Hellosailor posits that 10,000 shipping containers go over the side each year. It appears that these containers eventually sink or wash ashore. Let's just say they stay afloat for an average of six months. This means we've got about 5,000 containers floating out there at any given time. A standard shipping container is aprx. 40' x 8' resulting in a maximum surfaced area of 320 square feet. Five thousand of these results in 1.6 million square feet of hazard. Total surface area of the world's oceans are 3.6x10 the 15th power square feet. Dividing container sf by ocean sf ocean sf results in 4.4x10 to the negative 8th power or 0.00000000044 percent chance of encoutering a container at any given time.
This is very generalized, of course. Containers are certainly more concentrated near the shipping lanes and ocean currents may tend to concentrate them even further.
Not trying to pooh-pooh the concern of hitting one, but given the odds, it does not surprise me that we don't hear many stories of folks running into shipping containers.
Great intent on this, but it's not a surface area issue. Surface area would apply to the odds of a single, ocean-striking meteor hitting a boat, since the meteor slices through the "plain" of the ocean.
You boat is going to "slice through" the surface of the ocean/bay from one side to the other.
So, just rattling this off without too much thought in it... the odds of hitting a container is proportional to the length of your voyage, the number of containers afloat in the waters that you travel, the beam our your boat (kind of), and the beam of a shipping container (kind of). (Since shipping containers could be broadside to your path or not, use the average of the lenght and width of a shipping container. I'm ignoring height for this, although a container could be tilted, etc.) The odds are inversely proportional to the area of the waters you travel. (This along with the number of containers actually gives us the container-density).
Actually, the odds aren't exactly proportional to the beam of the boat and the beam of container. That would be true for one if the other had minicule width like a floating lobster pot buoy. Noodling it a bit, it's more proportional to the two beams added together.
So if I may do this with estimates and in the metric system to make the math easy...
. . . . . . . . . . TripLength * NumbConts * (BoatWidth + ContWidth)
. . . . .odds = ----------------------------------------------------------------
. . . . . . . . . . AreaOfWaters
Trip = 1,000km
Number of Containers currently floating in your ocean = 1,000
Boat width = 2 meters
Shipping container width = (13m + 3m)/2 = 8 m
Breath of ocean = 1,000km
Area of Ocean that containers are distributed across = 1,000km * 1,000km
. . . . odds = (1,000km * 1,000 * 10m) / (1,000km * 1,000km)
canceling out one set of "1,000km":
. . . . odds = (1,000 * 10m) / 1,000km
. . . . odds = 10km / 1,000km
canceling the "meters" from both side and dividing by 10
. . . . odds = 1 / 100
So if there were 1,000 containers floating in an smallish ocean, and you were to sail across that ocean, the change of hitting one is 1 in 100! (Even 100 containers floating in your small ocean would mean a 1 in 1000 chance of hitting one!)
Obviously there aren't that many containers still floating or there are fewer sailboats making such long trips. Either that or we just explained some of the sudden disappearances of sailboats.
(And yes, we could use the boat's smaller beam at the waterline instead. Like I said, this is quick noodling.)
Another way to picture this is to look at the area of your path, much like the area cleaned by a single push of a vacuum cleaner. And then compare that with the area of the ocean. If you path is longer, you have a greater chance of hitting something.
Hope this helps with a better approximation of the math. Not sure it's complete yet, but it's a bit better, and a bit scary.