How to Measure Speed Indoors — And the True Lap Distance in Skidome

As skiers in Gothenburg, we often train in Skidome. Having access to a high-quality indoor ski hall all year round is an incredible luxury. We truly want to give credit to all the staff and coaches who work continuously to improve the tracks and maintain excellent snow quality.

However, one small challenge — which I believe we share with many others training in the hall — is that our GPS watches do not work indoors, and it’s not entirely clear how long the lap actually is. Today we are so spoiled by always having accurate speed and distance data from every training session. It feels like a small gap in our statistics when all those indoor training hours fail to register distance.

For a long time, I have considered measuring the track with something like a measuring wheel — but it never happened. If anyone has done so, feel free to share the results!

Now, however, I have “measured the track.” Instead of using a traditional manual method — which, to be honest, would probably be more accurate — I did it in a way much more fun for an engineer. From the datasets we’ve collected during outdoor tests and treadmill sessions, we’ve observed correlations between several parameters, such as ground-contact time, impulse, frequency, and speed. Using these relationships, we developed an algorithm that estimates speed based on the data measured by the Skisens power grips. Voilà — we now have a speedometer that works indoors and can measure distance inside Skidome.

We evaluated this algorithm using both treadmill data and field data. Figure 1 below shows the agreement for three different skiers performing increasing-speed tests on the treadmill.

Fig. 1. Comparison between measured and estimated speed for three skiers on the treadmill.

In general, accuracy varies slightly between athletes, but except for a peak at the highest speeds, the difference is within 10% for all skiers at all levels. It should be noted, however, that this is the same dataset used to develop the model — so the method can of course be criticized.

To more accurately validate the speed-estimation algorithm, we found a straight outdoor section approximately one kilometer long. The terrain had slight variations, starting with a gentle downhill and ending with a climb of about 10 meters. We skied the section at three speeds — easy, moderate, and hard — and compared GPS speed and distance with data from our algorithm. Figure 2 shows the speed comparison across the three intensities.

Fig. 2. Comparison between GPS speed and algorithm-estimated speed.

Aside from deviations during rapid speed changes — for example when entering the climb — the agreement is within 5%. To further validate measurement accuracy, Figure 3 shows a comparison of accumulated distance across the three intervals. We see that distance estimation is very good at low and moderate speeds but somewhat less accurate at high speed, especially toward the end when entering the uphill.

Fig. 3. Comparison of accumulated distance measured by GPS and estimated by the algorithm.

After this verification, it felt appropriate to finally test the algorithm in the actual indoor track. So — how long is the lap in Skidome?

The test was performed by skiing a single lap at moderate speed. Ideally, I would have skied multiple laps, but due to time constraints — squeezing this in during youth training with SAIK Ski Club — one lap had to be enough. Figure 4 shows speed and accumulated distance from the test.

Fig. 4. Speed and distance measured by Skisens grips during a single lap in Skidome at moderate pace.

The magic result: one lap in Skidome is 870 meters long.
This number feels reasonable compared to lap times in different conditions, though there is some uncertainty regarding how the algorithm behaves in all the curves.

A fun observation: the test was performed on classic skis with fairly heavy grip wax. In my experience, Skidome snow can glide well with waxless skis but often feels slow on classic skis with grip wax. We saw an amusing effect of this in the results. In addition to estimating speed, the Skisens software also attempts to estimate gradient. According to this algorithm, the average incline of one lap in Skidome was 3%. Clearly not correct — but a humorous signal that the high drag fooled the algorithm into thinking we were skiing uphill the entire time.

We plan to repeat the test with skis of different glide properties and with more repetitions.

/Dan