# Research on Geometric Design Standards for Freeways under a Fully Autonomous Driving Environment
## 4 Geometric Design Standard
### Vertical Alignment
#### 4.2.1 Transition Slope
Figure 8: Blind area of convex vertical curve. Figure 9: The autonomous vehicles of different brands. (**a**) Uber autonomous vehicle. (**b**) Hong Qi autonomous vehicle. In the age of autonomous driving, autonomous vehicle eyes were replaced by LiDAR sensors. When calculating the minimum length of a convex vertical curve on an autonomous driving road [10], the autonomous vehicle is considered to be the same height as a 1.555 m tall SMART car. The height of the LiDAR is 0.283 m, so the visual height of the autonomous vehicle is 1.838 m. Google's autonomous driving project tested LiDAR on Toyota and Lexus RX450H autonomous vehicles, which were 1.470 m and 1.685 m [24]. [PERSON] [28] used the visual height of 2.27 m (vehicle height is 1.685 m, the height of radar sensor is 0.284 m, and the support height of the sensor is 0.3 m.) for the Lexus RX450h (SUV) and 1.84 m (vehicle height is 1.555 m, the height of radar sensor is 0.284 m, and the support height of sensor is not considered) for the Waymo autonomous vehicle when calculating the minimum length of a convex vertical curve. Autonomous driving passenger cars will be larger and taller than SMART cars, as will autonomous driving SUVs, trucks, and buses. The higher the visual height of vehicles, the lesser need for the length of the vertical curve. Taking the above factors into consideration, scholar [PERSON] conservatively takes the visual height of autonomous vehicles as 1.7 m.  
According to the above research, considering continuous development of technology and optimal design of sensors, the sensor height is chosen as 0.25 m. Normal passenger cars are typically less than 1.55 m tall, and SUVs are about 1.80 m tall. Due to the tolerance of safety, the height of the autonomous vehicle is rounded to 1.60 m from 1.55 m. Therefore, the visual height \(h_{1}\) of the autonomous driving passenger car is the sum of the above two heights, which is taken as 1.85 m (vehicle height 1.60 m and sensor height 0.25 m). In Formula (6), \(h_{2}\) is the height of the obstacle. The minimum height of the car chassis from the ground is 0.14-0.2 m [3]. On the one hand, autonomous vehicles are much better than drivers at recognizing road conditions. On the other hand, very small obstacles can cause a vehicle to lose control in a high-speed environment. Referring to Chinese standards, the obstacle height is still taken as 0.1 m in this paper. In Formula (6), \(S_{T}\) is the stopping sight distance. This paper adopts the recommended stopping sight distance based on automatic driving technology in Section 3.3. * Meet the impact mitigation requirements  
When an autonomous driving car travels at a high speed on a vertical curve, it can become overweight or weightless. When the phenomenon of becoming overweight or weightlessness reaches a certain degree, passengers will have uncomfortable psychological and physiological reactions. It will also bring adverse effects on the car's suspension system. Accordingly, in the autonomous driving environment, it is recommended to continue to apply the minimum radius value of the vertical curve in current specifications that considers alleviating impact, as shown in Formula (8):  
\[R_{\min}=\frac{V^{2}}{3.6}\;\text{or}L_{\min}=\frac{V^{2}}{3.6}\cdot\omega \tag{8}\]  
where \(R_{\min}\) is the minimum radius of the vertical curve (m); \(L_{\min}\) is the minimum length of the vertical curve (m); \(V\) is the design speed (km/h); \(\omega\) is the algebraic gradient difference between adjacent straight sections. * Meet the requirements of travel time  
In traditional manual driving environment, when the length of the vertical curve is very short, if the car is driving at a high speed through this section of the road, the driver is prone to the illusion of a large slope, and passengers will also feel uncomfortable. In an autonomous driving environment, although there is no driver's visual illusion, passengers will still feel uncomfortable.