
Estimating a nuclear blast with bits of paper - secretsinger
http://www.dannen.com/decision/fermi.html
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bdcs
Wikipedia 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/](https://thatsmaths.com/2014/09/18/how-big-was-the-bomb/)

~~~
anovikov
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.

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VLM
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.

~~~
mikeash
According to the NUKEMAP, the survival rate at 10 miles of a 1 megaton bomb
should be pretty good:

[https://nuclearsecrecy.com/nukemap/](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.)

~~~
wayn3
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.

~~~
ridgeguy
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](https://en.wikipedia.org/wiki/Little_Boy)
[2]
[https://en.wikipedia.org/wiki/Fat_Man](https://en.wikipedia.org/wiki/Fat_Man)

~~~
wayn3
about 1/3rd of a mile? weird units are weird :P

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Jedi72
One can only imagine what this moment must have been like for Fermi.

~~~
Hockenbrizzle
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.

------
rod_mdelc
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!

