# Lateral Oscillation Characteristics of Vehicle Trajectories on the Straight Sections of Freeways
## 5 Discussion  
The trajectory oscillation behavior of the vehicle is influenced by the combination of road alignment, vehicle performance, and driving ability. It serves as the main framework for researching driver lane-keeping behavior and practical lane-width design. For this objective, the variability between vehicle trajectory oscillation behaviors was discussed regarding vehicle type, lane position, and speed. These results suggest that the vehicle type is an integral factor in the variation of lateral offset [32]. Similarly, lane position and speed have varying degrees of influence on the lateral oscillation on straight sections of freeways [28]. It has been shown that the lane width is composed of lateral oscillation, vehicle width, and outside clearance [33]. However, [PERSON]'s study only used 70 questionnaires to determine the lateral offset at different speeds, which may lack powerful data support. Although previous research has also proposed suggested values for lane width [34; 35], their subjects and scenarios were inconsistent with this study. It is vital to determine how much each element influences the dependent variable because lane location and speed both considerably impact the magnitude of vehicle trajectory excursions. The analysis of covariance (ANCOVA) was used to explain the importance of this effect. Take passenger cars as an example; the average lateral amplitude at different speeds was divided into three groups based on the lane position; then, the lane position was used as the fixed factor, and speed was used as the covariate. The results of ANCOVA were obtained after the parallelism test (F = 0.019, \(p\) = 0.981 > 0.05) and the homogeneity of variance test (F = 1.986, \(p\) = 0.153 > 0.05). At the 0.05 level of significance, the F-value of the lane position was 2.850, with a concomitant probability of 0.073 (>0.05); the F-value of the speed was 19.732, with a concomitant probability of 0.000 (<0.05). Therefore, the speed greatly impacted how the lateral amplitude changed. Furthermore, the influence of lane position on the lateral amplitude was not significant once speed was taken into account. As a result, it may be concluded that speed, rather than lane position, primarily determines the vehicle trajectory's lateral amplitude. The variations in speeds may be the cause of the trajectory oscillations of cars in various lane positions. The difference in trajectory oscillation at different lane positions may be due to the variation in speed. The observation revealed a stepwise declining relationship between the driving speeds of vehicles in the inside, middle, and outside lanes, demonstrating that high-speed automobiles prefer to travel inside the roadway [19]. The evaluation of road alignment consistency based on operating speed is critical to improving highway safety design and road service quality [23]. The lateral amplitude versus speed model was constructed, as speed was the primary factor affecting the trajectory oscillation. To accommodate the driving behaviors of the majority of drivers, the upper and lower limits were taken as the 85 th percentile and the mean value of the lateral amplitude, respectively. Then, nonlinear regression analyses were adopted to quantify the relationship between speed and lateral amplitude. After comparing various nonlinear models, the mean and 85 th percentile values of the lateral amplitude for passenger cars were regressed using the 4 th-order polynomial and single exponential decay models. The adjusted goodness-of-fit of the models is 0.827 and 0.755, as shown in Equations (8)-(9). The average lateral amplitude of medium-large cars conforms to the periodic variation rule of the sine function. After excluding the outlier points, its 85 th percentile value likewise complies with the sinusoidal distribution. The goodness-of-fit of the two models for medium-large cars is 0.609 and 0.582, as shown in Equations (10)-(11).