Should Fermi Have Secured His Water Heater

A common student response to quantitative questions without obvious answers is “I have no idea.” Often these questions can be addressed by Fermi estimation, in which a difficult‐to‐estimate quantity is estimated by combining order of magnitude estimates of easier‐to‐estimate quantities. Although this approach is commonly used for numerical estimates, it can be applied to issues combining science and policy. Either application involves dividing an issue into tractable components and addressing them separately. To learn this method, our natural hazards seminar considered a statement by the Illinois Emergency Management Agency that homeowners should secure water heaters to prevent them from being damaged by earthquakes. We divided this question into subtopics, researched each, and discussed them to reach a synthesis. We estimated the net benefit: the difference between the expected value of damage and the cost of securing. This benefit is positive, indicating that securing is worthwhile, only if the probability of damage during the heater’s life is relatively large, approximately 1%–10%. To assess whether the actual probability is likely to be this high, we assume that major heater damage is likely only for shaking with modified Mercalli intensity VIII (“heavy furniture overturned”) or greater. Intensity data for 200 years of Illinois earthquakes show that this level was reached only in the southernmost part of the state for the 1811–1812 New Madrid earthquakes. As expected, the highest known shaking generally decreases northward toward Chicago, consistent with the fact that we find no cases of earthquake‐toppled water heaters in Illinois. We compared the rate of return on securing a water heater in Chicago to buying a lottery ticket when the jackpot is large and found the latter a better investment. This project let us explore ideas that might otherwise have seemed abstract and difficult to grasp, and suggests that other courses might consider similar projects.