# Slick Calculations

Mathematician Jeremy Teitelbaum plays by the numbers in an effort to comprehend the Gulf oil spill.

### Playing by the numbers in an effort to comprehend the Gulf oil spill.

On a hill overlooking the UConn campus stand three big blue water towers. For a long time I never noticed them – they’re the kind of landscape feature that the eye tends to edit out – but recently they were discussed at a meeting of the University’s Buildings and Grounds Committee, on which I serve.

Two of the three towers, holding together about a million gallons of water, are old and need to be replaced, and it was our job to approve the spending of \$2.5 million to do that work. (If you’re going to store a million gallons of water on a hill above campus, it’s a good idea to make sure that the tanks will not fail.)

The third, more modern tower holds a million gallons on its own.

The million-gallon figure struck me as particularly significant because the most recent estimate of the amount of oil spewing out of the damaged Deepwater Horizon well on the floor of the Gulf of Mexico is 60,000 barrels per day. A barrel of oil is about 42 gallons, so 60,000 barrels is 2.5 million gallons. Every 10 hours or so, a million gallons of oil – enough to fill the biggest of the three blue tanks overlooking UConn’s campus – pours into the Gulf of Mexico. Between the accident on April 20, 2010, and today, June 22, 64 days have elapsed, so something like 160 million gallons of oil have been released into the water. That’s equivalent to 160 of those big blue tanks, with more oil coming every minute.

Somehow, though, this isn’t a very satisfying picture of the scope of the mess. The oil isn’t neatly packaged in big blue tanks. As you can see from this image generated by UConn’s Department of Marine Sciences, there’s oil in a thin slick over a large stretch of ocean near the southern shore of the U.S.

I found a nice graph at this site, belonging to the Australian Maritime Safety Authority, that explains a little bit about the thickness of oil on water. According to that graph, a slick half a micron thick is barely visible on water, while one 100 microns thick forms a gloppy “mousse.”

To put those numbers in perspective, a piece of cheap copy paper is around 100 microns thick. So, to try to visualize a million-gallon slick that’s 100 microns deep, imagine taking the biggest blue UConn water tower, filling it up with neatly stacked pieces of paper, and then laying that paper out over the surrounding landscape. My calculations say that this amount of paper (or oil) forms a circle about 3.5 km, or about 2.2 miles, in radius.

This means that if a one-million gallon slick were centered at our water towers, it would stretch west to Eagleville Pond and north to Four Corners and beyond.

If it were 1 micron thick instead of 100 microns thick, it would be much larger. In fact, it would be large enough to completely cover the 1,400 square miles of Long Island Sound.

It’s a cliché that humans aren’t good at grasping large numbers. When I hear about a big number with some significance – the 60,000 barrels of oil a day – I make a point of turning that number around in my head in order to try to get some sort of comprehension of it. This visual calculation of the spill came out of such a mental exercise.

Now if I can just make some sense of the \$3 billion or so that represents the projected shortfall in Connecticut’s state budget, or the \$1.2 trillion that make up the federal deficit, I will really be making some progress.

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