Snow on narrowboats, and gauging loads

On her blog yesterday Heather of Takey Tezey mentioned that members of the local constabulary were handing out £50 fines to anyone driving around with snow on their vehicle's roof. In a comment I explained why driving with snow on the roof is dangerous, but then got thinking about how much snow would have to fall on a narrowboat's roof before its weight* became a hazard.

A foot of snow on a 60' narrowboat weighs about a ton. How do I know? Well, I worked it out.

60 feet is about 20m. That's 2,000cm. The boat's beam is about seven feet, or approximately 2m. That's 200cm. Multiplying together gives the area:

2,000cm x 200cm = 400,000 square centimetres.

Assuming that a foot of snow is equivalent to an inch of water, all we have to do is multiply this depth (1" = 2.5cm approx.) by the area:

2.5cm x 400,000 square centimetres = 1,000,000 cubic centimetres.

This is the total equivalent volume of water.

We know from car engine capacities that 1,000cc is 1 litre. So a million cc is 1,000 litres. A litre of water weighs 1kg, so a foot of snow on this narrowboat would weigh 1,000kg, or one tonne (or approximately one ton in old money).

The extra load would, assuming even distribution, merely serve to push the boat down in the water about an inch. (Why? Because that's the equivalent extra depth of water on top of the boat. It would displace its own weight of canal water, or an inch's worth.) That's if the ice were to relax its grip (and it probably would). OK, the boat's now a little less stable now, but dangerously so? Probably not. Most of the weight (I believe a modern steel narrowboat weighs about 17 tons) is still below water level.

Now if TWO feet of snow were to fall, that would mean two tons extra on the roof, or a possible increase in weight of more than ten percent. This could start to get significant, especially as this weight is a long way from where you'd normally want ballast.

In calculating the above I now understand why working boats sink about an inch for every ton of load. Yes, working boats are generally 72 feet long, but a cabin and the pointed bow would limit the hold to a maximum of 60 feet, so my calculation, although approximate, is directly applicable.

The photo is of Fulbourne heading up the Thames above Teddington Locks. It looks as though there's a good two feet of freeboard, so I would estimate that it could take an extra 24 tons of load. (That's 24 feet of snow!)

*Note: I have talked about "weight" (a force) where, strictly speaking, I should have used the word "mass" (a, er, mass). But, given that narrowboats are unlikely to be navigating in an environment where the acceleration due to gravity is much different from 9.81 metres per second squared, I think I can get away with it! Of course, if we discover narrowboats on the moon - in a snowstorm - I'm quite prepared to reconsider.