Maximum Take-Off Mass Estimation of a 19-Seat Fuel Cell Aircraft Consuming Liquid Hydrogen

Abstract

In this paper, the maximum take-off mass ($MTOM$) of a 19-seat fuel cell aircraft with similar characteristics to a conventional 19-seat aircraft is estimated using the combination of a rapid method and semi-empirical equations. The study shows that the $MTOM$ of a 19-seat fuel cell aircraft with current technology would be 25% greater than that of a conventional aircraft. However, with the expected technological improvements, the $MTOM$ of a 19-seat fuel cell aircraft could reach lower values than that of a conventional aircraft. The most important parameter affecting the $MTOM$ of fuel cell aircraft is the power-to-weight ratio of the fuel cells. If this ratio of fuel cell aircraft does not improve significantly in the future, fuel cell aircraft with lower power loading will become the preferred choice; thus, certain trade-offs in flight performance, such as a longer takeoff distance, will be accepted. The study provides the basis for further economic analysis of fuel cell aircraft, which has yet to be conducted.

1. Introduction

Since the beginning of the 20th Century and the first flights by the Wright Brothers, the internal combustion engine has driven aviation and led to massive mobilization in the air. Today, an interesting number of people are choosing to fly, because in many cases, it is a faster and more convenient way to travel than by road or rail. There is no doubt that the standard of travel and living has improved; however, the accelerated technological progress and improved quality of life brought about by the invention of the internal combustion engine has come at a price. First, toxic gases such as $CO$, $N{O}_X$, $S{O}_X$, as well as hydrocarbons cause various heart, lung, and liver diseases [1]. Second, $C{O}_2$ and $N_{2}0$ are not toxic, but can have lasting and devastating effects on the climate and environment due to the greenhouse effect. Third, fossil fuel reserves are not unlimited. Today, aviation contributes to 2% of global and 3% of European greenhouse gas emissions. Air traffic increased by 70% between 2005 and 2020 and will continue to grow in the future [2,3]. Projections from various studies suggest annual growth rates of 4.5% to 4.8% in air travel, which will double passenger numbers in the period from 2016 to 2035 alone [4,5]. If cleaner propulsion technologies are not introduced, this will lead to a 300% increase in $C{O}_2$ emissions by 2050 [3]. To meet environmental goals, breakthrough technologies such as electric and hydrogen-powered aircraft that partially or completely eliminate $C{O}_2$ and $N{O}_X$ emissions must be introduced.

Since the specific energy of batteries is too low, they can only be considered as an energy source for very light general aviation aircraft or as a supplement to primary energy sources to enable all-electric takeoff and landing [6]. On the other hand, the energy density of hydrogen is 2.75-times higher than that of kerosene (33 kWh/kg versus 12 kWh/kg), making hydrogen an interesting fuel for aviation. Unfortunately, hydrogen has a low volume density and must, therefore, be stored either in cryogenic tanks in a liquid state or in pressurized tanks, usually at 350 or 700 bar. Since these tanks are both large and heavy, any benefits that come from high energy density can be lost due to the high weight of the tanks. Since a much higher gravimetric ratio (ratio of hydrogen mass in hydrogen tank systems) can be achieved with cryogenic tanks [7,8] than with pressurized tanks [9], it is expected that hydrogen aircraft will use liquid hydrogen as fuel.

Hydrogen can either be burnt directly, similar to kerosene, or used in a fuel cell to generate electricity to power a propeller. Although hydrogen combustion produces no $C{O}_2$ emissions, it still releases $N{O}_X$ gases, while the only byproduct in fuel cell aircraft is water vapor. However, due to fuel cell specifications, fuel cell technology is only suitable for propulsion system in smaller aircraft (e.g., regional aircraft). The first aircraft to run on hydrogen was the Tupoljev Tu-155, which made its first flight in 1988s [10]. In 2011, AeroVironment tested the first unmanned aerial vehicle powered by fuel cells [11]. The first manned aircraft to use fuel cell technology exclusively was the DLR-HY2, developed by Lange Aviation and the German Aerospace Center in 2009, while the first fuel cell aircraft to be used for commercial passenger mobility was the four-seat DLR-HY4 fuel cell aircraft, which made its first flight in 2016 [12]. Following these initial successful trials, several companies (e.g., H2Fly, ZeroAvia, AeroDelft) and projects (e.g., Mahepa) are attempting to expand the technology to larger aircraft. However, commercialization of fuel cell aircraft can only be successful if the capital and operating costs of such aircraft are equal to or lower than those of conventional aircraft. Since operating costs are highly dependent on the maximum take-off mass ($MTOM$) of an aircraft, the $MTOM$ mass of a fuel cell aircraft must first be estimated in order to predict when and if a fuel cell aircraft will not only be technologically feasible, but also economically viable.

An overview of the characteristics of hydrogen-powered aircraft are discussed in [10]. Some technical characteristics of small (unmanned and two-seat) fuel cell aircraft are discussed in [13,14]. Verstraete et al. [15] demonstrated that burning hydrogen instead of kerosene can result in a 30% reduction in $MTOM$ and an 11% reduction in energy consumption for a 380-seat long-range aircraft. In another article, Verstraete et al. [16] showed that hydrogen combustion is not as favorable for medium- and short-range aircraft with 300 and 150 passengers, respectively. Although medium-range aircraft powered by hydrogen are expected to be about 10% lighter than their conventional counterparts, they would have higher energy requirements. In addition, short-range fuel cell aircraft are expected to have both a higher $MTOM$ and energy consumption than conventional aircraft. A similar study by Mukhopadhaya and Rutherford [17] showed that turboprop aircraft powered by liquid hydrogen and capable of carrying 70 or 170 passengers will be heavier than conventional aircraft in the same category, while larger narrow-body aircraft could be lighter than conventional jets. On the other hand, there is very little research on estimating the $MTOM$ of fuel cell aircraft. The first attempt was made by Trainelli et al. [18]. The study showed that converting 4- and 11-seat aircraft to fuel cell aircraft would result in significant losses in mission performance. In addition, a study by Vonhoff [19] showed that an 11-seat fuel cell aircraft would have a larger $MTOM$, while a 19-seat aircraft would have a similar $MTOM$ compared to a conventional aircraft with the same number of seats. However, these results are based on the current characteristics of fuel cells and electric motors. As the power-to-weight ratio of fuel cells and electric motors is expected to improve in the future, the $MTOM$ of fuel cell aircraft will also decrease.

In this paper, the $MTOM$ of a 19-seat fuel cell aircraft powered by liquid hydrogen is investigated using a combination of a rapid estimation method and semi-empirical formulas. The 19-seat aircraft was selected because it is the largest certified passenger aircraft that falls under the regulations of FAR–23. Therefore, it should be both easier to register than larger aircraft and have a more favorable $MTOM$ compared to lighter FAR-23 aircraft. Since wing and power loading determine aircraft performance characteristics (optimal cruise speed, takeoff and landing distance, rate of climb), this study examines aircraft with different ranges and wing and power loading in order to provide a more general overview of the parameter settings at which fuel cell aircraft may be more advantageous than conventional aircraft.

Section 2 illustrates the $MTOM$ calculation methodology, including a calculation of the aircraft empty weight in Section 2.1, a calculation of the fuel cell aircraft powertrain mass in Section 2.2, and a calculation of the fuel mass in Section 2.3. The results are shown and discussed in Section 3, while conclusions are given in Section 4.

2. Methodology

The maximum takeoff mass comprises the aircraft operational empty mass ($OEM$), payload mass $m_{pl}$, and fuel mass ($m_f$, $m_{rf}$):

$$MTOM=OEM+m_{pl}+m_f+m_{rf}.$$

(1)

The operational empty mass includes the mass of the aircraft components (manufacturer empty mass), the mass of the pilots, and the fluids in the system (oil and residual fuel) and is calculated using the method shown in Section 2.1. The fuel mass determines the range of the aircraft and comprises the fuel consumed during the mission ($m_f$) and the reserve fuel ($m_{rf}$). The calculation of the fuel mass is explained in Section 2.3. The payload consists of the cabin crew, passengers, luggage, and consumables (food, water, etc.). Different combinations of payload and fuel are possible, resulting in different possible ranges. The payload mass can be reduced at the expense of fuel to achieve a longer range, and vice versa. Since the operating empty weight and fuel mass depend on the $MTOM$, it is first roughly estimated and then calculated in an iterative process. The calculation method is schematically represented in Figure 1.

2.1. Calculation of Operational Empty Weight

Although a 19-seat fuel cell aircraft does not yet exist, it will consist of components already used in conventional aircraft, as well as those unique to fuel cell aircraft. The mass of the conventional components can be estimated using existing and well-established methods for estimating aircraft mass. Meanwhile, the mass of components unique to fuel cell aircraft can be determined by extrapolating the masses of components already used in small fuel cell aircraft prototypes such as HY4 [20], using data on existing suitable components from other industries, or using theoretical estimates.

There is a variety of aircraft mass estimation methods for conventional aircraft, generally classified into three categories [21]: rapid methods, graphical methods, and semi-empirical methods. In rapid methods, component masses are expressed as fractions of the $MTOM$. In graphical methods, component masses are determined by plotting the masses of aircraft components of previously manufactured aircraft and fitting the results to the regression curve. Both the rapid and graphical methods are fast, but do not provide the ability to capture the level of technology and types of materials used. Semi-empirical methods are the most accurate, use semi-empirical equations derived from theoretical expectations, and are fitted to actual data. There are several semi-empirical equations derived by different authors [22,23,24,25,26]. The decision on the appropriate method depends on the type of aircraft, the expectations and needs of the users, and the availability of data.

The most appropriate method for the needs of this study should have the following characteristics: first, it should be tailored to the mass estimation of a 19-seat aircraft; second, it should be independent of specific design and manufacturing details; third, it should be able to distinguish, at least roughly, between aircraft with different flight characteristics (cruise speed, ceiling altitude, landing and takeoff distance, rate of climb, etc.). Flight characteristics mainly depend on four parameters: payload, range, wing loading, and power loading. The methodology must therefore be based on these four parameters, while typical values for 19-seat aircraft should be used for the other parameters. After a careful study of the various available methods for mass estimation, the authors of this study developed and adopted a combination of a rapid and a semi-empirical method, similar to that proposed by [21], for a 19-seat fuel cell aircraft. The mass of the wing and fuselage is calculated using semi-empirical formulas, while the mass of the other components, except the engine system, is determined using rapid methods. The mass of the engine system is calculated separately using a method adapted for fuel cell aircraft.

The book by [21] provides a list of components as a fraction of $MTOM$ separately for different aircraft categories depending on engine type and aircraft size. Data for small twin-engine turboprop aircraft for 19 or fewer passengers are given in

Table 1. Mass fractions for a small turboprop twin-engine aircraft for 19 or less passengers. The mass fractions are expressed as percentages. The sum of the mass fractions represents the mass fraction of the $OEM$ in the $MTOM$.

Component	Fuselage	Wing	H-tail	V-tail
Fraction	10% to 11%	10% to 12%	1.5% to 2%	1% to 1.5%
Component	Nacelle and Pylon	Undercarriage	Engine	Engine control
Fraction	1.9% to 2.3%	4% to 6%	7% to 10%	1.5% to 2%
Component	Fuel system	Oil system	Flight control sys.	Hydraulics
Fraction	1% to 1.2%	0.3% to 0.5%	1.5% to 2%	0.5% to 1.5%
Component	Electrical sys.	Instrument	Avionic	ECS
Fraction	2% to 4%	0.5% to 1%	0.3% to 0.5%	2% to 3%
Component	Oxygen	Furnishing	Miscellaneous	Contingency
Fraction	0.3% to 0.5%	6% to 8%	0% to 0.5%	1% to 2%

. The components add up to a minimum aircraft empty weight that is 58–63% of the $MTOM$. Components that are not part of the fuselage, wing, or engine group can be divided into two categories: those that retain their mass when the aircraft is converted from a conventional to a fuel cell aircraft and those that would scale with the $MTOM$. It can be concluded from Raymer’s semi-empirical equations and component percentages for other aircraft types [21] that the components that retain their mass are electrical systems, instruments, avionics, oxygen, furnishing, miscellaneous, and contingencies. These components account for 10.1% to 16.5% of the $MTOM$ (13.3% of the $MTOM$ on average). The components that scale with the $MTOM$ are hydraulics, the environmental control system (ECS), the flight control system, and undercarriage, which account for between 8% and 12.5% of the $MTOM$ (on average, 10.25% of the $MTOM$).

The mass of the fuselage is calculated using the semi-empirical equation devised by Jenkinson and Howe [21]:

$$m_f=0.039·{(2·L·D·v_d^{0.5})}^{1.5},$$

(2)

where L and D are the length and average diameter of the fuselage in meters, while $v_D$ is the design dive speed in meters per second. The design dive speed can be estimated as 1.4-times the cruise speed at ceiling [27]. Note that the [27] standard applies to general aviation aircraft, including light sport aircraft, so this estimate is conservative. Since gravity and lift forces are equal in cruise flight, the equation for cruise speed can be derived and, consequently, the equation for dive speed (in SI units):

$$v_d=1.4\sqrt{\frac{2g{W}_l}{C_L{\rho }_c}}$$

(3)

where $g=9.81$m/s${}^2$ is the gravitational acceleration constant, $W_l$ is the wing loading in kg/m${}^2$, $C_L$ is the lift coefficient, and ${\rho }_c$ is the air density at the ceiling. The typical lift coefficient for a light turboprop aircraft is 0.5, while the typical flight altitude is $7600$m with an air density of $\rho =0.55$kg/m${}^3$ [28,29,30,31,32,33,34,35,36,37,38].

The wing mass is calculated using a semi-empirical equation for a wing-mounted, twin-engine aircraft [21]:

$$m_w=0.0211·{(MTOM·N_{ult})}^{0.48}·S_w^{0.78}·AR·\frac{K^{0.4}}{cos\Lambda },$$

(4)

where $AR$ is the wing aspect ratio, $S_w$ is the wing area in square meters, $N_{ult}$ is the ultimate load factor, $\Lambda$ is the quarter chord wing sweep, and K is a factor dependent on wing characteristics. Since small turboprop aircraft have no sweep, $cos\Lambda =1$ can be set. The aspect ratios for existing 19-seat turboprop aircraft are given in

Table 2. Technical data for a 19-seat aircraft.

Aircraft	Dornier 228	Twin Otter	Beechcraft 1900	Let L-410
Year of production	1981	2010	1982	1969
$MTOM$ (kg)	6575	5670	7764	6600
Performance characteristics
Power loading (kW/kg)	0.176	0.2	0.246	0.17
Wing loading (kg/m2)	200	245	270	189
Geometrical characteristics
Taper ratio	0.7	1	0.4	0.4
Aspect ratio	9	10	10.8	11.45
Length (m)	16.54	15.77	17.62	14.4
Av. fuselage diameter (m)	1.7	1.63	1.59	1.81
Fuel in the wing (kg)	1958	1175	2022	1045
$OEM$ (kg)
Model	3910	3894	4736	4170
Data	3900	3363	4732	4200

. The wing area is calculated from the wing loading and the $MTOM$ as $S_w=MTOM/W_l$. The ultimate load factor is calculated as [21]:

$$N_{ult}=2.1+\frac{\mathrm{24\; 000}}{2.205\ast MTOM+\mathrm{10\; 000}}$$

(5)

while the coefficient K is calculated as:

$$K=\frac{(1-m_{fw}/MTOM)(1+\lambda )}{(t/c)},$$

(6)

where $\lambda$ is the ratio of wing taper ratio, $t/c$ is the thickness to chord ratio, and $m_{fw}$ is the amount of fuel stored in the wings. The typical value of $t/c$ for 19-seat turboprop aircraft ranges from 0.12 at the root to 0.18 at the chord [28,29,30,31,32,33,34,35,36,37,38], while the values of the taper ratio can range from 0.4 to 1 (see Table 2). As a higher taper ratio means that more fuel can be stored in the wings, the factor K is similar for all 19-seat aircraft. According to Table 1, the empennage accounts for 27% of the wing mass; therefore, the mass of the wing group (wing with empennage) can be calculated as:

$$m_{wg}=1.27·m_w.$$

(7)

The engine group consists of a turboprop engine, propeller, oil system, fuel system, and engine controls. The nacelle and pylon are also included, since their mass depends on the dimensions and mass of the engine. According to [21], excluding the nacelle and pylon, the mass of the engine group is equal to that of 1.5 of the dry engine. Taking into account that turboprop engines for 19-seat aircraft have a power-to-mass ratio of ${\sigma }_{eg}=4$kW/kg and adding the mass fractions of the nacelle and pylon from Table 1, the mass of the engine group can be calculated from the power loading:

$$m_{eg}=1.75·\frac{W_p·MTOM}{{\sigma }_{eg}}$$

(8)

where $W_p$ is the power loading ($P/MTOM$) in kW/kg. Therefore, the operating empty mass ($OEM$) of conventional aircraft (in kilograms) can be calculated as follows:

$$OEM=0.2355·MTOM+m_{wg}+m_f+m_{eg}+m_{2p}$$

(9)

where $m_{wg}$, $m_f$, and $m_{eg}$ are calculated using Equations (2), (7), and (8), respectively, while $m_{2p}=154$kg is the mass of two pilots [39]. The factor $0.2355$ is the sum of the mass fractions of all $OEM$ components except the fuselage, wind, and engine group (see Table 1). The $OEM$ of fuel cell aircraft is determined in a similar way:

$$OEM=0.133·MTO{M}_c+0.1025·MTOM+m_{wg}+m_f+m_{eg}+m_{2p}$$

(10)

where $MTO{M}_c$ is the mass of the conventional aircraft with the same geometric characteristics. The $0.133$ and $0.1025$ factors are the mass fractions of the components that retain their mass when the aircraft is converted from a conventional to a fuel cell aircraft and those that scale with the $MTOM$, respectively, as explained at the beginning of the section. To validate the $OEM$ estimation method, the calculated $OEM$ is compared with the known $OEM$ of 19-seat turboprop aircraft. There are three known 19-seat turboprop aircraft models still in production: DHC-6 Twin Otter, Dornier 228, and Let L-410 Turbolet, while three models are no longer in production, but are still in service: BAe Jetstream, Beechcraft 1900, and Fairchild Swearingen Metroliner [40]. Data on 19-seat turboprop aircraft are compiled in Table 2. Data on the BAe Jetstream and Fairchild Swearingen Metroliner are not included because insufficient data were found for an $OEM$ calculation or the data obtained from different sources are incompatible. The operating empty weight calculated by the described method is compared with the operating empty weight data for a 19-seat aircraft in Table 2. It is found that the estimated $OEM$ is very close (within 1%) to the actual $OEM$ for the Dornier 228, Beechcraft 1900, and Let L-410 Turbolet, while the $OEM$ of the DHC-6 Twin Otter is overestimated by about 15%. This is understandable since the DHC-6 Twin Otter is a relatively new aircraft and newer technologies and lighter materials were used.

2.2. Fuel Cell Aircraft Power-Train Parametrization

In the fuel cell aircraft, only the mass of the engine group and the fuselage changes (due to the installation of the cryogenic tank), while the mass of other components remains the same. The fuel cell engine group consists of the hydrogen tank, electric motor, fuel cell system, propellers, nacelle and pylon, and support components. The fuel cell system includes fuel cells, the compressor, and the cooling system for the fuel cells. The support components include the power management system for transferring power from the fuel cells to the electric motor and all piping and mounting structures. The mass of the powertrain of a fuel cell aircraft can therefore be calculated as follows:

$$m_{egFC}=m_T+m_{FCs}+m_{em}+m_{prop}+m_{pn}+m_{pms}+m_{oth},$$

(11)

where $m_T$ is the mass of the empty tank, $m_{FCs}$ is the mass of the fuel cell system, $m_{em}$ is the mass of the electric motor, $m_{prop}$ is the mass of the propeller, $m_{pn}$ is the mass of the pylon and nacelle, $m_{pms}$ is the mass of the power management system, and $m_{oth}$ is the mass of the other support components such as piping and mounting structures.

Cryogenic hydrogen tanks for ground vehicles already exist; unfortunately, these types of tanks are unsuitable for use in aircraft due to the specific requirements of the aircraft industry. Nevertheless, several theoretical studies have been conducted on modeling and sizing cryogenic tanks for aircraft [7,8,41,42]. One study [41] focused on the most suitable materials for tank design. The studies by Verstreate et al. [7] and Winnefeld et al. [8] agree that the best solution would be a single cylindrical hydrogen tank integrated into the fuselage with a circular cross-section, while the study by Silberhorn et al. [42] suggests podded tanks. In addition, both [7,8] agree that the ratio between the length and diameter of a tank does not have a significant effect on the gravimetric storage density of the tank, as long as the length of the tank is not significantly larger than its diameter. The mass of a hydrogen tank is usually defined by the gravimetric storage density, which is expressed as the mass fraction of fuel in the total fuel tank system:

$${\mu }_{grav}=\frac{m_F}{m_F+m_T}$$

(12)

where $m_F$ is the maximum fuel mass that can be stored in the tank, while $m_T$ is the mass of the empty tank. From the gravimetric storage density, the tank mass can be calculated as follows:

$$m_T=m_F\left(\frac{1}{{\mu }_{grav}}-1\right).$$

(13)

Studies [7,8] predict that the cryogenic hydrogen tank for aircraft can achieve gravimetric densities between 0.6 and 0.7. To install a cryogenic tank in the aircraft fuselage, the fuselage must be extended by:

$$\delta L=\frac{m_F}{{\rho }_H}\frac{4}{\pi {(D-2d)}^2}+2d,$$

(14)

where ${\rho }_H=71$kg/m${}^3$ is the density of liquid hydrogen, D is the fuselage diameter, and d is the insulation thickness. The study by [7] implies that the thickness of the tank walls for regional aircraft would be between $11$cm and $14$cm.

The mass of the fuel cell system includes that of the fuel cells, compressor, and cooling system. The mass of the fuel cell stack is proportional to the power that the fuel cells must provide: power for propulsion $P_{FCpr}$, cooling system $P_{cool}$, and compressor $P_{comp}$, so $P_{FC}=P_{FCpr}+P_{cool}+P_{comp}$. The power for the cooling system and compressor is proportional to the power of the fuel cell system, while the power for the propulsion system must be higher than the power required for the electric motor due to the efficiency of the electric motor and the energy management system:

$$P_{FC}=\frac{P_{el}}{{\mu }_{el}{\mu }_{pms}}+C_{comp}{P}_{FC}+C_{cool}{P}_{FC}.$$

(15)

This results in:

$$P_{FC}=\frac{P_{el}}{{\mu }_{el}{\mu }_{pms}(1-C_{comp}-C_{cool})},$$

(16)

where ${\mu }_{el}$ and ${\mu }_{pms}$ are the efficiencies of the electric motor and power management system, respectively, while $C_{comp}$ and $C_{cool}$ are the fractions of fuel cell power used by the compressor and the cooling system, respectively. Since the efficiency of fuel cells is low when they are operated at maximum power, the fuel cell stack must be oversized. If the ratio between operating power and maximum power is denoted by $C_{FC}$, the maximum power designed for the fuel cell is $P_{FCmax}=\frac{P_{FC}}{C_{FC}}$.

The mass of the fuel cell system can now be written as:

$$m_{FCs}=m_{FC}+m_{cool}+m_{comp}=\frac{P_{FCmax}}{{\sigma }_{FC}}+\frac{P_{FC}{C}_{cool}}{{\sigma }_{cool}}+\frac{P_{FC}{C}_{comp}}{{\sigma }_{comp}}$$

(17)

where ${\sigma }_{FC}$, ${\sigma }_{cool}$, and ${\sigma }_{comp}$ are the power-to-mass ratios of the fuel cell, cooling system, and compressor, respectively. Combining Equations (16) and (17) gives:

$$m_{FCs}=P_{el}\frac{\left(\frac{1}{C_{FC}{\sigma }_{FC}}+\frac{C_{cool}}{{\sigma }_{cool}}+\frac{C_{comp}}{{\sigma }_{comp}}\right)}{{\mu }_{el}{\mu }_{pms}(1-C_{comp}-C_{cool})}.$$

(18)

According to [19], the efficiency of both the electric motor and power management system are estimated as $0.9$ and may reach values of $0.95$ in the future. The compressor should provide sufficient atmospheric oxygen to the fuel cell to achieve optimal performance at high altitudes. According to [19], ${\sigma }_{comp}=2$kW/kg and $C_{comp}$ can be estimated at 7.6%. The specifications of the cooling system depend on the fuel cell type. The most technologically advanced fuel cells that can be used in the aerospace industry are proton exchange membrane fuel cells (PEMFCs) [19,43,44]. This type of fuel cell can achieve high power-to-mass ratios of up to ${\sigma }_{FC}=2.9$kW/kg [45]. A study by [43] even predicts that PEMFCs could achieve power-to-mass ratios of $8$kW/kg in the future. The main drawback of PEMFC fuel cells is their low operating temperature, which means they need an effective cooling system. Another possibility would be solid oxide fuel cells (SOFCs) [19]. However, SOFCs are currently still in an experimental stage [44] and have a low power-to-mass ratio of only $0.7$W/kg [46]. However, they do not require such an advanced cooling system due to the higher operating temperature and can achieve higher efficiencies [44]. Only PEMFCs are considered in this paper. The efficiency of a PEMFC varies from 50% to 60%, depending on the power output—the lower the power, the higher the efficiency is. The relationship between efficiency and output power between 20% and 80% can be approximated by the linear function ${\mu }_{FC}=0.64-0.2C_{FC}$ [43], while the efficiency drops steeply at higher output powers.

The sizing of the cooling system depends on the efficiency of the fuel cell. According to the study by [47], power demand for cooling depends on the air temperature, the working temperature of the fuel cell, and the amount of heat to be removed. At an altitude of $7600$m, 50% fuel cell efficiency, and when all heat generated by the fuel cells is removed by the cooling system and not by natural ventilation, $C_{cool}$ varies between $0.04$ and $0.05$, depending on the working temperature of the fuel cells, and ${\sigma }_{cool}=2$kW/kg.

The study by [43] estimates the electric motor power-to-weight ratio (${\sigma }_{em}$) as $5.8$kW, while the study by [19] estimates the electric motor power-to-weight ratio as $5$kW. Both studies predict that the power-to-weight ratio of electric motors could reach $10$kW in the future. However, the electric motors that can potentially be used to power aircraft already have power-to-weight ratios with values that reach $40$kW [48,49] and are similar in diameter to turboprop engines. The power-to-weight ratio of the power management system estimated by [19] is $10$kW and is expected to reach $15$kW in the future.

Since electric motors are lighter and have similar dimensions to turboprop engines, the mass of the nacelle and pylon of fuel cell aircraft is expected to be less than that of turboprop aircraft. Therefore, to be on the safe side, the model assumes that the nacelle, pylon, and propeller have the same mass as conventional turboprop aircraft. The same assumption was also proposed by [19]. Similarly, the propeller of a fuel cell aircraft has the same size as that of a conventional aircraft. It is difficult to estimate the mass of the piping and the mounting structures. It can be assumed that it is similar to or less than the mass of the oil and fuel system in conventional aircraft. Since the pylon and nacelle mass fraction is 25% of the $MTOM$ of a conventional engine, the propeller mass fraction is 10% of the $MTOM$ of a conventional engine, and the oil and fuel system mass fraction is 20% of the $MTOM$ of a conventional engine, the mass of the propeller support and the piping and attachment structures can be estimated as follows:

$$m_{prpo}+m_{pn}+m_{oth}=0.55·\frac{W_p·MTOM}{{\sigma }_{eg}}$$

(19)

with $W_p$ and ${\sigma }_{eg}$ as previously defined. By combining the above equations, the mass of the fuel cell aircraft engine can be calculated as follows:

$$m_{egFC}=m_F\left(\frac{1}{{\mu }_{grav}}-1\right)+$$

$$W_p·MTOM\left(\frac{\frac{1}{C_{FC}{\sigma }_{FC}}+\frac{C_{cool}}{{\sigma }_{cool}}+\frac{C_{comp}}{{\sigma }_{comp}}}{{\mu }_{el}{\mu }_{pms}(1-C_{comp}-C_{cool})}+\frac{1}{{\sigma }_{em}}+\frac{1}{{\sigma }_{pms}}+\frac{0.55}{{\sigma }_{eg}}\right).$$

(20)

2.3. Calculation of Fuel Mass

The fuel consumption of the aircraft is proportional to its mass. It is calculated as the ratio of the mass of the aircraft at the beginning and at the end of the flight mission, which is called the mission fuel fraction:

$$M_{ff}=\frac{m_{stop}}{m_{start}}.$$

(21)

The mission fuel fraction is calculated by dividing the flight mission into flight phases:

$$M_{ff}=\sum _i\frac{m_i}{m_{i+1}}=\sum _i{k}_i,k_i=\frac{m_i}{m_{i+1}}$$

(22)

where $m_{i+1}$ is the mass at the beginning of each flight phase, $m_i$ is the mass at the end of the flight phase, and $k_i$ is the mission segment mass fraction. According to [24], the average mission segment mass fraction for conventional aircraft for engine start, taxi-out, and takeoff is 0.97 and for climb is 0.985, while for landing and taxi-in, it is 0.995, with the product being 0.95. Roskam’s values [23] for the aircraft types under consideration are summarized in the

Table 3. Average mission segment mass fractions for some typical aircraft types: SP—single piston engine, TP—twin piston engine, RT—regional turboprop, BJ—business jet.

Mission Segment	SP	TP	RT	BJ
start and taxi-out ($k_0$)	0.992	0.988	0.985	0.985
takeoff ($k_1$)	0.998	0.996	0.995	0.995
climb ($k_2$)	0.992	0.990	0.985	0.980
landing and taxi-in ($k_3$)	0.986	0.985	0.98	0.982
total ($k_t$)	0.968	0.960	0.946	0.943

.

The mass fraction in cruise flight is calculated using Breguet’s equation for propeller-driven aircraft:

$$k_c=e^{-R_c/B_s}{B}_s=\frac{L}{D}\frac{\eta }{SF{C}_{P}g},$$

(23)

where $SF{C}_P$ is the power-specific fuel consumption, $\eta$ is the propeller efficiency, $g=9.81$ is the gravitational acceleration constant, $L/D$ is the ratio of lift to drag at cruise, and $R_c$ is the distance traveled by the aircraft in cruise flight. The propeller efficiency is about 0.8 for all aircraft types, except for piston aircraft with a fixed pitch propeller during loiter (0.7). The typical lift-to-drag ratio of a 19-seat turboprop aircraft is 18, while the specific fuel consumption of a turboprop engine is $SF{C}_P=0.09·{10}^{-6}$kg/J. Therefore, the mass of the consumed fuel can be calculated from Equation (21):

$$m_f=m_{start}\frac{1-M_{ff}}{M_{ff}}=(OEM+m_{pl}+m_{rf})\frac{1-M_{ff}}{M_{ff}},$$

(24)

where $OEM$ is the operating empty mass of the aircraft calculated in Section 2.1, $m_{pl}$ is the mass of the payload (passengers, luggage, and cargo), and $m_{rf}$ is the mass of the reserve fuel. According to [39], the mass of the reserve fuel should be sufficient for a 30 min flight at full power, thus:

$$m_{rf}=SF{C}_P·W_p·MTOM·30\min =0.162\frac{\mathrm{kg}}{\mathrm{kW}}·W_p·MTOM.$$

(25)

For fuel cell aircraft, in Equations (23) and (25), the specific consumption of the turboprop engine must be replaced by that of the fuel cell propulsion system $SF{C}_{Pfc}$. In addition, the average mission segment mass fraction for the mission profiles in Table 3 must be recalculated taking into account the difference between the specific fuel consumption of the turboprop and fuel cell power-train systems. The consumption of fuel cells can be estimated from the energy content of fuel cells and the efficiencies of fuel cell power train system components. The energy contest of hydrogen is $w_H=120$MJ/kg, while the total efficiency of the fuel cell system is $\mu ={\mu }_{fc}{\mu }_{el}{\mu }_{pms}(1-C_{cool}-C_{comp})$, yielding the specific consumption of the fuel cell system:

$$SF{C}_{Pfc}=\frac{1}{w_H{\mu }_{fc}{\mu }_{el}{\mu }_{pms}(1-C_{cool}-C_{comp})}$$

(26)

3. Results and Discussion

The methodology explained in the previous section was used to calculate the $MTOM$ of fuel cell aircraft and its conventional version for comparison. Two types of aircraft were considered depending on the geometric characteristics of the wings and fuselage taper ratio, aspect ratio, fuel mass in the wings, length, and diameter: one with the geometric characteristics of the Dornier 228, referred to as the Dornier geometric type, and another with the geometric characteristics of the Beechraft 1900, referred to as the Beechcraft geometric type. The geometric characteristics of the two aircraft types are shown in Table 2. The payload mass was set to $1960$kg for all aircraft types and parameter settings. Two marginal parameter sets were chosen for the fuel cell aircraft, one representing the future/optimistic scenario and the other the present/pessimistic scenario. The fuel cell aircraft parameters for both options are listed in

Table 4. Parameters for the fuel cell aircraft.

	${\mathit{\mu }}_{\mathit{grav}}$	${\mathit{C}}_{\mathit{FC}}$	${\mathit{C}}_{\mathit{cool}}$	${\mathit{C}}_{\mathit{comp}}$	${\mathit{\sigma }}_{\mathit{FC}}$	${\mathit{\sigma }}_{\mathit{cool}}$	${\mathit{\sigma }}_{\mathit{comp}}$	${\mathit{\sigma }}_{\mathit{em}}$	${\mathit{\sigma }}_{\mathit{pms}}$	${\mathit{\mu }}_{\mathit{el}}$	${\mathit{\mu }}_{\mathit{pms}}$	d
					(kW/kg)	(kW/kg)	(kW/kg)	(kW/kg)	(kW/kg)			(cm)
present/pessimistic	0.6	0.8	0.05	0.076	2.9	2	2	5	10	0.9	0.9	14
future/optimistic	0.7	0.8	0.04	0.076	8.0	2	2	40	15	0.95	0.95	14

. The value of $C_{FC}$ was set to $0.8$ since lower values of $C_{FC}$ are less favorable and result in a larger $MTOM$. One of the performance parameters: range, power loading, and wing loading, was varied for both geometric types, while the other parameters remained fixed—range at full payload to $500$km, power loading to $0.18$kW/kg, and wind loading to $200$kg/m${}^2$.

The results are shown in Figure 2. The results show that for the same geometric and performance characteristics, the fuel cell aircraft with similar characteristics to the Dornier 228 is about 4% lighter than the conventional version for the future/optimistic version and about 25% heavier than the conventional version for the present/pessimistic version. Although the geometric Beechcraft aircraft type is slightly heavier than the geometric Dornier aircraft type, the ratio between the $MTOM$ of the fuel cell and the conventional versions is similar for both geometric types. Therefore, it can be concluded that the geometric characteristics do not have a major impact on the $MTOM$ of fuel cell aircraft. In addition, wing loading and range do not significantly affect the ratio between the $MTOM$ of fuel cell and conventional aircraft, although slight differences can be observed in favor of aircraft with a longer range and lower wing loading. In contrast, the difference in the $MTOM$ ratio of fuel cell and conventional aircraft is more pronounced for power loading, with lower values of power loading being preferred for fuel cell aircraft. The main reason for this is the relatively low power-to-weight ratio of fuel cells. The dependence of the fuel cell aircraft $MTOM$ on the fuel cell power-to-weight ratio is shown in Figure 3, where it can be seen that the improvement in the fuel cell power-to-weight ratio from $2$kW/kg to $4$kW/kg significantly affects the $MTOM$ of the fuel cell aircraft. It can be concluded that fuel cell development is a critical element that could determine the existence and feasibility of 19-seat fuel cell aircraft in the future. If the desired fuel cell power-to-weight ratio cannot be achieved, fuel cell aircraft design should move toward lower power and higher wing loading, which would result in longer takeoff distances and lower climb rates, while other performance characteristics remain similar to conventional aircraft. This may lead to changes in ground infrastructure and runway lengthening.

The mass fractions of the aircraft components, payload, and fuel are shown in Figure 4. As expected, the engine system accounts for a higher fraction of the overall aircraft $MTOM$ in fuel cell aircraft than in conventional aircraft due to the low power-to-weight ratio. In the present/pessimistic version, the share of the engine in the $MTOM$ of the fuel cell aircraft is more than twice that of the conventional aircraft. In contrast, due to the high specific energy of hydrogen compared to kerosene, the fuel fraction in the fuel cell aircraft is lower than in the conventional aircraft.

Installation of a liquid hydrogen tank in the fuselage increases the wetted area of the aircraft and thus the drag. The effect of increased drag was neglected in this study. According to [51], the wetted area of the aircraft is approximately six-times larger than the wing area. This means that increasing the fuselage area by installing a tank would increase the wetted area of the aircraft by 6%, consequently decreasing the lift-to-drag ratio by 3%. Such a change in the lift-to-drag ratio would have an insignificant effect on the $MTOM$ and can therefore be safely neglected. The additional thrust that may be provided from fuel cell cooling system was also neglected. Furthermore, in fuel cell aircraft, the hydrogen is moved from the wing to the fuselage, and the empty space is filled with fuel cells. This changes the bending moment of the wing, resulting in a change in the structural mass of the wing and adding uncertainty to the fuel cell aircraft mass estimate.

If the power-to-weight ratio of batteries is higher than that of fuel cells, some of the fuel cells could be replaced by batteries to provide power during takeoff. Currently, batteries achieve a power-to-weight ratio of $3.3$kW/kg compared to $2.9$kW/kg for fuel cells and, therefore, have only a slightly better power-to-weight ratio. Therefore, this scenario was not tested in this study.

Finally, the authors emphasize that this study is based on the results of theoretical studies of the gravimetric storage density of a tank [16], the cooling system [47], and assumptions about the properties of future components, which may prove to be different in the future.

4. Conclusions

The study predicts that future fuel cell aircraft could achieve a lower $MTOM$ than conventional aircraft while maintaining the important flight characteristics of conventional aircraft. This primarily depends on the future development of fuel cells, which must achieve a power-to-weight ratio of at least $4$kW/kg. Nevertheless, even at current fuel cell power-to-weight ratio values, the $MTOM$ of a 19-seat fuel cell aircraft is not unrealistically large, as is the case with battery-powered aircraft. Therefore, even in this case, fuel cell aircraft could be a possible future alternative to conventional aircraft with slightly inferior performance characteristics. Since the $MTOM$ of an aircraft affects the important cost elements such as production cost, fuel cost, and airport charges, this study provides the basis for further economic analysis of fuel cell aircraft, which has yet to be conducted. The economic competitiveness of fuel cell aircraft compared to kerosene aircraft primarily depends on the evolution of hydrogen and kerosene prices, as well as the environmental constraints imposed on conventional aircraft due to higher carbon costs, making them a less economic option compared to fuel cell aircraft.