# Determination and Evaluation of a Three-Wheeled Tilting Vehicle Prototype's Dynamic Characteristics
## 2 Three-Wheeled Vehicle Description
### Theoretical Determination of Acceleration
The dimensions of the square-shaped test chamber are 0.5 \(\times\) 0.5 m and 1 m in length, with walls made of 2 mm high-quality clear polycarbonate and a bottom made of 5 mm organic glass. Two weight scales, mounted at the bottom of the test chamber, were used for measuring vehicle air resistance and the clamping force of the three-wheeled vehicle, which is expressed in units of weight (grams). The maximum measured weight of these scales is 0.3 kg, with an accuracy of \(\pm\)0.01 g. The chamber has a built-in air flow speed and temperature sensor. The diffuser is the part connecting the test chamber and the fan. Its shape varies from square to round (\(\mathcal{O}\)0.720 m). The air flow rate in the diffuser decreases, and the pressure increases. The speed in the diffuser must decrease in order to minimize the energy losses. Due to the minimal energy losses the maximum pressure being guaranteed. The blower fan is mounted at the end of the wind tunnel. Its impeller is rotated by an electric motor. The electric motor power is 1.8 kW, and it is controlled by a frequency converter with frequencies from 0 Hz to 70 Hz. The maximum generated airflow rate is approximately 22 m/s. The fan flow at 60 Hz is 19,000 m\({}^{3}\)/h, and the impeller speed is 1715 min\({}^{-1}\). During the experimental testing, the scaled-down (1:16) model of the three-wheeled tilting vehicle (Figure 4) was placed in the test chamber to identify the air resistance. During the tests, the data were recorded at 9 frequency values, with different, increasing fan speeds from 30 Hz to 70 Hz. During the tests, the air flow rate (m/s), temperature (\({}^{\circ}\)C), three-wheeled air resistance force (N), and clamping force (N) were recorded. For more accurate results, the experiments were repeated for 4 cycles. The obtained data are presented in Table 2.  
Figure 4: Three-wheeled tilting vehicle model in a wind tunnel. Figure 2:0 Wind tunnel. Using Formula (6), the drag coefficient (\(K\)) was calculated at different speeds in the wind tunnel: 50 Hz--0.0968; 55 Hz--0.100; 60 Hz--0.103; 65 Hz--0.106; 70 Hz--0.102. The average of the drag coefficient is 0.102, which was used for the following calculations. The dynamic characteristic of a vehicle is called the graphical dependence between the dynamic factor (\(D\)) and the speed (\(v_{a}\)) of the vehicle. The dynamic factor is calculated according to the formula:  
Figure 2:1  
The acceleration of the vehicle (m/s\({}^{2}\)) is calculated, assuming that the vehicle with the driver accelerates on a horizontal road (\(i\) = 0) with a hard asphalt-concrete surface (\(f\) = 0.016) in the absence of wheel slip, according to the formula:  
Figure 2:2  
where \(g\)--gravity acceleration, 9.81 m/s\({}^{2}\);  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cycle** & **Test Number** & **Hz** & **Wind Speed, m/s** & **Air Temperature, \({}^{\circ}\)C** & **Clamping Force, N** & **Air Resistance Force (\(F_{o}\)), N** \\ \hline \multirow{8}{*}{1} & 1 & 30 & 10.6 & 15.6 & 1.2 & 20.2 \\  & 2 & 35 & 11.9 & 15.6 & 6.8 & 27.1 \\  & 3 & 40 & 13.3 & 15.6 & 7.8 & 33. \(\delta\)--coefficient estimating the rotating masses of vehicle. Figure 2:3  
In our case, the internal combustion engine is changed in an electric motor, so we must use \(\delta=1\). All previous dynamic parameters are calculated according to Formulas (1)-(10) and are presented in Figure 2:4