The last 8ft or so of the first floor has a flat roof. (Here already cleared.)

One end of my house has a flat "rubber" roof. After a heavy snow, I worry about the accumulated weight, and usually go out an upstairs window with a snow shovel to clear it off. Today, with the temperature rising into the tropical upper twenties (it bottomed out at 0

^{o}F last night), I decided it was time.

As I sent cubic-foot blocks
hurtling to the ground, I got to wondering just how much extra weight that roof
was supporting. How hard could it be to
figure out, at least roughly? If I knew
the weight of a given volume of snow--i.e. its density, then I could multiply
that by the volume of snow to get the total weight.

If you care about the details,
read on. Otherwise, photos might be enough.

Estimating density would be a bit
tricky: not only does snow differ in density from one snowfall to another, and
as it changes temperature, it also differs with depth in the same snow: the
deeper down you look, the more the snow will be packed down by the snow
overlying it. Finally, the density will
change as you handle snow to measure it, whether you accidentally pack it down,
or fluff it up.

Thinking about weighing snow on
our old kitchen spring scale gave me an idea.
The lid of the scale, which doubles as the weighing pan, is a short
cylinder with almost straight sides. It
reminds me a bit of a device soil scientists use to find the density of soil: a
bulk density corer. The idea is to drive
the short, fat cylinder of the corer into a body of soil, removing it intact
for measurement. Measurements will be
more true to the soil's natural state because the soil will be almost
undisturbed, and neither loosened nor packed-down.

My son passed the scale to me
through the window. A shovel thrust
straight down made a flat surface to push the scale pan into. Once the pan was in flush with this surface,
a big more careful work with the snow shovel got the core out intact for
weighing. Since I expected the density
to vary with depth, I pushed the pan into the snow about halfway down, to make
the core more "average."

Snow cut straight vertically for sampling.

Taking a bulk core with the scale pan, being careful not to disturb or pack it.

Weight full: 10.5oz.

Weight (approximately) empty: 5.5oz.

The scale pan with snow read 10
1/2 ounces, and 5 1/2 ounces empty. Because
it's easier to do math with metric units, I will call this 0.14 kg.* The pan's volume can be found from its radius
and height. Since it's inside is 14cm (o.14m)
in diameter and 8cm (0.08m) deep, the volume is the area of the circle times
the height, or pi

^{.}r^{2.}h=3.14X(0.075m)^{2}X0.08m=0.0014m^{3}. Giving the snow a density of mass/volume=99kg/m^{3}. (That sounds like a lot, until you consider how big a cubic meter is! In fact, pure water is about 1000kg/m^{3}--that's a bit over a ton per cubic meter, to mix my units a bit.) It nicely fits the generalization that snow is typically 90% air.
Now for the total volume of snow. I didn't think to get my
son to pass me a tape measure, but the depth of snow varied from about two
inches deeper than my foot-deep shovel blade to about two inches less deep.
That's 0.36m down to 0.25m. Since these is back-of-the envelope calculations, I'll
presume the snow depth varied smoothly for a roof width of 8ft (2.4m).
Imagining this cross-section as a rectangle with a thin triangle on top gives
it an area of (0.25mX2.4m)+(1/2X0.11mX2.4m)=0.73m

^{2}. Since the roof is about 27ft or 8m long, the total volume of snow is roughly 0.73m^{2}X8m=5.8m^{3}.### Result:

At a density of about 100kg/m3, this gives a total snow mass
of around 600kg, with a weight in English units of 1300lb. Impressive, but of
course that weight is spread over a roof that's 2.4mX8m=19m

^{2}in area, so it amounts to only 68lb per square meter. The guy shoveling it exerts 210lb on the much smaller area of his shoes--so it's high time he got the hell off the roof!
This little exercise isn't as
time-consuming to do as it is to write about.
Even so, I don't plan to repeat it.
I could probably guesstimate future snowfall weights by comparing them
to this one.

**is a measure of**

*Mass**how much "stuff"*something has, while

**is**

*weight**the*

*force gravity exerts*on that stuff. We can, however, relate them safely provided the force of gravity remains constant. Rather than "2.2lb=1kg," instead, think, "a mass of 1kg has a weight of 2.2lb at normal earth surface gravity."

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