Thursday, July 14, 2005
Fact, fiction, and forecast
Perhaps you've been sent a copy.
Here is the third fact on the list, coming after one assertion about butterflies and another about ducks:
In 10 minutes, a hurricane releases more energy than all of the world's nuclear weapons combined.
When my nephew announced this from across the room what I said was, "that seems unlikely."
"It's a fact," was his indignant reply. "It says so right here."
"You know," I said, "that's the sort of thing we could check out."
Not being acquainted with Fermi or his methods, my nephew was skeptical. I got to work, he continued his litany: A snail can sleep for three years; All polar bears are left handed; Thirty-five percent of the people who use personal ads for dating are already married.
It's surprisingly difficult to find out the total megatonnage of the world's nuclear arsenal -- surprising because I seem to remember seeing the figure thrown around in the press all the time back in the good old Cold War days. The Center for Defense Information (CDI) publishes a factsheet listing Current World Nuclear Arsenals, but it only provides information on the number of weapons, omitting any mention of yields. Bulletin of the Atomic Scientists (BAS) has a handy chart of Estimated U.S. and Soviet/Russian Nuclear Stockpile, 1945-94. That chart lists total U.S. megatonnage, but withholds similar information about the Soviet/Russian stockpile for appropriately footnoted reasons.
The key fact from the CDI is that the world's nuclear stockpile contains roughly 15,672 strategic nuclear weapons. The key fact from the BAS is that the average yield of an American strategic nuclear weapon in 1996 was 300 kilotons. On the assumption that the average yield of the strategic nuclear weapons in the world's nuclear stockpile today is the same as the average yield of the strategic weapons in the American arsenal in 1996, the total yield of the world's nuclear arsenal is around 4,700 megatons.
I told my nephew, and asked if he thought that a hurricane produced that many megatons of energy every ten minutes. "Probably," he said.
The Atlantic Oceanographic and Meteorological Laboratory (AOML) has a heck of a hurricane FAQ. Subject D7 is How much energy does a hurricane release? It turns out that there are a couple of ways of answering that question. Here's the one that gives the answer with the highest magnitude:
An average hurricane produces 1.5 cm/day (0.6 inches/day) of rain inside a circle of radius 665 km (360 n.mi) (Gray 1981). (More rain falls in the inner portion of hurricane around the eyewall, less in the outer rainbands.) Converting this to a volume of rain gives 2.1 x 1016 cm3/day. A cubic cm of rain weighs 1 gm. Using the latent heat of condensation, this amount of rain produced gives 5.2 x 1019 Joules/day or 6.0 x 1014 Watts.
It's unclear how the energy released by the average hurricane differs from the energy released by a really big storm, but let that pass. Simple math reveals that the average hurricane yields 3.61 x 1017 Joules/10 minutes.
I asked my nephew, who was by now sitting beside me, how many Joules he thought there might be in a kiloton. He didn't know.
This was a little more difficult to figure out than I anticipated, since Google's units calculator doesn't handle this particular conversion. If I'd had the wits to immediately consult wikipedia, all of my questions would have been answered in a straighforward way. Instead, I placed my trust in this geek1 and committed an unfortunate calculating error.2
Without getting into the details of my mistake, let me just say that it involved orders of magnitude (note the plural) and led to the conclusion that this particular weird thing you would never know was true, though it might not have been during the Reagan years. When I announced this conclusion, my nephew jumped to his feet and yelled, "BOO YA! I knew it!" We had a short and, he told me, boring discussion about the relation of justification to knowledge and then it was time for him to go home and for me to check my work.
According to Wikipedia's definition, a megaton is equivalent to 4.184 x 1015 Joules. The world's nuclear arsenal, therefore, amounts to something like 1.97 x 1019 Joules.
Not even close. Boo ya.
1 'geek' being, in my book, praise.
2 An error which was entirely my own, and for which the aforementioned geek bears no responsibility.