# Research on Geometric Design Standards for Freeways under a Fully Autonomous Driving Environment
## 4 Geometric Design Standard
### Horizontal Alignment
#### 4.1.3 Minimum Radius of Curve  
As a common alignment element in horizontal alignment, the selection of curve radius should be in line with the design speed. For safety and comfort of driving, the Chinese _Design Specification for Highway Alignment_ specifies the minimum radius of a curve according to Formula (3) [3,42]:  
\[R=\frac{V^{2}}{127(\mu\pm i_{h})} \tag{3}\]  
where \(R\) is the radius of a curve (m); \(V\) is the design speed (km/h); \(\mu\) is the lateral force coefficient; \(i_{h}\) is the superelevation value. * Limited Minimum radius of curve  
When calculating the limit minimum radius of a curve, the Chinese standard only considers the driving safety of a vehicle. It does not consider the requirements of stopping sight distance. This paper will study the minimum radius of a curve from two aspects: driving safety of autonomous vehicle and the requirements of lateral clear distance. According to the Chinese _Design Specification for Highway Alignment_, considering the comfort of passengers, when the lateral force coefficient \(\mu<0.10\), passengers cannot feel the curve when they turn, and the vehicle is very stable; when \(\mu=0.15\), passengers can feel the curve slightly when turning, and the vehicle is relatively stable; when \(\mu=0.20\), passengers can feel the curve exists when turning, and the vehicle is slightly unstable; when \(\mu=0.35\), passengers can feel the curve exists when turning, and the vehicle is unstable; when \(\mu>0.40\), the vehicle is very unstable, and there is a risk of tipping over. Therefore, the value of \(\mu\) must be limited when calculating the radius of the circular curve. In view of China's vast territory, geographical and climatic conditions vary greatly, so the standard needs to adapt to a variety of adverse conditions. In the Chinese _Design Specification for Highway Alignment_[35], on the basis of the most unfavorable situation when calculating the limit minimum radius of a freeway circular curve, the lateral force coefficients at the design speeds of 120 km/h, 100 km/h, and 80 km/h are taken as 0.10, 0.12, and 0.13. Obviously, the higher the design speed of a freeway, the more the passenger's comfort needs to be considered, so the restriction on the lateral force coefficient is also greater. Referring to the description of the meaning of the lateral force coefficient in the Chinese _Design Specification for Highway Alignment_, this paper takes the lateral force coefficients at design speeds of 140 km/h, 160 km/h, and 180 km/h as 0.09, 0.08, and 0.07 and then substituted them into Formula (3) to calculate the limit minimum radius in an autonomous driving environment, as shown in Table 8. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Length Type**} & \multicolumn{6}{c}{**Design Speed (km/h)**} \\ \cline{2-9}  & **80** & **100** & **120** & **140** & **160** & **180** \\ \hline Maximum tangent length (m) & — & — & — & — & — & — \\ \hline \multirow{3}{*}{Minimum tangent length (m)} & Equidirectional curve & 480 & 600 & 720 & 840 & 960 & 1080 \\ \cline{2-9}  & Reverse curve & 160 & 200 & 240 & 280 & 320 & 360 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Tangent length based on autonomous driving technology. \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 \multicolumn{2}{c}{**Lateral Force Coefficient**} & 0.07 & 0.08 & 0.09 & 0.10 & 0.12 & 0.13 \\ \hline \multirow{4}{*}{**Limit minimum radius of curve (m)**} & \(i_{h}=\)10\% & 1345 & 1120 & 910 & 570 & 360 & 220 \\ \cline{2-9}  & \(i_{h}=\)8\% & 1500 & 1260 & 1030 & 650 & 400 & 250 \\ \cline{2-9}  & \(i_{h}=\)6\% & 1700 & 1440 & 1200 & 710 & 440 & 270 \\ \cline{2-9}  & \(i_{h}=\)4\% & 1970 & 1680 & 1400 & 810 & 500 & 300 \\ \hline \hline \end{tabular}