*3.2. Electric Motor*

Electric motors used in eVTOL applications are primarily of two types: brushed DC motors (BDC) and brushless DC motors (BLDC). BLDC motors, known for their low resistance and high efficiency, are commonly used in heavyweight multicopters. They can be further categorized into two types: outrunner (OR) and inrunner (IR), based on the rotating part of the motor. Presently, OR BLDC motors are considered a preferable choice over IR motors. OR motors have lower Kv (rpm/V) values compared to other types of BLDC motors. This means they operate at lower rotational speeds but generate higher torque, which allows for direct propeller coupling (no gearbox) [24]. *Kv* (rpm/V) is the speed constant, which will determine the rotation speed of the electric motor when no-load and stable voltage is supplied. This is an important element for choosing a motor that is compatible with the power supply and propellers to achieve the required speed. In Figure 6, *Um* (V) is the supply voltage, *Im* (A) is the current absorbed by the motor coils, *Rm* (Ω) is the motor equivalent resistance, *Te* (Nm) is the electromotive torque produced by the motor, and *N* (rpm) is the shaft angular velocity. The equations describing the motor electric model are [19,24]:

$$\begin{cases} \mathcal{U}\_{\rm{m}} = \mathcal{e}\_{\rm{a}} + \mathcal{R}\_{\rm{m}} \cdot I\_{\rm{m}}, \\ T\_{\rm{c}} = \mathcal{K}\_{T} \cdot I\_{\rm{m}}, \\ E\_{\rm{a}} = \mathcal{K}\_{E} \cdot \mathcal{N} \approx \frac{\mathcal{N}}{\mathcal{K}\_{\rm{v}}}, \end{cases} \tag{6}$$

where *KE* (Vs/rad) represents the motor back EMF constant, *KT* (Nm/A) is the motor torque constant, and *N* is the motor rpm. *KT* and *KE* are related to *Kv* by

$$K\_E = \frac{1}{K\_v} = \frac{\pi}{30} \cdot K\_T.\tag{7}$$

The motor output torque and the propeller torque are related by

$$M = T\_{\mathfrak{e}} - T\_{\mathbb{O}} = K\_T \cdot (I\_m - I\_{m0}).\tag{8}$$

If the no-load current *Im*<sup>0</sup> is neglected, the propeller torque in this case is controlled uniquely by the motor load current. From Equations (1) to (4), the supply voltage *Um* and the motor current *Im* are given as follows:

$$\begin{cases} I\_m = \frac{\pi}{50 \cdot K\_v} \cdot M + I\_{m0\_V} \\ \mathcal{U}\_m = I\_m \cdot R\_m + \frac{N}{K\_v} . \end{cases} \tag{9}$$

**Figure 6.** BLDC motor electric model.

The mass regression model of the electric motor is given in Figure 7b. The motor data used in this model were collected from T-motor and KDEDirect [25]. The model input is the motor speed constant *Kv*, which is defined in the motor parameters database Equation (10) presents the regression model of the motor mass:

$$M\_{mo} = 0.00048K\_v^2 - 1.461K\_v + 840.617.\tag{10}$$

#### *3.3. Electronic Speed Controller*

The electronic speed controller (ESC) is an external device responsible for regulating the motor speed within a specific range based on the load and battery voltage. It converts the DC voltage from the battery pack into a three-phase alternating signal that is synchronized with the rotation of the rotor and applied to the armature windings. In the developed sizing methodology, the electric model of the ESC is not directly involved. However, it is essential to fix the maximum continuous current *Iemax* of the ESC, particularly during the selection and mass estimation steps [24,26]. Figure 7c presents the mass regression model of the ESC base on supplier data (collected from T-motor and KDEDirect). Equation (11) presents the regression model of the ESC mass:

$$M\_{ESC} = 0.016 I\_{cmax}^2 - 0.638 I\_{cmax} + 42.414.\tag{11}$$
