Introduction
World air traffic has grown significantly over the past
20 years. With the increasing number of aircraft, the air traffic's
contribution to climate change becomes an important problem. Nowadays,
aircraft emission (this includes still uncertain aviation-induced cirrus
cloud effects) contributes approximately 4.9 % (with a range of
2–14 %, which is a 90 % likelihood range) of the total
anthropogenic radiative forcing (; ;
). An Airbus forecast shows that the world air traffic
might grow at an average annual rate of 4.6 % over the next 20 years
(2015–2034, ), while Boeing forecasts a value of
4.9 % over the same period (). This implies a
further increase in aircraft emissions and therefore environmental impacts
from aviation rise. Reducing the impacts and building a climate-friendly air
transportation system are required for a sustainable development of
commercial aviation. The emissions induced by air traffic primarily comprise
carbon dioxide (CO2), nitrogen oxides (NOx), water vapor
(H2O), carbon monoxide, unburned hydrocarbons and soot. They lead to
changes in the atmospheric composition, thereby changing the greenhouse gas
concentrations of CO2, ozone (O3), H2O and methane (CH4).
The emissions also induce cloudiness via the formation of contrails,
contrail-cirrus and soot cirrus ().
The climate impact induced by aircraft emissions depends partially on local
weather conditions. That is, the impact depends on geographical location
(latitude and longitude) and altitude at which the emissions are released
(except for CO2) and time. In addition, the impact on the atmospheric
composition has different timescales: chemical effects induced by the
aircraft emissions have a range of lifetimes and affect the atmosphere from
minutes to centuries. CO2 has long perturbation lifetimes on the order
of decades to centuries. The atmosphere–ocean system responds to the change
in the radiation fluxes on the order of 30 years. NOx, released in the
upper troposphere and lower stratosphere, has a different lifetime ranging
from a few days to several weeks, depending on atmospheric transport and
chemical background conditions. In some regions, which experience a downward
motion, e.g., ahead of a high-pressure system, NOx has short lifetimes
and is converted to HNO3 and then rapidly washed out
(; ). The most localized and
short-lived effect is contrail formation, with typical lifetimes from minutes
to hours. Persistent contrails only form in ice supersaturated regions
() and extend a few hundred meters vertically and about
150 km along a flight path (with a standard deviation of
250 km) with a large spatial and temporal variability
().
The measures to counteract the climate impact induced by aircraft emissions
can be classified into two categories: technological and operational
measures, as summarized by Irvine et al. (2013). The former includes
aerodynamic improvements of aircraft (blended-wing-body aircraft, laminar
flow control, etc.), more efficient engines and alternative fuels (liquid
hydrogen, bio-fuels). The latter includes efficient air traffic control
(reduced holding time, more direct flights, etc.), efficient flight profiles
(continuous descent approach) and climate-optimized routing. Nowadays, flight
trajectories are optimized with respect to time and economic costs (fuel,
crew, other operating costs) primarily by taking advantage of tail winds,
e.g., jet streams, while the climate-optimized routing should optimize flight
trajectories such that released aircraft emissions lead to a minimum climate
impact. Earlier studies investigated the effect of systematic flight altitude
changes on the climate impact
(). They confirmed that
the changed altitude has a strong effect on the reduction of climate impact.
A number of studies have investigated the potential of applying
climate-optimized routing for real flight data. Matthes et al. (2012) and
Sridhar et al. (2013) addressed weather-dependent trajectory optimization
using real flight routes and showed a large potential of climate-optimized
routing. As the climate impact of aircraft emissions depends on local weather
conditions, Grewe et al. (2014a) optimized flight trajectories by considering
regions described as climate-sensitive regions and showed a trade-off between
climate impact and economic costs. That study reported that large reductions
in the climate impact of up to 25 % can be achieved by only a small
increase in economic costs of less than 0.5 %. The climate-optimized
routing therefore seems to be an effective routing option for the climate
impact reduction; however, this option is still unused in today's flight
planning.
This paper presents the new AirTraf submodel (version 1.0,
) that performs global air traffic simulations coupled
to the EMAC chemistry-climate model (). This paper
technically describes AirTraf and validates the various components for simple
aircraft routings: great circle and time-optimal routings. Eventually, we are
aiming at an optimal routing for climate impact reduction. The development
described in this paper is a prerequisite for the investigation of
climate-optimized routings. The research road map for our study is as follows
(): the first step was to investigate the influence of
specific weather situations on the climate impact of aircraft emissions
(). This results in climate cost functions
(CCFs, ) that identify climate
sensitive regions with respect to O3, CH4, H2O and contrails.
They are specific climate metrics, i.e., climate impacts per unit amount of
emission, and will be used for optimal aircraft routings. In a further step,
weather proxies will be identified for the specific weather situations, which
correlate the intensity of the climate-sensitive regions with meteorological
data. The proxies will be available from numerical weather forecasts, like
temperature, precipitation, ice-supersaturated regions, vertical motions or
weather patterns in general. These proxies are then used to optimize air
traffic with respect to the climate impact expressed by the CCFs. An
assessment platform is required to validate the optimization strategy based
on the proxies in multi-annual (long-term) simulations and to evaluate the
total mitigation gain of the climate impact – one important objective of the
AirTraf development.
This paper is organized as follows. Section 2 presents the model description
and calculation procedures of AirTraf. Section 3 describes aircraft routing
methodologies for the great circle and flight time routing options. A
benchmark test provides a comparison of resulting great circle distances with
those calculated by the Movable Type script (MTS, ). Another benchmark test compares the optimal solution to the
true-optimal solution. The dependence of optimal solutions on initial
populations (a technical terminology set in italics is explained in
Table in Appendix A) is examined and the appropriate
population and generation sizing is discussed. In Sect. 4,
AirTraf simulations are demonstrated with the two options for a typical
winter day (called 1-day AirTraf simulations) and the results are discussed.
Section 5 verifies whether the AirTraf simulations are consistent with
reference data and Sect. 6 concludes the study. Finally, Sect. 7 describes the
code availability.
AirTraf: air traffic in a climate model
Overview
AirTraf was developed as a submodel of EMAC () to
eventually assess routing options with respect to climate. This requires a
framework where we can optimize routings every day and assess them with
respect to climate changes. EMAC provides an ideal framework, since it
includes various submodels, which actually evaluate climate impact, and it
simulates local weather situations on long timescales. As stated above, we
were focusing on the development of this model. A publication on the climate
assessment of routing changes will be published as well.
Flowchart of EMAC/AirTraf. MESSy as part of EMAC provides interfaces
(yellow) to couple various submodels for data exchange, run control and data
input/output. Air traffic data and AirTraf parameters are input in the
initialization phase (messy_initialize, dark blue). AirTraf
includes the flying process in messy_global_end (dashed box, light
blue), which comprises four main computation procedures (bold-black boxes).
The detailed procedures are described in Sect. 2.4 and are illustrated in
Fig. . AirTraf is linked to three modules: the aircraft
routing module (light green), the flight trajectory optimization module (dark
green), and the fuel/emissions calculation module (light orange). Resulting
flight trajectories and global fields are calculated for output (rose red).
Various submodels of EMAC can be linked to evaluate climate impacts on the
basis of the output.
Figure shows the flowchart of the AirTraf
submodel. First, air traffic data and AirTraf parameters are read in
messy_initialize, which is one of the main entry points of the
Modular Earth Submodel System (MESSy, Fig. , dark
blue). Second, all entries are distributed in parallel following a
distributed memory approach (messy_init_memory,
Fig. , blue): AirTraf is parallelized using the
message passing interface (MPI) standard. As shown in
Fig. , the 1-day flight plan, which includes many
flight schedules of a single day, is decomposed for a number of processing
elements (PEs; here PE is synonymous with MPI task), so that each PE has a
similar workload. A whole flight trajectory between an airport pair is
handled by the same PE. Third, a global air traffic simulation (AirTraf
integration, Fig. , light blue) is performed in
messy_global_end, i.e., at the end of the time loop of EMAC. Thus,
both short-term and long-term simulations can take into account the local
weather conditions for every flight. This AirTraf integration is linked to
several modules: the aircraft routing module
(Fig. , light green) and the fuel/emissions
calculation module (Fig. , light orange). The
former is also linked to the flight trajectory optimization module
(Fig. , dark green) to calculate flight
trajectories corresponding to a selected routing option. The latter
calculates fuel use and emissions on the calculated trajectories. Finally,
the calculated flight trajectories and global fields (three-dimensional
emission fields) are output (Fig. , rose red).
The results are gathered from all PEs for output. The output will be used to
evaluate the reduction potential of the routing option on the climate impact.
Decomposition of global flight plans in a parallel environment of EMAC/AirTraf.
A 1-day flight plan is distributed among many processing elements (PEs) in
messy_init_memory (blue). A whole trajectory of an airport pair is
handled by the same PE in the time loop of EMAC (messy_global_end,
light blue). Finally, results are gathered from all the PEs for output (rose
red).
The following assumptions are made in AirTraf (version 1.0): a spherical
Earth is assumed (radius is RE=6371 km). The aircraft
performance model of Eurocontrol's Base of Aircraft Data (BADA Revision 3.9,
) is used with a constant Mach number M (the Mach number
is the velocity divided by the speed of sound). When an aircraft flies at a
constant Mach number, the true air speed VTAS and ground speed
Vground vary along flight trajectories. Only the cruise flight
phase is considered, while ground operations, take-off, landing and any other
flight phases are unconsidered. Potential conflicts of flight trajectories
and operational constraints from air traffic control, such as the
semi-circular rule (the basic rule for flight level) and limit rates of
aircraft climb and descent, are disregarded. However, a workload analysis of
air traffic controllers can be performed on the basis of the output data. The
following sections describe the used models briefly, while characteristic
procedures of AirTraf are described in detail.
Chemistry-climate model EMAC
The ECHAM/MESSy Atmospheric Chemistry (EMAC) model is a numerical chemistry
and climate simulation system that includes submodels describing tropospheric
and middle atmosphere processes and their interaction with oceans, land and
influences coming from anthropogenic emissions (). It
uses the second version of the MESSy (i.e., MESSy2) to link
multi-institutional computer codes. The core atmospheric model is the 5th
generation European Centre Hamburg general circulation model (ECHAM5,
). For the present study we applied EMAC (ECHAM5
version 5.3.02, MESSy version 2.41) in the T42L31ECMWF resolution, i.e., with
a spherical truncation of T42 (corresponding to a quadratic Gaussian grid of
approximately 2.8∘ by 2.8∘ in latitude and longitude) with 31 vertical
hybrid pressure levels up to 10 hPa (middle of the uppermost layer).
MESSy provides interfaces (Fig. , yellow) to
couple various submodels. Further information about MESSy, including the EMAC
model system, is available from http://www.messy-interface.org.
Air traffic data
Primary data of Airbus A330-301 aircraft and constant parameters used in AirTraf simulations.
Parameter
Value
Unit
Description
OEW
125 100
kg
Operational empty weighta
MPL
47 900
kg
Maximum payloada
S
361.6
m2
Reference wing surface areaa
CD0
0.019805
-
Parasitic drag coefficient (cruise)a
CD2
0.031875
-
Induced drag coefficient (cruise)a
Cf1
0.61503
kgmin-1kN-1
First thrust-specific fuel consumption (TSFC) coefficient (jet engines)a
Cf2
919.03
kt
Second TSFC coefficienta
Cfcr
0.93655
-
Cruise fuel flow correction coefficienta
M
0.82
-
Cruise Mach numbera
fref
0.228; 0.724; 2.245; 2.767
kg(fuel)s-1
Reference fuel flow at take-off, climb out, approach and idle conditions (sea level). CF6-80E1A2 (2GE051)b
EINOx,ref
4.88; 12.66; 22.01; 28.72
g(NOx) (kg(fuel))-1
Reference NOx emission index at take-off, climb out, approach and idle conditions (sea level). CF6-80E1A2 (2GE051)b
EIH2O
1230
g(H2O)(kg(fuel))-1
H2O emission indexc
OLF
0.62
-
ICAO overall (passenger/freight/mail) weight load factor in 2008d
SPD
86 400
sday-1
60×60×24=86 400 s in a day. Time (Julian date) ×SPD= Time (s)
g
9.8
ms-2
Gravity acceleration
γ
1.4
-
Adiabatic gas constant
P0
101 325
Pa
Reference pressure (sea level)
R
287.05
JK-1kg-1
Gas constant for dry air
T0
288.15
K
Reference temperature (sea level)
a ;
b ; c ;
d .
The air traffic data (Fig. , dark blue) consist
of a 1-day flight plan and aircraft and engine performance data.
Table lists the primary data of an A330-301 aircraft
used for this study. The flight plan includes flight connection information
consisting of departure/arrival airport codes, latitude/longitude of the
airports, and the departure time. The latitude and longitude coordinates are
given as values in the range [-90,90] and [-180,180], respectively. Any
arbitrary number of flight plans is applicable to AirTraf. The aircraft
performance data are provided by BADA Revision 3.9 ();
these data are required to calculate the aircraft's fuel flow. Concerning the
engine performance data, four data pairs of reference fuel flow
fref (in kg(fuel)s-1) and the corresponding NOx
emission index EINOx,ref (in
g(NOx) (kg(fuel))-1) at take-off, climb out, approach and
idle conditions are taken from the ICAO engine emissions databank
(). An overall (passenger/freight/mail) weight load factor
is also provided by ICAO ().
Calculation procedures of the AirTraf submodel
The calculation procedures in the AirTraf integration are described here step
by step. As shown in Fig. (light blue), the
flight status of all flights is initialized as “non-flight” at the first
time step of EMAC. The departure check is then performed at the beginning of
every time step. When a flight gets to the time for departure in the time
loop of EMAC, its flight status changes into “in-flight”. The time step
index of EMAC t is introduced here. The index is assigned t=1 to the
flight at the departure time. Thereafter the flight moves to the flying
process (dashed box in Fig. , light blue), which
mainly comprises four steps (bold-black boxes in
Fig. , light blue): flight trajectory
calculation, fuel/emissions calculation, aircraft position calculation and
gathering global emissions. The following parts of this section describe
these four steps and Fig. a to d illustrate the
respective steps.
Illustration of the flying process of AirTraf (dashed box in
Fig. , light blue). (a) Flight
trajectory calculation. (b) Fuel/emissions calculation.
(c) Aircraft position calculation. (d) Gathering global
emissions; the fraction of NOx,i corresponding to the flight
segment i is mapped onto the nearest grid point (closed circle) relative to
the (i+1)th waypoint (open circle). ETO: estimated time over;
Fcr: fuel flow of an aircraft; m: aircraft weight; t: time
step index of EMAC. The detailed calculation procedures are described in
Sect. 2.4.
The flight trajectory calculation linked to the aircraft routing module
(Fig. , light green) calculates a flight
trajectory corresponding to a routing option. AirTraf will provide seven
routing options: great circle (minimum flight distance), flight time
(time-optimal), NOx, H2O, fuel (which might differ from H2O,
if alternative fuel options can be used), contrail and CCFs
(). In AirTraf (version 1.0), the great
circle and the flight time routing options can currently be used. The great
circle option is a basis for the other routing options and the module
calculates a great circle by analytical formulae, assuming constant flight
altitude. In contrast to this, for the other six options, a single-objective
minimization problem is solved for the selected option by the linked flight
trajectory optimization module (Fig. , dark
green); this module comprises the Genetic Algorithm (GA,
) and finds an optimal flight trajectory
including altitude changes. For example, if the flight time routing option is
selected, the flight trajectory optimization is applied to all flights taking
into account the individual departure times. Generally, a wind-optimal route
means an economically optimal flight route taking the most advantageous wind
pattern into account. This route minimizes total costs with respect to time,
fuel and other economic costs; i.e., it has multiple objectives. AirTraf will
provide the flight time and the fuel routing options to investigate
trade-offs (conflicting scenarios) among different routing options. With the
contrail option, the best trajectory for contrail avoidance will be found.
The CCFs are provided by EU FP7 project REACT4C (Reducing Emissions from
Aviation by Changing Trajectories for the benefit of Climate,
) and estimate climate impacts due to some aviation
emissions (see Sect. 1). Thus, the best trajectory for minimum CCFs will be
calculated.
For all routing options, local weather conditions provided by EMAC at t=1
(i.e., at the departure day and time of the aircraft) are used to calculate
the flight trajectory. The conditions are assumed to be constant during the
flight trajectory calculation. No weather forecasts (or weather archives) are
used. Once an optimal flight trajectory is calculated, it is not re-optimized
in subsequent time steps (t≥2). The detailed flight trajectory
calculation methodologies for the great circle and the flight time routing
options are described in Sect. 3. After the flight trajectory calculation,
the trajectory consists of waypoints generated along the trajectory, and
flight segments (Fig. a). In addition, a number of
flight properties are available corresponding to the waypoints, flight
segments and the whole trajectory, as listed in
Table . Here, the waypoint index i is introduced (i=1,2,⋯,nwp); nwp is the number of waypoints
arranged from the departure airport (i=1) to the arrival airport (i=nwp). i is also used as the flight segment index (i=1,2,⋯,nwp-1).
Properties assigned to a flight trajectory.
The properties of the three groups (divided by rows) are obtained from the
nearest grid point of EMAC, the flight trajectory calculation
(Fig. a), and the fuel/emissions calculation
(Fig. b), respectively. The attribute type indicates
where the values of properties are allocated. “W”, “S” and “T” stand
for waypoints (i=1,2,⋯,nwp), flight segments (i=1,2,⋯,nwp-1) and a whole flight trajectory in column 3,
respectively.
Property
Unit
Attribute type
Description
P
Pa
W
Pressure
T
K
W
Temperature
ρ
kgm-3
W
Air density
u,v,w
ms-1
W
Three-dimensional wind components
ϕ
deg
W
Latitude
λ
deg
W
Longitude
h
m
W
Altitude
ETO
Juliandate
W
Estimated time over
a
ms-1
W
Speed of sound
VTAS
ms-1
W
True air speed
Vground
ms-1
W
Ground speed
d
m
S
Flight distance
h‾
m
T
Mean flight altitude. h‾=1/nwp∑i=1nwphi with waypoint number nwp.
FT
s
T
Flight time. FT=(ETOnwp- ETO1)×SPD
Fcr
kg(fuel)s-1
W
Fuel flow of an aircraft (cruise)
m
kg
W
Aircraft weight
EINOx,a
g(NOx) (kg(fuel))-1
W
NOx emission index
FUEL
kg
S
Fuel use
NOx
g(NOx) (kg(fuel))-1
S
NOx emission
H2O
g(H2O)(kg(fuel))-1
S
H2O emission
Next, fuel use, NOx and H2O emissions are calculated by the
dedicated module (Fig. , light orange); this
module comprises a total energy model based on the BADA methodology
() and the DLR fuel flow method
(; see Sects. 2.5 and 2.6 for more details). After this
calculation, additional flight properties are newly available (see
Fig. b and Table ). Note that
the flight trajectory calculation described above and this fuel/emissions
calculation are performed only once at t=1.
The next step is to advance the aircraft positions along the flight
trajectory corresponding to the time steps of EMAC
(Fig. c). Here, aircraft position parameters
posnew and posold are introduced to indicate the present
position (at the end of the time step) and previous position (at the
beginning of the time step) of the aircraft along the flight trajectory. They
are expressed by real numbers as a function of the waypoint index i
(integers), i.e., real(1,2,⋯,nwp). At t=1, the
aircraft is set at the first waypoint (posnew=posold=1.0). As the time loop of EMAC progresses, the
aircraft moves along the trajectory referring to the estimated time over
(ETO, Table ) (AirTraf continuously treats overnight
flights with arrival on the next day). For example,
Fig. c shows posnew=2.3 and posold=1.0 at t=2. This means that the aircraft moves 100 % of the
distance between i=1 and i=2, and 30 % of the distance
between i=2 and i=3 in one time step. posnew and
posold are stored in the memory and the aircraft continues the
flight from posnew=2.3 at the next time step. After the aircraft
moves to a new position, the arrival check is performed (dashed box in
Fig. , light blue). If posnew≥real(nwp), the flight status changes to “arrived”.
Finally, the individual aircraft's emissions corresponding to the flight path
in one time step are gathered into a global field (three-dimensional Gaussian
grid). This step is applied for all flights with “in-flight” or “arrived”
status. As shown in Fig. d, for example, the released
NOx emission along a flight segment i (NOx,i or the fraction of
it) is mapped onto the nearest grid point of the global field. For this
NOx,i, the coordinates of the (i+1)th waypoint are used to find the
nearest grid point. In this way, AirTraf calculates the global fields of
NOx and H2O emissions, fuel use and flight distance for output.
After this step, the flight status check is performed at the end of the
flying process. If the status is “arrived”, the flight quits the flying
process and its status is reset to “non-flight”. Therefore, the flight
status becomes either “in-flight” or “non-flight” after the flying
process. Once the status becomes “in-flight”, the departure check is false
in subsequent time steps t≥2 and the aircraft moves to the new
aircraft position without re-calculating the flight trajectory or
fuel/emissions (Fig. , light blue). For
simulations longer than 2 days, the same flight plan is reused: the departure
time is automatically updated to the next day and the calculation procedures
start from the departure check.
Fuel calculation
The methodologies of the fuel/emissions calculation module
(Fig. , light orange) are described. Fuel use,
NOx and H2O emissions are calculated along the flight trajectory
obtained from the flight trajectory calculation. A total energy model based
on the BADA methodology and the DLR fuel flow method is used. The fuel use
calculation consists of the following two steps: a first rough trip fuel
estimation and the second detailed fuel calculation (dashed boxes in
Fig. , light orange). The former estimates an
aircraft weight at the last waypoint (mnwp), while the
latter calculates fuel use for every flight segment and aircraft weights at
any waypoint by backward calculation along the flight trajectory, using the
mnwp as initial condition.
First, trip fuel (FUELtrip) required for a flight between a given
airport pair is roughly estimated:
FUELtrip=FBADAFT,
where FT is the estimated flight time (Table ) and
FBADA is the fuel flow. The BADA performance table provides cruise
fuel flow data at specified flight altitudes for three different weights
(low, nominal and high) under international standard atmosphere conditions.
Hence, FBADA is calculated by interpolating the BADA data (assuming
nominal weight) to the mean altitude of the flight (h‾,
Table ). Next, mnwp is estimated by
mnwp=OEW+MPL×OLF+rfuelFUELtrip,
where OEW, MPL and OLF are given in Table . The last
term represents the sum of an alternate fuel, reserve fuel and extra fuel. It
is assumed to be 3 % of the FUELtrip (rfuel=0.03). The burn-off fuel required to fly from i=1 to i=nwp
and contingency fuel are assumed to be consumed during the flight and hence
they are not included in mnwp. While the 3 %
estimation is probably not far from reality for long-range flights, it is
worth noting that typical reserve fuel quantities may amount to higher
values, depending on the exact flight route. Airlines have their own fuel
strategy and information about actual onboard fuel quantities is generally
unavailable.
Second, the burn-off fuel is calculated for every flight segment and the
aircraft weights are estimated at all waypoints (the contingency fuel is
disregarded in AirTraf (version 1.0)). With the BADA total energy model
(Revision 3.9), the rate of work done by forces acting on the aircraft is
equated to the rate of increase in potential and kinetic energy:
(Thr-D)VTAS=mgdhdt+mVTASdVTASdt,
where Thr and D are thrust and drag forces, respectively. m is the
aircraft weight, g is the gravity acceleration, h is the flight altitude
and dh/ dt is the rate-of-climb (or descent). For a cruise flight phase,
both altitude and speed changes are negligible. Hence, dh/ dt=0 as
well as dVTAS/dt=0 is assumed in AirTraf (version 1.0)
and Eq. () becomes the typical cruise equilibrium equation:
Thri=Di at waypoint i. To calculate Thri, the
Di is calculated:
CL,i=2migρiVTAS,i2Scosφi,CD,i=CD0+CD2CL,i2,Di=12ρiVTAS,i2CD,iS,
where CL,i and CD,i are lift and drag coefficients,
respectively. The performance parameters (S, CD0 and
CD2) are given in Table , ρi is
the air density (Table ) and VTAS,i is
calculated at every waypoint (Table ). The bank angle
φi is assumed to be zero. The thrust-specific fuel consumption
(TSFC) ηi and the fuel flow of the aircraft Fcr,i are
then calculated assuming a cruise flight:
ηi=Cf11+VTAS,iCf2,Fcr,i=ηiThriCfcr,
where Cf1, Cf2 and Cfcr are given in
Table . The fuel use in the ith flight segment
(FUELi) is calculated as
FUELi=Fcr,i(ETOi+1-ETOi)SPD,
where ETOi at the ith waypoint (in Julian date) is converted into
seconds by multiplying with seconds per day (SPD,
Table ). The FUELi incorporates the tail/head
winds effect on Vground through ETO. The relation between the
FUELi and the aircraft weight (mi) is obtained regarding the ith
and (i+1)th waypoints:
mi+1=mi-FUELi.
Given mnwp by Eq. (), the fuel use for the last
flight segment FUELnwp-1 and the aircraft weight at the last
but one waypoint mnwp-1 can be calculated. This calculation
is performed iteratively in reverse order from the last to first waypoints
using Eqs. () to (). Finally, the aircraft weight at
the first waypoint m1 is obtained.
Emission calculation
NOx and H2O emissions are calculated after the fuel calculations.
NOx emission under the actual flight conditions is calculated by the DLR
fuel flow method (). It depends on the engine type, the
power setting of the engine and atmospheric conditions. The calculation
procedure follows four steps. First, the reference fuel flow of an engine
under sea level conditions, fref,i, is calculated from the actual
fuel flow at altitude, fa,i (=Fcr,i/(number of
engines); see Eq. ):
fref,i=fa,iδtotal,iθtotal,i,
δtotal,i=Ptotal,iP0,
θtotal,i=Ttotal,iT0,
where δtotal,i and θtotal,i are correction
factors. Ptotal (in Pa) and Ttotal (in
K) are the total pressure and total temperature at the engine air
intake, respectively, and P0 and T0 are the corresponding values at
sea level (Table ). Ptotal and
Ttotal are calculated as
Ptotal,i=Pa,i(1+0.2M2)3.5,Ttotal,i=Ta,i(1+0.2M2),
where Pa,i (in Pa) and Ta,i (in K) are
the static pressure and temperature under actual flight conditions at the
altitude hi (Table ). Here, hi is the
altitude of the ith waypoint above the sea level (the geopotential altitude
is used to calculate hi). The cruise Mach number M is given in
Table .
Second, the reference emission index under sea level conditions,
EINOx,ref,i, is calculated using the ICAO engine emissions
databank () and the calculated reference fuel flow,
fref,i (Eq. ). Four data pairs of reference fuel
flows fref, and corresponding EINOx,ref, are
tabulated in the ICAO databank for a specific engine under sea level
conditions. Therefore, EINOx,ref,i values, corresponding to
fref,i, are calculated by a least squares interpolation
(second-order).
Third, the emission index under actual flight conditions,
EINOx,a,i, is calculated from the EINOx,ref,i:
EINOx,a,i=EINOx,ref,iδtotal,i0.4θtotal,i3Hc,i,Hc,i=e(-19.0(qi-0.00634)),qi=10-3e(-0.0001426(hi-12,900)),
where δtotal,i and θtotal,i are defined by
Eqs. () and (), respectively. Hc,i is
the humidity correction factor (dimensionless number) and qi (in
kg(H2O)(kg(air))-1) is the specific humidity at hi (the
unit ft is used here).
Finally, NOx and H2O emissions under actual flight conditions are
calculated for the ith flight segment using the calculated
FUELi (Eq. ):
NOx,i=FUELiEINOx,a,i,H2Oi=FUELiEIH2O,
where the H2O emission index is EIH2O =1230
g(H2O)(kg(fuel))-1 (). The H2O emission
is proportional to the fuel use, assuming an ideal combustion of jet fuel.
The NOx and H2O emissions are included in the flight properties
(Table ).
With regard to the reliability of the fuel/emissions calculation using these
methods, Schulte et al. (1997) showed a comparison of measured and calculated
EINOx for some aircraft/engine combinations (). The
study gave some confidence in the prediction abilities of the DLR method,
although it showed that the calculated values from the DLR method
underestimated the measured values on average by 12 %. In Sect. 5 we
verify the methods, using 1-day AirTraf simulation results. Detailed
descriptions of the total energy model and the DLR fuel flow method can be
found elsewhere ().
Demonstration of a 1-day AirTraf simulation
The aircraft routing methodologies corresponding to the great circle and
flight time routing options were verified in Sect. 3. Here, 1-day AirTraf
simulations were performed in EMAC (online) with the respective routing
options for demonstration.
Simulation setup
Information for the trajectories of the three selected airport
pairs; they were extracted from the 1-day AirTraf simulations. Columns 7 to
11 show the obtained flight times for the flight time and great circle
routing options. GC FL290: great circle at 29 000 ft.
Type
Departure airport
Arrival airport
Flight direction
Departure time, UTC
Mean flight altitude h‾, m (in ft)
Flight time FT, s
Time-optimal
GC FL290
GC FL330
GC FL370
GC FL410
I
New York (JFK)
Munich (MUC)
Eastbound
01:30:00
8841 (29 005)
23 986.2
24 100.1
24 472.1
24 772.6
24 931.9
Munich (MUC)
New York (JFK)
Westbound
14:27:00
8839 (29 000)
28 429.0
29 417.3
29 856.7
29 899.0
29 538.5
II
Minneapolis (MSP)
Amsterdam (AMS)
Eastbound
21:35:00
8839 (29 000)
25 335.6
25 958.4
25 957.9
25 989.3
26 043.9
Amsterdam (AMS)
Minneapolis (MSP)
Westbound
12:50:00
10 002 (32 815)
28 869.5
29 117.0
29 211.7
29 292.6
29 219.1
III
Seattle (SEA)
Amsterdam (AMS)
Eastbound
21:05:00
10 829 (35 527)
31 784.6
31 962.9
31 943.5
31 841.9
31 825.4
Amsterdam (AMS)
Seattle (SEA)
Westbound
12:30:00
9311 (30 546)
33 010.5
33 026.2
33 230.5
33 342.6
33 354.1
We focus on the trans-Atlantic region for the demonstration, because the
optimization potential is possibly large for this region.
Table lists the setup for the 1-day simulations. The
simulations were performed for 1 typical winter day in the T42L31ECMWF
resolution. The weather situation on that day showed a typical weather
pattern for winter characterized by westerly jet streams in the North
Atlantic region. The number of trans-Atlantic flights in the region was 103
(52 eastbound flights and 51 westbound flights). We assumed that all flights
were operated by A330-301 aircraft with CF6-80E1A2 (2GE051) engines. Thus,
the data shown in Table were used. Four 1-day
simulations were separately performed for the great circle routing option at
fixed altitudes FL290, FL330, FL370 and FL410 (see Sect. 3.1.1). In addition,
a single 1-day simulation was performed for the flight time routing option,
including altitude changes in the range of [FL290, FL410] (see
Sect. 3.2.2). For the two options, the Mach number was set to M=0.82 and
therefore the values of VTAS and Vground were
different at every waypoint (Eqs. and ). The
number of waypoints was set to nwp=101. As described in
Sect. 3.1.1, the flight distance was calculated by Eq. () for
the two routing options. The optimization parameters were set as follows:
np=100, ng=100 and other GA parameters were the
same as those used in the benchmark test in Sect. 3.2.3.
The 1-day simulation was parallelized on four PEs of Fujitsu Esprimo P900
(Intel Core i5-2500 CPU with 3.30 GHz; 4 GB of memory; peak
performance of 105.6 × 4 GFLOPS) at the Institute of Atmospheric
Physics, German Aerospace Center. The 1-day simulation required approximately
15 min for the great circle routing option, while it took approximately
20 h for the flight time routing option. Most of the computational time is
consumed by the trajectory optimizations. Therefore this time can be reduced
by choosing properly all GA parameters, using more PEs, or decreasing
np and ng. As discussed in Sect. 3.2.6, a large
reduction in computing time of roughly 90 % can be achieved by using
a small np and ng with still sufficient accuracy of
the optimizations.
Optimal solutions for selected airport pairs
The 1-day simulation results for the flight time routing option confirmed
that the optimized flight trajectories showed a large altitude variation. To
give an overview of the optimizations, we classified those optimized flight
trajectories according to their altitude changes into three categories. Type
I: eastbound and westbound time-optimal flight trajectories showed little
altitude changes; Type II: the eastbound time-optimal flight trajectory
showed little altitude changes, while the westbound time-optimal flight
trajectory showed distinct altitude changes; and Type III: eastbound and
westbound time-optimal flight trajectories showed distinct altitude changes.
We have selected three airport pairs of each type and
Table shows the details of them. Here, we mainly
discuss the selected solutions of Type II, which were eastbound and westbound
flights between Minneapolis (MSP) and Amsterdam (AMS).
Ten-thousand explored trajectories (black lines) between MSP and AMS
in the vertical cross section (top) and projection on the Earth (bottom),
including the time-optimal flight trajectories (red and blue lines).
(a) The eastbound flight from MSP to AMS. (b) The westbound
flight from AMS to MSP.
We examined first the optimal flight trajectories between MSP and AMS.
Figure shows all trajectories explored by GA
(black lines) and the time-optimal flight trajectories for eastbound and
westbound flights (red and blue lines). Figure a
and b show that GA explored diverse trajectories properly considering
altitude changes in the range of [FL290, FL410]. Similar results were
obtained for the selected solutions of Types I and III, as shown in Figs. S1
and S2 in the Supplement. In addition, the eastbound time-optimal flight
trajectory was located at FL290, while that for westbound flights showed
large altitude changes; i.e., it climbed, descended, climbed and then
descended again. The mean flight altitudes of these trajectories were
h‾=8839 m and h‾=10 002 m. These
time-optimal flight trajectories were compared to the prevailing wind fields.
To calculate tail/head winds in the eastern and western directions, the major
wind component is shown in Fig. . The
contours represent the zonal wind speed (u); black arrows show the wind
speed (u2+v2) and direction at the departure time at
h‾. Figure a and b show that the
eastbound time-optimal flight trajectory (red line) was located to the south
of the great circle (black line) to take advantage from the tail winds of the
westerly jet stream (red region), while the westbound time-optimal flight
trajectory (blue line) was located to the north of the great circle to avoid
the head winds (red region). Similar comparisons for the selected solutions
of Types I and III showed that the obtained optimal flight trajectories
effectively take advantage of the wind fields (see Supplement, Figs. S3 and
S4).
Trajectories for the time-optimal (red and blue lines) and great
circle cases (black lines) between MSP and AMS. The contours show the zonal
wind speed (u in ms-1); arrows (black) show the wind speed
(u2+v2) and direction. (a) The eastbound flight from
MSP to AMS with the wind field at h‾=8839 m at
21:35:00 UTC. (b) The westbound flight from AMS to MSP with the
wind field at h‾=10 002 m at 12:50:00 UTC.
Altitude distributions of the true air speed VTAS in
ms-1 (a, b) and the tail wind indicator
Vground/VTAS (c, d) along the time-optimal
flight trajectories (black line) between MSP and AMS. Note that (V ground/VTAS)≥1.0 means tail winds (TW, red), while
(Vground/VTAS)<1.0 means head winds (HW, blue) in the
flight direction. The contours were obtained at the departure time:
21:35:00 UTC (eastbound, a, c); 12:50:00 UTC (westbound,
b, d).
To understand the behavior of the altitude changes of the optimal flight
trajectories, Fig. shows the altitude
distribution of the true air speed (VTAS) and the tail wind
indicator (Vground/VTAS) along the time-optimal flight
trajectories. The indicator was calculated by Eq. () transformed
into Vground/VTAS=1+Vwind/VTAS;
this means tail winds ((Vground/VTAS)≥1.0) and
head winds ((Vground/VTAS)<1.0) in the flight
direction. Figure c shows that the core
tail winds region was located at 8.5 km and the tail winds were most
beneficial for the eastbound flight trajectory. On the other hand, the
westbound flight trajectory went through the regions where VTAS
was high, as shown in Fig. b. In
addition, Fig. d shows that the descent
at a flight time of 16 000 s was effective to counteract the head
winds. These results confirm that GA correctly takes into account the weather
conditions and finds the appropriate flight trajectories corresponding to the
flight direction. Similar results were obtained for the solutions of Types I
and III (see Supplement, Figs. S5 and S6).
Next, we compared the resulting flight times for the selected solutions.
Table shows the obtained flight times for the
time-optimal and great circle cases. As shown in
Table , the flight time is lower for the time-optimal
case compared to the great circle cases. In addition, the flight time is
lower for the eastbound time-optimal flight trajectories compared to that for
the westbound time-optimal flight trajectories. This supports the observation
that GA correctly takes into account weather conditions for the trajectory
optimization. With regard to the convergence behavior of the optimization,
Fig. shows the flight time vs. the number of
objective function evaluations corresponding to the GA simulations for the
three selected airport pairs. As expected, the solutions converged to each
optimal solution. Thus, GA successfully found the time-optimal flight
trajectories for the three airport pairs. It is also clear from
Fig. that a reduction in computing time can be
achieved by choosing properly np and ng, although the
solutions converged more slowly under the wind conditions than those under
no-wind conditions (Fig. ).
Flight time (in %) vs. number of function evaluations (=np×ng) for three selected airport pairs,
including the enlarged drawing in the early 1500 evaluations. The
population size np is 100 and the number of
generations ng is 100. Δf* means the
difference in flight time between the solution f and the obtained optimal
solution fopt, which was finally obtained after 10 000 function
evaluations. This was chosen because ftrue for the six flights
are unknown. The fopt for each flight corresponds to the flight
time for the time-optimal case (column 7, Table ). The
Δf* (in %) is calculated as (Δf*/fopt)×100.
One-day simulation results for all flights
Next, the 1-day simulation results for 103 trans-Atlantic flights are
analyzed. Figure shows the obtained flight trajectories
for the flight time and great circle routing options.
Figure a and c show that many eastbound time-optimal flight
trajectories congregated around 50∘ N over the Atlantic Ocean to
take advantage from the tail winds in the westerly jet stream. On the other
hand, the westbound time-optimal flight trajectories were located to the
north and south of that region to avoid head winds (as shown in
Fig. b and d). In addition, Fig. a and b
show that only 5 of 52 eastbound time-optimal flight trajectories showed
large altitude changes, in comparison to 35 of 51 westbound time-optimal
flight trajectories. The mean flight altitudes for the 52 eastbound, 51
westbound and total 103 flights were h‾= 9029 m,
9517 m and 9271 m, respectively.
Obtained flight trajectories from 1-day AirTraf simulations
corresponding to the time-optimal case including altitude changes in
[FL290, FL410] (a, b) and the great circle cases at FL290,
FL330, FL370 and FL410 (c, d). For each figure, the trajectories in
the vertical cross section (top) and projection on the Earth (bottom). The
1-day flights comprise 52 eastbound (red lines) and 51 westbound flights
(blue lines).
Values of the true air speed VTAS (a) and the
tail wind indicator Vground/VTAS (b) at
waypoints for the time-optimal and great circle flights. Linear fits of the
time-optimal (solid line, red (eastbound) and blue (westbound)) and great
circle cases (dashed line, red (eastbound) and blue (westbound)) are
included. VTAS of the international standard atmosphere (ISA) is
given in (a) (solid line, black) provided by the BADA atmosphere
table ().
As shown in Fig. , altitude changes were
due to variations of VTAS and prevailing winds. We now confirm
this behavior, focusing on the results for all flights.
Figure a and b show the values of VTAS and
Vground/VTAS at waypoints for the time-optimal and
great circle flights, with linear lines fitted by the least squares
algorithm. Figure a shows that VTAS is higher
at low altitudes. From Eq. (), high VTAS values
increase Vground values, thereby minimizing flight time. The mean
VTAS for the time-optimal and great circle cases are shown in
Table . The mean VTAS value (column 4)
for the time-optimal case is 245.1 ms-1, while that for the great
circle cases ranges from 241.2 to 244.9 ms-1, although the mean
flight altitude for the time-optimal case is h‾= 9271 m, which is higher than FL290 (=8839 m). GA
successfully found the flight trajectories with high VTAS values
as time-optimal flights.
The mean value of VTAS and Vground for the
time-optimal and great circle cases. The mean values were calculated using
VTAS and Vground values at all waypoints. Eastbound:
average of 52 eastbound flights; Westbound: average of 51 westbound flights;
and Total: average of 103 flights.
Case
VTAS, ms-1
Vground, ms-1
Eastbound
Westbound
Total
Eastbound
Westbound
Total
Time-optimal
245.1
245.1
245.1
268.7
231.2
250.2
GC FL290
245.0
244.8
244.9
265.3
223.7
244.7
GC FL330
242.8
242.6
242.7
262.7
222.0
242.6
GC FL370
241.3
241.1
241.2
260.4
221.7
241.2
GC FL410
241.2
241.1
241.2
258.7
223.1
241.1
With regard to the wind effects, Fig. b shows that the
fitted line for the eastbound time-optimal case (solid line, red) is larger
between FL290 (=8839 m) and 9500 m compared to that for
the eastbound great circle case (dashed line, red). These altitude bounds are
effective under the present weather condition to take advantage of tail winds
for the eastbound flights. Thus, almost all the eastbound time-optimal flight
trajectories were located at FL290, as shown in Fig. a
(top). On the other hand, the fitted line for the westbound time-optimal case
(solid line, blue) is distributed widely in altitude and is larger between
FL290 (=8839 m) and 12 000 m compared to that for the
westbound great circle case (dashed line, blue). The westbound time-optimal
flight trajectories certainly mitigated the head winds effect. Thus, many
westbound time-optimal flight trajectories showed large altitude changes, as
shown in Fig. b (top). The similar plot of
Vground is shown in the Supplement (Fig. S7), which
incorporates the influences of both VTAS and winds; the plot
indicates similar trends as shown in Fig. b.
Table also shows that the mean Vground
value (column 7) for the time-optimal case is 250.2 ms-1, while
that for the great circle cases ranges from 241.1 to 244.7 ms-1.
Therefore, the trajectories found by GA through altitude changes passed
areas, which correctly lead to larger Vground.
The mean fuel consumption (in kg(fuel)min-1) for the
time-optimal and great circle cases.
Eastbound: average of 52 eastbound flights; Westbound: average of 51 westbound flights; and Total: average of 103 flights.
Columns 5 to 7 show the reference cruise fuel consumption (in kg(fuel)min-1) for three different weights (low, nominal and high)
in the international standard atmosphere.
BADA provides the reference data at specific flight altitudes. Therefore, the reference values for the time-optimal case in parentheses were estimated
from the reference data at FL290 and FL330 by linear interpolation (the mean flight altitude of the time-optimal case was h‾=9271 m, which is the
value between FL290 (=8839 m) and FL330 (=10 058 m)).
Case
Simulation
Reference data*
Eastbound
Westbound
Total
Low
Nominal
High
Time-optimal
103.6
98.2
100.9
(99.8)
(104.0)
(111.9)
GC FL290
104.1
104.9
104.5
104.8
108.7
116.0
GC FL330
92.1
92.9
92.5
90.8
95.5
104.3
GC FL370
82.8
83.6
83.2
79.9
85.5
96.1
GC FL410
77.1
77.8
77.4
72.2
79.0
91.9
* .
Mean fuel consumption (in kg(fuel)min-1) vs. altitude
for the time-optimal and great circle flights. ◇: mean value of all
103 flights; these values are shown in column 4 of Table
.
These altitude changes affect the fuel consumption (the term is used
interchangeably with fuel flow). Figure shows the mean
fuel consumption (in kg(fuel)min-1) vs. altitude for the
time-optimal and great circle flights. The results show that the fuel
consumption is higher at low altitudes due to the increased aerodynamic drag
(i.e., increased air density). In addition, the mean value of the fuel
consumption for the time-optimal case is high, due to its low mean flight
altitude (h‾=9271 m, which is between FL290
(8839 m) and FL330 (10 058 m)).
Table lists the mean fuel consumptions for the
different cases. In the great circle cases, the mean value for the eastbound
cases is lower than that for the westbound cases (columns 2 and 3 of
Table ), because the eastbound flights benefit from
the tail winds of the westerly jet stream. On the other hand, the mean value
for the eastbound time-optimal case is higher owing to its low mean flight
altitude (h‾=9029 m) compared to that for the westbound
case (h‾=9517 m). Note that the fuel consumption was
not regarded as the objective function (Eq. ).
Flight time, fuel use, and NOx and H2O emissions for the
time-optimal and great circle cases obtained from 1-day AirTraf simulations.
Eastbound: sum of 52 eastbound flights; Westbound: sum of 51 westbound
flights; and Total: sum of 103 flights. Changes (in %) relative to
the time-optimal case are given in parentheses.
Case
Flight time, h
Eastbound
Westbound
Total
Time-optimal
348.2
395.9
744.1
GC FL290
351.2 (+0.9)
404.4 (+2.2)
755.6 (+1.5)
GC FL330
354.4 (+1.8)
408.0 (+3.1)
762.4 (+2.5)
GC FL370
357.4 (+2.7)
408.5 (+3.2)
765.9 (+2.9)
GC FL410
359.7 (+3.3)
405.6 (+2.5)
765.3 (+2.9)
Case
Fuel use, ton
Eastbound
Westbound
Total
Time-optimal
2155.4
2339.1
4494.5
GC FL290
2190.1 (+1.6)
2545.1 (+8.8)
4735.2 (+5.4)
GC FL330
1958.4 (-9.1)
2275.7 (-2.7)
4234.1 (-5.8)
GC FL370
1776.4 (-17.6)
2049.9 (-12.4)
3826.3 (-14.9)
GC FL410
1665.5 (-22.7)
1894.7 (-19.0)
3560.2 (-20.8)
Case
NOx emission, ton
Eastbound
Westbound
Total
Time-optimal
26.5
28.7
55.2
GC FL290
26.8 (+1.4)
31.2 (+8.8)
58.1 (+5.2)
GC FL330
22.2 (-16.0)
25.8 (-10.1)
48.1 (-12.9)
GC FL370
19.3 (-27.1)
22.2 (-22.8)
41.5 (-24.9)
GC FL410
18.3 (-31.0)
20.7 (-28.0)
39.0 (-29.4)
Case
H2O emission, ton
Eastbound
Westbound
Total
Time-optimal
2651.1
2877.0
5528.2
GC FL290
2693.8 (+1.6)
3130.5 (+8.8)
5824.3 (+5.4)
GC FL330
2408.9 (-9.1)
2799.1 (-2.7)
5208.0 (-5.8)
GC FL370
2185.0 (-17.6)
2521.4 (-12.4)
4706.4 (-14.9)
GC FL410
2048.5 (-22.7)
2330.5 (-19.0)
4379.0 (-20.8)
Comparison of the flight time for individual flights. A symbol
indicates the value for one airport pair, corresponding to the time-optimal
and great circle flights. If the value for the time-optimal flight is the
same as that of the great circle flight, the symbol lies on the 1:1 solid
line.
We also compared the total flight time, fuel use, NOx and H2O
emissions for the time-optimal and great circle cases.
Figure shows the flight time corresponding to
the 103 individual flights (similar figures for the fuel use, NOx and
H2O emissions are shown in Supplement Fig. S8). The results show that
all symbols lay on the right side of the 1:1 solid line. That is, the
flight time for the time-optimal flights is lower compared to that for the
great circle flights for all airport pairs. Table
shows the total flight time simulated by AirTraf for eastbound, westbound and
total flights. The total value is certainly minimal for the time-optimal
case, while in relative terms the value increases by +1.5, +2.5, +2.9
and +2.9 % for the great circle cases at FL290, FL330, FL370 and
FL410, respectively. Regarding the total value of fuel use,
Table indicates that the value increases by
+5.4 % for the great circle case at FL290 when compared with the
value of the time-optimal case. On the other hand, the fuel use decreased by
-5.8, -14.9 and -20.8 % for the great circle cases at FL330,
FL370 and FL410, respectively. The total values of NOx and H2O
emissions show a similar trend: the total value of NOx emission
increased by +5.2 % for the great circle at FL290, while it
decreased by -12.9, -24.9 and -29.4 % for the great circle
cases at FL330, FL370 and FL410, respectively. The changes in total H2O
emission were the same as those of the total fuel use, because EIH2O =1230 g(H2O)(kg(fuel))-1 was used. Figure
already shows that the mean fuel consumption for the time-optimal case is
high, owing to the low mean flight altitude. Thus, the total amount of fuel
use increased for this case, which increased total NOx and H2O
emissions. It is important to note that the variations in the flight time,
fuel use, NOx and H2O emissions are not representative for all
seasons and the whole world's air traffic, because they have been obtained
under the specific winter conditions using the trans-Atlantic flight plans.
Verification of the AirTraf simulations
To verify the consistency for AirTraf simulations, the 1-day simulation
results described in Sect. 4 are compared to reference data of flight time,
fuel consumption, EINOx and aircraft weight. Data obtained under similar
conditions (aircraft/engine types, flight conditions, weather situations,
etc.) were selected for the comparison, although the conditions are not
completely the same as the calculation conditions for the 1-day simulations.
Note that the verification of the aircraft weight is related to that of the
fuel use calculations, because the aircraft weight was calculated by adding
the amount of fuel use (Eq. ). In addition, H2O emission is
proportional to the fuel use assuming ideal combustion. Thus, its
verification would be redundant.
The flight time for time-optimal flight trajectories from 1-day
AirTraf simulations and optimal trajectories from earlier studies. The
original units of the flight times of the studies are converted into
seconds.
Airport pair
Flight time, s
Detailed information
Eastbound
Westbound
New York (JFK) – Shannon (SNN)
18 187.4
22 389.1
These seven time-optimal flight trajectories in this first group (divided by rows) were simulated by AirTraf.
New York (JFK) – Dublin (DUB)
18 853.2
23 150.6
Newark (EWR) – Amsterdam (AMS)
21 705.9
26 512.3
Newark (EWR) – Paris (CDG)
21 790.9
25 668.3
New York (JFK) – Frankfurt (FRA)
22 955.2
27 261.5
New York (JFK) – Zurich (ZRH)
23 450.9
27 246.7
New York (JFK) – Munich (MUC)
23 986.2
28 429.0
Newark (EWR) – Frankfurt (FRA)a
22 980
-
Wind-optimal flight trajectory (constant flight altitude, cruise phase)
New York (JFK) – London (LHR)b
18 000–22 200
21 600–27 000
Time-optimal flight trajectory (constant VTAS, constant flight altitude,
cruise phase, including wind fields)
Trans-Atlantic air trafficc
26 136–27 792
29 664–31 788
Climate-optimal/economic-optimal flight trajectories for real air traffic flight plans:
391 eastbound flights with 28 aircraft types/394 westbound flights with 30 aircraft types.
a ;
b ; c .
First, Table shows the flight time for the seven
time-optimal flight trajectories simulated by AirTraf and three reference
data (the seven airport pairs are geographically close to those of the
reference data). Sridhar et al. (2014) simulated the wind-optimal flight
trajectory from Newark (EWR) to Frankfurt (FRA) using a specific winter day,
and the flight time was 22 980 s. The flight time of the
time-optimal flight trajectory from JFK to FRA simulated by AirTraf was
22 955 s. This agrees well with the value reported by Sridhar et
al. (2014). Irvine et al. (2013) analyzed the variation in flight time of
time-optimal flight trajectories between JFK and London (LHR) using weather
data for three winters. The results showed that the flight time for eastbound
and westbound flights ranged from approximately 18 000 to 22 200 s,
and from 21 600 to 27 000 s, respectively (see Fig. 3 in Irvine et
al., 2013). In addition, Grewe et al. (2014a) optimized the trans-Atlantic
1-day air traffic (for winter) with respect to air traffic climate impacts
and economic costs to investigate routing options for minimizing the impacts.
The results showed that the mean flight time of the air traffic ranged from
26 136 to 27 792 s (eastbound), while it ranged from 29 664 to
31 788 s (westbound), depending on the degree of climate impact
reduction (see Tables 2 and 3 in Grewe et al., 2014a). The flight times
between the seven airport pairs are close to the reference data and the
variation shows a good agreement with the trend of the increased flight times
for westbound trans-Atlantic flights in winter due to westerly jet streams,
as indicated from the reference data.
Second, the fuel consumption was verified using the mean fuel consumption
value of 103 flights and the reference data, as shown in columns 4 to 7 of
Table . Note that the AirTraf simulations were
performed under the specific winter conditions
(Table ), while the reference data show the estimated
values under international standard atmosphere conditions.
Table shows that the mean fuel consumption values
for the time-optimal and great circle cases (column 4) were comparable to
those of the reference data corresponding to low and nominal weights (columns
5 and 6). In the AirTraf simulations, the overall load factor of the
worldwide air traffic was used (Table ). If a specific
load factor of A330-301 for international flights is available, the value is
possibly higher than 0.62 and the corresponding mean fuel consumption values
are expected to increase.
The mean value of EINOx (in g(NOx) (kg(fuel))-1) for 103 flights. Some reference data of EINOx are
provided by the literature in the table.
Case
EINOx, g(NOx) (kg(fuel))-1
Detailed information
Time-optimal
12.2
These values in this first group (divided by rows) were simulated by AirTraf.
GC FL290
12.2
GC FL330
11.3
GC FL370
10.8
GC FL410
10.9
21.8
Airbus A330-301 CF6-80E1A2, 1GE033 (1–9 km altitude band)
13.9
(10–13 km altitude band)
11.33
A330 (mean of 1318 flights, no profile completion option)
11.53
A330 (mean of 1318 flights, complete all operations option)
7.9–11.9
Typical emission for short haul
11.1–15.4
Typical emission for long haul
Third, the mean EINOx (in g(NOx) (kg(fuel))-1)
simulated by AirTraf were compared to the six reference data.
Table shows that the obtained mean EINOx value is
lower at high altitudes, and it ranged from 10.8 to
12.2 g(NOx) (kg(fuel))-1. These values are in the same range
as the reference data. Note that the reference data provided by Sutkus et
al. (2001) show higher EINOx values. They correspond to the values for
the CF6-80E1A2 (1GE033) engine instead of the CF6-80E1A2 (2GE051) engine used
in our simulations. NOx of aircraft engines, in general, decreases owing
to an installation of a new combustor. The 2GE051 utilizes the new 1862M39
combustor, which is known as a low-emissions combustor. Thus, the reference
EINOx value of 2GE051 will be lower than that of the 1GE033.
Finally, the aircraft weights simulated by AirTraf were verified to make sure
that the fuel use calculations were performed properly. AirTraf simulates
realistic fuel consumptions under cruising flight; i.e., the aircraft weight
decreases from the first waypoint (m1) to the last waypoint
(mnwp) as fuel is burnt (as described in Sect. 2.5). Thus,
m1 and mnwp correspond to the maximum and minimum
aircraft weights, respectively. Here the obtained m1 and
mnwp for the 103 flights were compared with three structural
weight limits (MTOW, MLW and MZFW), which are commonly used to provide flight
operations safety, and one specified weight limit (MLOW) of the A330-301
aircraft. Table shows the designated constraints among the
m1, mnwp and the four weight limits. Note that no model
that constrains the structural weight limits was included in AirTraf.
Constraints from the structural weight limits (MTOW, MLW and MZFW) and one specified weight limit (MLOW) of A330-301 aircraft.
m1 and mnwp correspond to the aircraft weight at the
first and last waypoints, respectively. OEW and MPL are given in Table
.
Constraint
Weight limit, kg
Description
m1 ≤ MTOW
212 000
Maximum take-off weight (weight variant 000 BASIC)a
mnwp ≤ MLW
174 000
Maximum landing weight (weight variant 000 BASIC)a
Zero fuel weight ≤ MZFW
164 000
Maximum zero fuel weight. MZFW = OEW + MPL. (weight variant 000 BASIC)a
mnwp ≥ MLOW
150 120
Planned minimum operational weight in the international standard atmosphereb. MLOW =1.2 × OEW.
a ; b .
Comparison of aircraft weights with structural weight limits (MTOW
and MLW) and one specified weight limit (MLOW). The aircraft weights of the
103 flights for the time-optimal and great circle cases are plotted. ∘:
aircraft weight at the last waypoint (mnwp). •:
aircraft weight at the first waypoint (m1). The description of the
limits is shown in Table .
As indicated in Table , the first constraint is on maximum
take-off weight (MTOW). The MTOW is limited for the aircraft so as not to
cause structural damage to the airframe during take-off.
Figure shows a comparison of m1 and
mnwp with the weight limits (MTOW, MLW and MLOW). The
results showed that almost all the m1 (closed circles) were less than
the MTOW. Only 15 of 515 flights (total of the time-optimal and great circle
cases: 5 cases × 103 flights) exceeded the MTOW. For these 15 flights,
actual flight planning data indicate higher flight altitudes to increase the
fuel mileage, leading to the decrease in m1. The second constraint is on
maximum landing weight (MLW). To prevent structural damage to the landing
gear and the fuselage, an aircraft has to reduce the total weight until MLW
prior to landing. Figure shows that all the
mnwp (open circles) were certainly less than MLW. The third
constraint is on maximum zero fuel weight (MZFW), which corresponds to the
maximum operational weight of the aircraft without usable fuel. The MZFW of
an A330-301 aircraft is 164 000 kg (), while the
calculated zero fuel weight (ZFW) was 154 798 kg for all flights.
This always satisfies the third constraint ZFW ≤ MZFW. Note that the ZFW
is calculated as ZFW = OEW + MPL × OLF, and hence it depends only
on the aircraft type and the load factor (Table ). In
addition, the fourth constraint is on the approximately minimum operational
weight of an A330-301 aircraft in the international standard atmosphere
(MLOW). The MLOW is used here as a measure of validity of fuel use
calculations and is not a strict constraint. As shown in
Fig. , all the mnwp (open circles)
were higher than the MLOW. As a result, almost all the m1 and
mnwp simulated by AirTraf satisfied the four constraints.
Thus, AirTraf simulates fairly good fuel use.
Conclusions
This study presents the AirTraf (version 1.0) global air traffic
submodel of EMAC. The great circle and flight time routing options can be
used in AirTraf 1.0. Two benchmark tests were performed without EMAC
(offline). First, a benchmark test was performed for the great circle routing
option using five representative routes. The results showed that the routing
methodology works properly and the great circle distances showed
quantitatively good agreement with those calculated by MTS. The accuracy of
the results was within -0.004 %. Second, a benchmark test was
performed for the flight time routing option by GA, focusing on a flight from
MUC to JFK. The results showed that GA explored diverse solutions and
successfully found the time-optimal solution. The difference in flight time
between the solution and its true-optimal solution was less than
0.01 %. The dependence of the optimal solution on the initial
population was investigated by 10 independent GA simulations from different
initial populations. The 10 obtained optimal solutions varied slightly;
however, the variability was sufficiently small (approximately
0.01 %). In addition, the population and generation sizing for the
trajectory optimization was examined by 1000 independent GA simulations. The
results show that there is a clear trade-off between the accuracy of GA
optimizations and the number of function evaluations (i.e., computational
costs). The present results indicate that a large reduction in the number of
function evaluations of around 92–97 % can be achieved with only a
small decrease in the accuracy of optimizations of around
0.05–0.1 %.
AirTraf simulations were demonstrated in EMAC (online) for a typical winter
day by using 103 trans-Atlantic flight plans of an A330 aircraft. Four 1-day
simulations were separately performed with the great circle routing option at
FL290, FL330, FL370 and FL410, while a single 1-day simulation was performed
with the flight time routing option allowing altitude changes. The results
confirmed that AirTraf correctly works online for the two options.
Specifically, we verified that GA successfully found time-optimal flight
trajectories for all airport pairs. A comparison of the simulations showed
that the total flight time was minimal for the time-optimal case, while it
increased, ranging from +1.5 to +2.9 %, for the great circle
cases. On the other hand, the total fuel use, NOx and H2O emissions
increased for the time-optimal case compared to the great circle cases at
FL330, FL370 and FL410. Compared to the time-optimal case, the total fuel use
and H2O emission increased by +5.4 % for the great circle
case at FL290, while they decreased by -5.8 %, -14.9 and
-20.8 % for the great circle cases at FL330, FL370 and FL410,
respectively. Similarly, the total NOx emission increased by
+5.2 % for the great circle case at FL290, while it decreased by
-12.9, -24.9 and -29.4 % for the great circle cases at FL330,
FL370 and FL410, respectively. Note that the changes are confined to the
specific weather conditions and that the changes can vary on longer
timescales.
The consistency of the 1-day simulations was verified with reference data
(published in earlier studies and BADA) of flight time, fuel consumption,
EINOx and aircraft weight (i.e., fuel use). Comparison of the flight
time between the selected trajectories and the reference data showed that the
values were similar and indicated a similar trend: an increased flight time
for westbound flights on the trans-Atlantic region in winter. The mean fuel
consumption values simulated by AirTraf were comparable to the reference
values of BADA corresponding to low and nominal weights. The mean EINOx
values were in the same range as the reference values of earlier studies.
Finally, obtained maximum and minimum aircraft weights were compared to the
three structural weight limits and one specified weight limit of the A330-301
aircraft. Almost all the values satisfied the four weight limits and only 15
of 515 flights exceeded the maximum take-off weight. Thus, AirTraf comprises
a sufficiently good fuel use model.
The fundamental framework of AirTraf has been developed to perform fairly
realistic air traffic simulations. AirTraf 1.0 is ready for more complex
routing tasks. Objective functions corresponding to other routing options
will be integrated soon, and AirTraf will be coupled with various submodels
of EMAC to evaluate air traffic climate impacts.