember correctly. He also poses the "how many piano tuners are in Chicago" problem, using a similar approximation technique. Great read, totally recommended!
Of course Taylor got an estimate within 2 as well, using photographs published in Life magazine.
https://thatsmaths.com/2014/09/18/how-big-was-the-bomb/