One of the interesting aspects of the 2016 winter storm from Jonas is the snow. Yes, there is lots of snow—but what do you do with all of it? If it wasn’t too much, you could just plow the streets and leave the extra snow on the side. With a bit more snow, you have to scoop it up on the side and ship it out to snow farms—yes, there is such a thing. A snow farm is a place where they just pile up extra snow (and it can take a long time to melt—last year’s snow in Boston didn’t melt until the summer).

But sometimes, a snow farm isn’t good enough. When you need snow removed right now, you need a snow melter. Again, yes—these things actually exist. It’s basically a big machine that you dump snow into and it melts the snow so you can pour it down the storm drain where it hopefully doesn’t freeze.

### How Much Power Do You Need to Melt Snow?

I’ll be honest. I don’t know much about snow melters. In fact, before this storm I didn’t even know they existed. However, I do know something about estimations. So, let’s get right to it.

• When it snows, people usually measure it in inches of accumulation (at least in the USA). But what really matters is the mass, which depends on the density. The density of snow can change a lot. Wet snow has a high density; dry snow is low. I remember hearing that 1 inch of rain would be like 10 inches of snow—so I will use that to get the mass of snow.
• You don’t need to remove all the snow—just the stuff on the streets. So, what percent of surface area for a city is covered by streets? Based on my rough estimations from Google Maps, a random block in Washington DC is about 10 percent street. Really, before looking at a map I was going to say 2 percent of the land is a street. Let’s just go with 10 percent.
• You might think that snow is frozen at 32°F (0°C), but really it could be colder. For this calculation, I am just going to assume the snow is at the freezing point. Also, what temperature do you want to bring the melt water up to? Just a ballpark figure of 40°F is what I will use.

Now let’s say that it’s snowing fast. Maybe 1 inch of snow an hour. If I want to melt the snow on the roads as it falls, what kind of power consumption would I need? Let’s start with a 1 square meter of ground. In one hour, 1 inch of snow would be a depth of 0.0254 meters. So the total snow on this square would be 0.0254 m3.

If only one tenth of this snow is water, that would just be 0.00254 m3 of frozen water. Also, I only want to melt 10 percent of this, so now I am down to a volume of ice/snow of 2.54 x 10-4 m3. Assuming an ice density of about 1,000 kg/m3 this makes 0.254 kg of ice per square meter that needs to be melted.

How much energy does it take to first melt the ice/snow and then heat that water up to 40 F? We call the energy per unit mass needed to melt stuff the latent heat of fusion. For water, this has a value of 334 x 103 Joules per kilogram. I also need to heat the water up, for this I will need the specific heat of water which has a value of 4181 Joules per kilogram per degree Celsius. I can write this energy as:

Putting in the values for the mass and temperature of water, the snow on this area would require 9.0 x 104 Joules. Over a time of 1 hour, this is a power of 24.8 Watts. Remember, that is 24.8 Watts per square meter. How big of an area do I need to clear? Again, I am going to use Washington DC. Here is my rough measurement—using Google Maps.