# Lateral Oscillation Characteristics of Vehicle Trajectories on the Straight Sections of Freeways
## 4 Data Analysis and Result
### Trajectory Oscillation of Different Speeds  
The speed concentration interval of each vehicle was used as the research range to analyze the variation regulation of vehicle trajectory oscillation. The speed study ranges were 80-150 km/h and 80-125 km/h for passenger cars and medium-large cars, with 15 and 10 measurement points divided at fixed intervals of 5 km/h. The speed distribution of extra-large trucks was more concentrated, so seven measurement points were split at a smaller fixed interval of 2.5 km/h. Figure 11 shows the LA and DTOC for each type of vehicle at each speed measurement point. The percentile of 15 th, 25 th, 50 th, 75 th, 85 th, and mean values were extracted, and the corresponding trend lines can be obtained by connecting the same eigenvalues.  
Figure 10: (**a**) Distribution of the LA in different lane positions; (**b**) Distribution of the DTOC in different lane positions.  
The ANOVA results showed the LA (F = 6.14, \(p\) < 0.01) and DTOC (F = 2.14, \(p\) = 0.008 < 0.01) had significant differences for passenger cars at different speed points. So, speed is also an essential factor affecting the trajectory oscillation of passenger cars. Figure 11a,c,e show that the trend of LA with speed for all vehicles is not a simple linear relationship. In the interval of 80-90 km/h, the LA of passenger cars tended to decrease with increasing speed and reached a local minimum of 90 km/h. In this interval, the LA of medium-large cars rose with growing speed and caught a local maximum of 90 km/h. In the interval of 90-110 km/h, both showed a parabolic trend of increasing and then  
Figure 11: The trend of trajectory oscillation indicators at different speed points. (**a**) The LA for passenger cars; (**b**) The DTOC for passenger cars; (**c**) The LA for medium-large cars; (**d**) The DTOC for medium-large cars; (**e**) The LA for extra-large trucks; (**f**) The DTOC for extra-large trucks.  
decreasing. In the subsequent process, the LA of passenger cars appeared to decline, while medium-large cars slowly increased. The tendency of LA with the speed of extra-large trucks was relatively smooth, and there was no sudden change.  
Figure 11b,d,f show the variation curves of DTOC for each vehicle type. It can be seen that: in the interval of 80-90 km/h, the DTOC of passenger cars decreased gradually, while medium-large cars showed an increase and then dropped, and extra-large trucks were smoothly changing. The only valley of the passenger cars occurred when the speed reached 135 km/h, at which point the DTOC was the global minimum. The DTOC of medium-large cars showed a valley at a rate of 110 km/h, followed by a gradual increase. The trough occurred at 92.5 km/h for extra-large trucks, and the DTOC increased rapidly when the speed exceeded it. In addition, because the medium-large cars' categories were more complex than the other two vehicle types and had the broadest coverage of dimensions, they exhibited a more volatile and less regular characteristic of trajectory oscillation.  
In conclusion, the trend of trajectory oscillation of passenger cars and medium-large cars has a more complicated pattern of variation with increasing speed. Meanwhile, the movement of extra-large trucks is more homogeneous. The LA of passenger cars is the largest, and that of extra-large trucks is the lowest under the same speed conditions. As a result, passenger cars are operating at a higher risk. A reasonable trajectory oscillation prediction scheme must be developed to ensure that all vehicles can perform at a superior safety level at high speeds.