# Determination and Evaluation of a Three-Wheeled Tilting Vehicle Prototype's Dynamic Characteristics
## 2 Three-Wheeled Vehicle Description
### Theoretical Determination of Acceleration  
The goal of this paper is to obtain theoretical acceleration results and verify them with experimental results using the prototype model MVP, which was built by the AKO team. According to this information, parameters for the electric motor and battery control module are chosen to optimize the three-wheeled tilting vehicle's dynamic characteristics. The first step is to acquire parameters of the electric motor (HPM-2000) (power and torque) using manufacturers' data (Figure 2) and three-wheeled tilting vehicle characteristics (body dimensions, weight, etc.) (Table 1). The battery consists of two series-connected LG Electronics LiMM-C.F/LGE (Model Name: Vista 2.0 Cell Module Assembly) modules with a rated energy capacity of 5.94 KW h and a rated voltage of 36 V each. The motor controller and other used parts and their solutions, as well as their parameters, are not presented by the AKO team in terms of a unique construction. For the theoretical determination of acceleration, a classical methodology presented by [PERSON] [39] was used. The three-wheeled tilting vehicle speed is calculated as follows:  
\[v_{a}=\frac{w_{e}\cdot r_{r}}{i_{pp}}; \tag{1}\]  
where \(w_{e}\)--engine rotations, rad/s;  
\(r_{r}\)--radius of rotating wheel, m.  
\(i_{pp}\)--gear ratio. \begin{table}
\begin{tabular}{c c c c} \hline
**Nr.** & **Parameter** & **Symbol** & **Dimension** & **Value** \\ \hline
**1.** & Gear ratio & \(i_{\text{PP}}\) & - & 4.365 \\
**2.** & Transmission efficiency coefficient & \(\eta_{tr}\) & - & 0.93 \\
**3.** & Three-wheeled tilting vehicle mass with driver & \(G_{a}\) & kg & 486 \\
**3.1.** & Mass to drive axle & \(G_{2}\) & kg & 212 \\
**4.** & Three-wheeled vehicle mass without driver & \(G_{0}\) & kg & 406 \\
**4.1.** & Mass to drive axle & \(G_{02}\) & kg & 177 \\
**5.** & Front axle wheel base & \(B_{a}\) & m & 0.892 \\
**6.** & Height & \(H_{a}\) & m & 1.6 \\
**7.** & Wheels dimensions & \(B\)–\(d\) & - & R17 170/60 \\ \hline \end{tabular}
\end{table} 
Table 1: Three-wheeled vehicle characteristics. Figure 2: Electric motor HPM-2000 power and torque parameters [38]. In our case, the radius of rotating wheel (\(r_{r}\)) is 0.2579 m and tire deformation coefficient \(\lambda\) = 0.93. The traction force of the three-wheeled vehicle is calculated as follows (N):  
\[F_{r}=\frac{M_{e}\cdot i_{pp}\cdot i_{pd}\cdot\eta_{tr}}{r_{r}}; \tag{2}\]  
where \(M_{e}\)--engine torque, Nm;  
\(i_{pd}\)--transmission gear ratio (\(i_{pd}\) = 1);  
\(\eta_{tr}\)--transmission efficiency coefficient. The radius of rotating wheel diameter is calculated (\(r_{r}\) = 0.2579). The equation of traction balance is as follows:  
\[F_{r}=F_{f}\pm F_{i}+F_{o}+F_{j}; \tag{3}\]  
where \(F_{f}\)--rolling resistance force, N;  
\(F_{i}\)--uphill resistance force, N;  
\(F_{o}\)--air resistance force, N;  
\(F_{f}\)--acceleration resistance force, N.  
If we are analyzing a case in which the three-wheeled tilting vehicle moves at a constant speed on a horizontal surface, then the equation of the traction balance is:  
\[F_{r}=F_{f}+F_{o}; \tag{4}\]  
Rolling resistance force:  
\[F_{f}=G_{a}\cdot f; \tag{5}\]  
where \(f\)--rolling resistance coefficient depending on the road surface. In our case, a hard asphalt-concrete surface was chosen (\(f\) = 0.016). Air resistance force:  
\[F_{o}=K\cdot S\cdot V_{a}^{2}; \tag{6}\]  
where \(K\)--drag coefficient;  
\(S\)--front part surface area, m\({}^{2}\). Front parts' surface area:  
\[S=0.6\cdot B_{a}\cdot H_{a}; \tag{7}\]  
where \(B_{a}\)--front axle wheel base, m;  
\(H_{a}\)--height, m.  
The drag coefficient is usually determined by vehicle producers, but in this case, the design is created by an AKO team, and coefficient (\(K\)) should be determined experimentally. For this solution wind tunnel were used (Figure 3). The test chamber is the most important part of the wind tunnel.