**1. Introduction**

The eVTOL concept represents one of the potential solutions to remedy the traffic congestion problem in big cities across the world. In the case of French metropolitan cities, such as Paris and Marseille, an average commuter loses over 80 h every year in traffic, resulting in increased stress and anxiety (R1). Such congestion also leads to 1.85 megatons per year of CO2 emissions into the atmosphere. In addition to having a detrimental impact on the health of commuters and the environment, it also contributes to economic loss. Therefore, it is imperative to explore new modes of transportation to facilitate faster daily commutes for passengers in urban areas and reduce traffic congestion. Several aircraft manufacturers, such as Airbus, Boeing, Lilium, and Volocopter, have actively embarked on the development of this drone taxi technology in recent years [1–5]. In addition to Uber, which estimates the launch of its air taxis (called Uber Elevate) in 2023, other companies,

**Citation:** Chahba, S.; Sehab, R.; Morel, C.; Krebs, G.; Akrad, A. Fast Sizing Methodology and Assessment of Energy Storage Configuration on the Flight Time of a Multirotor Aerial Vehicle. *Aerospace* **2023**, *10*, 425. https://doi.org/10.3390/ aerospace10050425

Academic Editors: Andreas Strohmayer, Spiros Pantelakis and Jordi Pons-Prats

Received: 28 February 2023 Revised: 27 April 2023 Accepted: 28 April 2023 Published: 30 April 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

such as Zephyr Airworks and Airbus, are also currently taking measures to conduct tests with their electric aviation taxis. Zephyr Airworks has developed Cora, while Airbus has developed Airbus Vahana. These companies are conducting tests in various countries across the world, including the USA, Japan, Singapore, New Zealand, France, and India.

eVTOL aircraft fit into four main categories: lift plus cruise, tilt rotor, ducted vector thrust, and multicopter (Figure 1). The first three categories fall under the powered lift aircraft classification, which includes winged aircraft that are capable of both VTOL and aerodynamic lifts during forward flights. The fourth category belongs to wingless aircraft, specifically multirotor aircraft with two or more lift/thrust units that have limited or no capability for wingborne forward flights. Powered lift eVTOLs can be further categorized based on whether they use a common power plant (tilt-rotor and ducted vector thrust) or an independent power plant (lift plus cruise) for both lifting and forward flights [6–8].

**Figure 1.** eVTOL propulsion configuration.

These categories are defined and characterized as follows [9,10]:


design of a more optimized propeller compared to a lift and cruise aircraft configuration. However, it comes with the trade-off of higher technical complexity and larger overall size and weight due to the inclusion of tilt and variable pitch mechanisms. Joby S4 is an example of this category; it is developed by Joby Aviation (Figure 2d) and is supposed to be commercialized by 2024 [12,13].

**Figure 2.** eVTOL categories.

As reported in [10], one of the main drawbacks of the multirotor configurations is the lack of wings, which limits their performances in long cruise flight missions. However, in the UAM mode, where the cruise phase durations are limited in comparison with extra-urban mobility, the multirotor configuration remains the best efficient solution to this transport market [10]. In this context, the Volocopter VC2X configuration, which is a non-coaxial, direct-lift one, presented in Figure 2b, will be tested in Paris, France, in 2024 [14]. Thus, the rest of the paper will focus on the multirotor wingless configuration.

One of the main steps in the eVTOL design process is to size and select the components of the propulsion system to meet the required specifications. To facilitate the assessment of proposed solutions, the development of precise and efficient sizing methodologies for the electric propulsion chain is necessary. The propulsion chain typically consists of a propeller for generating lift, a BLDC electric motor for energy conversion, an electronic speed controller (ESC) that supplies the required current to the load from the energy source, and a battery for energy storage. Multirotor design methods have been developed by Barshefsky et al. [15], Dai et al. [16], et Gur et al. [17]. In [15], the authors present a methodology that involves parameterizing the components of the propulsion chain to establish relationships between them. These relationships are then optimized to meet the specific requirements of the flight mission. In reference [16], an analytical method is proposed to estimate the optimal parameters of the propulsion system components. The approach involves modeling each component mathematically and then simplifying and decoupling the problem into smaller subproblems. By solving these subproblems, the optimal parameters for each component can be obtained. Moreover, selection algorithms are proposed based on these obtained parameters to determine the optimal combination of the propeller, motor, ESC, and battery products from their respective databases. Methodologies based on statistical data available from manufacturers for preliminary design are reported in

references in [17–19]. For example, reference [17] presents a multi-disciplinary optimization (MDO) approach for designing a propulsion system based on goals such as rate of climb and loiter time. It also provides a useful modeling analysis of motors and batteries. Moreover, a sensitivity analysis is conducted on certain propeller design elements.

In this study, on the one hand, a methodology for sizing and selecting the propulsion chain components was developed. This approach combines statistical methods based on data and analytical optimization techniques, allowing to maintain an acceptable level of precision and avoid increasing the calculation algorithm complexity. The technique of optimization is used for the optimal selection of the pair motor/propeller, based on the maximization of the specific efficiency. This optimization makes it possible to select the remaining components, namely the ESC and the energy storage system. The statistical methods are considered for the multirotor aerial vehicle *GTOW* evaluation, using the regression model for each component, based on supplier data. On the other hand, five energy storage configurations are considered, in order to evaluate their effect on the multirotor aerial vehicle performance, in particular on the flight time. These configurations are the lithium polymer battery (battery), hydrogen fuel cell (HFC), battery/hydrogen fuel cell (Bat/HFC), battery/supercapacitor (Bat/SC), and battery/supercapacitor/hydrogen fuel cell (Bat/SC/HFC). The five energy sources were sized to maximize the flight time and keep the gross take-off weight (*GTOW*) as low as possible.

This article is organized as follows. Section 2 presents the sizing methodology flowchart, including the optimization technique used to select the optimal motor/propeller pair and the remaining components of the propulsion chain. Section 3 presents the modeling of the propulsion chain components to formulate the optimization problem and maximize the efficiency of the motor/propeller pair. Section 4 is devoted to the formulation of the motor/propeller pair optimization problem. Section 5 presents the case study for the sizing approach validation, using a reduced-scale multirotor drone with a *GTOW* of 15 kg available in our laboratory. Section 6 presents the comparative study of the energy source configuration effect on the flight time, including the *GTOW* evaluation based on the regression model of each component. In Section 7, the conclusion is presented.

#### **2. Sizing Methodology**

The sizing methodology is based on a combination of analytical optimization techniques and data-based techniques. It takes the following input data: the required flight time, a database of electric motor parameters, including the voltage (*Um*), load current (*Im*), internal resistance (*Rm*), and speed constant (*Kv*) for *n* examples (at this stage, the optimal motor is not known), atmospheric conditions defining the altitude, temperature, and air density, and the initial gross take-off weight (*GTOW*). Subsequently, a global non-linear optimization is performed for each motor/propeller pair using the simulated annealing algorithm (SAA). The objective of this optimization is to maximize the pair motor/propeller efficiency, also known as specific efficiency *ηMP*(*N*/*W*). This efficiency index is widely used by industrial manufacturers, such as T-motor and Mejzlik [20,21] to measure the efficiency between the motor and the propeller. Constraints are applied to the propeller geometry, specifically the diameter (*Dp*) and the pitch angle *ϕp*. The optimized motor/propeller pair obtained from the optimization allows for checking the condition to avoid motor overheating, as stated in Equation (32). Subsequently, the maximum thrust *TMPmax* generated by the optimized motor/propeller pair was computed using Equation (34). By utilizing the maximum thrust *Tmax* imposed by *GTOW* as indicated in Equation (35), a filtering condition was established based on the relative error between *TMPmax* and *Tmax*, as shown in Equation (36). This filtering condition allows for an initial selection of the motor/propeller pairs. Subsequently, the selection of the optimal motor/propeller pair was determined based on the maximum specific efficiency achieved. The sizing of the energy sources was then performed to maximize the flight time. Finally, the last step of this sizing methodology involved verifying whether the total take-off mass, obtained using statistical mass models for each component of the propulsion chain based on supplier data, was within acceptable

limits. A detailed flowchart of this sizing methodology is provided in Figure 3. The specific efficiency maximization allows making a rapid and precise choice for each component in the propulsion chain. Figure 4 presents an overview of the different steps, based on which, the electric propulsion chain sizing is performed. The fact that the validation step was based on a reduced-scale multirotor drone with a *GTOW* of 15 kg explains the choice of the data scale used for the optimization of input data motors and regression models.

It is remarkable that in the developed sizing methodology, we do not consider a flight power mission in order to size the propulsion chain. However, in order to obtain a pair motor/propeller that can satisfy the take-off and cruise segment mission, the sizing methodology takes into consideration two constraints. The first one is related to the speed of rotation and the torque of the propeller reported in Equation (32). Through this constraint, the obtained motor/propeller pair is able to satisfy the cruise phase while avoiding motor overheating. The second constraint is the filter condition given in Equation (37). Through this constraint, the motor/propeller pair is able to succeed in the take-off phase.

**Figure 3.** Sizing approach for the eVTOL multirotor flowchart.

**Figure 4.** Overview of the sizing methodology steps.
