Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed...
Transcript of Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed...
![Page 1: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/1.jpg)
Prediction of Top of Descent Location forIdle-thrust Descents
Laurel Stell
NASA Ames Research Center
![Page 2: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/2.jpg)
Background
Vertical profile from cruise to meter fix
40-120 nmi
10,0
00–
30,0
00ft
idle thrust
.
Top of Descent
(TOD)
meterfix
Idle-thrust descent reduces fuel consumption and emissions.
2
![Page 3: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/3.jpg)
Example Meter Fix Time Errors for Operational Data
Numberof
Flights
−10 −5 0 5 10 150
10
20
30
40
50
Error (nmi)
Numberof
Flights
Top of Descent Path Distance
−30 −20 −10 0 10 20 300
10
20
30
40
50
Error (sec)
Meter Fix Crossing Time
Airbus 320B757B737−300B737−800
More than 90% of the meter fix crossing time predictionshave absolute error less than 30 sec.
3
![Page 4: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/4.jpg)
Example Prediction Errors for Operational Data
−10 −5 0 5 10 150
10
20
30
40
50
Error (nmi)
Numberof
Flights
Top of Descent Path Distance
−30 −20 −10 0 10 20 300
10
20
30
40
50
Error (sec)
Meter Fix Crossing Time
Airbus 320B757B737−300B737−800
Less than 50% of the TOD location predictions haveabsolute error less than 5 nmi.
4
![Page 5: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/5.jpg)
Outline of Presentation
Mathematical analysis and approximation of TOD locationbased on NASA trajectory predictorComparison of results with FMS test bench data and withoperational dataPossible applications
5
![Page 6: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/6.jpg)
Mathematical Analysis
6
![Page 7: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/7.jpg)
Treatment of Wind
For this mathematical analysis, wind is zeroIncorporating wind into the results is explained in paperAnalysis of operational data included wind
7
![Page 8: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/8.jpg)
Kinematic Equations
dsdt
= Vt
dhdt
= γaVt
t : times : the ground path distance relative to the meter fixh : the altitude
Vt : the true airspeedγa : is the flight path angle with respect to the air mass
8
![Page 9: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/9.jpg)
Kinetic Equation
mdVt
dt= T − D −mgγa
T : thrustD : dragm : aircraft massg : gravitational acceleration
9
![Page 10: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/10.jpg)
All Equations for Vertical Profile
1g
dVt
dt=
T − Dmg
− γa
dsdt
= Vt
dhdt
= γaVt
Specify 2 out of 3: flight path angle γa, airspeed Vt , thrust T
10
![Page 11: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/11.jpg)
Descent Procedure
bc bcbc
bc bc
cruise
.
Top of Descent
(TOD)constant Mach
constant
calibrated
airspeed (CAS)
deceleration
meter
fix• Idle thrust throughout descent• Known horizontal trajectory
11
![Page 12: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/12.jpg)
Constant Mach and CAS Segments
1g
dVt
dt=
T − Dmg
− γa
dsdt
= Vt
dhdt
= γaVt
Vt (h) specified:
dsdh
=1γa
=
(1 +
12g
dV 2t
dh
)mg
T − D
12
![Page 13: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/13.jpg)
Top of Descent Location
STOD = −∫ hfix
hcrz
(1 +
12g
dV 2t
dh
)mg
T − Ddh
− 1g
∫ Vfix
Vc
Vtmg
T − DdVt
STOD : TOD location as path distance relative to meter fixhcrz : cruise altitudehfix : meter fix altitudeVc : descent CAS
Vfix : meter fix CAS
GoalPolynomial approximation in terms of hcrz,Vc ,hfix,Vfix,W = mg
13
![Page 14: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/14.jpg)
Top of Descent Location
STOD = −∫ hfix
hcrz
(1 +
12g
dV 2t
dh
)mg
T − Ddh
− 1g
∫ Vfix
Vc
Vtmg
T − DdVt
GoalPolynomial approximation in terms of hcrz,Vc ,hfix,Vfix,W = mg
13
![Page 15: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/15.jpg)
Approach
Analyzed trajectories from NASA predictor to develop thepolynomial approximations
Test matrix with 9000 entries varyingcruise altitude hcrzcruise Machdescent speed Vcmeter fix altitude hfixmeter fix speed Vfixaircraft weight W
B737-700 and B777-200
14
![Page 16: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/16.jpg)
Approximation for Constant Mach and Constant CAS
∫ hfix
hcrz
(1 +
12g
dV 2t
dh
)W
T − Ddh
≈ P(Vc ,W )
∫ hfix
hcrz
(1 +
12g
dV 2t
dh
)dh
≈ −(∆h)V(Vc)P(Vc ,W )
≈ −(∆h)× [linear function of Vc ,W ]
≈ linear function of Vc ,W ,∆h
Each of the last three lines gives a polynomial approximation,with decreasing accuracy but increasing simplicity.
15
![Page 17: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/17.jpg)
Accuracy of Approximations for TOD Location
B737-700
−10 −5 0 5 100
0.2
0.4
0.6
0.8
1
residual (nmi)
cumulative distribution function
approx 1
approx 2
linear
16
![Page 18: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/18.jpg)
Accuracy of Approximations for TOD Location
B777-200
−15 −10 −5 0 5 10 150
0.2
0.4
0.6
0.8
1
residual (nmi)
cumulative distribution function
approx 1
approx 2
linear
16
![Page 19: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/19.jpg)
Validation Against Real-World Data
17
![Page 20: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/20.jpg)
FMS Test Bench Experimental Setup
Commercial FMS connected to flight simulatorSame aircraft types as in mathematical analysisTest matrix is (3 values of descent CAS Vc) × (3 values ofweight W )All other inputs the same in all runsRecorded TOD locations computed by FMS
18
![Page 21: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/21.jpg)
FMS Test Bench Data Results
Least squares fit with a model linear in Vc and W gaveabsolute errors less than 2 nmi for both aircraft typesMuch more accurate than expected from previous results
Approximations above partly explain thisTest matrix does not adequately exercise predictor
19
![Page 22: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/22.jpg)
Operational Data Collection Procedures
Collected data for flights arriving at Denver InternationalAirportSeptember 8–23, 2009United Air Lines and Continental Airlines participatedHumans in controller facility wrote down:
Flights that participated and whether descent interruptedSpeed profiles
Pilots wrote down aircraft weightExtracted cruise altitude and horizontal trajectory fromradar data
20
![Page 23: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/23.jpg)
Operational Data Results
Analyzed about 70 descents each for Airbus 319/320 andB757-200 from one airlineLeast squares fit with a model linear in ∆h, Vc , and Wgave absolute errors less than 4 nmi for all except:
Four (6%) of Airbus descentsSix (8%) of B757 descents
21
![Page 24: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/24.jpg)
Applications
22
![Page 25: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/25.jpg)
Possible Uses of These Approximations
Design of FMS test bench experimentsSimplified sensitivity analysisKinematic predictor of TOD location
Dynamic machine learning of coefficients to handle de-icingsettings, for exampleContinuously updated error modelsOnly 5-10 coefficients; NASA predictor has 2000 entries inits table for B777 thrust
23
![Page 26: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/26.jpg)
More About Kinematic Predictor
For “what-if” tool with data linkMight only consider changing Vc and horizontal trajectoryOnly need to assume STOD is linear in VcOnly need to estimate one coefficient
To fill in predicted trajectory between STOD and meter fixKinematic approach: straight line might be better thancurrent predictions with 10 nmi error in STODKinetic approach: modify W/(T − D) so that integratorgives STOD close to desired value
Replace with constantMultiply by constantAdd constant. . .
24
![Page 27: Prediction of Top of Descent Location for Idle-thrust Descents · 2011. 6. 6. · Analyzed trajectories from NASA predictor to develop the polynomial approximations Test matrix with](https://reader035.fdocuments.in/reader035/viewer/2022071217/604b59206b6a1a4563109851/html5/thumbnails/27.jpg)
Conclusions
Need to improve prediction of vertical profile to enablefuel-efficient descents in congested airspaceLargest source of error is difference in W/(T − D)between FMS and ground predictorTOD location can be approximated well by a simplefunction of hcrz,Vc ,hfix,Vfix,WThese approximations might guide research to improve thepredictor
25