Wind Field Simulation and Its Impacts on Athletes’ Performance, Based on the Computational Fluid Dynamics Method: A Case Study of the National Sliding Centre of the Beijing 2022 Winter Olympics

Abstract

The wind field plays an important role in the maintenance of large sport venues. Most wind field simulation research involves no quantitative analysis of the impacts of the wind environment on athletes’ safety and performance. Taking the National Sliding Centre (NSC) of the Beijing 2022 Winter Olympics as the research object, this paper conducts a wind field simulation study based on CFD, and innovatively explores the quantitative impact of building-scale wind environment characteristics on micro-athletes’ wind resistance and performance for the first time. First, an NSC model and a human body model of athletes are constructed and simplified. Grid independence verification is carried out, and the grid is divided and optimized. Second, wind environment simulation under different climatic conditions is completed, based on CFD technology. The defined wind speed dispersion indexes are calculated. The characteristics of the wind field outside the venue is quantitatively analyzed. Third, we define and calculate the main influencing parameters on athletes’ competition performance. The impacts of the wind field on micro-athletes’ performance are quantified. With a gradual increase in wind level (3.125, 3.5, 4.5, 5.5, 6.5, 7.5, 8.229), the optimized sliding route can reduce the air resistance by 0.2607 N, 0.3415 N, 0.4600 N, 0.6469 N, 0.9283 N, 1.1741 N, and 1.4535 N, which can improve the athletes’ competition results by 0.02 s, 0.03 s, 0.04 s, 0.06 s, 0.09 s, 0.11 s, and 0.14 s, respectively. This paper provides methodological support for exploring the mechanism of athlete performance from the perspective of a building-scale environment.

1. Introduction

Large single buildings are the main locations for hosting important activities in large cities. They are a type of building that has single or multiple functions, such as sports, scientific research, administration, education, commerce, and exhibitions. Large single buildings are characterized by their large volume, strong functionality, and strong comprehensiveness. The construction and maintenance process of such building facilities is complex, and has an important impact on the safety of relevant personnel. At the same time, the densely populated and highly closed characteristics of such buildings bring great challenges to their safe operation and maintenance management. To ensure the safe operation of large single buildings [1], it is necessary not only to maintain the management and operation of the building, but also to control the external climate environment of the building, that is, the wind field and thermal field inside and outside the building [2].

The impact of wind/thermal fields on large single buildings is one of the most important factors that must be considered in architecture and urban planning. Wind field analysis can help engineers to evaluate the structural stability of large single buildings under strong wind or hurricane conditions [3], ensure their structural safety and stability, and avoid related risks and accidents during the building planning and design stage. For building layout planning and design, by studying the spatiotemporal characteristics of its wind field, the shape and arrangement of the building can be optimized [4], thereby reducing wind loads [5], planning urban ventilation corridors [6], optimizing the wind and heat environment of the urban space, and reducing the occurrence of extreme weather [7]. For the setting of urban greening, wind and thermal field analysis can optimize the layout of green space [8] and help in arranging trees reasonably, thereby reducing the urban temperature, improving the outdoor thermal comfort of humans [9], and alleviating the heat island effect. The study of indoor and outdoor wind field characteristics of large sports venues is crucial for the design, construction, use, and maintenance of buildings, as well as for the comfort, safety, and competition results of athletes. For example, studying the optimization of natural ventilation [10] can reduce a building’s dependence on mechanical ventilation systems and optimize energy efficiency. When considering an emergency such as a fire, understanding the impact of wind direction and speed on smoke diffusion [11] can help in the design of effective emergency evacuation routes and safe exit layouts. By analyzing the wind field inside and outside the building, internal ventilation conditions can be optimized, and athletes can even be helped to avoid climatic conditions that have a negative impact on their athletic performance.

There are usually two methods to obtain the indoor and outdoor wind and heat field distribution of a single building or a group of buildings, namely, meteorological data collection and numerical simulation analysis. The sources of meteorological data collection [12] include meteorological station data, satellite remote sensing data, and drone data. Meteorological station data are historical and real-time meteorological data obtained from local meteorological stations or meteorological departments. Satellite remote sensing data can provide meteorological information in a wide range. Drone data acquisition uses drones to collect more detailed meteorological data, such as wind speed, temperature, and humidity. The main numerical simulation analysis methods include CFD simulation and atmospheric model simulation. Atmospheric model simulation uses atmospheric numerical models to perform meteorological simulations, such as the WRF (Weather Research and Forecasting) model [13], to obtain large-scale outdoor wind and thermal field information. Computational fluid dynamics (CFD) simulation can be used to simulate indoor and outdoor wind and thermal field distribution [14,15], and can be implemented using software such as ANSYS Fluent 2022 R2 and COMSOL6.3. Computational fluid dynamics (CFD) technology can simulate and analyze the behavior of wind in complex terrain and building environments. This information is very valuable for the design, construction, and long-term maintenance management of large-scale building projects.

The distribution of indoor and outdoor wind fields is an important factor affecting the safe operation of large single buildings; in particular, the wind fields of large stadiums will have an important impact on athletes’ performance.

Research on the outdoor wind fields of buildings mainly includes corridor ventilation, building layout, structural stability, and building wind load. Most scholars have mainly studied the relationship between wind field distribution characteristics and building form based on CFD technology or wind tunnel experiments. Lim et al. [16] developed a CFD and evolutionary algorithm-driven method to optimize building configurations for urban ventilation, and showed a 16% ventilation improvement in dense areas. Iqbal et al. [17] analyzed wind flow around cross-shaped high-rise buildings using CFD and wind tunnel tests, finding that building orientation, spacing, and wind angles critically affect pedestrian-level airflow, with oblique winds generating vortices, improving dispersion and comfort. Verma et al. [18] measured the wind load of high-rise building models at different incident angles through wind tunnel tests, and used CFD technology to complete a simulation study with the same parameters as the experimental study. They explored the wind pressure distribution of octagonal buildings at different wind incident angles (0°, 15°, and 30°) and measured the average area-weighted wind pressure on the surface of the building model.

In the study of indoor wind fields in buildings, most scholars mainly focus on the relationship between indoor wind field and fire smoke diffusion and the comfort of indoor occupants. Dong et al. [19] used FDS software to establish a numerical simulation model of high-rise building fires, and analyzed the changes in smoke layer height, temperature, visibility, and CO concentration over time in a high-rise building of a hospital in Shanxi Province, China. They established an emergency evacuation model, divided and optimized evacuation routes based on simulation results, and shortened the safe evacuation time. Tan et al. [20] analyzed the characteristics of indoor air flow organization by numerically simulating the velocity field and temperature field of a large sports stadium in Sichuan Province, China. Their study found that the use of air conditioning air supply in the form of seat air supply (downward air supply), side air supply, rear return air, and top exhaust makes the air flow distribution in the stadium uniform able to meet human comfort requirements.

We know that athletes’ performance is affected by many factors, such as technical level [21], physical fitness and strength, equipment quality and design [22], psychological factors [23], training and preparation [24], and other subjective factors of athletes. In addition to the above-mentioned subjective factors, it is also closely related to objective factors, such as track conditions [25] and climate conditions. Therefore, many scholars have begun to pay attention to the study of wind field changes and athletes’ performance. Jia et al. [26] established a three-dimensional human body model and a skeleton model, and used CFD numerical simulation technology to obtain the distribution law of aerodynamic parameters, such as pressure, streamline vorticity, and aerodynamic drag, around the skeleton and the athlete, providing a quantitative reference for the drag reduction of skeleton sports. Li et al. [27] used wind tunnel technology to study the wind resistance characteristics of a bobsleigh project during the sliding stage, thereby providing professional advice for the sliding posture of bobsleigh athletes. Barry et al. [28] measured the changes in air resistance under two different cycling team formations through wind tunnel experiments, and found that the resistance and lateral force between two riders are functions of their spatial positions. Belloli et al. [29] found through wind tunnel experiments that the resistance area of athletes in different postures is different, resulting in different wind resistance. This result can be used as a theoretical basis for athletes to adjust their sports postures. These studies show that different wind field distributions will cause athletes to experience different resistances, thereby affecting their competition results.

From the above-mentioned research on indoor and outdoor wind fields, we know that using CFD technology to simulate wind fields in large sports venues based on real scenarios is of great significance in the fields of sports and engineering. Wind field simulation of large sports venues based on real scenarios can be used to verify the rationality of venues’ architectural design, provide athletes with competition venue information adapted to different meteorological conditions to ensure athlete performance and safety, and analyze related parameters, providing support for the stability assessment of building structures [30]. The distribution of indoor and outdoor wind fields in large sports venues will significantly affect athletes’ performance. Existing research usually focuses on the study of outdoor wind fields, indoor wind fields, and small-scale wind fields around athletes. Research on the simulation of indoor and outdoor wind fields in real scenarios and their coupling with athletes’ movements is relatively rare.

To fill this research gap and better understand the quantitative relationship between the indoor and outdoor wind field distribution characteristics of large sports venues and athletes’ performance, we took the National Sliding Centre (NSC) of the Beijing 2022 Winter Olympics as the research object. BIM and CFD are used to simulate the building-scale wind field. The building-scale simulation not only considers the flow of the outdoor wind field at the building scale, but also focuses on the small-scale wind field of indoor athletes. Based on the CFD simulation results, we reveal the outdoor wind field characteristics of large single buildings under different climatic conditions. In addition, the wind resistance of athletes sliding and the parameters affecting athletes’ performance are calculated to explore the quantitative relationship between the outdoor wind field characteristics of the National Bobsleigh and Luge Center and the air resistance suffered by indoor athletes. We preliminarily explore the wind resistance reduction of athletes’ sliding routes under different outdoor climatic conditions, quantify the relationship between athletes’ competition time and wind resistance reduction, and plan and optimize athletes’ sliding routes to improve the overall performance of ski athletes.

2. Materials and Methods

2.1. Study Area and Meteorological Dataset

The National Sliding Centre (NSC), located in Yanqing District, Beijing, was the venue for bobsleigh, skeleton, and luge events during the 2022 Beijing Winter Olympics. Meteorological data show that northwest winds prevail in Beijing from February to March. The average wind speed in Yanqing District in winter (December to March) is 3.65 m/s, and the maximum wind speed reaches 18 m/s. According to the wind rose diagram of 700 hPa at the center of the Yanqing competition area from February to March 2009 to 2021, compiled by Liu et al., the wind direction in Yanqing District from February to March is mostly in the northwest quadrant, accounting for 83.74% of the total sample volume [31]. Within this quadrant, the three most frequently occurring wind direction ranges are WNW (270°~292.5°), NW (292.5°~315°), and NWN (315°~337.5°), as shown in Figure 1. The occurrence frequencies of WNW (270°~292.5°) and NW (292.5°~315°) both exceed 25.38%, and the occurrence frequency of NWN (315°~337.5°) exceeds 16.31%.

2.2. Establishment of Geometric Model

To conduct wind field research at the NSC based on real scenarios, it is necessary to establish a real geometric model of the NSC. The process of establishing the geometric model is shown in Figure 2. In addition, in order to show the semi-enclosed structure of the venue and the interaction of its indoor and outdoor air, Figure 3 was drawn.

The NSC covers a total area of 18.7 hectares, and has a large span. The three-dimensional geometric model of the NSC established based on BIM technology is relatively complex and highly fragmented. However, CFD calculation simulation does not need to consider overly detailed architectural details, so the existing three-dimensional BIM model needs to be simplified. Considering the characteristics of the venue model, with a large span, a large area, a complex model, and a high degree of fragmentation, it is difficult to simulate the wind field and windward resistance of the entire venue and all track positions. To effectively reduce the amount of model calculation and improve the efficiency of the model simulation, this study extracted typical areas and typical track sections of the NSC for wind field simulation, and simulated and analyzed the windward resistance of typical track sections that might affect athletes’ performance.

Firstly, four typical areas were selected. The tracks and some buildings in these four areas are relatively complex in shape. They are key areas that directly affect the athletes’ performance, including Starting area 1, the S-curve section, the 360-degree spiral curve section, and the end area (as shown in Figure 3). Starting area 1 is the starting area for bobsleigh, skeleton, and men’s luge events [32]. Starting area 1 is where the push-start phase of the skeleton competition occurs. The time spent in this phase is one of the most important factors affecting the performance of the competition [33,34]. Therefore, Starting area 1 was selected as the first typical area of the NSC, called Area I. The S-curve section is an important curve section of the NSC. The skiing level and skills at the S-curve are important factors affecting the athletes’ performance. Therefore, this paper selects an S-curve section as the second typical area, called Area II. The 360-degree spiral curve section is a characteristic curve of the NSC. The NSC is the only bobsleigh track in the world with a 360-degree spiral bend, so the 360-degree spiral bend section was selected as the third typical area, called Area III. The end area is the uphill section of the track and the deceleration area for skiers. This is obviously different from other sections of the track, so the end area was selected as the fourth typical area, called Area IV.

Secondly, the four typical areas were simplified. The detailed building components, such as window railings, internal equipment, and irrelevant internal walls, of the above four typical area models were removed. Then, CFD pre-processing was performed on the geometric models of the above typical areas to check and deal with their geometric errors.

Thirdly, simplified human body models of athletes were arranged on the track of the four typical area models. The simplified human body models of the athletes were in a prone position, which is the reference posture of the skeleton athlete. According to the principle of setting a simplified human body model every 30 m, 3, 5, 4, and 12 simplified human body models of athletes were added to Area I, Area II, Area III, and Area IV, respectively, so that they were evenly distributed on the track, as shown in Figure 3.

Finally, based on the principles for establishing the outer flow basin of buildings proposed by the German Engineers Association [35] and the Japanese AIJ Wind Engineering Group [36] (the building blockage rate should be less than 3%), the shells of four typical regional models were generated as their outer flow basins, as shown in the last stage in Figure 3.

2.3. CFD Simulation Method and Parameter Setting

2.3.1. CFD Simulation Principle

The flow of fluid follows three major equations, namely, the continuity equation, the momentum equation, and the energy equation. By solving the three equations, the wind field and thermal field of fluid flow can be obtained. In this study, CFD technology is used to simulate the steady-state wind field of the NSC. This study focuses on the wind field characteristics of the NSC, analyzes the impact of wind speed on athletes’ performance, and solves the wind speed and wind pressure in the fluid area. Therefore, the continuity equation and momentum equation of the fluid in the study area are established, as shown below.

Continuity equation:

$$div\left(\mathit{U}\right)=0$$

(1)

where $\rho$ represents density; and $u,v,w$ are velocity vectors in the x, y, and z directions. Since the CFD simulation performed in this study is a steady simulation, there is no time term in the continuity equation.

Momentum equation:

$$div\left(\rho u\mathit{U}\right)=div\left(\eta \mathit{g}\mathit{r}\mathit{a}\mathit{d}u\right)-{\displaystyle \frac{\partial p}{\partial x}}+S_u;$$

(2)

$$div\left(\rho v\mathit{U}\right)=div\left(\eta \mathit{g}\mathit{r}\mathit{a}\mathit{d}v\right)-{\displaystyle \frac{\partial p}{\partial y}}+S_v;$$

(3)

$$div\left(\rho w\mathit{U}\right)=div\left(\eta \mathit{g}\mathit{r}\mathit{a}\mathit{d}w\right)-{\displaystyle \frac{\partial p}{\partial z}}+S_w.$$

(4)

where η is the dynamic viscosity of the fluid. Similarly to the continuity equation, the transient time term of the momentum equation is also removed.

By performing CFD simulation of the steady state, the wind field distribution information of the NSC can be obtained.

2.3.2. Meshing and Independence Verification

The basic geometric model of the NSC was meshed. Area II is the most geometrically complex part of the NSC model. When Area II satisfies grid independence, all the NSC models satisfy grid independence. Therefore, the geometric model of Area II was selected for grid independence verification, and the fluid domain of Area II was divided into a refined grid, medium grid, and coarse grid, according to different mesh growth rates of 1.1, 1.15, and 1.2. The specific parameters are shown in

Table 1. Grid independence verification experimental parameters.

Grid Type	Elements	Nodes	Growth Rate
Coarse grid	16,950,209	3,123,716	1.2
Medium grid	20,832,355	3,775,180	1.15
Refined grid	28,427,397	5,049,341	1.1

. This study conducted CFD simulation calculations on the fluid domain under coarse grid, medium grid, and refined grid conditions, respectively. To demonstrate the grid independence, 20 sample points along the wind direction were selected from the above grid simulation wind fields with different resolutions to compare the wind speed values, as shown in Figure 4.

As shown in Figure 4, the difference in CFD-simulated wind speed between the coarse grid, medium grid, and refined grid is very small, with an average error of 0.012%. Therefore, the use of a coarse grid can meet the grid independence requirement. Considering that the number of coarse grids is 1.93 million lower than that of refined grids, this means that coarse grids consume less computing resources, calculate faster, and compute time is shorter. In this study, coarse mesh was used for CFD simulation. The meshing parameters were set according to the size of the geometric model. The most suitable meshing parameters for the above four typical areas are shown in

Table 2. Meshing parameters.

Area	Element Size (m)	Building Surface Defeature Size (m)	Growth Rate
Area I	0.2	0.1	1.2
Area II	0.15	0.075	1.2
Area III	0.15	0.075	1.2
Area IV	0.2	0.1	1.2

.

2.3.3. CFD Boundary and Input Parameter Setting

To comprehensively analyze the wind field characteristics of the NSC and its impact on athletes’ performance, this study combined different wind directions and wind speeds according to actual meteorological conditions, and simulated and calculated the wind field distribution under different climatic conditions in the NSC.

For the selection of wind direction in the simulation, based on the three most frequently appearing wind direction ranges, WNW (270°~292.5°), NW (292.5°~315°), and NWN (315°~337.5°), in the wind rose diagram of Yanqing, Beijing, in February and March from 2009 to 2021, the medians of these three wind direction ranges were selected as the initial input values of wind direction for this study, which are 281.25°, 303.75°, and 326.25°.

For the selection of wind speed, the average wind speed in the study area in winter (December to March) is 3.65 m/s and the maximum wind speed is 18 m/s. The wind speeds between 3.65 m/s and 18 m/s include level 3—breeze (3.4 m/s~5.4 m/s), level 4—mild wind (5.5 m/s~7.9 m/s), level 5—light wind (8.0 m/s~10.7 m/s), level 6—strong wind (10.8 m/s~13.8 m/s), and level 7—gale (13.9 m/s~17.1 m/s). We selected the medians of the wind speed ranges from level 3 to level 7 as the initial input values of the wind speed in this study, which are 3.65 m/s, 4.4 m/s, 6.7 m/s, 9.35 m/s, 12.3 m/s, 15.5 m/s, and 18.0 m/s, corresponding to values on the climate wind scale of 3.125, 3.5, 4.5, 5.5, 6.5, 7.5, and 8.229, respectively.

In summary, there were 21 climate conditions simulated by CFD in this study. For the turbulence model, we used the standard k-ε turbulence model [37], which has high computational accuracy, stability, and economy, and is suitable for CFD simulation of the outdoor wind environment of buildings. For the input wind speed at the flow field inlet, 3.65 m/s, 4.4 m/s, 6.7 m/s, 9.35 m/s, 12.3 m/s, 15.5 m/s, and 18.0 m/s were set, respectively. For boundary conditions, the flow field inlet boundary was the velocity inlet boundary, the flow field outlet boundary was the pressure outlet boundary, the building surface and the ground surface were both no-slip wall boundaries, and the top and two sides of the flow field were symmetrical boundaries.

3. Construction of Parameter Indicators for Analysis of Wind Field Characteristics

3.1. Wind Speed Dispersion Index

Wind speed dispersion is used to represent the wind speed difference characteristics of a certain plot in the study area. The smaller the dispersion, the more uniform the wind speed distribution of the plot. The larger the dispersion, the more uneven the wind speed distribution of the plot, which is prone to vortexes and extreme wind fields [38]. To evaluate the uniformity of wind speed distribution in the study area, this study established global wind speed dispersion and local wind speed dispersion indicators.

3.1.1. Global Wind Speed Dispersion

Wind speed dispersion is essentially a statistical indicator, and the parameters related to its definition include standard deviation, variance, and range. Considering that variance can better reflect the degree of deviation of all values from the mean, variance was used as an indicator to represent the global wind speed dispersion of the region:

$$\overline{L}={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(x_i-\mu )}^2.$$

(5)

where $\overline{L}$ is the global wind speed dispersion of the region, n is the number of grids in the region, $x_i$ is the wind speed value at the grid position, and $\mathsf{\mu }$ is the average wind speed of the entire region.

In this study, the four typical areas selected have different global wind speed dispersion, which can be expressed by the following formula:

$${\overline{L}}_a^b={\displaystyle \frac{1}{n_a}}{\sum }_{i=1}^{n_a}{\left(x_i-{\mu }_a^b\right)}^{2}a=\mathrm{1,2},\mathrm{3,4};b=\mathrm{1,2},3.$$

(6)

where a takes values of 1 to 4, corresponding to Area I, Area II, Area III, and Area IV, respectively. b takes values of 1 to 3, representing wind directions WNW, NW, and NWN, respectively. ${\overline{L}}_a^b$ is the global wind speed dispersion of area a when the wind direction is b. ${\mu }_a^b$ is the average wind speed of area a when the wind direction is b. $n_a$ is the number of grids in area a. $x_i$ is the wind speed value at each grid position.

3.1.2. Local Wind Speed Dispersion

The global wind speed dispersion is not enough to understand the local wind speed dispersion in the study region. Therefore, the local wind speed dispersion was established, with the following index:

$$L={(x-\mu )}^2$$

(7)

where L is the local wind speed dispersion, x is the wind speed value at the local position, and μ is the average wind speed of the entire region.

In this study, the local wind speed dispersion of the four typical areas can be expressed by Formula (8):

$$L_i^{a,b}={(x_i-{\mu }_a^b)}^2;i=\mathrm{1,2},3\dots \dots n_a$$

(8)

where $L_i^{a,b}$ is the local wind speed dispersion at the position of the i-th grid in area a, when the wind direction is b.

3.2. Construction and Quantification of Main Influencing Parameters on Athletes’ Competition Performance

Athletes’ performance is related to the air resistance and friction resistance they are subjected to. For the athletes of bobsleigh, skeleton, and luge events, the track slope is fixed so that their own gravity and friction resistance are relatively fixed. In this case, reducing air resistance becomes significant. An international consensus has been reached on improving athletes’ performance in bobsleigh, skeleton, and luge events through air resistance reduction [39].

Based on the results of CFD numerical simulation, the normal average wind resistance at 0.2 m in front of the athlete’s position can be calculated. The normal direction is the direction in which the athlete moves (as shown in Figure 5). On the track, each participating athlete must choose his lateral sliding position on the track, and this lateral sliding position can be briefly divided into the left, middle, and right sides in the Figure (as shown in Figure 5).

Based on the calculated normal average headwind resistance at the athlete’s track position, the lateral sliding position can be flexibly selected, thereby optimizing the sliding route of the entire track, so as to reduce air resistance and improve performance.

3.2.1. Athletes’ Normal Average Headwind Resistance

According to the location of the human body model, the calculation formula of the normal average headwind resistance is established. On the plane 0.2 m in front of the human body model, three circular surfaces are established, on the left, middle, and right sides, and the three circular surfaces are parallel to the top of the athlete’s head. The circular surface is established to indicate the track position of the athlete and to facilitate the algorithm of headwind resistance by taking sample points on the surface. For example, Figure 5 shows the situation at the first position of Area II. The formulas for the normal average headwind resistance on each circular surface are indicated in (9) to (15). In these formulas, the value of a ranges from 1 to 4, corresponding to typical Area I, Area II, Area III, and Area IV, respectively; b ranges from 1 to 3, representing wind directions WNW, NW, and NWN, respectively; c ranges from 1 to 12, corresponding to the location of the athlete human body model; d ranges from 1 to 7, representing the CFD-simulated climate wind levels 3.125, 3.5, 4.5, 5.5, 6.5, 7.5, and 8.229; and k can take values of L, M, and R, corresponding to the left, middle, and right sides 0.2 m in front of the athlete human body model.

$$A_{a-ck}^{b,d}=\left[\begin{array}{cc}{u\left(1\right)}_{a-ck}^{b,d}& {v\left(1\right)}_{a-ck}^{b,d}\\ ⋮& ⋮\\ {u\left(n\right)}_{a-ck}^{b,d}& {v\left(n\right)}_{a-ck}^{b,d}\end{array}\right];$$

(9)

$$B_{a-c}=\left[\begin{array}{c}\mathit{cos}{\theta }_{a-c}\\ \mathit{sin}{\theta }_{a-c}\end{array}\right];$$

(10)

$$V_{a-ck}^{b,d}=A_{a-ck}^{b,d}{B}_{a-c}=\left[\begin{array}{cc}{u\left(1\right)}_{a-ck}^{b,d}& {v\left(1\right)}_{a-ck}^{b,d}\\ ⋮& ⋮\\ {u\left(n\right)}_{a-ck}^{b,d}& {v\left(n\right)}_{a-ck}^{b,d}\end{array}\right]\left[\begin{array}{c}\mathit{cos}{\theta }_{a-c}\\ \mathit{sin}{\theta }_{a-c}\end{array}\right]=\left[\begin{array}{c}{m\left(1\right)}_{a-ck}^{b,d}\\ ⋮\\ {m\left(n\right)}_{a-ck}^{b,d}\end{array}\right];$$

(11)

$$v_{a-ck}^{b,d}={\left[\begin{array}{ccc}{\displaystyle \frac{1}{n}}& {\displaystyle \frac{1}{n}}& \begin{array}{cc}\dots & {\displaystyle \frac{1}{n}}\end{array}\end{array}\right]}_{1\times n}{V}_{a-ck}^{b,d}.$$

(12)

where $A_{a-ck}^{b,d}$ is the wind speed matrix on the k-surface 0.2 m in front of the c-th location in area a (Position a-ck for short), when the wind direction simulated by CFD is b and the wind level is d. n is the number of sample points taken on the circular surface. $B_{a-c}$ is the trigonometric function matrix of the normal headwind direction of the athlete at the c-th location in area a(location a-c for short). ${\theta }_{a-c}$ is the angle between the projection vector of the normal direction of the c-th location in area a (location a-c for short) on the xy plane, and the positive direction of the x-axis. $V_{a-ck}^{b,d}$ is the normal wind speed matrix at Position a-ck when the wind direction simulated by CFD is b and the wind level is d. $v_{a-ck}^{b,d}$ is the normal average wind speed at Position a-ck when the wind direction simulated by CFD is b and the wind level is d. When $v_{a-ck}^{b,d}$ is positive, the air flow is beneficial to the movement of the athlete at that position. When $v_{a-ck}^{b,d}$ is negative, the air flow will hinder the movement of the athlete at that position.

$${∆v}_{\mathrm{a}-\mathrm{c}\mathrm{k}}^{\mathrm{b},\mathrm{d}}={v\left(person\right)}_{a-c}-v_{a-ck}^{b,d}$$

(13)

$$f_{a-ck}^{b,d}={\displaystyle \frac{1}{2}}w\rho s_{\mathrm{a}-\mathrm{c}}{{∆v}_{\mathrm{a}-\mathrm{c}\mathrm{k}}^{\mathrm{b},\mathrm{d}}}^2$$

(14)

$$F_{a-ck}^{b,d}=f_{a-ck}^{b,d}/w={\displaystyle \frac{1}{2}}\rho s_{\mathrm{a}-\mathrm{c}}{{∆v}_{\mathrm{a}-\mathrm{c}\mathrm{k}}^{\mathrm{b},\mathrm{d}}}^2$$

(15)

where ${v\left(person\right)}_{a-c}$ is the speed of the athlete at location a-c. ${∆v}_{\mathrm{a}-\mathrm{c}\mathrm{k}}^{\mathrm{b},\mathrm{d}}$ is the speed difference between the athlete’s speed and the normal average wind speed at Position a-ck, when the wind direction is b and the wind level is d. $f_{a-ck}^{b,d}$ is the normal average headwind resistance (NAHR) at Position a-ck when the wind direction is b and the wind level is d. $s_{a-c}$ is the windward area of the athlete at location a-c; w is the appearance index, which is related to the athlete’s appearance and posture, usually measured by an experiment, and is a constant value. The average value of the product of the profile index and the windward area w × s of the base posture of the bobsled athlete in reference [27] is 0.04 m². The s value in this study is 0.0675 m², so the w value is taken as 0.6. $\rho$ is the air density. $F_{a-ck}^{b,d}$ is the relative value of the normal average headwind resistance (RNAHR) at Position a-ck when the simulated wind direction is b and the wind level is d.

3.2.2. Average Wind Resistance over Entire Journey

In this study, the average wind resistance over the entire journey (AWREJ) is defined as the average value of the normal average headwind resistance encountered by the athlete while sliding along the entire track. The formulas are shown in Formulas (16) and (17).

$$f_{a-c}^{b,d}=(f_{a-cL}^{b,d}+f_{a-cM}^{b,d}+f_{a-cR}^{b,d})\times {\displaystyle \frac{1}{3}};$$

(16)

$$f^{b,d}={\left[\begin{array}{ccc}{\displaystyle \frac{1}{23}}& {\displaystyle \frac{1}{23}}& \begin{array}{cc}\dots & {\displaystyle \frac{1}{23}}\end{array}\end{array}\right]}_{1\times 23}\left[\begin{array}{c}{f}_{1-2}^{b,d}\\ f_{1-3}^{b,d}\\ \begin{array}{c}{f}_{2-1}^{b,d}\\ f_{2-2}^{b,d}\\ \begin{array}{c}⋮\\ f_{2-5}^{b,d}\\ \begin{array}{c}{f}_{3-1}^{b,d}\\ f_{3-2}^{b,d}\\ \begin{array}{c}⋮\\ f_{3-4}^{b,d}\\ \begin{array}{c}{f}_{4-1}^{b,d}\\ f_{4-2}^{b,d}\\ \begin{array}{c}⋮\\ f_{4-12}^{b,d}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right]$$

(17)

In the equation, $f^{b,d}$ is the average wind resistance over the entire journey when the outdoor wind direction is b and the wind level is d. $f_{a-c}^{b,d}$ is the normal average wind resistance at location a-c when the outdoor wind direction is b and the wind level is d, which is equal to the average of the normal average headwind resistance at Position a-cL, Position a-cM, and Position a-cR.

3.2.3. Wind Resistance Reduction Indicators of Optimized Sliding Route

In order to reduce the air resistance of athletes competing in the NSC, the following method is used in this paper to optimize the athletes’ sliding routes: Based on the numerical simulation results of CFD under different climatic conditions, the relative values of the normal average headwind resistance $F_{a-cL}^{b,d}$, $F_{a-cM}^{b,d}$, and $F_{a-cR}^{b,d}$ on the left, middle, and right sides of each athlete’s human body model at 0.2 m in front of the athlete are calculated. Let the athlete choose the side with the smallest value among $F_{a-cL}^{b,d}$, $F_{a-cM}^{b,d}$, and $F_{a-cR}^{b,d}$ to slide, so as to optimize the sliding route of athletes in the NSC under different climatic conditions.

Based on this method, this paper defines the wind resistance reduction index of the optimized sliding route (WRDUI) and the time saved of the optimized sliding route (TS).

The wind resistance reduction index of the optimized sliding route (WRDUI) is defined as the ratio of the average wind resistance reduction of the optimized sliding route (AWRDU) to the average wind resistance over the entire journey (AWREJ), as shown in Formulas (18)–(20).

$$J_{\mathrm{a}-c}^{b,d}=f_{\mathrm{a}-cM}^{b,d}-min\left\{f_{\mathrm{a}-cL}^{b,d},f_{\mathrm{a}-cM}^{b,d},f_{\mathrm{a}-cR}^{b,d}\right\}.$$

(18)

$$J^{b,d}={\left[\begin{array}{ccc}{\displaystyle \frac{1}{23}}& {\displaystyle \frac{1}{23}}& \begin{array}{cc}\dots & {\displaystyle \frac{1}{23}}\end{array}\end{array}\right]}_{1\times 23}\left[\begin{array}{c}{J}_{1-2}^{b,d}\\ J_{1-3}^{b,d}\\ \begin{array}{c}{J}_{2-1}^{b,d}\\ J_{2-2}^{b,d}\\ \begin{array}{c}⋮\\ J_{2-5}^{b,d}\\ \begin{array}{c}{J}_{3-1}^{b,d}\\ J_{3-2}^{b,d}\\ \begin{array}{c}⋮\\ J_{3-4}^{b,d}\\ \begin{array}{c}{J}_{4-1}^{b,d}\\ J_{4-2}^{b,d}\\ \begin{array}{c}⋮\\ J_{4-12}^{b,d}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}\right]$$

(19)

$$C^{b,d}={\displaystyle \frac{J^{b,d}}{f^{b,d}}}$$

(20)

where $C^{b,d}$ is the WRDUI when the outdoor wind direction is b and the wind level is d. $J_{\mathrm{a}-c}^{b,d}$ is the wind resistance reduction of the optimized sliding route at locations a-c when the outdoor wind direction is b and the wind level is d. $J^{b,d}$ is the average wind resistance reduction of the optimized sliding route (AWRDU) when the outdoor wind direction is b and the wind level is d.

Yan Wengang won the third place in the skeleton event of the Beijing 2022 Winter Olympic Games, representing the highest level achieved in Chinese men’s skeleton technology. We take the result of skeleton athlete Yan Wengang in 2022 as an example and use it as a benchmark reference. The competition result of skeleton athlete Yan Wengang in 2022 was 241.77 s, and his average sliding speed was 32.6757 m/s. Here, the time saved of the optimized sliding route (TS) is defined as the number of seconds by which the athlete’s competition time after optimizing the route is improved compared with Yan Wengang’s competition time. The NSC track is 1975 m long, and the competition time of the skeleton event is the sum of the time of four laps of the sliding track. This study uses 241.77 s as the competition result of skeleton athletes before optimizing the route. We use 77 kg as the standard weight of skeleton athletes, and the formula for TS is shown in Formula (21).

$$S^{b,d}=241.77-{\displaystyle \frac{1975\times 4}{\frac{J^{b,d}}{77}+32.6757}}$$

(21)

where $S^{b,d}$ is the time saved of the optimized sliding route (TS) when the outdoor wind direction is b and the wind level is d.

4. Characteristics of Outdoor Wind Field at National Sliding Centre

Through CFD simulation, the wind field distribution information, including the wind speed distribution and wind pressure distribution, of the NSC under different climate conditions in Yanqing District in winter is obtained. The output simulation results are in the Supplementary Materials. Based on the CFD simulation results of Yanqing’s average winter wind level of 3.125 and different wind directions, we analyzed the outdoor wind field characteristics of the NSC.

4.1. Analysis of Outdoor Wind Field Distribution Characteristics

According to the simulation calculation results under the conditions of WNW, NW, and NWN wind directions, firstly, the wind field distribution result map was output. Secondly, the global wind speed dispersion and local wind speed dispersion of the areas were calculated. Finally, the average wind speed and average wind pressure in the windward region, venue region, and leeward region of the areas were calculated for wind field characteristic analysis. The specific output results are shown in Figure 6, Figure 7 and Figure 8.

For the CFD simulation results of the NSC when the wind direction is WNW, we found the following:

(1) Area I

The air in the windward region of the venue in Area I separates and refluxes due to collision with the track. Air separation zones are formed on the north and south sides of the venue in Area I, and air retention zones are formed in the windward region, with wind speeds ranging from approximately 1.81 m/s to 3.53 m/s.

The venue region interacts with the incoming wind, and the wind speed changes relatively greatly, ranging from approximately 0.0003 to 6.96 m/s. Due to the shielding effect of the venue in Area I on the incoming wind, there is an obvious low wind speed zone in the leeward region of the venue, and even a large zone of no wind. The minimum wind speed in the leeward region is as low as 0.02 m/s.

The wind pressure difference in the windward region of Area I is large, with the wind pressure ranging from about 0.91 Pa to 5.93 Pa, and the average wind pressure is 1.99 Pa. Due to the interaction between the venue in Area I and the incoming wind, a large-scale negative pressure zone is formed in the leeward region, with the wind pressure ranging from about −3.57 Pa to −0.22 Pa, and the average wind pressure is −1.37 Pa. The pressure difference between the windward region and leeward region is about 9.50 Pa. The wind speed in the venue region of Area I changes rapidly, forming vortices and complex wind fields, with a maximum wind speed value of 6.96 m/s; the global wind speed dispersion ${\overline{L}}_1^1$ of the venue region of Area I reaches 2.0194; and the wind field distribution is extremely uneven.

(2) Area II

The air in the windward region of Area II forms air backflow due to collision with the track, and an air stagnation zone is formed in the windward region, with wind speed ranging from about 1.99 m/s to 3.80 m/s. The venue region of Area II interacts with the incoming wind, and the wind speed varies greatly, ranging from about 0.0022 to 7.76 m/s. Due to the shielding effect of the venue on the incoming wind, there is an obvious low-wind-speed zone in the leeward region, and even a small zone of no wind, with the minimum wind speed in the leeward region as low as 0.20 m/s.

The wind pressure in the windward region of Area II varies greatly, ranging from −0.62 Pa to 5.71 Pa, with an average wind pressure of 0.40 Pa. Due to the interaction between the venue and the incoming wind, a large negative-pressure zone is formed in the leeward region, with wind pressure ranging from −3.24 Pa to 0.45 Pa, and an average wind pressure of −0.12 Pa. The pressure difference between windward region and leeward region is about 8.95 Pa. In the venue region of Area II, the wind speed distribution is uneven, the wind speed changes rapidly, forming vortices and complex wind fields, and there is a maximum wind speed value of 7.76 m/s. The global wind speed dispersion ${\overline{\mathrm{L}}}_2^1$ in the venue region of Area II reaches 0.1984.

(3) Area III

The air in the windward region of the venue in Area III is separated due to collision with the track. The separated air flows along the 360° curved loop until it reaches the north and south sides of the track. After that, the air leaves the track and flows around. Another part of the air in the windward region collides with the track and forms an air retention zone, with a wind speed ranging from about 1.93 m/s to 3.64 m/s. The venue region in Area III interacts with the incoming wind, and the wind speed varies greatly, ranging from about 0.0028 m/s to 6.01 m/s. Due to the shielding of the venue from the incoming wind, an obvious low-wind-speed zone appears in the leeward region. The indoor of the venue in this area, where the athletes slide on the track, is basically in the low-wind-speed zone and the windless zone, and the minimum wind speed in the leeward region is as low as 0.04 m/s.

The wind pressure difference in the windward region of Area III is large, with the wind pressure ranging from about 0.1653 Pa to 5.97 Pa, and the average wind pressure is 0.55 Pa. Due to the interaction between the venue of Area III and the incoming wind, a large-scale negative pressure area is formed in the leeward region, with the wind pressure ranging from about −2.61 Pa to 0.46 Pa, and the average wind pressure equaling −0.11 Pa. The pressure difference between windward region and leeward region is about 8.58 Pa. In the venue region of Area III, the wind speed distribution is uneven, the wind speed changes rapidly, forming a complex wind field, and a maximum wind speed value of 6.01 m/s is reached. The global wind speed dispersion ${\overline{\mathrm{L}}}_3^1$ in the venue region of Area III reaches 1.4146.

(4) Area IV

The air in the windward region of Area IV is separated due to collision with the track. The separated air flows along the surface of the track and then disperses. The wind speed in the windward region is approximately between 2.47 m/s and 3.70 m/s. The venue region interacts with the incoming wind, and the wind speed varies greatly, ranging from approximately 0.0012 m/s to 7.33 m/s. Due to the shielding of the venue from the incoming wind, there is an obvious low-wind-speed zone and a no-wind zone in the leeward region, and the minimum wind speed in the leeward region is as low as 0.15 m/s.

The wind pressure in the windward region of Area IV varies greatly, ranging from approximately −0.04 Pa to 4.46 Pa, with an average wind pressure of 0.34 Pa. Due to the shielding effect of the venue on the incoming wind, a large negative-pressure area is formed in the leeward region, with wind pressure ranging from −5.44 Pa to 0.69 Pa, and an average wind pressure of −0.12 Pa. The pressure difference between the windward region and the leeward region in Area IV is about 9.90 Pa. In the venue region of Area IV, the wind speed distribution is uneven, the wind speed changes rapidly, forming a complex wind field, and a maximum wind speed value of 7.33 m/s is reached. The global wind speed dispersion ${\overline{\mathrm{L}}}_4^1$ in the venue region of Area IV reaches 0.3825.

Similarly to the situation when the wind direction is WNW, the wind field distribution characteristics analysis of the NSC when the wind direction is NW and NWN are shown in

Table 3. The wind field distribution characteristics when the wind direction is NW.

Area		Area I	Area II	Area III	Area IV
Windward region	Wind speed	1.62~3.52 m/s	2.25~3.64 m/s	1.94~3.63 m/s	2.09~4.07 m/s
	Wind pressure	1.06~7.07 Pa	0.01~5.06 Pa	0.21~5.98 Pa	−1.91~5.50 Pa
	Average wind pressure	2.21 Pa	0.56 Pa	0.58 Pa	0.25 Pa
Venue region	Wind speed	0.0007~6.56 m/s	0.0029~7.57 m/s	0.0012~6.04 m/s	0.0018~8.90 m/s
	Maximum wind speed	6.56 m/s	7.57 m/s	6.04 m/s	8.90 m/s
	Global wind speed dispersion	${\overline{\mathbf{L}}}_1^2$ = 2.0187	${\overline{\mathbf{L}}}_2^2$ = 0.2879	${\overline{\mathbf{L}}}_3^2$ = 1.6350	${\overline{\mathbf{L}}}_4^2$ = 0.2590
Leeward region	Wind pressure	−7.99~−0.54 Pa	−4.34~0.77 Pa	−2.02~0.41 Pa	−5.74~0.64 Pa
	Average wind pressure	−2.33 Pa	−0.25 Pa	−0.10 Pa	0.00 Pa
Pressure difference between windward region and leeward region		15.06 Pa	9.39 Pa	7.99 Pa	11.25 Pa

and

Table 4. The wind field distribution characteristics when the wind direction is NWN.

Area		Area I	Area II	Area III	Area IV
Windward region	Wind speed	1.58~3.56 m/s	2.28~3.65 m/s	1.99~3.63 m/s	0.32~4.74 m/s
	Wind pressure	0.79~6.19 Pa	0.21~5.05 Pa	0.23~5.79 Pa	−13.30~5.80 Pa
	Average wind pressure	1.73 Pa	0.49 Pa	0.60 Pa	0.13 Pa
Venue region	Wind speed	0.0020~5.94 m/s	0.0011~8.38 m/s	0.0021~7.33 m/s	0.0011~6.82 m/s
	Maximum wind speed	5.94 m/s	8.38 m/s	7.33 m/s	6.82 m/s
	Global wind speed dispersion	${\overline{\mathbf{L}}}_1^3$ = 1.8248	${\overline{\mathbf{L}}}_2^3$ = 0.2498	${\overline{\mathbf{L}}}_3^3$ = 1.6657	${\overline{\mathbf{L}}}_4^3$ = 0.1749
Leeward region	Wind pressure	−4.28~−0.58 Pa	−2.69~0.56 Pa	−2.53~0.26 Pa	−3.39~0.64 Pa
	Average wind pressure	−2.16 Pa	−0.15 Pa	−0.31 Pa	0.04 Pa
Pressure difference between windward region and leeward region		10.47 Pa	7.74 Pa	8.32 Pa	9.19 Pa

.

4.2. Comparative Analysis of Outdoor Wind Field Characteristics

Based on the above analysis of the wind field distribution characteristics of the NSC, we established a line graph showing the variation in the global wind speed dispersion ${\overline{\mathrm{L}}}_{\mathrm{a}}^{\mathrm{b}}$ with the area and wind direction, as shown in Figure 9 and Figure 10.

As can be seen from Figure 9 and Figure 10, the global wind speed dispersion in Area I is generally larger than that in other areas. When the wind direction is NWN, the global wind speed dispersion is the smallest, and the wind speed distribution is relatively uniform. The global wind speed dispersion in Area III is generally smaller than that in Area I, but it is larger than the global wind speed dispersion in Area II and IV. When the wind direction is WNW, the global wind speed dispersion in Area III is the smallest, and the wind speed distribution is the most uniform. The global wind speed dispersions in Area II and IV are generally close, and both are smaller than those in Area I and III.

We took the average of ${\overline{\mathrm{L}}}_{\mathrm{a}}^1$, ${\overline{\mathrm{L}}}_{\mathrm{a}}^2$, and ${\overline{\mathrm{L}}}_{\mathrm{a}}^3$, and obtained the average global wind speed dispersion of Area I, Area II, Area III, and Area IV as 1.9543, 0.2454, 1.5718, and 0.2721, respectively. By calculating the average of ${\overline{\mathrm{L}}}_1^{\mathrm{b}}$, ${\overline{\mathrm{L}}}_2^{\mathrm{b}}$, ${\overline{\mathrm{L}}}_3^{\mathrm{b}}$, and ${\overline{\mathrm{L}}}_4^{\mathrm{b}}$, we obtained the average global wind speed dispersion of 1.0037, 1.0502, and 0.9788 when the wind directions are WNW, NW, and NWN, respectively. These data show that the global wind speed dispersion of different areas varies greatly, but the global wind speed dispersion of the same area under different wind directions varies very little. It can be seen that the decisive factor affecting whether the outdoor wind field of a large single building can be evenly distributed is the building shape, and the wind direction is a secondary factor.

5. Analysis and Discussion of Influence of Wind Resistance on Athletes

The bobsleigh, skeleton, and luge events held at the NSC are all racing events, and the time differences between the athletes participating in the events are extremely small, even as little as 0.01 s [26]. The resistance that affects the performance of the athletes is mainly air resistance. Therefore, understanding the magnitude of the windward air resistance that athletes experience on the track under different climatic conditions is crucial to improving the performance of the competition. Based on the CFD simulation results, this section calculates the normal average headwind resistance that athletes experience on the sliding track of the NSC under different climatic conditions. Based on the magnitude of the normal headwind resistance, the athlete’s sliding route is optimized, and the time saved of the optimized sliding route (TS) is calculated.

5.1. Calculation and Analysis of Average Wind Resistance over Entire Journey

First, based on the CFD simulation results of the NSC under different climatic conditions, we calculated the athlete’s normal average headwind resistance $f_{a-ck}^{b,d}$.

Then, for the CFD simulation results of the average winter climatic conditions in Yanqing District, i.e., wind level 3.125, the athlete’s AWREJ ($f^{b,1}$) under different outdoor wind directions was calculated using Formulas (9)–(17). The calculation results are shown as follows: ${\mathrm{f}}^{\mathrm{1,1}}$ (N) = 25.7083 N; ${\mathrm{f}}^{\mathrm{2,1}}$ (N) = 26.3088 N; ${\mathrm{f}}^{\mathrm{3,1}}$ (N) = 26.3334 N.

From the perspective of $f^{b,d}$, when the wind direction is WNW, the AWREJ is minimal, and this is most suitable for related events, followed by NW; but when the wind direction is NWN, holding related events has the greatest adverse impact on athletes’ performance.

For different climate conditions in Yanqing District, that is, different wind levels in the outdoor environment of the NSC, the AWREJ under different climate conditions was calculated using Formulas (9)–(17), and compared with the resistance value under average climate conditions, as shown in Appendix A (

Table A3. The average wind resistance over the entire journey under different climatic conditions.

Wind Direction	WNW	NW	NWN
${\mathbf{f}}^{\mathbf{b},2}$ (N)	25.7153	26.3604	26.5214
${\mathbf{f}}^{\mathbf{b},2}$-${\mathbf{f}}^{\mathbf{b},1}$ (N)	0.0070	0.0517	0.1880
${\mathbf{f}}^{\mathbf{b},3}$ (N)	25.7662	26.6459	26.6459
${\mathbf{f}}^{\mathbf{b},3}$-${\mathbf{f}}^{\mathbf{b},1}$ (N)	0.0579	0.3371	0.5687
${\mathbf{f}}^{\mathbf{b},4}$ (N)	25.7609	27.0870	27.7898
${\mathbf{f}}^{\mathbf{b},4}$-${\mathbf{f}}^{\mathbf{b},1}$ (N)	0.0525	0.7782	1.4563
${\mathbf{f}}^{\mathbf{b},5}$ (N)	25.8585	27.5592	28.4683
${\mathbf{f}}^{\mathbf{b},5}$-${\mathbf{f}}^{\mathbf{b},1}$ (N)	0.1502	1.2504	2.1349
${\mathbf{f}}^{\mathbf{b},6}$ (N)	25.9155	28.1387	29.1085
${\mathbf{f}}^{\mathbf{b},6}$-${\mathbf{f}}^{\mathbf{b},1}$ (N)	0.2072	1.8300	2.7751
${\mathbf{f}}^{\mathbf{b},7}$ (N)	26.5345	28.5795	29.8574
${\mathbf{f}}^{\mathbf{b},7}$-${\mathbf{f}}^{\mathbf{b},1}$ (N)	0.8262	2.2707	3.5240

). Based on this, a fitting curve of the AWREJ changing with wind level was established (see Formula (22)), and the fitting curve diagrams are shown in Figure 11 and Figure 12.

$$f^{b,d}=\left\{\begin{array}{l}22.41049+2.10388d-0.42688d^2+0.02811d^3, b=1\\ 24.75289+0.44807d,b=2\\ 24.04845+0.68569d,b=3\end{array}\right.$$

(22)

From Formula (22) and Figure 11 and Figure 12, it can be seen that no matter what wind direction, as the wind level continues to increase, the AWREJ of the NSC shows an increasing trend, but the growth rate is different. For the wind direction WNW, as the wind level increases, the AWREJ increases slightly, but the growth rate is small, showing a curve growth. For the wind direction NW, as the wind level increases, the AWREJ increases linearly, with a growth rate of 0.44807. For the wind direction NWN, as the wind level increases, the AWREJ also increases linearly, with a growth rate of 0.68569.

This phenomenon shows that when the wind direction is WNW, the wind field conditions of the NSC have little effect on the athletes’ performance, and the effect size hardly changes with an increase in wind level. However, when the wind direction is NW or NWN, the wind field conditions of the NSC have a greater impact on the athletes’ performance, and the greater the wind level, the greater the impact.

5.2. Optimization of Athletes’ Sliding Routes

Due to different climatic conditions, winds of different speeds will form on the track of the NSC, resulting in different headwind air resistance for athletes sliding at different lateral positions on the track. In order to reduce the impact of the wind field distribution on the athletes’ performance, this study uses the following method to optimize the sliding route of athletes at the NSC:

Based on the numerical simulation results of CFD under different climatic conditions, the relative values of the normal average headwind resistance $F_{a-cL}^{b,d}$, $F_{a-cM}^{b,d}$, and $F_{a-cR}^{b,d}$ on the left, middle, and right sides of each athlete’s human body model at 0.2 m in front of the athlete is calculated. Let the athlete choose the side with the smallest value among $F_{a-cL}^{b,d}$, $F_{a-cM}^{b,d}$, and $F_{a-cR}^{b,d}$ to slide, so as to optimize the sliding route of athletes in the NSC under different climatic conditions.

Among them, under the average winter climate conditions in Yanqing, $F_{a-cL}^{b,1}$, $F_{a-cM}^{b,1}$, and $F_{a-cR}^{b,1}$, are as shown in Appendix A (Figure A1, Figure A2 and Figure A3). According to the method of optimizing the sliding route, the optimized sliding route for athletes under different wind directions under the average winter climate conditions in Yanqing District is obtained, as shown in Appendix A (

Table A1. Suggestions of athletes’ sliding routes in a climate with an average wind level of 3.125 in Yanqing District (L represents sliding on the left side of the track, M represents sliding in the middle, and R represents sliding on the right side of the track).

Wind Direction	Area	Sliding Route Suggestion
WNW	Area I	1M−2M-3R
	Area II	1R-2R-3M-4R-5R
	Area III	1M-2R-3L-4L
	Area IV	1L-2L-3M-4M-5M-6M-7R-8L-9L-10R -11L-12R
NW	Area I	1M-2L-3R
	Area II	1M-2R-3R-4L-5L
	Area III	1L-2R-3R-4M
	Area IV	1L-2R-3R-4M-5R-6L-7R-8M-9R-10L -11L-12L
NWN	Area I	1R-2R-3L
	Area II	1L-2M-3L-4R-5L
	Area III	1M-2R-3R-4R
	Area IV	1L-2L-3L-4M-5M-6L-7R-8M-9M-10M -11M-12L

). Based on the optimized sliding route, the optimized sliding route map is completed, as shown in Appendix A (Figure A4, Figure A5 and Figure A6).

Formula (19) is used to calculate the AWRDU under the average winter climate conditions. The results are shown as follows: ${\mathrm{J}}^{\mathrm{1,1}}$ = 0.2274 N; ${\mathrm{J}}^{\mathrm{2,1}}$ = 0.1962 N; ${\mathrm{J}}^{\mathrm{3,1}}$ = 0.3586 N; $({\mathrm{J}}^{\mathrm{1,1}}+{\mathrm{J}}^{\mathrm{2,1}}+{\mathrm{J}}^{\mathrm{3,1}})/3$ = 0.2607 N.

When the outdoor wind level is d, optimizing the routes of the athletes sliding in the NSC can reduce the air resistance by an average of 0.2607 N. According to Newton’s second law (F = ma), an air resistance of 0.2607 N can cause an acceleration change of 0.0034 m/s² for an athlete weighing 77 kg. Thus, it can be seen that the optimization of the athlete’s sliding route can directly affect the athlete’s sliding competition results. It is very necessary to optimize the sliding route of the sliding athlete.

Therefore, according to the long-term local meteorological observation data of Yanqing, it was found that the wind directions of the winter wind field are mainly WNW, NW, and NWN, and the wind speed usually varies from level 3 to level 8. To this end, we optimized and determined the corresponding sliding routes based on the calculated quantitative impact of wind resistance on athletes under different wind speed and wind direction conditions, as shown in Appendix A (

Table A2. Suggestions of athletes’ sliding routes under different climatic conditions.

Wind Level	Wind Direction	Suggestion of Athletes’ Sliding Routes
3.5	WNW	Area I (1M-2R-3R), Area II (1R-2R-3M-4R-5R), Area III (1M-2R-3R-4L), Area IV (1L-2L-3M-4M-5M-6M-7R-8L-9L-10R-11L-12R)
	NW	Area I (1M-2L-3R), Area II (1R-2R-3R-4L-5L), Area III (1L-2R-3R-4M), Area IV (1L-2R-3R-4M-5R-6L-7R-8M-9R-10L-11L-12L)
	NWN	Area I (1R-2R-3L), Area II (1M-2R-3R-4R-5L), Area III (1M-2R-3R-4R), Area IV (1L-2L-3L-4M-5M-6L-7R-8M-9M-10M-11M-12L)
4.5	WNW	Area I (1M-2R-3R), Area II (1L-2R-3M-4R-5R), Area III (1L-2R-3R-4L), Area IV (1L-2L-3M-4M-5M-6M-7R-8L-9L-10R-11L-12R)
	NW	Area I (1M-2L-3R), Area II (1R-2R-3R-4L-5L), Area III (1L-2R-3R-4M), Area IV (1L-2R-3R-4M-5R-6L-7M-8M-9R-10L-11L-12R)
	NWN	Area I (1R-2R-3L), Area II (1M-2M-3R-4R-5L), Area III (1M-2R-3R-4R), Area IV (1L-2L-3L-4M-5M-6L-7R-8M-9M-10M-11M-12L)
5.5	WNW	Area I (1M-2R-3R), Area II (1M-2R-3M-4R-5R), Area III (1L-2R-3M-4L), Area IV (1L-2L-3M-4M-5M-6M-7R-8L-9L-10R-11L-12R)
	NW	Area I (1M-2L-3R), Area II (1M-2R-3R-4L-5L), Area III (1L-2R-3L-4M), Area IV (1L-2R-3R-4M-5R-6L-7M-8M-9R-10R-11L-12R)
	NWN	Area I (1R-2R-3L), Area II (1R-2M-3R-4L-5L), Area III (1M-2R-3R-4R), Area IV (1L-2L-3L-4M-5M-6L-7R-8M-9M-10M-11M-12L)
6.5	WNW	Area I (1M-2M-3R), Area II (1L-2R-3M-4R-5R), Area III (1M-2R-3R), Area IV (1L-2L-3M-4M-5M-6M-7R-8L-9L-10R-11L-12R)
	NW	Area I (1M-2L-3R), Area II (1L-2R-3R-4L-5L), Area III (1L-2R-3R-4L), Area IV (1L-2R-3R-4M-5R-6L-7M-8M-9R-10L-11L-12R)
	NWN	Area I (1R-2R-3L), Area II (1R-2M-3L-4R-5L), Area III (1M-2R-3R-4R), Area IV (1L-2L-3L-4M-5M-6L-7R-8M-9M-10M-11M-12L)
7.5	WNW	Area I (1M-2R-3R), Area II (1R-2R-3M-4R-5R), Area III (1M-2R-3R-4L), Area IV (1L-2L-3M-4M-5M-6M-7R-8L-9L-10R-11L-12R)
	NW	Area I (1M-2L-3R), Area II (1L-2R-3R-4L-5L), Area III (1L-2R-3R-4L), Area IV (1L-2R-3R-4M-5R-6L-7M-8M-9R-10R-11L-12M)
	NWN	Area I (1R-2R-3L), Area II (1L-2M-3R-4R-5L), Area III (1M-2R-3R-4R), Area IV (1L-2L-3L-4M-5M-6L-7R-8M-9M-10M-11M-12L)
8.229	WNW	Area I (1M-2M-3R), Area II (1R-2R-3M-4R-5R), Area III (1L-2R-3L-4L), Area IV (1L-2L-3M-4M-5M-6M-7R-8L-9L-10R-11R-12R)
	NW	Area I (1M-2L-3R), Area II (1L-2R-3R-4L-5L), Area III (1L-2R-3R-4M), Area IV(1L-2R-3R-4M-5R-6L-7M-8M-9R-10R-11L-12R)
	NWN	Area I (1R-2R-3L), Area II (1M-2M-3R-4R-5L), Area III (1M-2M-3R-4R-5L), Area IV(1L-2L-3L-4M-5M-6L-7R-8M-9M-10M-11M-12L)

).

When athletes do not have knowledge of the weather conditions on the day of the competition, or the weather on the day of the competition is more complicated, the optimized sliding route for athletes under the average winter climate conditions can be used as a basic reference for athletes’ competitions. Of course, if the climate conditions on the day of the competition are relatively stable or the wind force level is determined, athletes can refer to the optimized sliding route under different climate conditions.

5.3. Analysis of Wind Resistance Reduction of Optimized Sliding Route

According to the CFD numerical simulation results of the NSC under different climatic conditions, the wind resistance reduction of the optimized sliding route, the WRDUI, and the TS were calculated based on Formulas (18)–(21). The calculation results are shown in

Table 5. The wind resistance reduction index of the optimized sliding route (WRDUI).

Cb,d		Wind Direction
		WNW	NW	NWN
Wind level	3.125	0.89%	0.75%	1.36%
	3.5	1.20%	1.08%	1.63%
	4.5	1.78%	1.36%	2.08%
	5.5	2.20%	2.13%	2.87%
	6.5	3.47%	2.83%	3.89%
	7.5	4.50%	3.81%	4.42%
	8.229	6.11%	4.42%	4.94%

and

Table 6. The time saved of the optimized sliding route (TS).

Sb,d(s)		Wind Direction
		WNW	NW	NWN	Mean Value
Wind level	3.125	0.02	0.02	0.03	0.02
	3.5	0.03	0.03	0.04	0.03
	4.5	0.04	0.03	0.05	0.04
	5.5	0.05	0.06	0.08	0.06
	6.5	0.09	0.08	0.11	0.09
	7.5	0.11	0.10	0.12	0.11
	8.229	0.16	0.12	0.14	0.14

. At the same time, the fitting curves of the WRDUI and the TS with the change in the outdoor wind level were established according to Formulas (23) and (24). The fitting curves are shown in Figure 13 and Figure 14.

$${\mathrm{C}}^{\mathrm{b},\mathrm{d}}=\left\{\begin{array}{l}-0.0366+0.02574\mathrm{d}-0.0047{\mathrm{d}}^2+3.65477{\times {10}^{-4}\mathrm{d}}^3,\mathrm{b}=1\\ -0.01603+0.0071\mathrm{d},\mathrm{b}=2\\ -0.0096+0.00718\mathrm{d},\mathrm{b}=3\end{array}\right.$$

(23)

$${\mathrm{S}}^{\mathrm{b},\mathrm{d}}=\left\{\begin{array}{l}-0.07971+0.05889\mathrm{d}-0.0114{\mathrm{d}}^2+9.41481{\times {10}^{-4}\mathrm{d}}^3,\mathrm{b}=1\\ -0.04488+0.01941\mathrm{d},\mathrm{b}=2\\ -0.03935+0.02176\mathrm{d},\mathrm{b}=3\end{array}\right.$$

(24)

It can be seen from Appendix A (

Table A4. The average wind resistance reduction of the optimized sliding route (AWRDU).

Jb,d(N)		Wind Direction
		WNW	NW	NWN	Mean Value
Wind level	3.125	0.2274	0.1962	0.3586	0.2607
	3.5	0.3074	0.2847	0.4325	0.3415
	4.5	0.4593	0.362	0.5588	0.4600
	5.5	0.5668	0.5759	0.798	0.6469
	6.5	0.8971	0.7795	1.1083	0.9283
	7.5	1.165	1.0706	1.2866	1.1741
	8.229	1.6224	1.2624	1.4756	1.4535

) and Table 6 that with an increase in wind level (3.125, 3.5, 4.5, 5.5, 6.5, 7.5, 8.229), the optimized sliding route can reduce the air resistance by 0.2607 N, 0.3415 N, 0.4600 N, 0.6469 N, 0.9283 N, 1.1741 N, and 1.4535 N on average. According to Formula (21), the performance of athletes weighing 77 kg can be improved by 0.02 s, 0.03 s, 0.04 s, 0.06 s, 0.09 s, 0.11 s, and 0.14 s, respectively.

The bar graph in Figure 13 shows that, regardless of the wind direction, as the wind level increases, the average wind resistance reduction of the optimized sliding route (AWRDU) increases.

From Formula (23) and the fitting diagram in Figure 13, it can be seen that as the wind level increases, the wind resistance reduction index of the optimized sliding route (WRDUI) increases. It increases in a curve when the wind direction is WNW, and increases linearly when the wind directions are NW and NWN, with growth rates of 0.0071 and 0.00718, respectively.

From Formula (24) and Figure 14, it can be seen that as the wind level increases, the time saved of the optimized sliding route (TS) increases accordingly. It increases in a curve when the wind direction is WNW, and increases linearly when the wind directions are NW and NWN, with growth rates of 0.01941 and 0.02176, respectively.

These results also show the following:

(1) When the climatic conditions during the competition are more complex, or the wind level around the venue is higher, the optimized sliding route can reduce the wind resistance more, thereby enabling athletes to achieve relatively better competition results.

(2) In addition, the results also show that the shape and track design of the NSC are reasonable, so it can still effectively reduce the sliding wind resistance of athletes under complex climatic conditions.

6. Conclusions

Based on CFD technology, this study takes the Beijing 2022 Winter Olympic Stadium National Sliding Center as an example, carries out wind field simulation research at the building scale, applies the simulation results, and defines the related parameters of resistance reduction to quantify the influence of the wind field on micro-athletes’ performance, so that people can form a comprehensive understanding of the indoor and outdoor wind field characteristics of large stadiums and their influence on athletes’ performance. The main conclusions of this paper are as follows:

(1) The decisive factor affecting whether the outdoor wind field of a large single building can be evenly distributed is the building shape, and the climatic conditions are secondary. We obtained average global wind speed dispersion values of Area I, Area II, Area III, and Area IV of 1.9543, 0.2454, 1.5718, and 0.2721, respectively. In addition, we obtained average global wind speed dispersion values of 1.0037, 1.0502, and 0.9788 when the wind directions are WNW, NW, and NWN, respectively. This underscores the critical importance of aerodynamic design in large sports venues to mitigate turbulence and extreme wind zones.

(2) The design of the NSC is reasonable, allowing it to effectively reduce the sliding wind resistance of athletes even under complex climatic conditions. We optimized the sliding routes of athletes based on the quantitative impact of wind resistance on athletes under different climatic conditions. When the climatic conditions during the competition are more complex, or the wind level around the venue is higher, the optimized sliding routes can reduce wind resistance more effectively, thereby enabling athletes to achieve better competition results. With a gradual increase in wind level (3.125, 3.5, 4.5, 5.5, 6.5, 7.5, 8.229), the optimized sliding route can reduce the air resistance by 0.2607 N, 0.3415 N, 0.4600 N, 0.6469 N, 0.9283 N, 1.1741 N, and 1.4535 N, which can improve the athletes’ competition results by 0.02 s, 0.03 s, 0.04 s, 0.06 s, 0.09 s, 0.11 s, and 0.14 s, respectively.

This study not only innovatively provides methodological support for exploring the impact mechanism of athletes’ performance from the building-scale wind environmental perspective, but also has great significance for mastering the characteristics of outdoor wind fields, indoor personnel safety, building operation, and maintenance management of large stadiums. The research method in this paper has strong reusability, which can be used not only to improve the performance of skeleton athletes, but also to improve the performance of bobsleigh and luge athletes. This method has a low time cost and saves resources, and can shorten the training cycle of athletes and improve the personal utilization rate of sports venues. However, there are still some limitations to this study. For example, four typical areas that play a decisive role in athletes’ competition results are used, instead of the whole stadium. If we can overcome the contradiction that the simulation scale should not only reflect the geometric shape of the National Sliding Center well, but also monitor the small-scale climate characteristics of CFD, the real simulation of the whole stadium will significantly improve the accuracy of the analysis of athletes’ resistance reduction, and the optimized sliding route will be more credible. For another example, in view of the outdoor wind field characteristics of buildings, this study only focuses on the interaction characteristics between the National Sliding Center and the wind. If we can consider the buildings around the National Sliding Center at the same time, and analyze the interaction between the indoor and outdoor wind and heat fields of the National Sliding Center from the point of view of the thermal comfort of indoor athletes, this will constitute the basis for further research on this topic.