Scale Analysis VS Magnitude Comparisons

There are some subtle facts about scale analysis that make it more powerful than simply comparing orders of magnitude. A most remarkable example is that scale analysis can be applied, through a systematic use of dimensions, even when the precise equations governing the dynamics of a system are not known. The great physicist G. I. Taylor, a character whose prolific legacy haunts any aspiring scientist, gave a famous demonstration of this deceptively simple approach. In the 1950s, back when the detonating power of the nuclear bomb was a carefully guarded secret, the U.S. government incautiously released some unclassified photographs of a nuclear explosion. Taylor realized that whereas its details would be complex, the fundamentals of the problem would be governed by a few parameters. From dimensional arguments, he posited that there ought to be a scale-invariant number linking the radius of the blast, the time from detonation, energy released in the explosion, and the density of the surrounding air. From the photographs, he was able to estimate the radius and timing of the blast, inferring a remarkably accurate—and embarrassingly public—estimate of the energy of the explosion.

Giulio on how this technique was used to estimate the power of a secret nuclear blast from a photo.