In a nuclear attack, there’s no avoiding the brutal math

Like many Washingtonians, I try not to think about my proximity to a potential nuclear attack bull’s-eye. I live just over a mile from the U.S. Capitol, and I work three-quarters of a mile from the White House.

I’ve blithely assumed that if D.C. were ever bombed in a nuclear attack, I would just vaporize without ever knowing what hit me. But as I’ve learned from a recent analysis of where and when to take shelter, the kinds of nuclear weapons that would probably be used in an attack today are much smaller — and more survivable — than the megaton warheads stockpiled during the Cold War. The detonation could be 10 kilotons (equivalent to 10,000 tons of TNT) or less, and most people more than half a mile from ground zero would survive the initial blast from a 10-kiloton nuclear bomb, according to my new favorite government report, Planning Guidance for Response to a Nuclear Detonation. So I’ve got a fighting chance even at three-quarters of a mile from an attack on the White House.

One of the first things my fellow survivors and I will face is the highest-stakes math test we’ve ever taken. Let’s say you’re at work in a downtown area when the blast happens. You see a flash, your building shakes and a number of windows shatter. Through one of the gaping holes you see a mushroom cloud forming. There’s no basement, so you run to an interior windowless office. Now what? Hunker down and wait for rescue, or make a dash for your friend’s building three blocks over that has a basement break room?

You start having flashbacks to story problems involving trains.

Bob is receiving x Roentgens per hour in his office, but would receive only x/5 Roentgens per hour in a basement. The basement is 10 minutes away and the radiation outside is 10x. What the heck should Bob do now?

It could seem like a lost cause even for a worry-wart planner like me who memorizes the cabin safety information cards on airplanes (there’s no rear exit on a US Airways CRJ-200, in case you ever need to know).

Luckily atmospheric scientist Michael Dillon of Lawrence Livermore National Laboratory in California has developed some helpful rules of thumb. He focused on minimizing total radiation exposure regardless of blast size, wind direction or many other factors that could affect radiation levels. In math terms, you’re minimizing the area under the curve of your radiation exposure over time: the integral, for those who took calculus. (Yet more evidence that math skills really are useful.)

One way to minimize that total exposure is to get to a location that blocks more radiation. The best shelter is belowground — say, in a basement. Hiding in the basement of a large apartment or office building can bring radiation levels down to one two-hundredth of the outdoor dose, a protection factor of 200. Being inside a one-story wooden house, on the other hand, may only cut your exposure in half, a protection factor of 2. About 20 percent of U.S. houses are considered poor radiation shelters (we’re looking at you, California wood-frame cottages without basements).

So what to do if you are caught in a poor shelter but think you can get to a better one? Here’s where Dillon’s math comes in. Essentially, you’re comparing the extra area added to your exposure curve while you’re outdoors with the area you’ll save by spending time in the better shelter later. Radiation levels will be tailing off over time; one rule of thumb is called the 7-10 rule: Seven hours after a blast, you’ll be getting one-tenth the dose received in the first hour.

The most important factors, Dillon found, are how long it has been since the detonation and how long it will take you to get to the better shelter. To minimize the area under your curve, you’re going to want to minimize the ratio of the time you spend in an initial poor-quality shelter to the time you spend outdoors getting to better shelter.

If you have access to only a poor-quality shelter initially (something like a wooden house with no basement) but can get to an adequate shelter (with a protection factor of 10 or more, like the basement of a wooden house) within five minutes, you should ditch the poor shelter immediately and go to the better shelter, Dillon reports January 14 in the

Proceedings of the Royal Society A

. If it will take you 15 minutes to get to the adequate shelter, you can still reduce your total exposure as long as you make your move within 30 minutes of the detonation. After that, your savings decline along with the outdoor radiation levels.

If you are in or able to immediately enter adequate shelter right after a blast, federal guidelines say you shoud stay put. So if you’re our hypothetical office worker in downtown Washington, D.C., you should probably stay in an interior room near the center of the building unless you’re confident you can get to that supersafe basement before highly radioactive fallout starts raining down. According to a 2009 federal report that examined the effect of a 10-kiloton blast in downtown D.C. and in Los Angeles, “if you are outside of the building-collapse area immediately surrounding the detonation, you should have several minutes before fallout arrives.” After that, it’s unlikely you’re going to have enough information to calculate whether your total dosage would be reduced by moving from adequate to better shelter, even if you’ve memorized the equations.

Once you’re hunkered down, you can generally expect to stay put for at least a couple hours in a minimally adequate shelter before trying to evacuate the area, and 24 hours or more if you’re in a good shelter with a protection factor over 100 (again, minimizing your total exposure as outdoor levels fall). That decision can involve a different set of equations, based on wind speed and direction plus a whole host of other variables.

Still, that’s not nearly as long as movies would have us believe we need to hide out. Instead of living out my final days wishing I’d remembered a can opener, maybe I’ll just be glad I was such a worry wart up front.