[EN-041] A Study on Benefits Gained by Flight Trajectory
Optimization for Modern Jet Passenger Aircraft
EIWAC 2013
The Third ENRI International Workshop on ATM/CNS
19-21 February 2013, Tokyo Japan

N.K. Wickramasinghe†, H.Totoki, A. Harada and Y. Miyamoto
Graduate School of Engineering, Kyushu University
Fukuoka Japan

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft- Outline ■ Premise of Study■ Research Motivation■ Mathematical Formulation■ Dynamic Programming Method■ Utilized Models – Meteorological Model, Aircraft Performance Model■ Reference Data
■ Flight Trajectory Optimization – Examples & Effect of Wind Shear■ Conclusions

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A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

2- Premise of Study -NextGen Program

SESAR Program

CARATS Program

Trajectory-based ATM Operations

Reduce operational cost /environmental impact
Efficient and flexible airspacewith user priority
Increased Safety
Courtesy: CARATS Long Term Vision for the Future Air Traffic Systems

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft- Research Motivation Towards an Efficient Operational System... “Free Flight”
Safe and efficient User Priority flight path and speed selection inreal time according to weather conditions
System’s flexibility to manage capacity increase
Economic benefits such as Fuel Consumption Reduction withDeparture→Arrival direct approach

Reviewing the benefits obtained by flight trajectory
optimization by minimizing fuel consumption
considering the presence of winds in a Free
Flight based futuristic Air Transportation System3

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft- Requirements for Analysis Optimization Tool
Dynamic Programming Method
Meteorological Data
Numerical Weather Prediction Model Data
Aircraft Performance Model
Base of Aircraft Data (BADA) Model
Reference Data
Recorded Flight Data on GPS Logger

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A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

5- Mathematical Formulation -()(3D- Translational Motion : P1 φ1 ,θ1 , H1 ,VTAS1 → P2 φ2 ,θ 2 , H 2 ,VTAS2)

VTAS cos γ a cosψ a + Wv (φ ,θ , H )R+H
V cos γ a sinψ a + Wu (φ ,θ , H )θ& = TAS(R + H )cosφ
H& = V sin γ

φ& =TAS

amV&E cos(γ a − γ )V&TAS = T − D − mg sin γ aφθ: Latitude
R : Earth radius: Longitude
Wu : Zonal wind component
H : Altitude
Wv : Meridional wind component
VTAS : True airspeed
γ a : Flight path angle
ψ a : Heading angle
T : Engine thrust
D : Aerodynamic dragVE : Aircraft’s speed on Earth Frame

Definition of point mass equations

State Variables

Control Variables

φ , θ , H , VTAS

γ a ,ψ a , T

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

6- Dynamic Programming Method Performance Index : J opt =tf∫ FF dt ( FF : fuel flow)t0

Independent VariableηState Variables

H ,VCAS , ζηζ: Cross range angle

H: Altitude: Downrange angle

VCAS : Calibrated airspeed
Performance index calculations
Reference: [EN-040] Harada, A., Miyamoto, Y. and Wickramasinghe, N.K.,“Flight Trajectory Optimization Tool with Dynamic Programming Developed for Future Air Transportation System”

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

7- Meteorological Model Weather data from Japan Meteorological Agency (JMA)
Characteristics of GSM Japan Region Model
Data Format

GRIB2 Grid Point Value (GPV) Data

Initial Time Value00, 06, 12, 18 (UTC)RegionLongitude: 120 ~ 150 degoo[oo[Latitude: 20 ~ 50 deg]

Pressure Altitude] Latitude Direction: 0.20o [deg]1000,925,850,700,600,500,400,300,250,200,150,100[hPa ]Physical Elements

Geopotential Altitude, Zonal wind, Meridional wind, Temperature, vertical flow

Resolutiono[]

Longitude Direction: 0.25 deg

Barometric Pressure
Altitude: 12 layers

Latitude Grid Point Value

Longitude Grid Point Value

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

8- Aircraft Performance Model BADA (Base of Aircraft Data) by EUROCONTROL

Courtesy: EUROCONTROL

Utilized models
Aerodynamic Model
Thrust Model
Fuel Flow Model

Constraint Conditions
VMO ≥ VCAS ≥ 1.3 ×VSTALL

Tmax ≥ T

MMO ≥ Mach Number

FF = max (FFnom , FFmin )A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

9- Reference Data Lateral measurement error:
3 ~ 25 [m] at ground level(Courtesy: Google Maps)

Data recording

Accuracy check
Measured Data

Time of Measurement
Longitude [deg, mts, sec]Latitude [deg, mts, sec]
Ground Velocity [km/h]
Geometrical Altitude [m]Recorded total flight routes
Reference: [EN-039] Totoki, H. and Wickramasinghe, N.K.,“A Study on Flight Trajectory Estimation by Using GPS Data Measured in Airliner Cabin”

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

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Reference Data List- Problem Setting -Date(YY/MM/DD)

Calculation Conditions

Departure Flight Time(JST)/ Arrival

2011/06/18

FUK / HND

14:02 / 15:20

Reference
RouteHaneda ：35.54830N

139.90780E

2011/06/19

HND / FUK

20:00 / 21:48

Fukuoka：33.89030N

130.33170E

2011/06/26

HND / FUK

19:58 / 21:28

Downrange

30 Grid points

2011/07/31

HND / FUK

19:59 / 21:30

2011/08/28

HND / FUK

18:50 / 20:31

2011/09/02

FUK / HND

09:53 / 11:30

2011/09/24

FUK / HND

10:57 / 12:20

2011/10/01

FUK / HND

15:04 / 16:22

2011/10/02

HND / FUK

19:54 / 21:41

2011/10/08

FUK / HND

16:11 / 17:29

2011/10/10

HND / FUK

11:22 / 12:59

2011/10/15

FUK / HND

16:04 / 17:42

2011/10/17

HND / FUK

10:20 / 12:00

2011/10/21

FUK / HND

9:55 / 11:20

AltitudeCalibrated
Airspeed

Minimum

3000[m]Maximum

13000[m]Minimum

100[m/s]

Maximum

160[m/s]

100
Grid Points
60
Grid Points

2.5[deg] on each side of Great
Cross range Circle Route100 Grid Points

Boundary values: Identical 3D-position and Calibrated Airspeed
Initial mass of aircraft: Reference mass from BADA model
Aircraft configuration: Clean Configuration of a twin engine wide body jet aircraftA Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

11- Application example (1) [Date: 2011/10/08] FUK→HND

Fuel Consumption

Fuel Flow

Mach Number

Lift Drag Ratio

Thrust for Optimal RouteThrust for GPS RouteAltitude

Calibrated Airspeed

True Airspeed

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft- Application example (1) -Flight Path Angle

Heading Angle

Downrange Wind

Lateral Flight Profile

Cross range Wind

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A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

13- Application example (2) [Date: 2011/06/19] HND→FUK

Fuel Consumption

Fuel Flow

Mach Number

Lift Drag Ratio

Thrust for Optimal RouteThrust for GPS RouteAltitude

Calibrated Airspeed

True Airspeed

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft- Application example (2) -Flight Path Angle

Heading Angle

Downrange Wind

Lateral Flight Profile

Cross range Wind

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A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

15- Application example (3) [Date: 2011/10/15] FUK→HND

Fuel Consumption

Fuel Flow

Mach Number

Lift Drag Ratio

Thrust for Optimal RouteThrust for GPS Route

AltitudeCalibrated Airspeed

True Airspeed

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

16- Application example (3) -Flight Path Angle

Heading Angle

Downrange Wind

Lateral Flight ProfileCross range Wind

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft- Quantitative Evaluation Results -Tradeoff between Fuel Consumption and Flight Time

Average fuel consumption efficiency: -10%
Average exceeding flight time: 5%17

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft

18- Effect of Wind Shear [Date: 2011/12/17] HND→FUK

Fuel Consumption

Fuel Flow

Mach Number

Lift Drag Ratio

Thrust for 4D RouteThrust for 3D Route

AltitudeCalibrated Airspeed

True Airspeed

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft- Effect of Wind Shear -Lateral Flight Profile Comparison

3D- Optimal Route
Fuel Consumption : 9651.08[kg]Flight Time: 6031[sec]4D- Optimal Route
Fuel Consumption : 9349.9[kg]Flight Time: 5948[sec]19

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger Aircraft20- Conclusions ■Flight trajectory optimization plays an important role in the development of a futuristic ATS
system and optimized flight trajectories in presence of winds would greatly increase thebenefits such as fuel consumption of modern jet passenger aircraft.

■

Dynamic Programming Method is introduced as an optimization tool for flight trajectory
optimization. → Reference: EN-040■

Numerical weather prediction models provided Weather Data are highly accurate and can bewell used to predict future weather conditions at flight planning.

■

The used aircraft performance model, BADA Model possesses highly accurate aircraft
performance data which can be used to evaluate fuel consumption.

■

Using a simple GPS data logger to record a very few number of flight data parameters in anairliner cabin was sufficient to implement a substantial research and understand the structureof the ATC system. → Reference: EN-039■

An average fuel efficiency of 5% ~ 10% could be obtained by choosing a lower descent
speed and a smoother descent rate with the application of Trajectory Based Operations.

■Overall optimization considering the tradeoff of fuel consumption and flight time would
eventually contribute towards a futuristic Air Transportation System with great benefits.

A Study on Benefits Gained by Flight Trajectory Optimization
for Modern Jet Passenger AircraftThank you for your kind attention.

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