## 3 Construction of Parameter Indicators for Analysis of Wind Field Characteristics
### Construction and Quantification of Main Influencing Parameters on Athletes' Competition 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. \[A_{a-ck}^{b,d}= \begin{bmatrix}u(1)_{a-ck}^{b,d}&v(1)_{a-ck}^{b,d}\\ \vdots&\vdots\\ u(n)_{a-ck}^{b,d}&v(n)_{a-ck}^{b,d}\end{bmatrix} ; \tag{9}\]  
\[B_{a-c}= \begin{bmatrix}cos\theta_{a-c}\\ sin\theta_{a-c}\end{bmatrix} ; \tag{10}\]  
Figure 5: Schematic diagram of normal average headwind resistance and its solution. \[V_{a-ck}^{b,d}=A_{a-ck}^{b,d}B_{a-c}= \begin{bmatrix}u(1)_{a-ck}^{b,d}&v(1)_{a-ck}^{b,d }\\ \vdots&\vdots\\ u(n)_{a-ck}^{b,d}&v(n)_{a-ck}^{b,d}\end{bmatrix}\begin{bmatrix}cos\theta_{a-c} \\ sin\theta_{a-c}\end{bmatrix} = \begin{bmatrix}m(1)_{a-ck}^{b,d}\\ \vdots\\ m(n)_{a-ck}^{b,d}\end{bmatrix} ; \tag{11}\]  
\[v_{a-ck}^{b,d}= \begin{bmatrix}\frac{1}{n}&\frac{1}{n}&\dots&\frac{1}{n}\\ \end{bmatrix} _{1\times n}V_{a-ck}^{b,d}. \tag{12}\]  
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. \[\Delta v_{a-ck}^{b,d}=v(person)_{a-c}-v_{a-ck}^{b,d} \tag{13}\]  
\[f_{a-ck}^{b,d}=\frac{1}{2}w\rho s_{a-c}\Delta v_{a-ck}^{b,d} \tag{14}\]  
\[F_{a-ck}^{b,d}=f_{a-ck}^{b,d}/w=\frac{1}{2}\rho s_{a-c}\Delta v_{a-ck}^{b,d} \tag{15}\]  
where \(v(person)_{a-c}\) is the speed of the athlete at location \(a\)-\(c\). \(\Delta v_{a-ck}^{b,d}\) 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 \(d\).