Towards the Development of a Multi-disciplinary Flight Trajectory Optimization Tool - GATAC

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Proceedings of ASME Turbo Expo 2012

GT2012

June 11-15, 2012, Copenhagen, Denmark

GT2012-69862Towards the Development of a Multi-disciplinary Flight Trajectory Optimization Tool — GATAC

Weiqun Gu①, Rukshan Navaratne①, Daniele Quaglia①, Yang Yu①, Kenneth Chircop②, Irfan Madani①

Huamin Jia①, Vishal Sethi①, Roberto Sabatini①, David Zammit-Mangion①②

① - Cranfield University, ② - University of Malta

ABSTRACT

Reducing the impact on the environment and the associated

commercial implications are two major challenges that the global

commercial aviation industry is addressing with significant

commitment today. In this respect, Clean Sky, which is a €1.6 billion

Joint Technology Initiative part funded by the European Commission is

the largest ever programme addressing the greening of air

transportation in response to the Advisory Council for Aeronautics

Research in Europe (ACARE) goals of reducing CO2 and perceived

noise emissions by 50% and NOx by 80% by 2020 compared to 2000

condition.

This paper presents research work carried out within the Systems

for Green Operation Integrated Technology Demonstrator (ITD) of

Clean Sky that is associated with GATAC, a trajectory and route

planning tool to enable the multi-objective optimization of flight

trajectories and missions. The design and operational methodology of

the tool, the optimization algorithms and models are discussed and the

results of a preliminary application for a long-range commercial flight

are presented.

INTRODUCTION

Aviation has become an essential commodity in today's global

society, with 2.2 billion passengers travelling every year. As a result, the

air transport industry is addressing growing public concern on the

impact of air travel on the environment, which includes air pollution,

noise and climate change. Although today air transport only produces

two percent of CO2 emissions through the burning of fossils fuels, this is

expected to increase to 3% by 2050 with the continuous and steady

growth of traffic. In recent years, emissions from combustion processes

have become a great public concern due to their impact on health and

the environment. Indeed, the past decade has witnessed rapid changes

both in the regulations for controlling gas turbine emissions and in the

technologies used to meet these regulations. During this period, air

transport grown rapidly and is now perceived as one of the world’s

fastest growing energy-use sector and aviation is directly impacted by

energy trends and the perceived impact of fossil fuel burn on the

environment.

Clean Sky is a Joint Technology Initiative (JTI) that aims to

identify, develop and validate the key technologies necessary to achieve

major steps towards the ACARE 2020 environmental goals of reducing

CO2 by 50%, NOx by 80% and perceived noise by 50% compared to

2000 figures. It is organized in six Integrated Technology Demonstrators

(ITDs) and a Technology Evaluator (TE) to evaluate and demonstrate

the outputs of the ITDs [1]. An activity under the System for Green

Operations (SGO) ITD is focusing on the development of a trajectory

and route planner that can optimize trajectories under multiple

constraints, including air traffic constraints. This involves the

development of models, optimization algorithms and the software

environment in which the optimization can be performed. The SGO ITD

will also optimize trajectories and missions to demonstrate the

environmental gains that can be achieved if such optimized flight

profiles are flown.

This paper reflects the research on trajectory optimization work

carried out by Cranfield University within the Clean Sky SGO-ITD. It

describes the techniques used for multi-disciplinary optimization of

flight trajectories, software environment developed (referred as to as

the optimization framework), the models and tools as well as a

preliminary application of a long-haul flight in terms of fuel

consumption and time. The paper concludes with a discussion of

further work that can follow on the achieved results.

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MATHEMATICAL DESCRIPTIONS AND CHARACTERISTIC

ANALYSIS OF MULTI-DISCIPLINARY FLIGHT

TRAJECTORY OPTIMIZATION

Optimization is defined as the science of determining the best

solution of mathematical problems which represent reality [2]. In

practice, flight trajectory for green operations has several and often

conflicting performance indices to minimize to obtain a trajectory

which satisfy all the constraints imposed. Therefore multi-objective (or

multi-disciplinary) optimization is involved in the process. The number

of objectives involved might vary from a phase of flight to another;

hence different objectives can be applied to flight trajectory planning

optimization. For example a combination of fuel consumption, flight

time, gaseous emissions like NOx or CO2, contrails and noise generated

by aircraft activity can be taken into account within the optimization

process.

Generally, a multi-disciplinary optimization problem is defined as

follow [3]:

UL

Tm

qk

pj

FFF

xxx

x

x

xxxxF

,,2,1,0)(h

,,2,1,0)(g

tosubject

)](,,)(,)([)(min

k

j

21

(1)

Where m is the number of objective functions, p and q are

respectively the number of inequality and equality constraints, x is a

vector of decision variables, )(xiF is the ith objective function and

Lx andUx are respectively the lower and upper boundary vectors.

For a generic three-dimensional flight trajectory optimization,

assuming a flat-Earth frame of reference (Fig.1), the vector x of

decision variables can be expressed by a list of aircraft states and

controls along the flight trajectory as shown in following:

Tnnnniiii VVV ],,,,,,,,,,,,,[ 1111 PPPx (2)

Here, iP is the position vector of the i୲୦ flight node (i.e.

Tiiii zyx ],,[P ) on a total of n flight segments, V is the

aerodynamic speed, is the flight path angle and is the heading

angle. In practice, iP is not always a vector of variables; ix and iy

can be defined by the position of specific navigation fixed point in

space and iz has specific boundaries imposed by ATM rules.

Simplifying the problem considering only the vertical motion of the

aircraft along the symmetric plane, a 2-D trajectory optimization is

obtained (Fig.2). Introducing a fixed space division of the whole flight

range, a further simplification is added and the vector x of decision

variables becomes:

Tnnii VzVzVz ],,,,,,,[ 11 x (3)

In addition to the multi-objectives feature, other considerable flight

optimization characteristics are as follows:

a) Multi-dimensional: The system enables a number of parameters or

variables to be involved during the optimization process.

b) Constrained: Design constraints can be used to limit the range of the

design variables, which are illustrated in Eqn. (1).

c) Nonlinear: The functions relating inputs (design variables) and

outputs (objective function values) are extremely complicated and

cannot be expressed simply or easily by a single or a set of equation(s).

Therefore, they are presumed to be nonlinear, non-smooth and

non-differentiable.

d) Real-valued: These design variables are allowed to take any real

value.

e) Deterministic parameters.

f) Multi-modal: Several local minima (or maxima) occur during the

optimization process.

Fig.1 Full 3-D flight trajectory Fig.2 Simplified 2-D flight trajectory

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METHODOLOGY AND OPTIMIZATION FRAMEWORK

Based on the characteristics of the optimization problem explained

in the previous section, a tool which is based on a framework called

GATAC (Green Aircraft Trajectory under ATM constraints) [4]

equipped with Genetic Algorithm (GA) optimizer and aircraft airframe

and system models as the core as well as cost function models such as

noise and emission models has been developed by SGO ITD [1].

The architecture of the optimization framework comprises two

system-level components, the GATAC Core and the Model Suite. The

GATAC Core is where the optimization process takes place. The Model

Suite serves the GATAC Core on request by executing models and

transferring data to the GATAC Core. The GATAC Core is the heart of

the optimization tool. It is made up of an Optimization Suite and an

Evaluation Handler. The Optimization Suite is the module that defines

the values of the variable parameters and analyses the resulting

constraints and criteria values. The Evaluation Handler is the unit that

handles the models and controls the direct data transfer between the

models in the Model Suites, the Optimization Suite and other modules

in the GATAC Integration Framework. In addition, the Evaluation

Handler also performs simple mathematical calculations on the model

data to create composite parameters as defined in the problem

formulation. On request from the Optimization Core, the Evaluation

Handler invokes the relevant model through the Models Interface to

obtain the required data [5].

The GATAC software can run either on a single stand-alone

machine or a distributed system with multiple computers. The Model

Suite is distributed on one or more machines acting as hosts. The data

exchange between different components is carried out through Ethernet

LAN. The Fig.4 illustrates the architecture and operating principle of

GATAC distributed system [5].

Fig.3 Methodology and optimization framework [5]

Fig.4 Distributed operation of optimization framework [5]

SIMULATION MODELS

Aircraft Performance Model (APM)

Aircraft Performance Model (APM) is developed by Cranfield

University as one of the core modules within GATAC tool. APM

handles multi-dimensional trajectory problems; it simply elaborates the

aircraft flight states and controls required for a generic aircraft to fly

between two pre-defined positions in space.

In general, an aircraft can be correctly modeled using rigid body

problem with varying mass undertaking aerodynamic, propulsive and

gravitational forces. Following the assumption of spherical and

nonrotating Earth, rigid and symmetrical aircraft, symmetric flight and

thrust parallel to the motion direction, it is possible to describe the

aircraft motion by using point mass with three degrees of freedom

representation. In the additional assumption of no wind, it is possible to

list the differential algebraic equations (DAE) referred to stability axes

system as follow:

sin

sincoscos)(

coscos)(

),(

coscos

sincos

sin),,(

Vdt

dh

Vdt

dhR

Vdt

dhR

ThVcdt

dm

mgLdt

dmV

Ldt

dmV

mgLhVDTdt

dVm

E

E

(4)

where:

m : Aircraft mass

V : Aerodynamic speed

T : Thrust magnitude

h : Altitude

L : Lift magnitude

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D : Drag magnitude

g : Gravity acceleration

: Flight path angle

: Heading angle

c : Specific fuel consumption

: Geodetic latitude

: Geodetic longitude

ER : Earth radius

: Bank or roll angle

This formulation provides seven state variables

( mhV ,,,,,, ) and three control variables ( ,, LT ).

Additionally, to be able to solve the problem, an atmospheric model

based on the International Standard Atmosphere (ISA) with constant

gravity acceleration and a generic aircraft aerodynamic model based on

the drag polar characteristics have also been integrated into the APM.

The input module within the model allows the user to define all

the parameters related to the state of the aircraft. Several input

parameters such as initial and final positions, aircraft mass, flap setting

and initial velocity can be pre-defined to calculate all other parameters.

In order to drive the subsequent engine model (Turbomatch model, see

the following Section) in GATAC environment, the APM is required to

output essential parameters such as calculated flight altitude, calculated

flight Mach number and the thrust required. These variables are used by

the Turbomatch model to estimate the engine performance. The APM

algorithm uses two methods of calculation: Linear estimation, where

the algorithm assumes that the angle of attack of the aircraft and the

atmospheric conditions remain constant throughout the simulation

nodes, and Non-linear estimation using a numerical integration to

model the behavior of the aircraft at different selected intermediary

points.

Engine Performance Simulation Model-Turbomatch

Turbomatch, developed by Cranfield University, is an in-house gas

turbine software for the purpose of engine performance simulation and

fault diagnostics.

Turbomatch is made up of pre-programmed modules termed as

“Bricks”. Most of Bricks are correlated to individual component

models namely Compressors, Combustor, Turbine, Mixers, Nozzles,

Heat Exchangers, etc., and others blocks which provide support

functionalities of arithmetic operations, overall engine performance

calculations and result-plotting.

Turbomatch is capable of simulating the performance of both Industrial

Engine Cycle and Aero-engine Cycle spanning from Single-shaft

turbojets to multi-spool turbofans with mixed/ separated exhaust(s) and

complex secondary air systems. In addition to steady-state performance

simulation capability, transient performance calculations can also be

performed by Turbomatch.

Currently, Turbomatch has already been used in extension

applications by several European Union projects like VIVACE, VITAL,

NEWAC, DREAM and Clean Sky.

Gaseous Emission Prediction Model (Hephaestus)

Currently, there are three broad strategies to be used for gas Turbine

Combustor emission prediction:

a) Empirical Correlation

b) Physics-based model

c) Comprehensive numerical simulations involving CFD

Calculations.

Hephaestus, a gaseous emission prediction tool developed at

Cranfield University, can provide the first two methodologies to

estimate the level of gaseous emissions produced by gas turbine

combustors. Based on the consideration of limitations of Empirical

correlation method and Numerical Simulation method, the second

approach-Stirred Reactor Model in Hephaestus is applied in this paper.

In order to model a Combustion Chamber and predict the gaseous

emission levels including ones of CO2, NOx (Oxides of Nitrogen,

which refers collectively to NO (Nitric Oxide) and NO2 (Nitrogen

Dioxide)), several different stirred reactors are adopted, based on the

main principles of Stirred Reactor Modeling theory, including

Perfectly-Stirred Reactor (PSR) Model, a Series of Perfectly-Stirred

Reactor (PSRS) Model, and Partially-Stirred Reactor (PaSR) Model.

The following Fig.5 and Fig.6 respectively illustrates the schematic of a

Combustion Chamber and its stirred Reactor based emission model.

Fig.5 Combustion Chamber Schematic [6]

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From the above two figures, it can be clearly observed that the whole

flame tube in this Combustion Chamber is artificially divided into four

segments, that is, Flame Front (FF), Primary Zone (PZ), Intermediate

Zone (IZ), and Dilution Zone (DZ), and each segment except DZ is

further divided into the core and the near-wall (NW) regions.

On the basis of this division, different reactor models are applied:

for FF where the initial mixing and reaction of the fuel with the nozzle

and swirled air, PaSR is used for the core region to consider

inhomogeneities and PSR for the NW region, and for the other

segments (PZ, IZ, DZ), no metter core and NW regions, PSRS model is

used. As we know, currently the gaseous emissions of interest for the

aero-engines are CO2, H2O (contrail formation), NOx (note, in this

paper, just CO2 and NOx are investigated). During the Emission

Simulation, it can be properly assumed that CO2 and H2O are formed at

chemical equilibrium condition and the corresponding emission indices,

EICO2 and EIH2O can be obtained readily from equilibrium

calculations (In Hephaestus, the NASA CEA program-Chemical

Equilibrium with Applications is applied for this purpose), but NOx

formation does not meet chemical equilibrium conditions and its finite

rate chemistry is therefore required in this emission model in this paper,

kinetic calculation of NOx is included. Once the gas conditions, flow

rates at the inlet and outlet of these reactors, and their lengths are

known, the residence times can be computed and further used for the

integration of the reaction rates of NOx. More details can be found in

Reference [6].

Fig.6 Stirred Reactor Based Emission Model [6]

OPTIMIZATION ALGORITHM

As mentioned in the above section 3, Genetic Algorithms are used

for Optimization Algorithm. Genetic Algorithms (GAs) are a stochastic

approach used for optimization and search processes based on the

mechanisms of genetic inheritance and natural selection (Darwin’s

survival of the fittest).

GAs follows a step-by-step evolution procedure. During the

optimization process, GAs search from a population of chromosomes

(or called strings, or individuals). Each chromosome is made of genes,

and each chromosome represents a potential solution to the

optimization problem. Each chromosome is evaluated to give measure

of its “fitness”. Then a new population is formed by the selection of

chromosomes which fit best. Some members of this new population

undergo alterations through genetic operators like “Crossover” and

“Mutation” to produce new chromosomes. The process is repeated

iteratively until given “stopping criteria” is satisfied. The final

population will contain better chromosomes (solutions) than those in

the initial population. Therefore, the GAs’ evolution process running on

a population of chromosomes corresponds to a search through a space

of potential solutions. The following Fig.7 illustrates the GAs’ search

evolution optimization process.

Compared with typical calculus-based optimization methods, GAs have

several distinctive features:

(1) No derivatives are needed so any non-smooth function can be

optimized.

(2) Constraints can be dealt with in a very different way, such as by

means of penalty functions or design of specific operations.

(3) Global search is used to avoid getting stuck in a local minimum.

(4) Probabilistic rather than deterministic transition rules are used to

create the next generation of strings from the current one.

Cranfield University has accumulated a lot of experience in GAs

application into practical engineering problems so far and GAs-based

optimizer which is being used in Cranfield University has also

undergone great developments compared with the simple GAs

described preciously. These improvements include:

(1) The introduction of the concept of Pareto optimality (Pareto

fronts), which can enhance the optimizer’s capabilities to perform

multi-objective optimization problems.

(2) The development of chromosome modules to support real-number

parameter encoding in conjunction with a definition of the

allowable range for the parameters (genes), which can avoid the

problem of “Hamming Cliffs” encountered by the Binary encoding

method.

(3) The introduction of some concepts like elitism, steady state

replacement, and fitness scaling.

(4) The adoption of more advanced and efficient GA operators.

For Mutation Operator, besides the standard random mutation operator,

others like Creep Mutation with and without delay, and Dynamic

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Vectored Mutation (DVM) have been introduced in the optimizer.

When Creep Mutation is applied, the decay rate reduces the mutation

range with GAs population aging, and therefore a broad capability to

explore at optimization initial stages and fine local searches at later

stages (which strikes a remarkable balance between “Exploiting the

best solutions and exploring the search space”). For Crossover Operator,

several crossover techniques have been adopted, such as the weighting

averaging crossover method, the Blend crossover (BLX-α) method, and

the Simulated Binary crossover (SBX) method. For the Selection

Operators, a modified roulette wheel selection operator, and the

Stochastic Universal Sampling (SUS) technique can be implemented in

the current version optimizer in Cranfield University. Additionally

improvements in tournament replacement and the ranked replacement

have been also achieved as Replacement Operators.

The optimization of practical engineering problems needs a large

number of parameters to be accommodated. Take the flight trajectory

optimization as an example; describing properly a flight path requires a

number of flight segments, each of which includes several design

variables and constraints (for instance, altitudes, speeds, etc.).

Therefore, the optimizer used in this project adopts a unique

optimization technology based on Wienke’s idea of Target Vector

Optimization. Hence, through the achievement of the targets, the

possibility of range-violation and the optimization of chosen

parameters, the quality of the optimization/ design can be assessed.

Moreover, this technology enables users to have entire control over two

optimization process with no needs for too much knowledge about two

optimization algorithms and to create a fitness function.

Finally, the optimizer utilized in this project has been established

with a high degree of modularity to cope with large changes and

extensibility features, and Java is the main programming language and

is of significant advantages when optimization process is implemented

on a heterogeneous set of computers due to Java’s platform

independence.

Fig.7 Genetic Algorithm Reproduction Cycle

MULTI-DISCIPLINARY TRAJECTORY OPTIMIZATION OF A

LONG-RANGE CIVIL AIRCRAFT

As a preliminary application of GATAC in flight trajectory, a

multi-disciplinary optimization case was performed for optimization of

modern long-haul civil aircraft powered by 4 high ByPass Ratio (BPR)

turbofan engines with the flight mode of constant cruise altitude and

Mach number. In this case, the optimized objective functions are fuel

consumption and flight time, with the NOx and CO2 as outputs as well,

and the optimization variables are speeds and altitudes at points 1, 2, 3,

16 and 17 shown as the Fig.8. The initial weight of simulated aircraft is

260,000kg, the flight altitudes and speeds at both initial point and end

point are specified as 457.2 meters and 0.39 (Mach Number), and the

flight distance is designed as 6840 km. The following schematic gives a

graphical description about this optimization.

Fig.8 Schematic representation of flight trajectory optimization

Moreover, Table 1, Table 2, Table 3 and Fig.9 show the aircraft

performance model, engine performance model and engine emission

model which are utilized in the application case. Fig.10 to Fig.13

further illustrate the engine off-design behavior in terms of the

influences of flight altitude, flight Mach number, TET and ambient

temperature on net thrust and SFC respectively. Fig.14 displays the

model integration and data exchange among them.

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Table 1 Aircraft Performance Model Parameters

Fig.9. Engine Performance Model [7]

Table 2 Engine Design-point Parameters [7]

Flight altitude m 0

Temperature deviation from ISA K 0

Flight Mach number 0

Air flow rate kg/s 860

Fan pressure ratio 1.5

Fan isentropic efficiency 0.88

Bypass ratio 7.5

IPC pressure ratio 5.5

IPC isentropic efficiency 0.85

HPC pressure ratio 4.21

HPC isentropic efficiency 0.88

HPT cooling air 20%

Combustor total pressure recovery 0.94

Combustion efficiency 0.998

Turbine entry temperature K 1680

HPT isentropic efficiency 0.89

IPT isentropic efficiency 0.91

LPT isentropic efficiency 0.92

Net thrust N 234771

Fig.10. Net thrust vs. flight Mach number and altitude [7]

Fig.11. SFC vs. flight Mach number and altitude [7]

Fig.12. Net thrust vs.TET & ambient temperature at SLS [7]

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Fig.13. SFC vs.TET & ambient temperature at SLS [7]

Table 3 Engine Emission Model

Here, FACT1:Fuel fraction reaching FF NWR; FACT2: Air fraction

going to FF core reactor; FACT3: Comb gases fraction reaching PZ

NWR; FACT4: Fraction of FRAIRP going to PZ NWR; FACT5:

Fraction of FRAIRI going to IZ NWR; FFIA: Flame Front Inlet Area

(m2); FFOA: Flame Front Outlet Area (m2); FFL: Flame Front Length

(m); FRAIRFF: Flame front air mass flow fraction; FRAIRP: Primary

air mass flow fraction; FRAIRI: Intermediate air mass flow fraction;

FRAIRD: Dilution air mass flow fraction; IZIA: Intermediate Zone

Inlet Area (m2); IZOA: Intermediate Zone Outlet Area (m2); IZL:

Intermediate Zone Length (m); DZIA: Dilution Zone Inlet Area (m2);

DZOA: Dilution Zone Outlet Area (m2); DZL: Dilution Zone Length

(m); PZIA: Primary Zone Inlet Area (m2); PZOA: Primary Zone Outlet

Area (m2); PZL: Primary Zone Length (m).

Fig.14 Model integration and data exchange

The following Fig.15 to Fig.18 illustrate briefly the corresponding

optimization results.

The following several points can, from these figures, be observed:

1) The Pareto Front Line has been formed with total fuel consumption and

total flight time as optimization objectives simultaneously, namely, a

set of optimization solutions which are unique and not dominant each

other have been achieved with different trade-offs between these two

objectives. In practical application, the decision on which solution to

implement can be made based on customers’ requirements.

2) For the purpose of preliminary analysis, two extreme points

(solutions) on this Pareto Front Line, i.e., the optimized flight

trajectories respectively based on min. fuel consumption and min. flight

time are chosen. Their trajectories in terms of altitude versus flight

distance and Mach number versus flight distance are shown in Fig.16

and Fig.17. Here, the discussion is only concentrated on the results

from cruise phase because the phase covers the major part of flight

distance and is of the most significant importance. From these two

figures, the optimized results suggest that for the purpose to minimize

flight time, the aircraft has to fly as low altitude as possible and as fast

as possible (the optimized flight altitude and Mach number at cruise

phase are respectively 8000m and 0.86 which are the lower boundary

of altitude variable and upper boundary of speed variable for cruise

phase). The results are reasonable conceptually because lower cruise

altitude means less climb and descent time, and in the meantime, the

lowest flight altitude and highest flight Mach number allowed means

the maximum permissible True Airspeed during the cruise phase can be

achieved, which will doubtlessly result in the significant reduction in

flight time. However, unfortunately, this benefit in terms of flight time

saving has to be obtained at the expense of large fuel consumption

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because larger drag resulted from higher air density (lower flight

altitude) and higher flight speed has to be overcome and therefore

higher thrust requirement (high TET and high fuel consumption) has to

be met by engine. Conversely, in order to minimize the fuel

consumption, the optimization results suggest that the aircraft has to fly

as high altitude and as low Mach number as possible at the cruise phase

(the optimized flight altitude and Mach number at cruise phase are

respectively 12309 m and 0.78 which are basically the upper boundary

of altitude variable and lower boundary of speed variable for cruise

phase) due to the lower air density and True Airspeed, and hence the

drag as well as the corresponding thrust requirements. Similarly, this

gain is obtained at the cost of flight time because more time is taken for

the climb and descent and lower flight speed during cruise.

3) Fig.18 also gives the comparisons between these above

extreme flight cases in terms of CO2 and NOx emissions.

From this figure, it can be observed that, compared with the

min. time flight, the emissions of CO2 and NOx from min.

fuel flight is reduced to 61.4% and 27.6% respectively

because of the lower fuel consumption and lower engine

power requirement (so lower engine operation temperature)

for the latter one.

Fig.15 Pareto Front Line

Fig.16 Optimized Trajectories-Alt. vs. Range

Fig.17 Optimized Trajectories-Flight Mach Number vs. Range

Fig.18 Gaseous emission comparison

CONCLUSIONS AND FUTURE WORK

With the increasing global concerns about pollution issues and

climate change as well as shortage in fossil-fuel supply, aviation

industry is facing up to unprecedented challenges and pressures in

terms of Environment and Economy.

Clean Sky Project is one of a number of efforts to deal with these

challenges from aviation industry, launched by the European Union.

Flight trajectory optimization, as one of subprojects of Clean Sky, is an

important research direction and solution.

Based on the characteristics of flight trajectory multi-disciplinary

optimization, Cranfield University and other European research

partners adopted the methodology of Architecture-centered,

Model-based and GA-driven to deal with this complicated mathematic

and engineering problem, and newly developed a multi-disciplinary

optimization framework-GATAC as well as corresponding aircraft,

engine performance and emission simulation modules.

The preliminary application of GATAC in flight trajectory, which

is flown by a modern long-haul civil aircraft driven by 4 high BPR

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turbofan engines using the flight mode of constant cruise altitude and

Mach Number, and with fuel and flight time as objective functions

simultaneously, shows clearly that an encouraged optimized result has

been achieved and the good capability of GATAC frame work as an

optimization tool in obtaining optimum solution at multi-disciplinary

level. However, the present work is just preliminary. More research

efforts are needed in this field with several directions, for example,

selecting flight time vs. NOx or flight time vs. CO2 as objective

functions; introducing noise as new objective function; introducing

practical ATM constraints into the trajectory optimization process,

evolving the current 2-D optimization to 3-D and 4-D trajectory

optimization (SESAR / NextGen) and changing automatically

optimization objectives during the flight to adapt to the different

requirements of different phases. These activities are currently being

conducted by Cranfield University and its research partners and the

corresponding research results are expected to be published in the near

future.

ACKNOWLEDGEMENTS

The research has received funding from the European Union's

Seventh Framework Program (FP7/2007-2013) for the Clean Sky Joint

Technology Initiative under grant agreement no

CJSU-GAMSGO-2008-001, and also got valuable support from

partners of Clean Sky, through the GSAF(Green Systems for Aircraft

Foundation) cluster including mainly the University of Malta, TU Delft

and the National Aerospace Center NLR of the Netherlands.

The authors are also especially grateful to Mr. Matthew Xuereb, Mr.

Raymond Muscat, Mr. William Camilleri, Mr. Hugo Pervier and Mr.

Devaiah Nalianda for their invaluable advices and supports during this

research.

NOTATIONS

EI: Emission Index, (g/kg fuel)

M: Mach number

SFC: Specific Fuel Consumption, (mg/(N·s))

TET: Turbine Entry Temperature, (K)

X: Fuel carbon atoms

Y: Fuel hydrogen atoms

REFERENCES

[1] Clean Sky JTI (Joint Technology Initiative), Clean Sky,

available at: http//ww.cleansky.eu, (accessed 9th July 2011).

[2] Fletcher, R., 1987, “Practical Methods of Optimization”, 2nd

Edition, John Wiley, Chichester, UK.

[3] Narzisis, G., “Multi-Objective Optimization” - A quick

introduction to’, Courant Institute of Mathematical Sciences,

New York University, January, 2008.

[4] Chircop, K., Xuereb, M., “A Generic Framework for

Multi-Parameter Optimization of Flight Trajectories”, ICAS,

27th Int. Congress of the Aeronautical Sciences, 2010.

[5] Dimech, E., Chircop, K., “GATAC V2 Beta User Manual”,

University of Malta, Cranfield University, 2010. (Ref. not

available in the public domain)

[6] Celis, C., “Evaluation and Optimization of Environmentally

Friendly Aircraft Propulsion Systems”, PhD Thesis,

Department of Power and Propulsion, Cranfield University,

UK, 2010.

[7] Murugaiyan, J., “Multi-disciplinary Civil Aircraft

Trajectory Optimization Studies”, MSc Thesis, Cranfield

University, UK, September, 2011.

BIBLIOGRAPHY

(1) Betts, J., “Survey of Numerical Methods for Trajectory

Optimization”, Journal of Guidance, Control and dynamics,

Vol.21 No.2, p193-207, 1998.

(2) Velenzuela, A., “Conflict Resolution in Converging Air

Traffic Using Trajectory Patters”, Journal of Guidance,

Control, and Dynamics, Vol. 34 No. 4, p. 1172-1189, 2011.

(3) Gen, M., Cheng, R., “Genetic Algorithm and Engineering

Optimization”, Mishikaga Institute of Technology, Ashikaga,

Japan.

Towards the Development of a Multi-disciplinary Flight Trajectory Optimization Tool - GATAC

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