# Wind Speed Spectrum of a Moving Vehicle under Turbulent Crosswinds
## 4 Wind Speed Spectrum of a Moving Vehicle  
### Results  
By putting the parameter results from Table 1 into Equation (23), the wind speed spectrum of a moving point can be obtained. Figure 6 shows the spectrum results of a moving point corresponding to the static point in the wind tunnel simulated turbulence field at a wind yaw angle of 15\({}^{\circ}\)\(\sim\)175\({}^{\circ}\) for 12 total working conditions. In Figure 6, \(V_{T}\) is the vehicle's moving speed, \(\overline{V}\) is the incoming wind speed and \(\phi\) is the wind yaw angle. \(V_{\rm ratio}\) represents the ratio between the vehicle's moving speed \(V_{T}\) and the incoming wind speed \(\overline{V}\). When the vehicle's moving speed is zero, it is the wind speed spectrum of the static point corresponding to the spire's turbulent flow field in the wind tunnel tests. The turbulent integral scale adopts the results of Table 1. The main results are shown in Figure 6.  
The ratios of the vehicle's moving speed to the incoming wind speeds are 0-5. If the train vehicle's moving speed is 200 km/h and the wind speed is 11 m/s, the \(V_{\rm ratio}\) value can reach 5. For a moving car on highway, the moving speed is 120 km/h and the wind speed is 11 m/s, so the \(V_{\rm ratio}\) value is about 3.3. The once-in-a-century wind speed in mountainous areas can reach 30 m/s or higher. The ratio of the vehicle's moving speed to the wind speed is thus approximately 2. Therefore, ratios of 0-5 are considered in this investigation.  
As can be seen in Figure 6, the basic shape of the wind velocity spectrum varies little. The main differences are found at the wind speed spectrum peaks and the corresponding frequencies.  
When the \(V_{\rm ratio}\) =1 and the wind yaw angle \(\phi\) = 15\({}^{\circ}\), the wind speed spectrum peak is the same as that of the static point, while the frequency corresponding to the peak is larger than that of the static point. The wind speed spectrum peak of the moving point gradually becomes larger than that of the static point. As the wind yaw angle \(\phi\) increases, the wind velocity spectrum peak and the corresponding frequency of the moving point also gradually increase. At different wind yaw angles, the wind speed spectrum peak of the moving point gradually moves to higher frequencies.  
When the wind yaw angle \(\phi\) is 15\({}^{\circ}\)\(\sim\)45\({}^{\circ}\), the peak wind speed spectrum values of the moving point remain unchanged as the \(V_{\rm ratio}\) values increase. The wind spectrum peak just corresponds to a larger frequency. When the wind yaw angle \(\phi\) is 60\({}^{\circ}\), the peak values and the corresponding frequencies increase as the \(V_{\rm ratio}\) value increases. The wind yaw angle continues to increase, and the peaks also gradually increase. When the wind yaw angle is 135\({}^{\circ}\), the frequencies corresponding to the wind speed spectrum peak gradually decrease. When the wind yaw angle is 175\({}^{\circ}\), the wind speed spectrum in conditions of \(V_{\rm ratio}\) = 2 and \(V_{\rm ratio}\) = 0 roughly coincide.  
Additionally, in Figure 7, the wind speed spectrums at different wind yaw angles are shown when the \(V_{\rm ratio}\) =1, 3 and 5. It can be seen that as the wind yaw angles increase, the wind speed spectrum peak and the corresponding frequency are increased firstly. When the wind yaw angle is from 135\({}^{\circ}\) to 175\({}^{\circ}\), the frequency corresponding to the wind speed spectrum peak is decreased as the wind yaw angles increase, and the wind speed spectrum peak is decreased when the \(V_{\rm ratio}\) values are 3 and 5.