## 3 Racetrack Wind Field Model  
To master the influence of the ski field wind on the athlete's sliding, it is necessary to obtain the field wind parameters of the ski racetrack, such as the wind speed and wind direction. Field wind information can be collected in real time by installing several anemometers near the ski racetrack, and the field wind information of the racetrack location outside the anemometer needs to be calculated by establishing a ski field racetrack wind model. The racetrack wind field model is based on the measured data of several anemometers installed around the racetrack and is a mathematical expression of the field wind parameters for the entire racetrack formed by a mathematical regression calculation.  
As shown in Figure 2, anemometers are installed at the starting points of different stages in the entire track, and the position of the anemometer is marked as \(P_{j}\) (\(j=1\sim m\)).  
For the starting and ending points of a certain stage \(S_{j}\), the wind speed and wind direction monitoring values at height \(h\) from the ground at the corresponding position are \(u_{j,i}^{*}\), \(u_{j+1,j}^{*}\), \(\theta_{j,i}^{*}\), \(\theta_{j+1,i}^{*}\). As shown in Figure 3a, at the position of the curved stage, the wind speed \(u_{j,i}^{\wedge}\) at point \(G_{0}\) (\(x_{j,i}\), \(y_{0}\)) of the ski field racetrack coordinate system is approximately equal to the wind speed \(u_{j,i}\) at point \(G\) (\(x_{j,i}\), \(y_{j,i}\)) of the geographic coordinate system. As shown in Figure 3b, at time \(i\), the triangular similarity relationship between wind speed \(u_{j,i}\) at the athlete's position \(x_{j,i}\) (\(x_{j,i}\in[x_{p_{j}},x_{p_{j+1}}]\)) in \(S_{j}\) stage and the wind speed \(u_{j,i}^{*}\), \(u_{j+1,j}^{*}\) at the monitoring point positions \(x_{p_{j}}\), \(x_{p_{j+1}}\) is as follows:  
\[\frac{u_{j,i}^{*}-u_{j+1,i}^{*}}{L_{j}}=\frac{u_{j,i}^{*}-u_{j+1}^{*}}{x_{p_{ j+1}}-x_{j,i}} \tag{15}\]  
In the formula, \(L_{j}\) is the linear distance (\(L_{j}=x_{p_{j+1}}-x_{p_{j}}\)) between the start point and the end point of the two anemometer positions in stage \(S_{j}\). Formula (15) is rearranged. The wind speed at different positions in the ski field racetrack coordinate system is as follows:  
\[u_{j,i}=\frac{\left(u_{j,i}^{*}-u_{j+1,i}^{*}\right)\left(x_{p_{j+1}}-x_{j,i} \right)}{x_{p_{j+1}}-x_{p_{j}}}+u_{j+1}^{*} \tag{16}\]  
According to the wind speed relationship between point \(G_{0}\) of the ski field racetrack coordinate system and point \(G\) of the geographic coordinate system in Figure 3a, the wind speed at different positions near ground \(h\) in the stage is expressed as follows:  
\[u_{j,i}=\frac{\left(u_{j,i}^{*}-u_{j+1,i}^{*}\right)\left(x_{p_{j+1}}-x_{j,i} \right)}{x_{p_{j+1}}-x_{p_{j}}}+u_{j+1}^{*} \tag{17}\]  
The wind direction of the racetrack wind field model is obtained using the same mathematical method as in Figure 3a. The wind direction at different positions near the ground \(h\) in the stage can be expressed as follows:  
\[\theta_{j,i}=\frac{\left(\theta_{j,i}^{*}-\theta_{j+1,i}^{*}\right)\left(x_{p_ {j+1}}-x_{j,i}\right)}{x_{p_{j+1}}-x_{p_{j}}}+\theta_{j+1}^{*} \tag{18}\]  
The same method is used to establish the racetrack wind field model of other stages and to obtain the wind environment information at any position in the entire track.  
Figure 2: Schematic diagram of dividing the ski field racetrack.