Nuclear explosions
No article about Taylor would be complete without including the often told story about his calculation of the energy in a nuclear blast. Fables of this story abound. As told by Taylor himself,16 during the early years of World War II he was told by the British government about the development of the atomic bomb, and was asked to think about the mechanical effect produced by such an explosion. He realized that the energy released from the bomb would quickly lose memory of its initial shape and distribution, and would produce a strong shock in the air. The structure of the shock far from the ground would be well-approximated as spherical.
With these simplifications Taylor recognized that the parameters in the problem are the energy E, the density r of air, the pressure p in the air, the radius R(t) of the blast wave, and the time t since the blast. Because the blast is very strong, the air pressure will not affect the wave very much, and so p is not a relevant parameter. Taylor realized that this implies that there is a single dimensionless number characterizing the process; the reader can verify that Et2/rR5 is dimensionless.
Because this quantity does not depend on any aspect of the problem, it must be a constant. This implies that the radius of the blast wave is given by
R(t) = c(Et2/r)1/5,
where c is a constant. In fact, it turns out that for air c~1.033 according to a calculation. Therefore, given a picture that shows the radius of the blast, a reference length scale, and the time since the blast, one can deduce the energy.
Much after the fact, Taylor analyzed photographs taken by J. E. Mack of the first atomic explosion in New Mexico. These pictures were taken at precise time intervals from the instant of the explosion, and Taylor confirmed that the scaling law agrees very nicely with the data. It is interesting to note that, of the papers written in the early 1950s reporting independent discoveries of the blast scaling law (authors including John von Neumann and Leonid Sedov), only Taylor’s paper took publicly available data to show that the above equation agrees with experiments.
There are many topics that we have not been able to cover in this article, or in our course—among them, the bulk of Taylor’s contributions to solid mechanics. Another effort to design a course around Taylor’s papers would likely arrive at a completely different list of topics. We encourage interested readers to browse Taylor’s collected works and to design their own course using his papers as a gateway to the modern literature.
http://www.seas.harvard.edu/brenner/taylor/physic_today/taylor.htm
