Impact of Hybrid-Electric Aircraft on Contrail Coverage

Aviation is responsible for approximately 5% of global warming and is expected to increase substantially in the future. Given the continuing expansion of air traffic, mitigation of aviation’s climate impact becomes challenging but imperative. Among various mitigation options, hybrid-electric aircraft (HEA) have drawn intensive attention due to their considerable potential in reducing greenhouse gas emissions (e.g., CO2). However, the non-CO2 effects (especially contrails) of HEA on climate change are more challenging to assess. As the first step to understanding the climate impact of HEA, this research investigates the effects on the formation of persistent contrails when flying with HEA. The simulation is performed using an Earth System Model (EMAC) coupled with a submodel (CONTRAIL), where the contrail formation criterion, the Schmidt–Appleman criterion (SAC), is adapted to globally estimate changes in the potential contrail coverage (PCC). We compared the HEA to conventional (reference) aircraft with the same characteristics, except for the propulsion system. The analysis showed that the temperature threshold of contrail formation for HEA is lower; therefore, conventional reference aircraft can form contrails at lower flight altitudes, whereas the HEA does not. For a given flight altitude, with a small fraction of electric power in use (less than 30%), the potential contrail coverage remained nearly unchanged. As the electric power fraction increased, the reduction in contrail formation was mainly observed in the mid-latitudes (30◦ N and 40◦ S) or tropical regions and was very much localized with a maximum value of about 40% locally. The analysis of seasonal effects showed that in non-summer, the reduction in contrail formation using electric power was more pronounced at lower flight altitudes, whereas in summer the changes in PCC were nearly constant with respect to altitude.


Introduction
Civil aviation satisfies modern society's needs for mobility and is an essential economic driver. Air transportation demand increases at around 4.4% per annum and is forecast to maintain that growth rate for the next few decades [1]. Although the global COVID-19 pandemic has put a great challenge on the aviation industry, we expect that aviation will eventually recover, as aviation has become a fundamental part of the modern world, providing long-range mobility. Aviation is responsible for approximately 5% of the anthropogenic causes of global warming [2], and it is expected to increase substantially in the future. Given the continuing expansion of air traffic, mitigation of aviation's climate impact becomes challenging but imperative. Because of its long lifetime, aviation's climate impact from CO2 is mainly determined by the amount of CO2 emissions. The induced perturbation of the atmospheric CO2 concentration is determined by several lifetimes that are associated with individual processes, such as land-uptake (biosphere; 1-100 years) and sediment formation (1000 to 10,000 years) [11]. Due to the long lifetimes, the concentration change can be estimated to first-order by accumulating CO2 emissions over aviation history. On the contrary, the short-lived non-CO2 effects depend not only on the emission quantity but also on the geographical location, altitude, time, and the local weather conditions. It is possible to mitigate aviation's climate impact via operational measures to avoid climate-sensitive regions associated with non-CO2 effects, e.g., to contrail avoidance [12][13][14][15][16][17].
The formation of persistent contrails depends on environmental conditions and aircraft/engine technologies. The well-known Schmidt-Appleman criterion (SAC) [18,19] suggests that the possible measures to reduce aviation's contrail formation are reducing the H2O emission index, increasing the fuel lower heating value, or decreasing the overall propulsion efficiency. Various options can affect these three measures, e.g., new aircraft design [20] and alternative fuels [21][22][23][24].
Electric aircraft is one of the possible options as well, since using a battery will eliminate exhaust emissions. Due to technology limitations, a purely electric aircraft would not be feasible. Instead, hybrid-electric aircraft is proposed for regional/narrow-body airliners [25,26]. For long-range flights, the electric propulsion system's additional weight makes it difficult to achieve substantial fuel saving. A hybrid-electric propulsion system consists of a gas turbine engine combined with an electric motor (EM) and a battery pack. There are several possible ways to connect these components in a power train. The most frequently proposed configurations are the series and parallel type, as demonstrated in Figure 2. In a series configuration, the gas turbine generates electricity via a generator. EM then uses the electricity to drive a fan/propeller. Batteries can assist in supplying power to the EM. In the parallel type, a gas turbine and EM drive the fan/propeller simultaneously, with different hybridization degrees. In addition, the operational flexibility of the parallel hybrid-electric system Because of its long lifetime, aviation's climate impact from CO 2 is mainly determined by the amount of CO 2 emissions. The induced perturbation of the atmospheric CO 2 concentration is determined by several lifetimes that are associated with individual processes, such as land-uptake (biosphere; 1-100 years) and sediment formation (1000 to 10,000 years) [11]. Due to the long lifetimes, the concentration change can be estimated to first-order by accumulating CO 2 emissions over aviation history. On the contrary, the short-lived non-CO 2 effects depend not only on the emission quantity but also on the geographical location, altitude, time, and the local weather conditions. It is possible to mitigate aviation's climate impact via operational measures to avoid climate-sensitive regions associated with non-CO 2 effects, e.g., to contrail avoidance [12][13][14][15][16][17].
The formation of persistent contrails depends on environmental conditions and aircraft/engine technologies. The well-known Schmidt-Appleman criterion (SAC) [18,19] suggests that the possible measures to reduce aviation's contrail formation are reducing the H 2 O emission index, increasing the fuel lower heating value, or decreasing the overall propulsion efficiency. Various options can affect these three measures, e.g., new aircraft design [20] and alternative fuels [21][22][23][24].
Electric aircraft is one of the possible options as well, since using a battery will eliminate exhaust emissions. Due to technology limitations, a purely electric aircraft would not be feasible. Instead, hybrid-electric aircraft is proposed for regional/narrow-body airliners [25,26]. For long-range flights, the electric propulsion system's additional weight makes it difficult to achieve substantial fuel saving. A hybrid-electric propulsion system consists of a gas turbine engine combined with an electric motor (EM) and a battery pack. There are several possible ways to connect these components in a power train. The most frequently proposed configurations are the series and parallel type, as demonstrated in Figure 2. In a series configuration, the gas turbine generates electricity via a generator. EM then uses the electricity to drive a fan/propeller. Batteries can assist in supplying power to the EM. In the parallel type, a gas turbine and EM drive the fan/propeller simultaneously, with different hybridization degrees. In addition, the operational flexibility of the parallel hybrid-electric system (HEPS) may allow for full electrical power through the climate-sensitive regions, such as contrail-vulnerable parts of a flight, hence eliminating contrail formation.
Aerospace 2020, 7, x FOR PEER REVIEW 3 of 18 (HEPS) may allow for full electrical power through the climate-sensitive regions, such as contrailvulnerable parts of a flight, hence eliminating contrail formation.
As the first step towards understanding the climate impact of hybrid-electric aircraft, this research investigates the effects on the formation of contrails when flying with hybrid-electric aircraft (HEA). A parallel hybrid configuration, as described in Figure 2b, is considered. In terms of the baseline aircraft, an earlier study suggested a possible mission range of 1000 km for a parallel hybridelectric plane to allow reasonable benefits of fuel savings [26]. The A320 type aircraft is then our potential baseline. Figure 3 shows an example of a power management strategy for a parallel configuration. The degrees of hybridization between fuel and electricity can be varied to achieve different mission performance. For contrail avoidance, it would be better to have a 100% electric flight at the contrail-sensitive regions of the cruise flight only, which is analyzed in detail in the current paper.  [26]. During taxi-out/taxi-in phases, 100% electrical power is used, whereas during take-off, climb, and cruise conditions, battery and turbofan engine are used in parallel. The arrow on the mission profile indicates different flight stages.
The paper is organized as follows. In Section 2, the methods used to predict the potential contrail coverage (PCC), defined as the atmospheric ability to form contrails for a given aircraft and fuel type [28], are elaborated. The conditions of contrail formation for parallel hybrid-electric configuration are also discussed. Section 3 analyses the effects of the variation of cruise altitude, degrees of hybridization, and seasons on PCC changes. Finally, conclusions are drawn in Section 4.

Methodology
We have envisaged a research roadmap (as presented in Figure 4) to investigate the potential of flying a hybrid-electric plane for contrail avoidance. The complete research chain contains the relevant technical aspects of HEA for contrail formation (the green box), the PCC calculation procedure, the operational strategy of HEA to avoid contrails, and the actual mitigation potential when flying HEA. In this paper, we present the first steps of the roadmap (marked in blue). Subsequent research will cover the later steps (marked in orange). This section elaborates on the details of the methodology of the first steps (those in blue). As the first step towards understanding the climate impact of hybrid-electric aircraft, this research investigates the effects on the formation of contrails when flying with hybrid-electric aircraft (HEA). A parallel hybrid configuration, as described in Figure 2b, is considered. In terms of the baseline aircraft, an earlier study suggested a possible mission range of 1000 km for a parallel hybrid-electric plane to allow reasonable benefits of fuel savings [26]. The A320 type aircraft is then our potential baseline. Figure 3 shows an example of a power management strategy for a parallel configuration. The degrees of hybridization between fuel and electricity can be varied to achieve different mission performance. For contrail avoidance, it would be better to have a 100% electric flight at the contrail-sensitive regions of the cruise flight only, which is analyzed in detail in the current paper.
Aerospace 2020, 7, x FOR PEER REVIEW 3 of 18 (HEPS) may allow for full electrical power through the climate-sensitive regions, such as contrailvulnerable parts of a flight, hence eliminating contrail formation.
As the first step towards understanding the climate impact of hybrid-electric aircraft, this research investigates the effects on the formation of contrails when flying with hybrid-electric aircraft (HEA). A parallel hybrid configuration, as described in Figure 2b, is considered. In terms of the baseline aircraft, an earlier study suggested a possible mission range of 1000 km for a parallel hybridelectric plane to allow reasonable benefits of fuel savings [26]. The A320 type aircraft is then our potential baseline. Figure 3 shows an example of a power management strategy for a parallel configuration. The degrees of hybridization between fuel and electricity can be varied to achieve different mission performance. For contrail avoidance, it would be better to have a 100% electric flight at the contrail-sensitive regions of the cruise flight only, which is analyzed in detail in the current paper.  [26]. During taxi-out/taxi-in phases, 100% electrical power is used, whereas during take-off, climb, and cruise conditions, battery and turbofan engine are used in parallel. The arrow on the mission profile indicates different flight stages.
The paper is organized as follows. In Section 2, the methods used to predict the potential contrail coverage (PCC), defined as the atmospheric ability to form contrails for a given aircraft and fuel type [28], are elaborated. The conditions of contrail formation for parallel hybrid-electric configuration are also discussed. Section 3 analyses the effects of the variation of cruise altitude, degrees of hybridization, and seasons on PCC changes. Finally, conclusions are drawn in Section 4.

Methodology
We have envisaged a research roadmap (as presented in Figure 4) to investigate the potential of flying a hybrid-electric plane for contrail avoidance. The complete research chain contains the relevant technical aspects of HEA for contrail formation (the green box), the PCC calculation procedure, the operational strategy of HEA to avoid contrails, and the actual mitigation potential when flying HEA. In this paper, we present the first steps of the roadmap (marked in blue). Subsequent research will cover the later steps (marked in orange). This section elaborates on the details of the methodology of the first steps (those in blue).  [26]. During taxi-out/taxi-in phases, 100% electrical power is used, whereas during take-off, climb, and cruise conditions, battery and turbofan engine are used in parallel. The arrow on the mission profile indicates different flight stages.
The paper is organized as follows. In Section 2, the methods used to predict the potential contrail coverage (PCC), defined as the atmospheric ability to form contrails for a given aircraft and fuel type [28], are elaborated. The conditions of contrail formation for parallel hybrid-electric configuration are also discussed. Section 3 analyses the effects of the variation of cruise altitude, degrees of hybridization, and seasons on PCC changes. Finally, conclusions are drawn in Section 4.

Methodology
We have envisaged a research roadmap (as presented in Figure 4) to investigate the potential of flying a hybrid-electric plane for contrail avoidance. The complete research chain contains the relevant technical aspects of HEA for contrail formation (the green box), the PCC calculation procedure, the operational strategy of HEA to avoid contrails, and the actual mitigation potential when flying HEA. In this paper, we present the first steps of the roadmap (marked in blue). Subsequent research will cover the later steps (marked in orange). This section elaborates on the details of the methodology of the first steps (those in blue).  An Earth System Model (EMAC) coupled with a CONTRAIL submodel was used to predict the hybrid-electric aircraft's PCC. The CONTRAIL submodel includes a revision of the contrail formation criterion for HEA. Please note that in this analysis, we focus on the contrails formed at the engine exhaust, whereas aerodynamic contrails are not considered. The formation of aerodynamic contrails mainly depends on the aerodynamic design of aircraft, especially the airfoil [29], which is assumed to be unchanged in this analysis and of minor importance concerning their climate impact [30].

The Base Model EMAC
The ECHAM/MESSy Atmospheric Chemistry (EMAC) model is a numerical chemistry and climate simulation system that includes submodels describing tropospheric and middle atmosphere processes and their interaction with oceans, land, and human influences [31]. For the present study, we applied EMAC (ECHAM5 version 5.3.02, MESSy version 2.52.0) in T42L31ECMWF-resolution, corresponding to a horizontal grid of about 310 km and a vertical resolution of roughly 1 km up to an altitude of approximately 30 km. The simulation time step is 12 min. Such a model resolution will provide us with reasonable weather data to calculate the potential contrail coverage.
EMAC has been extensively validated with other models, for instance, ACCMIP presented in [32], concerning atmospheric dynamics, cloud occurrence, chemistry, etc. An overview is given in [33]. In this paper, we use the submodel CONTRAIL V1.0. Section 2.2 discusses details on the CONTRAIL submodel.

The CONTRAIL Submodel
CONTRAIL is one of the submodels in EMAC, developed by Frömming et al. (supplement of [12]) to calculate the potential coverage of persistent contrails instantaneously, with the EMAC resolution specified in the previous section. The thermodynamic condition of contrail formation is given by the Schmidt-Appleman criterion [18,19], the derivation of which is presented in Section 2.3 of this paper. In the CONTRAIL submodel, the PCC is calculated as the difference between the An Earth System Model (EMAC) coupled with a CONTRAIL submodel was used to predict the hybrid-electric aircraft's PCC. The CONTRAIL submodel includes a revision of the contrail formation criterion for HEA. Please note that in this analysis, we focus on the contrails formed at the engine exhaust, whereas aerodynamic contrails are not considered. The formation of aerodynamic contrails mainly depends on the aerodynamic design of aircraft, especially the airfoil [29], which is assumed to be unchanged in this analysis and of minor importance concerning their climate impact [30].

The Base Model EMAC
The ECHAM/MESSy Atmospheric Chemistry (EMAC) model is a numerical chemistry and climate simulation system that includes submodels describing tropospheric and middle atmosphere processes and their interaction with oceans, land, and human influences [31]. For the present study, we applied EMAC (ECHAM5 version 5.3.02, MESSy version 2.52.0) in T42L31ECMWF-resolution, corresponding to a horizontal grid of about 310 km and a vertical resolution of roughly 1 km up to an altitude of approximately 30 km. The simulation time step is 12 min. Such a model resolution will provide us with reasonable weather data to calculate the potential contrail coverage.
EMAC has been extensively validated with other models, for instance, ACCMIP presented in [32], concerning atmospheric dynamics, cloud occurrence, chemistry, etc. An overview is given in [33]. In this paper, we use the submodel CONTRAIL V1.0. Section 2.2 discusses details on the CONTRAIL submodel.

The CONTRAIL Submodel
CONTRAIL is one of the submodels in EMAC, developed by Frömming et al. (supplement of [12]) to calculate the potential coverage of persistent contrails instantaneously, with the EMAC resolution specified in the previous section. The thermodynamic condition of contrail formation is given by the Schmidt-Appleman criterion [18,19], the derivation of which is presented in Section 2.3 of this paper. In the CONTRAIL submodel, the PCC is calculated as the difference between the maximum possible coverage of both contrails and cirrus and the natural cirrus coverage alone. Supersaturation with respect to ice is used to determine if the contrails are persistent or not.

The HEA Extended Schmidt-Appleman Criterion
Contrails form when the mixture of engine exhaust and ambient air reaches water saturation at a sufficiently low temperature, and they persist when the ambient air is ice-supersaturated. The mixing process is assumed to be isobaric; therefore, the mixing trajectory is represented as a straight line on the T-e diagram (see Figure 1 of [34]; e is the partial pressure of water vapor in the mixture; T is the static temperature of the mixture). The slope of this straight line (G) determining the temperature threshold of contrail formation is given by the SAC and calculated using Equation (1).
where p is the ambient pressure in Pa; ε is the ratio of the molar mass of water vapor and dry air (0.622 constant); c p is the isobaric heat capacity of air (1004 J/kg/K); Q is the lower heating value of fuel in MJ/kg; EIH2O is the water vapor emission index in kg/kg(fuel); and the notation (η K ) is the overall propulsion efficiency of the pure kerosene aircraft (reference), for which we assumed a value of 0.4 in the current study. This efficiency value was in line with the value computed using the aircraft/engine performance model presented in [27]. For HEA, the thrust power is provided by two energy sources, as defined by Equation (2).
where F is the thrust requirement in N, V is the flight speed in m/s, . m f is the fuel flow rate of kerosene in kg/s, η E is the overall efficiency of the aircraft when electric power is working alone, the notation (P E ) is the electric power in watts.
Accordingly, the original SAC was adapted using the assumption that kerosene plus electric power are combined to the necessary power FV results (details are discussed in Appendix A). The revised calculation procedure for slope G leads to Equation (3), which considers the effects of various degrees of hybridization.
For the same thrust power, the maximum fuel flow rate ( . m f max ) corresponds to the fuel consumption of the reference aircraft, where only kerosene is used. Hence, at pure liquid-fuel operation, R = 1, and pure electric operation, R = 0. The notation (Q 0 E ) is a quasi-electric energy content, defined in Equation (4): Note that the SAC derivation in this paper only applies to the situation where batteries provide electric power. A battery has no water vapor emission. Suppose the electric power is provided by a fuel cell or another gas turbine via a generator. In that case, water vapor is emitted by these components. A different form of the Schmidt-Appleman criterion must be derived to consider the effects of water vapor emitted by, e.g., the fuel cell.

The Threshold of Contrail Formation Calculated by SAC
On the basis of the SAC derivation in Section 2.3, we studied the threshold of contrail formation for HEA. Figure 5 shows how the contrail factor G varies with the share of electric propulsion. It is zero for pure electric propulsion (R = 0) and increases non-linearly with the fraction of liquid-fuel propulsion until it reaches its maximum at full liquid-fuel propulsion. The shape of the curve depends on the efficiency η E of the electric powertrain. The higher is η E , the flatter the relation close to R = 1.
Aerospace 2020, 7, x FOR PEER REVIEW 6 of 18 depends on the efficiency of the electric powertrain. The higher is , the flatter the relation close to = 1. For the maximum temperature ( ,) ( [35], Equation (5)), at which contrail formation is possible, we studied the effects of various with respect to the fraction of electric power (see Figure  6). For a more efficient electric system with a high , it needs a relatively high electric share (R is very small) to achieve a substantial lowering of . In our example, the maximum temperature at which contrails can be formed when only liquid fuel is used ( = 1) is −40 °C. To reduce this by 5 K, to achieve a maximum temperature of −45 °C, it needs roughly = 0.3, or 70% of the thrust power needs to be provided by the electric motor when its efficiency is 0.8. For the smaller efficiency, the reduction in is larger. This may sound paradoxical, but it is the consequence of the simple physical fact that contrail formation is easier when the exhaust gas is colder, for what is higher combined overall propulsion efficiencies.
For the maximum temperature (T max ,) ( [35], Equation (5)), at which contrail formation is possible, we studied the effects of various η E with respect to the fraction of electric power (see Figure 6). For a more efficient electric system with a high η E , it needs a relatively high electric share (R is very small) to achieve a substantial lowering of T max . In our example, the maximum temperature at which contrails can be formed when only liquid fuel is used (R = 1) is −40 • C. To reduce this by 5 K, to achieve a maximum temperature of −45 • C, it needs roughly R = 0.3, or 70% of the thrust power needs to be provided by the electric motor when its efficiency is 0.8. For the smaller efficiency, the reduction in T max is larger. This may sound paradoxical, but it is the consequence of the simple physical fact that contrail formation is easier when the exhaust gas is colder, for what is higher combined overall propulsion efficiencies.
Aerospace 2020, 7, x FOR PEER REVIEW 6 of 18 depends on the efficiency of the electric powertrain. The higher is , the flatter the relation close to = 1. For the maximum temperature ( ,) ( [35], Equation (5)), at which contrail formation is possible, we studied the effects of various with respect to the fraction of electric power (see Figure  6). For a more efficient electric system with a high , it needs a relatively high electric share (R is very small) to achieve a substantial lowering of . In our example, the maximum temperature at which contrails can be formed when only liquid fuel is used ( = 1) is −40 °C. To reduce this by 5 K, to achieve a maximum temperature of −45 °C, it needs roughly = 0.3, or 70% of the thrust power needs to be provided by the electric motor when its efficiency is 0.8. For the smaller efficiency, the reduction in is larger. This may sound paradoxical, but it is the consequence of the simple physical fact that contrail formation is easier when the exhaust gas is colder, for what is higher combined overall propulsion efficiencies.  This paper considered the technology level of 2030 for electric motor, inverter, and battery, as summarized in [27,36]. Furthermore, a typical value of 0.9 for fan efficiency was used. Eventually, the value of η E was about 0.8. This value was then used in the further analysis of PCC.
A further example of the parameters for SAC on different aircraft is presented in Table 1. The numbers were calculated for an altitude of 11 km. Figure 7 shows three critical mixing lines: one for conventional aircraft with an overall efficiency of 0.4, one for HEA with 40% electric power, and one for HEA with 80% electric power. These three mixing lines ran from the engine exhaust conditions and were tangential to the water saturation pressure line. At the same flight altitude, the temperature threshold and the slope G decreased with the increase of electric power in use. Therefore, the chance for HEA to form contrails reduced as the electric power fraction increased. A further example of the parameters for SAC on different aircraft is presented in Table 1. The numbers were calculated for an altitude of 11 km. Figure 7 shows three critical mixing lines: one for conventional aircraft with an overall efficiency of 0.4, one for HEA with 40% electric power, and one for HEA with 80% electric power. These three mixing lines ran from the engine exhaust conditions and were tangential to the water saturation pressure line. At the same flight altitude, the temperature threshold and the slope G decreased with the increase of electric power in use. Therefore, the chance for HEA to form contrails reduced as the electric power fraction increased.

Changes in Potential Contrail Coverage
We studied the variations of potential contrail coverage caused by different effects, for instance, altitude, degree of hybridization, and seasons. In this section, we present the results. The data are based on a one-year simulation with EMAC, including the updated CONTRAIL submodel (see above). For illustration purposes, we first present results for an arbitrary day in winter to give an impression of an actual weather situation and then present climatological values. All the results were obtained with 0.8 electric power efficiency and 0.4 kerosene system efficiency.

Changes in Potential Contrail Coverage
We studied the variations of potential contrail coverage caused by different effects, for instance, altitude, degree of hybridization, and seasons. In this section, we present the results. The data are based on a one-year simulation with EMAC, including the updated CONTRAIL submodel (see above). For illustration purposes, we first present results for an arbitrary day in winter to give an impression of an actual weather situation and then present climatological values. All the results were obtained with 0.8 electric power efficiency and 0.4 kerosene system efficiency. Figure 8a shows the PCC of conventional aircraft at 300 hPa (FL300) on a specific day. In contrast, the changes in PCC caused by 50% electric hybridization of HEA (i.e., R = 0.5 in Equation (3)) at the same altitude is given in Figure 8b. For the pure kerosene case, the contrails were mainly formed at the mid-latitudes and polar regions, where the local temperature was sufficiently low to form contrails. With 50% thrust power supplied by the battery, the reduction in contrail formation was observed at about 30 • N and 40 • S, where the tropopause climbed to the higher altitudes. The local temperature in this region was close to the temperature threshold for the pure kerosene aircraft. A transition to HEA lowered the temperature threshold by a few degrees Celsius. It was also noticeable that the contrail formation's reduction was very much localized with a maximum value of around 0.4, which might have been related to the local temperature and humidity.

One-Day Case Study
Aerospace 2020, 7, x FOR PEER REVIEW 8 of 18 Figure 8a shows the PCC of conventional aircraft at 300 hPa (FL300) on a specific day. In contrast, the changes in PCC caused by 50% electric hybridization of HEA (i.e., R = 0.5 in Equation (3)) at the same altitude is given in Figure 8b. For the pure kerosene case, the contrails were mainly formed at the mid-latitudes and polar regions, where the local temperature was sufficiently low to form contrails. With 50% thrust power supplied by the battery, the reduction in contrail formation was observed at about 30° N and 40° S, where the tropopause climbed to the higher altitudes. The local temperature in this region was close to the temperature threshold for the pure kerosene aircraft. A transition to HEA lowered the temperature threshold by a few degrees Celsius. It was also noticeable that the contrail formation's reduction was very much localized with a maximum value of around 0.4, which might have been related to the local temperature and humidity. When increasing the flight altitude from 300 hPa to 250 hPa (FL340), for the conventional reference aircraft, we found the areas of potential contrail coverage in the tropical regions as well (Figure 9a). For HEA, with 50% of electric hybridization, the reduction of contrail formation was more pronounced in the tropical regions, as seen in Figure 9b. When increasing the flight altitude from 300 hPa to 250 hPa (FL340), for the conventional reference aircraft, we found the areas of potential contrail coverage in the tropical regions as well (Figure 9a). For HEA, with 50% of electric hybridization, the reduction of contrail formation was more pronounced in the tropical regions, as seen in Figure 9b. When we increased the flight altitude further to 200 hPa (FL390), HEA with 50% of electric hybridization had no significant change in contrail formation. At this level, the ambient temperature was far below the threshold for contrail formation for conventional aircraft. HEA did not lead to a sufficient lowering of that temperature threshold with 50% electric power. However, increasing the hybridization to 90% allowed for a further reduction of the temperature threshold for contrail formation. Accordingly, a reduction in contrails was observed in several locations of the tropical region, as shown in Figure 10b. When we increased the flight altitude further to 200 hPa (FL390), HEA with 50% of electric hybridization had no significant change in contrail formation. At this level, the ambient temperature was far below the threshold for contrail formation for conventional aircraft. HEA did not lead to a sufficient lowering of that temperature threshold with 50% electric power. However, increasing the hybridization to 90% allowed for a further reduction of the temperature threshold for contrail formation. Accordingly, a reduction in contrails was observed in several locations of the tropical region, as shown in Figure 10b.

Effect of Degree of Hybridization
In Figure 11, we present a statistical analysis of the local reduction of contrail coverage when different hybridization degrees were considered. The annual mean PCC was used. We observed that the contrail coverage remained nearly unchanged with a smaller fraction of electric power in use (less than 30%). As the hybridization rate increased from 10-90%, an exponential reduction trend was found, which was already indicated by the theoretical analysis in Figures 5 and 6.

Effect of Degree of Hybridization
In Figure 11, we present a statistical analysis of the local reduction of contrail coverage when different hybridization degrees were considered. The annual mean PCC was used. We observed that the contrail coverage remained nearly unchanged with a smaller fraction of electric power in use (less than 30%). As the hybridization rate increased from 10-90%, an exponential reduction trend was found, which was already indicated by the theoretical analysis in Figures 5 and 6.

Climatology of Contrail Formation
The zonal annual mean values of PCC for the reference aircraft and various hybridization degrees are presented in Figure 12. Figure 12a shows the potential contrail coverage for the conventional aircraft, which was also used as a baseline to evaluate different degrees of hybridization effects. From Figure 12b-d, the degree of hybridization increased from 30% to 50% and up to 90%.

Climatology of Contrail Formation
The zonal annual mean values of PCC for the reference aircraft and various hybridization degrees are presented in Figure 12. Figure 12a shows the potential contrail coverage for the conventional aircraft, which was also used as a baseline to evaluate different degrees of hybridization effects. From Figure 12b-d, the degree of hybridization increased from 30% to 50% and up to 90%. Again, corresponding to the SAC theory, HEA did not form contrails at the higher temperature and could not form contrails in the lower region of the potential contrail coverage of conventional contrails. Therefore, the reduction of HEA in contrail formation occurred mostly at the lower flight altitudes. However, as the hybridization increased, the altitude range, where contrail formation was reduced, grew.

Seasonal Effects
On the basis of the annual simulation results, we studied the seasonal effects. Figure 13 presents the variations in PCC for 90% of hybridization. The results were grouped into four seasons at four pressure altitudes. Generally, we expected the largest effect (i.e., the greatest reduction in PCC) on the lowest pressure level, since the temperatures on that level were closest to the SAC-temperature threshold. Similarly, we expected the PCC reduction to become smaller towards higher pressure altitudes with their lower temperatures. This pattern was evident in the figure, except for summer. There were more substantial reductions on 150 hPa (FL450) and 200 hPa (FL390) levels in summer than in the other seasons. This behavior was partly due to higher temperatures, closer to the SAC-

Seasonal Effects
On the basis of the annual simulation results, we studied the seasonal effects. Figure 13 presents the variations in PCC for 90% of hybridization. The results were grouped into four seasons at four pressure altitudes. Generally, we expected the largest effect (i.e., the greatest reduction in PCC) on the lowest pressure level, since the temperatures on that level were closest to the SAC-temperature threshold.
Similarly, we expected the PCC reduction to become smaller towards higher pressure altitudes with their lower temperatures. This pattern was evident in the figure, except for summer. There were more substantial reductions on 150 hPa (FL450) and 200 hPa (FL390) levels in summer than in the other seasons. This behavior was partly due to higher temperatures, closer to the SAC-threshold, but lower relative humidity than those in different seasons may contribute to PCC reduction. The reduction was found to be more or less constant in summer at all flight levels (differences were insignificant), although the difference between the actual and the SAC-threshold temperature increased with flight level. It is likely that a decreasing frequency of high humidity (including ice-supersaturation) cases balanced the temperature effect such that the PCC reduction in summer depended little on the flight altitude.

Discussion
This study demonstrated the effects of hybrid-electric aircraft on potential contrail coverage. The actual contrail properties-the number of soot particles related to using a hybrid-electric propulsion system, the lifetime of contrails, etc.-were not considered. Earlier research shows that the number of soot particles produced by a turbofan engine is strongly dependent on the thrust setting [37]. A higher thrust setting would lead to an increase in the combustion temperature, hence, increasing the rate of soot formation, and vice versa. As different degrees of electric hybridization were considered, the gas turbine engine's thrust setting and the number of soot particles varied accordingly. The change in soot particles will affect the contrails' actual optical properties, thus the resulting contrail radiative forcing.
Furthermore, the Schmidt-Appleman criterion's derivation in this paper is applicable for a hybrid-electric propulsion system, for which the electric power is generated by battery. If the choice goes for a fuel cell hybrid-electric propulsion system, one would require a different consideration. The SAC for the fuel cell type of hybrid system depends on how the fuel cell's exhaust is handled. If a heat exchanger is used to collect the fuel cell's exhaust heat, the water vapor at the fuel cell's exhaust is then condensed into a liquid. In this case, contrails are only formed from the gas turbine exhaust. The SAC derivation in the current paper can still be valid. However, if no condensation process is involved, the fuel cell then also produces water vapor in the exhaust, which must be considered to derivate an alternative SAC.

Discussion
This study demonstrated the effects of hybrid-electric aircraft on potential contrail coverage. The actual contrail properties-the number of soot particles related to using a hybrid-electric propulsion system, the lifetime of contrails, etc.-were not considered. Earlier research shows that the number of soot particles produced by a turbofan engine is strongly dependent on the thrust setting [37]. A higher thrust setting would lead to an increase in the combustion temperature, hence, increasing the rate of soot formation, and vice versa. As different degrees of electric hybridization were considered, the gas turbine engine's thrust setting and the number of soot particles varied accordingly. The change in soot particles will affect the contrails' actual optical properties, thus the resulting contrail radiative forcing.
Furthermore, the Schmidt-Appleman criterion's derivation in this paper is applicable for a hybrid-electric propulsion system, for which the electric power is generated by battery. If the choice goes for a fuel cell hybrid-electric propulsion system, one would require a different consideration. The SAC for the fuel cell type of hybrid system depends on how the fuel cell's exhaust is handled. If a heat exchanger is used to collect the fuel cell's exhaust heat, the water vapor at the fuel cell's exhaust is then condensed into a liquid. In this case, contrails are only formed from the gas turbine exhaust. The SAC derivation in the current paper can still be valid. However, if no condensation process is involved, the fuel cell then also produces water vapor in the exhaust, which must be considered to derivate an alternative SAC.
As observed from our analysis, the reduction in contrail coverage by hybrid-electric aircraft is mostly localized. The consequences are twofold. In a case where the flight route does not cross a region of reduction (that is, the temperature is significantly lower than the contrail formation threshold even for a high portion of electric power), flying with a hybrid-electric aircraft does not affect the contrail formation. Still, the contrail properties (lifetime, optical thickness, and eventually individual radiative forcing) may change with the degree of hybridization. In another case where the contrail reduction is possible along the flight route (that is, the temperature is close to the contrail formation threshold), using a large fraction of electric power at that specific location would effectively reduce contrail formation. For the second case, a specific power management strategy can be developed to design the hybrid-electric system. Eventually, we expect the actual effect to be a convolution of the existing air traffic patterns with the PCC-reduction patterns. In further analysis, we will investigate the effectiveness of contrail avoidance by hybrid-electric aircraft, considering the routing effects.
In addition, in our analysis, we used a typical value of 0.4 as the overall propulsion efficiency, and we left it constant regardless of the amount of electrical power used. As more electrical energy is used, the gas turbine engine's thrust setting is reduced; correspondingly, the propulsion efficiency would decrease slightly. If we consider such efficiency deterioration, the temperature threshold of contrail formation for the hybrid-electric system is reduced further (see, e.g., Equation (1) and Figure 6 of this paper). The lower temperature threshold implies that contrail formation is more likely to decrease, but it requires a thorough analysis in future research.

Conclusions
This paper presents the changes in potential contrail coverage when flying with hybrid-electric aircraft. On the basis of the analysis, we have drawn the following conclusions: • The atmospheric areas of contrail formation of hybrid-electric aircraft are smaller than those of conventional aircraft and require lower atmospheric temperatures.

•
The reduction in contrail formation by hybrid-electric aircraft is more pronounced in a tropical region where the temperatures are higher.

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With a small degree of hybridization (below 30% in the current study), the contrail coverage remains nearly unchanged. A maximum reduction of about 40% in contrail coverage was observed locally, with 90% electric power in use.

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In non-summer, the reduction in potential contrail coverage by hybrid-electric aircraft was more noticeable at lower flight altitudes. In contrast, the changes in potential contrail coverage were nearly constant (about 20%) for all flight altitudes studied in summer.  that the vapor partial pressure at the engine exit is composed of that carried by the air needed to burn the fuel plus the contribution from the fuel itself. Since an electric motor does not emit water vapor, there is hence no contribution. Thus, the numerator in the formula for G is where the approximation is possible since EIH2O q a . The aircraft needs a thrust F to overcome drag and friction. When it flies with a velocity V, the engines must produce a power That is, two sources of energy, from the liquid fuel and the electric motor, add their powers with their respective thermodynamic efficiencies, η x . The notation (P E ) is the (variable) power of the electric engine. P E varies in response to variable fuel flow, such that the above sum equals FV. Thus, P E is a function of . m f .
Here, P 0 E is the electric power when it is driving the aircraft alone. The higher the fuel flow, the lower P E is. The maximum fuel flow to achieve a thrust power of FV is . m f max = FV/η K Q. It turns out to be useful also to define a quasi-electric energy content, namely, From here, it is relatively straightforward to formulate a generalization to more than two energy sources. Let