# Feasibility of a Quasi-Static Approach in Assessing Side-Wind Hazards for Running Vehicles
## 1 Introduction  
Vehicles crossing long-span bridges over open seas are often exposed to strong side winds. Accidents involving side-slipped and overturned vehicles occur often on spans such as the Gwangan and Seohae Bridges in Korea. Typhoon Jebi hit Japan in 2018, and videos taken during Jebi showing a heavy truck overturned on a bridge are available on the internet [1]. Estimating the vulnerability of vehicles crossing sea bridges begins with an evaluation of the critical wind speed, which is defined as the point at which vehicles will side-slip or overturn. Once the critical wind speed curve is developed for different vehicle types, the risk assessment of a bridge in terms of vehicle safety for strong side winds can be estimated [2]. Accordingly, appropriate numerical analysis models are required for the evaluation of the critical wind speeds for vehicles.  
The quasi-static model, which is basically utilizing static equilibrium equations, and the full dynamic model with sophisticate modeling of vehicle parts are two typical vehicle models utilized for the evaluation of the critical wind speed [3; 4; 5]. Both the quasi-static and the dynamic approaches have pros and cons.  
The merit of the dynamic approach is that it simulates more realistic vehicle motions by considering various interactions among vehicle components based on vehicle dynamics. CarSim and TruckSim [6]are examples of the commercial software that is available to support the dynamic approach. The dynamic approach can simulate the time histories of vehicle responses for each part of a vehicle, which includes tire forces, displacement, and acceleration. The results can be used to assess not only vehicle safety but also discomfort experienced by drivers [7]. The construction of a reliable dynamic model, however, requires tremendous effort and detailed data, which are usually not available to general researchers. Furthermore, vehicles consist of many parts with different characteristics depending on the vehicle. These differing parts include tires, suspension springs, shock absorbers, and brake systems. Therefore, if there is a small error in the modeling of these components, the complexity of the dynamic model can cause a large propagation error [8].  
The quasi-static vehicle model, on the other hand, is convenient to use, because it requires only a few basic dimensional and aerodynamic configurations of vehicle information. The quasi-static model is also intuitive because it focuses on the equilibrium condition of static forces acting on vehicles. For these reasons, the quasi-static model has been utilized for the risk assessment of vehicle safety in side winds, even though it is less realistic than the dynamic approach [2; 9; 10]. A very important question remains, however, as to whether the quasi-static model can accurately evaluate the tire reaction forces and/or the critical wind speeds with sufficient precision when it ignores the dynamic interactions between the mechanical parts of a vehicle. [PERSON] [8] proved the feasibility of the quasi-static train model by using it to estimate the wheel load and comparing the results with estimations using the dynamic train model. However, there are no reports of a feasibility study for road vehicles.  
Therefore, the focus of this study is to confirm the feasibility of the quasi-static approach in assessing the safety of vehicles exposed to strong side winds. Two types of vehicles, vans and trailers, were considered. The TruckSim software was utilized to provide target responses for the dynamic approach. The novel approach in this study includes three dimensions: (1) the proposition of a quasi-static approach for trailers; (2) a feasibility assessment of the proposed quasi-static approach by comparing the reaction forces of tires with that proposed by the full dynamic approach for turbulent wind; and (3) an enhancement of the conventional quasi-static approach based on a cause investigation of the differences identified between the two approaches.