# Hybrid Power System Design for Multifunctional Mini-Loader Vehicles
## 2 Materials and Methods
### Design of the Hybrid Power System
#### 2.2.1 Design of the Drive Specifications  
In addition to the start, acceleration, deceleration, stop, and climbing changes during the normal road driving process, different road surfaces and loads are considered for the vehicle. When designing, the weight can be divided into unloaded and fully loaded weights. The unloaded weight indicates the weight of general mini agricultural tractors of 270 kg, and the fully-loaded weight is the total weight that includes the hydraulic cylinder system along with the tool module, set to 470 kg. For the design of the vehicle moving speed, in this study, the average adult walking speed of 3.75-5.34 km/h is considered, with the maximum speed being set to 4 km/h. To ensure that the vehicle can operate in different conditions, the drive system design is determined by calculating the maximum power required by the vehicle, as shown in Equation (1) [24]:  
\[\mathrm{P}\geq\frac{1}{\eta_{r}}\bigg{(}\frac{mg_{f}r}{3600}V_{max}+\frac{C_{d }A}{76140}V_{max}{}^{3}\bigg{)}. \tag{1}\]  
Figure 1: Belt-starter generator structure.  
Figure 2: Hybrid power system design.  
In Equation (1), drive force p in the left side is the power consumption to overcome the resistance and the right side refers to the conditions of pure electric vehicles. Under good road conditions, pure electric vehicles can drive at its highest speed, thus the required power should not be less than the sum of kinetic energy of automobile and all the resistance. \(f_{r}\) is the drag coefficient corresponding to the ground deformation, \(V_{max}\) is the maximum driving speed, and \(\eta_{r}\) is the transmission coefficient. Because the maximum travel speed of this study is set to slow, the wind resistance is omitted. The equation is simplified as  
\[\text{p}\geq\frac{1}{\eta_{r}}\frac{mgf_{r}}{3600}V_{max}. \tag{2}\]  
The weight of the vehicle is 720 kg when considered to be driving fully loaded on a normal road surface. The transmission efficiency of the tracked vehicle is 0.89, and the track-to-ground resistance coefficient is 0.15; the fully loaded maximum speed is set to 3 km/h, and then the values of m \(=720\) kg, \(f_{r}=0.15,\ \eta_{r}=0.89,\ \text{and}\ V_{max}=3\) km/\(h\) are substituted into Equation (2) to obtain the following:  
\[\text{p}\geq 0.99\text{ kw}.\]  
The power consumption when the vehicle climbs a slope at a certain speed is shown in Equation (3):  
\[\text{p}\geq\frac{1}{\eta_{r}}\bigg{(}\frac{mgf_{r}\cos\alpha}{3600}V_{max}+ \frac{mg\sin\alpha}{3600}V_{max}+\frac{C_{d}A}{76140}V_{max}{}^{3}\bigg{)}. \tag{3}\]  
Because the speed is slow, the power consumption by wind resistance in Equation (3) can be omitted, and the formula is simplified as  
\[\text{p}\geq\frac{1}{\eta_{r}}\bigg{(}\frac{mgf_{r}\cos\alpha}{3600}V_{max}+ \frac{mg\sin\alpha}{3600}V_{max}\bigg{)}. \tag{4}\]  
Assuming a 30% slope is climbed fully loaded, to enhance safety, the maximum speed is reduced to 2.5 km/\(h\), and then substituting m \(=720\) kg, \(f_{r}=0.15,\ \eta_{r}=0.89\), and \(V_{max}=2.5\) km/\(h\) into Equation (4), p is obtained as follows:  
\[\text{p}\geq 3.47\text{ kw}.\]  
This value shows that the power required to travel on flat grounds is greater than 0.99 kw, and the power required to climb slopes is greater than 3.47 kW. To ensure that the vehicle can be used in various conditions, the drive system of this study needs to be greater than 3.5 kW. The design specifications and performance index of the entire vehicle are listed in Table 1.