Falling with Class(ical Physics)

When you are going over your first ski jump of the season, do you ever wonder, “How can I reach the farthest distance possible?” Not a skier? That is quite alright. Have you ever watched ski jumping and wondered, “What is the longest possible distance an athlete can go?” Well, this question can be answered with the use of classical physics.

Today I will take you skiing and together we will obtain the world record for the greatest distance obtained by a ski jump. Scared of skiing? Don’t worry, as this is just a blog post and not reality. Scared of physics? There is nothing to be scared of, I will be here every step of the way so you can learn. Let us get started!

As we go down a take-off ramp together, we will be launched with an initial speed. Before we move on, I will introduce the physics term velocity. Velocity is the speed of an object in a certain direction, for example, if you are throwing a snowball at a friend, the speed at which the snowball is going before it hits your friend is its velocity. Now taking this term, we can sprinkle physics language into our jump by renaming our take-off speed as our initial velocity. Let us assume our journey is only being affected by gravity pulling downwards, which will cause us to follow an upside-down U-shaped curve. You may believe that our initial velocity plays a factor in obtaining a large distance from the ramp; however, due to our assumptions, it does not.

So, what in our ski setup can we adjust to obtain the farthest distance possible? Before adjusting anything, I will introduce the terms horizontal and vertical. Horizontal is a direction that runs flat from left to right, for example, if you were to throw a snowball forward, the distance where the snowball was launched to where it lands is the horizontal distance covered. Vertical is another direction that runs directly up and down, like when you throw a snowball upwards, the distance from your hands to the sky would be the vertical distance traversed. Using our new physics terms, let us focus on the amount of space between the end of the ski ramp and the horizontal direction which we will refer to as the angle, and the vertical direction will come into play soon.

By adjusting our ski ramp angle, we also need to consider the angle of our landing platform. If our landing platform is completely flat to the ground, the takeoff angle to obtain the furthest distance would be halfway between the horizontal and vertical directions as shown in scenario two below [1]. However, if the angle of the landing platform is steeper, the angle of the take-off ramp will get flatter in order to obtain the farthest distance illustrated in scenario one below [1]. 

For fun, let us consider a case where our landing platform is vertical – this may seem ridiculous, but please trust the process. The angle of the take-off ramp would become completely flat and as a result, we would shoot straight off horizontally [1]. We would never hit the ground and keep moving forward while falling downwards due to gravity. Congratulations, we have obtained the world record of longest ski jump together. I hope you are comfortable with me because we are falling together… forever. 

Now that we have gone through a situation together where we assumed gravity is the only force acting on the skier, let us go into a real-world situation and learn how professional skiers obtain large distances from a ski-ramp. In a real-world situation, the professional ski-jumpers do not have a say in the angles of the ski-ramp or landing platform, therefore their initial velocity matters.

When an athlete is standing at the top of the ski hill, they contain potential energy. The potential energy is the energy stored in them based on their height to the bottom of the ski hill. The higher an object is compared to the ground, the higher its potential energy. As the athlete begins skiing down the hill, the potential energy stored gets converted into kinetic energy, which is the energy that powers the downhill skiing motion.

To obtain greater speed before the athlete takes off from the ski-ramp, they must minimize resistance from the air. Ski jumpers decrease this factor by considering their body positioning. The problem ski jumpers run into when going down a ski hill is the air pushing in the opposite direction of their motion, causing their motion to slow down. This problematic effect is called drag. To overcome this issue, ski jumpers follow a body formation called the streamlined position [2].The streamlined position is when the ski jumper bends their knees, places their head forward while maintaining their arms behind them in a straight line [2]. As a result of these positioning adjustments, they minimize the amount of area that air drag opposes, hence reducing the effects of slowing down. 

As the ski jumper is taking off the ski jump, most of their potential energy has been converted to kinetic energy which will power the athlete’s motion to reach an initial velocity. Now comes an exciting section, the athlete takes flight into the air. To maintain the athlete's body in the air, they must use the initial velocity from the ramp and control the effects of lift and drag. Lift is produced when an object pushes air out of the way as it moves through it. As the air is pushed down on the skier, the skier is pushed upwards, which is the act of lift [2]. 

The relationship between drag and lift is that as drag increases, the lift decreases [2]. So, for a competitive ski jumper who wants to stay in the air for as long as possible, the goal is to maximize their lift while minimizing drag. To do this, the ski jumper aligns their skis and body parallel to the ground and places the skis in a V-shape formation just outside of the body [2].

By utilizing this position, the surface areas that create lift are increased. Eventually, the drag will reduce the speed of the skier, the lift will decrease, and gravity will pull downwards on them until they land, obtaining their farthest distance from the ski jump. 
Now, the next time you are at the ski hill, or stumble upon a ski jumping competition on television, you can tell yourself, “I know how to obtain the farthest distance after a ski jump; I simply have to remember that ski jumps fall with classical physics.”

References

[1] Nahin, P. J. (n.d.). Hurtling Your Body through Space. In In Praise of Simple Physics: The Science and Mathematics behind Everyday Questions (pp. 178–180). 
[2] Falling with style: The science of ski jumping. Smithsonian Science Education Center. (2018, February 1). Retrieved September 24, 2022, from https://ssec.si.edu/stemvisions-blog/falling-style-science-ski-jumping 

Celeste Wolske, an undergraduate student at the University of Guelph, produced this article in the context of the 3rd-year course IPS3000 on Science Communication in the Fall 2022 semester (course instructor: Alex Gezerlis, TA: Carley Miki).