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Comparative Study
. 2005 Aug 7;272(1572):1561-9.
doi: 10.1098/rspb.2005.3121.

Human locomotion on snow: determinants of economy and speed of skiing across the ages

Federico Formenti  1 , Luca P Ardigò, Alberto E Minetti
Affiliations
Comparative Study

Human locomotion on snow: determinants of economy and speed of skiing across the ages

Federico Formenti et al. Proc Biol Sci. .

Abstract

We explore here the evolution of skiing locomotion in the last few thousand years by investigating how humans adapted to move effectively in lands where a cover of snow, for several months every year, prevented them from travelling as on dry ground. Following historical research, we identified the sets of skis corresponding to the 'milestones' of skiing evolution in terms of ingenuity and technology, built replicas of them and measured the metabolic energy associated to their use in a climate-controlled ski tunnel. Six sets of skis were tested, covering a span from 542 AD to date. Our results show that: (i) the history of skiing is associated with a progressive decrease in the metabolic cost of transport, (ii) it is possible today to travel at twice the speed of ancient times using the same amount of metabolic power and (iii) the cost of transport is speed-independent for each ski model, as during running. By combining this finding with the relationship between time of exhaustion and the sustainable fraction of metabolic power, a prediction of the maximum skiing speed according to the distance travelled is provided for all past epochs, including two legendary historical journeys (1206 and 1520 AD) on snow. Our research shows that the performances in races originating from them (Birkebeiner and Vasaloppet) and those of other modern competitions (skating versus classical techniques) are well predicted by the evolution of skiing economy. Mechanical determinants of the measured progression in economy are also discussed in the paper.

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Figures

Figure 1
Figure 1
(a) Cave graffiti representing early ‘skiers’; (b) a painting representing the Birkebeiners' feat in 1207 AD; (c) late nineteenth-century photograph of Finnish skiers; (d) a Chukchi hunter who is representative of the hundreds of thousands of people in the Arctic (the Inuit/Eskimo in Alaska, northern Canada and Greenland; the Saami/Lapps in upper Scandinavia; the Nenet and Evenk in northern Russia; the Chukchi in northeastern Siberia) who still use skis as a means of transport for hunting, herding and foraging; (e) a modern athlete while skating.
Figure 2
Figure 2
The first ski is shown as it was found; the remaining band that passed around the heel is only partially visible (drawing, National Board of Antiquities, Helsinki, Finland).
Figure 3
Figure 3
We used a digital elevation model of the Scandinavian area (E020N90, edcdaac.usgs.gov/main.asp) providing the altitude (m a.s.l.) every 941 m of latitude and every 340–430 m of longitude. We sampled a (700 by 700 points) subarea of about 177 520 km2 mainly located in central and northern Finland (square inset) and wrote a custom programme (LabView, National Instruments, USA) to measure 977 202 gradients in the area and work out their frequency distribution. The result was a quasi-exponential distribution (mean=0.0148, mode=0.0050, s.d.=0.0187, Skewness=3.038, Kurtosis=18.331) whose cumulative function showed that 95% of the gradients were within the range of 0–5%. The typical uplands, with lots of lakes and bogs, were paradoxically more easily travelled during winter when most of the soft ground was frozen.
Figure 4
Figure 4
The metabolic cost of transport (means with standard deviations) is plotted against the speed for all the investigated skis (the one marked 3200 BC refers to the replica of ‘Salla’, a debated ski-like specimen under which no fur was found in the archaeological site). The units have been changed from ml O2 to J according to the breath-by-breath measured respiratory exchange ratio. Walking and running costs on firm terrain (grey curves) are reported for the sake of comparison (Cavagna & Kaneko 1977). The double circle symbol refers to walking on snow in the tunnel. The slowest point for each ski relates to the ‘migration’ speed. The three hyperbolae represent different iso-metabolic power curves (cost×speed=constant). While the metabolic cost is the analogous of fuel consumption (per unit distance travelled), the hyperbolae show cost/speed combination at which the effort (approximately proportional to the heart rate) is the same. Bars show s.d.
Figure 5
Figure 5
The metabolic cost for each ski model is here shown as partitioned in its main mechanical components equivalent: the external work (Wext, black, obtained from C−Wint/eff−Wfriction/eff), the internal work (Wint, dark grey) and the work performed against friction (Wfriction, light grey). While the work against friction has to be considered part of the external work, here we keep on using Wext to represent the mechanical work done to raise and accelerate the body centre of mass only.
Figure 6
Figure 6
The three-colour curves represent the maximum speed/distance relationships for constant metabolic cost, each of which refers to a different ski. They have been obtained by combining the relationships between the time to exhaustion and the available fraction of the metabolic power used, as suggested by Wilkie, Saltin and Davies for different exercise duration ranges (blue: 40 s–10 min; light orange: 10 min–1 h; green: 1 –24 h, respectively). In this computational frame, 20.3 W kg−1 has been assumed as the maximum metabolic power available. In the graph, the grey curves show iso-duration speed/distance pairs and the open square symbols represent recent records in cross-country skiing, from sprint events to endurance races. Grey and black symbols are explained in the text. For further details refer to the text and to appendix B.
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