Between 1945 and 1962 the United States conducted 210 atmospheric nuclear tests. Each event was captured with special cameras, able to record at around 2,400 frames per second. Many declassified films of these tests have been recently retrieved by the Lawrence Livermore National Laboratory (LLNL) and
released on Youtube. Below I'll show that is possible to determine the total energy liberated during these tests by estimating the expansion rate of the blast wave. Something that can be done solely from the video of the explosion. This is exactly what two physicists, British Geoffrey I. Taylor and his Russian colleague Leonid Sedov, did after the United States exploded the first atomic bomb in 1945 (the famous Trinity test in New Mexico). Using a few images of the explosions that were shared with the rest of the world by the US army, they determined the total energy released by the new weapon, an information that was highly classified at the time.
A nuclear weapon releases, almost instantaneously, a very large amount of energy. This is deposited in a relatively small area, leading to a spherical blast wave expansion. The evolution of this blast wave turns out to be a relatively simple physical problem, since the only important variables of the problem are the total deposited energy
\(E_0\) and the density
\(\rho_0\) of the medium in which the explosion occurs. This means that the radial evolution of the fireball depends only on the energy yield of the weapon and the density of the material in which it exploded (in this case air). Conversely, if one can measure the expansion rate of the fireball in a medium of known density, one can retrieve the energy of the explosion. I tried reproducing what Sedov and Taylor did in 1945 with the Trinity test, using one of the newly released footage from the Tesla test, part of
operation Teapot. This particular bomb was exploded on the 1st of March 1955 in the Nevada test site, some 65 miles north west of Las Vegas. In Figure
\ref{279461} six frames extracted from the youtube video show the expansion of the blast wave. Below I re-derived the Sedov-Taylor solution, which I used to fit the data and estimate the total energy of the blast in Figure
\ref{483223}. The data and the code I used is accessible through the data icon in that figure. The best fit is obtained for an energy of 4.3 kilotons, which given the approximations and the very rudimental way I used to determine the location of the blast wave radius, is in very good agreement with the value declared by LLNL (7 kilotons). Science
works! You can try doing this with some of the
other videos, and check if the declared energy of the weapon matches what you find. For more details on the Taylor-Sedov solution see
\citet{Taylor_1950,SEDOV_1959}.