During the first test of an atomic bomb on 16 July, 1945, one important question was the yield of the weapon. During the test, the Nobel-prize winning physicist Enrico Fermi, one of the leaders of the team, estimated that it was about 10 kilotons.
This was more than a mere guess. As the shockwave from the explosion hit the Base Camp where Fermi was observing the test, he method threw a handful of paper scraps into the air and watched how far the shock moved them.
Then. with a few straightforward assumptions, he made an estimate that turned out to be reasonably accurate. The actual yield turned out to be 19 kilotons.
Fermi was a master of estimation, an art that is worth acquiring. He famously set his students problems such as estimating the number of piano tuners in Chicago. This involves making a number of reasonable assumptions such as as the number of people living in Chicago, in how many houses there is a piano, how often a piano should be tuned, how long it takes for a tuner to do the work and so on.
In this spirit, Hernan Asory and Arturo Lopez Davalos at the Comision Nacional De Energia Atomica in Argentina, have set themselves (and their students) a similar estimation task. The problem is to estimate the energy release as well as the volume and mass of sand ejected during the eruption of the Puyehue-Cordon Caulle volcano in Chile on 4 July.
You can look up the calculations and the assumption they make in the paper. You might want to try the estimate yourself.
I’ll just leave you with a couple of very general but impressive figures: These guys conclude that the volcano produced 24 million truckloads of sand and released as much energy as the entire Argentinian electric power grid generates in 2.3 days.
Ref: arxiv.org/abs/1109.1165: Fermi Problem: Power developed at the eruption of the Puyehue-Cordon Caulle volcanic system in June 2011