# Research on Geometric Design Standards for Freeways under a Fully Autonomous Driving Environment
## 4 Geometric Design Standard
### Vertical Alignment  
#### 4.2.1 Transition Slope  
At present, different scholars have different views on whether it is scientific and reasonable to set a transition slope between long and steep slopes. [PERSON] [43] found through the simulation experiment that when the average longitudinal slope of the road is large, the transition slope can play a role in restoring the speed of trucks on the slope. [PERSON] [44] and others believe that some European countries tend to design a single longitudinal slope, mainly because the transition slope will make drivers relax their vigilance. [PERSON] [45] put forward the suggested values of the transition slope gradient and slope length at different altitudes. It can be seen that most scholars are quite sure of the positive effect of the transition slope section in an upgrade. Compared with the traditional self-driving vehicle, the dynamic performance of the autonomous vehicle does not change qualitatively in the autonomous driving environment. Second, the autonomous vehicle's \"eyes\" have become sensors. In other words, the insertion of transition slopes between consecutive downhill sections will not cause the illusion of flatness or an anti-slope. It is conducive to downhill vehicle deceleration. Therefore, this paper refers to the maximum longitudinal slope value of each design speed of superhighway [23], combined with the stipulations of each country, and the maximum \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Design Speed (km/h)**} & **180** & **160** & **140** & **120** & **100** & **80** \\ \hline \multirow{2}{*}{**Minimum radius of curve without superelevation**} & **Cross slope \(\leq\) 2\%** & 12,800 & 10,100 & 7750 & 5500 & 4000 & 2500 \\ \cline{2-8}  & **Cross slope \(>\) 2\%** & 17,050 & 13,500 & 10,300 & 7500 & 5250 & 3350 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Minimum radius of curve without superelevation (m). According to Figure 7, Formula (6) can calculate the minimum radius that satisfies the sight distance requirement:  
\[\left. \begin{array}{c}S_{T}=\sqrt{2R}\big{(}\sqrt{h_{1}}+\sqrt{h_{2}}\big{)}\\ L_{\min}=\frac{5r^{2}\omega}{2\left(\sqrt{h_{1}}+\sqrt{h_{2}}\right)^{2}}\end{array} \right\} \tag{6}\]  
where the parameter meanings are the same as before. When calculating the minimum radius of the convex vertical curve, the most conservative case should be selected, that is, the equation with a larger \(L_{\min}\) value should be used. Subtract Formula (6) from Formula (5) and bring the values of \(h_{1}\) and \(h_{2}\) into the formula. \[L_{\min 1}-L_{\min 2}=2S_{T}-\frac{4}{\omega}-\frac{S_{T}{}^{2}\omega}{4}=- \frac{\left(S_{T}\omega-4\right)^{2}}{4\omega} \tag{7}\]  
Obviously, the calculation result \(L_{\min 2}\) of Formula (6) is larger than the calculation result \(L_{\min 1}\) of Formula (5). Accordingly, this paper chooses Formula (6) (vertical curve length is greater than the stopping sight distance) to calculate the minimum radius of the convex vertical curve. * Satisfy sight distance requirements  
Autonomous vehicles may also have blind spots when driving on a convex vertical curve, similar to traditional manual driving, as shown in Figure 8. When designing a convex vertical curve, to ensure driving safety, it is necessary to meet the stopping sight distance requirements of an autonomous vehicle. The calculation models and method for convex vertical curves in the design specifications of various countries are also applicable to the autonomous driving environment. The difference is the variation of some parameters in the formula, such as the visual height of autonomous vehicle elevation, stopping sight distance requirement, and so on. In Formula (6), \(h_{1}\) is the visual height. Autonomous vehicles are no longer controlled by the driver but by a variety of on-board sensors and CPUs. The position and height of its viewpoint change accordingly, as shown in Figure 9. Both the Hong Qi and Uber autonomous vehicles have video cameras and radar sensors positioned on the roof.