# The Contribution of Ski Poles to Aerodynamic Drag in Alpine Skiing

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## Abstract

**:**

_{p}) to the total aerodynamic drag during alpine skiing. At three different wind speeds in a wind tunnel, 10 skiers assumed typical alpine skiing postures (high, middle, and tuck), and their frontal aerodynamic drag was assessed with a force plate and their cross-sectional area, along with that of their ski poles, determined by interactive image segmentation. The data collected were utilized to examine intra-subject variation in S

_{p}, the effects of S

_{p}on the coefficient of aerodynamic drag (C

_{d}), and the product of C

_{d}and total cross-sectional area (C

_{d}∙S. The major findings were as follows: (i) S

_{p}ranged from 0.0067 (tuck position) to 0.0262 m

^{2}(middle position), contributing 2.2–4.8% of the total cross-sectional area, respectively; (ii) S

_{p}was dependent on wind speed in the high and middle positions; (iii) intra-subject variations ranged from 0.0018 m

^{2}(27.6%) in the tuck position to 0.0072 m

^{2}(30.5%) in the high position; (iv) S

_{p}exerted a likely effect on C

_{d}and C

_{d}∙S. The extensive intra- and inter-skier variability in S

_{p}can account for as much as ~5% of the total frontal cross-sectional area and future investigations on how elite skiers optimize their positioning of the poles in a manner that reduces aerodynamic drag are warranted.

## 1. Introduction

_{d}) and cross-sectional area (S), as well as C

_{d}∙S, the product of these two, in wind tunnels have attempted to optimize body posture, showing that height, joint angles, and positioning of the arms and head all influence the aerodynamic drag [5,6,16]. Moreover, C

_{d}∙S for the technical disciplines ranged from 0.63–0.66 in the high, 0.51–0.55 in the middle, and 0.23–0.24 in the tuck positions, which is generally lower than the corresponding values reported for the speed disciplines (0.15–0.4) [8,13].

_{p}) to the skier’s total cross-sectional frontal area (S); (ii) intra-subject variation in this respect; and (iii) the influence of S

_{p}on the coefficient of aerodynamic drag (C

_{d}) and the product C

_{d}∙S.

## 2. Materials and Methods

#### 2.1. Participants

#### 2.2. Instruments, the Experimental Design and Data Collection

_{p}) and the total cross-sectional area of the skier (S) were assessed by application of click-based interactive segmentation [18] to the images taken in the coronal plane from behind with an HDR-HC7 camcorder purchased from the Sony Corporation (Tokyo, Japan) (Figure 1). Fifteen images (5 in each of the three positions) were re-processed to determine the reproducibility of the measurement of cross-sectional area, resulting in a difference of 0.31 ± 0.24% (mean ± SD).

_{d}) was considered to be the 5-s average of the force in the direction in which the wind was blowing, once this signal had stabilized completely.

#### 2.3. Calculations

_{d}) was obtained from the Rayleigh drag equation C

_{d}∙S = 2∙F

_{d}/(ρ·V

^{2}). In this equation, F

_{d}represents the aerodynamic drag, V the wind speed, and ρ the density of the air. The cross-sectional areas, both total (S) and of the ski poles (S

_{p}) alone, were derived from image processing as described above. The value of S obtained by interactive segmentation was in pixels and special calibration marks in the wind tunnel were utilized to convert these pixels into square meters. Division of C

_{d}∙S by S provided C

_{d}. Since in the combined tuck and high positions, the skier obstructed roughly 6–12% of the airflow in the wind tunnel, C

_{d}was corrected for blockage as proposed by Elfmark and colleagues [19].

#### 2.4. Statistical Analyses

_{p}are presented as means and standard deviations, as well as the percentage of S accounted for by S

_{p}(i.e., (S

_{p}/S)∙100). The individual variation in S

_{p}for each skier was expressed as the difference between the maximal and minimal measured values of S

_{p}and S

_{p}/S (min–max range), together with the coefficient of variance (CV) for S

_{p}.

_{p}and S

_{p}/S, respectively. In these models, the speed and position were fixed factors, and a random intercept was utilized for each athlete. To examine the effect of S

_{p}on C

_{d}and C

_{d}∙S, linear Bayesian multilevel models were fitted for each position, S

_{p,}and body cross-sectional area, again employing a random intercept for each skier. Weakly informative priors were included on standardized values in each model, with intercept and coefficients of ~N(0, 2.5) and residuals of ~exp(1). With each model, 4 chains of 4000 warm-up and 4000 sampling iterations were performed, for a total of 16,000 sampling iterations. There were no diverging transitions, the minimal effective sample size to total sample size ratio of >0.26, and maximal Rhat value < 1.0016.

## 3. Results

_{p}) in the different positions and at different wind speeds are shown in Table 1, together with the intra-skier variation between trials. Figure 2 illustrates the cross-sectional area of the poles for each skier during all of the trials and the images of Skier 8 presented in Figure 3 highlight the extent to which the positioning of the poles and corresponding S

_{p}obtained at 40, 60, and 80 km/h varied. Also noteworthy is the asymmetric positioning of the left and right poles (which was common for this particular skier), as well as the variation in the height of the shoulders and head.

#### 3.1. The Cross-Sectional Area of the Ski Poles

_{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–Middle = −0.5%, 95% CI [−0.7, −0.3%], pd = 1.000; High–Tuck = 2.1%, 95% CI [1.9, 2.3%], pd = 1.000; Middle–Tuck = 2.6%, 95% CI [2.4, 2.7%], pd = 1.000).

_{p}at a wind speed of 40 km/h was probably higher than at 60 km/h and was certainly higher than at 80 km/h (40–60 km/h = 0.0013 m

^{2}, 95% CI [0.0003, 0.0022 m

^{2}], pd = 0.994; 40–80 km/h = 0.0018 m

^{2}, 95% CI [0.0008, 0.0028 m

^{2}], pd = 1.000; 60–80 km/h = 0.0005 m

^{2}, 95% CI [−0.0005, 0.0015 m

^{2}], pd = 0.849). At the same time, in the tuck position, it was unclear whether wind speed influenced S

_{p}(40–60 km/h = −0.0001 m

^{2}, 95% CI [−0.0015, 0.0013 m

^{2}], pd = 0.561; 40–80 km/h = −0.0008 m

^{2}, 95% CI [−0.0021, 0.0006 m

^{2}], pd = 0.863; 60–80 km/h = −0.0007 m

^{2}, 95% CI [−0.0020, 0.0007 m

^{2}], pd = 0.830).

_{p}in the tuck position was again unclear (40–60 km/h = 0.0%, 95% CI [−0.3, 0.2%], pd = 0.587; 40–80 km/h = −0.2%, 95% CI [−0.5, 0.1%], pd = 0.928; 60–80 km/h = −0.2%, 95% CI [−0.5, 0.1%], pd = 0.894).

#### 3.2. Effects of the Cross-Sectional Area of the Poles on C_{d} and C_{d}·S

^{2}increase in the cross-sectional area of the ski poles on the C

_{d}and C

_{d}· S with all wind speeds (controlling for S) can be seen in Table 2. In the case of the high position, S

_{p}had an unclear effect on C

_{d}, while exerting a likely positive effect on C

_{d}·S. With the middle position, there were likely positive effects on both C

_{d}and C

_{d}·S. Finally, in the tuck position, there was a probable negative effect on C

_{d}and possible negative effect on C

_{d}·S. The general relationship between the cross-sectional area of the ski poles and C

_{d}and C

_{d}·S is illustrated in Figure 4.

_{p}by the average range for all the skiers combined at each position on C

_{d}and C

_{d}·S (m

^{2}).

## 4. Discussion

_{p}) ranged from 0.0067 in the tuck position to 0.0262 m

^{2}in the middle position; (ii) these areas accounted for 2.2–4.8% of the total cross-sectional area; (iii) the contribution of the ski poles to the total cross-sectional area was dependent on wind speed in the high and middle positions; (iv) at 80 km/h, the inter-subject variations in this contribution ranged from 0.0018 m

^{2}(27.6%) in the tuck position to 0.0072 m

^{2}(30.5%) in the high position; and, finally, (v) S

_{p}exerted a likely effect on the coefficient of drag (C

_{d}) and C

_{d}∙S (product of coefficient of drag and total cross-sectional area).

_{p}could account for as much as 5.0 ± 0.8% of the total frontal cross-sectional area (Table 1), making the greatest absolute contribution in the high position and the most pronounced relative contribution in the middle position. Furthermore, the intra-skier variations in S

_{p}were relatively extensive (17.1–34.8%), more so apparently at the two highest speeds examined. This variation for all of the skiers combined was even more pronounced (35.6–63.0%), as were the absolute differences between skiers (Figure 2). Knowing that aerodynamic drag is one of the two resistive forces in alpine skiing [4,7,24,25] contributing to energy dissipation [6,26], these observations indicate that the ski poles may be responsible for variations in total energy loss as great as 1% (considering that maximally 28% of the energy loss during giant slalom is due to aerodynamic drag [Supej et al., 2013] [6], a 5.8% relative cross-sectional area of the poles, and 63% variation), with an average of approximately 0.3% (considering that, on average, 15% of the energy loss during giant slalom is due to aerodynamic drag [Supej et al., 2013] [6], a 4.5% relative cross-sectional area of the poles and 40% variation (the latter two values being approximately the mean values for the middle and high positions). No more than a fraction of a second often separates the finishing times of the gold and silver medallists [12], e.g., 0.01 s or 0.015% in the case of the Super Giant Slalom for men in the recent 2023 Alpine Skiing World Championships.

_{p}for the poles declined with increasing wind speed, whereas the graph in Figure 2 shows that the opposite was more often observed for this particular Skier 8. The variation in the positioning of the poles between skiers was even greater than this variation for one and the same subject (Table 1) and it would be worthwhile investigating further the pole position (for example, more or less parallel to the direction of skiing, i.e., to the wind flow) that minimizes drag optimally. However, this potential improvement in performance indicated here is considerably lower than the ~40% reduction in aerodynamic drag that could be achieved by training the arms according to previous reports [17,24] and future investigation should take both the arms and poles into consideration.

_{p}to aerodynamic drag was associated with the tuck position, even though this is the position where the total frontal cross-sectional area of the skier is by far the smallest (Table 1). Perhaps the fact that the poles are held much more parallel to the ground in the tuck position reduces their cross-sectional area to approximately one-quarter of that in the high and middle positions. To further reduce drag, some skiers who specialize in the speed disciplines use folded poles that allow them to align the shape of their poles to that of their bodies. However, even in such a situation, the poles can give rise to strong vortices that increase aerodynamic drag [27].

_{p}on C

_{d}in both the middle and high positions and on C

_{d}∙S in the high position, such that a change in S

_{p}of 0.01 m

^{2}might alter C

_{d}and C

_{d}∙S by as much as 0.02 m

^{2}(Table 2). More surprising were the negative effects of S

_{p}on C

_{d}and C

_{d}∙S in the tuck position, implying that these values both decrease with increasing S

_{p}. The finding is probably due to the fact that the less favorable positioning of the poles (larger S

_{p}) allows more favorable aerodynamic positioning of the skier. For example, if the skier inclines the poles slightly more forwards (tips higher than the grips), this would allow a lower, more aerodynamic positioning of the head and torso, which contribute strongly to the total aerodynamic drag [8,28].

_{p}and its relative contribution to the total aerodynamic drag were on average higher in the middle and high positions at 40 km/h than at 60 and 80 km/h, even though the skiers were instructed to assume the same position at all three wind speeds. Whether the skiers instinctively changed their position somewhat to reduce the aerodynamic drag (i.e., by positioning the poles in a manner that reduced their cross-sectional area) and/or whether this was a consequence of the drag on the poles forcing them into a more inclined position is not possible to know and it is difficult to predict whether similar behavior would occur during actual skiing.

## 5. Conclusions

_{p}) and S

_{p}was found to account for as much as ~5% of the total frontal cross-sectional area, with estimated inter-skier differences in total energy loss being as much as 1%. Since the finishing differences between elite skiers in competitions are extremely small, sometimes no more than 0.015% between the gold and silver medallists, further investigation of the pole position that reduces aerodynamic drag maximally is clearly motivated.

_{p}on C

_{d}and C

_{d}∙S reveal clearly that it is necessary to differentiate between the effect of the poles during more intense turns (involving high and middle positions) and during less intense turns or on flat terrain (tuck position). With higher postures, the poles may increase drag directly, whereas the less favorable pole positioning in a tuck position may reduce overall aerodynamic drag. Although our present work has focused on the technical disciplines, our findings concerning the middle and high positions are likely to be even more relevant to the speed disciplines as well, where skiers adopt positions similar to those utilized in the technical disciplines during more intensive turns on challenging terrain. To make the best use of this knowledge in practice, we recommend that elite skiers train in a wind tunnel with real-time feedback during annual pre-season training to hold their ski poles in a manner that reduces aerodynamic drag, and then apply this when training on snow.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The coronal plane of a skier in the wind tunnel (

**right**) and the corresponding interactive segmentation (

**left**).

**Figure 2.**The cross-sectional area of the ski poles (S

_{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.

**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

_{p}—cross-sectional area of the poles.

**Figure 4.**The values of C

_{d}(coefficient of drag) and C

_{d}·S (product of coefficient of drag and total cross-sectional area) are predicted by the cross-sectional areas of the ski poles (S

_{p}). Gray shaded areas represent a 95% confidence interval.

**Table 1.**The cross-sectional area of the skiers and poles at different wind speeds and body positions.

Cross-Sectional Area | Within-Skier Variation of Pole Cross-Sectional Area | |||||
---|---|---|---|---|---|---|

Speed | Skier (m^{2}) | Poles (m^{2}) | Poles (%) | Min-Max Range (m ^{2}) | Min-Max Range (%) | CV (%) |

High position | ||||||

40 km/h | 0.5615 ± 0.0383 | 0.0262 ± 0.0034 | 4.5 ± 0.7 | 0.0047 ± 0.0013 | 18.4 ± 6.0 | 7.4 ± 2.4 |

60 km/h | 0.5747 ± 0.0422 | 0.0253 ± 0.0030 | 4.2 ± 0.7 | 0.0043 ± 0.0007 | 17.1 ± 3.0 | 7.1 ± 1.0 |

80 km/h | 0.5704 ± 0.0439 | 0.0243 ± 0.0047 | 4.1 ± 1.0 | 0.0072 ± 0.0033 | 30.5 ± 17.1 | 12.6 ± 6.4 |

Overall | 0.5689 ± 0.0402 | 0.0253 ± 0.0030 | 4.3 ± 0.7 | 0.0106 ± 0.0032 | 42.8 ± 14.4 | 12.2 ± 4.7 |

Middle position | ||||||

40 km/h | 0.5143 ± 0.0400 | 0.0273 ± 0.0049 | 5.0 ± 0.8 | 0.0035 ± 0.0014 | 12.7 ± 4.8 | 5.4 ± 2.3 |

60 km/h | 0.5281 ± 0.0473 | 0.0256 ± 0.0043 | 4.6 ± 0.7 | 0.0051 ± 0.0029 | 20.6 ± 12.2 | 8.1 ± 4.8 |

80 km/h | 0.5269 ± 0.0405 | 0.0257 ± 0.0043 | 4.7 ± 0.9 | 0.0052 ± 0.0025 | 20.7 ± 10.6 | 8.3 ± 4.2 |

Overall | 0.5231 ± 0.0415 | 0.0262 ± 0.0039 | 4.8 ± 0.7 | 0.0093 ± 0.0033 | 35.6 ± 11.9 | 10.8 ± 4.5 |

Tuck position | ||||||

40 km/h | 0.3000 ± 0.0189 | 0.0064 ± 0.0025 | 2.1 ± 0.8 | 0.0018 ± 0.0011 | 29.3 ± 20.3 | 12.4 ± 10.4 |

60 km/h | 0.3008 ± 0.0232 | 0.0065 ± 0.0025 | 2.1 ± 0.8 | 0.0021 ± 0.0019 | 34.8 ± 26.6 | 14.9 ± 11.7 |

80 km/h | 0.3045 ± 0.0205 | 0.0072 ± 0.0020 | 2.3 ± 0.7 | 0.0018 ± 0.0008 | 27.6 ± 13.6 | 11.2 ± 5.3 |

Overall | 0.3018 ± 0.0200 | 0.0067 ± 0.0022 | 2.2 ± 0.7 | 0.0041 ± 0.0015 | 63.0 ± 20.6 | 18.2 ± 7.8 |

C_{d} | C_{d}·S (m^{2}) | |||||
---|---|---|---|---|---|---|

Position | b | 95% CI | pd | b | 95% CI | pd |

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 |

_{d}and C

_{d}·S (m

^{2}) caused by a 0.01 m

^{2}increase in the cross-sectional area of the ski poles; CI = confidence interval; pd = probability of direction; C

_{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.

**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

_{d}and C

_{d}·S (m

^{2}).

The Average Range (Avg) in S_{p} for All Skiers Combined | C_{d} | C_{d}·S (m^{2}) | ||||
---|---|---|---|---|---|---|

Position | Avg (m^{2}) | Avg % | Diff | 95% CI | Diff | 95% CI |

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] |

_{d}and C

_{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

_{p}; CI = confidence interval; C

_{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.

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**MDPI and ACS Style**

Supej, M.; Kalén, A.; Verdel, N.; Ogrin, J.; Holmberg, H.-C.
The Contribution of Ski Poles to Aerodynamic Drag in Alpine Skiing. *Appl. Sci.* **2023**, *13*, 8152.
https://doi.org/10.3390/app13148152

**AMA Style**

Supej M, Kalén A, Verdel N, Ogrin J, Holmberg H-C.
The Contribution of Ski Poles to Aerodynamic Drag in Alpine Skiing. *Applied Sciences*. 2023; 13(14):8152.
https://doi.org/10.3390/app13148152

**Chicago/Turabian Style**

Supej, Matej, Anton Kalén, Nina Verdel, Jan Ogrin, and Hans-Christer Holmberg.
2023. "The Contribution of Ski Poles to Aerodynamic Drag in Alpine Skiing" *Applied Sciences* 13, no. 14: 8152.
https://doi.org/10.3390/app13148152