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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
3 |
Outline
•ATM aircraft performance models
•Aeronautical fundamentals •BADA
• BADA 3 • Difference with BADA 4
•Alternatives to BADA
4 |
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
5 |
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
6 |
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
7 |
Forces
V
γ θ
α
horizon
airspeed
x-axis aircraft body
Faerodynamic
Vhor = V cos γ
Vvert = V sin γ
8 |
Forces
V
γ θ
α
horizon
airspeed
x-axis aircraft body
L
D
W
T
9 |
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):
10 |
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
11 |
Total energy (rate) equation
dh dV
mg mV T D Vdt dt
Drag?
12 |
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
13 |
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:
14 |
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
15 |
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
16 |
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
17 |
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
18 |
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
19 |
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
20 |
International Standard Atmosphere
T Change in standard conditions:
V VM
a RT
( )f h
21 |
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
22 |
Profile of a descent
Cruise Top of Descent
Level deceleration Arrival approach
Descent
23 |
Profile of a descent
Cruise Top of Descent
Level deceleration Arrival approach
Constant Mach Descent
Constant CAS Descent
Crossover altitude
24 |
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
25 |
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
26 |
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
27 |
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
28 |
Downloaded BADA and then what?
29 |
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)
30 |
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
31 |
So what is in BADA 3 for this model?
File: A306__.OPF
32 |
TOL = Take-off Length LDL = Landing Length
33 |
APF file: Airline Procedure file: speeds
34 |
*.PTD Performance Test/Table Data
35 |
*.PTF Performance Table Fuel Flow
36 |
BADA Families: Introduction
BADA User Group Meeting 2015 - BADA Theoretical Fundamentals
36
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
41
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
42
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
43
BADA 4 sub-models: Drag (clean configuration)
Drag polar formula: CD = a(M) + b(M) · CL2 + c(M) · CL
6
Main improvement: dependency on airspeed (compressibility)
44
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
45
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
46
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
47
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
48
Altitude [ft]
49
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
50
Advanced capabilities: Cost Index in cruise (1)
Typical presentation of Cost Index data in aircraft manuals
51
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
52
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:
54 |
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
55 |
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