The Math Of Snow

 Snow is a wonderful thing. It can be light and airy or it can be quite dense and heavy.  You can ski or snowboard on it.  It can be used to make ice cream or a snowman but there is so much math associated with it.

For instance, we see ratios used when discussing how much snow has to fall in order to get one inch of water.  If it is an average snow which is neither too wet or too dry, you need ten inches of snow to equal one inch of water.  On the other hand, if your snow is wet, it only takes five inches of snow to equal one inch of water but if your snow is dry, you'll need 15 inches to get the same one inch of water.  Knowing these ratios means you can figure out how much water it equals.  For instance if you only get four inches of wet snow, you'd set up a proportion of 4/x = 15/1, so if you solve for x, you'll get 0.27 inches of water.

Furthermore, if your snow is such that you can create a proper snowman, one made of of three spheres decreasing in size, but the ratio is based on different ratios depending on who you talk to.  There is the  the 1:2:3 ratio, or the 3:5:8 (top to bottom) ratio for the spheres,  all suggestions based on the Fibonacci series. Thus, if you know the radius of the top sphere, you can calculate the radii of the other two so that your snowman has the proper proportions.  A mathematician in Poland actually created a Snowman calculator which allows people to determine the maximum sized snowman they can build based on the amount of snow in their backyard based on the golden ratio.

This article gives some interesting information on how much it cost the city of Boston to clear out 99 inches of snow or snow that was 8 feet 3 inches tall.  Back in 2015, Boston got hit with 99 inches of snow and the city had to send out every truck they could just to keep the snow from completely shutting everything down.  The workers spent 185,000 man hours and drove about 293,000 miles which is about 12 times around the earth. In addition, they had to use 76,000 tons of salt and the whole process cost them about $35 million dollars.

Now to figure out the best way to clear the snow, mathematicians have to apply the Chinese Postman problem in which the postman wants to deliver to every house, on every street, backtracking as little as possible.  It boils down to finding the best routes between intersections with an odd number of streets. This lead to a mathematician in the 1990's to design an algorithm focused on optimizing snowplowing. Since most cities use more than one snow plow and have to cover large areas, the best way is to break the down the network of streets into smaller units for the best results.

I hope you find these tidbits interesting.  Let me know what you think, I'd love to hear.  Have a great day.