The Math Of Skiing

It is winter time and many people head off to the local ski resort to spend time out on the hills.  They love flying down the hill as fast as they can and once they reach the bottom, they head up again.

I tried it once but between being intimidated by 6 year old's whizzing down expert slopes and skiing backwards down a hill, I've never been back.  If you are wondering, the only reason I stopped was that a lovely tree stopped me when I ran into it butt first.

The only skiing we have around here is cross country skiing. There is quite a bit of math associated with down hill skiing in terms of the hotel, cost of skiing, and the course itself.  People have to calculate the cost of driving to the resort, the cost of the rooms, the cost of renting equipment, lift tickets, etc so they can determine the amount of money needed to finance the trip.  The cost may not be as much if a person skies down a local hill.

In addition, the ski resorts use mathematics to determine the current amount of snow and can predict possible snow fall based on mathematical modeling.  When predicting the amount of snow, they have to know wind direction and speed because that gives a good idea of where the snow will fall. 

Then there is the steepness of the slope.  If its too steep, only extreme skiers will chance it but if its too flat, you won't do much on it.  The ideal slope is 15 to 25 degrees.  In addition, they keep track of vertical drop or the distance from the top to the bottom because usually the larger the vertical drop, the longer  the ski run if its within the proper steepness. 

When planning a ski resort, the designers have to plan for carrying capacity which in this case refers to the vertical transport system.  They need to plan enough lifts to move the skiers up the hill so they can ski down.  It is vertical transport in feet per day divided by vertical demand.  Vertical transport in feet per day is found by multiplying vertical rise of the lift, by the hourly capacity of the lift by the number of number of hours in operation each day while vertical demand is the typical number of round trip runs made by a skier on one of the lifts.

If the resort has a ski rental place, the workers have to make sure the edges of the skies are set between one and three degrees. In addition angles are used when making turns, too sharp and you mess up, too shallow and you don't make the turn.  Furthermore, its good to know the turning radius which is marked on the ski.  It lets the skier know how tight a turn they can make.

Imagine assigning a project where students research what it takes to build a ski resort before creating their own.  There are a couple places on the web which have projects already set up for this.  One is at Teach Hub and the other looks at slopes.   Years ago I took a physics of avalanches class which was great because it included an assignment where we had to figure out where to put barriers so resorts or houses would not be crushed during an avalanche.  That was fun.