# Application of Wind Tunnel Device for Evaluation of Biokinetic Parameters of Running

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Design

#### 2.2. Participants

#### 2.3. The Basic Characteristics of the Wind Tunnel

#### 2.4. Experimental Procedure

^{3}/s with a nominal average velocity calculated from the volume flow <v

_{nom}> (m

^{3}/s) and the surface of the flow tunnel A = 10.5 m

^{2}; <v

_{nom}> = V/A. The velocity was measured at 1 m from the entry to the treadmill running belt in the direction of the airflow in the meridian plane, positioned on the treadmill’s longitudinal axis. The measurement uncertainty of the recorded and nominal velocities was within the $\left[\begin{array}{c}+\\ -\end{array}\right]$2% limit. The running speed was determined using a marker that was mounted onto the treadmill surface. Based on the length of the running belt and the number of camera frames per second, we were able to calculate the athlete’s speed. To determine the speed of the treadmill, we used a Nikkon D 3000 camera to record the markers on the treadmill belt, with a frequency of 60 Hz.

_{nom}> in the wind tunnel, are presented below. The basic parameters of the run are first provided in the introductory portion of the analysis. A description of the methodology for evaluating the time course of the horizontal and vertical loads on the treadmill sensors, depending on the time course of the load on the runner’s feet on the surface of the running belt, follows. The results are provided with time series F

_{vert}(t) and F

_{vert}(t), which were obtained as the load sum of the four vertical force sensors and the two horizontal force sensors:

- –
- Vertical reaction impulse J
_{vert}, braking impulse J_{dec}, and accelerator impulse J_{acc}:$${J}_{vert}={{\displaystyle \int}}_{{t}_{0}}^{{t}_{1}}{F}_{vert}dt$$$${J}_{dec}={{\displaystyle \int}}_{{t}_{3}}^{{t}_{2}}{F}_{hor}dt$$$${J}_{acc}={{\displaystyle \int}}_{{t}_{2}}^{{t}_{4}}{F}_{hor}dt$$ - –
- Contact time:$${t}_{k}\left(i\right)={t}_{2L}\left(i\right)-{t}_{0L}\left(i\right)+{t}_{2D}\left(i\right)-{t}_{oD}\left(i\right),{t}_{kD}\left(i\right)={t}_{2D}\left(i\right)-{t}_{oD}\left(i\right),{t}_{kL}\left(i\right)={t}_{2L}\left(i\right)-{t}_{oL}\left(i\right)$$
- –
- Time-averaged contact time:$${t}_{k}={{\displaystyle \sum}}_{i}{t}_{k,i}/N$$
- –
- Running frequency:$$f\left(i\right)=\frac{1}{\left({t}_{0D}{}_{i+1}\right)-\left({t}_{0D}{}_{i}\right)}\cong \frac{1}{\left({t}_{0L}{}_{i+1}\right)-\left({t}_{0L}{}_{i}\right)}$$
- –
- Time-averaged frequency:$$\langle {f}_{i}\rangle =1/N{{\displaystyle \sum}}_{i}{f}_{i}$$
- –
- Stride length$${L}_{i}=\frac{{{\displaystyle \sum}}_{i=1}^{N}\frac{{v}_{i}}{{t}_{2D,i}-{t}_{oL,i}}}{N}$$
- –
- Time-averaged stride length:$$\langle {L}_{i}\rangle =1/N{\displaystyle \sum}_{i=1}^{N}{L}_{i}$$

## 3. Results

#### 3.1. Simultaneous Analysis of the Running Topology and the Measured Forces of the Athlete on the Running Surface

#### 3.2. Integral Analysis of Kinematic and Dynamic Running Characteristics and the Impact of Airflow in the Wind Tunnel

## 4. Discussion

#### 4.1. The Analysis of the Running Topology and the Forces Measurement on the Treadmill Surface

_{vert}(t) of the left—L and right—R foot, which is repeated throughout the course of the experiment in seemingly stationary chronological sequence. Minor differences between the loads of the left and right foot can be observed. This is expected based on the training pattern of the athletes. According to some studies, trained runners generally have very little asymmetry of force development between the left and right leg; the asymmetry is less than 1.5% [13,18,23]. The red curve on the diagram represents the braking and accelerating phase of the runner’s take-off on the running belt. The time series between t

_{0}to t

_{2}represents the braking phase, and the t

_{2}to t

_{3}interval represents the acceleration phase. At this point, it is worth noting that, during the analysis of the dynamics shown in Figure 4 (the transition from A to B), time segments were selected when the runner’s left or right leg generated a vertical force on the surface of the running belt. Figure 4B illustrates the occurrence of a “delayed” horizontal force signal behind the vertical force, at its transitional point where the values shift from positive to negative. This phenomenon is attributed to the force transfer properties from the running belt to the runner’s foot (at contact) onto the horizontal force sensors. This transfer occurs due to the deformability of the belt, mechanical transmissions between the belt and the underlying support rollers, and the force sensors. It is assumed that the time delay is a function of the mechanical properties of the set of individual elements and the airiness between each of them, which results in the time delay of the measured signal. We also estimate that this phenomenon does not significantly affect the amplitude of the measured horizontal forces.

#### 4.2. The Impact of Airflow on Kinematic and Dynamic Characteristics of Running

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**A**) represents the wind tunnel’s physical model, tested by the water flow in the model with an M:1:36 ratio (wind tunnel designed size: wind tunnel model size); (

**B**) represents the computational fluid dynamics (CFD) model of the airflow in the wind tunnel flow tract.

**Figure 2.**Treadmill positioning (

**A**) with marginal conditions—airflow velocity profile in the meridian plane (

**B**).

**Figure 3.**The horizontal x-oriented force sensors and the vertically oriented sensors–schematic representation (

**A**); images of the sensors in the x orientation and y orientation (

**B**).

**Figure 4.**Snapshot of the step load of the runner time series, consisting of the left—L and right—R leg load on the treadmill. original signal (

**A**); a snapshot of the time series specifying the time limits of the foot’s contact with the surface of the treadmill (

**B**).

**Figure 6.**Achieving the local extreme of the on its outer side. the Fy force load on the inner side of the foot.

**Figure 8.**Reduction of the vertical force on the outer side of the foot. Fy load on the inner side of the foot.

**Figure 15.**Step frequency, contact times, and flight phases as functions of the time sequence of running.

**Figure 16.**Time-averaged forces in vertical and horizontal directions: (

**A**)—Fy, (

**B**)—force Fx during the braking phase, (

**C**) force Fx during the acceleration phase, at different airflow velocities, and running Athletes 1, 2, and 3.

**Figure 17.**Relationship between the acceleration and deceleration force for individual athletes under different aerodynamic conditions.

**Figure 19.**Contact times (

**A**) and flight phases (

**B**) of individual athletes depending on aerodynamic characteristics.

Athlete 1 | Athlete 2 | Athlete 3 | |

Age (years) | 26 | 22 | 28 |

Height [cm] | 171 | 186 | 183 |

Body Mass [kg] | 58 | 72 | 74 |

1500 m (PR) * | 03.59, 0 | 03.58, 75 | 03.58, 8 |

Nominal volume flow rate in the wind tunnel | 510 m^{3}/s |

Cross-section of the vertical section | Φ 3.6 m |

Maximum airflow velocity in the vertical section of the wind tunnel | 61 m/s |

Nominal total pressure differential on installed fans | 4300 Pa |

Air density range in the wind tunnel | 1.1–1.2 kg/m^{3} |

Nominal electrical power of fans | 2.2 MW |

Nominal volume flow rate in the wind tunnel | 124 m^{3}/s |

Transverse section of horizontal section A | 10.5 m^{2} |

Maximum airflow velocity in the vertical section of the wind tunnel | 45 m/s |

V1 (m/s) | V2 (m/s) | V3 (m/s) | V4 (m/s) | V5 (m/s) | |
---|---|---|---|---|---|

Athlete 1 | 5 | 3 | 0 | −5 | −7 |

Athlete 2 | 5 | 3 | 0 | −5 | |

Athlete 3 | 3 | 0 | −5 | −7 |

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**MDPI and ACS Style**

Širok, B.; Gostiša, J.; Sečnik, M.; Mackala, K.; Čoh, M.
Application of Wind Tunnel Device for Evaluation of Biokinetic Parameters of Running. *Symmetry* **2021**, *13*, 505.
https://doi.org/10.3390/sym13030505

**AMA Style**

Širok B, Gostiša J, Sečnik M, Mackala K, Čoh M.
Application of Wind Tunnel Device for Evaluation of Biokinetic Parameters of Running. *Symmetry*. 2021; 13(3):505.
https://doi.org/10.3390/sym13030505

**Chicago/Turabian Style**

Širok, Brane, Jurij Gostiša, Matej Sečnik, Krzysztof Mackala, and Milan Čoh.
2021. "Application of Wind Tunnel Device for Evaluation of Biokinetic Parameters of Running" *Symmetry* 13, no. 3: 505.
https://doi.org/10.3390/sym13030505