ski training with purpose

What is Roller Skiing?

Cross-country skiing is constrained by snowfall. So what do skiers do when they don't have snow?

They roller ski! Roller skiing is cross country ski training that trades in skis and snowy trails for roller skis and paved trails or roads.

Roller skiing is a way to train for skiing once the snow comes. Meaning roller skiing with correct form is important so that people are training correctly and truly improving their skiing

ski training with purpose

Analyze Roller Skiing Forms

The Project

In this project, we will be analyzing a skier's motion to provide feedback on their technique so they can improve their roller skiing. We will specifically be focusing on skate skiing, and differentiating between two forms of skate skiing called V1 and V2. We differentiate between these forms by collecting acceleration data of a skier doing each form and analyzing the data by pulling out key frequencies that appear in each form.

V1

V1 is the easiest and most common skate skiing form. This form involves planting both poles in sync with one foot stepping down and then gliding with your other foot (Terko). In the video below the skier is poling with the right foot plant and gliding with the left foot. This means there is more acceleration when the right foot goes down because there is acceleration coming from the left foot pushing off and from the pole push.

When to use: V1 is the technique to start with when learning to skate ski. It should be used when going up hills or for going on long skis (Backcountry).

V2

V2 is a more difficult technique to balance on. This form involves pushing off with both poles with each foot plant (skixc). This is a more powerful technique with more acceleration because there is a full leg and pole push on each step versus V1 where you only get that full force on every other step.

When to use: V2 is worked on after skiing with V1 for a little while. It should be used to gain speed and power up short hills (Backcountry).

Our Model

We hypothesized that the V1 technique would have two similar and relatively high peaks in the frequency domain since the V1 technique includes pole push only when the skier plants one foot while the skier glides with the other foot. So one of the peaks is the push with the pole and the foot and we guess the other peak is just the movement of the leg by itself without a pole push.

For the V2 technique, we guess that we will see two relatively high but very distinct peaks. We expect the highest peak to represent both the push with the dominant leg and the push with the weaker leg with a frequency around one and a lesser peak with the half frequency that represents the push with the weaker leg. So mathematically, we think that to represent the strong push and weaker push, we need two sin functions, smaller amplitude with one unit frequency and bigger amplitude with two unit frequencies.

Data Collection

To collect data, we used a phone app called Phyphox. We only needed the accelerometer data to collect data on roller skiing acceleration. Phyphox measured and saved the acceleration in each dimension (x, y, z) and calculated the absolute acceleration with a sample rate of 100 samples per second.

We hypothesized that the main moving parts of a body during roller skiing are feet, hands, and, torso. In order to collect all the data from all these three sections, we initially planned to place three phones on the roller skier’s body for data collection, one in her right pocket (screen facing out), one on her right ankle (again screen facing out) and one on her forearm. Sadly, we were only able to place two phones on the roller skier’s body, one in the pocket and one on the ankle. You can see in the images above how the phones were placed and attached.

Data Analysis

After we gathered our data from Declan roller skiing, we began analyzing it by manually removing the parts of the data where she wasn’t actually roller skiing using one of the two forms (when we were placing the phones, removing them, or when she was stopping and turning around). To figure out where she was and wasn’t roller skiing in the data, we manually looked at the time-domain plot of absolute acceleration, observed where there seemed to be a periodic motion, and trimmed everything else.

This left us with four data sets, two each for V1 and V2. Since we knew we were looking for the frequencies of the motion, we decided to use a Fourier Transform on the data, and use the resulting plot of frequency vs amplitude of the frequencies present in the data to tell the two forms apart. Since we knew the motion we were looking for was happening about once a second, we filtered out any frequencies above 1.75Hz or below 0.2Hz, and plotted the resulting Fourier Transform.

Just as we expected, we saw the Form 2 data had one primary frequency at almost exactly 1Hz, corresponding to Declan’s once-a-second pushing with both her foot and her poles, with the next highest distinguishable peak at half the frequency of the highest. By distinguishable, we mean we didn’t consider any peaks within a small frequency range around the first peak, as the subpeak directly next to the main peak is likely noise from slight differences in how fast Declan was roller skiing. Since Declan pushes harder on one side than the other (source: Declan said so), this lower amplitude, lower frequency peak corresponds to her pushing on one side, and the higher amplitude, higher frequency peak corresponds to each pushing motion.

For the V1 data, we weren’t as sure what we’d see. We expected to see a periodic motion in the time-domain graph, with large and small peaks at roughly even intervals representing Declan pushing with and without the poles respectively. Since the intervals would be roughly even, we thought we’d see two component waves of roughly equal frequency and very different amplitudes, so we weren’t sure how that would show up in the frequency-domain plot. We ended up seeing two peaks of roughly equal amplitude in the frequency domain at frequencies of 1.3Hz and 1.6Hz, which we weren’t sure how to interpret. This behavior was relatively constant among different slices of the V1 data though, so we decided to use it as part of our quantitative analysis.

Results

Once we’d confirmed our expectations for the qualitative appearance of our plots, we began developing an algorithm to quantify the difference and attempt to classify the data as representing Form 1 or Form 2. Based on our data observations, we decided to take the ratio of the frequencies of the two highest (post-filtering) amplitudes and use that ratio to classify a data set as Form 1 or Form 2. In practice, this meant we would find the two highest amplitudes in the Fourier Transform of a dataset, find the corresponding frequencies, and divide the higher frequency by the lower frequency. For Form 1, we expected this ratio to be a little over one, and we expected the ratio to be closer to two for Form 2, so we decided to make a ratio “threshold” at 1.5. If a dataset’s “ratio” was above 1.5 we classified it as Form 2, and if the ratio was below 1.5 we classified it as Form 1.

Once we’d developed this algorithm to take in data and classify it as V1 or V2 (using the data from Declan skiing one direction), we tested it on subsets of the data from her skiing the other direction. Using 30 subsets of a length from 30-40 seconds, our classification algorithm correctly identified V1 skiing 97% of the time, and V2 90% of the time.

Next Steps

To more accurately analyze the data and draw more solid conclusions, we would collect data from the initial three locations that we identified. Also, we would have more than one person roller ski for data collection because right now we are bound to one individual’s way of applying different forms. We think the data will vary marginally based on the roller skiing habits and proficiency level of the roller skier. Finally, we would try experimenting with and without poles to see how much difference that would apply to our raw data.

ABOUT US

Han

I’m an Engineering:Robotics major who loves building things, working with my hands, and writing code that makes things move.

Declan

A current electrical and computer engineer at Olin. Loves cross country skiing and dragged her team mates into a rolling skiing motion analysis project where she got to ski for class.

EFE

A current Mech: E at Olin College. I think it is fascinating to be able to represent real-life with mathematical equations. I really want to be a better mathematician to increase my capabilities in helping people and solving real-life problems with mathematics.