# Lateral Oscillation Characteristics of Vehicle Trajectories on the Straight Sections of Freeways
## 4 Data Analysis and Result
### Trajectory Oscillation of Different Lane Positions  
Based on the test road segments, the lanes were divided into three categories: the inside lane (near the left herb and central median), the outside lane (near the hard shoulder), and the middle lane (between the inside and outside lanes). The inside lanes included Lane 1 of the four-lane and six-lane divided highways. Lane 2 of the four-lane divided highway and Lane 3 of the six-lane divided highway were classified as outside lanes. The middle lane covered only Lane 2 of the six-lane divided highway (see Figure 2). After the detailed division of the lanes, the trajectory oscillation patterns of the three vehicles in different lane positions were analyzed separately. Details about the trajectory oscillation are shown in Figure 10. The results in Figure 10 are as follows. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{5}{c}{**LogNormal Fitting Coefficients**} & \multicolumn{5}{c}{**Index Value**} \\ \cline{2-10}  & \(A\) & \(w\) & \(x_{e}\) & \(y_{0}\) & \(\mathbb{R}^{2}\) & **15 th** & **50 th** & **85 th** & **Mean** & **SD** \\ \hline \hline \multicolumn{10}{l}{_Lateral Amplitude (m)_} \\ \hline Passenger cars & 0.052 & 0.47 & 0.49 & \(-8.6\times 10^{-4}\) & 0.99 & 0.29 & 0.48 & 0.75 & 0.52 & 0.23 \\ Medium-large cars & 0.054 & 0.47 & 0.50 & \(-2.1\times 10^{-3}\) & 0.99 & 0.30 & 0.49 & 0.76 & 0.52 & 0.22 \\ Extra-large trucks & 0.053 & 0.48 & 0.48 & \(-1.7\times 10^{-3}\) & 0.98 & 0.28 & 0.46 & 0.72 & 0.49 & 0.21 \\ \hline \multicolumn{10}{l}{_Distance Travelled in the Oscillation Cycle (m)_} \\ \hline Passenger cars & 11.43 & 0.45 & 203.37 & \(-2.0\times 10^{-3}\) & 0.98 & 127.14 & 196.07 & 290.06 & 204.94 & 72.82 \\ Medium-large cars & 12.47 & 0.52 & 199.26 & \(-3.8\times 10^{-3}\) & 0.96 & 115.55 & 187.11 & 288.16 & 197.04 & 76.72 \\ Extra-large trucks & 13.07 & 0.56 & 205.61 & \(-4.4\times 10^{-3}\) & 0.95 & 112.48 & 188.22 & 295.58 & 198.95 & 80.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The coefficients of LogNormal and eigenvalues of the trajectory oscillation index. Figure 9: (**a**) Distribution of the LA for extra-large trucks; (**b**) Distribution of the DTOC for extra-large trucks. (1) The LA (F = 96.17, \(p\) < 0.01) and DTOC (F = 9.81, \(p\) < 0.01) showed significant differences for passenger cars in all three lane categories. Passenger cars had the smallest LA in the inside lane (mean = 0.498 m) and the giant LA in the outside lane (mean = 0.552 m). The DTOC gradually decreased in the three lanes, with a minimum of 139.29 m and a maximum of 258.32 m. Thus, it reveals that the trajectory oscillation of passenger cars is the most intense when driving in the outside lane. The larger oscillation amplitude and shorter oscillation period are more likely to lead to lane departure. (2) The LA (F = 4.99, \(p\) = 0.0068 < 0.01) and DTOC (F = 3.43, \(p\) = 0.033 < 0.05) were also significantly different for medium-large cars at different lane locations. Contrary to passenger cars, medium-large cars had the least amount of LA in the middle lane and oscillated more in other lanes. All three lanes experienced a gradual decline in DTOC performance, but the decline was more significant between the middle and outside lanes and less pronounced between the inside and middle lanes. Consequently, driving in the middle lane is the safest option for medium-large cars. (3) Among the three lanes, the LA for extra-large trucks (F = 18.26, \(p\) < 0.01) was significantly different, with performance comparable to that of passenger cars but with a modest increase over them. However, the DTOC for extra-large trucks (\(p\) = 0.12 > 0.05) was not significantly different across lanes. It might be because these vehicles are usually oversized and most of them are located in the right lane of traffic. (4) Passenger cars have narrower widths and more lateral clearance when lane departing. Therefore, compared to the other two vehicle classes, the LA of passenger cars in the same lane is generally higher.