Monday, January 25, 2016

Proportion and Snow Removal

I don’t imagine that the big weekend storm qualified as a blizzard based on the conditions I saw in my town, but we did get two feet of snow. It ended before dawn Sunday but the cleanup has taken more than one day. People who have gone out today tell me the roads are narrow and icy. Some side streets are plowed so narrowly there isn’t room for two cars to pass. Some icy patches are the length of a tractor-trailer. Roads will improve as temperatures rise above freezing every day this week, but that’s happening for the first time just now. For those who have that option, the easy thing is to stay home until more melting occurs. More than a few workers between Virginia and Connecticut are working at home today.

The difficulty in clearing two feet of snow is surprising to some people. It’s just snow, right? What could be so difficult about it? This reaction is an indication of how poorly humans are equipped with a sense of proportion. Intuition suggests to many people that clearing two feet of snow should be about twice as hard as clearing two inches of snow. It’s a case where intuition misleads.

It’s easy to see how far off this kind of intuition can be when you consider that part of snow removal is simply transportation, or carrying the snow from point to point, even if those points are just ten steps apart. The work of transporting snow is proportional to the weight of snow that has to be carried between two points. But wait. With more snow, some of it has to be carried farther. A snow pile is not a point, but is a heap that spreads out in proportion to the amount of snow added.

When you try to create a physical model of snow removal and look at it mathematically, it is easy to see that some parts of the work are proportional to the snow depth, some are proportional to the square of the snow depth, and some are fixed (for example, you might retrieve the same shovel from storage regardless of snow depth). Put it all together, and two feet of snow might be about ten times as much work as two inches of snow.

That kind of physical model assumes you are working efficiently, but efficiency comes more easily with work that is familiar. Around here a two-foot snowfall occurs about once every eight years. It will never be routine work. Any miscalculation from the unfamiliarity of the work adds to the effort.

It shouldn’t be too surprising, then, if it takes days to get roads in good order after a two-foot snowfall or if corners are cut along the way. It helps that the snow came late in the season. If the cleanup is a bit messy, it’s a temporary problem. All but the larger snow piles will melt away within a few weeks.