2.2.1 Emissions modelling

The combustion emissions other than CO $_2$ are more problematic. Modelling fuel burn is easier than modelling the combustion chemistry in the general case, because too many parameters are unknown. To begin with, the ICAO publishes data on emission indices at four conventional points. LTO emissions are calculated according to the time-in-mode at each operational point, unlike the prescription from the ICAO reference durations and engine speeds. These operating points and their duration do not correspond to reality.

It is necessary to resort to a model of engine emissions that yields emission indices. Emission indices (CO, NO $_x$ , UHC, soot) from non regulated engines (turboprops, small turbofans with rating below 26.7 kN) are either found by a method described in Ref. [Reference Filippone and Bojdo18] or inferred from machine learning techniques whose benefits are being researched. All emissions are modelled and associated with tropospheric and stratospheric. The tropopause is by default 36,000 feet. We are aware of models that consider the troposphere at variable altitudes, both seasonal and geographical [Reference Mateus, Mendes and Pires19], but an attempt to judge a change in the results did not lead to a useful demonstrated result.

Emission indices measured at sea level, in specified atmospheric conditions [20], must be corrected for atmospheric effects (altitude, pressure, humidity), flight effects (Mach number or true air speed) and operational conditions (part throttle, or engine rpm or fuel flow fraction). One of the popular methods is the Boeing Fuel Flow Model, Version 2 (BBFM2), but it covers engines that are 40 or more years old and only a few of the emission species [Reference Baughcum, Tritz, Henderson and Pickett21]. There is a later method called P3T3 [Reference DuBois and Paynter22], which relies on `proprietary’ engine and airplane performance. In the present approach, we have all the parameters to conduct such analysis, e.g. $T_3$ (compressor exit temperature), $P_3$ (compressor exit pressure) and a host of other aero-thermodynamic quantities at every operational condition of the engine (temperature, altitude, Mach number and part throttle) – about two dozen, in fact. In the BFFM2, the flight Mach number correction depends on the factor $0.2 \, M^2$ . In this instance, there is no such correction, because all the aero-thermodynamic parameters are calculated at the corresponding Mach number. In other words, parameters such as $W_1$ are already corrected for Mach number or intake ram effects. Alternative methods for fuel flow have appeared in the technical literature since, for example Chati et al. [Reference Chati and Balakrishnan23], and most recently Poll et al. [Reference Poll and Schumann24]. These methods have not been implemented.

The emission of pollutants such as particulate matter, non-volatile particulate matter (nvPM) is calculated with the method called ImFOX of Reference [Reference Abrahamson, Zelina, Andac and Vander Wal25]. The volumetric flow rate is replaced by $W_1$ (air flow rate), but most likely this is $W2.5$ (core mass flow rate, since there is no combustion in the bypass). However, concentration of black carbon will depend on where the reference section is and how the particulate is collected. The temperature $T_4$ (combustor absolute temperature) is calculated exactly as in ImFOX, although the engine data include actual calculation of $T_4$ , which could be used. The fuel-to-air ratio is taken from the engine simulation rather than the values suggested by ImFOX. There will be some variability in results as a consequence, and differences with the original method and later First Order Approximation version 3 (FOA3) method [Reference Wayson, Fleming and Iovinelli26]. It has been demonstrated previously [Reference Filippone and Bojdo18] that at low engine rpm the approximation of the various methods depends critically on how the interpolating function is chosen among the ICAO reference points.

2.2.2 Assumptions and approximations

The origin and destination of the flights are generally not known. Therefore, it is not possible to make precise inferences about many aspects of the flights. The effect is compounded by the absence of critical data such as gross weight, passenger load, freighter load and weight and many other important parameters that are not known. An approach was proposed in Reference [Reference Filippone and Rotherham27]. Since then, the origin-destination pairing has become available, and re-analysis has revealed that inferences on distances and weight profile are not always accurate, though this is the only possibility in absence of critical data. The following discussion focuses on the overflights when origin and destination are known. For the case when they are not, refer to Reference [Reference Filippone and Rotherham27].

In the first place, the flight of the origin-destination pairing (for ex. EGLL-KJFK) waypoint in the reference box is calculated. The total distance flown is the sum between two great circle distances; this approximates the actual range.

The actual fuel burn $E_1$ and emissions $E_2$ are calculated from the flight distance within the region of interest, Figure 6, and two regression parameters $a$ and $b$

(1) \begin{eqnarray} E_1 = \frac {x_o}{x_1} \left ( a_i + b_i x_i \right ) \end{eqnarray}

(2) \begin{eqnarray} E_2 = \frac {x_o}{x_1} \left ( a_i + b_i x_i + c_i x^2 \right ) \end{eqnarray}

where $x_o$ is the length across the reference box and $x_1$ is the actual distance calculated previously; $x_o/x_1$ is the relative flight length within the box. The coefficients $a_i$ , $b_i$ , $c_i$ are calculated by appropriate least squares of the existing data.

For example, in the database, the A388 flies on average for 4,500 n-miles ( $X_{max} =$ 7,150 n-miles; $X_{min} =$ 3,200 n-miles). If a flight over the region of interest is 94 n-miles, the corrected fraction of flight distance is $x_c = 94/4,500 = 0.020888$ .

In a previous simulation [Reference Filippone and Rotherham27], it was shown that a long-range passenger service with an A388 yields $\overline {X}_{min} = 2,516$ n-miles and $X_{max} = 7,558$ n-miles (OMDB to KLAX); from there, the most likely estimate of the average range was 6,046 n-miles; the corrected fraction of flight distance was $x_o/x_1 = 0.01555$ .

The law of large numbers compounds to our advantage, and in fact we found the following results for the A388: carbon-dioxide emissions when the origin-destination was unknown is $W_{CO2} =$ 167.74 tons (old method); when the pairing is known, $W_{CO2} =$ 163.67 tons (new method). Therefore, the difference is less than 2.5% of the original findings.

We are not so fortunate for shorter-range and business aircraft. In fact, the smaller the weight profile of the airplanes, the larger the difference between the old and new methods. For example, in the case of the Pilatus PC-12, the difference is $W_{CO2} =$ 4.06 tons (old method), $W_{CO2} =$ 1.73 tons (new method), leading to a difference which is over a factor of two. In this case, there is no alternative to retrieving the origin-destination pair to make a realistic analysis.

An example is shown in Figure 2 for the A350-900 (A359) as a function of the flight distance from space-based trajectory data. The minimum distance in this case is 250 n-miles, although shorter flights are done for operational reasons (these flights have been excluded from the analysis). The charts also show the difference between a linear regression and a quadratic one. The difference increases with larger flight distances, as a result of the aircraft having to tanker more fuel as the range is increased. Both mathematical approximations have been used to understand the role of the data modelling on the overall results. It is only beyond 6,000 n-miles that there are practical differences between the interpolation methods.

Once the ICAO code for a specific aircraft has been identified, fuel consumption and all emissions are correlated with the appropriate regression law, subject to a minimum distance being 150 n-miles (short), 200 n-miles (medium), 250 n-miles (long range), respectively. The shorter-range targets mostly domestic overflights or repositioning.

Figure 2.

Fuel burn rates and NO $_x$ emissions from flights of the A350-900 (ICAO $=$ A359).

Figure 3.

Fuel burn rates simulated for the Boeing B787-9 and the Pilatus PC-24.

2.2.3 Atmospheric data

Atmospheric data are sourced from the relevant Meteorological Aerodrome Report (METAR) stations in the region of interest to evaluate temperature, winds, cloud cover, all related to some aspect of emissions. The temperature is of no concern in the period analysed; the maximum range is noted as between 15–20 degrees Celsius in Northern England and Ireland, and lower and depending on the altitude in the Eastern Alps (Appendix C).

2.2.4 Sensitivity analysis

Numerical analysis conducted on least squares approximations, both linear and polynomial (Equations. 1 and 2) reveal a negligible difference in results, less than 2% on NO $_x$ emissions and ${\sim}3\%$ on the fuel burn, overall. Therefore, the use of polynomial regressions like the one shown in Figure 2 is not materially different from the linear approximation. Each circle is a simulated flight using the actual range.

Alternatively, we can use an average fuel burn expressed in fuel/available-seat/n-mile (FASM), which was previously calculated over a large number of flights. An example is given in Figure 3 for two different airplane classes. Graph 3a illustrates the performance of the Boeing B787-9 (a long-range commercial airliner); graph 3b shows the performance of a mid-range business jet, the Pilatus PC-24. There are two things to note. First, the FASM is relatively constant for each aircraft, providing the range is not too short. Second, there is a substantial difference in FASM between the two aircraft shown in Figure 3a: there is a factor 3.7:1 between the PC-24 and the B787-9 for the most common range (4,000 and 400 n-miles, respectively). For clarity, in the middle range, we expect a fuel burn rate of $\sim$ 0.035 kg/seat/n-mile ( $\sim$ 2.25 lit/100 km) in the former case and $\sim$ 0.16 kg/seat/n-mile ( $\sim$ 8.5 lit/seat/100 km) in the latter case, assuming an 8-seat configuration.

The trajectories used are in 1-second parsing. Analysis on coarser time steps of the A359, up to 1/60, reveals small changes in fuel burn, below 6% (Figure 4); the difference between the great-circle distance and actual distance is 5–10% for up to 80 distance-destination pairs. This aircraft carries out intercontinental service with an average of ${\sim}4,000$ n-miles (middle of Figure 2) but also some extremely long flights. Some origin-destination pairings are shown in Figure 4. The difference in estimated fuel burn is relatively modest, depending on the route and trajectory.

Figure 4.

Sensitivity analysis on fuel burn rates from flights of the A359 with IATA codes.

2.2.5 Verification of results

Verification and validation are always a complicated matter due to the sparse availability of data that have been provided independently, and due to the long chain of calculations leading to a final result. It is necessary to establish the correct initial conditions, the actual taxi times, the gross take-off weight, the atmospheric conditions during the flight and particularly winds. Hence, we use default settings. There are too many parameters to mention, which depend on aircraft, route, passenger load, destination airfield, hold altitude, baggage allowance, diversion fuel and more. Outbound and inbound taxi times are considered constant, though there is indication that this is not the case in reality from data reported by Eurocontrol.

We use the EEA/EMEP Corinair Version 2023 [10] for the Airbus A320 Neo (A20N) and calculate the fuel burn and carbon dioxide CO $_2$ emissions for a flight range up to 3,000 n-miles, which is the range detected for 700 random flights. This is shown in Figure 5.

Figure 5.

Comparison of fuel burn for the A320 Neo (A20N with Leap 1A engines) with the EEA/EMEP Corinair data [10] (dashed line).

Simulations have been carried out with and without LTO. Two cases were considered: (1) emissions above 24,500 feet, and (2) complete trajectories from wheel-up to wheel-down. It has been assessed that especially when the required range is short to medium, the overall flight must be considered to accurately capture the amount of emissions at altitude.