## Monday, February 16, 2009

### Nuclear submarine collision what are the chances?

"A Royal Navy nuclear submarine was involved in a collision in the middle of the Atlantic, it was reported.

The crash between HMS Vanguard and French submarine Le Triomphant, which was also carrying nuclear warheads, is believed to have occurred on February 3 or 4, The Sun claimed."

A nuclear submarine seems to be about 140 meters with a radius of 12. So that's a volume of about 63360 cubic meters.

The Atlantic ocean is 354,700,000 cubic kilometers. There are 1 000 000 000 cubic metres is a cubic kilometer. Of course subs can only dive to about 400 metres. So say they stay in the top 300 meters then the volume might be more like 106.4 million km squared * 300 meters=30 million cubic km. More likely they avoid the top 20 meters where ships might hit them, so their range is estimated to be 20-2320 meters deep.

This is assuming a submarine is a cylinder which it isn't.
How many nuclear submarines are there? There seems to be about 50 in the world. Navies will keep their own submarines separate. But that still means there are in the Atlantic maybe 25 submarines that the French or UK subs could run into. This does reduce the number of subs the Russians Or Americans can hit significantly though. They have a top speed of about 40 km per hour. So I assume they are wandering around at 20kph. So assuming all the worlds submarines are in the Atlantic ocean at the same time how often would you expect one to hit another if they were traveling round at random?

Thom said...

Every 4.2 seconds. They just keep quiet about it.

krusty said...

If it they were travelling around at random, I’d say never. The time frame between subs being built and the Earth being devoured by the great space insect on the eve of the next millennium celebration is basically a thousand years. Given a fairly static population of subs, and each randomly changing direction and wandering far from any collective points of interest, the chances of such small objects in a huge system meeting would be equivalent to Garda finding incriminating documents in a bank that is state owned and already given over all the documents it was going to, having shredded the rest.
K

Fergal said...

I don't think a Fermi argument applies here.

First, submarines follow either submarines or surface ships, and surface ships follow narrow shipping lanes across the ocean. So the actual area of ocean in which you are likely to find a submarine is orders of magnitude lower than the total area of ocean. Even the subs that are doing their best to hide from the other subs would only do so in regions of the ocean that are mapped, which is a very small percentage.

Once you determined the that area and assuming (incorrectly, but reasonably) that all subs can dive to the same depth, you could start making estimates of volumes occupied per hour per sub.

But even then, I don't think you can assume uniform random variables for sub positions. Half the subs are spending their time watching the other subs, and satellites are doing the same, so some sort of incompetence would have to happen for two subs to collide.

David Curran said...

"I don't think you can assume uniform random variables for sub positions. Half the subs are spending their time watching the other subs, and satellites are doing the same, so some sort of incompetence would have to happen for two subs to collide."

I thought the whole point of nuclear subs was that no one knew where they were? If they spend their time following each other around that kind of messes up MAD doesn't it? On the incompetance issue that is what im trying to put a figure on "how unlikely is a collision" and so how much evidence do we have that it was nto a chance event?