# Numerical Investigation on Handling Stability of a Heavy Tractor Semi-Trailer under Crosswind
## 1 Introduction  
In recent years, with the development of highways and logistics industries, more and more heavy tractor semi-trailers have been introduced into road transport. The crosswind stability, which is related to the safety of truck driving, has attracted wide concern. Due to its high center of gravity, narrow wheelbase (compared with the body height) and large area of container, the heavy tractor semi-trailer driving at high speed is more prone to lateral tilt and rollover when encountering strong crosswind [1]. Serious traffic accidents or strong psychological burden to the driver will be induced [2]. As shown in Figure 1, a sequence of scenes vividly displays some cases of wind-induced rollover of a tractor semi-trailer. The study related to crosswind effect on vehicle performance could be basically classified into two aspects: one is crosswind aerodynamics [3], and the other is crosswind stability [4]. About crosswind aerodynamics [5], the influence of the crosswind on aerodynamic characteristics was mainly discussed, such as the fluctuation of the six aerodynamic components and the change of flow field. The most common evaluation methods for evaluating the aerodynamic performance of vehicles indifferent wind environments are road tests, static wind tunnel tests and simulations with varying yaw angles [6]. As for the crosswind stability, experimental and dynamic modeling simulation methods were adopted to investigate the dynamic response of the vehicle under crosswind, the deviation from the original driving path and the driver's handling of the vehicle. Some previous works have already concentrated on dynamic aerodynamics, which clearly demonstrate the importance of time-related changes under aerodynamic forces. When driving at high speed, the influence of aerodynamic force on vehicle performance is particularly important, especially under complex crosswind circumstances. For instance, [PERSON] et al. [7] investigated the aerodynamic coefficients with different yaw angles on Ahmed vehicle by the wind tunnel test and Particle image velocimetry (PIV) measurements, which visualized the velocity flow field under the crosswind vividly and thoroughly revealed the underlying flow phenomena related to crosswind sensitivity of the ground vehicles. [PERSON] et al. [8] discussed the crosswind aerodynamics of a sedan, and their research illustrated that the drag coefficient, lift coefficient and the yaw moment would increase with the growth of yaw angle and velocity of crosswind. [PERSON] et al. [9] analyzed a road vehicle's aerodynamic response in transient crosswinds. [PERSON] et al. [10] proposed a framework to analyze a vehicle running on a long bridge in windy circumstances. On this basis, the aerodynamic response of vehicles running on highways or bridges can be analyzed and the critical wind speed can be evaluated to avoid potential accidents. In the aspect of crosswind stability, scholars have had extensive discussions on theoretical analysis, model simulation and experiments. [PERSON] et al. [11] carried out an investigation on the riding stability of a passenger car under crosswind by the full-scale wind tunnel test and on-road test with a crosswind generator. Their results revealed the major parameter that affects the crosswind sensitivity of passenger cars was the yawing moment. In addition, high-speed stability would be improved with the reduction of lift force, lateral force and yawing moment. [PERSON] et al. [12] evaluated vehicle behavior under crosswind by using a full-vehicle dynamic simulation model with aerodynamic forces and moments, which were obtained by numerical simulation added on the gravity center. [PERSON] [13] conducted vehicle dynamics simulations to analyze the effect of unsteady aerodynamics of a simplified truck under transient crosswinds. In his study, the horizontal motion of the vehicle was considered, and the vertical motion was assumed to be balanced statically. To investigate the influence of crosswind on directional deviation and handling performance, [PERSON] et al.