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Traffic Synchronization with Controlled Time of Arrival for Cost-Efficient Trajectories in High-Density Terminal Airspace

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The main objective of this PhD thesis is to develop methods to efficiently schedule arrival aircraft in terminal airspace, together with concepts of operations compliant with the trajectory based operations concept.
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Traffic Synchronization with Controlled
Time of Arrival for Cost-Efficient Trajectories
in High-Density Terminal Airspace
RAÚL SÁEZ GARCÍA
Aeronautical Engineer
Advisor
DR. XAVIER PRATS I MENÉNDEZ
Doctorate program in Aerospace Science and Technology
Department of Physics - Aerospace Engineering Division
Technical University of Catalonia - BarcelonaTech
A dissertation submitted for the degree of
International Doctor of Philosophy
September 2021
Traffic Synchronization with Controlled Time of Arrival for Cost-Efficient Trajectories in High-
Density Terminal Airspace
Author
Raúl Sáez García
Advisor
Dr. Xavier Prats i Menéndez
Reviewers
Dr. Eri Itoh
Dr. Michael Schultz
Thesis committee
Dr. Eri Itoh
Dr. Michael Schultz
Dr. Karim Zeghal
Doctorate program in Aerospace Science and Technology
Technical University of Catalonia - BarcelonaTech
September 2021
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Contents
List of Figures ............................................ ix
List of Tables ............................................ xiii
List of Publications ......................................... xv
Acknowledgements .........................................xvii
Abstract ............................................... xix
Resumen .............................................. xxi
Resum ................................................xxiii
Notation ...............................................xxviii
List of Acronyms ..........................................xxxi
CHAPTER I Introduction ..................................... 1
I.1 Environmental Impact of Descents ............................ 2
I.2 CDO Adherence in the Current Air Transportation System: Efficiency vs. Capacity 4
I.3 Motivation of this PhD ................................... 10
I.4 Objectives of this PhD Thesis ............................... 13
I.5 Scope and Limitations of this PhD Thesis ........................ 14
I.6 Outline of this PhD Thesis ................................. 15
CHAPTER II Framework on Trajectory Optimization ..................... 17
II.1 Models ............................................ 18
II.2 Optimal Trajectory Planning ................................ 24
CHAPTER III Evaluation of Historical-Flights Databases for Efficiency Assessments 33
III.1 State of the Art ....................................... 34
III.2 Methodology ......................................... 35
III.3 Experimental Setup ..................................... 37
v
III.4 Results ............................................ 40
III.5 Discussion .......................................... 44
CHAPTER IV Achieving RTAs outside the Energy-Neutral Time Window: Energy-
Neutral CDOs vs. Powered Descents ...................... 45
IV.1 State of the Art ....................................... 46
IV.2 Concept of Operations ................................... 47
IV.3 Experimental Setup ..................................... 50
IV.4 Results ............................................ 56
IV.5 Discussion .......................................... 62
CHAPTER V Enabling CDOs in Trombone Sequencing and Merging Procedures ... 65
V.1 State of the Art ....................................... 67
V.2 Concept of Operations ................................... 68
V.3 Methodology ......................................... 70
V.4 Experimental Setup ..................................... 73
V.5 Results ............................................ 81
V.6 Discussion .......................................... 88
CHAPTER VI Enabling CDOs in Dynamic Arrival Routes in Terminal Airspace ..... 91
VI.1 State of the Art ....................................... 92
VI.2 Concept of Operations ................................... 93
VI.3 Methodology ......................................... 98
VI.4 Experimental Setup .....................................100
VI.5 Results ............................................105
VI.6 Discussion ..........................................116
CHAPTER VII Concluding Remarks ...............................119
VII.1 Summary of Contributions .................................119
VII.2 Future Research ......................................121
APPENDIX A Grid-Based MIP Formulation ...........................123
A.1 Tree Constraints and Objective Function .........................124
A.2 Degree Constraints .....................................125
A.3 Turn angle Constraints ...................................126
A.4 Auxilliary Constraints to Prevent Crossings .......................126
A.5 Integration of Temporal Separation ............................127
A.6 Integration of Different Speed Profiles for Aircraft ....................129
A.7 Consistency between Trees of Different Time Periods .................132
A.8 Flexibility at the Entry Points of the dynamic-trajectories area ............132
vi
A.9 Separation with Different Wake Turbulence Categories ................133
A.10 The Complete MIP .....................................134
vii
List of Figures
I-1 Illustrative comparison of a CDO and a conventional descent operation . . . . . . . 3
I-2 Open-loop vs. closed-loop instructions (lateral view) . . . . . . . . . . . . . . . . . 5
I-3 Vectoring instructions used by the ATC at Barcelona-El Prat airport during a typ-
ical day (Dalmau,2019)................................... 5
I-4 Scheme of the 3D-path arrival management concept (Coppenbarger et al.,2010) . . 8
I-5 continuous descent operations (CDOs) with controlled times of arrival (CTAs) and
xedroutes.......................................... 8
II-1 Theoretical and empirical weather models (Dalmau,2019) .............. 23
II-2 Optimal speed profile for a typical narrow-body jet aircraft in international stan-
dard atmosphere (ISA) and no-wind conditions . . . . . . . . . . . . . . . . . . . . . 26
III-1 performance indicators (PIs) computation process . . . . . . . . . . . . . . . . . . . 35
III-2 Comparison of demand data repository (DDR) and OpenSky data: vertical and
lateral profiles for arrival flights in Stockholm-Arlanda-airport terminal maneu-
veringarea(TMA)...................................... 40
III-3 Lateral profile of the arrival flight with callsign SAS410 in Stockholm Arlanda
airport TMA from DDR and OpenSky data on January 01, 2018. . . . . . . . . . . . 41
III-4 Additional fuel burn (in %) in the TMA of actual flown trajectories with respect to
CDOs (values per day February 2018). . . . . . . . . . . . . . . . . . . . . . . . . . . 42
III-5 Average fuel burn (in kg) in the TMA of actual flown trajectories and of CDOs
(values per day of February 2018). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
IV-1 Neutral and powered time windows if the published route is flown . . . . . . . . . 47
IV-2 Scenario 1 - Powered descents flying the published route (procedure) . . . . . . . . 48
IV-3 Scenario 2 - Neutral CDO flying longer/shorter predefined (up-linked) routes . . . 49
IV-4 Time windows for already initiated descents . . . . . . . . . . . . . . . . . . . . . . 49
IV-5 Illustrative example for earliest and latest trajectories (representative narrow-
body-jet aircraft, no wind, 90% maximum landing weight (MLW)) . . . . . . . . . . 54
IV-6 Baseline case study: results for the whole powered time window . . . . . . . . . . 57
IV-7 Sensitivity of fuel consumption differences to cruise altitude . . . . . . . . . . . . . 58
IV-8 Sensitivity of fuel consumption differences to longitudinal wind . . . . . . . . . . . 59
ix
IV-9 Sensitivity of fuel consumption differences to aircraft mass . . . . . . . . . . . . . . 60
IV-10 Sensitivity of fuel consumption differences to aircraft type . . . . . . . . . . . . . . 61
IV-11 Sensitivity of fuel consumption differences to required time of arrival (RTA) as-
signmentaltitude ...................................... 62
V-1 Simplified diagram of a tromboning procedure . . . . . . . . . . . . . . . . . . . . . 66
V-2 Arrival traffic on September 14th, 2018 in Frankfurt airport obtained from Open-
Sky (The OpenSky Network,2019) automatic dependent surveillance-broadcast
(ADS-B)trajectories..................................... 66
V-3 Simplified diagram of a point merge procedure (Eurocontrol,2018b) ........ 67
V-4 concept of operations (CONOPs): trajectories . . . . . . . . . . . . . . . . . . . . . . 68
V-5 CONOPs: RTA and route negotiation process . . . . . . . . . . . . . . . . . . . . . . 69
V-6 Proleassignmentprocess................................. 70
V-7 Independent Set (IS) diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
V-8 Frankfurt am Main Airport (EDDF) GPS/FMS area navigation (RNAV) 25L/C/R
Tromboning (Eurocontrol,2018a)............................. 74
V-9 Example of optimal speed profiles for an Airbus A320 Neo and several required
times of arrival in ISA and no wind conditions . . . . . . . . . . . . . . . . . . . . . 76
V-10 Illustrative earliest and latest trajectories for an A320 Neo in ISA and no wind
conditions .......................................... 77
V-11 Frankfurt airport demand per hour on August 10th, 2017. The 3 case studies are
highlighted. ......................................... 78
V-12 Time window and candidate profiles for a given route . . . . . . . . . . . . . . . . . 79
V-13 Three new shortcuts in Frankfurt am Main Airport (EDDF) GPS/FMS RNAV
25L/C/R trombone procedure (source: German AIP) . . . . . . . . . . . . . . . . . 79
V-14 Time windows for the baseline case of the 3 traffic case studies . . . . . . . . . . . . 82
V-15 Time windows for the available routes of an A320 Neo flying the EMPAX arrival
procedure .......................................... 82
V-16 Delays for the baseline case of the 3 traffic case studies . . . . . . . . . . . . . . . . . 84
V-17 Extra distance flown for the baseline case of the 3 traffic case studies . . . . . . . . 84
V-18 Delay distribution and percentage of aircraft scheduled for each case study and
for different model enhancements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
VI-1 Concept of operations: trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
VI-2 Concept of operations: RTA and route negotiation process for naircraft and m
routes............................................. 95
VI-3 Dynamic scheduling workflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
VI-4 Feasible times at the dynamic-trajectories horizon for profiles corresponding to
different route lengths inside the dynamic-trajectories area . . . . . . . . . . . . . . 99
VI-5 Overlaying Arlanda TMA with a 15x11 grid . . . . . . . . . . . . . . . . . . . . . . . 101
VI-6 Entry-time-window offset effect on the number of aircraft scheduled and on the
sum of paths lengths for each case study (0% light aircraft) . . . . . . . . . . . . . . 107
VI-7 Results of the entry time deviation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
VI-8 Arrival trees as a function of the entry-time-window offset for the average-traffic
casestudy(0%lightaircraft)................................109
VI-9 Arrival trees as a function of the entry-time-window offset for the high-traffic case
study(0%lightaircraft)...................................110
VI-10 Arrival trees as a function of the entry-time-window offset for the low-traffic case
study(0%lightaircraft)...................................110
VI-11 Actual flown trajectories vs. optimized trajectories for low, average and high-
traffic case studies: arrival routes and minimum time to final . . . . . . . . . . . . . 112
x
VI-12 Actual trajectories vs. optimized trajectories for low, average and high-traffic case
studies: sequence pressure and spacing deviation . . . . . . . . . . . . . . . . . . . 114
VI-13 Vertical profiles for the different traffic case studies . . . . . . . . . . . . . . . . . . . 115
VI-14 Distance in TMA for the different traffic case studies . . . . . . . . . . . . . . . . . . 116
Figures in Appendices
A-1 Limited turn: if edge e= (i, j )is used, only edges within the green region are allowed,
that is, edges with an angle of at least θwith e. If edges in the light red region, Γe, are
used, xemust be set to zero. Here: Γe={e1, e2, e3}, e4/Γe.................126
A-2 Four cases with entry point (marked in red) in a grid square: missing edges are
shown in red. The figures in order refer to Eqs. (A.15),(A.16),(A.17) and (A.18),
respectively. .........................................127
A-3 Grid edges are shown in gray, edges of the arrival tree are shown in black. From its
location at iat time t, the black aircraft acan reach the green position at jat time t+u,
the red positions cannot be reached: is not on any path, and for kthere is xj,k = 1, but a
is not at jat time t.......................................128
xi
List of Tables
III-1 Vertical Efficiency of Stockholm Arlanda Airport Arrivals During the Year 2018 . . 41
IV-1 Phases and associated constraints from cruise phase to the runway for a generic
arrivalprocedure ...................................... 52
IV-2 Design matrix for the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
V-1 Potential routes for Frankfurt trombone procedure (North and South cases) . . . . 75
V-2 Percentage of aircraft scheduled per case study . . . . . . . . . . . . . . . . . . . . . 83
V-3 Results for the low-traffic baseline case study . . . . . . . . . . . . . . . . . . . . . . 85
V-4 Results for the medium-traffic baseline case study . . . . . . . . . . . . . . . . . . . 86
V-5 Results for the high-traffic baseline case study . . . . . . . . . . . . . . . . . . . . . 86
V-6 Modelenhancementresults ................................ 87
VI-1 Design matrix for the experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
VI-2 Resultssummary ......................................106
VI-3 Minimum time to final (ttf), spacing deviation (sd) and sequence pressure (sp):
Min/Max/Average/Standard deviation . . . . . . . . . . . . . . . . . . . . . . . . . 111
VI-4 CDOs vs actual flown trajectories: Distance and time in TMA . . . . . . . . . . . . 115
xiii
List of Publications
The list of publications resulting from this PhD. work is given in inverse chronological order as
follows:
Journal Papers
• SÁEZ, RAÚL & PRATS, XAVIER. 2021. Achieving RTAs outside the Energy-Neutral Time
Window of Nominal Aircraft Descents - Fuel Consumption of Powered Descents along Pub-
lished Routes vs. Neutral CDOs along Pre-Defined Routes. Submitted to Transportation Re-
search Part C: Emerging Technologies.
• SÁEZ, RAÚL, POLISHCHUK, TATIANA, SCHMIDT, CHRISTIANE, HARDELL, HENRIK,
SMETANO, LUCIE, POLISHCHUK, VALENTIN & PRATS, XAVIER. 2021. Automated Se-
quencing and Merging with Dynamic Aircraft Arrival Routes and Speed Management for
Continuous Descent Operations. Submitted to Transportation Research Part C: Emerging Tech-
nologies.
• SÁEZ, RAÚL, PRATS, XAVIER, POLISHCHUK, TATIANA & POLISHCHUK, VALENTIN. 2020.
Traffic synchronization in terminal airspace to enable continuous descent operations in trom-
bone sequencing and merging procedures: An implementation study for Frankfurt airport.
Transportation Research Part C: Emerging Technologies. D.O.I: 10.1016/j.trc.2020.102875. 121.
• SÁEZ, RAÚL, PRATS, XAVIER, POLISHCHUK, TATIANA, POLISHCHUK, VALENTIN &
SCHMIDT, CHRISTIANE. 2020. Automation for separation with continuous descent oper-
ations: dynamic aircraft arrival routes. Journal of Air Transportation. D.O.I: 10.2514/1.D0176.
28(4), 144–154.
Conference Proceedings
• POLISHCHUK, TATIANA, POLISHCHUK, VALENTIN, SCHMIDT, CHRISTIANE, SÁEZ, RAÚL,
PRATS, XAVIER, HARDELL, HENRIK & SMETANO, LUCIE. 2020 (Dec.). How to achieve
CDOs for all aircraft: automated separation in TMAs - enabling flexible entry times and
accounting for wake turbulence categories. In: 10th SESAR Innovation Days (SIDS). Virtual
event: SESAR JU.
xv
• SÁEZ, RAÚL & PRATS, XAVIER. 2020 (Jun.). Comparison of Fuel Consumption of Con-
tinuous Descent Operations with Required Times of Arrival: Path Stretching vs. Powered
Descents. In: 9th International Conference on Research in Air Transportation (ICRAT). Virtual
Event: EUROCONTROL/FAA.
• LEMETTI, ANASTASIA, POLISHCHUK, TATIANA, POLISHCHUK, VALENTIN, SÁEZ, RAÚL &
PRATS, XAVIER. 2020 (Jun.). Identification of significant impact factors on Arrival Flight Ef-
ficiency within TMA. In: 9th International Conference on Research in Air Transportation (ICRAT).
Virtual Event: EUROCONTROL/FAA.
• LEMETTI, ANASTASIA, POLISHCHUK, TATIANA & SÁEZ, RAÚL. 2019 (Nov.). Evaluation
of flight efficiency for Stockholm Arlanda Airport using OpenSky Network data. In: 7th
OpenSky Workshop. Zurich, Switzerland: EasyChair.
• LEMETTI, ANASTASIA, POLISHCHUK, TATIANA, SÁEZ, RAÚL & PRATS, XAVIER. 2019 (Oct.).
Analysis of weather impact on flight efficiency for Stockholm Arlanda Airport arrivals. In:
6th ENRI International Workshop on ATM/CNS (EIWAC). Tokyo, Japan: ENRI.
• SÁEZ, RAÚL, PRATS, XAVIER, POLISHCHUK, TATIANA, POLISHCHUK, VALENTIN &
SCHMIDT, CHRISTIANE. 2019 (Jun). Automation for separation with continuous descent
operations: dynamic aircraft arrival routes. In: 13th USA/Europe Air Traffic Management Re-
search & Development Seminar. Vienna, Austria: FAA/EUROCONTROL. Best paper in track
award.
• SÁEZ, RAÚL, DALMAU, RAMON & PRATS, XAVIER. 2018 (Sept.). Optimal assignment of 4D
close-loop instructions to enable CDOs in dense TMAs. In: IEEE/AIAA 37th Digital Avionics
Systems Conference (DASC). London, UK: IEEE.
Book Chapters
• LEMETTI, ANASTASIA, POLISHCHUK, TATIANA, SÁEZ, RAÚL & PRATS, XAVIER. 2021 (Feb.).
Analysis of weather impact on flight efficiency for Stockholm Arlanda Airport arrivals. Lec-
ture Notes in Electrical Engineering (LNEE) - Air Traffic Management and Systems IV: Selected
Papers of the 6th ENRI International Workshop on ATM/CNS. Springer. ISBN: 1876-1100.
xvi
Acknowledgements
Siempre he pensado que la palabra “gracias” ha perdido todo el significado en la mayoría de
las lenguas que se hablan actualmente. Se ha vuelto meramente una palabra vacía que se usa
rutinariamente sin pensar realmente lo que significa en realidad. Y es por eso que yo no la suelo
usar muy a menudo. Sin embargo, durante estos 4 años de doctorado sí que han habido personas
a las que tengo que dar las “gracias” con todo su significado, ya que de una manera u otra han
ayudado a que pueda acabar esta tesis satisfactoriamente.
Els meus primers i possiblement els més importants agraïments són pel Dr. Xavier Prats.
Gràcies Xevi per la confiança, l’entusiasme i les teves idees. Tot i tenir mil coses entre mans sempre
has trobat temps durant aquests 4 anys per guiar-me de manera impecable durant el doctorat.
Mereixes jubilar-te als 40!
I would like to thank as well the guys from Linköping University in Norrköping, Sweden,
where I lived for 4 months. Thank you Tatiana and Valentin for your kindness, and of course
for helping me out with new ideas for my PhD. I hope we will carry on working together in
the future! Thanks also to Christiane, Leonid, Anastasia, Henrik and Lucie. I believe we have
succeeded in writing very nice papers together over these years, and I hope we can meet soon in
some conference!
I would also like to thank Dr. Eri Itoh from The University of Tokyo and Priv.-Doz. Dr.-
Ing. habil. Michael Shcultz from Dresden University of Technology (TU Dresden) for agreeing
to review this PhD dissertation and being members of the committee. I really appreciate your
time and commitment, which resulted in valuable comments to improve the quality of the final
document. I must also acknowledge Dr. Karim Zeghal, from the European Organisation For The
Safety Of Air Navigation (Eurocontrol), for agreeing to be part of the committee and for reviewing
some chapters of the thesis.
Òbviament, no m’oblido dels companys de la universitat. Gràcies al Ramon Dalmau per la
seva ajuda en els primers mesos de doctorat, ets un crack! Gràcies també al Marc Melgosa, que
ha estat present des que vaig arribar, sempre disposat a ajudar. A veure si podem repetir una
conferència com la de San Diego ben aviat! També al Yan i al Leo, que tot i que ja estaven acabant
els seus doctorats quan vaig arribar, vam compartir molt bons moments. I would also like to thank
Homeyra, my officemate and guardian of the castle during COVID times! And of course Jovana,
for being always very positive and being always there to give me a hand. I no m’oblido de les
noves incorporacions a l’equip, que han fet la vida a la uni molt més interessant aquests últims
xvii
mesos: Júlia, Martí, Antoni, David i Jordi.
Per últim, agraïr a la meva família i amics... o potser no... en veritat, puc pensar en moltes
més coses que van abans del doctorat que agraïr-los a ells, no creieu? Però clar, els agraïments
sempre solen acabar així. Suposo que el més adient seria dir simplement “gràcies per ser-hi”.
Castelldefels, September 2021
Raúl Sáez García
xviii
Abstract
The growth in air traffic has led to a continuously growing environmental sensitivity in aviation,
encouraging the research into methods for achieving a greener air transportation. In this context,
continuous descent operations (CDOs) allow aircraft to follow an optimum flight path that deliv-
ers major environmental and economic benefits, giving as a result engine-idle descents from the
cruise altitude to right before landing that reduce fuel consumption, pollutant emissions and noise
nuisance. However, this type of operations suffers from a well-known drawback: the loss of pre-
dictability from the air traffic control (ATC) point of view in terms of overfly times at the different
waypoints of the route. In consequence, ATC requires large separation buffers, thus reducing the
capacity of the airport.
Previous works investigating this issue showed that the ability to meet a controlled time
of arrival (CTA) at a metering fix could enable CDOs while simultaneously maintaining airport
throughput. In this context, more research is needed focusing on how modern arrival managers
(AMANs)—and extended arrival managers (E-AMANs)—could provide support to select the ap-
propriate CTA. ATC would be in charge to provide the CTA to the pilot, who would then use
four-dimensional (4D) flight management system (FMS) trajectory management capabilities to
satisfy it. A key transformation to achieve a more efficient aircraft scheduling is the use of new air
traffic management (ATM) paradigms, such as the trajectory based operations (TBO) concept. This
concept aims at completely removing open-loop vectoring and strategic constraints on the trajec-
tories by efficiently implementing a 4D trajectory negotiation process to synchronize airborne and
ground equipment with the aim of maximizing both flight efficiency and throughput.
The main objective of this PhD thesis is to develop methods to efficiently schedule arrival
aircraft in terminal airspace, together with concepts of operations compliant with the TBO concept.
The simulated arrival trajectories generated for all the experiments conducted in this PhD thesis,
to the maximum possible extent, are considered to be energy-neutral CDOs, seeking to reduce the
overall environmental impact of aircraft operations in the ATM system. Ultimately, the objective
of this PhD is to achieve a more efficient arrival management of traffic, in which higher levels
of predictability and similar levels of capacity are achieved, while the safety of the operations is
kept. The designed experiments consider a TBO environment, involving a high synchronization
between all the involved actors of the ATM system. Higher levels of automation and information
sharing are expected, together with a modernization of both current ATC ground-support tools
and aircraft FMSs to comply with the new TBO paradigm.
xix
First, a trajectory optimization framework is defined in order to generate the simulated trajec-
tories for the experiments conducted in this PhD thesis. Then, the benefits of flying energy-neutral
CDOs are assessed by comparing them with real trajectories, which are obtained from historical
flight data. Two sources of data are compared, concluding which is more suitable for efficiency
assessments in terminal airspace. Energy-neutral CDOs are the preferred type of trajectories from
an environmental point of view but, depending on the amount of traffic, it might be impossible for
the ATC to assign a CTA achievable by the arriving aircraft when flying this kind of descents along
the published route. In this PhD thesis, two strategies are compared in order to achieve the as-
signed CTA: flying energy-neutral CDOs along longer/shorter routes vs. flying powered descents
along the published route. The sensitivity of the fuel consumption of both strategies to several pa-
rameters, such as the initial cruise altitude or wind speed, is analyzed. Finally, two strategies are
analyzed in this PhD in order to efficiently schedule arriving aircraft in terminal airspace. First,
an interim strategy between full 4D negotiated trajectories and open-loop vectoring is used: a
methodology is proposed to effectively schedule arrival traffic flying energy-neutral CDOs along
a trombone area navigation (RNAV) procedure. Then, a novel methodology is proposed to gener-
ate dynamic arrival routes that automatically adapt to the current air traffic demand. Once again,
energy-neutral CDOs are enforced for all arrival traffic.
There are several factors to be considered that may limit the benefits of the proposed solu-
tions. The arrival traffic amount and distribution greatly affect the results obtained, limiting in
some cases the successful scheduling of all the arrival aircraft. Furthermore, some of the solutions
proposed involve high computational loads that may limit their applicability in operational prac-
tice, encouraging future research in order to optimize the models and methodologies involved.
Finally, allowing some aircraft to fly powered descents might ease the scheduling of the arrival
aircraft in the experiments focusing on the trombone procedure and on the dynamic generation of
arrival routes.
xx
Resumen
El incremento de tráfico aéreo ha llevado a una mayor sensibilidad medioambiental en la avia-
ción, motivando la investigación de métodos para conseguir un transporte aéreo más ecológico.
En este contexto, las operaciones de descenso continuo (CDOs) permiten a las aeronaves seguir
una trayectoria que aporta grandes beneficios económicos y ambientales, dando como resultado
descensos con los motores al ralentí desde la altitud de crucero hasta justo antes de aterrizar. Estas
trayectorias reducen el consumo de combustible, las emisiones contaminantes y el ruido generado
por las aeronaves. No obstante, este tipo de operaciones tiene una gran desventaja: la pérdida de
predictibilidad desde el punto de vista del controlador aéreo (ATC) en términos de tiempos de
paso en los diferentes puntos de la ruta. Como consecuencia, el ATC necesita asignar una mayor
separación entre las aeronaves, lo cual comporta una reducción en la capacidad del aeropuerto.
Estudios previos investigando este problema han demostrado que la capacidad de cumplir
con un tiempo controlado de llegada (CTA) en un punto de la ruta (utilizado para secuenciar las
aeronaves) podría habilitar las CDOs manteniendo al mismo tiempo la capacidad del aeropuerto.
En este contexto, es necesario investigar más en cómo los gestores de llegadas (AMANs)—y los
gestores de llegadas extendidos (E-AMANs)—podrían dar soporte en la selección de la CTA más
adecuada. El ATC sería el encargado de enviar la CTA al piloto, el cual, para cumplir con la CTA,
usaría la capacidad de gestión de trayectorias de un sistema de gestión de vuelo (FMS) de cuatro
dimensiones (4D). Una transformación clave para conseguir una gestión más eficiente del tráfico
de llegada es el uso de nuevos paradigmas de gestión del tráfico aéreo (ATM), como por ejem-
plo el concepto de operaciones basadas en trayectorias (TBO). Este concepto tiene como objetivo
eliminar completamente de las trayectorias la vectorización en “bucle abierto” y las restricciones
estratégicas. Para conseguirlo, se propone implementar de manera eficiente una negociación de
la trayectoria 4D, con el objetivo de sincronizar el equipamiento de tierra con el de la aeronave,
maximizando de esta manera la eficiencia de los vuelos y la capacidad del sistema.
El principal objetivo de este doctorado es desarrollar métodos para gestionar aeronaves de
manera eficiente en espacio aéreo terminal, junto con conceptos de operaciones que cumplan con
el concepto de TBO. Las trayectorias de llegada simuladas para todos los experimentos definidos
en esta tesis doctoral, en la medida de lo posible, son CDOs de energía neutra. De esta manera,
la idea es reducir lo máximo posible el impacto medioambiental de las operaciones aéreas en el
sistema ATM. En definitiva, el objetivo de este doctorado es conseguir una gestión del tráfico de
llegada más eficiente, obteniendo una mayor predictibilidad y capacidad, y asegurando que la
seguridad de las operaciones se mantiene. Los experimentos diseñados consideran una situación
xxi
donde el concepto de TBO está presente, lo que comporta una sincronización elevada entre todos
los actores implicados en el sistema ATM. Asimismo, se esperan mayores niveles de automati-
zación y de compartición de información, junto con una modernización de las herramientas de
soporte en tierra al ATC y de los FMSs de las aeronaves, todo con el objetivo de cumplir con el
nuevo paradigma de TBO.
Primero de todo, se define un marco para la optimización de trayectorias utilizado para gene-
rar las trayectorias simuladas para los experimentos definidos en esta tesis doctoral. A continua-
ción, se evalúan los beneficios de volar CDOs de energía neutra comparándolas con trayectorias
reales obtenidas de datos de vuelo históricos. Se comparan dos fuentes de datos, concluyendo
cuál es la más adecuada para estudios de eficiencia en espacio aéreo terminal. Las CDOs de ener-
gía neutra son el tipo preferido de trayectorias desde un punto de vista medioambiental pero,
dependiendo de la cantidad de tráfico, podría ser imposible para el ATC asignar una CTA que
pueda ser cumplida por las aeronaves mientras vuelan la ruta de llegada publicada. En esta te-
sis doctoral, se comparan dos estrategias con el objetivo de cumplir con la CTA asignada: volar
CDOs de energía neutra por rutas más largas/cortas o volar descensos con el motor accionado por
la ruta publicada. Para ambas estrategias, se analiza la sensibilidad del consumo de combustible a
diferentes parámetros, como la altitud inicial de crucero o la velocidad del viento. Finalmente, en
esta tesis doctoral se analizan dos estrategias para gestionar de manera eficiente el tráfico de llega-
da en espacio aéreo terminal. Primero, se utiliza una estrategia provisional a medio camino entre
la negociación completa de trayectorias 4D y la vectorización en “bucle abierto”: se propone una
metodología para gestionar de manera eficaz tráfico de llegada donde las aeronaves vuelan CDOs
de energía neutra en un procedimiento de navegación de área (RNAV) conocido como trombón.
A continuación, se propone una nueva metodología para generar rutas de llegada dinámicas que
se adaptan automáticamente a la demanda actual de tráfico. De igual manera, se aplican CDOs de
energía neutra a todo el tráfico de llegada.
Hay diferentes factores a considerar que podrían limitar los beneficios de las soluciones pro-
puestas. La cantidad y distribución del tráfico de llegada tiene un gran efecto sobre los resultados
obtenidos, limitando en algunos casos una gestión eficiente de las aeronaves de llegada. Ade-
más, algunas de las soluciones propuestas comportan elevadas cargas computacionales que po-
drían limitar su aplicación operacional, motivando mayor investigación en el futuro con el fin de
optimizar los modelos y metodologías utilizados. Finalmente, permitir a algunos aviones volar
descensos con el motor accionado podría facilitar la gestión de las aeronaves de llegada en los ex-
perimentos que se centran en el procedimiento de trombón y en la generación de rutas de llegada
dinámicas.
xxii
Resum
L’increment de trànsit aeri ha portat a una major sensibilitat mediambiental en l’aviació, motivant
la recerca en mètodes per aconseguir un transport aeri més ecològic. En aquest context, les opera-
cions de descens continu (CDOs) permeten a les aeronaus seguir una trajectòria que aporta grans
beneficis econòmics i ambientals, donant com a resultat descensos amb els motors al ralentí des
de l’altitud de creuer fins just abans d’aterrar. Aquestes trajectòries redueixen el consum de com-
bustible, les emissions contaminants i el soroll generat per les aeronaus. No obstant això, aquest
tipus d’operacions té un gran desavantatge: la pèrdua de predictibilitat des del punt de vista del
controlador aeri (ATC) en termes de temps de pas als diferents punts de la ruta. Com a conse-
qüència, l’ATC necessita assignar una major separació entre les aeronaus, la qual cosa comporta
una reducció en la capacitat de l’aeroport.
Estudis previs investigant aquest problema han demostrat que la capacitat de complir amb
un temps controlat d’arribada (CTA) a un punt de la ruta (utilitzat per seqüenciar les aeronaus)
podria habilitar les CDOs tot mantenint la capacitat de l’aeroport. En aquest context, es necessita
investigar més en com els gestors d’arribades (AMANs)—i els gestors d’arribades extesos (E-
AMANs)—podrien donar suport en la selecció de la CTA més adequada. L’ATC seria l’encarregat
d’enviar la CTA al pilot, el qual, per tal de complir amb la CTA, faria servir la capacitat de gestió
de trajectòries d’un sistema de gestió de vol (FMS) de quatre dimensions (4D). Una transformació
clau per aconseguir una gestió més eficient del trànsit d’arribada és l’ús de nous paradigmes de
gestió del trànsit aeri (ATM), com per exemple el concepte d’operacions basades en trajectòries
(TBO). Aquest concepte té com a objectiu eliminar completament de les trajectòries la vectorització
en “bucle obert” i les restriccions estratègiques. Per aconseguir-ho, es proposa implementar de
manera eficient una negociació de la trajectòria 4D, amb l’objectiu de sincronitzar l’equipament
de terra amb el de l’aeronau, maximitzant d’aquesta manera l’eficiència dels vols i la capacitat del
sistema.
El principal objectiu d’aquest doctorat és desenvolupar mètodes per gestionar aeronaus de
manera eficient en espai aeri terminal, juntament amb conceptes d’operacions que compleixin
amb el concepte de TBO. Les trajectòries d’arribada simulades per tots els experiments definits en
aquesta tesi doctoral, en la mesura que s’ha pogut, són CDOs d’energia neutra. D’aquesta manera,
la idea és reduir el màxim possible l’impacte mediambiental de les operacions aèries al sistema
ATM. En definitiva, l’objectiu d’aquest doctorat és aconseguir una gestió del trànsit d’arribada
més eficient, obtenint una major predictibilitat i capacitat, i assegurant que la seguretat de les ope-
racions es manté. Els experiments dissenyats consideren una situació on el concepte de TBO és
xxiii
present, el que comporta una sincronització elevada entre tots els actors implicats en el sistema
ATM. Així mateix, s’esperen nivells majors d’automatització i de compartició d’informació, junta-
ment amb una modernització de les eines de suport en terra a l’ATC i dels FMSs de les aeronaus,
tot amb l’objectiu de complir amb el nou paradigma de TBO.
Primer de tot, es defineix un marc per l’optimització de trajectòries utilitzat per generar les
trajectòries simulades pels experiments definits en aquesta tesi doctoral. A continuació, s’avaluen
els beneficis de volar CDOs d’energia neutra comparant-les amb trajectòries reals obtingudes de
dades de vol històriques. Es comparen dues fonts de dades, concloent quina és la més adequada
per estudis d’eficiència en espai aeri terminal. Les CDOs d’energia neutra són el tipus preferit de
trajectòries des d’un punt de vista mediambiental però, depenent de la quantitat de trànsit, podria
ser impossible per l’ATC assignar una CTA que pugui ser complida per les aeronaus mentre volen
la ruta d’arribada publicada. En aquesta tesi doctoral, es comparen dues estratègies amb l’objectiu
de complir amb la CTA assignada: volar CDOs d’energia neutra per rutes més llargues/curtes o
volar descensos amb el motor accionat per la ruta publicada. Per les dues estratègies, s’analitza la
sensibilitat del consum de combustible a diferents paràmetres, com l’altitud inicial de creuer o la
velocitat del vent. Finalment, en aquest doctorat s’analitzen dues estratègies per gestionar de ma-
nera eficient trànsit d’arribada en espai aeri terminal. Primer, s’utilitza una estratègia provisional
a mig camí entre la negociació completa de trajectòries 4D i la vectorització en “bucle obert”: es
proposa una metodologia per gestionar de manera eficaç trànsit d’arribada on les aeronaus volen
CDOs d’energia neutra en un procediment de navegació d’àrea (RNAV) conegut com a trombó.
A continuació, es proposa una nova metodologia per generar rutes d’arribada dinàmiques que
s’adapten automàticament a la demanda actual de trànsit. D’igual manera, s’apliquen CDOs d’e-
nergia neutra per tot el trànsit d’arribada.
Hi ha diversos factors a considerar que podrien limitar els beneficis de les solucions proposa-
des. La quantitat i distribució del trànsit d’arribada afecta en gran mesura els resultats obtinguts,
limitant en alguns casos una gestió eficient de les aeronaus d’arribada. A més, algunes de les
solucions proposades comporten elevades càrregues computacionals que podrien limitar la seva
aplicació operacional, motivant una major recerca en el futur per tal d’optimitzar els models i
metodologies emprats. Finalment, permetre a alguns avions volar descensos amb el motor acci-
onat podria facilitar la gestió de les aeronaus d’arribada en els experiments que es centren en el
procediment de trombó i en la generació de rutes d’arribada dinàmiques.
xxiv
Notation
Throughout this PhD thesis and as a general rule, scalars and vectors are denoted either with
lower or upper case letters. Vectors are noted with the conventional overhead arrow, like for
example a or
ψ. Sets are denoted using calligraphic fonts, like for example A,Bor X, while
matrices use the same font but in bold series, like R. The time derivative of magnitude a(t)with
respect to tis expressed by da(t)
dt= ˙a. Furthermore, if not otherwise noted, all vectors are column
vectors and a transposed vector is denoted by [·]T. In the notation , (·)indicates optimal. Next, the
principal symbols that are used throughout this dissertation are shown along with their meaning.
The reader should note that this list is not exhaustive.
BB-Spline basis function
CDdrag coefficient
CLlift coefficient
CD0parasite drag coefficient
CD2induced drag coefficient
Daerodynamic drag
Ekkinetic energy of the aircraft
Eppotential energy of the aircraft
Esspecific energy of the aircraft
Ettotal energy of the aircraft
Jcost function of the optimal control problem
Laerodynamic lift force
MMach number
Nnumber of discretisation intervals in the whole time horizon
Njnumber of discretisation intervals in the jth phase
Pnumber of phases of the optimal control problem
xxv
Rperfect gas constant
Swing surface area
Tengine thrust
Tidle idle thrust
Tmax maximum thrust
τdiscretisation step
τjdiscretisation step in the jth phase
Πquadrature function of the running cost
Ξpenalty cost function
αHellman exponent
βspeed brakes deflection
χaaerodynamic heading angle
χgground track angle
δnormalised pressure of the air
δ11 normalised pressure of the air at the tropopause
ηlanding gear status
γaerodynamic flight path angle
γgground flight path angle
γmin minimum aerodynamic flight path angle
λhstandard temperature lapse rate
Rset of real numbers
Eset associating the index of the last time sample to its corresponding phase
Iset associating the index of each time sample to its corresponding phase, excluding the last time
sample of each phase
Llagrangian of the nonlinear programming optimisation problem
Palgorithm that solves the nonlinear programming optimisation problem
Qalgorithm that solves the quadratic programming optimisation problem
Tset associating the index of each time sample to its corresponding phase
φend cost or Mayer term
πrunning cost or Lagrange term
ρdensity of the air
σnormalised density of the air
τSSL temperature of the air at standard sea level
θnormalised temperature of the air
θ11 normalised temperature of the air at the tropopause
xxvi
Fevolution function of the state vector
χ current states vector
λdual variables associated with inequality constraints
µ dual variables associated with equality constraints
ψterminal constraints
ϕ equality algebraic path constraints
ϑeq equality interior-point constraints
ϑin inequality interior-point constraints
bpath constraints
dfixed parameters of the model
e vector of slack variables
fdynamics of the state vector
g inequality constraints of the nonlinear programming problem
hequality constraints of the nonlinear programming problem
p vector of parameters of the nonlinear programming problem
u controls vector
w wind vector
x states vector
ζaerodynamic configuration of the aircraft
fcost function of the nonlinear programming optimisation problem
ggravity acceleration
hgeometric altitude
hrreference altitude of the Hellman model
h11 standard altitude of the tropopause
kjkth discretisation time sample
mmass of the aircraft
nzload factor
pSSL pressure of the air at standard sea level
qnominal fuel flow
qidle idle fuel flow
sdistance to go
ttime
tFfinal time of the time horizon
tIinitial time of the time horizon
xxvii
tjinitial time of the jth phase
vtrue airspeed
vCAS calibrated airspeed
weeast wind component
whvertical wind component
wnnorth wind component
wrreference speed of the Hellman model
wslongitudinal wind component
wxcross wind component
xxviii
List of Acronyms
2D two-dimensional
3D three-dimensional
3D-PAM 3D-path arrival management
4D four-dimensional
AAL above aerodrome level
ADS-B automatic dependent surveillance-broadcast
ADS-C automatic dependent surveillance-contract
AGL above ground level
AIP aeronautical information publication
AMAN arrival manager
ANSP air navigation service provider
APM aircraft performance model
ATC air traffic control
ATCO air traffic control officer
ATFM air traffic flow management
ATM air traffic management
ATS air traffic services
BADA base of aircraft data
CARATS collaborative actions for renovation of air traffic systems
CAS callibrated airspeed
CDO continuous descent operation
CI cost index
CONOP concept of operation
CPR correlated position report
CTA controlled time of arrival
DAE differential algebraic equation
DCB demand and capacity balance
DDR demand data repository
E-AMAN extended arrival manager
E-TMA extended terminal maneuvering area
ECAC european civil aviation conference
ECMWF european centre for medium-range weather forecasts
EDA efficient descent advisor
EPP extended projected profile
ETA estimated time of arrival
xxix
FAA federal aviation administration
FAB functional airspace block
FAP final approach point
FAS final approach speed
FCOM flight crew operating manual
FIM flight-deck interval management
FL flight level
FMS flight management system
GAMS general algebraic modelling system
GD green dot speed
GFS global forecast system
GRIB gridded binary
GS glide slope
i4D initial four-dimensional
IAF initial approach fix
ICAO international civil aviation organization
IF intermediate fix
ILS instrumental landing system
IM interval management
INAP integrated network ATC planning
ISA international standard atmosphere
KKT Karush-Kuhn-Tucker conditions
KPI key performance indicator
MILP mixed integer linear programming
MIP mixed integer programming
MLW maximum landing weight
MMO maximum operative Mach
NASA national aeronautics and space administration
NextGen next generation air transportation system
NLP non-linear programming
NMOC network manager operations centre
NOAA national oceanic and atmospheric administration
NWP numerical weather prediction
ODE ordinary differential equation
OEM original equipment manufacturer
OPTIMAL optimised procedures and techniques for improvement of approach and landing
PARTNER partnership for air transportation noise and emission reduction
PI performance indicator
PRU performance review unit
RAP rapid refresh
RBT reference business trajectory
RMSE root-mean-square error
RNAV area navigation
RNP required navigation performance
RTA required time of arrival
SESAR single european sky ATM research
SLQP sequential linear-quadratic programming
SNOPT sparse nonlinear optimiser
SQP sequential quadratic programming
SSL standard sea level
STAM short-term air traffic flow capacity measure
STAR standard terminal arrival route
STATFOR statistics and forecast service
SWIM system-wide information management
TA tailored arrival
xxx
TAAM total airport and airspace model
TAS true airspeed
TBO trajectory based operations
TDDA three-degrees deceleration approach
TMA terminal maneuvering area
TOD top of descent
TRL technology readiness level
UPC technical university of Catalonia
UPS united parcel service
VFE vertical flight efficiency
VLS lowest selectable speed
VMO maximum operative CAS
xxxi
える場所これらが
うだけできくわるわ
[Any new position from which you view your re-
ality will change your perception of its nature. It’s
all literally a matter of perspective.]
マヤ (新世エヴァンゲリオン)[Maya
Ibuki (Neon Genesis Evangelion)]
I
Introduction
Air transportation has been experiencing a continuous growth over the last decades and, although
the 2020 setback might slow down this upward trend, high levels of air traffic are still projected
for the future (Iacus et al.,2020). Despite the desirable growth of the global economy, the higher
volume of traffic has also increased the environmental impact of aviation and the workload faced
by air traffic control officers (ATCOs). This is especially evident in terminal maneuvering areas
(TMAs), which are areas of controlled traffic surrounding one or more aerodromes. Specifically
in large airports, TMAs are very congested and experience large levels of noise and emissions
produced by aircraft. This leads to the need for research into methods for achieving a greener
air transportation and for lessening the ATCO workload, which would allow for an increase in
capacity.
Numerous ongoing air traffic management (ATM) improvement programs are being under-
taken by a number of international civil aviation organization (ICAO) member states, like the
single european sky ATM research (SESAR) in Europe, the next generation air transportation sys-
tem (NextGen) in the United States, the collaborative actions for renovation of air traffic systems
(CARATS) in Japan or SIRIUS in Brazil, among others. Through these programs, organizations
like the SESAR Joint Undertaking and the federal aviation administration (FAA)—in charge of
SESAR and NextGen programs, respectively—are addressing the impact of air traffic growth by
developing new or improved procedures and technologies that aim to increase the capacity and
efficiency of the ATM system, while simultaneously improving safety and reducing the environ-
mental impact.
In Europe, SESAR aims at increasing the capacity of the whole ATM system by 80-
100% (SESAR JU,2020) by 2035. Enhancements to conflict and separation management processes
and increased automation for both on-board and ground systems will help to safely handle the
1
2Chapter I - Introduction
increasing traffic demand in the TMA and en-route environments. At airspace and air traffic flow
management (ATFM) level, more dynamic optimization and allocation of airspace (see for in-
stance Sergeeva et al. (2017)) is foreseen to enable airspace users to access required airspace with
minimum constraints. Finally, airport throughput is expected to increase by improving the traffic
sequencing and merging techniques and by reducing separation requirements for both arrivals
and departures, which would lead to a 5-10% capacity improvement in highly congested airports
(SESAR JU,2020).
Another SESAR ambition is to achieve a total reduction of between 4% and 10% in fuel burn
per flight (SESAR JU,2020). In this context, improvements to the design of engines over the past
years have greatly reduced fuel consumption and gaseous emissions. Promising procedural so-
lutions, which have the advantage to provide fuel benefits without modifying aircraft engines or
airframe, have been also proposed. For instance, in the en-route environment, a fuel reduction of
around 2.5% is expected due to more direct routes and more efficient vertical profiles (altitude and
speed). Optimal vertical profiles for en-route operations were investigated, for instance, by Betts
& Cramer (1995) and Soler et al. (2012), and the actual quantitative benefits in terms of fuel and
time savings with respect to current profiles were assessed by Dalmau & Prats (2015) and Dalmau
& Prats (2017a). In the TMA environment, the SESAR target is to enable an average reduction of
around 10% in fuel burn by enabling continuous climb and descent profiles with fewer tactical
interventions from air traffic control (ATC). The introduction of more fuel-efficient profiles, how-
ever, could be achieved at the cost of a reduction of capacity, provided new concepts of operation
are not implemented. Major challenges involved with the implementation of new concepts of
operation include the upgrade of current flight management systems (FMSs) planning and guid-
ance capabilities; changes in airspace and procedure design; and modernization of current ATC
separation, sequencing and merging techniques and their ground decision support tools.
I.1 Environmental Impact of Descents
One of the strategies to achieve a greener air transportation system is the use of continuous de-
scent operations (CDOs), which allow aircraft to follow an optimum flight path that delivers major
environmental and economic benefits, giving as a result engine-idle continuous descents that re-
duce fuel consumption, pollutant emissions and noise nuisance (Erkelens,2000;Warren & Tong,
2002;Clarke et al.,2004). A CDO is understood as a trajectory executed with the engines at idle
during the whole descent, no matter how many level-offs are performed. In the case of a level-
off at idle thrust, the aircraft will rapidly reduce the kinetic energy without requiring additional
drag devices. In addition, a CDO could also be executed with the engines at non-idle, but with
no level-offs. In this PhD thesis, the concept of energy-neutral CDO (or simply neutral CDO) is
introduced. This concept refers to a descent in which the total energy is not increased by means of
thrust higher than idle nor removed by using active drag devices (e.g. speed brakes).
Figure I-1 shows an illustrative comparison between the altitude profile of a conventional
descent and that of a CDO for an aircraft planning to land at Barcelona airport (LEBL). A con-
ventional descent leaves the cruise altitude earlier, typically as a result of an ATC clearance. The
aircraft descends by performing a series of level-offs caused by tactical ATC instructions (as dis-
cussed in Section I.2.1) or constraints defined at the waypoints of the particular procedure being
flown. During these segments at constant altitude, additional thrust is typically required to main-
tain the altitude without decelerating too much.
During a CDO, the aircraft remains at the cruise altitude for a longer distance, thus, con-
suming a lower quantity of fuel. Then, at the optimal top of descent (TOD), the point at which
the aircraft starts the descent, the engines are set to idle and the aircraft starts a continuous de-
scent towards the interception of the instrumental landing system (ILS) glide slope (GS). A short
I.1 Environmental Impact of Descents 3
Figure I-1: Illustrative comparison of a CDO and a conventional descent operation
level-off is required in order to properly intercept the GS. In general, a CDO is performed (as far
as possible) at higher altitudes, lower thrust settings and lower drag configurations all along the
descent.
Extensive research has been conducted to assess the environmental benefits of CDOs. For
instance, a series of simulations and field tests were performed within the optimised procedures
and techniques for improvement of approach and landing (OPTIMAL) program initiated by the
European Commission in 2004 (European Comission,2020) and the partnership for air transporta-
tion noise and emission reduction (PARTNER) program established by the FAA in support of the
NextGen initiative in 2003 (Massachusetts Instritute of Technology,2020). It is worth mention-
ing that these programs are only two of the many research activities that have been performed to
quantify the benefits and to identify the limitations of CDOs.
In the OPTIMAL program, field tests were performed at two major European airports to
assess the trade-off between environmental benefits and operational flexibility of CDOs, including
predictability of the descent trajectories, ATC coordination procedures and workload of the flight
crew. The results obtained from field tests at London Heathrow airport (LHR) were reported
by Reynolds et al. (2005), while the main findings obtained at Amsterdam Schiphol airport (AMS)
were presented by Wat et al. (2006). Similar experiments were performed within the PARTNER
project at Louisville international airport (SDF) (Clarke et al.,2004,2006), Atlanta international
airport (ATL) (Clarke et al.,2007) and Los Angeles international airport (LAX) (Clarke et al.,2013).
With no exception, all the aforementioned experiments concluded that CDOs lead to fuel
savings, noise nuisance and gaseous emission reduction if compared to conventional descents.
For instance, results from united parcel service (UPS) flight tests during night-time operation at
SDF reported fuel savings of about 200 kg per flight for B767 models (Clarke et al.,2004,2006),
while results from flight tests at ATL, which considered flights from two airlines, suggested fuel
savings of around 460 kg and 600 kg per flight for B757 and B767 models, respectively (Clarke
et al.,2007). Finally, an analysis over more than 480,000 flights at 25 airports in the US national
airspace system during a four-month period concluded that fuel savings of CDOs were lower than
25 kg for 45% of the flights, and less than 100 kg for 87% of the flights (Robinson & Kamgarpour,
2010).
Based on this diversity of fuel savings figures, it can be concluded that comparison of results
across different experiments is difficult due to the substantial differences in assumptions, types of
data, models, and methods being used. Nevertheless, Thompson et al. (2013) quantified the bene-
fits of CDOs in Paris and New York regions using similar sources of data, analytical methods and
models, and concluded that discrepancies in fuel saving figures across different experiments are
also caused by the differences in traffic intensity, as well as the distribution of level-off segments in