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Aircraft performance models for ATM Research

Jacco Hoekstra

BADA parts: ©2009 The European Organisation for the Safety of Air Navigation. All rights reserved

BADA Overview

Angela Nuic

BADA Project manager

VIF/ Validation Infrastructure

Directorate SESAR and Research

EUROCONTROL

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Outline

•ATM aircraft performance models

•Aeronautical fundamentals •BADA

• BADA 3 • Difference with BADA 4

•Alternatives to BADA

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ATM performance models

• Goal:

• Realistic aircraft behaviour:

• Dynamics (accelerations, turn rate)

• Flight envelope (max altitude, speed, climb speed, descent speed)

• Procedure

• Fuel consumption => benefits new ATM proecdeures

ATM performance

model

Flight state: Speed

Altitude Flight path angle or V/S

Turning or not Accelerating/Decelerating

Limited flight state Limited speed

Limited Altitude Limited Flight path angle

or V/S Bank angle

Actual accel/decel Fuel consumption/Thrust

setting

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ATM performance models

• Goal:

• Realistic aircraft behaviour:

• Dynamics (accelerations, turn rate)

• Flight envelope (max altitude, speed, climb speed, descent speed)

• Procedure

• Fuel consumption => benefits new ATM proecdeures

ATM performance &

procedure model

Flight plan (3D) Trajectory 4D

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Kinematics: angles and speeds

γ θ

α γ = flight path angle

θ = pitch angle

α = angle of attack

horizon

V airspeed

x-axis aircraft body

Vhor = V cos γ

Vvert = V sin γ

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Forces

V

γ θ

α

horizon

airspeed

x-axis aircraft body

Faerodynamic

Vhor = V cos γ

Vvert = V sin γ

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Forces

V

γ θ

α

horizon

airspeed

x-axis aircraft body

L

D

W

T

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Forces

V

γ θ

α

horizon

airspeed

x-axis aircraft body

L

D

W

T

cos ( )sin

sin ( )cos

vert

hor

F L W T D

F L T D

Inertial axes (x=horizon):

cos

sin

vert

hor

F L W

F T D W

Stability axes (x=airspeed):

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Forces along stability axes (speed)

sindV

m T D Wdt

No speed & equilibrium

Speed & acceleration

cos

sin

vert

hor

F L W

F T D W

dV dhmV TV DV W

dt dt

dh dVW mV TV DV

dt dt

dh dV

mg mV T D Vdt dt

pot kindU dU

Force speeddt dt

21

122

2

kin

d mVdU dV dV

mV mVdt dt dt dt

Force x speed = power

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Total energy (rate) equation

dh dV

mg mV T D Vdt dt

Drag?

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Aerodynamic forces

α

horizon

airspeed

x-axis aircraft body

L

D

CL

α

CL

CD

m W L

cos

sin

vert

hor

F L W

F T D W

W

γ

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Total energy (rate) equation

dh dV

mg mV T D Vdt dt

Drag

21

2DD C V S

21cos

2LL C V S m g

0 , ( , )DC k f flaps gear

L DC C

2

2

0 0L

LD D D

CC C C k C

Ae

Drag polar:

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dh dV

mg mV T D Vdt dt

Total energy (rate) equation

Vertical speed

Acceleration

Thrust Drag

Possible control variables

Speed

Three variables and one equation: two free

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Total energy (rate) equation

dh dV

mg mV T D Vdt dt

Speed setting, throttle => V, T => result is vertical speed dh/dt

Vertical speed, throttle => dh/dt, T => result is speed V

Speed setting, vertical speed => V, dh/dt => result is required thrust T

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Climb/descent performance

dh dV

mg mV T D Vdt dt

Speed setting, throttle => V, T => result is vertical speed dh/dt

Vertical speed, throttle => dh/dt, T => result is speed V

Speed setting, vertical speed => V, dh/dt => result is required thrust T

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Horizontal Flight: Manual Thrust

dh dV

mg mV T D Vdt dt

Speed setting, throttle => V, T => result is vertical speed dh/dt

Vertical speed, throttle => dh/dt, T => result is speed V

Speed setting, vertical speed => V, dh/dt => result is required thrust T

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Horizontal Flight: Speed select

dh dV

mg mV T D Vdt dt

Speed setting, throttle => V, T => result is vertical speed dh/dt

Vertical speed, throttle => dh/dt, T => result is speed V

Speed setting, vertical speed => V, dh/dt => result is required thrust T

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Climb descent :Constant CAS/Mach

dh dV

mg mV T D Vdt dt

dh dV dh

mg mV T D Vdt dh dt

dh V dV dh

mg T D Vdt g dh dt

1V dV dh

mg T D Vg dh dt

1

1

T D Vdh

V dVdt mg

g dh

T D Vdhf M

dt mg

Energy share factor

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International Standard Atmosphere

T Change in standard conditions:

V VM

a RT

( )f h

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Energy share factor: Constant Mach

( ) 1.0f M Constant Temperature: (h>11 km)

Temperature gradient β:

(h<11 km)

2( ) 12

R T Tf M M

g T

κ =heat capacity ratio of air 1.40p

v

cfor air

c

T = Temperature

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Profile of a descent

Cruise Top of Descent

Level deceleration Arrival approach

Descent

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Profile of a descent

Cruise Top of Descent

Level deceleration Arrival approach

Constant Mach Descent

Constant CAS Descent

Crossover altitude

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Energy share factor: Constant CAS

Constant Temperature: (h>11 km)

Temperature gradient β : (h<11 km)

1

1 12 2 2

1( )

1 11 1 1 1

2 2 2

f M

R T TM M M

g T

1

1 12 2

1( )

1 11 1 1 1

2 2

f M

M M

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Total energy (rate) equation

dh dV

mg mV T D Vdt dt

Speed setting, throttle => V, T => result is vertical speed dh/dt

Vertical speed, throttle => dh/dt, T => result is speed V

Speed setting, vertical speed => V, dh/dt => result is required thrust T

T => Fuel consumption

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Fuel consumption linear with Thrust?

FF T η = specific fuel flow [kg/s N] or:

η = specific fuel flow [kg/min N]

Specific fuel flow varies with: - Type of engine - Speed - Altitude - Thrust rating (flight phase)

And how this varies is different for turboprop and jet

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BADA 3

•

• Current version v 3.13 license: https://badaext.eurocontrol.fr/licence/bada/v3last

• Link: http://www.eurocontrol.int/services/bada

• BADA 3 document: http://www.eurocontrol.int/sites/default/files/field_tabs/content/docu

ments/sesar/bada-aircraft-performance-modelling.pdf

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Downloaded BADA and then what?

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File types:

• For each type (also see synonym file) SYNONYM.NEW file contains

aircraft type identifiers and corresponding file names, e.g.:

CC A/C MANUFACTURER NAME OR MODEL FILE ICAO

CD - A306 AIRBUS A300B4-600 A306__ Y

• APF = Airline Procedures file • OPF = Aircraft Operations Performance File • PTD = Performance Table Data (results to check) climb speeds etc

• PTF = Performance Table for Fuel Flow

• BADA.GPF = General performance file (typical default values max

acceleration, bank angels used by AP)

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Fuel consumption BADA 3 model

FF T η = specific fuel flow [kg/s N] or:

η = specific fuel flow [kg/min N]

Idle descent: min 3

4

1f

f

hFF C

C

fcrC

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So what is in BADA 3 for this model?

File: A306__.OPF

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TOL = Take-off Length LDL = Landing Length

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APF file: Airline Procedure file: speeds

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*.PTD Performance Test/Table Data

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*.PTF Performance Table Fuel Flow

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BADA Families: Introduction

BADA User Group Meeting 2015 - BADA Theoretical Fundamentals

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BADA 3 family

BADA 4 family

Today’s standard APM, widely used by the ATM community

New model developed to meet requirements

of future ATM systems

BADA Families: BADA 3

Objective: provide credible modelling of aircraft performances

for nominal part of aircraft operational envelope

for a great number of aircraft types

Developed 20 years ago to meet requirements of that time

Currently used all over the world for R&D, strategic planning, ground

operational systems, real-time and fast-time simulations...

Will continue to be used in the future, so:

No modifications in model specifications and data characteristics

Improvement of aircraft type models by using better performance

reference data and addition of new models

BADA User Group Meeting 2015 - BADA Theoretical Fundamentals 37

BADA Families: BADA 4

Objective: provide accurate modelling of aircraft performances

for entire aircraft operational envelope

to support modelling of complex operations (e.g. optimization)

New model developed using today’s resources that did not exist

when BADA was created:

Better aircraft performance reference data

Higher computing power

BADA User Group Meeting 2015 - BADA Theoretical Fundamentals 38

BADA Theoretical Fundamentals: Content

Meet the BADA families

Commonalities between BADA 3 and 4

Overview of BADA 3 sub-models and their limitations

Overview of BADA 4 sub-models and new uses they enable

BADA User Group Meeting 2015 - BADA Theoretical Fundamentals 39

Commonalities: Model structure, sub-models

BADA User Group Meeting 2015 - BADA Theoretical Fundamentals 40

Airline Procedure Model

<<model>>

ActionsActions

<<model>>

MotionMotion <<model>>

Operations<<model>>

{a1, a2, …}{o1, o2, …}

{l1, l2, …}

<<model>>

Actions

<<model>>

Motion <<model>>

Operations<<model>>

Limitations

{a1, a2, …}{o1, o2, …}

{l1, l2, …}

<<model>>

Aircraft Characteristics

<<model>>

Speed modelSpeed model

{a1, a2, …}

<<model>>

Speed model

{a1, a2, …}

<<model>>

Speed modelSpeed model

{a1, a2, …}

<<model>>

Configuration

1 c2, …}{c

Aircraft Performance Model

thrust,

drag...

speed envelope,

max altitude...

engine ratings,

flap positions...

BADA Theoretical Fundamentals: Content

Meet the BADA families

Commonalities between BADA 3 and 4

Overview of BADA 3 sub-models and their limitations

Overview of BADA 4 sub-models and new uses they enable

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BADA Theoretical Fundamentals: Content

Meet the BADA families

Commonalities between BADA 3 and 4

Overview of BADA 3 sub-models and their limitations

Clean drag

Climb thrust (jet, turboprop, piston)

Fuel consumption (jet)

Overall behaviour and use cases

Overview of BADA 4 sub-models and new uses they enable

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BADA Theoretical Fundamentals: Content

Meet the BADA families

Commonalities between BADA 3 and 4

Overview of BADA 3 sub-models and their limitations

Overview of BADA 4 sub-models and new uses they enable

Clean drag

Climb thrust (jet, turboprop, piston)

Fuel consumption (jet)

Optimized flight operations

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BADA 4 sub-models: Drag (clean configuration)

Drag polar formula: CD = a(M) + b(M) · CL2 + c(M) · CL

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Main improvement: dependency on airspeed (compressibility)

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Typical reference polar Typical BADA 4 polar

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.2

0.4

0.6

0.8

1

1.2

1.4

1.6

CD [dimless]

CL [

dim

less]

M = 0.25

M = 0.3

M = 0.35

M = 0.4

M = 0.45

M = 0.5

M = 0.55

M = 0.6

M = 0.65

M = 0.7

M = 0.75

M = 0.8

M = 0.85

M = 0.86

different

aircraft

BADA 4 sub-models: Jet thrust

Thrust formula (MCMB, flat-rated):

Thr(δ, M..M5, δT..δT5)

δT,MCMB,flat(M..M5, δ..δ5)

Main improvement 1: dependency on airspeed

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BADA 4 sub-models: Piston thrust

Thrust and efficiency formulas: Thr = f1(η, VTAS-1), η = f3(VTAS

3)

Main improvement 1: accurate dependency on airspeed

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Typical reference climb perf. Typical BADA 4 climb perf.

best rate speed VX best rate speed

Climbing speed KIAS

RO

CD

BADA 4 sub-models: Jet fuel consumption (1)

Fuel (not TSFC) formula: F = f(Thr..Thr4, M..M4, δ, √θ)

Main improvement 1: TSFC (= F/Thr) depends on altitude and thrust

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Altitude effect in ref. fuel Altitude effect in BADA 4 fuel

TS

FC

TS

FC

TAS [kt] TAS [kt]

BADA 4 sub-models: Jet fuel consumption (2)

Cruise phase (T=D): combines improvements of drag and fuel models

Main improvement 2: optimum altitude can be estimated

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Altitude [ft]

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Advanced capabilities: Optimized flight operations

Increased accuracy of BADA 4 enables management of

complex and optimized flight operations

Examples:

Optimum cruise altitude

Maximum endurance cruise speed (MEC)

Maximum or Long range cruise speed (MRC/LRC)

ECON cruise speed based on Cost Index

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Advanced capabilities: Cost Index in cruise (1)

Typical presentation of Cost Index data in aircraft manuals

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Advanced capabilities: Cost Index in cruise (2)

5.5 6 6.5 7 7.5

x 104

0.73

0.74

0.75

0.76

0.77

0.78

0.79

0.8

0.81

Weight [kg]

Mach [

dis

s]

CI = 0

CI = 20

CI = 40

CI = 60

CI = 100

BADA 4 ECON cruise speed in function of

CI and altitude (constant weight)

2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7

x 104

0.68

0.7

0.72

0.74

0.76

0.78

0.8

Hp [ft]

Mach [

dis

s]

CI = 0

CI = 20

CI = 40

CI = 60

CI = 100

BADA 4 ECON cruise speed in function of

CI and weight (constant altitude)

BADA 4 ECON cruise speed consistent with expectations

e.g. higher CI => higher speed

BADA Theoretical Fundamentals: Conclusions

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BADA 3:

proper physical relations not

included in some sub-models

limited accuracy of individual

sub-models

domain of validity:

nominal flight envelope

BADA 4:

proper physical relations

included in all sub-models

improved accuracy of individual

sub-models

domain of validity:

complete flight envelope

For more info

Consult BADA web site:

https://www.eurocontrol.int/services/bada

Contact BADA team:

eec.bada@eurocontrol.int

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Alternative approaches (1/2)

• Flight Envelope data can be observed and gained in other ways

• Fuel consumption can also be replaced by work by thrust = energy

consumed: integrate required thrust x speed over time

• Independent measure for energy also when new engine types are being

developed

1

0

t

T

t

E T V dt

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Alternative approaches (2/2) • Eurocontrol has helped ATM as a science enormously by providing

BADA

• Allows comparing studies in terms of a/c perf models used

• Although BADA 3 license is/was nearly open and BADA 4 is quite

accurate, but more restrictive and per project licensing

• There are alternative efforts to develop no-license, fully open and still accurate model using e.g. ADS-B big data/machine learning and public-

only sources

• Check out presentations for example of this effort: check Track 2

Advanced Modelling in Conference Hall 2 this afternoon • Big thanks to Eurocontrol and in particular Angela Nuic for

providing Eurocontrol BADA 3 vs 4 slides