Walkable Ice

In the absence of significant global warming, Minnesotans still need to contend with ice on the sidewalks (to be clear, in the presence of significant global warming, we would have other problems; and in the presence of significant global cooling, we would face snow and glaciers rather than freezing rain and ice).
My own house suffers this problem, despite (or because of) snow clearance, ice re-forms on the sidewalks and steps, or freezing rain falls on the cleared sidewalks, making them slick, rather than on snow-covered sidewalks, making them crunchy. Further, water drips from the house and gutters because of ice dams, and then freezes on the ground.
My alma mater, Georgia Tech, while not typically subject to much snow or ice, has many sidewalks just above steam-heat pipes, which would clear those sidewalks pretty readily in most conditions. The University of Minnesota does a pretty good job with snow clearance, all things considered, using a lot of labor and snow clearance machines in the process.
Ice clearance is hard in this freeze-melt cycle, especially when the water has no where to drain because (1) the sidewalks are convex (along either width or length), (2) the boulevards are covered in snow creating no place for run off to go and creating a source for new melted water, (3) the storm drains are covered in snow, and (4) the ground is still frozen and/or the soil above the freeze line is super-saturated.
I see a lot of attention to ice-free roads, and very little for ice-free sidewalks. This would greatly enhance walkability, reduce the likelihood of severe injury, and increase the number of pedestrians.
There are a variety of ways to address icy sidewalks:

  • Mechanical: clearing sidewalks with shovels and pick-axes and snow-bots.
  • Friction: Sand, Grit, Gravel make the ice more walkable (by increasing friction);
  • Chemical: Salt (reduces ice via melting);
  • Radiant: heated sidewalks (using a variety of techniques);
  • Protection: covered sidewalks; and

If we consider the cost of an icy sidewalk equal to the probability of a fall multiplied by the cost of a fall, multiplied by the number of people who face that probability per day, times the number of days the sidewalk is icy, we can get a sense of the amount we should invest to avoid the ice.
Let’s say I fall once a year on the ice (typical), after traveling 2.6 km * 2 times a day * 10 ice days = 52 km. My fall rate: is 1 fall per 52 km of ice.
For a house with 10 m of frontage, with 100 pedestrians a day, it gets 1 km of pedestrian traffic per day. Once every 52 icy days, it will see someone fall.
The cost of a fall is unclear, since most falls are unreported. For reported falls which require medical care, the estimate is on the order of $10,000. Let’s assume 10% of falls require medical attention, meaning the average cost per fall is $1,000.
This implies that every 52 icy days (once every 5.2 years if there are 10 icy days per year), each house with icy sidewalks imposes $1,000 in costs. In that case, if we want to minimize social costs, we should be willing to invest $19 day in effective ice clearance. This is about an hour of labor (or two hours of undergraduate labor) to operate simple machines plus some cheap (Friction or Chemical based) treatments). Unfortunately, I am unclear whether $19/day is effective.
We could add delay costs, due to people walking slower on ice, which I estimate to be about a 10% reduction in walking speed. With a travel speed typically of 1.44 m/s, we might decrease that to 1.3 m/s. So instead of the 100 pedestrians taking 7 seconds each to walk in front of the house, they are taking 7.7 seconds. That is 70 person-seconds per day, which has an economic value of (@ $15/hour) of $0.30 per day, two orders of magnitude lower than the fall costs, and so not really worth discussing further.
But can we prevent the ice from forming?
For $1000 every 5.2 years, we get $5000 for a 26 year expected life of a capital investment. If we can make a capital investment of less than $5000 to eliminate falls on our public sidewalk, it would be socially worthwhile.
The cost of heating sidewalks is about $20 per square foot (or about $215 per square meter). A 10 meter by 2 meter sidewalk is 20 meters square, giving us a cost of $4305.
We must consider operating costs, which are estimated at $.60/hour. If it is operating 240 hours per year (this is a guess, I don’t know how long it needs to operate to keep the sidewalk ice free), this is $144 year. (You might run it to melt snow, but that has fewer benefits, just avoiding shoveling, not reduced falling in this simple model, so I don’t consider that). $144 per year is $3744 over 26 years (no discounting), so is a large fraction of the capital costs.
Unfortunately, $4305+$3744 > $5000, so 100 pedestrians is not enough to justify heating. However 160 pedestrians would be a break-even point.
Covering the sidewalks (200m of roofing) could cost $80/square foot ($860/square meter). This lasts 15 years. For 20 square meters, this costs $17,200, well out of range for our residential sidewalk if the only objective is ice reduction, especially since it only lasts 15 years. It might have other benefits, such as reducing our exposure to nature and street-life though.
Policy recommendation: Use student labor to clear sidewalks with low pedestrian flows. Heat sidewalks which have high pedestrian flows. Cover sidewalks with very high pedestrian flows.
Yes, I did fall this year. This post was written between my vertical and horizontal positions, so I apologize in advance for its rushed nature.