Introduction

The concept of electric aviation is driven by the growing concern over the aviation industry’s contribution to greenhouse gas emissions and climate change1,2. To put this into perspective, the per-passenger emissions produced by a round-trip flight from Lisbon to New York are approximately equivalent to the emissions generated by an average person in the European Union when heating their home for an entire year3, which is large enough to rank the aviation industry among the top 10 emitters in the world if it was considered a country3. The significance of emissions from the aviation industry is amplified by the fact that most of the carbon dioxide (CO2) produced by aviation is international, falling outside the scope of the Paris Agreement4. This emphasized the necessity of electric propulsion to reduce CO2 emissions5. Electric aviation would also address some non-CO2 emissions, including the excessive noise associated with conventional jet propulsion6. While electric aviation shows promise for a greener and more sustainable future, it faces various technical, regulatory, and infrastructure challenges. One major hurdle is the limitation of current battery technology, which can affect electric aircraft’s range and payload capacity7. Additionally, developing a reliable and extensive charging infrastructure for electric planes is crucial for widespread adoption.

A practical approach to address this challenge involves employing fuel cells (FC) for on-site power generation on the aircraft, eliminating the need for battery storage and charging infrastructure. Similar hybrid approaches have also been proposed for marine transportation8. A few projects are investigating the feasibility of developing large electric airplanes beyond the size of training aircraft using liquid hydrogen and FC. Nevertheless, this idea presents logistical hurdles, primarily the necessity to maintain hydrogen in its liquid state, which requires storage at a frigid -252.8 °C. An initiative sponsored by the U.S. National Aeronautics and Space Administration, namely the C arbonL ess E lectric A viatioN (CLEAN) project9, led by our team in collaboration with several other institutions, also utilizes FC to tackle the electric aviation challenge. The CLEAN project focuses on using ammonia as the fuel, which remains liquid at atmospheric pressure with a less extreme requirement of -33.6 °C.

Our power generation method to make electric aviation feasible involves hybridizing a traditional gas turbine (GT) with a solid oxide fuel cell (SOFC)10. This approach offers a substantial increase in thermal efficiency when compared to existing state-of-the-art aircraft propulsion systems. The enhanced efficiency in converting chemical energy into electrical energy reduces fuel consumption. Preliminary simulations of the SOFC-GT hybrid system under commercial flight conditions of a Boeing 737 have demonstrated a propulsion efficiency greater than 60%11,12,13. This efficiency almost doubles the performance of the current state-of-the-art LEAP-1B engine used in the Boeing 737 MAX. The electrical power generated by the SOFC, along with the generator connected to the GT’s shaft, enables the system to power a set of electric motors responsible for generating the necessary thrust for the aircraft. A schematic of this power generation and propulsion system is depicted in Fig. 1.

Fig. 1
figure 1

The proposed hybrid electric propulsion system.

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The high efficiencies of the SOFC-GT system stem from the synergistic integration of the GT and SOFC. The SOFC utilizes pressurized air to generate electricity and high-temperature waste heat. On the other hand, the GT relies on a high-temperature heat source, which can be provided by a combustor or the SOFC itself. The GT’s compressor produces warm, compressed discharge air, which is later combusted with the anode exhaust (hydrogen) to heat the incoming cathode air to attain the required SOFC operational temperatures of approximately 750 °C. The combustion of the compressed air with the anode off-gas allows for precise and rapid thermal control of the SOFC operational temperature through a single fuel valve. This unique characteristic also eliminates the necessity for a bulky and heavy heat exchanger, making the system more streamlined and efficient. Thermal control of the SOFC stack is crucial when operating an FC hybrid system, which ideally would operate the SOFC isothermally. The SOFC first converts the chemical energy stored in the fuel to electrical energy through electrochemical reactions. The waste heat generated by the SOFC is transferred to the cathode air via convection. The high-temperature exhaust from the cathode is subsequently directed through the turbine, where work is extracted by expanding the hot gases. The work generated by the turbine is transmitted via a shaft to provide work for the compressor and generator.

A general SOFC electrochemical reaction is between hydrogen on the anode electrode and oxygen on the cathode electrode to form the product of steam on the anode electrode14,

$$6{{{{{\rm{H}}}}}}_{2}+3{{{{{\rm{O}}}}}}_{2}\,\to \,6{{{{{\rm{H}}}}}}_{2}{{{{\rm{O}}}}}.$$
(1)

For the FC to generate electricity, it first needs a supply of hydrogen and oxygen. The oxygen supply is obtained by directing ambient air through the compressor discharge. The supply of hydrogen is obtained by utilizing hydrogen-carrying fuel. In the CLEAN project, ammonia is employed as fuel since it does not include many of the constraints a liquid hydrogen aircraft contains, such as the needed fuel volume for sufficient range and thermal control to maintain cryogenic temperatures. The ammonia can be broken down into hydrogen and nitrogen through thermal cracking15,16,17. This cracking can be done internally on the SOFC anode or with an externally heated catalyst bed as

$$4{{{{{\rm{NH}}}}}}_{3}\to 6{{{{{\rm{H}}}}}}_{2}+2{{{{{\rm{N}}}}}}_{2.}$$
(2)

Assuming all fuel is completely oxidized, the proposed system’s exhaust products will include oxygen, nitrogen, and steam, assuming NOx formation is minimized through controlling post-combustion temperatures.

As technology advances through such projects and the industry and governments continue to invest in electric aviation research, one can expect to see more hydrogen-based electric aircraft taking to the skies in the coming years. While employing hydrogen-based fuels will eliminate CO2 emissions, it might lead to more non-CO2-related climate effects, defeating the purpose of such efforts. Hydrogen fuels increase water content in the exhaust gas, potentially leading to a higher and more persistent occurrence of contrails. Contrails can influence the Earth’s climate by affecting the balance of incoming and outgoing radiation, warming the atmosphere. This climate impact is more pronounced in regions with heavy air traffic. Literature provides valuable insight into the significance of the contrail effect, highlighting that contrails can diminish incoming shortwave radiation at the surface and reduce photovoltaic power production by up to 10%18. Contrails contribute to more than 50% of aviation’s total radiative forcing19.

This article employs a thermodynamic analysis to investigate essential distinctions between contrails induced by the proposed ammonia-based propulsion system and those formed by conventional jet fuel. The thermodynamic analysis presented herein is a crucial prerequisite for future high-fidelity computational fluid dynamics simulations, as it identifies the contrail-forming conditions under which one must conduct those studies. Identifying contrail-forming regions would also allow airplanes to avoid them by adopting alternative flight trajectories20 or elevations21 with minimal increased fuel consumption to mitigate contrail effects. Since only a small percentage of flights cause the most contrail effect, strategic flight routes and altitude planning can somewhat alleviate the issue. For example, only 12% of flights within the North Atlantic-recognized as one of the globe’s busiest air traffic routes-contribute to 80% of the annual contrail climate forcing in this area22. Another study indicates that a mere 2.25% of flights contribute to approximately 80% of the contrail energy forcing within the airspace of Japan20. This article primarily focuses on flights at 11,470 m, corresponding to 21,000 Pa. The impact of relative humidity (RH) and axial distance from the aircraft, which correlates to the entrainment of fresh air into the contrail, is studied for both fuels (ammonia and kerosene). Relative humidity of the background air is employed to model the effect of pre-existing cirrus on contrail properties, and as demonstrated by large-eddy simulations reported in the literature, they appear to elevate the critical temperature23. The analysis reveals that powering the aircraft with ammonia instead of kerosene exhausts 2.74 times more water into the atmosphere, assuming it burns an equal mass of each fuel. The ratio would be 6.11 on an equal energy basis, as one needs to burn 2.23 grams of ammonia to achieve the energy that burning 1 gram of kerosene yields. The analysis reports that switching to ammonia increases the critical temperature required for supersaturation while showing how this temperature varies with entrainment ratio and axial distance from the airplane. It also discusses whether the absence of soot in the ammonia-powered airplane’s exhaust is sufficient to dismiss concerns about increased contrails.

Methodology

Moisture to temperature ratio

A flying airplane injects water and heat into the atmosphere. The added water increases relative humidity, while the added heat decreases relative humidity due to increased temperatures. Thus, when comparing the impact of different fuels on contrail formation and persistence, it is essential to compute the ratio of the change in temperature to the change in mixing ratio caused by the fuels. The mixing ratio, denoted as X in g kg−1, represents the quantity of water vapor in grams contained within one kilogram of air. This section computes this ratio for jet fuel and ammonia. Throughout the remainder of this document, we will frequently use the values.

Consider an airplane burning jet fuel C11H22,

$$2{{{{{\rm{C}}}}}}_{11}{{{{{\rm{H}}}}}}_{22}+33{{{{{\rm{O}}}}}}_{2}\to 22{{{{{\rm{H}}}}}}_{2}{{{{\rm{O}}}}}+22{{{{{\rm{CO}}}}}}_{2}.$$
(3)

Based on Equation (3), burning each gram of jet fuel generates 1.284 grams of water and 3.140 grams of CO2. Jet fuel possesses an energy density of approximately 41,840 J g−1, with g standing for grams. Similar to air entrainment of fire plumes24, fresh air dilutes contrails. Let’s consider an entrainment ratio denoted as N, indicating the amount of air (in grams) that mixes into the contrail for every gram of CO2 produced. The entrainment ratio varies with the axial distance from the exhaust, being 0 at the exhaust and increasing to an infinitely large value far away from the exhaust, where the contrail eventually ceases to exist due to a substantial influx of fresh air. Applying the heat equation Q = mcΔT and assuming that all the heat generated from the reaction, described in Equation (3), is transferred to the contrail, one can make an approximation of the increase in air temperature within the contrail domain for each gram of fuel as:

$$Q=mc\Delta T\to \Delta T=\frac{10,000}{3.14N\times 0.240}$$
(4)

with 0.240 cal g−1 K−1 being the specific heat capacity of air, m = 3.14N being the mass of air that absorbs the heat, Q = 41, 840 J being the amount of heat released from burning one gram of the fuel, and ΔT being the change in air temperature. The mixing ratio, denoted as X in g kg−1, represents the quantity of water vapor in grams contained within one kilogram of air. Hence, the change in mixing ratio is,

$$\Delta X=\frac{1.284}{3.14N/1,000}=\frac{1,284}{3.14N}.$$
(5)

Airplane exhaust gases consist of both moisture and heat, wherein the former contributes to increasing the relative humidity, while the latter leads to its reduction. Given that the impacts of increased temperature (Equation (4)) and the additional mixing ratio (Equation (5)) on relative humidity counteract each other, it becomes essential to calculate the ratio between the two,

$${\frac{\Delta X}{\Delta T}}_{{{{{\rm{jetfuel}}}}}}=\frac{\frac{1,284}{3.14N}}{\frac{10,000}{3.14N\times 0.240}}\approx 0.031\,{{{{\rm{g}}}}}\,{{{{{\rm{kg}}}}}}^{-1}\,{{{{{\rm{K}}}}}}^{-1}.$$
(6)

Consequently, per each degree Kelvin increase in air temperature caused by the aircraft burning jet fuel, it adds 0.031 grams of water moisture to every kilogram of air. Notably, the entrainment ratio between the two terms cancels out, rendering \(\frac{\Delta X}{\Delta T}\) independent of N. Ammonia, on the other hand, burns as

$$4{{{{\rm{N}}}}}{{{{{\rm{H}}}}}}_{3}+3{{{{{\rm{O}}}}}}_{2}\to 2{{{{{\rm{N}}}}}}_{2}+6{{{{{\rm{H}}}}}}_{2}{{{{\rm{O}}}}}$$
(7)

which leads to the release of 18,799 J g−1 of heat and 1.588 grams of water per every gram of fuel burnt. Hence, \(\frac{\Delta X}{\Delta T}\) for ammonia is

$${\frac{\Delta X}{\Delta T}}_{{{{{\rm{ammonia}}}}}}=\frac{\frac{1,588}{0.823N}}{\frac{4,493}{0.823N\times 0.240}}\approx 0.085\,{{{{\rm{g}}}}}\,{{{{{\rm{kg}}}}}}^{-1}\,{{{{{\rm{K}}}}}}^{-1}.$$
(8)

Therefore, when the aircraft utilizes ammonia, it introduces 0.085 grams of water to each kilogram of air for every degree Kelvin increase in the air temperature it induces. Comparing \(\frac{\Delta X}{\Delta T}\) for the two fuels as

$$\frac{{\frac{\Delta X}{\Delta T}}_{{{{{\rm{ammonia}}}}}}}{{\frac{\Delta X}{\Delta T}}_{{{{{\rm{jetfuel}}}}}}}=2.74$$
(9)

indicates that the aircraft using ammonia puts 2.74 times more moisture in every kilogram of air per every degree Kelvin temperature increase it causes.

As explained before, in addition to the SOFC unit, the proposed hybrid electric propulsion system utilizes a combustor right after the FC, acting as an afterburner to provide additional thrust (see Fig. 1). The FC directly powers the electric motor while the combustor powers a GT attached to a generator. The generator then contributes to the electric motor’s input power. This system’s performance and efficiency depend on the FC/GT power ratio. The optimal FC/GT power ratio is still unknown as the authors are developing a comprehensive multidisciplinary, multi-objective, system-level optimization to identify this ratio to maximize aerodynamic lift/drag, minimize thrust-specific fuel consumption, minimize NOx formation, and minimize exhaust relative humidity—all while avoiding aeroelastic flutter. Thus, since the optimal FC/GT power ratio is still unknown, the analysis needed to choose some arbitrary FC/GT ratio or present the results for various FC/GT ratios in order to take into account the system’s efficiency. That was doable; however, it would distract from the central message of this article and make this work more about system performance for various FC/GT ratios. Thus, this study did not include the efficiencies of the hybrid-electric system and the conventional propulsor in the analysis.

With all that considered, it is also essential to point out that the fuel’s oxidization in the combustor or the fuel cell follows the same reaction (i.e., Equation (7)). While the FC and GT efficiencies differ, as mentioned above, this study did not account for efficiencies upon determining how much of the fuel’s energy was released upon oxidization and how much of the released energy was absorbed via the contrail. Instead, the analysis assumed that the entire energy of the fuel was released upon oxidizing, and all the released energy was absorbed entirely via the air within the contrail. The same assumption was applied to both ammonia and kerosene fuels. Assuming that all of the released heat affects the contrail for jet fuel and ammonia is fairly reasonable because even under non-ideal conditions, the entire energy released by burning the fuel will eventually be converted to heat (whether useful or waste). All the released heat has nowhere to go but into the airplane’s wake, either through the exhaust or the aircraft’s exterior surface.

Flying through saturated atmosphere

It is essential to establish a way to determine whether an airplane burning a specific fuel flying through an already saturated atmosphere would maintain saturation or would result in undersaturation (negative contrail). Let us assume the aircraft is flying through saturated air at a background pressure and temperature of pa (in Pa) and T1 (in K), respectively, and raises the temperature by ΔT. The maximum quantity of water vapor that one kilogram of air can hold before condensation occurs, denoted as Xs (where s stands for saturation), is given by25:

$${X}_{{{{{\rm{s}}}}}}=\frac{621.98{p}_{{{{{\rm{ws}}}}}}}{{p}_{{{{{\rm{a}}}}}}-{p}_{{{{{\rm{ws}}}}}}}$$
(10)

where pa is air pressure and pws is the maximum saturation pressure of water in the air with dry bulb temperature of T in K, computed via the Clausius-Clapeyron equation as26,27,

$${p}_{{{{{\rm{ws}}}}}}={p}_{0}.\exp \left[\frac{L}{{R}_{{{{{\rm{v}}}}}}}\left(\frac{1}{{T}_{0}}-\frac{1}{T}\right)\right]$$
(11)

where the water–vapor gas constant is Rv = 461 J K−1 kg−1, T0 = 273.15 K, p0 = 0.6113 kPa, and L is a latent-heat parameter in J kg−1. By substituting the background pressure and temperature (pa and T1) into Equations (10) and (11), we obtain the value of X1. When replacing T1 with T2 = T1 + ΔT, we arrive at X2. Consequently, one can compute the minimum required increase in the mixing ratio as ΔX = X2−X1. Finally, to determine if this flight would maintain the saturation, one must divide this computed ΔX by the given ΔT and compare the outcome against 0.031 g kg−1 K−1 for jet fuel and 0.085 g kg−1 K−1 for ammonia. If the computed ΔX/ΔT is smaller than 0.031 g kg−1 K−1 (for jet fuel) or 0.085 g kg−1 K−1 (for ammonia), then the fuel not only maintains the saturation, it can push it to supersaturation. If larger, it would lead to undersaturation, i.e., if clouds already existed in the atmosphere, the airplane would diminish them.

Flying through unsaturated atmosphere

Another critical scenario is an airplane flying through sub-saturated air with a relative humidity RH  < 1. The relative humidity is defined as the ratio of the air’s moisture content (mw in kg) to the maximum amount of moisture the air can hold (\({m}_{{{{{\rm{w}}}}},\max }\) in kg), denoted as RH = \(\frac{{m}_{{{{{\rm{w}}}}}}}{{m}_{{{{{\rm{w}}}}},\max }}\). It is critical to establish whether jet fuel and ammonia can transform a given unsaturated air to saturated and then maintain that saturation.

A conventional aircraft powered by jet fuel adds 0.031 g of moisture to every kilogram of air for every degree Kelvin increase in the air’s temperature. On the other hand, the proposed electric aircraft consuming ammonia adds 0.085 g of moisture for each degree Kelvin temperature rise it causes. Initially, the added moisture saturates the unsaturated air at the atmosphere’s initial temperature. Any remaining moisture, if present, will be utilized to maintain saturation as the air’s temperature increases due to exhaust gases. This section aims to investigate whether the moisture added by 0.031 g kg−1 K−1 and 0.085 g kg−1 K−1 is sufficient to raise the unsaturated air’s moisture to saturation. Additionally, it explores whether the remaining moisture, after reaching saturation, is adequate to keep the air saturated. The answers to these questions are contingent on the initial humidity, background pressure, initial temperature, and temperature increase.

Suppose the initial relative humidity is RH and the maximum amount of water vapor that one kilogram of air can hold is Xs. Hence, the actual mixing ratio can be computed as X = RH × Xs because \({{{{\rm{RH}}}}}\times \scriptstyle{X}_{{{{{\rm{s}}}}}}=\frac{{m}_{{{{{\rm{w}}}}}}}{{m}_{{{{{\rm{w}}}}},\max }}\times \frac{{m}_{{{{{\rm{w}}}}},\max }}{{m}_{{{{{\rm{air}}}}}}}=\frac{{m}_{{{{{\rm{w}}}}}}}{{m}_{{{{{\rm{air}}}}}}}\). The moisture required to reach saturation is Xs−X, or Xs−RH × Xs = Xs(1 − RH). This required moisture to reach saturation can be presented in per degree Kelvin as \(\frac{{X}_{{{{{\rm{s}}}}}}}{\Delta T}(1-{{{{\rm{RH}}}}}).\) Hence, the \({(\frac{\Delta X}{\Delta T})}_{{{{{\rm{r}}}}}}\) that remains available for keeping the air saturated after bringing it up from unsaturated to a saturated state is,

$${\left(\frac{\Delta X}{\Delta T}\right)}_{{{{{\rm{r}}}}}}=0.031-\frac{{X}_{{{{{\rm{s}}}}}}}{\Delta T}(1-{{{{\rm{RH}}}}})$$
(12)

and

$${\left(\frac{\Delta X}{\Delta T}\right)}_{{{{{\rm{r}}}}}}=0.085-\frac{{X}_{{{{{\rm{s}}}}}}}{\Delta T}(1-{{{{\rm{RH}}}}})$$
(13)

for jet fuel and ammonia, respectively. Note that Equations (12) and (13) yielding a negative value means the unsaturated air cannot reach saturation, thus \({(\frac{\Delta X}{\Delta T})}_{{{{{\rm{r}}}}}}=0\). Also, note that \({(\frac{\Delta X}{\Delta T})}_{{{{{\rm{r}}}}}}\) represents the amount of available moisture to keep the saturation after some of the available moisture in the exhaust gases has been consumed to bring the sub-saturation state to saturation.

Results and Discussion

Flying through saturated atmosphere

Equations (10) and (11) produce the data needed to compare the potential of jet fuel and ammonia in maintaining air saturation. Suppose an airplane flies through the air with pressure and temperature of 10 kPa and -50 °C (=223.15 K) and increases the temperature in its wake by 5 °C to -45 °C (=228.15 K). Inserting 223.15 K in Equation (11) yields 6.363 Pa, leading to Xs1 = 0.3960 using Equation (10), which increases to Xs2 = 0.6918 at -45 °C. So, the mixing ratio needs to increase by ΔX = 0.2958 g kg−1. Dividing this by ΔT = 5 °C, \(\frac{\Delta X}{\Delta T}=0.059\) g kg−1 K−1 is needed to keep the air saturated. A fuel that produces more than 0.059 grams of water per kilogram of air per every degree temperature would lead to supersaturation, and a smaller value would lead to undersaturation, i.e., a negative contrail. Considering Equations (6) and (8), a conventional propulsion using jet fuel can provide 0.031 g kg−1 K−1, which is less than the required 0.059 g kg−1 K−1; thus, leads to a negative contrail. However, an ammonia-powered propulsive provides 0.085 g kg−1 K−1, more than what is required to keep the atmosphere saturated, leading to a supersaturated atmosphere. Therefore, the provided conditions would lead to the formation of contrails with ammonia but not jet fuel.

Table 1 reports the required added moisture into every kilogram of air per every degree Kelvin increase in the temperature in order to keep the air saturated at nearly 5486 m and 11,470 m. Values smaller than 0.085 g kg−1 K−1 indicate that supersaturation occurs if the proposed ammonia-based aircraft flies through these atmospheric conditions. These values are marked by *. Values smaller than 0.031 g kg−1 K−1 indicate conditions where the conventional aircraft with jet fuel would also lead to supersaturation. These values are marked by +. This table is an example of the type of data the presented analysis can provide. Using the theory described herein, one can extend this table to cover a broader range of background temperatures and pressures as needed, determining the conditions that can lead to contrail formation.

Table 1 Required grams of water per every kilogram of air to keep the air saturated at 21,000 and 50,000 Pa if the temperature increases from T (C) by ΔT
Full size table

Flying through unsaturated atmosphere

When flying through an unsaturated atmosphere, within which cloud formation is impossible, the aircraft might cause saturation. To determine this, one must compare the values obtained from Equations (12) and (13) against those presented in Table 1 to understand whether the remaining moisture is sufficient to raise the relative humidity of the unsaturated air to 1 while leaving enough moisture to sustain the saturated state. Data produced using Equations (12) and (13) is presented in Tables 2 and 3. These tables share the grams of water left in every kilogram of air per every Kelvin temperature increase after the unsaturated air reaches saturation.

Table 2 Remaining moisture to maintain the saturated state of an initially unsaturated atmosphere after raising it to saturation at  ~ 11,470 m (21,000 Pa)
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Data points denoted by * and + signify that the moisture available, after elevating the unsaturated air to saturation, is adequate to maintain the air saturated as its temperature increases by ΔT. As an illustration, suppose an airplane burning ammonia flies through the air at an altitude of 11,470 m. Also suppose air’s initial relative humidity and temperature are 50% and -40 °C, respectively, and the airplane causes a temperature increase of 5 °C. Table 2 suggests that this flight can result in saturation at -40 °C while leaving 0.0458 g kg−1 K−1. Is this remaining 0.0458 g kg−1 K−1 sufficient to maintain the saturation after the air temperature increases by 5 °C? According to Table 1, under the said conditions (i.e., 21,000 Pa, T = -40 °C, and ΔT = 5 °C), 0.0739 g kg−1 K−1 is required to maintain saturation. Thus, what remains after raising the sub-saturated air to saturation (i.e., 0.0458 g kg−1 K−1) is insufficient to maintain saturation when the air’s temperature increases by 5 °C. Therefore, this point is not marked with * in Table 2. However, when the initial RH is 75%, the remaining moisture after bringing 75% to 100% is 0.0654 g kg−1 K−1, exceeding the required moisture of 0.0517 g kg−1 K−1. As a result, the data point is marked with * to indicate that the moisture available after raising the unsaturated air to saturation is sufficient to maintain saturation when the air’s temperature increases by 5 °C.

Critical temperatures

The primary objective of this section is to determine the temperature necessary for the formation of contrails under specific conditions. Referred to as the critical temperature (Tc), it can be obtained by intersecting the data provided in Table 1 with the information presented in Tables 2 and 3. Figure 2 illustrates this process for ammonia and jet fuel at nearly 11,470 m (i.e., p = 21,000 Pa), assuming that the airplane leads to a 5-degree increase in the air temperature. The red line represents data provided in Table 1, while the black lines show the data in Table 2. The blue points where these lines intersect represent critical temperatures where the remaining moisture in the air, after reaching saturation, matches the moisture required to maintain saturation. Consequently, for a contrail to form, the air temperature must be Tc or lower. Upon comparing Fig. 2a, b, it becomes evident that ammonia possesses a higher critical temperature. This implies that with ammonia, the air doesn’t need to be as cold for a contrail to form, reaffirming the conclusion drawn from Equation (9) that the likelihood of observing a visible contrail is substantially greater with ammonia than with jet fuel.

Table 3 Remaining moisture to maintain the saturated state of an initially unsaturated atmosphere after raising it to saturation at  ~ 5,486 m (50,000 Pa)
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Fig. 2: Critical temperatures found by intersecting Tables 1 and 2 when ΔT = 5 °C.
figure 2

a Jet fuel. b Ammonia.

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Figure 3 duplicates Figure 2 with a single distinction: the assumed increase in air temperature is now 15 °C. It’s essential to highlight that the value of the temperature increase depends on the quantity of air that mixes into the contrail, as indicated by Equation (4). The larger the entrainment ratio, the smaller the temperature increase. Also, note that the entrainment ratio increases with axial distance from the exhaust. Hence, a temperature increase of 15 °C occurs closer to the aircraft compared to 5 °C, which is pretty intuitive. Comparing Figs. 2 and 3 reveals that a greater temperature increase (indicating less air entrainment) results in a narrower range of critical temperatures when relative humidity changes from 0 to 100%. The range for critical temperature Tc for jet fuel has become more restricted, shifting from (-45 °C – -54 °C) to (-51 °C – -53 °C). Similarly, for ammonia, the range changed from (-34 °C – -44 °C) to (-40 °C – -43 °C). An intriguing observation is that when the air is already saturated (RH=100%), Tc experiences minimal changes with axial distance from the exhaust, as the upper limit of the range stays almost unchanged. On the other hand, the lower the humidity, the more sensitive the system becomes to temperature increases, thus, to axial distance from the exhaust.

Fig. 3: Critical temperatures found by intersecting Tables 1 and 2 when ΔT = 15 °C.
figure 3

a Jet fuel. b Ammonia.

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To provide additional clarity, we present the critical temperature in relation to the entrainment ratio (N) in Fig. 4. As was mentioned above, the entrainment ratio, which represents fresh air mixing into the contrail, increases with axial distance from the aircraft. Also note that Fig. 4 displays data corresponding to an altitude of approximately 11,470 m (21,000 Pa). It is evident that lower humidity necessitates colder temperatures for a contrail to form. This graph also indicates that critical temperatures associated with ammonia are higher than those for jet fuel. For instance, at a temperature of -43 °C, ammonia can result in contrail formation even when the background atmosphere’s relative humidity is 0%, whereas jet fuel would necessitate considerably colder temperatures for a contrail to form and would not result in a contrail at -43 °C even when the relative humidity is 100%.

Fig. 4
figure 4

The variation of the critical temperature of ammonia and jet fuel with entrainment ratio with final saturation with respect to water.

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Figure 4 also highlights an entrainment ratio (N) that enables contrail formation at higher temperatures, except when the relative humidity is very high (note the curve’s maximum and its disappearance at large RHs). The curve’s maximum disappears when the relative humidity reaches 98%. This means when RH < 98%, the temperature required for contrail formation increases and then decreases with distance from the aircraft. In other words, colder air is required in the near wake and far wake for the contrail to form compared to the mid wake region where the critical temperature curve maximizes. This is an interesting observation since the mixing monotonically increases with axial distance, but the critical temperature does not. Another interesting observation is that the entrainment ratio that leads to a maximum critical temperature is independent of the fuel type.

The data provided in Tables 2 and 3, along with Figs. 2-4, was generated based on the assumption of a final saturation with respect to liquid water. It’s essential to note that the results would vary if the final saturation were assumed with respect to ice. When comparing water and ice at the same temperature, the saturation vapor pressure over water is higher than that over ice28. This means that at a specific temperature, water molecules have a higher tendency to evaporate and enter the vapor phase compared to ice molecules’ tendency to sublimate and enter the vapor phase. The reason behind this difference lies in the energy required for the phase transitions. When water evaporates, it changes from a liquid to a gas, and this process requires energy to overcome the intermolecular forces holding the liquid together. On the other hand, when ice sublimates, it changes directly from a solid to a gas, which requires breaking the intermolecular forces holding the ice lattice together. Sublimation generally requires more energy compared to evaporation. One can model for both scenarios by modifying L in Equation (11). To illustrate the impact of such differences on contrail formation, Fig. 5 compares the critical temperature versus entrainment ratio when the final saturated state is calculated with respect to water and ice for ammonia. While the entrainment ratio associated with the maximum critical temperature appears to remain relatively constant, two changes are observed:

  1. 1.

    Within a specific distance from the aircraft, the critical temperatures associated with the final saturation with respect to water are higher compared to those obtained when considering the final saturation state with respect to ice. However, this trend reverses at large entrainment ratios (farther away from the aircraft). The transition between these behaviors occurs approximately at N = 3000−4000.

  2. 2.

    The humidity threshold below which the critical temperature curve does not have a maximum decreases from 98% to approximately 60%.

Fig. 5: The critical temperature variation with entrainment ratio in the wake of an ammonia-powered engine.
figure 5

Dashed lines display supersaturation with respect to ice, and solid lines show supersaturation with respect to water (Altitude= 11,470 m and p= 21,000 Pa).

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Figure 6 illustrates the comparison of critical temperatures versus entrainment ratio for the two investigated fuels when the final saturation state is with respect to ice. Critical temperatures linked to jet fuel consistently remain lower than those of ammonia under an equal relative humidity. However, this discrepancy diminishes as the axial distance from the airplane’s exhaust outlet (larger N) increases. This convergence occurs more quickly as the relative humidity rises. Additionally, it is apparent that the maximum critical temperature for jet fuel disappears at a lower relative humidity compared to that observed for ammonia.

Fig. 6
figure 6

The variation of the critical temperature of ammonia and jet fuel with entrainment ratio with final saturation with respect to ice.

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A Discussion on the Effect of Reduced Atmospheric Aerosols

Note that the proposed analysis only focused on the effect of temperature, pressure, humidity, and air entrainment and did not account for the aerodynamics of the aircraft wake, engine size29, exhaust geometry30, and reduced soot emissions, which would substantially decrease the number of ice-crystal forming nuclei. While this article left the investigation of soot reduction to future work, it is important to note that soot reduction does not necessarily decrease contrail’s radiative forcing when alternative fuels are used as they induce competing effects31. In the case of conventional jet fuel, however, when there is a smaller number of initial ice crystals, they tend to grow more rapidly, assuming a constant amount of ambient water vapor available for deposition. This, in turn, leads to an earlier and greater sedimentation loss of ice crystals, resulting in reduced contrail cirrus optical depth, shorter lifetimes, and diminished radiative forcing32.

Furthermore, in certain clouds, water droplets have the ability to supercool to temperatures where homogeneous ice nucleation becomes the primary freezing mechanism, even without the involvement of ice nuclei. As opposed to the widespread belief that homogeneous ice nucleation in water droplets only takes place below a specific threshold temperature, typically set at -40 °C, laboratory measurements indicate that there is a measurable rate of nucleation at temperatures warmer than this threshold33. Therefore, the lack of soot particles in the exhaust gases of carbon-free aviation systems must not automatically imply that ice crystals, and consequently visible contrails, will not develop. As an example, experimental research revealed that within the temperature range of -34.5 to -37.5 °C, the volume nucleation rate coefficient, representing the number of ice nucleation events per unit volume per unit time, exhibited variation spanning approximately 105 to 10834.

Dust, metallic, and other atmospheric aerosols that pre-exist in the atmosphere, including the upper troposphere, serve as the primary heterogeneous ice nucleating particles responsible for creating natural cirrus clouds. These same particles, derived from diverse sources including desert dust, wildfire smoke, sea salt, volcanic aerosols, and human activities such as fossil fuel combustion from industries, energy use, agricultural land clearing, and transportation, can also serve as the nucleation sites for the formation of visible ice crystals in the wake of airplanes. Notably persistent, observations from cloud-aerosol lidar and infrared pathfinder satellite data35 combined with simulations conducted through aerosol transport models indicate that upper troposphere dust can be transported for more than a complete circuit around the globe before eventual removal36. Hence, it would be premature to dismiss the possibility of hydrogen-based, carbon-free fuels in generating contrails solely based on the absence of soot particles in their exhaust gases.

With all that said, how can we know how contrails will change with switching from kerosene to hydrogen with more certainty? A potential approach is developing a high-fidelity computational model. This work aimed to make a case for the necessity of developing such a model, allowing us to investigate the impact of other aerosol particles as potential cloud condensation nuclei and consider their impact by modeling their entrainment into a hydrogen plane’s plume. Such an investigation would be very challenging, mainly due to the complexities of creating a realistic background condition in the model regarding other aerosol particle species’ dimensions and concentrations and modeling their entrainment in a realistically non-linear rate, spatially and temporally. Here, we aim to create the momentum for taking on this challenging task.

Conclusions

Aviation’s contribution to global CO2 emissions is 2.5%37 while being responsible for 3.5% of the net anthropogenic effective radiative forcing38, a measure of climate change. For instance, a Boeing 777, using the full capacity of both fuel tanks, produces 1 million pounds of CO2, which is equivalent to the CO2 emissions generated by 130 cars in one year, assuming each car is driven approximately 22,000 km annually. Given the large number of flights, estimated at around 100,000 per day (excluding military and private jets), there is a pressing need for the scientific and engineering communities to take decisive action toward enabling electric aviation.

Through the CLEAN project, our team, partnering with leading aerospace industries, aims to address this challenge by introducing a propulsion system that is partially powered by a SOFC and utilizes ammonia as its fuel source. Although this system effectively eliminates CO2 emissions, it poses potential climate challenges by potentially increasing cloudiness in the sky. Therefore, one of the project’s long-term goals includes understanding this propulsion system’s contrail formation, evolution, persistence, and impact on radiative forcing and climate sensitivity by employing various analytical tools, including thermodynamic analysis, computational fluid dynamics, and mesoscale models, such as the Weather Research and Forecasting model39. This article presents the initial findings of the team’s thermodynamic analysis, which aims to establish a fundamental understanding of contrails formed by ammonia compared to jet fuel. Moving forward, the team plans to share further insights and discoveries on this subject in the upcoming years as the results of computational fluid dynamics simulations and the Weather Research and Forecasting model become available.

Some highlights from the present study are summarized below.

  • An aircraft introduces both heat and moisture into the surrounding air. The heat decreases relative humidity due to the elevated temperature (ΔT), while the added moisture (ΔX) increases relative humidity. Therefore, the ΔX/ΔT ratio would be suitable for assessing a fuel’s potential in forming contrails.

  • The interaction of contrails with the surrounding atmosphere was modeled by introducing the entrainment ratio, N, representing the mass of fresh air entrained into the contrail for every kilogram of exhaust gas. Notably, the entrainment ratio N was eliminated when calculating the ΔX/ΔT ratio. The entrainment ratio N, solely dependent on ΔT for a specific fuel, provides valuable insights into how particular contrail characteristics, such as the critical temperature, evolve with distance from the aircraft.

  • The analysis revealed that jet fuel introduces 0.031 grams of water to each kilogram of exhaust gases for each degree K increase in air temperature. In contrast, ammonia exhibits a higher value of 0.085 g kg−1 K−1. Thus, on an equal mass basis, ammonia-power aircraft exhausts 2.74 times more moisture content. The ratio would be 6.1 on an equal energy basis as one needs to burn 2.23 grams of ammonia to achieve the energy that burning 1 gram of kerosene yields. On the other hand, the higher efficiency of the ammonia-powered aircraft is expected to lower these ratios (2.74 and 6.1); however, one cannot quantify that without knowing the precise efficiencies of both kerosene and ammonia-powered airplanes. The efficiency of the ammonia-powered airplane is yet unknown as the aircraft design is still underway.

  • The study explored two scenarios.

    1. 1.

      In the first scenario, the investigation focused on flying through saturated air. This analysis depends on the air’s initial temperature, pressure, and air entrainment ratio. This work examined several combinations to determine if each fuel could maintain the air in a saturated state. The outcomes of this analysis are detailed in Table 1.

    2. 2.

      The second scenario centered on a sub-saturated environment. The objective was to investigate whether the moisture and heat generated by ammonia and jet fuel would cause the sub-saturated state to become saturated and subsequently sustain it. The findings from this analysis are documented in Tables 2 and 3.

  • The investigation of the critical temperature involved assessing the final saturation states with respect to both water and ice. Across all scenarios, ammonia consistently exhibited higher critical temperatures than jet fuel. This implies that the air temperature does not need to be as cold for contrail formation when using ammonia. Moreover, when the final saturation state is computed with respect to ice, the difference between the critical temperatures of the two fuels diminishes as the distance from the exhaust outlet increases.

  • The critical temperature varies with the entrainment ratio (N), which, in turn, changes with distance from the aircraft. When the relative humidity is relatively low, the temperature needed for contrail formation first increases and then decreases with distance from the exhaust outlet. However, beyond a specific relative humidity (RHthreshold), the peak vanishes, and the critical temperature continuously increases with distance from the aircraft. For ammonia, the RHthreshold was 98% when saturation was computed with respect to water and 60% when calculated with respect to ice. Notably, the thresholds are lower for jet fuel.