Saturday, January 4, 2014

Domestic Science

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 0oF 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.r2.h=3.14X(0.075m)2X0.08m=0.0014m3.  Giving the snow a density of mass/volume=99kg/m3.  (That sounds like a lot, until you consider how big a cubic meter is!  In fact, pure water is about 1000kg/m3 --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)=0.73m2.  Since the roof is about 27ft or 8m long, the total volume of snow is roughly 0.73m2X8m=5.8m3.


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=19m2 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.

While I'm up here, I'll take a couple of photos of the Wild Place I often write about.
*A pet peeve of mine (yes, I've got a zoo-full) is the misconception that weight (e.g. pounds) and mass (e.g. kilograms) are the same thing.  They are not.  I sigh deeply when someone says that one kilogram "equals" 2.2 pounds.  It doesn't.  Mass is a measure of how much "stuff" something has, while weight is 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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