# The Contribution of Ski Poles to Aerodynamic Drag in Alpine Skiing
## 3 Results
### The Cross-sectional Area of the Ski Poles  
The skiers demonstrated a somewhat smaller S\({}_{\rm p}\) in the high and middle positions compared to the tuck position, as well as in the middle versus high position (High-Middle = \(-\)0.0009 m\({}^{2}\), 95% CI [\(-\)0.0017, \(-\)0.0001 m\({}^{2}\)], pd = 0.987; High-Tuck = 0.0186 m\({}^{2}\), 95% CI [0.0178, 0.0194 m\({}^{2}\)], pd = 1.000; Middle-Tuck = 0.0195 m\({}^{2}\), 95% CI [0.0186, 0.0202 m\({}^{2}\)], pd = 1.000). The percentage of the total cross-sectional area occupied by the poles differed between the positions, being greatest in the middle position, followed by the high position (High \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & & & & & & \\ \multicolumn{6}{c}{**Cross-Sectional Area**} & \multicolumn{4}{c}{**Within-Skier Variation of**} \\  & & & & & & & \\ \multicolumn{6}{c}{**Pole Cross-Sectional Area**} \\ \hline \multicolumn{6}{c}{**Speed**} & **Skier (m\({}^{2}\))** & **Poles (m\({}^{2}\))** & **Poles (\%)** & **Min-Max Range (m\({}^{2}\))** & **Min-Max Range (\%)** & **CV (\%)** \\ \hline \multicolumn{6}{c}{High position} \\
40 km/h & 0.5615 \(\pm\) 0.0383 & 0.0262 \(\pm\) 0.0034 & 4.5 \(\pm\) 0.7 & 0.0047 \(\pm\) 0.0013 & 18.4 \(\pm\) 6.0 & 7.4 \(\pm\) 2.4 \\
60 km/h & 0.5747 \(\pm\) 0.0422 & 0.0253 \(\pm\) 0.0030 & 4.2 \(\pm\) 0.7 & 0.0043 \(\pm\) 0.0007 & 17.1 \(\pm\) 3.0 & 7.1 \(\pm\) 1.0 \\
80 km/h & 0.5704 \(\pm\) 0.0439 & 0.0243 \(\pm\) 0.0047 & 4.1 \(\pm\) 1.0 & 0.0072 \(\pm\) 0.0033 & 30.5 \(\pm\) 17.1 & 12.6 \(\pm\) 6.4 \\ Overall & 0.5689 \(\pm\) 0.0402 & 0.0253 \(\pm\) 0.0030 & 4.3 \(\pm\) 0.7 & 0.0106 \(\pm\) 0.0032 & 42.8 \(\pm\) 14.4 & 12.2 \(\pm\) 4.7 \\  & & & Middle position & & & \\
40 km/h & 0.5143 \(\pm\) 0.0400 & 0.0273 \(\pm\) 0.0049 & 5.0 \(\pm\) 0.8 & 0.0035 \(\pm\) 0.0014 & 12.7 \(\pm\) 4.8 & 5.4 \(\pm\) 2.3 \\
60 km/h & 0.5281 \(\pm\) 0.0473 & 0.0256 \(\pm\) 0.0043 & 4.6 \(\pm\) 0.7 & 0.0051 \(\pm\) 0.0029 & 20.6 \(\pm\) 12.2 & 8.1 \(\pm\) 4.8 \\
80 km/h & 0.5269 \(\pm\) 0.0405 & 0.0257 \(\pm\) 0.0043 & 4.7 \(\pm\) 0.9 & 0.0052 \(\pm\) 0.0025 & 20.7 \(\pm\) 10.6 & 8.3 \(\pm\) 4.2 \\ Overall & 0.5231 \(\pm\) 0.0415 & 0.0262 \(\pm\) 0.0039 & 4.8 \(\pm\) 0.7 & 0.0093 \(\pm\) 0.0033 & 35.6 \(\pm\) 11.9 & 10.8 \(\pm\) 4.5 \\  & & & Tuck position & & & \\
40 km/h & 0.3000 \(\pm\) 0.0189 & 0.0064 \(\pm\) 0.0025 & 2.1 \(\pm\) 0.8 & 0.0018 \(\pm\) 0.0011 & 29.3 \(\pm\) 20.3 & 12.4 \(\pm\) 10.4 \\
60 km/h & 0.3008 \(\pm\) 0.0232 & 0.0065 \(\pm\) 0.0025 & 2.1 \(\pm\) 0.8 & 0.0021 \(\pm\) 0.0019 & 34.8 \(\pm\) 26.6 & 14.9 \(\pm\) 11.7 \\
80 km/h & 0.3045 \(\pm\) 0.0205 & 0.0072 \(\pm\) 0.0020 & 2.3 \(\pm\) 0.7 & 0.0018 \(\pm\) 0.0008 & 27.6 \(\pm\) 13.6 & 11.2 \(\pm\) 5.3 \\ Overall & 0.3018 \(\pm\) 0.0200 & 0.0067 \(\pm\) 0.0022 & 2.2 \(\pm\) 0.7 & 0.0041 \(\pm\) 0.0015 & 63.0 \(\pm\) 20.6 & 18.2 \(\pm\) 7.8 \\ \hline \end{tabular} The values presented are means \(\pm\) standard deviations. Poles % = the percentage contribution of the cross-sectional area of the poles to the total cross-sectional area. CV = coefficient of variation.  
\end{table} 
Table 1: The cross-sectional area of the skiers and poles at different wind speeds and body positions. Figure 3: The middle position was taken by ”Skier 8” during one of the tests at 40 (**left**), 60 (**middle**), and 80 km/h (**right**). At the top is the posterior view and at the bottom is the sagittal view. S\({}_{\rm p}\)—cross-sectional area of the poles. Figure 2: The cross-sectional area of the ski poles (S\({}_{\rm p}\)) with different wind speeds and positions for each individual skier. The means for all 10 athletes are represented by the black lines and the standard deviations for these means by the grey shaded areas.