3.4.1. Battery

Due to the high energy density and discharge rate, eVTOL aerial vehicles use lithium polymer (LiPo) batteries. A LiPo pack consists of identical LiPo cells, each with a nominal voltage of 3.7 V and power density of *ρ<sup>b</sup>* = 140 (Wh/kg) [24,27]. The parallel connection of battery packs raises the battery's total capacity while keeping the nominal total voltage the same. The nominal voltage of a LiPo battery is:

$$
\Omega I\_b = 3.7 n\_{\odot} \tag{12}
$$

where *nc* is the number of cells connected in series in the battery pack. Each cell has a capacity *Ccs*. The total battery capacity is

$$\mathbb{C}\_b = n\_p \cdot \mathbb{C}\_{cs} \tag{13}$$

where *np* is the number of battery packs connected in parallel. As we can see from Figure 5, the motor power *Pm* is converted by the ESC and supplied by the battery. The battery output power *Pb* can be estimated by

$$P\_b = N\_m \cdot \frac{P\_m}{\eta\_c \cdot \eta\_b} \, \tag{14}$$

where *Nm*, *ηe*, and *η<sup>b</sup>* are, respectively, the propulsion chain number, the conversion efficiency of ESC, and the battery efficiency. An oversizing of the battery is taken into account the drop in battery capacity with the discharge time, utilizing the battery efficiency. A value of *η<sup>b</sup>* = 0.75 is considered suitable for battery sizing, as reported in [24].

The flight time *tflight* (min) of the eVTOL aerial vehicle, which is equivalent to the battery discharge time, is given by

$$t\_{f\text{light}} = \frac{60 \cdot \rho\_b \cdot m\_b}{N\_{\text{m}} \cdot P\_{\text{m}}} \cdot \eta\_{\varepsilon} \cdot \eta\_{b\text{\textdegree}} \tag{15}$$

where *ρ<sup>b</sup>* and *mb* are, respectively, the battery power density (Wh/kg) and the battery mass (kg). Thus, for a given embedded LiPo battery mass *mb*, and a load, an equivalent flight time is determined. Once the battery mass *mb* (kg) is located with an objective to maximize the flight time with the *GTOW* constraint, the battery capacity *Cb* (mAh) is computed using the following equation:

$$\mathbb{C}\_{b} = \frac{\rho\_{b} \cdot m\_{b}}{\mathcal{U}\_{b}}.\tag{16}$$
