[WalterBright]

My fluid mechanics prof told the class that a scientist in the 1940's published the yield of the Hiroshima bomb. Since this was top secret, he got investigated. But he showed how the yield could be calculated from the film of the explosion - how fast the blast radius expanded.

So I imagine the yield of the Beirut explosion could be calculated the same way from the video.

[rmm]

Paper in question.

http://sites.science.oregonstate.edu/~restrepo/MTH481/Classn...

From videos:

R=450m

t=1.5s

rho=1.2kg/m3

E=9.84E12 kg.m2/s2 or 9.84E19 erg

Equiv TNT = 2.5kTonnes -TNT

Equiv AN = 5400 Tonnes

So double what current media is saying.

edit:formatting.

[Denvercoder9]

You have to be careful about your errors though with this method, because you get higher-order powers. If the radius estimation was wrong by only 10%, your final answer will be wrong by almost 50%.

[WalterBright]

You da man! Thank you.

[selimthegrim]

It was G.I. Taylor.

[tigerlily]

Using the Buckingham Pi theorem.

[hanche]

And data from smaller explosions of known magnitude, in order to determine the dimensionless constant that cannot be determined from Buckingham’s theorem alone.

[raverbashing]

There's a story about Feynman estimating yield by dropping pieces of paper and seeing how far they'd travel in the shockwave

[kleton]

Feynman told that story about Fermi.

[mhh__]

Imagine being so good that Feynman tells stories about you (rather than himself).

Fermi also put Dyson down gently once "A successful theory must have either a strong physical intuition or a rigorous mathematical basis: you have neither"

[lordgrenville]

Fermi was an inveterate experimentalist, always trying to measure and test things. Hence the idea of the Fermi estimate.

There's a good piece about him here: https://www.lrb.co.uk/the-paper/v40/n10/steven-shapin/think-...

>Fermi saw the Trinity Test as an opportunity for one of his famous exercises of rational estimation, a Fermi problem. First, he offered to take wagers from other scientists on whether the bomb would ignite the atmosphere, destroying New Mexico or even the entire world. Then, the evening before, he carefully prepared an experiment to estimate the bomb’s explosive yield:

> "About forty seconds after the explosion the air blast reached me, I tried to estimate its strength by dropping from about six feet small pieces of paper before, during and after the passage of the blast wave. Since, at the time, there was no wind, I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2.5 metres, which, at the time, I estimated to correspond to a blast that would be produced by ten thousand tons of TNT."

> "He was so profoundly and totally absorbed in his bits of paper," his wife recorded, "that he was not aware of the tremendous noise." The answer later calculated by the instrumentation specialists was 18 kilotons, but Fermi’s answer was arrived at on the spot – and it was correct within an order of magnitude.

[Udik]

> First, he offered to take wagers from other scientists on whether the bomb would ignite the atmosphere, destroying New Mexico or even the entire world.

Of course if you bet on the bomb not causing the end of the world, you can only win.

[raverbashing]

Ah you're right!