## 3 Results
### The Effects of Time Delay in Drivers' Steering Inputs on the Vehicle's Reaction to the Crosswind
The subfigure in each figure shows the instant differences between the results obtained for \(t_{S,delay}=0\) s, and \(t_{S,delay}=0.5\) s, and \(1.0\) s.  
maximum magnitude of the steering input of Driver 3 at the first peak was 1.4 times larger than that of Driver 1 at the delay time of \(t_{\delta,delay}=1.0\) s. Additionally, in the case of Driver 3, the magnitude of the steering input at the first peak at \(t_{\delta,delay}=1.0\) s was around 3 times greater than the corresponding one at \(t_{\delta,delay}=0\) s. Furthermore, the steering efforts needed to bring the vehicle on its original track increased significantly as the delay time in the steering input of the driver increased to \(t_{\delta,delay}=1.0\) s.  
The total steering wheel inputs of each driver at three distinct delay times are compared in Figure 13. On an individual basis, each driver's total steering inputs were roughly the same at \(t_{\delta,delay}=0\) s and 0.5 s. Conversely, at \(t_{\delta,delay}=1.0\) s, the total steering inputs of drivers were at least 1.4 times higher than those at \(t_{\delta,delay}=0\) s and 0.5 s. [PERSON] and [PERSON] [16] specified the importance of the promptness of drivers in controlling the different crosswind sensitivity of vehicles. The findings of the current study unequivocally demonstrated that the delay time of \(t_{\delta,delay}=0.5\) s was important in controlling the vehicle motion after the crosswind hit it. Additionally, there were significant differences between the drivers' steering inputs. For example, the steering wheel inputs of Driver 1 were 1.7 and 1.3 times larger than those of Driver 3 at \(t_{\delta,delay}=0\) s and 1.0 s, respectively. In conclusion, there were both significant differences between the drivers' steering inputs at certain delay times and significant increases in the drivers' steering efforts as the delay time extended to \(t_{\delta,delay}=1.0\) s.  
Figure 12: The steering inputs, \(\delta\), of three drivers with different skills at three delay times of \(t_{\delta,delay}=0\) s, 0.5 s, and 1.0 s in the steering inputs. Figure 13: Total steering wheel inputs of drivers with different driving skills, \(\sum\delta_{\mathrm{zw}}\), at three different delay times, \(t_{\delta,delay}=0\) s, 0.5 s and 1.0 s.  
The Effects of Drivers' Steering Inputs on the Aerodynamic Force and Moments Acting on the Vehicle Subjected to Crosswind  
Previous research studies indicated the significance of the aerodynamic yaw moment, lateral force, and roll moment in influencing the vehicle's response to crosswind [8, 21, 33]. The findings demonstrated in the current study revealed that the steering inputs made by the drivers had an impact on the aerodynamic forces and moments acting on the vehicle as a result of the crosswind. The characteristics of lateral force, yaw moment, and roll moment acting on the vehicle due to the crosswind, with and without steering inputs from the driver, are depicted in Figure 14. They revealed that both the drivers' driving skills and the delay times in their steering inputs caused differences between the aerodynamic forces and moments exerted on the vehicle due to the crosswind. Thus, the differences in the amount of force and moments arose after the steering started, i.e., \(t_{\delta,delay}=0\). For all delay times, the drivers' steering inputs increased the yaw moment at various amounts towards the end of the crosswind, whereas they reduced the lateral force and roll moment. Rapid alterations in the vehicle's yaw angle resulting from the drivers' steering inputs led to notable variations in the yaw moment outcomes. For example, the yaw moment results at \(t_{\delta,delay}=0\) s and \(0.5\) s reached their maximum values at around \(t\)\(\sim\)3.9 s, while the yaw moment results at \(t_{\delta,delay}=1.0\) s reached their maximum at a later time of \(t\)\(\sim\)4.5 s.  
Furthermore, the other outcomes of aerodynamics simulation, such as the analysis of velocity fields, were not included in the present study due to the specific scope outlined for this research.