## 3 Results and Discussion
### Effects of VIDD on Vehicle Speeds in Middle of Long Downhill Tunnel
#### 3.2.3 Effect on Average Vehicle Acceleration  
The average vehicle accelerations in the middle of the tunnel are shown in Figure 18. In Sections 2 and 3, the 40\({}^{\circ}\) slash-line VIDD gave the most obvious deceleration effect, with average vehicle accelerations of \(-\)0.39 and \(-\)0.21 m/s\({}^{2}\), respectively. However, the average vehicle accelerations with the 55\({}^{\circ}\) slash-line VIDD were positive in those two sections, exhibiting continuous acceleration. In the whole experimental section, the most obvious deceleration behavior was given by the 1Y1W and 4Y4W VIDDs; the vehicles speeds in Sections 1 and 2 decreased the most quickly, where the average accelerations were \(-\)0.58 and \(-\)0.59 m/s\({}^{2}\), respectively. In Sections 3 and 4, the 90\({}^{\circ}\) fold-line and 4Y4W VIDDS gave obvious acceleration characteristics.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**VIDD Type**} & \multirow{2}{*}{**None**} & \multicolumn{3}{c}{**Slash Lines**} & \multicolumn{3}{c}{**Fold Lines**} & \multicolumn{3}{c}{**Alternating Yellow and**} \\  & & & **15\({}^{\circ}\)** & **40\({}^{\circ}\)** & **55\({}^{\circ}\)** & **60\({}^{\circ}\)** & **90\({}^{\circ}\)** & **120\({}^{\circ}\)** & **1Y1W** & **2Y2W** & **4Y4W** \\ \hline Speed difference (km/h) & 47.8 & 54.6 & 52.3 & 58.8 & 65.8 & 44.2 & 61.3 & 52.9 & 60.5 & 47.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Differences between maximum and minimum speeds of vehicles with VIDDs.  
Figure 15: Minimum speeds of vehicles controlled by VIDD: (a) slash lines; (b) fold lines; (c) alternating yellow and white lines.  
Each VIDD on the side wall of the tunnel had a different influence on driving behavior, but the overall performance was to reduce the average speed and standard deviation of vehicles in the middle of tunnel. Among them, the 90\({}^{\circ}\) fold-line VIDD had the most significant effect on reducing the average speed, as well as on the standard deviation of speed. Compared with the vehicles with no VIDD, the average and standard deviation of vehicle speeds with the 90\({}^{\circ}\) fold-line VIDD decreased by 18.3% and 24.8%, respectively.  
Figure 16: Average speeds at every point for vehicles controlled by different types of VIDD: (**a**) slash lines; (**b**) fold lines; (**c**) alternating yellow and white lines.  
With no VIDD, when vehicles passed from Section 1 to Section 5, the speed and standard deviation showed no apparent change, and the driving state of vehicles was basically unchanged. However, after setting a VIDD, the average speed and standard deviation at each observation point decreased initially and then increased. The reason for this is that the visual intervention of the VIDD tends to cause drivers to overestimate the vehicle speed and then take measures to decelerate. The impact of a VIDD on drivers disappears when they have passed it, so that the vehicle speeds recover. A VIDD influences the drivers' visual frame of reference and can effectively reduce the average speed and its dispersion of vehicles in the middle of the tunnel, thereby reducing the accident rate and improving traffic safety.  
Figure 17: Average speeds and standard deviations of vehicles in middle of tunnel with and without VIDD.  
Figure 18: Average acceleration of vehicles in middle of tunnel with and without VIDD.