## 4 Results
### Time-Varying Aerodynamic Coefficients
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Coefficient**} & \multirow{2}{*}{**Car**} & \multicolumn{4}{c}{**Entering**} & \multicolumn{4}{c}{**Exiting**} \\ \cline{3-10}  & & **H = 0 m** & **H = 2 m** & **H = 4 m** & **H = 6 m** & **H = 0 m** & **H = 2 m** & **H = 4 m** & **H = 6 m** \\ \hline \multirow{3}{*}{\(c_{s}\)} & Head & 0.441 & 0.279 & 0.157 & 0.228 & 0.925 & 0.661 & 0.544 & 0.787 \\  & Intermediate & 0.219 & 0.127 & 0.241 & 0.204 & 0.426 & 0.226 & 0.460 & 0.393 \\  & Tail & 0.137 & 0.221 & 0.552 & 0.309 & 0.226 & 0.169 & 0.433 & 0.513 \\ \hline \multirow{3}{*}{\(c_{l}\)} & Head & 0.092 & 0.079 & 0.076 & 0.033 & 0.574 & 0.342 & 0.244 & 0.231 \\  & Intermediate & 0.370 & 0.275 & 0.065 & 0.009 & 0.606 & 0.298 & 0.313 & 0.249 \\  & Tail & 0.419 & 0.312 & 0.074 & 0.081 & 0.393 & 0.227 & 0.270 & 0.196 \\ \hline \multirow{3}{*}{\(c_{M_{x}}\)} & Head & 0.050 & 0.022 & 0.017 & 0.011 & 0.110 & 0.049 & 0.073 & 0.064 \\  & Intermediate & 0.022 & 0.004 & 0.005 & 0.007 & 0.047 & 0.021 & 0.021 & 0.019 \\  & Tail & 0.002 & 0.030 & 0.015 & 0.012 & 0.032 & 0.028 & 0.015 & 0.010 \\ \hline \multirow{3}{*}{\(c_{M_{y}}\)} & Head & 0.014 & 0.097 & 0.137 & 0.075 & 0.238 & 0.453 & 0.474 & 0.462 \\  & Intermediate & 0.096 & 0.078 & 0.092 & 0.084 & 0.532 & 0.435 & 0.649 & 0.481 \\  & Tail & 0.223 & 0.198 & 0.170 & 0.124 & 0.331 & 0.256 & 0.392 & 0.352 \\ \hline \multirow{3}{*}{\(c_{M_{x}}\)} & Head & 0.772 & 0.515 & 0.255 & 0.283 & 1.780 & 1.509 & 1.668 & 1.644 \\  & Intermediate & 0.116 & 0.134 & 0.184 & 0.215 & 0.305 & 0.504 & 0.830 & 0.729 \\ \cline{1-1}  & Tail & 0.678 & 0.703 & 0.158 & 0.409 & 0.655 & 0.490 & 0.637 & 0.527 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Peak-to-peak values of the aerodynamic coefficients when each car entered and left the crosswind region with different wind barriers. and \(c_{M_{x}}\) values is that it was geometrically symmetrical in the length direction, while the head and tail cars have a strong asymmetric flow due to the presence of streamlined structures so that different time-varying \(c_{M_{y}}\) and \(c_{M_{z}}\) values were generated. Figure 7 and Table 1 show that almost all the aerodynamic coefficient fluctuations of cars exiting the crosswind region were larger than that entering the region. Their changes also reflected the effect of the height of the wind barrier on the wind-protection performance, taking into consideration the over-protection. The influence of the running speed of the train on the aerodynamic forces and moments is also shown in Figure 8. The table showing their peak-to-peak value of the aerodynamic coefficients when each car of the train entering and leaving the crosswind area is also given in Table 2.  
Figure 8: The time-varying aerodynamic coefficients of each car of the train passing the bridge with various running speeds: (**a**) \(c_{s}\) of the head car; (**b**) \(c_{s}\) of the intermediate car; (**c**) \(c_{s}\) of the tail car; (**d**) \(c_{l}\) of the head car; (**e**) \(c_{l}\) of the intermediate car; (**f**) \(c_{l}\) of the tail car; (**g**) \(c_{M_{x}}\) of the head car; (**h**) \(c_{M_{x}}\) of the intermediate car; (**i**) \(c_{M_{y}}\) of the head car; (**k**) \(c_{M_{y}}\) of the intermediate car; (**l**) \(c_{M_{y}}\) of the tail car; (**m**) \(c_{M_{x}}\) of the head car; (**n**) \(c_{M_{x}}\) of the intermediate car; (**o**) \(c_{M_{x}}\) of the tail car. Compared to the influence given by the height of the wind barrier, the running speed of the train seemed to provide a difference in the aerodynamic coefficient values instead of the developing pattern. With the same crosswind, when the train runs at a lower speed, a larger yaw angle can result from a synthesis between the train speed and the crosswind. Therefore, at a lower vehicle speed, it was easier to obtain a greater aerodynamic coefficient when calculating the aerodynamic coefficient. On the one hand, the yaw angle directly changed the contribution of the resultant wind to the lateral force of the train.