# Analysis and Assessment of a Brushless DC Outrunner Motor for Agriculture Drones Using JMAG
## 4 Results and Discussion  
### Efficiency and Autonomy  
Efficiency maps (EMs) are contour plots used to relate torque, speed, and efficiency in electric machine applications. EMs allow for the evaluation of design choices taken throughout motor development and represent a powerful tool with which to assess electric machines' performance in specific load cases. However, in order to obtain accurate EM results, motor loss components should be considered [22]. Out of the various components, the joule and core losses represent the highest power dissipation in electric machines on electrical vehicle applications. The core loss frequency-based approach in JMAG allows for accurate results [22], while the Finite Element Analysis (FEA) technique permits individual part loss analysis. Additionally, windage and friction losses (mechanical loss) can be considered in the efficiency map computation. A reduced efficiency map for the U12 II motor is shown in Figure 22, where the maximum efficiency reaches 79.3% for the specified operating range. The total losses, excluding converter contributions, are reported in Figure 23.  
Iron losses are highly dependent on source frequency, flux density, and core characteristics [22]. And they represent the highest loss contribution (Figure 24). On the other hand, copper losses directly relate to winding current, motor torque, and speed, becoming significant in high-torque low-speed applications (Figure 25). Velocity effects dominate in mechanical loss contributions; in assuming a 6 W/k rpm mechanical loss [23], the low-speed characteristics of UAV agriculture applications account for up to 10.69% of the total losses (Figure 26). \begin{table}
\begin{tabular}{l c c c} \hline
**Variable** & **JMAG** & **Experimental** & **Error** \\ \hline Phase current & 18.707 A & 18.8 A & 0.49\% \\ Line voltage & 23.08 V & 22.1 V & 4.43\% \\ \hline \end{tabular}
\end{table} 
Table 11: Quantitative comparison: JMAG and experimental driving signals for 40% throttle. Figure 21: Driving signals for 40% throttle from JMAG. (**a**) Phase currents from JMAG. (**b**) Line voltages from JMAG. Figure 23: Total losses for the expected velocity range. Figure 24: Iron losses for the expected velocity range. Figure 22: Reduced motor efficiency map obtained for the expected velocity range. For a battery with a 40 percent minimum reserve capacity, assuming a linear consumption behavior and hover conditions, Equation (10) from [24] can be used to obtain the battery capacity and minimum C-rate. \[Cp_{battery}=\frac{Time_{flight}\times I_{hover}}{36} \tag{10}\]  
and  
\[K_{p}=\frac{I_{total}}{Cp_{battery}} \tag{11}\]  
where \(Cp_{battery}\) is the battery capacity in Ah; \(Time_{flight}\), the flight time in minutes; \(I_{hover}\), the hover current; and \(K_{p}\), the minimum C-rate. Through the use of the design requirements and values obtained in the electromagnetic analysis, the battery chosen was the Tattu 28 Ah 14 SP1, with a continuous C-rate of 6.07 and burst C-rate of 7.85. For the chosen battery, the overall propeller-motor efficiency can be related with autonomy as  
\[Droneautonomy\ (minutes)=\frac{36\times E_{battery}}{Weight_{Total}}\underbrace{ \times\frac{Thrust}{Power_{Mechanical}}\times\eta_{BLDC}}_{\text{Propeller-motor efficiency}} \tag{12}\]  
Figure 26: Mechanical losses for the expected velocity range. Figure 25: Copper losses for the expected velocity range. where \(E_{buttery}\), \(Weight_{Total}\), and \(\eta_{BLDC}\) are the power of the battery, the total mass of the UAV in grams, and the motor efficiency, respectively. With the data obtained from Figure 7, to have a 12-min flight time, the motor efficiency should be above 75%. From Figure 22, it is clear that for a vehicle mostly in hover mode, the U12 II KV120 motor will suffice. Agriculture UAV applications set the starting torque in a medium-duty range category using large inertia loads [25].