Article written for Courtyard by Beth Utter
Math in the Real World
I qualified for the NASTAR National Championship that was held in Winter Park, CO and it just happened to occur during our Spring break! You may be wondering “NASTAR…what is NASTAR?” NASTAR was developed by SKI Magazine in 1968, NASTAR (NAtional STAndard Race) and is the largest recreational ski and snowboard race program in the world. The mission is to provide a fun and competitive racing program that allows racers of all abilities and ages a means to compare their race results to other competitors across the country from any ski area that has NASTAR races by using a handicap. Basically, it is giant slalom course (GS), meaning that you ski or snowboard around the gates in the fastest time possible. Speeds can approach 40 mph!
Now let me throw in a little math. What is a NASTAR handicap and how is it used to rank recreational ski racers? AJ Kitt, a four time Olympian, (’88, ’92, ‘94, ’98) is the NASTAR traveling pacesetter. Each year AJ races against the fastest skier on the US Ski Team. For 2010 AJ’s handicap is 1.87%. Thus, AJ is 1.87% slower than the fastest US Ski Team racer. During November – December, AJ travels throughout the US and conducts race pacesetting trials. All resorts, like Gore Mountain where I ski, have ski instructors race against AJ in the trials. Based on each instructor’s raw time against AJ, a handicap is established. Again, the handicap is a measure of how much longer it takes the instructor to ski the racecourse compared to the fastest US Ski Team racer. Each instructor who races then has a handicap for the ski season. Each day the instructor pacesetter runs the course first at their home mountain. Based on his/her handicap, a par time is calculated for that day. The par time is how long it would take the fastest US Ski Team racer to complete that course. My best race in 2010 yielded a handicap of 17.57%. The par time for that day was 20.94 seconds; my raw time was 24.62 seconds. Thus, I was 3.68 seconds longer in the course than the fastest US Ski Team racer would have been. All NASTAR ski racers have a handicap. I qualified for the NASTAR National Championships by being one of the top three racers (top three lowest handicaps) in the “gold division” for my gender and age bracket at Gore Mountain.
At the National Championships in Winter Park there was a two day race format. I had two races on Friday, 3/26 and two races on Saturday 3/27. The fastest times from each day were averaged for a final time. I was in the Gold division. After Friday’s race, I was in 5th place, but that changed to 4th place after a competitor was injured. After Saturday’s race, I was in 2nd place in my division, so I really did not know where I stood overall yet! I ended up winning my division with a Gold medal (ranked #1) and a current Olympian named Steve Nyman put the gold medal around my neck during the Medal Ceremonies! He just came back from competing in the Olympics in Vancouver, Canada! I met many Olympians that night, took pictures with them and obtained their autographs. Since I won my division, I was invited to compete in the Race of Champions on Sunday, 3/28. Only competitors who received a gold medal on Saturday were invited to compete on Sunday.
How about some more math trivia? During my visit to Winter Park, I said I had the opportunity to meet several current and former US Ski Team Olympians. Jimmy Cochran, had just returned from Vancouver, and mentioned calculus was his favorite subject in college! Having a strong mathematics background helps you understand the technology of ski racing. Today’s skis are “shaped” meaning they are wider at the tips and the tails compared to the width under your foot/binding. What is the purpose of this? Using algebra and geometry, it is easy to calculate a ski’s natural turning radius. If you are standing on your skis with your boots in the bindings, and you look down at your skis, you can notice a subtle curve or shape along the ski’s edge. The wider the tips and tails compared to under your foot, the smaller the ski’s natural turning radius. This ski will want to turn naturally on this radius when put on edge. A straight ski, uniform width along its entire length, has an infinite radius. Ski racers will select skis with the proper natural radius for the course they are racing. Slalom racecourses are characterized by many closely spaced gates. Thus, having a ski with a smaller natural turning radius is best. Therefore, you will notice slalom skiers have shorter skis with wider tips and tails. Typical slalom skis have a radius in the 12-13 meter range. NASTAR racing is on a GS course, the gates are further apart, about 30 ft. GS racers select skis that have a natural turning radius in the 17-20 meter range. My race skis have a 17-meter radius. Any ski can be forced to ski a tighter radius than its natural radius but that takes more work and energy from the racer. Energy conservation is key. This is a good example of how mathematics is leveraged in the sport of ski racing.
Back to Winter Park and Sunday’s race. The course was steeper, longer and the gates were closer together, which means it was going to be fast! I was competing against all alpine female racers and I came in 6th with a discounted time (based on handicap and age). I stood on the winning podium stand for about 10 minutes in 3rd place and it was very exciting! All the Olympians were milling about and I obtained more autographs and many pictures! This was a fantastic experience that I will remember always!
And…whoever thought that ski racing involved mathematics?!?!
Click on picture of me racing! Once you retrieve the picture, you need to right click on mouse, click on ’rotate clockwise’ until picture is upright. NASTAR Picture of Mrs. Utter Ski Racing
