One of our readers, John Frewen-Lord, has been housebound for four days by the recent heavy snow falls – about 60 cm deep in his area. This has prompted him to provide an illustration of the comparative simplicity of calculating snow loads in metric units.

John writes:

“Two winter calculations. Which is easier?

Like many parts of the UK in the beginning of December 2010, we in North East Lincolnshire have had a lot of snow. Up to now we’ve had around 60 cm. On the roofs of our cars it is about 50 cm deep. Like all good motorists, and having just spent three days digging one car out, we do not drive off with snow like this on the roof. Apart from it being dangerous to vehicles behind (and possibly illegal as well), it is a huge amount of extra weight to carry around! Carrying all that extra weight not only increases fuel consumption unnecessarily, but it is more likely to get you stuck in deep snow – a lighter vehicle will not bog down in snow as much as a heavier one.

So how much extra weight does this 50 cm of snow amount to? In metric it is a very easy calculation. The only things we need to know are that snow has about 1/10^{th} the density of liquid water, 1 litre (L) is 1000^{th} of a cubic metre, and that 1 L of water weighs 1 kg. Now from this it can be seen that 1 L = 1 m² x 1 mm deep.

Now I measured the pile of snow on the roof of my car, and it was approximately 2 m long x 1.5 m wide, or 3 m². Using the above information, 3 m² of snow x 50 cm deep is equivalent to 3 m² of water x 50 mm deep. Therefore the snow on the roof of my car will have an equivalent water volume of 3 x 50 = 150 L. Which will weigh 150 kg.

As the average adult person weighs 75 kg, that is equivalent to carrying an extra two people around. I think you will agree that those calculations are pretty simple, and could be easily done in your head. Could you do the same in imperial units? I very much doubt it.

Let’s say the snow on the roof of my car is 6ft 6 in long by 5 ft wide, and that it is 20 in deep. We need to convert the feet and inches to feet only, so the area becomes 6.5 x 5 = 32.5 ft². The 20 in of snow is equivalent to 32.5 ft² x 2 in deep of water. Where we do we go from here? The easiest way is to calculate the volume of water in cubic feet, by converting the 2 in to decimals of a foot. This then becomes 32.5 x 0.167 = 5.43 ft³. Now 1 ft³ = 6.22883288 imperial gallons (let’s round that to 6.23 gallons). Our water therefore has a volume of 5.43 x 6.23 = 33.8 gallons. How much does 1 gallon of water weigh? The imperial gallon (but not the US gallon) happens to weigh 10 lbs, so the weight of the snow on the roof of my car would be 33.8 x 10 = 338 lbs.

We’re not finished yet. That weight of 338 lbs, representing the weight of two people of 169 lbs each, needs to be converted to those stones that we British seem to love. There are 14 lbs in a stone, therefore 169 lbs = 12.07 stones = 12 stone 1 lb.

While you may not want to calculate the weight of snow on the roof of your car (though it is an eye-opener as to just how much it does weigh), this sort of calculation is surely typical of the kind that most of have to make continually in our lives. Whereas the metric calculations in this example involved just 4 calculations which were easily done in your head, and involved NO conversion factors, the imperial calculations involved no fewer than 9 calculations, of which 6 involved a conversion factor of one sort or another. And unless you have lots of time on your hands and like doing calculations manually with some awkward numbers, a calculator is necessary.

I am still amazed that we in the UK still want to torture ourselves with calculations like this.”

John,

I agree metric is easier, and with all your calculation methods. However, be aware that 10% of water density is a very crude approximation to snow density. It varies considerable with conditions. If the snow packs well into snowballs, it is appreciably heavier, 2X or more. You may find this article helpful. Apparently attempts to predict density from temperature and other conditions are only rough guides, and you really need to melt a core for snow-water-equivalent.

http://www.or.nrcs.usda.gov/Snow/about/swe.html

Many people deprecate the use of the decimetre (dm), but I found it useful here as 1 dm³ = 1 L. Hence, weight of snow = 20 x 15 x 5 x 0.1 = 150 kg. Just one step, compared with imperial's nine.

John has chosen a topical example of the simplicity of metric calculations, but others can be found in every walk of life, at work and in the home. Time will show if those people, companies and countries which prefer expensive and inefficient practices can survive and prosper in global markets.

Just as a point of interest, I do know of an incident where someone was fined £60 and 3 penalty points for driving their car with snow on the roof.

I strongly agree with Derek about the usefulness of the decimetre.

We don't have to limit ourselves to rectangular shapes either. For example the volume of a cylinder is quite close to 80% of the enclosing box shape (actually it's pi/4 = 0.785 to 3 d.p.). So consider a tin can 70 mm in diameter and 100 mm tall, then converting to dm we have 0.7 x 0.7 x 1 x 0.8 = 0.392 or about 400 ml

Critics would point out that the convenient fluid mass relationship to the litre only applies to water. True, but at least the basic unit used for liquids does relate sensibly to linear units. Can't say that for the pint versus the cubic inch or the gallon versus the cubic foot etc.

John raised the interesting question – “Which is the easier to calculate”. The answer is self-evident, but was John asking the right question? In reality there is a mood of “Am I bovvered?” in the UK – fuelled by, amongst other things, the complex calculations needed in situations that could be simplified by using metric units.

This brings up another point, should we bother? Well, yes, we should. The point, houses, buying, doing them up and furnishing. Here in UK we have room sizes almost exclusively in ft and ins times the number of rooms as the single guide to spending hundreds of thousands of pounds on a house. Try asking the floor area of the house, try working it out! I have only bought one house outside UK but have rented plenty. Always the first thing you know is the area in sq. m.,the land in hectares, often a ground plan as well. No need to look at 100 homes to see that 95 of them are not what you want. Yet we seem to love the system here. Then buying materials, in France just about everything is sold buy the sq.m, just measure the room then buy the same amout of material and mostly the job is done. Replacing the boiler? already got the house size job done.

Everything is ok, I was looking at the statement you give, 1 / 10 density, only a little error; you forgot to divide 150 with 10, so that was only 15 kilos !!! It's another question whether the density is constant; it could be a light snow but other times wetter like ...I'm living on mountain...Kopaonik in Serbia, former Yugoslavia...

@Tibor

I just shovelled snow off a trampoline and found this calculation.

It is 3.4 m * 3.4 m and it was very heavy.

Regarding your correction. Please note the calc already has reduced by 10.

"3 m² of snow x 50 cm deep is equivalent to 3 m² of water x 50 mm deep"

3 m² of snow x 500 mm deep is equivalent to 3 m² of water x 50 mm deep

The 500mm to 50 mm here is the division by 10.

My snow was 20 cm deep and I definitely shoveled off 230 kg of snow rather than 23 kg.