Forces at work on the ski slope
By Paul Swenson EBS COLUMNIST
Now that we are a couple weeks into the ski season, hopefully your legs are not hurting as much as they did at first. I always know that I should work out before the season starts, but usually I’m not in good enough shape. I suppose the silver lining in a slow opening like this year is that it gives me the chance to ski lots of groomers to build up the endurance before powder days in January and beyond.
Of course, that’s about the only good thing. Let’s look at the forces that skiers have to endure just on a groomer and why all these early season runs are good workouts.
Lines showing the horizontal centripetal and slanted “normal” forces acting on a skier or boarder. PHOTOS BY PAUL SWENSON
To understand the forces involved in skiing, we need a few definitions. In middle school, force is defined as a “push or pull” acting on an object. In high school, it is defined as a quantity that causes an object to accelerate. Acceleration is a time-based rate of change in velocity, and velocity is a speed with an associated direction. So, if a skier changes direction they must experience a force, even if their speed does not change. I will get back to that in a second.
The one force that is always acting on us is the force due to gravity, your weight. This force is directed toward the center of the Earth. If there are no other forces acting on you, you would be in freefall, accelerating toward the Earth at 9.8 meters per second per second (32 ft/s/s for old school learners). Of course, as you are sitting here reading this article you are not hurtling downward because another force is acting on your feet or derrière: the normal force. It is applied to you perpendicular to the surface you are standing or sitting on and is applied upward to you with a size equivalent to your weight force. These two forces add to zero, so there is no acceleration experienced and you stay put.
So, let’s put on a pair a skis and just stand there. You apply your weight to the skis, and the skis in return apply a normal force to you. Your legs experience a force equal to your weight. Now suppose we are gently gliding down the beginners’ slope at a constant velocity. Your legs still experience your weight since there is no acceleration. Move up to Mr. K. at a faster constant velocity, no turns yet, still the same force.
But as soon as you start to turn, your direction—therefore your velocity—changes. An acceleration occurs. By definition, there must be a new unbalanced force causing this turn. To navigate a turn there is a force called the centripetal force that is directed toward the center of the curve. If you are driving the canyon, the friction between the tires and road is responsible for this force going around a curve, but when you are skiing this force is provided by the angle of the skis carving the turn. The snow pushes on the ski which, in turn, pushes on your legs to make your turn possible. It is the normal force applied by the ski that has a component equal to your weight and another toward the center of the turn. This force is felt by your legs and increases with your speed and the sharpness of the turn.
In these photographs, the normal force applied to the skier’s or boarder’s legs is indicated by the diagonal red line directed from the boots through the person’s center of mass. This force can be calculated by the angle the skier leaning into the turn. Here are a few examples: in the image of the skier there is a 60-degree angle. To achieve this, they need to be able to support 115% of their body weight. The border displays an angle of 30 degrees, so their legs must be able to support 200% of their weight. As the angle gets smaller and smaller, the force increases drastically.
Pictures of Olympic skiers display angles of 10 degrees or less, and these athletes must be able to support 600% of their weight. Luckily it is for short bursts, but much of this force must be transferred through knees and hips. Add compressions, ruts and bumps, and technique, and it’s a wonder how these racers can do it year after year.
So back to us regular skiers. Carving your way down Ambush, you might be experiencing forces of 200% to 300% of your weight on each turn. As the day progresses and your legs fatigue, please be careful—call it a day when you know that your legs cannot support 300, 400 or 500 pounds of force.
Paul Swenson has been living in and around the Big Sky area since 1966. He is a retired science teacher, fishing guide, Yellowstone guide and naturalist. Also an artist and photographer, Swenson focuses on the intricacies found in nature.
