## 2 Co-Simulation System
### TruckSim Model  
#### 2.1.1 The Road Model  
The establishment of the road model is based on the characteristics of typical high-grade highway longitudinal slope sections, determining the coordinates of the road centerline and the road width. The design criteria comply with the relevant provisions of the Chinese road standard \"Design Specification for Highway Alignment\" (hereinafter referred to as the \"Specification\") [31]. The road model simulates the environment of one-way travel on one side of a two-way, four-lane highway, with a lane width of 3.75 m and a total length of 3.1 km for the section. Asphal is commonly used for road surfaces on Chinese highways; thus, the road surface material is set to asphalt, with a friction coefficient of 0.6. The longitudinal profile consists of straight lines (uniform slope lines or straight slope sections) and vertical curves, as shown in Figure 1. When the vehicle's front axle passes the starting point of a vertical curve, the vehicle has already started climbing. Ignoring the vehicle operation within the vertical curve segment before the slope may lead to an overestimation of the vehicle's predicted speed. Therefore, the investigation of the road's longitudinal slope grade suitable for the climbing ability of pure electric heavy-duty vehicles and its corresponding maximum longitudinal slope length should commence from the starting point of the vertical curve. Considering the visual characteristics of road users and driving comfort, the experimental road adopts a combination of straight horizontal alignments and sag vertical curves in the longitudinal profile. Regarding the sag vertical curves, to ensure the authenticity of the experimental results and to align with the design practices of industry professionals, the lengths of the sag vertical curves are set to the normal value specified in the \"Specification\" for roads of different design speeds, as shown in Table 1.  
The text simulates a one-way travel environment on one side of a two-way, four-lane highway. Therefore, the sag vertical curve profile adopts the commonly used parabolic curve profile for high-grade roads, as shown in Equation (1):  
\[y=\frac{x^{2}}{2R} \tag{1}\]  
In the equation, \(x\) is the horizontal distance from any point on the vertical curve to the starting point of the curve measured in meters. \(R\) is the radius of the sag vertical curve measured in meters. Under the constraint of controlling the length of the vertical curve, the coordinates of the intersection point between the vertical curve and the uphill road segment, as well as the radius \(R\) of the vertical curve, are obtained, as shown in Equation (2):  
\[\frac{x}{R}=i_{p} \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **120** & **Design Speed (km/h)** & \\
**Normal value of minimum radius of crest vertical curve (m)** & 17,000 & 10,000 & 4500 \\ Normal value of minimum radius of sag vertical curve (m) & 6000 & 4500 & 3000 \\ Normal value of length of vertical curve (m) & 250 & 210 & 170 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Minimum radius and length of vertical curve [31]. Figure 1: Road model. (**a**) Profile view; (**b**) actual effect. In the equation, \(i_{p}\) represents the slope gradient of the experimental road measured as a percentage. According to Equation (1), we can calculate the coordinates of points on the vertical curve. When the design speeds of the experimental road are 120, 100, and 80 km/h and the longitudinal slope gradient of the vertical curve is 3%, the arrangement of the vertical curves is as it is shown in Figure 2.  
According to the \"Specification\" regarding the maximum grade values for roads with different design speeds, we grouped roads with various design speeds and established road models for experimentation.