Comparative Study of Hybrid Electric Distributed Propulsion Aircraft Through Multiple Powertrain Component Modeling Approaches

Abstract

Aircraft design is an ever-expanding field of research. Disruptive aircraft architectures and the long-standing need for fast design processes are the main drivers behind the domain growth. Novel concepts like distributed propulsion, Vertical Take-Off and Landing, electrification, hybridization, etc., require new models and design strategies to achieve a significant degree of fidelity at every stage of the design. This paper proposes a framework targeting key techniques and assumptions to improve the accuracy of the preliminary aircraft design stage. Based on a review of modern design strategies, a model-based method has been developed. Two distinct approaches to component modeling have been compared for a hybrid-electric distributed propulsion aircraft. To complement this comparative study, the second modeling approach has been tested for three different hybrid electric architectures. The results showcase the feasibility of the three architectures, with promising results for the hydrogen powertrain system.

1. Introduction

In recent years, a notable rise in public and governmental awareness toward the environmental crisis has been occurring. Therefore, authorities supported by researchers have been building schemes to reduce the transportation sector’s contribution to climate change. In aeronautics, the coordination of the environmental targets is shared between international organizations, such as the ICAO, while the technology developments are driven by research organizations and private companies. In 2016, a historic agreement by the ICAO [1] led to the introduction of specific standards and targets for ${\mathrm{CO}}_2$ emissions in the aviation industry. Research and industrial sectors promptly reacted with the launch of new or renewed aircraft concepts.

Driven by this need, aeronautic partakers strive to answer the following question: how can we produce more efficient aircraft? To answer this question, the life cycle of the aircraft must be carefully studied and considered. Such an endeavor takes aircraft manufacturers several years and thousands of people. Therefore, researchers tend to investigate specific domains such as aircraft operations, end of life, or design stage. The latter has been a research and engineering topic for a long time. The introduction of Computer-Aided Design (CAD) into aircraft designer practices has led to the build-up of processes and methods based on physics, know-how and historical data. Several authors [2,3,4,5,6] have spent a considerable amount of time and effort compiling and harmonizing these results into largely accepted methods and models. From these works sprung the conventional three-step aircraft design: conceptual, preliminary, and detailed design. During the conceptual and preliminary design stage, empirical or semi-empirical models are used. However, these models are not applicable to aircraft concepts far from the state of the art. To solve this issue, researchers tend to develop high-fidelity models of the new concepts. Surrogate models are resulting from these studies and then grafted to early design procedures. Such procedures have already been developed for aerodynamic purposes [7]. However, as de Vries [8] pointed out, the considerations around the powertrain design are currently too restricted.

The research work presented hereafter accounts for these considerations. The objectives of the study are the following:

• Quantifying the influence of the new powertrain design assumptions compared with the current ones.
• Studying the feasibility of several powertrain architectures using new powertrain design assumptions.
• Refining the aircraft hybrid powertrain architecture during the preliminary design stage.

The concept of Distributed Hybrid Electric Propulsion (DHEP) will be developed for a general aviation aircraft in this study. It is the authors’ belief that faster-paced design in general aviation will benefit commercial aviation. Ideas and innovations can be tested on a smaller scale with lighter regulations and then translated to commercial aviation aircraft. In the case of general aviation, DHEP concept is made viable by the hybrid powertrain flexibility and its components’ compactness [9]. The study is split into four sections. The Section 1 introduces the aircraft and powertrain concepts. The Section 2 presents the method, models and key assumptions made during the study. The Section 3 highlights two sets of results. The first set of results compares two component modeling approaches. The second set of results showcases a trade-off study on three powertrain architectures. The Section 4 concludes with the study limitations and further work.

2. Aircraft Concept

The requirement for the aircraft concept proposed hereafter where set by the partnering aircraft manufacturer. The objective was to develop a CS23 [10] aircraft for nine passengers and a pilot. Following such regulations, the aircraft’s Maximum Take-Off Mass (MTOM) could not exceed 8618 kg. Considering a certification basis, like the CS23, during preliminary design is mandatory to be able to certify the aircraft produced. However, as DHEP concepts are rather peculiar, the authors would advise reaching out to certification authorities as soon as possible during the development of the powertrain certifiability. Recently, Special Condition E-19 EHPS was introduced to cover hybrid and electric powertrains. However, it is not sufficient for DHEP systems, especially regarding the energy management capabilities.

2.1. Aircraft Mission Profile

The mission profile is the main aircraft design requirement during the early design stage. For this case study, the aircraft range is 1600 km with a maximal flight altitude of 3000 m. The mission is composed of 5 flight phases with specific requirements: take-off, climb, cruise, descent and landing. Take-off and landing ground roll should not exceed 300 m. Each phase is composed of multiple segments with different requirements. The mission profile shown in Figure 1 is composed of nine flight segments and is the typical flight profile in the case study.

The mission is built as follows:

• Take-off and landing are, respectively, represented by the first and the last segments (Seg.1 and Seg.9). Their durations are approximately 15 s.
• Three climb segments (Seg.2 to Seg.4) are made to test several power requirements at different flight levels. Their durations are, respectively, 2 min, 6 min and 11 min.
• Cruise is split into two segments (Seg.5 and Seg.6) to test a maximal cruise speed and a “hybrid” maximal cruise speed. During the latter, the Primary Energy Source (PES) is assisted by the battery to fulfill the power and energy requirements. The segment durations are 4 h 30 min and 30 min.
• Two descent segments (Seg.7 and Seg.8) represent a fast descent and the approach phase. Their durations are 20 min and 1 min 40 s.

2.2. Aircraft Architecture

As stated in the Section 1 the DHEP concept has been chosen. This concept stands out as a suitable choice based on the requirements of this case study. The literature on DHEP shows improvements in the lift and the drag at low speed and a reduction in the take-off and landing distances [11,12,13]. Several cases reported energy savings while using DHEP [14,15]. This can be translated into either a higher range or more passengers on board.

Two trends are observed in the distribution strategy of the propellers. On one hand, Lilium or DRAGON [16] are distributing identical small fans along the wing span. With this approach, the DHEP is the only thrust provider for the aircraft. Therefore, the fan design should be carefully thought out to provide sufficient thrust at low and high speeds. On the other hand, Eco-Pulse [17] or X-57 Maxwell [18] are designed with a distributed drivetrain and a more conventional drivetrain. The latter concept was chosen for the case study as it brings flexibility over a wide range of flight conditions. Figure 2 showcases two examples of the concept with different propeller distributions.

2.3. Powertrain Architectures

Three different powertrain architectures have been selected for this case study. The first two architectures are hybrid series with different Primary Energy Sources (PES). The first one uses a turbine (HS-T) while the second uses a fuel cell (HS-FC). The third architecture is a hybrid parallel architecture with a turbine as a PES (HP-T). Figure 3 showcases the HS-T architecture. This type of architecture benefits from the flexibility of electric wires to carry energy [19]. They offer a high degree of freedom during integration, which facilitates the integration of the components. However, compared with the HS-FC or HP-T architecture, this architecture usually displays a lower efficiency.

As represented in Figure 4, a hybrid series can also use fuel cell systems as PES. A fuel cell system brings two main benefits to the aircraft. Firstly, a fuel cell consumes hydrogen, which can be produced through electrolysis. Therefore, as long as the electricity required for electrolysis comes from low-carbon sources, hydrogen is a low-carbon aviation fuel [20]. Secondly, a fuel cell system also has a higher efficiency than a turbine. In the automotive sector, testing on Proton-Exchanger Membrane Fuel Cell (PEMFC) systems reports maximal efficiencies from 60% [21] to 67% [22] with a nominal power efficiency around 50%. Regarding aeronautical literature, the results are more pessimistic. A study from Datta [23] showcases maximal efficiency around 40% for two PEMFC systems. This efficiency difference stems from the maturity of the system in aeronautics. On the other hand, three limits are hindering fuel cell system development in aeronautics. The first limit is the production and supply of low-carbon hydrogen. Direct operation costs are expected to rise from the use of low-carbon hydrogen [24]. The second is the hydrogen storage in the aircraft. Hydrogen tanks are currently heavy and bulky as showed by Usman [25]. The third limit is that fuel cell system performance is highly dependent on the air pressure and density. Therefore, at high altitudes, the fuel cell system efficiency decreases, especially at high loads [26]. Some light aircraft concepts already surpassed some of these challenges, as shown in Adler and Martin’s review [27].

Lastly, a hybrid parallel architecture has been selected and is displayed in Figure 5. The main benefit of this architecture is its high efficiency. Some studies also highlighted a potential mass gain compared with a conventional powertrain [28]. However, such improvement is highly dependent on the aircraft concept. Usually, the mass reduction results from a downsizing of either the PES, the battery, or the hybridization system. Downsizing some of these elements might also limit the aircraft’s range or the powertrain system’s responsiveness.

3. Method and Models

The design method applied is a top-down approach, from Top-Level Aircraft Requirements (TLAR) and component specifications to the evaluation of the aircraft’s Key Performance Indicator (KPI). Figure 6 illustrates the methodology. Two major systems, aircraft and powertrain, encapsulate several models.

3.1. Aircraft Model

As the objectives of the study are oriented towards the powertrain design, the models selected will only represent the aircraft performance. These models are efficient when designing a significant number of configurations, which, in turn, allows for more detailed powertrain components’ models. However, they are not sufficient to complete the full preliminary design of the aircraft. Complementary studies are discussed in Section 5.2.

First, Newton’s second law is applied to the aircraft to obtain the aerodynamic flight requirements. The assessed forces are represented in Figure 7. First, the forces are projected in the Eiffel coordinate system. Second, the angle of attack is small, leading to $sin\left(\alpha \right)=0$. With these hypotheses, the lift requirement is expressed as a function of the weight as shown in Equation (1). Regarding the thrust requirement four forces are considered in Equation (2): weight, drag, acceleration forces, and ground forces.

$$L_{req}=W_0·cos\left(\theta \right)$$

(1)

$$T_{req}=W_0·sin\left(\theta \right)+F_{acc}+D+F_{Gnd}$$

(2)

Second, the lift requirement is provided to the lifting-line theory model. Associated with the flight conditions and aircraft characteristics, the lifting line theory assesses the wing aerodynamic capabilities [4]. They are presented either using a wing lift curve or $C_{L_{\alpha }}$, the slope of the lift curve.

Third, the lift assessment model compares the requirements to the aircraft’s aerodynamic capabilities. The difference between these two elements results in the lift that the distributed propulsion has to provide ($L_{DHEP}$). It is expressed using Equation (3).

$$\overrightarrow{L_{req}}=\overrightarrow{L_{Wing}}+\overrightarrow{L_{DHEP}}$$

(3)

Fourth, the DHEP lift requirement is translated to a propeller-induced speed requirement. This model uses the formulation provided by Patterson et German [29].

$${\displaystyle \frac{L_{DHEP}}{L_{tot}}}={\displaystyle \frac{S_{blown}}{S_{Wing}}}\left(1-{\displaystyle \frac{v_{Prop}·sin{i}_{Prop}}{v_{\infty }·sin\alpha }}\right){\displaystyle \frac{\sqrt{{v_{\infty }}^2+2v_{\infty }·v_{Prop}·cos(\alpha +i_{Prop})+{v_{Prop}}^2}}{v_{\infty }}}-1$$

(4)

Figure 8 illustrates the influence of each variable in Patterson’s model.

Fifth, the Froude–Rankine theory is applied. This model returns the thrust as a function of the propeller-induced speed as shown in Equation (5).

$$T=2{\rho }_{air}(\pi ·{r_{Prop}}^2)(v_{\infty }+v_{Prop})v_{Prop}$$

(5)

Figure 9, illustrates the Froude–Rankine theory. The propeller is modeled as a disk that increases the pressure. The pressure difference accelerates the airflow. The induced propeller speed ($v_{Prop}$) results from this acceleration [30].

Lastly, the main propeller thrust is defined using the drag assessment. Equation (2) is associated with Equation (6), which provides the relationship between thrust requirement, main propeller thrust and distributed propeller thrust.

$$\overrightarrow{T_{req}}=\overrightarrow{T_{main}}+\overrightarrow{T_{DHEP}}$$

(6)

As shown in Figure 6, the main propeller thrust is subjected to a decision algorithm. Two cases have been identified:

• If ${\mathrm{T}}_{\mathrm{Main}}<0$, excessive thrust is generated by the distributed propulsion. In order to maintain the thrust equilibrium presented in Equation (6), the main propeller has to provide a breaking force. Such a case happening during the flight seems counterproductive. Therefore, modifications are required in either the aircraft configuration or the mission profile to fulfill the requirements.
• If ${\mathrm{T}}_{\mathrm{Main}}\ge 0$, the main propeller is used and the lift requirement is achieved. This concept is valid.

The aircraft wing, fuselage and tail masses are based on Raymer’s work [3]. The use of these models can be discussed for disruptive concepts like DHEP. For example, the wing structure is highly influenced by the distributed propulsion integration. Adding propellers increases the mass on the wing, which is balanced with the lifting force. Hospodàř et al. [31] modeled these aspects for a distributed propulsion aircraft. On one hand, they showed that for the same requirements, using a distributed propulsion can reduce the wing area up to 35%. On the other hand, they showed that the wing mass can be reduced up to 130 kg, which represents 32% of an unblown wing mass designed under the same conditions.

3.2. Powertrain Model

The powertrain model defines the characteristics of the powertrain components. In this work, two novel directions have been tried out. On the one hand, an Energy Management Strategy (EMS) has been added. The objective of the EMS module is to model the power allocation between the components. A specific set of rules has been defined based on the two following constraints:

• The PES must provide a baseline power level. Therefore, it is sized on the longest flight phase requirement.
• The battery system compensates when the power requirement exceeds the PES capabilities.

On the other hand, two modeling approaches were explored to represent the components. Models referred to as level-1 follow the current trends in aircraft design. Component performance is modeled using solely the nominal operating efficiency throughout the mission. A component mass is estimated using component power density. Models referred to as level-2 are built upon a database of commercially available components and their efficiency maps. The efficiency is expressed as a function of different variables that are listed in

Table 1. Variables influencing component efficiency.

Component	Variables
Electric motors	Rotational speed *, torque *, temperature
Power converters	Current *, voltage, voltage conversion ratio [32], temperature
Turbine	Power *, air pressure *, air density *, air temperature *
PEM Fuel Cell	Current *, gases pressure *, fuel-air stoichiometry, temperature

* Variables considered for the case study.

.

As the level-2 models use a database, the selection of the reference components follows two criteria:

• At any flight point, power through the component should never exceed 110% of its nominal power.
• The lightest component shall be selected.

Level-1 and level-2 models provide the component mass and power setting for each flight segment. The component power setting and its efficiency are used to evaluate the thermal management system (TMS). This model uses the specific heat rejection (SHR) of the cooling system to define its mass [33].

Both approaches are efficient for modeling the powertrain components. The level-1 approach is interesting for long-term projects, where sufficient time is allocated for the development of components from scratch. The level-2 approach is more accurate as it is based on manufactured components operations and characteristics. This approach benefits short-term projects, where components must be found off the shelf. Moreover, with this design procedure, the component selected can also serve as a detailed specification for further improvements. However, uncertainties could be brought into the design due to inaccurate or misinterpreted manufacturer data. Component technology should also be carefully examined as some components might not be compatible with each other.

3.3. Design Variables and Input Data

This section presents the design variables and input data. As previously stated, the study provides insight into the powertrain design for a given aircraft configuration. The aircraft characteristics that influence the powertrain design the most should be selected. Therefore, this study proposes a trade-off between four design variables: MTOM, number of distributed propellers, wing area and wing aspect ratio. They are likely to be the key contributors to the overall aircraft and powertrain optimal design, as shown by Legrand et al. [34]. The

Table 2. Design variable range for the case study.

Variable	Range	Increment Step	Unit
MTOM ($MTOM$)	[2500, 4000]	100	kg
Distributed propeller count ($n_{Prop}$)	[6, 32]	2	-
Wing area ($S_{Wing}$)	[20, 35]	1	${\mathrm{m}}^2$
Aspect ratio ($AR$)	[5, 12]	0.5	-

provides the range studied for each design variable. In order to highlight the influence of the models selected, the authors opted for a sensitivity study. As a consequence, the design variables are swept over the range presented. The combination of the four variables is selected, leading to 53,760 different aircraft configurations for each powertrain architecture.

Table 3. Case study main aircraft TLAR.

Name	Value	Level-1	Level-2	Unit
Wing profile	NACA 2418	✓	✓	-
${\mathrm{C}}_{{\mathrm{L}}_{\max }}$	1.5	✓	✓	-
${\alpha }_{C_{L_{max}}}$	15	✓	✓	°
Wing sweep angle	0	✓	✓	°
Flaps additional ${\mathrm{C}}_{\mathrm{L}}$	0.7	✓	✓	✓
Fuselage length	11	✓	✓	m
Fuselage diameter	1.7	✓	✓	m
Tail total surface	2.25	✓	✓	${\mathrm{m}}^2$
Tail AR	3	✓	✓	-
Tail sweep angle	30	✓	✓	°
Tail relative thickness	0.12	✓	✓	-
Maximal load factor	6	✓	✓	-

and

Table 4. Case study main propulsion TLAR.

Name	Value	Level-1	Level-2	Unit
$\eta$ electric motor	0.95	✓		-
Power density electric motor	2.5	✓		kW/kg
$\eta$ power electronics	0.95	✓		-
Power density power electronics	10	✓		kW/kg
$\eta$ turbine	0.25	✓		-
Power density turbine	3	✓		kW/kg
Power density battery	1.6	✓	✓	kW/kg
Energy density battery	0.2	✓	✓	kWh/kg
LH2 storage gravimetric index	0.2	✓	✓	-
Battery integration factor	1.6	✓	✓	-
Specific Heat Rejection	2.5	✓	✓	kW/kg

regroups the main TLAR. The wing and tail taper ratios are one. The wing does not have a sweep angle. In order to accurately assess the differences between level-1 and level-2 models, the level-1 model assumptions are built upon linear regression of the databases used by level-2 modeling.

Table 5. Database component range.

Component	Power (kW)	Mass (kg)	Number of Components
Electric machines	6–2800	1.56–220	22
DC-DC converters	90–500	10.5–25.2	7
AC-DC converters	6–300	1.5–18	20
Turbine	74.5–471	40–206.8	14
Fuel cell	31–300	72–250	11

, provides an insight into the database size for level-2 models.

4. Results

The result section is split into two subsections. The Section 4.1 highlights the differences between level-1 and level-2 modeling approaches for aircraft design. The Section 4.2 compares the three powertrain architectures previously defined. The level-2 modeling approach is used for this part of the study. Of the 53,760 configurations, 28,159 configurations cleared the thrust analysis stage.

As previously stated, the authors opted for a sensitivity analysis instead of using optimization algorithms. During the study, optimization algorithms were investigated. These processes can lead to significant computing cost reduction, especially for studies with a vast design space. Moreover, as only the best aircraft configuration results from the optimization algorithm, the evaluation of the results is easier and faster. On the other hand, sensitivity studies might be time-consuming as every possibility is computed. However, sensitivity studies provide all the results in a given design space. This specificity makes sensitivity studies mandatory to highlight the influence of the powertrain modeling.

4.1. Powertrain Modeling Approach Comparison

The comparison between level-1 and level-2 models is based on the HS-T architecture. As stated in Section 3.3, the level-1 powertrain assumptions are built with the level-2 components databases. Figure 10 highlights the useful load dispersion using level-1 and level-2 models. It appears that level-1 models overestimate the achievable useful load. As the design method is influenced by multiple parameters, finding a specific reason as to why the level-1 models overestimate the mass is complex. Here, two results could explain the global trend. First, for 61% of the configurations, the battery mass is lower using level-1 models. For identical aircraft configurations, level-2 overestimates the battery mass by at most 257 kg. The fuel mass is the second element. Level-1 models always result in a lower fuel mass than the level-2 models. The average difference is 100 kg, while the lowest and largest differences are, respectively, 23 kg and 374 kg. These results are explained by the turbine efficiency hypothesis, as level-1 tends to overestimate this efficiency.

Figure 11 and Figure 12 represent the two configurations with the highest useful load. Contrary to the average useful load values, level-1 showcases a lower maximum useful load (1094 kg) than the level-2 configuration (1174 kg). It is interesting to note that the two modeling approaches do not achieve the same aircraft configuration in Figure 11. Level-2 optimal is achieved for a lower wing area and a higher number of distributed propellers. These variations have an effect on the aircraft aerodynamic performance, explaining part of the component mass differences. As wing area increases, drag increases, which leads to a higher overall thrust requirement. Therefore, with the level-1 configuration, the propellers require more energy to carry out the mission than the level-2 configuration. The variation in the number of distributed propellers influences the thrust ratio between the main and distributed propellers. A high distribution tends to lead to a higher main propeller thrust requirement and a heavier main drivetrain.

Figure 12 provides an insight into these assumptions. First of all, as highlighted in the analysis of Figure 10, battery and fuel are heavier with the level-2 modeling. This mass difference even overshadows the energy gain produced by the lower wing area of the level-2 configuration.

As highlighted in Figure 11, level-2 has a higher propeller distribution. Therefore, the level-2 main drivetrain components should be heavier than the level-1. Similarly, the level-1 distributed drivetrain components should be heavier than the level-2. While this assumption is verified for the inverters, it is not for the electric motors. It would appear that the electric motor specific power assumption is true only in a given power range. Such a hypothesis is confirmed by the correlation coefficient of the level-2 database. The linear regression correlation coefficient equals 0.77 [35], which indicates only a good yet not strong correlation. In fact, low-power electric motors tend to reach higher power density, between 3.5 and 4 kW/kg, than what is hypothesized with level-1 models. Moreover, high-power motors are more sparse and display a higher variation in their characteristics.

The PES generator highlights a significant variation. In this case, level-2 models select two mechanically coupled HPDM-250 [36]. These machines are designed for low torque and high rotational speed (20,000 rpm). Such a design greatly reduces the size of the winding and magnets compared with a high torque, low speed machine. Moreover, the HPDM-250 manufacturer offers a gearbox to reduce the rotational speed to around 3000 rpm without significant mass penalties.

The aircraft-related masses do not show significant evolution except for the wing. This difference is explained by the lower wing area and the fuel mass requirement. From Raymer’s [3] formula, increasing the fuel storage reduces the wing mass. Lastly, level-1 and level-2 best configurations achieve rather close useful loads. Level-2 shows an increase in useful load of 79 kg, which represents almost a passenger.

4.2. Aircraft and Powertrain Design Comparative Study

After assessing the differences between the two modeling levels’ results, the architectures presented in Section 2.3 are compared. First, the useful load distribution of the three architectures is illustrated. In addition, the number of configurations allowing from 8 to 12 passengers (PAX) is identified. Second, the study is focused on the highest useful load configurations for the three architectures. The share of eight types of components in the aircraft MTOM will be assessed. Third, the energy consumption of the three architectures will be compared with the energy consumption of a reference aircraft, the Cessna208 (Caravan). Except for the relaxed take-off length, this reference aircraft is modeled on the same mission as the three other configurations. Fourth, the architectures presented in Section 2.3 are amended using the results of the design method. Specific components are identified and the method limitations will be highlighted.

Figure 13 displays the results of the useful load for the three architectures. Of the three architectures, the HP-T provides the highest useful load configurations. Comparing the configurations one by one, useful load is lowered by 172 kg to 1179 kg for the HS-T and by 316 kg to 1263 kg for the HS-FC when compared with HP-T architectures.

Similar tendencies have been showcased in other design exploration case studies. An example of such is provided by Finger et al. [28], who presented a hybrid parallel architecture with a lower MTOM than the hybrid series architecture (−8.6% MTOM). Another case study by Vries et al. [37] showcased the design of a hybrid series and a Partial TurboElectric (PTE) aircraft. The PTE aircraft showed an MTOM 5.3 t lower than the hybrid series (19% of the hybrid series MTOM). Adding the batteries to the PTE aircraft, the MTOM reduction would be close to 3.8 t. However, some interesting cases highlighted a lower mass using a series architecture. Friedrich et al. reference the case of the DA-36 E-Star and E-Star 2 [38]. The latter version, E-Star 2, uses a hybrid series powertrain with an overall aircraft mass of 100 kg lighter.

Comparing the HS-T and HS-FC architectures provides an interesting standpoint on the conceptual feasibility of hydrogen in aviation. First, the average useful load of the 28,159 HS-T configurations is 26 kg higher than the HS-FC average. However, when compared one by one, the HS-FC architecture achieves a higher useful load 47% of the time. It would appear that over the design space, the HS-FC configurations remain competitive against the HS-T. Moreover, 222 HS-FC configurations exceed an 850 kg useful load (10 PAX of 85 kg). Of these 222 configurations, 37 display a higher useful load than the HS-T configurations. These numbers highlight that a significant number of HS-FC configurations (≈17%) are feasible and could outperform the HS-T architectures in terms of useful load.

To conclude the study of the design space, the number of configurations that can carry a given number of passengers is showcased in

Table 6. Count of configurations abiding by a given passenger requirement.

PAX	8	9	10	11	12
HS-T	3648 (13%)	1623 (6.8%)	832 (3%)	322 (1.1%)	114 (0.4%)
HS-FC	2671 (9.5%)	1019 (3.6%)	222 (0.8%)	12 (0.04%)	0
HP-T	19,045 (67.6%)	15,875 (56.4%)	12,942 (46%)	9955 (35.4%)	7259 (25.8%)

. A mass of 85 kg was deemed appropriate to represent a passenger with light luggage. The HS-FC architecture is the only architecture that does not reach the 12-passenger requirement.

Following the design space study, the configurations with the highest useful loads are showcased. Figure 14 presents the aircraft configurations for each powertrain architecture. While HS-T and HP-T configurations are similar, the HS-FC configuration appears rather different. First, this configuration MTOM is lowered by 200 kg. As a result, the overall lift requirement is lowered by around 5%. Compared with the other architecture, the wing area of the HS-FC configuration is smaller. Such evolution reduces the lift and the drag the wing produces. On the other hand, the increase in the aspect ratio tends to increase the lift and the induced drag produced by the wing. In the case of this study, the combination of these effects induces almost the same wing capabilities for the HP-T and HS-FC architectures. A 0.5% wing lift variation has been observed while the drag is increased by 3.5% for the HP-T architecture during take-off. Lastly, the HS-FC configuration showcases a higher distribution of the distributed drivetrains. This characteristic lowers the propeller diameter, thus reducing the overall thrust provided by the distributed drivetrains. Consequently, the mass of the distributed drivetrains should be lowered. On the other hand, a higher part of the take-off constraint will fall on the main drivetrain.

To complement the architecture analysis, the contributors to the mass budget have been identified and reported in Figure 15. First of all, it appears that the HS-T configuration is greatly hindered by the mass of its electric machines. The share of the electric machines for the HS-T architectures is around 8%, while it does not exceed 3.8% for the two other architectures. This difference is due to the higher number of electric machines in the HS-T architecture as well as its main drivetrain power requirement. The HS-T main drivetrain power requirement is 518 kW during take-off, while it is 50 kW lower for the HS-FC architecture. However, for this power range, a significant gap is visible in the electric motor database. Therefore, the mass of the main drivetrain electric motor is doubled for the HS-T architecture (HS-T: 206 kg, HS-FC: 96 kg). Despite this observation, the mass of power converters remains low for the three architectures. The lowest share is for the HP-T architecture, which, by design, benefits from a lower number of power converters. Thirdly, the turbine and fuel cell masses can be compared. The fuel cell mass share is around 7.3%, while a turbine is between 3.1% and 3.5%. Regarding the fuel and its storage, it seems that the HP-T is once more the lightest. For this system, the HS-T architecture is hindered by its lower efficiency, while the HS-FC architecture is hindered by the hydrogen tank mass. Adding the battery and the TMS, the powertrain of the three architectures accounts for 43.8%, 44.9% and 34.5% for the HS-T, HS-FC and HP-T architectures. Such results are higher than the values expected for conventional aircraft (20 to 30% [4]). The aircraft system (wing, fuselage and tail) accounts for 26 to 30% of the overall aircraft mass. In this case, it would seem that the models used underestimate the mass of the aircraft system as it should be between 35% and 50% of the overall aircraft mass, according to [4]. Lastly, the useful load accounts for 26% up to 49.5% of the maximum take-off mass. For conventional aircraft, this share goes from 30% to 45%.

To the authors, such results on preliminary design are highly encouraging, especially for the HS-FC architectures. Designing a hydrogen aircraft is a novel and complex task requiring the development of very specific components. As previously stated, the mass of the hydrogen tank is an issue that must be addressed. Literature showed that hydrogen tank gravimetric index should rise from 6–10% to 25–30% to design financially viable aircraft [39]. Moreover current research results highlight feasible tanks with gravimetric indexes above 30% [40]. Therefore, the 20% gravimetric index selected for this design showcases a realistic yet pessimistic perspective on the development of the technology. In addition, the fuel cell model developed by Datta [23] and used in this study depicts poor fuel cell nominal operations. As stated in Section 2.3, while this model only achieves 40% maximal efficiency at sea level, current technologies achieve around 50% efficiency. Therefore, more savings should be expected.

Another KPI is the aircraft configuration energy cost. This cost represents the quantity of primary energy used per kilometer traveled or per person carried. It reflects the energetic performance of the aircraft, which could be further optimized during the detailed design stage. In addition, energy cost can serve as a basis for a life-cycle assessment study. Equations (7) and (8) provide insights as to how this cost is calculated.

$$E_{cost-m_u}={\displaystyle \frac{E_{con{s}_{batt}}+E_{con{s}_{fuel}}}{m_u}}$$

(7)

$$E_{cost-range}={\displaystyle \frac{E_{con{s}_{batt}}+E_{con{s}_{fuel}}}{range}}$$

(8)

Figure 16 highlights the two energy costs of the three architectures. They are compared with the reference aircraft. It appears that the HS-T architecture has the highest energy costs out of the three architectures. Looking at the cost per kilogram of useful load, the HS-T configuration is followed by the HS-FC and then the HP-T architectures. However, looking at the cost per range, the HS-FC configuration outperforms the HP-T architecture by 37.5%. This discrepancy is explained by the low useful load of the HS-FC configuration (982 kg) compared with the HP-T configuration (1520 kg).

Compared with the reference aircraft, the HS-T architecture showcases higher energy costs. These additional costs are explained by the accumulation of system efficiencies in series. While Cessna208 powertrain efficiency ranges from 25% to 30%, the HS-T powertrain efficiency ranges from 19% to 25%. In contrast, the HS-FC configuration outperforms the reference aircraft. Energy cost per useful load is 15% lower, while the energy cost per range is 32% lower. Once more, the efficiency of the system is key in this comparison, as the HS-FC powertrain efficiency ranges from 32% to 53%. Lastly, the HP-T architecture showcases an in-between. The energy cost per useful load is lower than that of the Cessna, as the latter can carry around 1360 kg. It is of note that these results are preliminary. The use of complex energy management strategies, as presented in references [41,42], leads to significant changes in the energy cost.

Lastly, it appears that most of the energy is provided by the fuel. The primary energy provided by the battery ranges from 0.60 to 1.18% of the total primary energy used by the aircraft. It remains low for turbomachines architecture (0.60 to 0.68%), while it reaches almost 1.2% when fuel cells are used.

Table 7. Components selection for each architecture.

System	Component	Parallel Component Count	Mass per Component (kg)	Nominal Component Power (kW)	Sizing Segment	Supplier Reference
Hybrid series turbine (HS-T)
Distributed	Motor	44	1.56	6	1	DHA
drivetrain	Inverter	22	1.7	15	1	MC15
Main	Motor	1	206	640	1	Magnix650
drivetrain	Inverter	2	14.6	278	1	CM350-SiC
PES	Rectifier	4	6.75	113	5	CM200
	Generator	2	17	200	5	HPDM-250
	Turbine	1	122.5	450	5	Arriel 1D
Battery	Boost converter	1	20	500	1	DCUHV
	Battery	1	494	494	1
Hybrid series fuel cell (HS-FC)
Distributed	Motor	32	1.56	6	1	DHA
drivetrain	Inverter	32	1.5	6	1	HPS
Main	Motor	2	48	230	1	AXM4
drivetrain	Inverter	2	14.6	278	1	CM350-SiC
PES	Boost converter	1	20	500	1	DCUHV
	Fuel cell	1	280	300	5	SP300
Battery	Boost converter	1	20	500	1	DCUHV
	Battery	1	508	508	1
Hybrid parallel turbine (HP-T)
Distributed	Motor	48	1.56	6	1	DHA
drivetrain	Inverter	24	1.7	15	1	MC15
Hybridization	Motor-generator	1	48	230	1	AXM4
system	Inverter-rectifier	1	18	225	1	PM250
PES	Turbine	1	139.2	360	5	Arriel 2E
Battery	Boost converter	1	20	500	1	DCUHV
	Battery	1	458	458	1

showcases the component selection. Interestingly, the design procedure opts to arrange several components of the main drivetrain in parallel for the three architectures. Firstly, the HP-T and HS-T distributed drivetrains use two mechanically linked motors. Reducing the number of distributed propellers from 32 to 24 multiplies the power required of each propeller by 1.5. This evolution in the requirement leads to the use of two motors in the design. However, the mechanically associated motors are controlled by a single inverter. Having one inverter for both motors is beneficial as it simplifies the control. The risk of rotor blockage can also be reduced as long as both motors are monitored by the inverter. Secondly, for the HS-FC architecture, two lighter motors are selected and associated with one inverter each. As a comparison, the single motor closest in the database weighs 206 kg for 640 kW of nominal power. This motor has been selected for the HS-T architecture. It is associated with two inverters to reach the power requirement. Lastly, the HS-T PES generator and rectifier are redundant. Regarding the motors, the closest trade-off here would be to swap the HPDM-250 for the AXM4. However, this last machine provides only 30 kW more (+15%) for a mass increase of 31 kg (+182%). Each HPDM-250 machine [36] is controlled by two rectifiers.

The sizing segment column highlights which segment requirement is selected to size a given component. In accordance with the EMS design constraints, the PES is designed during the max speed cruise segment, for the three architectures. The other systems are sized for the take-off requirement, where the power should be maximized. However, it appears from the study of the design space that the main drivetrain components, as well as the battery system, can be sized for other segments. Over the 28,159 configurations, the main drivetrain is sized for the last climb segment (Seg.4) 23.8% of the time. Similarly, from 8.5% to 15.8% of the time, the battery is sized with the energy requirement over the whole mission rather than the power requirement during take-off.

5. Discussion

5.1. Study Limitations

Several limits to this study have been identified. Two categories have been defined to regroup the limits resulting from design uncertainties and from the methodology.

The first category is related to the design assumptions and models. Two limits were reached in this research work: the parasite drag assumption and the aircraft mass models. Currently, the literature provides neither data nor methods for estimating the parasite drag from a distributed drivetrain. Such models are especially challenging to define as they should translate the influence of the propellers’ operation, the propeller hub design, the cooling systems, etc. Regarding aircraft masses, tendencies were found in the literature. The DHEP concept seems to lighten the mass of the wing elements. However, it appeared that these mass gains are highly dependent on how the DHEP is integrated into the aircraft.

The second category is related to the design methodology and the tool architecture. Two limits were also reached. Firstly, with the current tool, the increasing number of configurations designed leads to higher computing time. Therefore, adding an optimization layer could prove beneficial to study more design variables. However, as this process converges toward a single optimal solution, design space exploration, as shown in this paper, is not feasible. Secondly, the design is based on a nine-segment mission profile, relating to nine stationary operations. This point-wise design procedure does not account for the dynamics of the aircraft or its components. This could lead to design discrepancies at later stages.

5.2. Further Work

This study is part of a larger research project on aircraft and powertrain design. It has already been furthered by work on the detailed design stage. The influence of several energy management strategies on the concepts presented was showcased. In addition, several other directions have been identified to complement this study:

• Further work should consider the well-to-propeller efficiency when comparing hydrogen and conventional fuels. As several hydrogen production processes are available, such a study will highlight the overall aircraft energetic use. In addition, the implementation of life-cycle assessment in the method would provide another indicator driving the selection of the aircraft configuration.
• In order to prove the feasibility of the aircraft concepts here presented, an extensive analysis on the stability and control. Such work is pivotal in the evaluation of DHEP benefits and limits [43].
• Regarding the parasitic drag and aircraft mass, further studies could categorize the effect of specific elements, such as the cooling systems, propeller wing interaction, etc.
• Regarding hydrogen maturity in an aircraft, several aspects still need to be studied. First, high gravimetric hydrogen tanks should be tested under operational conditions. Then, the operation and maintenance of hydrogen aircraft should be considered. Lastly, the production of hydrogen has to be competitive with conventional aircraft fuels.

6. Conclusions

This paper aims to provide the reader with key elements on the influence of powertrain architectures, models, and design assumptions on DHEP aircraft design. First, a design method for a DHEP light aircraft is presented. The method is established around several models representing aircraft and powertrain components. Two models representing the aeropropulsive coupling and the energy management of the powertrain are added. Built upon four constraints, these two models define the operation and requirements associated with the distributed propulsion and energy flow in the powertrain. Lastly, the two KPIs, useful load and energy cost, were presented. These KPIs provide vital information on the feasibility and performance of the aircraft configuration.

A first set of results presented the differences arising from two different powertrain component modeling approaches. The first approach uses current design assumptions, such as fixed efficiency and power density, to estimate the component mass. The second approach is based on manufactured components and black box component models. These models represent the component operational conditions based on a requirement. A comparison of the two modeling approaches was built for the same component technology level. Results showed that the first approach tends to overestimate the aircraft capabilities. The comparison of the configurations one by one showed that the battery and fuel mass budgets are underestimated most of the time. The estimation of the highest useful load configurations resulted in different aircraft characteristics for the two modeling approaches. Such results can lead to design discrepancies at later design stages if the limits of the level-1 models are not properly assessed.

A second set of results provided a comparison of three aircraft propulsion architectures. This comparison shows that over the same design space, the hybridization technology is closely linked to the aircraft design. The HP-T architecture provides the highest useful load and the highest number of configurations that abide by a 12-passenger requirement. Despite lower performance, the two hybrid series architectures show a significant number of configurations that can carry 8 to 10 passengers. Such results show that even though hydrogen systems are not fully mature, a number of aircraft configurations are feasible if the payload constraint is lowered. The analysis of the best configurations confirms this observation. While the HS-FC powertrain system is 1.1% heavier than its HS-T counterpart, its useful load is only lowered by 4% (≈200 kg). This study also showed that a flexible approach to component modeling can improve results with slight modifications of the powertrain architecture. Power segmentation allows multiple lighter components to replace a heavier one, as shown for the three architectures’ drivetrains or PES. Moreover, such results improve the safety of the aircraft through a redundant system at the expense of some complexity. Lastly, the energetic cost of the three highest useful load configurations was compared to a reference aircraft (Cessna208). While the HS-T configuration consumes more energy than the reference aircraft, the HS-FC and to some extent the HP-T configurations might outperform current aircraft. Depending on the KPI used, energy consumption is reduced by 15 to 32% using an HS-FC powertrain.