# Optimal Design of an Ecofriendly Pickup Truck Overhang and Roof to Reduce the Drag Coefficient
## 3 Numerical Analysis  
### CAD Geometry of a Pickup Truck  
Figure 1 shows the overall geometry of the pickup truck used in this study. The pickup truck consisted of a cabin, bed floor, sidewalls, and tailgate. The scale was one-tenth that of an actual commercial vehicle. Unnecessary parts such as side-view mirrors were excluded from the modeling to investigate the flow characteristics of the roof and overhang length of the pickup truck, and the geometry was simplified as much as possible.  
The reason for specifying the parameters is that research on the drag coefficient of pickup trucks has mainly focused on the bed. In the case of electric pickup trucks, there is no need for an engine room, which increases freedom in the design of the cabin geometry. The parameters were chosen because the design of the cabin is mainly influenced by the overhang and roof. Six factors (\(L_{T},L_{O},L_{C},L_{F},\theta_{F}\), and \(\theta_{R}\)) were considered in this study. Four of these are related to the length, and two are related to the angle. Two factors (\(L_{T}\) and \(L_{O}\)) were used to analyze the flow characteristics of the total vehicle length and front overhang length. \(L_{T}\) represents the total vehicle length from the starting point of the engine room to the endpoint of the bed, including the tailgate. \(L_{O}\) is the front overhang length, which represents the distance from the starting point of the engine room to the center of the front wheel. Four factors (\(L_{C},L_{F},\theta_{F}\), and \(\theta_{R}\)) were used to analyze the flow characteristics of the pickup truck roof. \(L_{C}\) is the length from the starting point to the endpoint of the cabin roof. \(L_{F}\) is the distance from the starting point of the cabin roof to the position at which the angle changes. \(\theta_{F}\) is the front angle of the roof, and \(\theta_{R}\) is the rear angle of the roof. X is the distance from the front of the vehicle, and Y is the height from the bottom of the vehicle. This is used for non-dimensionalization. Table 2 lists the conditions for these six factors. All length-related conditions were dimensionless. Table 3 lists 54 cases obtained by combining the conditions in Table 2. Three cases with overlapping factors were excluded; therefore, the drag coefficient was derived for 51 cases.  
\begin{table}
\begin{tabular}{c c c c} \hline \(\frac{L_{O}}{L_{T}}\) & \(\frac{L_{F}}{L_{C}}\) & \(\theta_{F}\) & \(\theta_{R}\) \\ \hline
0.16 & 0.5 & 0\({}^{\circ}\) & 0\({}^{\circ}\) \\
0.13 & 0.66 & 3\({}^{\circ}\) & 5\({}^{\circ}\) \\
0.1 & 0.66 & 5\({}^{\circ}\) & 10\({}^{\circ}\) \\ \hline \end{tabular}
\end{table}
Table 2: Roof and overhang conditions used in this study.  
Figure 1: Schematic of pickup truck geometry. (**a**) Side view; (**b**) top view.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Case** & \(\frac{L_{\Omega}}{L_{T}}\) & \(\frac{L_{\epsilon}}{L_{\epsilon}}\) & **Front Angle** & **Rear Angle** \\  & \(\frac{L_{\epsilon}}{L_{T}}\) & \(\frac{L_{\epsilon}}{L_{\epsilon}}\) & **[Degree]** & **[Degree]** \\ \hline Base model & 0.16 & 0.5 & 0 & 0 \\
1-1 & 0.16 & 0.5 & 0 & 5 \\
1-2 & 0.16 & 0.5 & 0 & 10 \\
1-3 & 0.16 & 0.5 & 3  
To minimize the drag according to the front overhang and roof conditions of the pickup truck, the drag coefficient, which is the derived objective function, was defined as shown in (1). \(F_{D}\) is the drag force exerted on the pickup truck by the working fluid. The \(\rho\) is the density, and \(U_{\infty}\) is the freestream velocity of the working fluid. \(A\) is the projected area of the pickup truck in the main flow direction.  
\[C_{D}=\frac{F_{D}}{0.5\rho AU_{\infty}^{2}} \tag{1}\]