Nuclear Mangos

This blog is intended to provide reliable technical analysis of nuclear issues with non-state actors and nuclear beginner states. Some technical issues have important policy implications that citizens in a democracy should be able to make informed decisions about. The motivation for the blog has been the incredible amount of lies & hyperbole on the Iran situation of early 2006. The blog title is to remind you constantly of the quality of minds in charge of our nuclear security today.

Location: MA

Until recently I was a physics professor at Harvard, where I taught the nuclear and particle physics course, among others. I've recently left that position to work as an R&D physicist in security applications. I have never done classified weapons work.

Monday, September 10, 2007

What's the Risk?

As a gruesome homework problem, just what was the expected fatality risk that the errant B-52 flight presented?

The flight from Minot to Barksdale is about 1200 miles as the crow flies. The airplane death rate is about 1.9 deaths per 100 million miles; if the average crash kills 19 people (to keep the numbers easy), the crash rate is once per billion miles. So the odds of a crash are about one in 800,000.

Suppose that the plane leaves a swath of destruction 0.1 square miles in size. By eye, the average population density along the path is about 30 per square mile.

What is the radiation risk in a crash? There are several ways to estimate it.

1. One is the "worst case" calculation, which assumes the plutonium is perfectly evenly dispersed in respirable particles through the atmosphere of the planet, where it remains until breathed in by a human. There were 6 warheads on the plane. An oft-cited number is 6kg of Pu for a warhead; and the fatal respirable quantity is about a microgram. This upper limit gives 36 billion people killed. A more stringent upper limit can be estimated by simply noting that the human population of the planet is only 6 billion people.

This assumption may also be dubious on the grounds that is suggests plutonium is more dangerous if it does not initiate a nuclear explosion, but merely hits the ground with a big thud. If true, that would make X-Division's life much easier!

2. However, this is not a very realistic assumption. Most of the Pu will be in unrespirable particles, most of which settle to the ground quickly and form a radiation hazard over a few hundred meters from the site. This is messy, but unless you're right in this area, not fatal. "Plumes" of a few square miles with sufficient concentration might possibly form.

This gives an estimate at the outside of say ten square miles per warhead, or sixty square miles. On average over the flight path this is about 1800 fatalities.

3. As a third "upper limit" (i.e. number we know the value must be less than), we may take the expected number of casualties from a nuclear explosion at the worst point along the flight path, which surely must be near Kansas City. Note I do not think the path passes over KC! This is just for estimation's sake. A detonation over KC might bring 200,000 fatalities.

So we need to weight the outcomes by their probabilities, which as we saw above was about 1 in 800,000. So the expected "badness" of the flight was

1. In the ultimate planet-killing worst case upper-limit, the expected fatalities per flight are less than 7500.
2. Given the "best estimate" available on what Pu actually does, the expected fatalities per flight is probably in the neighborhood of 0.002.
3. Given another extreme upper limit, as if the warheads actually initiated a thermonuclear explosion in Kansas City, the expected fatalities per flight are less than 0.25 . (nb in principle I ought to reweight this downward by a large factor since KC is only a small part of the flight path, but then we'd have to do a horrible sum over the flight path which I'd prefer to avoid if it's just a very loose upper limit.)

So the best available estimate probably gives about 0.002 fatalities per flight; and the number is surely less than 0.25 per flight.

0.002 fatalities actually doesn't sound as low as I might like for any activity that might be regular. But the practice of flying nuclear warheads on B-52's is no longer a regular activity.

Update: CKR points out that this has actually happened! A B-52 crashed in Palomares, Spain, in 1966, with four hydrogen bombs. One fell into the Mediterranean Sea, three on land. Of the three on land, two had their conventional explosives detonate--precisely a classic "dirty bomb". 2 square kilometers were contaminated, and no fatalities were attributed to the crash.

According to Milnet:

By 1969, a U.S.Commission had settled 522 claims by Palomares residents totalling $600,000. It also gave the town of Palomares the gift of a desalting plant, which cost about $200,000 to build.

There was also a crash at Thule Air Base in Greenland in 1968, in which a B-52 crashed, and all four weapons were destroyed by fire:

After it was abandoned, the plane did a 180 degree turn and crashed onto the ice of North Star Bay, seven and one-half miles southwest of Thule, whereupon it skidded across the ice in flames and exploded. It is believed that the high explosives in the outer coverings of the four 1.1 megaton H-Bombs aboard detonated, releasing radiation from the plutonium in the bombs and causing fires which destroyed all four. Wreckage of the plane was widely scattered in an area about 300 yards on either side of the plane's path, much of it in "cigarette box-sized" pieces.

Again, no fatalities were attributed to the crash.

In both cases there were substantial cleanup operations lasting many months.


Anonymous Anonymous said...

The numbers you are using are far beyond what has actually happened in air crashes involving nuclear weapons, like the one in Palomares, Spain.

That was probably the worst.


11:17 AM  
Blogger Andrew Foland said...

Wow, thanks!

I was trying to make the most "conservative" reasonable assumptions to set the outer limits (following a discussion at Digby's place), but there's nothing like data!

10:54 PM  
Anonymous Anonymous said...

You're welcome. Thanks yourself for doing some work to dig out the details.

I left out the Thule crash because the population density there was much, much less than any of the country that the Minot-Barksdale nuclear express flew over.

There have been a number of accidents involving nuclear weapons, but I think Palomares and Thule are the only two in which the weapons caught fire or the conventional explosive detonated.


10:27 AM  

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