Avalanches and Math

  Avalanches occur anywhere there are slopes and snow.  Some avalanches occur in areas with little to no human interaction while others occur in populated areas.  Years ago, I took a class on the physics of avalanches and there was more to it than I'd ever imagined. 

Its interesting that there is not one type of avalanche.  There are many depending on the type of snow, the snow pack and other factors.  For instance there is a snow sluff or point release avalanche which involves new snow being released from a point and spreading outwardly as it goes down hill.  There is a slab avalanche which is when bonded blocks of snow move and are among the most dangerous type of avalanche.  Although about eighty percent of slab avalanches happen on a hill with a slope between 30 and 45 degrees, the most common slope is 38 degrees.

There is also math involved in predicting the chances of avalanches happening in certain areas due to populations, etc. One way of learning to predict possible avalanches was done by several scientists who discovered by dropping ping pong down an Olympic Ski jump,  they got a better idea of how powder snow reacts.  Apparently, they are light enough to be caught up by the air in the same way as powder snow avalanches.

As a result the scientists were able to develop simple models for momentum and for the volume of snow fall.  These models are being tested in real situations in Switzerland. Powder snow avalanches can reach speeds of one hundred miles per hour and can easily bury people.  If you'd like to present activities in your classroom that would give students a flavor of working with avalanches, there are these:

1. Discovery Education has a lovely activity which allows students to discover the angle needed for avalanches to start moving. It does not require a lot of materials but what it does require can be easily gotten, especially if planned for ahead of time as it uses pebbles, sand, talcum powder, and marbles.

2. PBS has this activity to help students understand more about how weak and strong layers of snow lead to avalanches. It uses flour, sugar, and mashed potato flakes to illustrate how it happens. 

3. This activity has students use different substances to see how they form heaps. The heaps are then measured for area, height, and angle before being graphed to visually compare results.  Students are expected to reach conclusions on the type of event after researching different kinds of avalanches.

I love it when I can teach a topic that extends beyond just the math classroom.  There actually is a lot of math involved but some of it is a bit advanced for my students especially when  looking at the turbulent flow of two component mixture used to describe the density and volume distribution.  Or the avalanche release and flow parameters.

Let me know what you think.  I'd love to hear.