# Research on Geometric Design Standards for Freeways under a Fully Autonomous Driving Environment
## 4 Geometric Design Standard
### Vertical Alignment
#### 4.2.3 Concave Vertical Curve  
A concave vertical curve is mainly affected by sight distance requirements for vehicles under overpass bridges and sight distance requirements at night. In an autonomous traffic environment, [PERSON] [10] noted in his study that the Waymo team has developed a range of sensors that enable autonomous vehicles to detect 360-degree environments both during the day and at night. In other words, at night, an autonomous vehicle's radar sensors work as well as they do during the day, so vehicles are no longer limited by headlight illumination distance at night. In his research, [PERSON] [28] believed that the function of headlights was replaced by sensors on the roof. Therefore, when studying the minimum radius of a concave vertical curve, this paper does not consider the requirement of headlight illumination distance; it only considers travel time, impact mitigation, and sight distance requirements for vehicles under overpass bridges. Since the requirements for cushioning impact and minimum travel time are the same for a convex vertical curve, it is only necessary to focus on sight distance requirements for vehicles under overpass bridges. The blind area under an overpass is shown in Figure 11.  
In calculating sight distance requirements for vehicles under overpass bridges, _Design Specification for Highway Alignment_ uses the results of calculation when the vertical curve length is not less than the stopping sight distance as an effective basis. The schematic diagram of calculation is shown in Figure 12.  
Figure 11: Blind area under an overpass. Figure 12: Calculation of radius of concave vertical curve under overpass bridge. \[M=0.0103V_{2}+0.46 \tag{13}\]  
where \(D\) is the safety distance between the edges of the rear wheels of two vehicles (m); \(M\) is the safety distance from the outer edge of the left rear wheel to the left side of the lane (m); \(y\) is the safety distance from the outer edge of the right rear wheel to the right side of the lane (m); \(V_{2}\) and \(V_{1}\) are the speed (km/h) of the overtaking vehicle and the vehicle being overtaken. It can be seen from this model that lane width is positively correlated with speed. In the autonomous driving environment, the driving speed of the vehicle will achieve further breakthroughs. If the lane width of the autonomous driving freeway is still calculated according to this model, it will cause unnecessary waste. It also does not match the real need for lane width in autonomous vehicles. [PERSON] et al. (2019), in their research on lane width, believed that the demand for lane width would be reduced for cars equipped with a lane-keeping assistance system. Their results divide the lane lateral width into safety width and swing width, which includes performance pendulum and driving pendulum (swing caused by the driver steering). [PERSON] (2017) established a model of the lateral safety distance and speed difference between different vehicles based on the trajectory data of the vehicle. The results of study found that lane width specified in the Chinese _Design Specification for Highway Alignment_ is too large. Many domestic scholars (2018, 2019, 2020) reach the conclusion that the lane width in China is on the large side by analyzing the irrationality of the application of the Poliankefu model in the calculation of the road width of our country. In an autonomous driving environment, the vehicle's running state will be more stable, and the speed change will be smoother. With the rapid development of the automobile industry, the driving stability of vehicles will be better and better. For autonomous vehicles, the driving pendulum caused by the drivers no longer exists, and the swing width of the vehicle will be effectively controlled. The lateral distance between parallel vehicles is reduced. The autonomous vehicle can sense the driving state of the surrounding vehicles in all directions.