# Performance Analysis in Ski Jumping with a Differential Global Navigation Satellite System and Video-Based Pose Estimation

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## Abstract

**:**

## 1. Introduction

^{−1}[6,7]. To avoid the pitfalls of qualitative analysis, the objective quantification of sport performance is of great interest [8]. To study sport performance with high internal and external validity, first, the sport should be assessed in competition or in competition-like situations, in the absence of instrumentation that can hamper performance. Second, the performance level of athletes should represent the population to be studied and the number of subjects should be sufficiently high to allow for generalisation of the findings to the given population. Third, the measurement equipment needs to be sufficiently accurate and precise despite the outdoor conditions [9].

## 2. Materials and Methods

#### 2.1. Video Based PosEst Method

^{−1}. The camera was horizontally levelled and slightly angled on the trajectory to capture as much as possible of the flight and the take-off ($6.5$ $\mathrm{m}$ prior to take-off to 22 $\mathrm{m}$ after). The image space was calibrated using the ski jumpers segment lengths, measured with a measuring tape prior to testing. The image calibration was conducted by first rotating the image plane in such way that the average segment length of the leg, thigh and arm of the ski jumpers in the 16 jumps remained constant during the flight. Second, calibration was achieved from the image space in pixels to the object space in meters using the athletes’ segment lengths.

#### 2.2. dGNSS Based Method

#### 2.3. Parameter Definition and Calculation

#### 2.4. Part I: Comparison of PosEst and dGNSS Method

#### 2.5. Part II: Case Study

## 3. Results and Discussion

#### 3.1. Part I: Comparison of PosEst and dGNSS Data

^{−1}and ± $0.97$ m s

^{−2}as a maximum for the velocity and acceleration respectively. The largest difference was observed in the horizontal direction, with an MAE of ± $0.41$ m s

^{−1}and ± $1.56$ m s

^{−2}as a maximum for the region 5–20 $\mathrm{m}$. Altogether, the uncertainty in the measurements was high the first 5 $\mathrm{m}$ and deviated from the edge of the in-run. All measurements showed good agreement from 5 $\mathrm{m}$ after the in-run. The consistency and agreement 5$\mathrm{m}$ indicates that these methods are reliable for use in such analyses.

#### 3.2. Part II: Case Study

#### 3.2.1. External Data

^{−1}. For more information about the simulation, the reader is referred to [6].

#### 3.2.2. In-Run

^{−1}was observed, with the difference in the velocity components being $0.86$ m s

^{−1}and $0.60$ m s

^{−1}in ${v}_{x}$ and ${v}_{y}$, respectively. During the in-run, the difference in ${v}_{y}$ diminished to zero and ${v}_{x}$ to approximately half, and thus the difference in v was $0.43$ m s

^{−1}approaching the edge of the in-run. About $0.3$ m s

^{−1}of the speed difference was expected due to the lower start gate in Jump 2 [6], but $0.1$ m s

^{−1}( $0.36$ $\mathrm{k}$$\mathrm{m}$ h

^{−1}, equivalent to the effect of 1 gate) cannot be explained by the gate difference. In other words, Jump 1 showed a $0.1$ m s

^{−1}better performance regarding in-run speed. This is a substantial difference, since a difference in in-run speed at take-off of ∼ $0.3$ m s

^{−1}can increase the jump distance by 3.8–$10.1$ $\mathrm{m}$ approximately, depending on hill size and wind conditions [51,52].

#### 3.2.3. Take-Off and Early Flight Phase

#### 3.2.4. Flight Phase

#### 3.3. Possibilities and Limitations

#### 3.4. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CoM | Center of Mass |

ConvNet | Convolutional Neural Network |

dGNSS | differential Global Navigation Satellite System |

${F}_{b}$ | Braking force |

${F}_{D}$ | Drag force |

${F}_{f}$ | Friction force |

${F}_{L}$ | Lift force |

${F}_{L}$/${F}_{D}$-ratio | Lift-to-drag ratio |

${F}_{N}$ | Normal force |

${F}_{p}$ | Perpendicular force |

FIS | International Ski Federation |

IMU | Inertial Measurement Units |

MAE | Mean Absolute Error |

PosEst | Markerless Video-based Pose Estimation |

SPM | Statistical Parametric Mapping |

## Appendix A. Statistical Parametric Mapping Analysis

**Figure A1.**Statistical parametric mapping t-test analysis of the paired difference between the methods compared to zero difference of trajectory (

**a**), horizontal and vertical velocity (

**b**,

**c**) and acceleration (

**d**,

**e**) (n = 16). The red, dashed, horizontal lines indicate the threshold t${}^{*}$ test-values and the values are reported in each plot. Significant supra-threshold clusters are marked with a grey shade, together with their corresponding p-values.

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**Figure 1.**Camera view for the experiment together with examples of the cropped and tracked windows during the in-run, take-off and flight phase.

**Figure 2.**Ski jumpers with the dGNSS antennae mounted on their helmets and the receivers in backpacks that were carried under the ski jumping suit.

**Figure 3.**Gravitational ($mg$), normal (${F}_{N}$), friction (${F}_{f}$), drag (${F}_{D}$) and lift (${F}_{L}$) forces acting on a ski jumper in an in-run, together with the coordinate system and angle of the hill ($\phi $).

**Figure 4.**Definition of parameters calculated from the PosEst data: (

**a**) shows the knee angle ($\theta $) and the hip angle ($\gamma $). (

**b**) the centre of mass (CoM), gravitational force (${F}_{g}$), drag force (${F}_{D}$), lift force (${F}_{L}$), body angle of attack ($\psi $) and the resultant speed of the ski jumper (v).

**Figure 5.**Comparison of data of the PosEst system and the dGNSS. (

**a**) show the average trajectory (

**a1**), vertical and horizontal velocity (

**a2**) and acceleration (

**a3**). The shaded error bands indicate the standard deviation with n = 16. PosEst data are indicated in red and dGNSS in blue. (

**b**) shows the average paired difference of the same variables between the systems. The shaded error bands indicate the standard deviation with n = 16 and the dashed line zero difference. The paired differences in the x-direction are indicated in red and in the y-direction in blue. The SPM statistical information is represented by the horizontal bars for the paired difference. The black bar represents the statistical difference between the paired difference and zero in (

**b1**). In (

**b2**,

**b3**), the light gray color represents statistical difference in the x-direction, dark gray in the y-direction and black in both directions, where ** denotes p < 0.001.

**Figure 6.**Velocity components of the in-run phase for the two jumps in the case analysis. (

**a**) shows the resultant velocity v, (

**b**) the horizontal velocity ${v}_{x}$ and (

**c**) the vertical velocity ${v}_{y}$. The horizontal length from the in-run edge is shown on the x-axis and velocity is shown on the y-axis.

**Figure 7.**Perpendicular force action on the ski jumper during the in-run. The horizontal length from the in-run edge is shown on the x-axis and velocity is shown on the y-axis.

**Figure 8.**Braking force acting on the ski jumper during the in-run phase measured with the dGNSS. The horizontal length from the in-run edge is shown on the x-axis and velocity is shown on the y-axis.

**Figure 9.**CoM trajectory during the take-off and early flight phase for the two jumps in the case analysis. The horizontal and vertical distance from the in-run edge are shown on the x-axis and y-axis, respectively.

**Figure 10.**Velocity components of the CoM in the take-off and early flight phase for the jumps in the case study. (

**a**) shows the resultant velocity v, (

**b**) the horizontal velocity ${v}_{x}$ and (

**c**) the vertical velocity ${v}_{y}$. The horizontal length from the in-run edge is shown on the x-axis and velocity is shown on the y-axis. A negative sign on the x-axis indicates the area before take-off.

**Figure 11.**External forces acting on the ski jumper during the early flight phase for the jumps in the case study. (

**a**) shows the lift-to-drag ratio (${F}_{L}/{F}_{D}$), (

**b**) the aerodynamic lift (${F}_{L}$) and (

**c**) the aerodynamic drag (${F}_{D}$). The horizontal length from the in-run edge is shown on the x-axis. On the vertical axis the unit less ratio is shown in (

**a**) and the force [$\mathrm{N}$] in (

**b**,

**c**).

**Figure 12.**Knee angle ($\theta $), hip angle ($\gamma $) and body angle of attack ($\psi $) measured during the take-off phase for the jumps in the case analysis. (

**a**) shows the angles and (

**b**) the respective angular velocity. The horizontal length from the in-run edge is shown on the x-axis, angles in $\mathrm{rad}$ on the vertical axis in (

**a**) and angular velocity in $\mathrm{rad}$ s

^{−1}in (

**b**).

**Figure 13.**Trajectory from the dGNSS in the flight phase for the two jumps. The gray shaded areas highlight the take-off and landing phases. The horizontal and vertical distances from the in-run edge are shown on the x-axis and y-axis, respectively.

**Figure 14.**Velocity components in the flight phase for the jumps in the case study. The gray shaded areas highlight the take-off and landing phases: (

**a**) shows the resultant velocity v, (

**b**) the horizontal velocity ${v}_{x}$ and (

**c**) the vertical velocity ${v}_{y}$. The horizontal length from the in-run edge is shown on the x-axis and velocity is shown on the y-axis.

**Figure 15.**Forces acting on the ski jumper in the flight phase. (

**a**) shows the lift-to-drag ratio (${F}_{L}/{F}_{D}$), (

**b**) the aerodynamic lift (${F}_{L}$) and (

**c**) the aerodynamic drag (${F}_{D}$). The horizontal length from the in-run edge is shown on the x-axis with a unit less ratio in (

**a**) and the forces [$\mathrm{N}$] in (

**b**,

**c**) on the vertical axis. The gray shaded areas highlight the take-off and landing phases.

**Table 1.**Overview of the performance parameters measured in the different phases of the ski jump and the method used for the analysis. Dist. is the horizontal distance from the jump edge and Tr. the trajectory of the head for the dGNSS and CoM for the PosEst.

Phase | Dist. | Method | Tr. | v | ${\mathit{v}}_{\mathit{x}}$ | ${\mathit{v}}_{\mathit{y}}$ | ${\mathit{F}}_{\mathit{b}}$ | ${\mathit{F}}_{\mathit{p}}$ | ${\mathit{F}}_{\mathit{D}}$ | ${\mathit{F}}_{\mathit{L}}$ | ${\mathit{F}}_{\mathit{L}}/{\mathit{F}}_{\mathit{D}}$ | $\mathit{\psi}$ | $\mathit{\theta}$ | $\mathit{\gamma}$ | ${\mathit{v}}_{\mathit{\psi}}$ | ${\mathit{v}}_{\mathit{\theta}}$ | ${\mathit{v}}_{\mathit{\gamma}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

[$\mathrm{m}$] | [$\mathrm{m}$] | [m s^{−1}] | [$\mathrm{N}$] | [] | [$\mathrm{rad}$] | [$\mathrm{rad}$ s^{−1}] | |||||||||||

in-run | −65–0 | dGNSS | X | X | X | X | X | X | |||||||||

Take-off | −5–20 | PosEst | X | X | X | X | X | X | X | X | X | X | X | X | X | ||

Flight | 0–90 | dGNSS | X | X | X | X | X | X | X |

**Table 2.**Mean absolute error (MAE) for phases of 5 $\mathrm{m}$ between the paired difference and zero difference (Figure 5b).

Phase [$\mathbf{m}$] | −5–0 | 0–5 | 5–10 | 10–15 | 15–20 |
---|---|---|---|---|---|

Tr [$\mathrm{m}$] | 0.10 | 0.04 | 0.02 | 0.03 | 0.03 |

${v}_{x}$ [m s^{−1}] | 0.49 | 0.15 | 0.41 | 0.34 | 0.15 |

${v}_{y}$ [m s^{−1}] | 0.41 | 0.10 | 0.08 | 0.13 | 0.15 |

${a}_{x}$ [m s^{−2}] | 2.45 | 2.19 | 0.43 | 1.44 | 1.56 |

${a}_{y}$ [m s^{−2}] | 1.44 | 1.89 | 0.57 | 0.97 | 0.92 |

**Table 3.**External data for the two jumps chosen for the case study. Distance points and wind points showing the length and wind compensation points in an FIS competition.

Gate | Distance | Total Wind Score | Wind Measurements at [m s^{−1}] | |||||||
---|---|---|---|---|---|---|---|---|---|---|

[#] | [$\mathbf{m}$] | Points | [m s^{−1}] | Points | 10 m | 38 m | 57 m | 76 m | 95 m | |

Jump 1 | 15 | 96 | 62 | 0.40 | −3.2 | 1.63 | 0.80 | 0.71 | 0.52 | 0.29 |

Jump 2 | 12 | 91 | 52 | 0.46 | −3.7 | 1.44 | 0.94 | 0.50 | 0.78 | 0.92 |

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**MDPI and ACS Style**

Elfmark, O.; Ettema, G.; Groos, D.; Ihlen, E.A.F.; Velta, R.; Haugen, P.; Braaten, S.; Gilgien, M.
Performance Analysis in Ski Jumping with a Differential Global Navigation Satellite System and Video-Based Pose Estimation. *Sensors* **2021**, *21*, 5318.
https://doi.org/10.3390/s21165318

**AMA Style**

Elfmark O, Ettema G, Groos D, Ihlen EAF, Velta R, Haugen P, Braaten S, Gilgien M.
Performance Analysis in Ski Jumping with a Differential Global Navigation Satellite System and Video-Based Pose Estimation. *Sensors*. 2021; 21(16):5318.
https://doi.org/10.3390/s21165318

**Chicago/Turabian Style**

Elfmark, Ola, Gertjan Ettema, Daniel Groos, Espen A. F. Ihlen, Rune Velta, Per Haugen, Steinar Braaten, and Matthias Gilgien.
2021. "Performance Analysis in Ski Jumping with a Differential Global Navigation Satellite System and Video-Based Pose Estimation" *Sensors* 21, no. 16: 5318.
https://doi.org/10.3390/s21165318