Estimating a nuclear blast with bits of paper
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&#x2F;0.2e3 or 50 Zeppelins of gas when it goes boom aka 50 * 10 M cu ft = 500 million cu feet of gas.<p>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&#x27;t expand the dirt so the sphere result is 1.25 meters or 4 feet or assuming about 5000 feet per mile we&#x27;re talking a thousandth of a mile.<p>So my adjusted &quot;done in my head&quot; 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.<p>So if V = 4&#x2F;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?<p>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.<p>That would imply to me that he measured a good 5 kilotons of air displacement.<p>There&#x27;s a heck of a lot of &quot;round to one sig fig&quot; and &quot;spherical cows&quot; 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&#x27;s a realistic way to do in your head what he did.<p>The atmosphere is not a perfectly linear gas, its not constant pressure with height, blah blah.<p>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 &quot;prove&quot; it should be about 1 meter of displacement  for every 4 kilotons then his real &quot;in the head math&quot; was 2.5 times 4.<p>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&#x27;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&#x27;d expect.