Tuesday, July 31, 2012

Fun with math

Yeah, that's right. Having fun by playing with numbers. It's what I do.

Remember this photo of the Sandy Drake from two days ago?

When I took it, I noticed how big the piles of coal in the barges were. The ones closest to the boat especially looked big. If you look at the depth marker on this particular barge, you'll see that the barges is loaded to almost 11 feet deep.

The Corps of Engineers is required to maintain a nine-foot-deep channel in the Ohio River, although in practice it maintains 12. So, most times you see a loaded barge in summer, when the river is at its lowest, it's loaded to nine feet.

But the river was running a few feet high last weekend, and in times like that companies try to get a little more coal -- or a lot more coal -- onto each barge.

An empty barge drafts about two feet (more or less) and a loaded barge nine feet. A rule of thumb is that a loaded coal barge hauls 1,500 tons, so each foot of coal in a barge is roughly 200+ tons. If you load it to 11 feet instead of nine, you can get an additional 400 tons of coal on there. That's about 28 percent extra cargo with one boat and one crew.

To verify that, do the math. A coal barge is about 195 feet long and 35 feet wide. That's 6,825 cubit feet per foot of draft. Double that for the two extra feet of coal and you have 13,650 cubic feet. A cubit foot of water weighs about 62.43 pounds. Multiply13,650 by 62.43 and you get about 852,169 pounds, or about 426 tons of displacement.

After I did the math, I wondered what it must be like for a pilot to steer all that coal on a boat with a boat like the Sandy Drake, which has less than 2,000 hp, I believe, as opposed to a 6,000-hp boat like some of the newer ones. But that's one of many questions I would like to ask people in the river industry, top to bottom, should I ever get the chance again.

ONE MORE THING: In winter, when Crounse and other companies load barges down like this, a lot of ice builds up on the head of the tow. A heavy barge sits lower in the water, and when there are waves driven by wind or current, water splashes up onto the front of the barge and freezes. I've seen and photographed several instances of that, and I'm always glad I'm not the guy who has to go out there and get that ice off of there, if anyone ever has to.