Frictionless Skiing

downhill vs cross country skiing

Downhill skiing is better.

Unsurprisingly, the answer lies in physics. Over this break, I attempted cross country skiing and decided that I like skiing on big sticks (aka downhill skiing) better.

Why is that?

Downhill skiing Conditions: -steep terrain -20-35 degrees Snow: -powdery snow -groomed in corduroy lines -icy patches -moguls (like camel humps) Equipment: -thick and heavy skis -ski edges that are sharpened for grip on the snow -boots that firmly lock into skis -gear to protect against falling and wind Technique: -make turns to control speed

Cross country skiing Conditions: -mild, easily walkable terrain -around 0-19 degrees of elevation Snow: -carved tracks -easily icy, frictionless Equipment: -thin lightweight skis -extremely dull edges on skis -boots that lock in loosely at the toe -gear for a hike Technique: -stay in the tracks, keep balance

Here's the physics of downhill skiing

Here is a video of my brother skiing at Stowe, VT

𝚫x: (?) 76 meters

Vi: 0 m/s

Vf: 11.18 m/s

a: (?) 1.9 m/s^2

t: 13 sec

𝚫x = 1/2(Vi + Vf)t

     = 0.5 (11.18)(13)

     = 76 meters travelled

Vf = Vi + at

     = 0 + 13a

     = 1.9 m/s^2 acceleration

*speed obtained from Sean's ski tracking app

Here's the physics of cross country skiing

Here is cross country skiing, filmed out of my pocket 

𝚫x: (?) 13.8 meters

Vi: 0 m/s

Vf: 1.38 m/s

a: (?) 0.069 m/s^2

t: 20 sec

𝚫x = 1/2(Vi + Vf)t

     = 0.5 (1.38)(20)

     = 13.8 meters travelled

Vf = Vi + at

1.38   = 0 + 13a

     = 0.069 m/s^2 acceleration

Now, a comparison:

Distance

In a mere 13 seconds, my brother is able to travel 76 meters downhill, while cross country speed takes me 20 seconds to travel 13.8 meters.

Speed

The downhill skiing is faster, but more controlled. The tight turns that my brother does in the video are using the ski weight and friction against the snow, allowing him to maintain steady control. In the cross country video, I have no control over my speed besides using my poles to accelerate and keep balance. My skis are stuck in a deep straight track made by other cross country skiers, and without the grip or weight in the skis, I am unable to use friction and turning to control my speed.

This combination creates a huge gap in ability to control your speed and direction. I am happy at the meager speed for cross country because it allows me time to react to obstacles. In contrast, downhill skiing at that speed would be a snooze.

Acceleration

Unaccounted for in the math, but a large factor is the angle of elevation of the hills. Downhill skiing is at a greater angle for the aforementioned reason of speed and control. Being on a steeper hill allows the skier to accelerate faster due to gravity acting upon them. This would be bad for cross country skiing, because a steeper decline would have them accelerating to a point out of their control almost instantaneously.

Time

The difference in speed means that it takes a cross country skier much longer to complete the same distance as a downhill skier. 

Conclusion

Downhill skiing is better because you can do more than walking, and develop skills for controlling speed. It's more exciting because you can go faster and try different trail types.

Also, this happens

Sources:

http://www.skibum.net/do-it-up/comparing-steepness-of-ski-trails/

http://www.trailstobuild.com/articles/bc%20trail%20standards/4-4.htm