Should Fermi Have Secured his Water Heater Against Earthquakes?

Abstract:

A common student response to quantitative questions in science with no obvious answer is "I have no idea." Often these questions can be addressed by Fermi estimation, in which an apparently difficult-to-estimate quantity for which one has little intuitive sense can be sensibly estimated by combining order of magnitude estimates of easier-to-estimate quantities. Although this approach is most commonly used for numerical estimates, it can also be applied to issues combining both science and policy. Either application involves dividing an issue into tractable components and addressing them separately. To learn this method, our natural hazard policy 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 weekly to reach a synthesis. We used a simple model to estimate the net benefit, the difference between the expected value of damage and the cost of securing a water heater. 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 water heater damage is likely only for shaking with MMI intensity VIII ("heavy furniture overturned") or greater. Intensity data for the past 200 years of Illinois earthquakes show that this level was reached only in the very southernmost part of the state for the 1811-1812 New Madrid earthquakes. As expected, the highest known shaking generally decreases northward toward Chicago. This history is consistent with the fact that we find no known 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 that the latter would be a better investment. This project gave our seminar an interesting way to explore ideas that might otherwise have seemed abstract and difficult to grasp, and suggests that other classes might consider similar projects.