A Volcanic Fermi Problem

Enrico Fermi not only estimated the number of piano tuners in Chicago, one of his most famous estimates was the one he made during the first atom bomb test on 16 July, 1945. There was an important question in the minds of the bomb makers on the yield of this new class of weapon. During the test Fermi estimated that it was about 10 kilotons.

Fermi didn't guess - as the shockwave from the explosion hit Fermi he threw a handful of paper scraps into the air and watched how far they moved. Using this data and some assumptions he made his estimate. It was surprisingly accurate. Not only to the correct order of magnitude, but within a very respectable factor of 2. The actual yield was 19 kilotons.

Fermi used the "piano tuner" approach to train his students to be able to conceptualise and evaluate "order of magnitude" estimates.

For a very recent Fermi estimate - of the energy released (and volume and mass of sand ejected) during the eruption of the Puyehue-Cordon Caulle volcano in Chile on 4 July see here = http://arxiv.org/abs/1109.1165.

Fermi Problem: Power developed at the eruption of the Puyehue-Cordón Caulle volcanic system in June 2011

By Hernan Asorey & Arturo López Dávalos

Abstract of the paper reads;

On June 4 2011 the Puyehue-Cordon Caulle volcanic system produced a pyroclastic subplinian eruption reaching level 3 in the volcanic explosivity index. The first stage of the eruption released sand and ashes that affected small towns and cities in the surrounding areas, including San Carlos de Bariloche, in Argentina, one of the largest cities in the North Patagonian Andean region. By treating the eruption as a Fermi problem, we estimated the volume and mass of sand ejected as well as the energy and power released during the eruptive phase. We then put the results in context by comparing the obtained values with everyday quantities, like the load of a cargo truck or the electric power produced in Argentina. These calculations have been done as a pedagogic exercise, and after evaluation of the hypothesis was done in the classroom, the calculations have been performed by the students. These are students of the first physics course at the Physics and Chemistry Teacher Programs of the Universidad Nacional de Rio Negro