# Feasibility of a Quasi-Static Approach in Assessing Side-Wind Hazards for Running Vehicles
## 4 Feasibility of the Quasi-Static Approach Under Turbulent Winds
### Enhanced Quasi-Static Approach Considering an Additional Rolling Moment  
The wind data measured at the tops of the pylons, located at 182 m from the sea level, of an actual sea-crossing cable-stayed bridge were utilized for the feasibility analysis of quasi-static and dynamic procedures for turbulent winds. The data were collected with a sampling rate of 100 Hz for a duration of 10 min during a typhoon. Since the wind speed measured at the top of the pylon was too high to investigate the triggering of vehicle instability, the magnitude of the wind speed was scaled down by half, as shown in Figure 11a. The time history of the wind direction is also given in Figure 11b. The 10 min average and standard deviations in wind speeds were 10.8 m/s and 2.9 m/s, respectively. Wind data for a duration of 1 min were utilized in the analysis. The wind direction was measured in the direction of a running vehicle at a starting point of 1 min for analysis in the clockwise direction. A vehicle speed of 40 km/h was assumed on a curved road with a curvature radius of 700 m at a cant of 2%. The total analysis time was 70 s, which includes the stabilization time, and the wind direction was modified according to the direction of a vehicle running on a curved road. The tire forces were evaluated at a time step of 0.01 s in the quasi-static approach and of 0.001 s in the dynamic approach. Figure 10: Windward vertical reaction force of the trailer by the enhanced quasi-static approach. Figures 12 and 13 show the tire forces for the van and the trailer, respectively, for the 1 min turbulent wind. According to these figures, under turbulent wind conditions, the quasi-static approach also provided results that were comparable to those of the dynamic approach. First, we will discuss lateral friction forces. A comparison of the quasi-static and dynamic approaches in Figure 12b shows slight differences in the lateral friction forces of the front axle of the van. The difference originated from the application of sophisticated tire dynamics on a curved road in the TruckSim analysis, which was not further investigated in the present study. Meanwhile, Figure 13b shows that the lateral tire friction of the trailer obtained by the dynamic approach oscillated around that of the quasi-static approach, which was not observed under uniform wind conditions. This was due to the fluctuation components of wind velocity, which excited the trailer body in a dynamic fashion. We identified larger differences in the vertical reaction forces than in the lateral friction forces, as shown in Figures 12a and 13a. In the case of the van, the minimum vertical reaction forces from the quasi-static and dynamic approaches were 2.61 and 3.07 kN, respectively. However, when the same stiffness and the same position of the suspension springs was applied to all tires in the dynamic approach, the minimum vertical reaction force was reduced to 2.45 kN, which approximates that of the quasi-static approach. The cause of the difference was previously identified under a uniform wind velocity. Figure 11: Time history of wind data: (**a**) wind speed and (**b**) wind direction. Figure 12: _Cont._  
A difference of approximately 10% was identified between the two approaches with respect to the vertical reaction forces of the trailer, as shown in Figure 13a. As with uniform wind velocity, the enhanced quasi-static approach was also applied to the trailer. Figure 14a shows the time history of the vertical reaction forces acting on a windward tire obtained from the enhanced quasi-static approach, and Figure 14b lists the results for the first 10 s. As shown in Figure 14a, the enhanced quasi-static approach provided a vertical reaction force that approximated that of the dynamic approach. This illustrates how the difference in Figure 13a originated from the additional moment induced by the lateral displacement of the sprung mass, as was demonstrated in the uniform wind velocity case.