## 4 Discussion  
When investigating the crosswind sensitivity of vehicles, previous research studies often used a traditional approach that ignored the driver's contributions and concentrated only on the vehicle-crosswind interactions. [PERSON] and [PERSON] [19] stated that the response of a less crosswind-sensitive vehicle to crosswind might be different when including the driver's reactions. Thus, in the current study, the responses of a heavy vehicle to a crosswind were investigated by including the steering inputs of three drivers who had different driving skills. Accordingly, the vehicle dynamics results were acquired both with and without the driver's steering inputs for comparative analysis. Comprehensive discussions regarding the vehicle's response to crosswind without any driver's steering input were elaborated in previous studies by [PERSON] et al. [7, 9, 9]. When examining the lateral dynamic properties of vehicles, yaw velocity and lateral acceleration and their relationship with steering-wheel angle were generally specified as important characteristics. For instance, [PERSON] et al. [33] reported that lateral acceleration,  
Figure 14: Lateral force, \(F_{a,g}\), yaw moment, \(M_{a,z}\), and roll moment, \(M_{a,x}\), obtained in the case of three drivers with different skills at three delay times in their steering inputs, i.e., \(t_{\delta,delay}=0\) s, \(0.5\) s, and \(1.0\) s. The green lines depict the corresponding forces and moments obtained when there is no driver’s steering input. yaw velocity, and the time lag between those parameters are the primary factors influencing the driver's perception of vehicle movements, next to perception limits. In this perspective, the corresponding results are compared in Figure 9, given in the previous section. However, the outcomes presented in Figure 9 demonstrated an intricate interaction among the crosswind, vehicle, and driver's steering inputs, which made it difficult to compare the results of different driver's steering efforts and draw any general conclusions regarding them. For example, in Figure 9a, the second peak of the lateral acceleration of Driver 3 occurred inside the crosswind, whereas the second peak of the lateral acceleration of Driver 1 occurred just after the crosswind ceased. That means the larger second peak of the lateral acceleration of Driver 1 could also be due to the reduction in crosswind, not necessarily only due to the steering input. Thus, it is more appropriate to talk about the vehicle-driver system instead of considering their individual effects in the study of the crosswind sensitivity of vehicles [34]. In line with the aim of investigating the driver-vehicle-crosswind interactions, a driver model that reproduced a realistic human driver's steering response was used in the study. The maximum steering wheel rate after the first steering manoeuvres of all drivers was smaller than \(\dot{\delta}\) = 240 deg/s, given in Figure 7c, indicating that the steering responses of drivers in the study corresponded to normal human driving conditions as described by [PERSON] and [PERSON] [35] and [PERSON] [36]. Based on empirical observations, [PERSON] and [PERSON] [35] identified three driving regimes described as \"normal\", \"spirited\", and \"accident avoidance\", which were characterised by steering rates of 0 to 400 deg/s, 400 to 700 deg/s, and 700 to 1200 deg/s, respectively. Also, [PERSON] [36] stated that normal driving requires an average steering rate of 500 deg/s. In general, the study's findings indicated that the vehicle dynamics became more stable after the onset of crosswind with higher levels of driver driving skill. The drivers' steering inputs, aimed at mitigating the unfavourable effects of crosswind on vehicle motion, decreased with increasing driving skills. These outcomes were anticipated, given that the driver model employed in the study was based on proportional gain parameters.