Estimating a nuclear blast with bits of paper
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Re: Estimating a nuclear blast with bits of paper
#2One can only imagine what this moment must have been like for Fermi.
Re: Estimating a nuclear blast with bits of paper
#3One 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.
Re: Estimating a nuclear blast with bits of paper
#4Wikipedia says the Trinity test was 20 kilotons. With Fermi estimating 10 kt, he was off by a factor of only two.
Of course Taylor got an estimate within 2 as well, using photographs published in Life magazine.
Re: Estimating a nuclear blast with bits of paper
#5Wikipedia says the Trinity test was 20 kilotons. With Fermi estimating 10 kt, he was off by a factor of only two. 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/
It wasn't off at all. It was spot on. He estimated BLAST power, not total yield. Half of energy was released in form of prompt radiation, flash, and fallout.
Re: Estimating a nuclear blast with bits of paper
#6Wikipedia says the Trinity test was 20 kilotons. With Fermi estimating 10 kt, he was off by a factor of only two. 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/
It's called Fermi estimation for a reason!
Re: Estimating a nuclear blast with bits of paper
#7Lets 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.
Re: Estimating a nuclear blast with bits of paper
#8Lets 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…
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.)
Re: Estimating a nuclear blast with bits of paper
#9Lets 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…
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 we…
I think that the reason why people dismiss "duck and cover" is that they think it's issued as a recommendation for surviving inside the lethal radius.
Re: Estimating a nuclear blast with bits of paper
#10Earlier quoted context omitted.
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 we…
I think that the reason why people dismiss "duck and cover" is that they think it's issued as a recommendation for surviving inside the lethal radius .
Definitely less silly than get inside the fridge.