# The Contribution of Ski Poles to Aerodynamic Drag in Alpine Skiing
## 3 Results
### Effects of the Cross-Sectional Area of the Poles on \(C_{d}\) and \(C_{d}\):S  
The intra-athlete influence of a 0.01 m\({}^{2}\) increase in the cross-sectional area of the ski poles on the \(C_{\rm d}\) and \(C_{\rm d}\) - S with all wind speeds (controlling for S) can be seen in Table 2. In the case of the high position, \(S_{\rm p}\) had an unclear effect on \(C_{\rm d}\), while exerting a likely positive effect on \(C_{\rm d}\) - S. With the middle position, there were likely positive effects on both \(C_{\rm d}\) and \(C_{\rm d}\) - S. Finally, in the tuck position, there was a probable negative effect on \(C_{\rm d}\) and possible negative effect on \(C_{\rm d}\) - S. The general relationship between the cross-sectional area of the ski poles and \(C_{\rm d}\) and \(C_{\rm d}\) - S is illustrated in Figure 4.  
Table 3 documents the effects of increasing \(S_{\rm p}\) by the average range for all the skiers combined at each position on \(C_{\rm d}\) and \(C_{\rm d}\) - S (m\({}^{2}\)).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline  & & \multicolumn{2}{c}{\(C_{\rm d}\)} & \multicolumn{3}{c}{\(C_{\rm d}\)**-S (m\({}^{2}\))**} \\ \cline{2-7}
**Position** & **b** & **95\% CI** & **pd** & **b** & **95\% CI** & **pd** \\ \hline High & 0.0087 & [\(-\)0.0128, 0.0292] & 0.797 & 0.0185 & [0.0016, 0.0360] & 0.982 \\ Middle & 0.0148 & [\(-\)0.0053, 0.0344] & 0.928 & 0.0237 & [0.0089, 0.0378] & 0.999 \\ Tuck & \(-\)0.0791 & [\(-\)0.1515, \(-\)0.0181] & 0.993 & \(-\)0.0192 & [\(-\)0.0416, 0.0034] & 0.960 \\ \hline  & & & & & & \\ \end{tabular} Note. b = change in \(C_{\rm d}\) and \(C_{\rm d}\) - S (m\({}^{2}\)) caused by a 0.01 m\({}^{2}\) increase in the cross-sectional area of the ski poles; Cl = confidence interval; pd = probability of direction; \(C_{\rm d}\)—aerodynamic drag coefficient; S—total cross-sectional area of the skier. These values were obtained employing a mixed effects model with the skier’s cross-sectional area as a covariate and a random intercept for the skiers. Trials at all wind speeds were incorporated into this model.  
\end{table}
Table 2: Relationship between the cross-sectional area of the ski poles and \(C_{\rm d}\) and \(C_{\rm d}\) - S.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{2}{c}{**The Average Range (Avg) in**} & \multicolumn{2}{c}{\(C_{\rm d}\)**} & \multicolumn{2}{c}{\(C_{\rm d}\)**-S (m\({}^{2}\))**} \\ \cline{2-7}
**Position** & **Avg (m\({}^{2}\))** & **Avg \%** & **Diff** & **95\% CI** & **Diff** & **95\% CI** \\ \hline High & 0.0106 & 42.8 & 0.0092 & [\(-\)0.0135, 0.0309] & 0.0197 & [0.0017, 0.0382] \\ Middle & 0.0093 & 35.6 & 0.0137 & [\(-\)0.0049, 0.0318] & 0.0219 & [0.0082, 0.0349] \\ Tuck & 0.0041 & 63.0 & \(-\)0.0321 & [\(-\)0.0615, \(-\)0.0073] & \(-\)0.0078 & [\(-\)0.0169, 0.0014] \\ \hline  & & & & & & \\ \end{tabular} Notes. Diff = the change in \(C_{\rm d}\) and \(C_{\rm d}\) - S (m\({}^{2}\)) that would result from an increase in the cross-sectional area of the ski poles equivalent to the average range in \(S_{\rm p}\); Cl = confidence interval; \(C_{\rm d}\)—coefficient of aerodynamic drag; S—total cross-sectional area of the skier. These values were obtained employing a mixed effects model with the skier’s cross-sectional area as a covariate and a random intercept for the skiers. Trials at all wind speeds were incorporated into this model.  
\end{table}
Table 3: Effect of increasing the cross-sectional area of the ski poles by the average range of all of the skiers combined on \(C_{\rm d}\) and \(C_{\rm d}\) - S (m\({}^{2}\)).