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The Buckingham π theorem and the atomic bomb

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On 16 July 1945, the first nuclear test, ‘Trinity’, was carried out and with it the nuclear age began. The explosion was huge, but the actual calculation of the amount of energy released was rather difficult due to the large number of physical and chemical processes involved in the detonating reaction; even the rough estimates were far from accurate. It was not until the publication of the photographs of the explosion that scientists became aware of its magnitude. With just these photographs and some clever mathematical arguments, British physicist GI Taylor,  Soviet physicist LI Sedov and Hungarian–American mathematician John von Nuemann estimated independently an energy of about 17 kilotons of TNT.  Taylor published this result in 1950, with the US Army not at all thrilled that this sensitive piece of information was now in the public domain. Although the estimates of Taylor, Sedov and von Neumann required the use of some complex mathematics, dimensional analysis and the Buckingham π theorem allow us to come to the same conclusion with a minimum amount of knowledge of physics.

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