Modeling and Analysis of Noise Emission Using Data from Flight Simulators

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Potential use by aerodrome operators for strategic noise mapping as a cheaper alternative to contemporary methods. Subject of further research.

Abstract

The main goal of this article is to examine the impact of various factors, including the aircraft take-off weight and configuration, on the noise and gaseous emissions. The analysis was based on trajectory data obtained from the X-Plane 11 simulator and a MATLAB noise engine created in accordance with ECAC.CEAC (European Civil Aviation Conference) Doc 29 recommendations. It allowed us to present various noise metrics in the form of noise maps and conduct a general analysis of how certain factors, e.g., flap settings, impact the noise and gaseous emissions. The study indicates that, from the “global” perspective (i.e., the entire airport vicinity), the NADP1 procedure shows better noise reduction, while the NADP2 procedure exhibits lower $C{O}_2$ emissions. Conversely, from the perspective of individual observers (i.e., the local perspective), it may (but not necessarily) be the case that the NADP2 procedure allows for achieving both minimal noise and $C{O}_2$ emissions compared to the NADP1 procedure. For example, reducing take-off thrust may reduce the SEL > 85 [dB] area in NADP2 by twice as much as in NADP1, but at the cost of almost four times less $C{O}_2$ emission reductions. The study may be further developed to find an algorithm for designating individual noise-abatement procedure parameters that will account for various factors in order to minimize the aforementioned emissions.

1. Introduction

Commercial civil aviation is currently characterized as a vigorously growing branch of the global economy. ICAO estimates that the Revenue per Passenger Kilometers (RPK) is going to continue to grow by 4.3% per annum, which will result in its being doubled by the year 2040. Should this trend be sustained, commercial aviation will create over fifteen million new workplaces and contribute almost $1.5 trillion to the global GDP [1]. It is worth noting that these predictions do not account for the growth of the tourism sector.

One can distinguish numerous side effects of the dynamic growth driven by the popular demand for air travel. One of these effects is the reaching of capacity limits by major airports and transportation hubs. This leads to an increased number of operations at airports, which are typically located in suburban areas inhabited by thousands or tens of thousands of people. Unlike heavily urbanized city centers, or the neighborhoods of large industrial plants, these areas are usually only exposed to noise from taking-off and landing aircraft. During these phases of flight, the jet engine’s core exhaust noise is the factor that highly contributes to the overall noise levels [2]; however, the fan noise is dominant during landing [3]. Jet engine’s fan noise is also a major contributor to airplane noise during take-off [3]. Some cities consider redirecting part of the traffic from the main airports to smaller aerodromes that are not faced with the problem of managing such a heavy load of air traffic. One of the challenges of such maneuvers is to ensure that the residents of previously calm neighborhoods will not experience a sudden increase in overall noise exposure, for example by properly preparing the airport vicinity with appropriate acoustic isolation [4]. The maximum noise levels perceived in these areas is only a small part of the effective management of the aircraft-generated acoustic footprint. This is because the sound timbre and frequency spectrum of aircraft makes their noise more annoying to people than other noises at the same sound intensity level. This has been confirmed by numerous organizations and is supported by various studies [5,6,7], which indicate that frequency spectrum-oriented research is gaining significance. An increasing number of operations of UAVs may be a motive for further research in this field. Their electrically powered rotors produce high-pitched noise that can cause greater annoyance to residents, especially in combination with maneuvers in close proximity to populated areas [8,9,10].

Prolonged exposure to the noise that causes some form of irritation may lead to a number of health-related risks. A document published by the World Health Organization, titled “Guidelines for Community Noise”, points out that among the negative effects that noise can have on human health and quality of life, we can distinguish progressive hearing impairment, insomnia, and a range of psychological effects [11]. Many further studies back this up, providing additional insights and tools to help officials and airport managers in developing solutions for quieter airport neighborhoods [12,13].

The emission of noise, however, is not the only type of pollution that poses a threat to communities. Many of the harmful substances derived from the combustion of aviation fuel are considered to be significant sources of pollution, especially in areas directly adjacent to airports [14]. The physical compounds, which are the subject of concern in this study, include carbon dioxide ($C{O}_2$), nitrogen oxides, sulfur oxides, and particulate matter (PM), which contribute to the formation of smog, for example. They have a documented negative impact on human health and the overall condition of the environment [15].

At present, it seems that minimizing the impact of aviation on the natural environment remains one of the most significant issues in the industry. Despite the development of aircraft that introduce increasingly innovative solutions to reduce emissions, the continuous growth in the number of operations seems to neutralize the positive impact of these solutions [16]. Furthermore, these solutions appear to be effective mostly in from a long-term perspective, as they require many years of extensive research before they can be implemented, i.e., it may take additional years before airlines incorporate these solutions into their fleets [17].

Standardizing the maneuvers performed by departing aircraft may lead to achieving more uniform flight profiles in its initial stages, when the engines are operating at high-power settings and at relatively low altitudes. This may provide an opportunity to optimize the aircraft’s initial climb trajectory and, to a certain extent, be a more immediate solution to noise and gaseous emissions in the airport vicinity.

In the Doc 8168, the ICAO recommends that commercial operators shall enforce a maximum of two Noise Abatement Departure Procedures to be used during the take-off and climb-out phase of each flight. The recommendation is implemented by the majority of airlines in their respective Standard Operating Procedures, and despite some differences specific to the airline and aircraft type, these procedures can be divided into two basic categories:

• Procedures that minimize the effect of noise in areas closer to airports (in ICAO’s nomenclature—NADP1);
• Procedures that minimize the effect of noise in areas more distant from the airport (in ICAO’s nomenclature—NADP2).

It is worth noting, that there are no set boundaries between what can be classified as “distant” and “close-in” areas. Both procedures differ in specific altitudes, at which the crew commences the maneuver of acceleration to a speed that will enable them to clean up the aircraft configuration (typically 250 KIAS (KIAS—Knots of Indicated Air Speed) under 10,000 feet, although individual departure procedures may specify lower values). The simplicity and independence from multiple factors suggest that for specific initial conditions, there may exist solutions that optimize both noise and gaseous emissions, such as $C{O}_2$. In general, studies have shown that compliance with these procedures allow for savings both in noise and in gaseous emissions [18,19]. A schematic representation of both procedures is depicted on Figure 1.

The clean configuration speed, excess thrust produced by engines, climb gradient, and many other performance parameters are closely related and depend on many factors, including the aircraft’s mass and atmospheric conditions, such as wind and temperature, which also change with time and altitude. Relationships describing the interplay of thrust and specific aerodynamic forces and moments acting on aircraft are similarly complex. In general, one can describe the maneuver of acceleration to be the issue of optimal trade-off between potential and kinetic energy (e.g., lowering the climb gradient may speed up the acceleration process, which allows for quicker clean-up and saves excess drag generated by flaps, thus saving some fuel).

Noise Abatement Departure Procedures are not the only way to mitigate the degree of noise and gaseous emissions. Usually, they are used in conjunction with other methods, such as reduced take-off thrust, Standard Instrument Departures (SIDs), noise preferential runways, or other airport-specific procedures.

According to the Directive 2002/49/WE of European Parliament, aerodrome operators are obliged to assess and revise, every five years, current levels of noise pollution in the vicinity of the airport [20]. This process relies on drawing up strategic noise maps, which portray areas that are particularly vulnerable to higher noise levels. These maps usually depict cumulative noise metrics, such as $L_{DN}$ (day–night average sound level) or $L_{night}$ (night average sound level) that account for multiple noise events caused by different departing and arriving traffic in a specified timeframe. The downside of this type of depiction is that it lacks in accounting for abrupt and short changes in noise exposure, e.g., caused by delaying maneuvers, such as holdings or procedural turns, which are shown to inflict more negative residents’ responses [21]. For the purpose of this study, only single-event noise metrics were used—$SEL$ (sound exposure level) and $L_{Amax}$ (the maximum A-weighted level of noise recorded by the observer). It is emphasized that although the ICAO Doc 9911 recommends that the aircraft noise calculations shall only be applied to model the long-term averaged noise metrics, the methodology for calculating the single noise event remains unchanged.

During the process of creating the software that would allow for generating such noise maps, the modelers often need to rely on incomplete data sets and simplification techniques. With the scarcity of aircraft’s trajectories and precise radar data, or even more commonly, the lack of data of thrust settings or aircraft’s body angles, which can be only acquired from an on-board Flight Data Recorder, modelers often need to synthesize aircraft trajectories that are based upon simplified methods, such as default procedure profiles or steps [22] The steps are then evaluated based on statistical characteristics (e.g., Gaussian distribution) [23]. Some researchers acquire flight data through an ADS-B equipment, which is nowadays mounted onboard most large aircraft [24], while others suggest that a specially trained Neural Network might help to predict the weight, thrust, and flap settings for a given flight using only surveillance equipment (such as ADS-B) [25].

Until recently, assessing an aircraft’s trajectory using simulation methods was considered a very precise, but also costly, process with a limited scope of application. Work in [26] presents a unique rapid prototyping environment, which enables an evaluation of the aircraft’s noise impact. The NOSIM system, presented in this work, combines a flight simulator, a noise model, and a geographic information system (GIS). The flight simulator component of NOISIM uses advanced performance data from the Boeing 737 [27]. The Aircraft Noise Simulation Working Group (ANSWr) was established by DLR, ONERA, and NASA to compare simulation tools, establish guidelines for noise prediction, and assess uncertainties associated with the simulation [28]. ANSWr develops its own scientific simulation tools for the prediction of overall aircraft system noise. PANAM (the Parametric Aircraft Noise Analysis Module) by DLR [29], ANOPP (Aircraft Noise Prediction Program) by NASA [30], and CARMEN by ONERA [31] are advanced simulation tools developed for many years (2000—PANAM, 1970s—ANOPP, and 2008—CARMEN) [28]. Nowadays, widely available and popular flight simulators, such as X-Plane or Microsoft Flight Simulator present a possible new, cheaper way of flight data acquisition for use in Noise and Emission modeling. The difference in the simulation of aircraft dynamics in these two popular simulators is significant. Microsoft Flight Simulator software uses the classic six degree of freedom 6DOF model of motion [32], while X-Plane uses the blade element theory developed originally to evaluate the behavior of the propeller [33]. In the blade theory method, each element of the aircraft is divided into small elements, for which the forces and moments are calculated individually. The obtained results are summed to obtain an overall result for the simulation object. Certain add-ons for various airliners made by third-party developers, such as Fenix Simulations or PMDG, allow for almost a study-level experience and very close representation of the aircraft’s handling and performance characteristics, e.g., a climb gradient specific to the aircraft’s mass or air density, which is of paramount importance in proper noise modeling. This may prove to be a very efficient method, as all important data can be exported from the simulator in a convenient format straight to the appropriate modeling software. Furthermore, simulators allow for virtual flights to be conducted in very specific conditions manually selected by the user. This may include, for example, the atmospheric conditions, airport location, aircraft’s mass, balance and take-off configuration, and more.

It needs to be emphasized that the simulation only allows for acquiring data in regards to the aircraft’s trajectory, configuration, and power settings, but the “power-specific” and “distance-specific” noise metric values are still acquired from the Noise–Power–Distance (NPD) relationships from aircraft’s type database. These so-called NPD Tables are a standard way of expressing the base noise levels in almost every software for noise modeling. In practical noise assessments, the NPD data are subjected to various adjustments that allow for a further increase in the accuracy of noise calculations.

2. Methods of Noise Modeling

Methodology for noise pollution determination was based on existing models for real-world use. Aforementioned models are developed in accordance with recommendations published in ECAC.CEAC Doc 29 [34]. The created model is based on flight trajectory data acquired from X-Plane 11.55 that are used in conjunction with Noise—Power—Distance characteristics for type Boeing 737–800 that were accessed through the ANP (Aircraft Noise and Performance) Database, which is managed by Eurocontrol [35].

Analysis was performed for five factors that influence aircraft trajectory to a large degree, and thus, it is noise and pollutant emissions. The degree of this influence was assessed on the canvas of two departure procedures—NADP1 and NADP2. Due to the simplistic character of the carried out studies, the simulation scenarios were limited to the One Factor at a Time (OFAT) method, i.e., modifying only one factor during a single simulation while keeping the rest at their default setting.

The red-colored cells correspond to the procedure NADP1, while blue-colored cells correspond to the procedure NADP2, as visible in the thrust reduction/acceleration column. This color scheme prevails through the entire paper to aid in differentiation between the two procedures.

Although the modeling was based on the methodology presented in ECAC.CEAC Doc 29, it must have been simplified in certain areas, which were not objectives of the study. One of those simplifications was the negligence of modeling the effect of the aircraft’s bank angle on noise propagation, as the established trajectories were a straight line extending on the runway track, i.e., no turns were made by the aircraft. Figure 2 presents only a broad overview of the steps in determining $L_{Amax}$ and SEL parameters for a single noise event, and it shall not be treated as a technical guide of any sort due to its simplistic nature. All of the mathematical background regarding the modeling software created in MATLAB is provided in great detail as a part of the document [34]. It is not presented in this paper, as this paper would not provide any additional insight into the modeling process, which in itself is not vital to the proper understanding of the presented analysis.

As depicted in Figure 2, the modeling process begins from carrying out simulations in a suitable Flight Simulator of choice. For the purposes of this paper, simulations were conducted in X-Plane 11.55 on a ZIBO Mod Boeing 737–800 fitted with CFM56-7B26 engines. The adequate data from the simulator concerning the aircraft’s distance covered, altitude, True airspeed, thrust generated, and fuel burned are then imported into the modeling software and initially processed. The software chosen as a main computing environment for further modeling was MathWorks MATLAB R2022a.

The take-off was performed using a standard method of engaging the auto-throttle with the TOGA pushbutton during take-off roll, which set the appropriate power setting programmed earlier in the virtual Flight Management Computer (FMC). The take-off was performed manually until 500 ft when the autopilot was engaged and followed the appropriate noise-abatement departure procedure (with thrust reduction altitude programmed in the FMC and acceleration altitude commanded manually by increasing the target speed bug on the Mode Control Panel (MCP)).

Simultaneously with the process related to the flight trajectory, equally important NPD data from the ANP Database can be acquired. The database comprises a set of tabulated values of various noise metrics, such as $L_{Amax}$ or $SEL$. Each value corresponds to a specific value of thrust and distance from the observer. The data of the aircraft’s thrust values and trajectory acquired from the flight simulator present a much broader spectrum of thrust values and distances than the NPD noise metrics in the database, so naturally, the noise data must be interpolated. In accordance with Doc 29, a linear interpolation is used between tabulated power settings, whereas a logarithmic interpolation is used between tabulated distances.

After defining the area of observers with one of them in each node of the created grid, preliminary results of a noise map can be generated. However, because the values acquired from NPD data sets are only baseline, uncorrected noise levels, the model needs to account for a variety of effects that are specific to the nature of sound propagated from the aircraft. All of the corrections and adjustments are based on numerous simplifications by means of semi-empirical equations introduced in Doc 29, which were created through many years of preceding research in this field. The adjustments include, but are not limited to, the effect of engine installation in relation to the fuselage (i.e., are the engines mounted under the wings or near the empennage) or the bearing of the observer relative to the temporary position of the aircraft, which allows us to mimic the lobed pattern of jet exhaust during the take-off run.

The calculations are carried out individually for each of the thousands of observers in the defined grid, for a given position of the aircraft, thus producing a value of a desired noise metric ($L_{Amax}$ or $SEL$) for a single segment of the aircraft’s trajectory: $L_{Amax}^{seg}$ or $SE{L}^{seg}$. This is performed by simply adding up all the values of the previously described adjustments to the baseline NPD values:

$$L_{A_{max}}^{seg}=L_{A_{max}}^{NPD}+AI+EI-LA+DIR$$

(1)

$$SE{L}^{seg}=L_{SEL}^{NPD}+AI+EI-LA+DIR+DUR+NF$$

(2)

The calculations are repeated for each of hundreds of segments yielding a multi-million-celled matrix of noise values corresponding to each observer and each segment of the aircraft’s trajectory. Through appropriate calculations, the final values of $L_{Amax}$ and $SEL$ for each observer can be obtained:

$$L_{A_{max}}=\max \left(L_{A_{max}}^{seg}\right)$$

(3)

$$SEL=10\cdot \log \left(\sum {10}^{0.1\cdot SE{G}^{sel}}\right)$$

(4)

Validation of the model with the default data from Doc 29 Vol. 3 App. A, which is shown in Figure 3, shows encouraging results as the compliance is on a satisfactory level. This and all of the following noise maps present a top-down view of the aircraft’s trajectory, with the axis system attached to the threshold of the departure runway with the X-axis aligned with the runway track.

No measurements or experiments in real-life conditions were performed for the needs of validation of the created model as it was created in accordance with the guidelines of ECAC.CEAC Doc 29, which are themselves based on the experimental and semi-empirical basis.

A quantitative determination of substances generated as a result of aviation fuel combustion during flight operations is based on empirically determined emission factors. These factors are developed for each type of engine and depend on the operating phase (e.g., a different emission factor during climb compared to taxiing). Basic data regarding the analyzed aircraft in this project are available in the ICAO Engine Exhaust Emissions Databank in the form of the unit of mass of the emitted substance per unit of mass of burned jet fuel, e.g., grams of $C{O}_2$ per kilograms of Jet A-1 [36]. This document, however, does not provide the emission index for $C{O}_2$, and hence, the standard value of 9.75 kg $C{O}_2$ per US gallon was used. It is assumed that the density of Jet A-1 is constant and is equal to 3.04 kg per one US gallon.

3. Comparative Analysis

Due to the abundance of results that the model is able to provide, this section focuses only on presenting the range of parameters that can be used for the quantitative and qualitative analysis based on the example of one randomly chosen factor.

In Section 1, a comparison of base scenarios of both noise-abatement procedures NADP1 and NADP2 is provided. Section 2 contains a general description of the parameters for an analysis of the impact of single-factor modifications. The influence of take-off thrust reduction is examined as an example. Section 3 provides a holistic overview of all the scenarios in the form of trade-off charts between the reduction of noise and reduction of $C{O}_2$ emissions.

3.1. Baseline Scenario Comparison

Presented in

Table 1. Characteristic factor values for analyzed scenarios.

ID.	Take-Off Mass [kg]	Take-Off Thrust [lbf]	Outside Air Temperature [°C]	Take-Off Flap Configuration	Thrust Reduction/Acceleration [ft AAL]
1.	79,000	26,000	15	F5	1500/3000
2.	65,000	26,000	15	F5	1500/3000
3.	79,000	26,000	32	F5	1500/3000
4.	79,000	26,000	15	F1	1500/3000
5.	79,000	26,000	15	F15	1500/3000
6.	79,000	24,000 + ATR	15	F5	1500/3000
7.	79,000	26,000	15	F15	1500/1500
8.	79,000	26,000	15	F5	1500/1500
9.	65,000	26,000	15	F5	1500/1500
10.	79,000	26,000	32	F5	1500/1500
11.	79,000	26,000	15	F1	1500/1500
12.	79,000	24,000 + ATR	15	F5	1500/1500

, the first and seventh scenario are referred to as “baseline scenarios” for procedures NADP1 (red-colored) and NADP2 (blue-colored), respectively. They correspond to an aircraft taking off at a maximum take-off weight, in a standard flap configuration, and in standard ISA conditions (i.e., $15 °\mathrm{C}$ temperature and $1013.25 \mathrm{hPa}$ sea level pressure) using a maximum take-off thrust of 26,000 pounds of force. Both procedures assume 1500 feet above aerodrome elevation as a thrust reduction height but differ in the acceleration altitude, which is 3000 feet for NADP1 and 1500 feet for NADP2.

Figure 4 presents the profile view of aforementioned baseline scenarios alongside two differential noise maps that were created through the subtraction of $L_{Amax}$ and $SEL$ noise levels of both scenarios for each observer: $L_{A_{max}}^{NADP2}-L_{A_{max}}^{NADP1}$ and $SE{L}_2-SE{L}_1$. The subtraction order implies the following interpretation of colors on the noise maps:

• Warmer colors (shifted towards red)—the red trajectory (NADP1) is quieter from the perspective of this particular observer;
• Cooler colors (shifted towards blue)—the blue trajectory (NADP2) is quieter from the perspective of this particular observer.

The noise maps present the difference based on a sixteen-point scale between values of $\left[-2 \mathrm{dB}, 2 \mathrm{dB}\right]$ so that every color change corresponds to the change of $0.25 \mathrm{dB}$ between the two scenarios.

It is evident that for the majority of the observers, i.e., in the most areas, there is little to no difference in noise between the two procedures. The most pronounced effect is observed between 6 and 12 km from the start of roll. Along this segment, the NADP1 presents the most visible advantage directly underneath the aircraft’s trajectory, which is most apparent on the $L_{A_{max}}^{NADP2}-L_{A_{max}}^{NADP1}$ noise map (the middle one).

However, due to excess lateral attenuation of the trajectory at a lower altitude, i.e., the blue one (of NADP2), the observers alongside the same segment (between 6 and 12 km), which are laterally displaced from the trajectory, experience lower noise levels from the NADP2 trajectory. The ECAC.CEAC Doc 29, Vol. 2 provides more insight into the lateral attenuation theory, which this model accounts for, despite there being an increasing number of articles criticizing present methods of modeling this effect [37].

After the “crossover point”, at which the trajectories of both scenarios cross in the vertical plane, the blue NADP2 trajectory offers a minimal advantage over the red NADP1 trajectory, although the difference is less than $1 \mathrm{dB}$.

3.2. Parameters for Single-Factor Impact Analysis

Factors distinguished in Table 1 for which the influence on noise and other substance emissions are the subject of analysis, can be divided into two categories:

• Random factors: variables independent of the flight crew’s choice. These include the aircraft mass and atmospheric conditions;
• Non-random factors: all other factors influenced to some extent by the crew or the appropriate flight management system. These include the wing mechanization configuration (selection of flap positions for takeoff), engine power setting for takeoff, and thrust reduction and acceleration.

It should be emphasized that although the influence of both random and non-random factors will be analyzed, any potential optimization of selecting their appropriate values should focus only on non-random factors. In practice, it should also consider other unmentioned aspects specific to each airport, special conditions, and the airline operator.

In order to conduct such an analysis, a number of reliable metrics or parameters shall be defined, the most useful of which are as follows:

• An area $S_{\ge 85}^{SEL}$, which contains all the observers, for which the $SEL$ noise metric is equal to or greater than $85 \mathrm{dB}$. The calculation of these area boils is a matter of counting the number of observers whose $SEL$ level meets the criteria and multiplying this number by the area of a single tile on the defined grid, which is a rectangle of 100 × 50 m;
• Change in $C{O}_2$ emissions relative to the baseline procedure expressed in $[\%]$;
• The values of the $SEL$ noise metric for the three observers, for which the position in relation to the start of the roll point is specified in Figure 5. Although their specific positions are not relevant, they are selected to allow for the analysis in both “close-in” and “distant” areas. The axis system is anchored to the starting position of the simulation, located on the beginning of the departure runway, with the X-axis aligned parallel to the runway track.

As an example, the influence of take-off thrust reduction is provided. It is perceived as one of the most common methods for emission reductions at the source. However, it needs to be emphasized that the lower engine thrust setting will result in reduced excess thrust, which will negatively impact the climb gradient during the initial climb phase, thus reducing the distance between the aircraft and observers on the grid. During the simulation, the thrust reduction was achieved by de-rating the thrust from 26,000 to 24,000 pounds of force, further reducing it by means of the Assumed Thrust Reduction.

A comparison between scenarios 6 and 1 (NADP1), as well as 12 and 7 (NADP2), is presented in the profile view in Figure 6.

It is worth noting that the almost level flight segment corresponding to the acceleration phase is significantly extended for the solid red NADP1 trajectory in comparison with the solid blue NADP2 trajectory. Both scenarios have a visibly reduced climb profile gradient, which in turn moves the crossover point by almost 1 km further away from the start of the roll point. Behind the crossover point, a greater difference in height between trajectories is observed in comparison with the baseline scenarios (dashed line).

For the observers $O_1, O_2, O_3$, whose position was specified in Figure 5, the following values of the SEL metric can be listed (Figure 7):

In compliance with the previous analysis, it can be seen that the values of $SEL$ for observers $O_1, O_3$ located underneath the aircraft’s trajectory are increasing for up to $1.5 \mathrm{dB}$. Observer $O_2$, located aside, benefits from the reduced thrust. This effect is mainly caused by the increased lateral attenuation. Based on this factor, it is apparent that the distance from the noise source to the observer (i.e., the climb gradient/trajectory) has a greater impact on the overall noise exposure, compared to the power of the noise source (i.e., engine thrust setting). The following

Table 2. $S_{\ge 85}^{SEL}$ contours and area.

NADP1 $26\mathbf{k}$	NADP1 $24\mathbf{k}+\mathit{A}\mathit{T}\mathit{R}$	NADP2 $26\mathbf{k}$	NADP2 $24\mathbf{k}+\mathit{A}\mathit{T}\mathit{R}$
				$\mathrm{Area} \mathrm{of} SEL\ge 85 \mathrm{dB} \left[{\mathrm{km}}^2\right]$
$S_{\ge 85}^{SEL}=10.70 \left[{\mathrm{km}}^2\right]$	$S_{\ge 85}^{SEL}=8.92 \left[{\mathrm{km}}^2\right]$	$S_{\ge 85}^{SEL}=11.09 \left[{\mathrm{km}}^2\right]$	$S_{\ge 85}^{SEL}=9.87 \left[{\mathrm{km}}^2\right]$
$SE{L}_{mean}=76.2 \left[\mathrm{dB}\right]$	$SE{L}_{mean}=74.8 \left[\mathrm{dB}\right]$	$SE{L}_{mean}=75.9 \left[\mathrm{dB}\right]$	$SE{L}_{mean}=74.5 \left[\mathrm{dB}\right]$	Mean $SEL \left[\mathrm{dB}\right]$

compiles the “over $85 \mathrm{dB}$ noise contours” and their area, along with the total mean value of the SEL metric for the entire grid of observers.

It should be noted that the reduced engine power has caused two significant changes in the shape of the analyzed areas. For both procedures, they have been elongated due to flying at a lower trajectory, but more importantly, they have been significantly narrowed, which correlates with the engine power setting. Therefore, it can be inferred that while the distance component has the greatest impact on the length of the noise footprint, the engine power component influences the transverse dimension of the area. In this example, although some observers noted increased levels of noise exposure, the overall surface area exposed to the highest $SEL$ was decreased by 19.9% for NADP1 and 12.4% for NADP2, alongside with the mean value of $SEL$ for the entire grid of observers.

Figure 8 illustrates the relative change in carbon dioxide emitted with the reduced thrust.

As expected, thrust reduction in combination with an appropriately chosen noise-abatement procedure allows for $C{O}_2$ reductions of nearly 10% for the take-off and initial climb phases. Moreover, the blue NADP2 procedure results in a greater $C{O}_2$ reduction in comparison with the red NADP1 procedure.

3.3. Trade-Off Global and Local Analysis

The remaining factors were subjected to the analysis presented in Section 3.2 of this paper. Grouping the relative parameters on a trade-off chart enables the analysis for minimizing the noise reduction or $C{O}_2$ emission reduction. The X-axis presents the relative change in the total $C{O}_2$ emissions, while the Y-axis presents the change in the $S_{\ge 85}^{SEL}$ surface area. It is clear that the most desirable configuration is for the points to be in the third quarter with both of the coordinates having a negative value—this implies that this factor reduces both the noise, as well as the $C{O}_2$ emission metric. Figure 9 presents the trade-off chart for the global analysis.

From the chart, it is apparent that almost all factors positively impact both types of aircraft’s emissions. However, as the name implies—a certain trade-off exists, which refers to the degree of impact that a single factor has. It can be observed that all the blue points, representing NADP2 procedures, have lower values of the X coordinate and greater values of the Y coordinate in comparison with all their respective red points representing the NADP1 procedures. Based on this chart, it can be concluded that the NADP2 is more efficient at minimizing $C{O}_2$ emissions, while the NADP1 is more efficient at minimizing the noise. The most pronounced reduction in both types of emissions comes from the random factors of take-off mass and air temperature, while the reduced thrust has the most prominent impact on the emissions reduction from the remaining non-random factors. Again, it is important to emphasize that all of the comparisons presented above are in relation to the baseline scenario number 1, and hence, it is at the center of the XY-axis system.

Usually, however, the aerodrome operator may benefit from a more locally oriented approach, i.e., a direct comparison of the impact between two specific locations (e.g., two villages in the vicinity of the aerodrome). Figure 10 presents the trade-off chart for the locations of observers $O_1$ and $O_3$. The Y-axis presents the absolute $SEL$ metric change relative to the baseline scenario number 1, while the X-axis remains unchanged from Figure 9 and presents the relative change in CO₂ emissions.

From the perspective of these observers, only reduced take-off mass and the F1 flap configuration is capable of reducing both noise and gaseous emissions. Nevertheless, the trade-off chart visualizes, in an elegant manner, an important change between those two locations. For observer $O_1$, the key outcome remains unchanged from the global analysis—the NADP2 is better for reducing $C{O}_2$, while NADP1 is better for reducing noise. However, for observer $O_3,$ it becomes apparent that the NADP2 procedure provides the minimization of both noise and $C{O}_2$ emissions. It can be thus concluded that the more locally oriented approach to aircraft emissions analysis might provide better insight into a means of possible optimization.

4. Conclusions

An analysis was conducted to assess the impact of selected factors on noise and gaseous emissions in currently adapted noise-abatement procedures.

Noise measured in aviation can be expressed using various metrics, which can be classified as maximum-based, exposure-based, and an overall cumulative indicator. For the purpose of this research, the analysis focused primarily on the Sound Exposure Level (SEL) indicator, which takes into account both the maximum sound intensity level, as well as the duration of noise exposure during a single aircraft event, such as a single aircraft overflight. For the purpose of this study, SEL is a sufficiently advanced indicator of noise exposure; however, in practical applications, more complex indicators shall be considered.

The presented MATLAB environment for the noise and gaseous emissions calculation is of a simplified nature, although it was created in accordance with recommendations for real noise modeling software provided in ECAC.CEAC Doc 29. The main novelty and advantage over commonly used noise engines is the use of flight trajectory data acquired from flight simulators instead of trajectories from Flight Data Recorders, which can be costly, or trajectories synthesized using procedural steps and motion equations.

Section 3 provides a broad description of some of the parameters that can be implemented in the software, which can aid in assessing the capabilities of noise-abatement procedures in given conditions or in comparative analysis of various solutions. The parameters were described using an example of a reduced take-off thrust scenario; however, the analysis was performed for all the examined factors.

This enabled the global and local trade-off analysis between the noise and gaseous emissions reduction to be performed with the aid of trade-off charts. The charts presented as Figure 9 and Figure 10 provide a holistic overview and indicate which factors influence the emissions in the most beneficial way, as well as which of the two procedures (NADP1 or NADP2) is more effective at noise reduction, as well as $C{O}_2$ emissions reductions.

The main finding from the trade-off analysis is that aerodrome operators may benefit from the locally oriented approach in assessing the best noise-abatement procedure having given the location of the most noise-sensitive areas. It is however important to note that usually Standard Instrument Departures (SIDs) are equally significant for efficient noise reduction by means of laterally vectoring aircraft alongside the track that minimizes the time or the ground run over noise-sensitive areas.

Considering the fact that the global trade-off chart indicates that neither NADP1 nor NADP2 can minimize both noise and gaseous emissions regardless of the analyzed scenario, it implies that an optimal noise-abatement procedure exists, which can maximize the possible emissions reduction. Further research into the issue of aircraft’s emissions might include the noise-abatement procedure optimization or developing the existing noise model to integrate the effect of the terrain surrounding the airfield or flying with a non-zero bank angle along a curved trajectory. Additionally, the possibility of modeling with more complex noise indicators may be examined. This should require abundant data of simulated flight trajectories, which would allow for a calculation of time-averaged cumulative noise metrics that are more common in real applications of airport noise mapping.