**3.1 Methods and data**

high latitudes have a 5% decrease in NSAD or MTOW. Considering that a 1% reduction in MTOW corresponds to a 2% (for larger aircraft such as a Boeing 747-800 or an An-24) to 3.6% (for small aircrafts such as an Embraer ERJ-145) reduction in effective payload, the 5% reduction in MTOW means a 8.5–19% reduction in effective payload year-round. As we stated earlier, at the costs of extra maintenance, aircraft still can operate with the manufacturer-labeled MTOW, which is lower than MTOW, under the unfavorable condition of warming. There may be no apparent passenger or cargo reduction. However, there will be hidden

*Actual payload equivalence of a 1% reduction in near-surface air density (NSAD). Percentages of maximum*

Based on the diagnosis of stresses (and forces) exerted on aircraft, a suitable invariant entity was identified for investigating climate change effects on aviation payload. Assuming no changes in technical aspects of aircraft and no changes to FAA regulations on takeoff performance, near-surface air density is the single most significant atmospheric parameter. Reanalyses data indicated clearly that the Earth's

Consequently, the near-surface air density experienced significant decreases globally. The 27 climate models showed a high level of consensus in simulated nearsurface air density variations. The ensemble mean of their twenty-first century simulations in NSAD trends was used to examine future reduction to effective payload. In line with Ref. [18], our study aimed to illustrate the potential for rising temperatures to influence weight restriction at takeoff stage. All technical aspects as commented on by Ref. [19] were assumed to be invariants during the analyses period. The simple fact that during extreme hot weather in summertime cargo airplanes have to reduce the effective payload indicates the validity of such analyses. The difference found with seasonal cycle is that these superimposed effects

atmosphere had expanded in volume in the past half century.

extra costs from a warming atmosphere.

*payload equivalence are shown in parenthesis.*

*Environmental Impact of Aviation and Sustainable Solutions*

**2.3 Discussion**

**182**

**Table 2.**

During different stages of flying, the force balance situation on an aircraft is different. At the takeoff and climbing stages, there are vertical and forward accelerations. The vertical component of thrust aids the lift in overwhelming gravity. Similarly, the horizontal component of thrust also overwhelms drag. At cruising

#### **Figure 5.**

*Typical flight profile of an aircraft and the fuel-burning rate in each stage. Except the cruising stage, other six stages last from 10 to 40 minutes only. In all, cruising stage is the most fuel-consuming stage.*

stage, thrust is reduced mainly to counteract drag, and the weight is balanced primarily by lift. Inevitable work done to the aircraft involves lifting it to the cruise elevation. The potential energy cannot be reclaimed at descending stage, unlike electronics cars. This portion of energy only is sensitive to warming when tropopause height changes as climate warms. The far larger term in energy cost would be that used to overcome drag. While it is apparent that drag is proportional to fuel cost, the picture for how total drag is affected by climate change is more sophisticated, because of the multiple sources involved. Classifying the many drag terms into pressure drag (e.g., induced drag, wave drag, and form drag) and skin friction drag (second term on right-hand side of Eq. (3)) is convenient because the pressure drags tend to be proportionally affected by air temperature and density changes. For example, for a specific design, the effects from environmental air on induced drag and net lift are usually proportional. Thus, the changes in skin friction are decisive for the sign of extra drag on top of total drag stress. To separate out climate change effects on aviation, it is assumed that there is no technological advance in design of subsonic aircrafts used for commercial airliners during the timespan of consideration:

$$F\_d = \iint\limits\_{\mathcal{S}} (p - p^\*) \hat{n} \hat{i} dA + \iint\limits\_{\mathcal{S}} \pi \hat{t} \hat{i} dA \tag{3}$$

airline or from several partner airlines are considered to be several connected direct flights, with distinct flight profile legs and usually carried out using different types of aircraft. For example, the Xiamen Airline schedule from Beijing to Singapore is looked upon as a direct flight from Beijing to Zhoushan, followed by a direct flight from Zhoushan to Xiamen, and another direct flight from Xiamen to Singapore. In this specific case, the same types of aircrafts are used. However, for intercontinental flights, usually different types of aircrafts are involved and intercontinental legs

In the estimation of fuel efficiency change by the end of this century, atmospheric parameters (i.e., air temperature and humidity) from multiple climate models (all under RCP 8.5 scenario) are used to drive expressions (Eqs. (3)–(5)), weighted by airplane-specific aerodynamic parameters. Ensemble averages are taken after the along trajectory integrations driven, respectively, by all climate models (**Table 1**). The climate model outputs are obtained from the IPCC Deutsches Klimarechenzentrum (DKRZ) Data Distribution Centre (http://www. ipcc-data.org/sim/gcm\_monthly/AR5/Reference-Archive.html). For models providing multiple perturbation runs, only *r*1*i*1*p*1 runs are used. There still is quite a large uncertainty with emission scenario. The results presented here thus should not be taken too literally. Instead, its values primarily are quantitatively accurate.

From the discussion in Section 3.1, we see that the total energy an aircraft needs to perform is the one overcoming the drag force (Eq. (3)) and the one overcoming gravity to the cruising altitude. The drag forces do work all stages taking off and before landing (all the suspension stages), whereas the potential energy increases only during the taking off and climbing to the cruising altitude (usually tropopause elevation for best visibility and thermal efficiency—to be discussed soon). Because the cruising stage is of very different lengths, in the following discussion, we estimate the percentage change in energy (fuel) costs relative to each stage in the A-G profile against their respective values (e.g., changes in fuel cost in each flight

From **Figure 6**, tropopause has apparent latitudinal distribution: reaching lower pressure (higher altitudes) at the tropical region and drops to higher pressure levels at the polar regions. As climate warms, tropopause was lifted to higher elevations (**Figures 6b** and **7a** and **b**), except very localized regions around the South Pole. This is in agreement with Refs. [20, 21]. Different emission scenarios differ primarily in magnitudes, with decreasing regions totally disappeared for the strong emission scenario RCP 8.5. For the bustling North Atlantic Corridor (NAC, 305–350E; 30–60N), not only the trend but even the differences between the two scenarios (**Figure 7c**) pass a *t*-test with 95% confidence interval. The tropopause altitude increase rate reaches 6 m/year for a weak emission scenario (RCP 4.5). This is about 4% increase in the fuel cost at the ascending stage for normal commercial flights. In the ascending stage, (in the vertical direction) the aircraft not only overcomes

gravity, but it also experiences drag (both terms in Eq. (3)). As a result, the ascending at the lower altitudes is more fuel-consuming, because of the higher air density. As a result of this fact, the elevated tropopause elevation is only an increase of less than 0.2% in fuel costs for long-range international flights. Except for very short-range flights, the cruising stage is the most fuel-consuming stage. Factors

cruise at a higher elevation than the domestic legs of flights.

*Climate Warming and Effects on Aviation DOI: http://dx.doi.org/10.5772/intechopen.86871*

stage, rather than vaguely relative to the total seven stages).

*3.2.1 Fluctuation of the tropopause height*

**3.2 Results**

**185**

where *Fd* is the total drag, *n*^ and ^*t* are, respectively, unit vectors in the direction perpendicular and parallel to the local surface element (d*A*), *p* is pressure, and ^*i* is the flow (drag) direction (align with the aircraft trajectory in **Figure 5**). For a specific type of airplane, the second term on the right-hand side of Eq. (3) can be parameterized as *p*<sup>∗</sup> *Sc*1*Rc*<sup>2</sup> *<sup>e</sup>* , where *S* is wing area and *Re* is Reynolds' number. Coefficients *c*<sup>1</sup> (�0.074 for well-painted un-dented surfaces) and *c*<sup>2</sup> (approximately�0.2) are aircraft dependent. The drag coefficient is inversely related to the Reynolds number. Increased flow speed tends to increase *Re*, while increased temperature, with consequently increased dynamic viscosity, tends to reduce *Re*. Without resorting to strict model calculation, it is difficult to estimate accurately the net effect from climate warming to total drag.

To have an estimate of the effects by the end of the twenty-first century, we followed a line-by-line analysis of available commercial airliners. For this purpose, online commercial ticketing databases are browsed for available flights among global airports. Non-direct flights are decomposed to several "direct flights" in a row. An annual, global, direct flight database is thus archived for this research. To estimate the total annual fuel consumption, we follow a line-by-line adding method that considers all available (in operation as of 2010) commercial airliners and their scheduled flights. The integration is along the flying trajectory. There are all sorts of alliances and partnerships between the commercial airliners. A trip involving multiple stops is likely carried out by different airliners in collaboration. For example, between Beijing and Singapore, there are 14 companies having such a transportation service at sub-weekly frequency. Asiana and Air China, for example, have a service to take passengers to Seoul first before heading to Singapore. Cathay Pacific and Thai Airlines stop, respectively, in Hong Kong and Bangkok. Xiamen Airlines even make two stops in between (Beijing ! Zhoushan ! Xiamen ! Singapore). To eliminate possible recounting of the flying legs, only direct flights (each involves one takeoff, cruise, and one landing) between airports are analyzed. In the above case between Beijing and Singapore, there are only five such daily flights, from Air China (A975 and A976, Airbus 330 s) and Singapore Airlines (SA801, 805, Boeing 777 s as carrier, and SA 807, an Airbus 380-800). Connecting flights from the same

#### *Climate Warming and Effects on Aviation DOI: http://dx.doi.org/10.5772/intechopen.86871*

airline or from several partner airlines are considered to be several connected direct flights, with distinct flight profile legs and usually carried out using different types of aircraft. For example, the Xiamen Airline schedule from Beijing to Singapore is looked upon as a direct flight from Beijing to Zhoushan, followed by a direct flight from Zhoushan to Xiamen, and another direct flight from Xiamen to Singapore. In this specific case, the same types of aircrafts are used. However, for intercontinental flights, usually different types of aircrafts are involved and intercontinental legs cruise at a higher elevation than the domestic legs of flights.

In the estimation of fuel efficiency change by the end of this century, atmospheric parameters (i.e., air temperature and humidity) from multiple climate models (all under RCP 8.5 scenario) are used to drive expressions (Eqs. (3)–(5)), weighted by airplane-specific aerodynamic parameters. Ensemble averages are taken after the along trajectory integrations driven, respectively, by all climate models (**Table 1**). The climate model outputs are obtained from the IPCC Deutsches Klimarechenzentrum (DKRZ) Data Distribution Centre (http://www. ipcc-data.org/sim/gcm\_monthly/AR5/Reference-Archive.html). For models providing multiple perturbation runs, only *r*1*i*1*p*1 runs are used. There still is quite a large uncertainty with emission scenario. The results presented here thus should not be taken too literally. Instead, its values primarily are quantitatively accurate.

#### **3.2 Results**

stage, thrust is reduced mainly to counteract drag, and the weight is balanced primarily by lift. Inevitable work done to the aircraft involves lifting it to the cruise elevation. The potential energy cannot be reclaimed at descending stage, unlike electronics cars. This portion of energy only is sensitive to warming when tropopause height changes as climate warms. The far larger term in energy cost would be that used to overcome drag. While it is apparent that drag is proportional to fuel cost, the picture for how total drag is affected by climate change is more sophisticated, because of the multiple sources involved. Classifying the many drag terms into pressure drag (e.g., induced drag, wave drag, and form drag) and skin friction drag (second term on right-hand side of Eq. (3)) is convenient because the pressure drags tend to be proportionally affected by air temperature and density changes. For example, for a specific design, the effects from environmental air on induced drag and net lift are usually proportional. Thus, the changes in skin friction are decisive for the sign of extra drag on top of total drag stress. To separate out climate change effects on aviation, it is assumed that there is no technological advance in design of subsonic aircrafts used for commercial airliners during the timespan of

> *Fd* ¼ ðð

*Environmental Impact of Aviation and Sustainable Solutions*

*S*

Coefficients *c*<sup>1</sup> (�0.074 for well-painted un-dented surfaces) and *c*<sup>2</sup>

accurately the net effect from climate warming to total drag.

(approximately�0.2) are aircraft dependent. The drag coefficient is inversely related to the Reynolds number. Increased flow speed tends to increase *Re*, while increased temperature, with consequently increased dynamic viscosity, tends to reduce *Re*. Without resorting to strict model calculation, it is difficult to estimate

To have an estimate of the effects by the end of the twenty-first century, we followed a line-by-line analysis of available commercial airliners. For this purpose, online commercial ticketing databases are browsed for available flights among global airports. Non-direct flights are decomposed to several "direct flights" in a row. An annual, global, direct flight database is thus archived for this research. To estimate the total annual fuel consumption, we follow a line-by-line adding method that considers all available (in operation as of 2010) commercial airliners and their scheduled flights. The integration is along the flying trajectory. There are all sorts of alliances and partnerships between the commercial airliners. A trip involving multiple stops is likely carried out by different airliners in collaboration. For example, between Beijing and Singapore, there are 14 companies having such a transportation service at sub-weekly frequency. Asiana and Air China, for example, have a service to take passengers to Seoul first before heading to Singapore. Cathay Pacific and Thai Airlines stop, respectively, in Hong Kong and Bangkok. Xiamen Airlines even make two stops in between (Beijing ! Zhoushan ! Xiamen ! Singapore). To eliminate possible recounting of the flying legs, only direct flights (each involves one takeoff, cruise, and one landing) between airports are analyzed. In the above case between Beijing and Singapore, there are only five such daily flights, from Air China (A975 and A976, Airbus 330 s) and Singapore Airlines (SA801, 805, Boeing 777 s as carrier, and SA 807, an Airbus 380-800). Connecting flights from the same

*<sup>p</sup>* � *<sup>p</sup>*<sup>∗</sup> ð Þ*n*^^*idA* <sup>þ</sup>

where *Fd* is the total drag, *n*^ and ^*t* are, respectively, unit vectors in the direction perpendicular and parallel to the local surface element (d*A*), *p* is pressure, and ^*i* is the flow (drag) direction (align with the aircraft trajectory in **Figure 5**). For a specific type of airplane, the second term on the right-hand side of Eq. (3) can be

ðð

*τ*^*t*^*idA* (3)

*S*

*<sup>e</sup>* , where *S* is wing area and *Re* is Reynolds' number.

consideration:

**184**

parameterized as *p*<sup>∗</sup> *Sc*1*Rc*<sup>2</sup>

From the discussion in Section 3.1, we see that the total energy an aircraft needs to perform is the one overcoming the drag force (Eq. (3)) and the one overcoming gravity to the cruising altitude. The drag forces do work all stages taking off and before landing (all the suspension stages), whereas the potential energy increases only during the taking off and climbing to the cruising altitude (usually tropopause elevation for best visibility and thermal efficiency—to be discussed soon). Because the cruising stage is of very different lengths, in the following discussion, we estimate the percentage change in energy (fuel) costs relative to each stage in the A-G profile against their respective values (e.g., changes in fuel cost in each flight stage, rather than vaguely relative to the total seven stages).

#### *3.2.1 Fluctuation of the tropopause height*

From **Figure 6**, tropopause has apparent latitudinal distribution: reaching lower pressure (higher altitudes) at the tropical region and drops to higher pressure levels at the polar regions. As climate warms, tropopause was lifted to higher elevations (**Figures 6b** and **7a** and **b**), except very localized regions around the South Pole. This is in agreement with Refs. [20, 21]. Different emission scenarios differ primarily in magnitudes, with decreasing regions totally disappeared for the strong emission scenario RCP 8.5. For the bustling North Atlantic Corridor (NAC, 305–350E; 30–60N), not only the trend but even the differences between the two scenarios (**Figure 7c**) pass a *t*-test with 95% confidence interval. The tropopause altitude increase rate reaches 6 m/year for a weak emission scenario (RCP 4.5). This is about 4% increase in the fuel cost at the ascending stage for normal commercial flights.

In the ascending stage, (in the vertical direction) the aircraft not only overcomes gravity, but it also experiences drag (both terms in Eq. (3)). As a result, the ascending at the lower altitudes is more fuel-consuming, because of the higher air density. As a result of this fact, the elevated tropopause elevation is only an increase of less than 0.2% in fuel costs for long-range international flights. Except for very short-range flights, the cruising stage is the most fuel-consuming stage. Factors

#### **Figure 6.**

*GFDL2.1 simulated tropopause height (shades in (a), in km) and tropopause temperature (contour lines in (a)) during a control period (1980–2000). The projected differences between (2080–2100) and the control period, under the RCP 8.5 emission scenario, are shown in (b). The increases in tropopause height are a global phenomenon. For most areas, tropopause temperatures also increase.*

affecting the cruising stage needed to be examined to have an estimate of the fuel efficiency issue of climate warming.

#### *3.2.2 Thermal, mechanical, and total efficiency*

Aircraft engines are breathing thermal engines. That is, they use oxygen in the environmental air fanned into the burning chamber, rather than carrying the oxidizers (as rocket engines do) for burning the fuel. The working fluid is the hightemperature and thus high-pressure exhausts (gases resulting from burning of fuel plus other components in the inhaled air). As fuel and inhaled air are "locked" in the burning chamber moving with the aircraft, the overall efficiency (in providing thrust) is a multiplication of thermal efficiency and mechanical efficiency. Applying Newton's third law of motion (or momentum theory) *F*Δ*t* ¼ *m*Δ*V*, it is straightforward to ascertain that the overall efficiency, *η*, is the multiplication of mechanical efficiency (*ηM*) and thermal efficiency (*ηT*), or *η* = *η<sup>M</sup>* � *η<sup>T</sup>* (e.g., Ref. [22]).

As aircraft engines are thermal engines, their thermal efficiency is adversely affected by environmental temperature rise. The second law of thermodynamics puts a fundamental limit on thermal efficiency (*ηT*):

$$
\eta\_T = \varepsilon (\mathbf{1} - T\_{\rm C}/T\_H) \tag{4}
$$

where *ε* is a technical limiting factor (0.57) indicating actual engines' closeness

, and 4.94 <sup>10</sup><sup>4</sup>

thermal efficiency from climate change are transferred to the air temperature variations along the flying routes (legs). As the oxygen is inhaled from environmental air (common to breathing engines), and the density decrease due to climate warming does not result in incrementing oxygen concentration in the

. The effects on engine

to ideal engine [9],*TH* is the absolute temperature at which the heat enters the engine cycle (also called turbine entry temperatures, TETs), and *Tc* is the absolute temperature of the exhaust gases. *Tc* closely follows the environmental air temperature,*Ta*, with only a cooling technology-dependent constant difference. The efficiency of thermal engines increases with higher operating temperature and lower environmental temperature. There have been active efforts in improving TETs during the past 50 years (Section 7.4.1.2 of IPCC AR5: aviation and the global atmosphere). In this study, for simplicity, we assume that both *TH* and *ε* are not going to improve in the projection period (between 2010 and 2100). *Tc* is the only variable being considered varying along the cruising route. For all commercial brands in operation, the TETs published during 2010–2014 are used. Except for several well-known engine types, most engine companies are very protective of actual engine data and operating conditions, although there is much discussion in the literature and also clues such as in EASA (and FAA) type of certificates (certificates for all of the engine types are publicly available), which have detailed listings of actual engine values in regions where engine measurements are made. The TETs can be deduced from the emission data. According to Eq. (4), a decrease in thermal efficiency for common commercial engines, GE90, RB211, LAEV2500, and Lyulka, in response to a 1 K increase in environmental temperature (*Tc*), are respectively,

*GFDL2.1 simulated tropopause height changes (shades in (a) and (b), in hPa) between periods 1980–2000 and 2080–2100, represented in pressure levels. The area averaged time series over the NAC (305–350E; 30–60N) is shown in (c), for two emission scenarios (RCP 4.5 and RCP 8.5). The two differs only quantitatively.*

5.62 <sup>10</sup><sup>4</sup>

**187**

**Figure 7.**

, 5.88 <sup>10</sup><sup>4</sup>

*Climate Warming and Effects on Aviation DOI: http://dx.doi.org/10.5772/intechopen.86871*

, 5.07 <sup>10</sup><sup>4</sup>

#### *Climate Warming and Effects on Aviation DOI: http://dx.doi.org/10.5772/intechopen.86871*

**Figure 7.**

affecting the cruising stage needed to be examined to have an estimate of the fuel

*GFDL2.1 simulated tropopause height (shades in (a), in km) and tropopause temperature (contour lines in (a)) during a control period (1980–2000). The projected differences between (2080–2100) and the control period, under the RCP 8.5 emission scenario, are shown in (b). The increases in tropopause height are a global*

Aircraft engines are breathing thermal engines. That is, they use oxygen in the environmental air fanned into the burning chamber, rather than carrying the oxidizers (as rocket engines do) for burning the fuel. The working fluid is the hightemperature and thus high-pressure exhausts (gases resulting from burning of fuel plus other components in the inhaled air). As fuel and inhaled air are "locked" in the burning chamber moving with the aircraft, the overall efficiency (in providing thrust) is a multiplication of thermal efficiency and mechanical efficiency. Applying Newton's third law of motion (or momentum theory) *F*Δ*t* ¼ *m*Δ*V*, it is straightforward to ascertain that the overall efficiency, *η*, is the multiplication of mechanical efficiency (*ηM*) and thermal efficiency (*ηT*), or *η* = *η<sup>M</sup>* � *η<sup>T</sup>* (e.g., Ref. [22]). As aircraft engines are thermal engines, their thermal efficiency is adversely affected by environmental temperature rise. The second law of thermodynamics

*η<sup>T</sup>* ¼ *ε*ð Þ 1 � *TC=TH* (4)

efficiency issue of climate warming.

**Figure 6.**

**186**

*3.2.2 Thermal, mechanical, and total efficiency*

*phenomenon. For most areas, tropopause temperatures also increase.*

*Environmental Impact of Aviation and Sustainable Solutions*

puts a fundamental limit on thermal efficiency (*ηT*):

*GFDL2.1 simulated tropopause height changes (shades in (a) and (b), in hPa) between periods 1980–2000 and 2080–2100, represented in pressure levels. The area averaged time series over the NAC (305–350E; 30–60N) is shown in (c), for two emission scenarios (RCP 4.5 and RCP 8.5). The two differs only quantitatively.*

where *ε* is a technical limiting factor (0.57) indicating actual engines' closeness to ideal engine [9],*TH* is the absolute temperature at which the heat enters the engine cycle (also called turbine entry temperatures, TETs), and *Tc* is the absolute temperature of the exhaust gases. *Tc* closely follows the environmental air temperature,*Ta*, with only a cooling technology-dependent constant difference. The efficiency of thermal engines increases with higher operating temperature and lower environmental temperature. There have been active efforts in improving TETs during the past 50 years (Section 7.4.1.2 of IPCC AR5: aviation and the global atmosphere). In this study, for simplicity, we assume that both *TH* and *ε* are not going to improve in the projection period (between 2010 and 2100). *Tc* is the only variable being considered varying along the cruising route. For all commercial brands in operation, the TETs published during 2010–2014 are used. Except for several well-known engine types, most engine companies are very protective of actual engine data and operating conditions, although there is much discussion in the literature and also clues such as in EASA (and FAA) type of certificates (certificates for all of the engine types are publicly available), which have detailed listings of actual engine values in regions where engine measurements are made. The TETs can be deduced from the emission data. According to Eq. (4), a decrease in thermal efficiency for common commercial engines, GE90, RB211, LAEV2500, and Lyulka, in response to a 1 K increase in environmental temperature (*Tc*), are respectively, 5.62 <sup>10</sup><sup>4</sup> , 5.88 <sup>10</sup><sup>4</sup> , 5.07 <sup>10</sup><sup>4</sup> , and 4.94 <sup>10</sup><sup>4</sup> . The effects on engine thermal efficiency from climate change are transferred to the air temperature variations along the flying routes (legs). As the oxygen is inhaled from environmental air (common to breathing engines), and the density decrease due to climate warming does not result in incrementing oxygen concentration in the

environmental air (as a matter of fact, if vapor content is considered, a decrease in oxygen concentration is expected), a natural consequence is that this may result in incomplete fuel oxidization, without technological improvements to the combustion system to increase the volumetric air inhaling rate. This detrimental effect on thrust production is not considered here but is apparently proportional to air density decrease.

As the airplane moves forward by ejecting exhausts backward, the way in which the kinetic energy (extracted from the fuel-burning chemical energy) is partitioned between aircraft and exhaust jet (i.e., used for pushing aircraft forward versus removed by the exhaust) is measured by the mechanical (propulsive) efficiency (*ηM*):

$$\eta\_M = \frac{2}{1 + V\_\varepsilon / V\_a} \tag{5}$$

direction. A *t*-test was performed for the overall decrease in fuel efficiency time series. For 22-year periods centered at year 2010 and 2090, a *P*-value of 0.0017 (*dof* = 38) was obtained. At this significant level, it means at a possibility of 99.84%, the trend is not by mere coincidence. Thus, the net decrease in fuel efficiency is

*Decreases in thermal efficiency (a) and mechanical efficiency (b), increase in skin frictional drag (c), and the overall decrease in fuel efficiency (d) during 2000–2100, for entire commercial aviation sector as a whole. Multiple climate model ensemble means (shown as thick red lines), and the ranges of the variability (thick yellow lines) are shown for 24 climate models under RCP 8.5 emission scenarios (for clarity only, the other two models both are within the range). The flight schedules of year 2010 are assumed unchanged during the entire period. Note that the control period is centered on 2010 (2005–2015), so the values at starting (2000) is not*

To conclude, factors affecting aviation fuel efficiency are thermal and propulsive efficiencies and overall drag on aircrafts. An along-the-route integration is made for all direct flights in baseline year 2010, under current and future atmospheric conditions from nine climate models under the representative concentration pathway (RCP) 8.5 scenario. Thermal and propulsive efficiencies are affected oppositely by environmental warming. The former decreases 0.38%, but the latter increases 0.35% over the twenty-first century. Consequently, the overall engine efficiency decreases only by 0.02%. Over the same period, skin frictional drag increases 5.5%, from the increased air stickiness. This component is only 5.7% of the total drag, the 5.5% increase in air viscosity accounts for a 0.275% inefficiency in fuel consumption, one order of magnitude larger than that caused by engine efficiency reduction. The total decrease in fuel efficiency equals to 0.24 billion gallons of extra fuel annually, a qualitatively robust conclusion but quantitatively with

The effects on fuel cost from increased airplane potential energy still is one order of magnitude smaller than factors considered here, due to the fact that it is a less than a 1% increase in the climbing stage (at most 1 hour). The fuel cost, in the

small but statistically significant.

*Climate Warming and Effects on Aviation DOI: http://dx.doi.org/10.5772/intechopen.86871*

significantly inter-climate model spread.

**3.3 Conclusion**

**189**

**Figure 8.**

*exactly united.*

where *Ve* is effective exhaust speed (jet speed relative to airplane) and the airplane speed, *Va*, is relative to the ground. *η<sup>M</sup>* reaches maximum when the jet exhaust is stationary relative to the ground (all extracted energy from fuel burning is used as thrust to push forward the aircraft). Here exhaust speed is retrieved from TETs and engine pressure ratios [23]. Equation (5) is derived in the inertial frame coordinates based on energy and momentum conservation. The commercial passenger aircrafts generally have effective jet speeds, *Ve*, within the range of 600–850 m/s. The lower the effective jet speed (i.e., close to the cruising speed), the more sensitive the mechanical efficiency is to airplane cruising speeds. Overall efficiency *η* is the multiplication of mechanical efficiency and thermal efficiency (*η* = *η<sup>M</sup>* � *ηT*). Factors lowering (enhancing) overall efficiency result in more (less) fuel cost.

In the global belt between 65°S and 70°N, which contains most of the trajectories of commercial flights, the tropopause temperature increased �0.8–1.2°C over a 100-year period (the difference between (2080–2100) and (1980–2000)). For most commercial engines, thermal efficiency reduces only 0.06% during the cruising stage of the flight profile. Due to air density decrease, the mechanical efficiency is affected by warming the opposite way. As a result, the total efficiency was affected only by �0.03%. The most significant effect from a warming flying environment is in fact from the increased air stickiness—the body drag acting on the aircraft.

#### *3.2.3 Drag on aircraft*

The percentage change in skin friction drag is caused primarily by the increase in the kinematic viscosity of air, within the cruising space, which has a temperature lapse rate of about 8 � <sup>10</sup>�<sup>8</sup> <sup>m</sup><sup>2</sup> <sup>s</sup> �<sup>1</sup> K�<sup>1</sup> . **Figure 8c** indicates that, for all operating airliners considered, there could be a 3.5% increase in skin frictional drag by 2100 (Δ*τ=τ*<sup>0</sup> <sup>¼</sup> <sup>0</sup>*:*035, with superscript means the value at reference year 2010), whereas the skin friction drag is only �5.7% of the total drag. The increase in skin frictional drag accounts only for a �0.2% reduction in efficiency in fuel consumption. Thus, due to increased air viscosity and decreased engine overall efficiency, the annual fuel consumption in 2100 would be �0.9% higher than around 2010. The spread in the estimation is wide among climate models, but all indicate more fuel consumption as climate warms. The corresponding absolute change of 0.9% reduction in efficiency in fuel consumption is considerable, about 0.68 billion gallons of fuel annually. The reduction in thermal efficiency is complementary to the IPCC AR5 perspective, but the fact that the increased drag and mechanical efficiency may be a supplant concept (a new rubric) will hopefully stimulate further studies in this

#### **Figure 8.**

environmental air (as a matter of fact, if vapor content is considered, a decrease in oxygen concentration is expected), a natural consequence is that this may result in incomplete fuel oxidization, without technological improvements to the combustion system to increase the volumetric air inhaling rate. This detrimental effect on thrust production is not considered here but is apparently proportional to air den-

*Environmental Impact of Aviation and Sustainable Solutions*

As the airplane moves forward by ejecting exhausts backward, the way in which the kinetic energy (extracted from the fuel-burning chemical energy) is partitioned between aircraft and exhaust jet (i.e., used for pushing aircraft forward versus removed by the exhaust) is measured by the mechanical (propulsive)

*<sup>η</sup><sup>M</sup>* <sup>¼</sup> <sup>2</sup>

where *Ve* is effective exhaust speed (jet speed relative to airplane) and the airplane speed, *Va*, is relative to the ground. *η<sup>M</sup>* reaches maximum when the jet exhaust is stationary relative to the ground (all extracted energy from fuel burning is used as thrust to push forward the aircraft). Here exhaust speed is retrieved from TETs and engine pressure ratios [23]. Equation (5) is derived in the inertial frame coordinates based on energy and momentum conservation. The commercial passenger aircrafts generally have effective jet speeds, *Ve*, within the range of

600–850 m/s. The lower the effective jet speed (i.e., close to the cruising speed), the more sensitive the mechanical efficiency is to airplane cruising speeds. Overall efficiency *η* is the multiplication of mechanical efficiency and thermal efficiency (*η* = *η<sup>M</sup>* � *ηT*). Factors lowering (enhancing) overall efficiency result in more (less)

In the global belt between 65°S and 70°N, which contains most of the trajectories

The percentage change in skin friction drag is caused primarily by the increase in the kinematic viscosity of air, within the cruising space, which has a temperature

airliners considered, there could be a 3.5% increase in skin frictional drag by 2100 (Δ*τ=τ*<sup>0</sup> <sup>¼</sup> <sup>0</sup>*:*035, with superscript means the value at reference year 2010), whereas the skin friction drag is only �5.7% of the total drag. The increase in skin frictional drag accounts only for a �0.2% reduction in efficiency in fuel consumption. Thus, due to increased air viscosity and decreased engine overall efficiency, the annual fuel consumption in 2100 would be �0.9% higher than around 2010. The spread in the estimation is wide among climate models, but all indicate more fuel consumption as climate warms. The corresponding absolute change of 0.9% reduction in efficiency in fuel consumption is considerable, about 0.68 billion gallons of fuel annually. The reduction in thermal efficiency is complementary to the IPCC AR5 perspective, but the fact that the increased drag and mechanical efficiency may be a supplant concept (a new rubric) will hopefully stimulate further studies in this

. **Figure 8c** indicates that, for all operating

�<sup>1</sup> K�<sup>1</sup>

of commercial flights, the tropopause temperature increased �0.8–1.2°C over a 100-year period (the difference between (2080–2100) and (1980–2000)). For most commercial engines, thermal efficiency reduces only 0.06% during the cruising stage of the flight profile. Due to air density decrease, the mechanical efficiency is affected by warming the opposite way. As a result, the total efficiency was affected only by �0.03%. The most significant effect from a warming flying environment is in fact from the increased air stickiness—the body drag acting on the aircraft.

1 þ *Ve=Va*

(5)

sity decrease.

efficiency (*ηM*):

fuel cost.

**188**

*3.2.3 Drag on aircraft*

lapse rate of about 8 � <sup>10</sup>�<sup>8</sup> <sup>m</sup><sup>2</sup> <sup>s</sup>

*Decreases in thermal efficiency (a) and mechanical efficiency (b), increase in skin frictional drag (c), and the overall decrease in fuel efficiency (d) during 2000–2100, for entire commercial aviation sector as a whole. Multiple climate model ensemble means (shown as thick red lines), and the ranges of the variability (thick yellow lines) are shown for 24 climate models under RCP 8.5 emission scenarios (for clarity only, the other two models both are within the range). The flight schedules of year 2010 are assumed unchanged during the entire period. Note that the control period is centered on 2010 (2005–2015), so the values at starting (2000) is not exactly united.*

direction. A *t*-test was performed for the overall decrease in fuel efficiency time series. For 22-year periods centered at year 2010 and 2090, a *P*-value of 0.0017 (*dof* = 38) was obtained. At this significant level, it means at a possibility of 99.84%, the trend is not by mere coincidence. Thus, the net decrease in fuel efficiency is small but statistically significant.

#### **3.3 Conclusion**

To conclude, factors affecting aviation fuel efficiency are thermal and propulsive efficiencies and overall drag on aircrafts. An along-the-route integration is made for all direct flights in baseline year 2010, under current and future atmospheric conditions from nine climate models under the representative concentration pathway (RCP) 8.5 scenario. Thermal and propulsive efficiencies are affected oppositely by environmental warming. The former decreases 0.38%, but the latter increases 0.35% over the twenty-first century. Consequently, the overall engine efficiency decreases only by 0.02%. Over the same period, skin frictional drag increases 5.5%, from the increased air stickiness. This component is only 5.7% of the total drag, the 5.5% increase in air viscosity accounts for a 0.275% inefficiency in fuel consumption, one order of magnitude larger than that caused by engine efficiency reduction. The total decrease in fuel efficiency equals to 0.24 billion gallons of extra fuel annually, a qualitatively robust conclusion but quantitatively with significantly inter-climate model spread.

The effects on fuel cost from increased airplane potential energy still is one order of magnitude smaller than factors considered here, due to the fact that it is a less than a 1% increase in the climbing stage (at most 1 hour). The fuel cost, in the

cruising stage is much greater, because of the length of time (up to 14 hours). Also, at higher altitudes, the fuel cost for climbing is reduced (the increased tropopause height's effect is the upper level part of the trajectory). The common statement that the climb stage is more fuel-consuming refers to the rate, not the total value (except for very short flights, e.g., from Oklahoma City to Tulsa).

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Climate effects on aviation are a burgeoning but promising research field. Our study here focused on the rudimentary aspects that are of concern to the commercial airlines: the effects on maximum payload and on fuel costs. Other directions such as customer comfort and safety also are profoundly affected, especially the circulation changes (winds and turbulence [24]). These will be addressed in future studies in this walk of line.
