# Feasibility of a Quasi-Static Approach in Assessing Side-Wind Hazards for Running Vehicles
## 5 Conclusions  
This paper examines the feasibility of using the quasi-static approach in evaluating the reaction forces of tires, which could be utilized to limit the occurrences of overturning and side-slip accidents of vehicles under strong side winds. The performance of the quasi-static approach was examined by comparing the calculated tire forces to calculations using the dynamic vehicle analysis software, TruckSim. The governing equations were formulated for two types of vehicle, vans and trailers, by taking force-equilibrium, compatibility conditions, and several assumptions into consideration. The centrifugal forces created by the curvature and cant of a curved road were also considered. Both uniform and turbulent wind conditions were applied. Based on this feasibility study, the following conclusions were drawn:  
* The quasi-static approach for the van model provided vertical and lateral tire forces that were similar to those estimated using the dynamic approach for both turbulent and uniform winds. However, the quasi-static approach showed a discrepancy in vertical forces when the stiffness of the suspensions differed between the front and rear axles. According to the present case study, however, this discrepancy in the quasi-static approach would not prevent it from being considered a conservative estimation of vehicle safety. \begin{table}
\begin{tabular}{c c c} \hline
**Quasi-Static Approach** & **Enhanced Quasi-Static Approach** & **Dynamic Approach** \\ \hline
15.2 m/s & 14.1 m/s & 13.9 m/s \\ \hline \end{tabular}
\end{table} 
Table 2: Determined critical wind speed for the overturning accident of the trailer. Figure 17: Vertical reaction force of windward tire of each trailer model. * The quasi-static approach for the trailer model also created lateral tire forces similar to those created by the dynamic approach for both turbulent and uniform winds. However, the quasi-static approach returned a certain discrepancy in vertical forces by neglecting the additional rolling moment induced by a large lateral offset in the sprung mass. Accordingly, this study proposed an enhanced quasi-static approach for the trailer model, which added the rolling moment effect to the equilibrium equation. The vertical tire forces estimated by the enhanced quasi-static approach agreed well with those estimated by the dynamic analysis. However, additional information on both the roll stiffness and the position of the roll center are required for the enhanced quasi-static approach. * The realistic modeling of a suspension system in the dynamic approach resulted in an attenuation of the high-frequency components and a phase lag in the time history of the vertical tire force when the vehicle was exposed to turbulent winds. However, the magnitude and overall variations in the reaction forces of the quasi-static approach were in good agreement with those in the dynamic approach. * The critical wind speeds estimated by the quasi-static approach were almost identical to those used in the dynamic approach for the parameters of both side-slip and overturning accidents. Accordingly, the proposed quasi-static vehicle model is an efficient alternative to the dynamic model in estimating vehicle safety against strong side winds. Conceptualization, S.-J.K. and H.-K.K. ; methodology, S.-J.K. and H.-K.K. ; software, S.-J.K. and H.-K.K. ; formal analysis, S.-J.K.; investigating, S.-J.K.; writing--original draft preparation, S.-J.K.; writing--review and editing, H.-K.K. ; supervision, H.-K.K. This research was supported by a Grant (19 SCIP-B119963-04) from the Ministry of Land, Infrastructure and Transport of the Korean Government through the Korea Bridge Design and Engineering Research Center (KBRC) at Seoul National University. This work was also supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (2017R1A2B4008973). The authors declare no conflict of interest.