# Mission Performance Analysis of Hybrid-Electric Regional Aircraft

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Hybrid-Electric Aircraft Design

#### 2.1. Hybrid-Electric Aircraft Requirements

#### 2.2. Conceptual Design Methodology

#### 2.3. Mission Simulation and Performance Analysis

#### 2.3.1. Overview

#### 2.3.2. Mission Simulation: Aeromechanics

_{V}, Z

_{V}); the force scheme considered is reported in Figure 4.

_{c}is the power-specific fuel consumption and P

_{e}is the supplied power. All the quantities are time functions, except for g and k

_{c}, which are constants. Dotted variables indicate the time derivative of the considered quantity. The trajectory of the aircraft and the related performance, such as fuel consumption, travel time, distance covered, etc., can be obtained by time-integrating differential Equation (2), given the initial conditions and the proper flight programmes selected for each mission phase. Specifically, in this work it was decided to use the Euler forward method as a technique for numerical integration of the equations of motion. Such a model is given in Equation (3) for a generic y function of time t; $\dot{y}$ represents the time derivative of the considered function, while $\mathsf{\Delta}\mathrm{t}$ is the finite timestep in which the mission is discretised.

- Taxi-out: ground manoeuvring with constant power supply for 240 s;
- Take-off: full-power supply for 45 s;
- Climb: constant indicated air speed (IAS) and rate of climb (RoC);
- Cruise: constant speed and altitude;
- Descent: constant indicated air speed (IAS) and rate of descent (RoD);
- Loiter: 30 min of level flight at maximum L/D;
- Approach: constant RoD;
- Landing: neglected;
- Taxi-in: ground manoeuvring with constant power supply for 240 s.

#### 2.3.3. Mission Simulation: Power Supply

- Taxi-out/Taxi-in: taxiing is performed with only electrical power supply, in order to suppress all air-polluting emissions on the ground;
- Take-off: all the available power on board, both electrical and thermal, is supplied;
- Climb, Cruise, Descent: for each phase, electrical and thermal power are supplied in different quotas to match the total power required for the flight, according to a strategy set by the designer/operator.

**x**are those related to the sizing of the propulsion system by means of a matching chart, i.e., the wing loading W/S and the hybridisation factor H

_{P}, and those related to the power supply strategy Φ. As described above, at each time, given the total required power ${\mathrm{P}}^{\mathrm{nec}}$, it is sufficient to identify the fraction of supplied thermal power to also know the electric power fraction, or vice versa. In this case, it was chosen to select the thermal power fractions ${\mathsf{\Phi}}_{i}^{ice}$ for the three i-th phases (climb, cruise, descent) as optimisation variables, and to compute the electrical power fractions ${\mathsf{\Phi}}_{\mathrm{i}}^{\mathrm{el}}$ accordingly. Furthermore, since the power fractions ${\mathsf{\Phi}}_{\mathrm{i}}$ are functions of time, a further simplifying assumption was imposed: the thermal power fractions, used as optimisation variables, are kept constant within the i-th phase considered, while the electrical power fractions can vary over time in the i-th phase, depending on the matching with the total required power. A summary overview of the choices related to the power supply strategy is given in Table 3.

## 3. Hybrid-Electric Aircraft Performance Analysis

#### 3.1. Analysis of the Design Mission Performance

_{max}, which restricts the maximum amount of batteries that can be taken on board. In line with the requirement set by the designer, there is no use of electrical energy in diversion.

#### 3.2. Analysis of the Off-Design Mission Performance

_{TO}> MTOW, the ${\mathsf{\Phi}}^{\mathrm{el}}$ values have to be reduced and the power request has to be fulfilled, increasing the supplied thermal power. This causes a lighter battery pack and hence the fulfilment of the MTOW constraint, including for the most energy-demanding passengers–range combinations. The thermal and electric power fractions found with this strategy, for each payload–range pair evaluated, are reported in Figure 12. As in the case of the design point, in this case the ${\mathsf{\Phi}}^{\mathrm{ice}}$ are also constant within each phase, whereas ${\mathsf{\Phi}}^{\mathrm{el}}$ are time variables, depending on $\mathsf{\Phi}\left(\mathrm{t}\right)$; so, at the bottom of Figure 12, the values of ${\mathsf{\Phi}}^{\mathrm{el}}$ at the beginning of the climb (left) and cruise (right) are reported.

_{TO}(right). The trend of fuel consumption basically follows the trend of thermal power fraction supplied in cruise (Figure 12—top right). When the energy demand of the assessed mission decreases, i.e., as the payload and/or range decreases, it is possible to exploit a larger supply of electrical power (Figure 12—bottom right), thus allowing reduction of the fuel consumption. In a 40-passenger 250 nm mission, which can be considered the mission of typical use of this class of aircraft [50], it can be seen that the fuel consumption becomes very limited (approximately 50 kg), thus favouring a significant reduction in direct emissions from the operation of such an aircraft.

_{TO}reaches the MTOW value; beyond this line, the MTOW cannot be exceeded (Figure 13—right), and it is necessary to swap battery mass for fuel mass in order to accomplish the missions. This is carried out by increasing the thermal power fraction and reducing the electric power fraction in cruise, as Figure 12 (right) shows. In contrast to the conventional thermal aircraft, for which the W

_{TO}= MTOW condition only occurs on one point of the diagram edge, in this case a large area within the envelope is subject to this condition (Figure 13—right). In this area of the envelope, once the payload is fixed, the gradual mass exchange between batteries and fuel occurs.

## 4. Beyond the Design Point: Payload–Range Diagram Analysis

#### 4.1. Payload–Range Diagram for Aircraft with Thermal Propulsion

_{eo}), which is constant and therefore subtracted from the total aircraft weight, for simplicity. The weight contributions represented in Figure 14 are: (i) the payload weight W

_{pay}; (ii) the fuel weight W

_{fuel}, which has the origin starting from the maximum value of the payload weight (W

_{pay max}); (iii) the aircraft take-off weight W

_{TO}, i.e., the sum of payload, fuel and empty operating weight, limited at the top by the maximum take-off weight MTOW. Once the payload weight is set equal to its maximum, the fuel weight required to accomplish the mission is the key factor which determines the take-off weight of the aircraft; W

_{fuel}depends on the aerodynamic, ponderal and propulsive characteristics of the aircraft, and it assumes a distinct value for each range considered. Therefore, there is a monotonically increasing correlation between the W

_{TO}and the flight range, which is valid up to the so-called harmonic point [86], at which the take-off weight reaches the MTOW limit. This point of the payload–range diagram indicates the maximum range the aircraft can fly with the maximum payload, i.e., the harmonic range (R

_{H}).

_{fuel}“slides” on the W

_{pay max}line, thus giving a concise and general interpretation of this diagram. In this segment of the envelope, the take-off weight of the aircraft W

_{TO}is always equal to the maximum weight MTOW.

_{fuel max}, as represented in Figure 15 (right). When the payload weight decreases to zero, the aircraft reaches its maximum range, defined as ferry range. This situation is of minor commercial interest, unless for the conditions of aircraft delivery or transfer. Figure 15 (right) thus represents the complete generic payload–range diagram for an aircraft with conventional thermal propulsion. The edge of the envelope represents the limiting conditions in terms of payload maximisation; all the combinations within the envelope are feasible missions for the considered aircraft.

#### 4.2. Payload–Range Diagram for Aircraft with Hybrid-Electric Propulsion

_{TO}depends on the fuel–battery mass distribution, depending on the split of the power supply during the different stages of the mission; Figure 16 provides a qualitative clarification of this point. In Figure 16 (left) (Case 1), the strategy adopted is targeted at maximising the mass of batteries on board; due to the low energy density of the batteries, W

_{TO}reaches the MTOW limit well before the harmonic point. On the other hand, in the case of Figure 16 (right) (Case 2), a different fuel–battery mass distribution is adopted, in which a higher fuel consumption is allowed. In this instance, W

_{TO}reaches the MTOW for a longer range than in the previous case.

_{TO}= MTOW always occurs. This segment should end at the harmonic point, which is defined as the point with the maximum range for the maximum payload, and where W

_{TO}equals MTOW for the first time. This definition of harmonic point is clearly no longer valid in the case of hybrid-electric aircraft; it is therefore more consistent to generically identify this point as the design point, i.e., the point that, according to the specifications, sets the requirements to size and/or op-528 timise the aircraft.

_{TO}= MTOW condition is maintained. In the second strategy, the payload mass is exchanged for battery mass, while the fuel mass is kept constant. In this case, the battery mass increases until the maximum volume available for the batteries is saturated (Figure 18—right). Since the gravimetric energy density of batteries is about 25 times lower than fuel, the range for which the volume saturation is achieved could be significantly anticipated. Figure 18 shows a qualitative comparison between these two strategies: given the low gravimetric energy density of batteries compared to fuel, the second strategy does not appear to be effective in extending the range; however, it may be suitable if cutting the fuel consumption is the priority.

_{pay max}(Figure 19). As fuel has a much higher gravimetric energy density than batteries, very large design range extensions could be obtained.

_{P}. The maximum range, defined in the following as extended range E

_{R}, depends on the specific characteristics of the aircraft and the propulsion system; in particular, following the diagrams in Figure 20, in which qualitative details of the payload–range diagrams in the area beyond the design point are represented, the following cases occur:

- Case 1: the extended range is limited by the saturation of the maximum volume available for fuel; this depends on the design of the aircraft, in particular on the allocation of internal volumes for fuel and/or batteries.
- Case 2: the extended range is limited because the MTOW is reached, no further battery–fuel mass swap is possible, hence it is necessary to start reducing the payload.
- Case 3: the extended range is limited by the lack of available energy or power, which depends on the sizing of the propulsion system and in particular on the hybridisation factor. Two subcases are possible:
- ◯
- 3a: electrical energy is not sufficient to accomplish one or more stages of the mission;
- ◯
- 3b: the power provided by the thermal engine is not sufficient to accomplish one or more mission stages.

^{ice}limited, as it shows a cruise thermal supplied power fraction ${\mathsf{\Phi}}_{\mathrm{cruise}\mathrm{opt}}^{\mathrm{ice}}$ near to the maximum available value ${\mathsf{\Phi}}_{\mathrm{max}}^{\mathrm{ice}}$. This condition is representative of Case 3b of Figure 20. The second regional hybrid-electric configuration has also been designed by means of the tools described in Section 2.2; this aircraft is here labelled as Swap limited, and is representative of Case 2 of Figure 20.

^{ice}limited configuration. The cruise-required thermal power saturates its allowed maximum for ranges slightly larger than the design range, thus limiting the extended range to 800 nm; the ferry range is about 1500 nm.

_{TO}= MTOW and no further battery–fuel mass swap is possible. In this case, the extended range is equal to 2000 nm, and the ferry range is about 3200 nm. The mass swap between batteries and fuel allows an extension of the maximum range of the aircraft beyond the design point. Essentially, this is caused by the large amount of battery mass that can be exchanged for fuel, whose specific energy is one order of magnitude higher. Consequently, this improved operating flexibility comes at the cost of a higher fuel consumption.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 9.**Mission simulation outcomes: trajectory (

**left**), slope angle (

**centre**), lift–drag ratio (

**right**).

**Figure 10.**Mission simulation outcome: thermal (

**left**), electric (

**centre**), total (

**right**) power supplied.

**Figure 12.**Thermal (

**top**) and electrical (

**bottom**) supplied power fractions in climb (

**left**) and cruise (

**right**) for the missions inside the pax–range diagram.

**Figure 13.**Block fuel (

**left**), battery mass (

**centre**), and take-off weight W

_{TO}(

**right**) for the missions inside the pax–range diagram.

**Figure 16.**Effects of different fuel–battery mass distributions on the first segment of the payload–range diagram for hybrid-electric aircraft.

**Figure 18.**Strategies to extend the range beyond the design point: mass exchange between payload and fuel (

**left**), and between payload and batteries (

**right**).

TLARs | |
---|---|

Number of seats | 40 |

Cruise Mach | 0.4 |

Cruise altitude | 20,000 ft |

Design mission range | 600 nm |

Balanced field length | 1100 m |

Landing distance available | 1100 m |

Mission | Diversion | |
---|---|---|

Climb | IAS = 170 kt RoC = 900 ft/min | IAS = 150 kt RoC = 600 ft/min |

Cruise | Mach = 0.4 h = 6100 m | Mach = 0.27 h = 3050 m |

Descent | IAS = 220 kt RoD = −1100 ft/min | IAS = 150 kt RoD = −1100 ft/min |

Thermal Power Fraction | Electric Power Fraction | ||
---|---|---|---|

Mission | Taxi-out/in | ${\mathsf{\Phi}}^{\mathrm{ice}}$(t) = 0 | ${\mathsf{\Phi}}^{\mathrm{el}}$(t) = 0.07${\mathrm{P}}_{\mathrm{inst}}^{\mathrm{tot}}$ |

Take-off | ${\mathsf{\Phi}}^{\mathrm{ice}}$(t) = 1 | ${\mathsf{\Phi}}^{\mathrm{el}}$(t) = 1 | |

Climb | ${\mathsf{\Phi}}^{\mathrm{ice}}$(t) = const. = ${\mathsf{\Phi}}_{\mathrm{climb}\mathrm{opt}}^{\mathrm{ice}}$ | ${\mathsf{\Phi}}^{\mathrm{el}}$(t) = f(${\mathsf{\Phi}\left(\mathrm{t}\right),\mathsf{\Phi}}_{\mathrm{climb}\mathrm{opt}}^{\mathrm{ice}}$) | |

Cruise | ${\mathsf{\Phi}}^{\mathrm{ice}}$(t) = const. = ${\mathsf{\Phi}}_{\mathrm{cruise}\mathrm{opt}}^{\mathrm{ice}}$ | ${\mathsf{\Phi}}^{\mathrm{el}}$(t) = f(${\mathsf{\Phi}\left(\mathrm{t}\right),\mathsf{\Phi}}_{\mathrm{cruise}\mathrm{opt}}^{\mathrm{ice}}$) | |

Descent | ${\mathsf{\Phi}}^{\mathrm{ice}}$(t) = const. = ${\mathsf{\Phi}}_{\mathrm{desc}\mathrm{opt}}^{\mathrm{ice}}$ | ${\mathsf{\Phi}}^{\mathrm{el}}$(t) = f(${\mathsf{\Phi}\left(\mathrm{t}\right),\mathsf{\Phi}}_{\mathrm{desc}\mathrm{opt}}^{\mathrm{ice}}$) | |

Diversion | Climb_{div} | ${\mathsf{\Phi}}^{\mathrm{ice}}$(t) = $\mathsf{\Phi}\left(\mathrm{t}\right)$ | ${\mathsf{\Phi}}^{\mathrm{el}}$(t) = 0 |

Cruise_{div} | ${\mathsf{\Phi}}^{\mathrm{ice}}$(t) = $\mathsf{\Phi}\left(\mathrm{t}\right)$ | ${\mathsf{\Phi}}^{\mathrm{el}}$(t) = 0 | |

Descent_{div} | ${\mathsf{\Phi}}^{\mathrm{ice}}$(t) = $\mathsf{\Phi}\left(\mathrm{t}\right)$ | ${\mathsf{\Phi}}^{\mathrm{el}}$(t) = 0 |

Number of Passengers | 40 |

Design range | 600 nm |

MTOW | 22,935 kg |

OEW | 17,879 kg |

Wing surface | 70.6 m^{2} |

Wingspan | 28.7 m |

Fuselage length | 21.9 m |

Fuselage diameter | 2.88 m |

Installed thermal power | 3.21 MW |

Installed electric power | 2.49 MW |

H_{P} | 0.43 |

Block fuel mass | 937 kg |

Battery mass | 4054 kg |

Design Point Features | Φ^{ice} Limited | Swap Limited |
---|---|---|

H_{P} | 0.43 | 0.27 |

${\mathsf{\Phi}}_{\mathbf{climb}\mathbf{opt}}^{\mathbf{ice}}$ | 0.28 | 0.37 |

${\mathsf{\Phi}}_{\mathbf{cruise}\mathbf{opt}}^{\mathbf{ice}}$ | 0.55 | 0.33 |

${\mathsf{\Phi}}_{\mathbf{desc}\mathbf{opt}}^{\mathbf{ice}}$ | 0.20 | 0.53 |

MTOW | 22,935 kg | 22,960 kg |

Installed thermal power | 3.21 MW | 4.39 MW |

Installed electric power | 2.49 MW | 1.67 MW |

Block fuel mass | 937 kg | 1041 kg |

Battery mass | 4054 kg | 4065 kg |

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## Share and Cite

**MDPI and ACS Style**

Palaia, G.; Abu Salem, K.
Mission Performance Analysis of Hybrid-Electric Regional Aircraft. *Aerospace* **2023**, *10*, 246.
https://doi.org/10.3390/aerospace10030246

**AMA Style**

Palaia G, Abu Salem K.
Mission Performance Analysis of Hybrid-Electric Regional Aircraft. *Aerospace*. 2023; 10(3):246.
https://doi.org/10.3390/aerospace10030246

**Chicago/Turabian Style**

Palaia, Giuseppe, and Karim Abu Salem.
2023. "Mission Performance Analysis of Hybrid-Electric Regional Aircraft" *Aerospace* 10, no. 3: 246.
https://doi.org/10.3390/aerospace10030246