Transcript
AIRCRAFT DESIGN WITH ACTIVE LOAD ALLEVIATION AND
NATURAL LAMINAR FLOW
A DISSERTATION
SUBMITTED TO THE DEPARTMENT OF AERONAUTICS &
ASTRONAUTICS
AND THE COMMITTEE ON GRADUATE STUDIES
OF STANFORD UNIVERSITY
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
Jia Xu
March 2012
http://creativecommons.org/licenses/bync/3.0/us/
This dissertation is online at: http://purl.stanford.edu/hz528zb1688
© 2012 by Jia Xu. All Rights Reserved.
Redistributed by Stanford University under license with the author.
This work is licensed under a Creative Commons Attribution
Noncommercial 3.0 United States License.
ii
I certify that I have read this dissertation and that, in my opinion, it is fully adequate
in scope and quality as a dissertation for the degree of Doctor of Philosophy.
Ilan Kroo, Primary Adviser
I certify that I have read this dissertation and that, in my opinion, it is fully adequate
in scope and quality as a dissertation for the degree of Doctor of Philosophy.
Juan Alonso
I certify that I have read this dissertation and that, in my opinion, it is fully adequate
in scope and quality as a dissertation for the degree of Doctor of Philosophy.
Antony Jameson
Approved for the Stanford University Committee on Graduate Studies.
Patricia J. Gumport, Vice Provost Graduate Education
This signature page was generated electronically upon submission of this dissertation in
electronic format. An original signed hard copy of the signature page is on file in
University Archives.
iii
Abstract
In this thesis we incorporate maneuver load alleviation (MLA), gust load alleviation
(GLA), and natural laminar ﬂow (NLF) into aircraft conceptual design. While existing
conceptual design frameworks tend to reduce the impact of these technologies to
empirical weight and drag corrections, the present work uses physicsbased methods
to capture the dynamic interplay among natural laminar ﬂow and load alleviation.
The results demonstrate that the simultaneous application of MLA and GLA can
tilt the balance of the transonic Machsweepthickness (MT) trade in favor of high
aspect ratio, lowsweep natural laminar ﬂow wings. A minimum cost turbulent aircraft
designed concurrently with MLA and GLA control systems can achieve a signiﬁcant
10% reduction in fuel burn and 3.4% reduction in cost relative to a baseline design
without load control. The fuel and cost savings grow to 15% and 5% respectively when
we introduce natural laminar ﬂow into the design process. Sensitivity studies conﬁrm
that the control and actuator requirements of eective active load alleviation are
consistent with the performance parameters of modern aircraft. Results also suggest
that the combination of aggressive active load control and lowsweep NLF wing can be
a viable alternative to a 3D NLF wing design or complex active laminar ﬂow control
(LFC) schemes. Finally, the aeroservoelastic conceptual design framework developed
in this thesis can serve as a platform for assessing future aircraft conﬁgurations and
operational paradigms aimed at reducing aircraft fuel consumption and environmental
impact.
iv
This dissertation is dedicated to my parents Sarah and Yan;
and to my loving wife, Donna
v
Acknowledgments
My deepest gratitude goes to my advisor, Professor Ilan Kroo, who has taught me
by example to seek out interesting questions and pursue them with rigor, intensity
and integrity. I shall miss the precious ahha moments in our conversations about
research and aircraft design
I would like to thank my committee members Professor Jameson and Professor Alonso.
I shall miss my discussions with Professor Jameson on all things airplane. It was my
honor and pleasure to be his course assistant in the wellloved Case Studies in Aircraft
Design. Professor Alonso has always been there with incisive comments and timely
encouragement. I am deeply grateful for the long discussions on both research and
career paths. It is also entirely possible that I only learned aerodynamics by working
with him on AA200B.
I want to thank Dr. Steve Smith for serving on my oral committee and for his
leadership and insights in the NASA NRA that ultimately led to this thesis. Professor
David Freyberg responded enthusiastically to my lastminute request for an oral
examination chair. I am grateful for his time and for his questions and perspectives
in the examinations.
I am deeply indebted to the members of the Aircraft Design Group. Most of all I
thank Tristan Flanzer, Andrew Ning, Geo Bower and Emily Schwartz. The FYI
team eort was a highlight of my years at Stanford. I am grateful and proud to
have you all as friends. While we were cruelly robbed of our 30,000 e prize money,
what I cherish in its place are the priceless adventures and laughters – I will always
vi
have Paris with my friends. I reserve a very special thanks to Tristan and Elyssa, for
feeding me, for listening, and for being such awesome human beings. My best wishes
for the two of you in all of life’s journeys.
My experience at Stanford would be rendered incomplete – perhaps all too literally
– without the words of wisdom and encouragement from Mathias Wintzer and Sara
Smoot. I shall miss our long conversations. The same is true of former ADG members
Peter Sturdza, Dev Rajnarayan and Brian Roth. And many thanks go to Alex Haas
and Alex Stoll for the enlightening discussions.
A special thanks Aero/Astro alum Prasun Bansal for his joviality, hospitality, and for
his long, arduous journey across the Himalayas (by Boeing 777) to my wedding.
I am indebted to the miracle workers in the Aero/Astro oce. I want to give a big
thanks to Jay Subramanian and Robin Murphy for their patience with my consistent
procrastinations on all matters paperwork and deadline. I thank Ralph Levine, the
departmental manager, for his constant encouragements, and for lunch.
I am grateful for the generous support from the National Science Foundation, the
NASA Subsonic Fixed Wing Program and Airbus. I owe much to mentors and ad
vocates beyond Stanford: Professor Jewel Barlow at the University of Maryland,
Professors P.K.Yeung, Jerry Seitzman and Carol Senf at Georgia Tech, and Professor
Christopher Coker at the LSE. I am forever indebted to the Marshall Aid Commemo
ration Commission for the opportunity of a lifetime to study in the UK.
Most importantly, none of this would have been possible without the unconditional
love and tireless patience of my parents. My dream may have be an impossible one
without their courage to start life anew in this once foreign land. And they, more than
anyone else, have had to endure too many Christmases, thanksgivings and Chinese
New Years without their son by their side.
Finally, I could not have walked this far without the constant, enveloping love of
my dear wife Donna. And the journey would be rendered meaningless without her.
Thanks to Donna I live with the joy and anticipation of a soontobe father. Why
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built airplanes if not to see the faces of our loved ones that much faster; why travail
in life if not to see the same people made happy and safe. Finally, it bears mention
that this thesis would not be complete without Donna’s patience, encouragements,
warm hugs, and her timely realization that the deadline for thesis submission is in
fact in two weeks.
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Contents
Abstract iv
v
Acknowledgments vi
1 Introduction 7
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Natural Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Maneuver Load Alleviation . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4 Gust Load Alleviation . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.5 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Design Framework 15
2.1 Aircraft Parameterization . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Mission Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Wing Design 20
3.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Aerodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 High Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.5 Inverse Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5.1 Pressure Distribution . . . . . . . . . . . . . . . . . . . . . . . 29
ix
3.5.2 Airfoil Geometry . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.3 Boundary Layer Solution . . . . . . . . . . . . . . . . . . . . . 35
4 Active Load Alleviation 38
4.1 MLA and GLA Parameterization . . . . . . . . . . . . . . . . . . . . 38
4.2 Maneuver Load Alleviation . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Gust Load Alleviation . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.1 GLA Parameterization . . . . . . . . . . . . . . . . . . . . . . 41
4.3.2 Gust Load Design Criteria . . . . . . . . . . . . . . . . . . . . 42
4.3.3 Gust Encounter Simulation . . . . . . . . . . . . . . . . . . . 46
4.3.4 Structural Dynamics . . . . . . . . . . . . . . . . . . . . . . . 47
5 Design Studies 54
5.1 Optimizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2 Baseline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.4 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.5 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6 Results 60
6.1 Turbulent Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.1.1 Point Optimizations . . . . . . . . . . . . . . . . . . . . . . . 61
6.1.2 Mach Number Sweeps . . . . . . . . . . . . . . . . . . . . . . 68
6.2 Laminar Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.1 Point Optimizations . . . . . . . . . . . . . . . . . . . . . . . 70
6.2.2 Mach Number Sweeps . . . . . . . . . . . . . . . . . . . . . . 77
6.3 Turbulent and Laminar Comparison . . . . . . . . . . . . . . . . . . . 78
7 Sensitivity Studies 81
7.1 NLF Wing Sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2 MLA and GLA Control Surface Deﬂection . . . . . . . . . . . . . . . 85
7.3 GLA Control Surface Bandwidth . . . . . . . . . . . . . . . . . . . . 87
x
7.4 GLA with Only Ailerons . . . . . . . . . . . . . . . . . . . . . . . . . 88
7.5 Lower Surface Laminar Flow . . . . . . . . . . . . . . . . . . . . . . . 90
7.6 Gate Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8 Conclusions and Future Work 98
A Airfoil Inverse Design 101
B Numerical Solution of SecondOrder ODEs 105
C Cost Model 107
C.1 Direct Operating Cost . . . . . . . . . . . . . . . . . . . . . . . . . . 108
C.1.1 Fuel Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
C.1.2 Pilot Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
C.1.3 Depreciation and Insurance Costs . . . . . . . . . . . . . . . . 109
C.1.4 Maintenance Cost . . . . . . . . . . . . . . . . . . . . . . . . . 110
C.2 Indirect Operating Cost . . . . . . . . . . . . . . . . . . . . . . . . . 111
Bibliography 113
xi
List of Tables
2.1 Engine parameters for the PW2037 (reference engine deck) and CFM
567B27 turbofans. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
5.1 Key cost assumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2 Summary of all optimization variables. . . . . . . . . . . . . . . . . . 57
5.3 Summary of all optimization constraints. . . . . . . . . . . . . . . . . 59
6.1 Summary of optimized Mach 0.78 turbulent aircraft design parameters. 62
6.2 Summary of Mach 0.78 high sweep NLF aircraft parameters. . . . . . 72
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List of Figures
1.1 The Boeing Sugar Volt – part of the NASA N+3 advanced subsonic
transport study.
1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Representative airfoil geometries and C
p
distributions. . . . . . . . . . 10
1.3 A plot of NLF transition as a function of wing sweep based on the
results of historical laminar ﬂow experiments.
2
. . . . . . . . . . . . . 10
1.4 An illustration of typical compressibility drag rise trend as a function
of streamwise t/c and wing sweep. . . . . . . . . . . . . . . . . . . . . 11
1.5 Lift distribution for conventional and MLA aircraft at the same ma
neuver load factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 The design mission proﬁle and ﬂight conditions. . . . . . . . . . . . . 18
3.1 The wing break sections that deﬁne the planform and twist. The
innermost section (÷ = 0) corresponds to the wing root. The next
section deﬁnes the wingfuselage intersection. . . . . . . . . . . . . . . 21
3.2 The wing structure box conﬁguration. . . . . . . . . . . . . . . . . . . 21
3.3 The parameterization of the wing box cross section. . . . . . . . . . . 22
3.4 An illustration of wing aerodynamic control points and C
lmax
constraints. 23
3.5 Section C
lmax
as a function of t/c and Mach number. The airfoil is in
its clean conﬁguration and the chord Reynolds number is ﬁxed at 20
million. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.6 Section C
lmax
as a function of t/c and wing sweep in degrees. The
airfoil is in its clean conﬁguration and the chord Reynolds number is
ﬁxed at 20 million. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
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3.7 Section C
lmax
as a function of the t/c and ﬂap deﬂection in degrees.
The Reynolds number is ﬁxed at 20 million. . . . . . . . . . . . . . . 26
3.8 Wing static stress constraints. . . . . . . . . . . . . . . . . . . . . . . 27
3.9 The aileron reversal constraint placed on the outboard deﬂections ”
4
. 28
3.10 The wing breakpoints with inverse design sections highlighted. The
blue sections can be designed for NLF while the red wingfuselage inter
section is always assumed to be turbulent to account for the dominant
role of attachment line instabilities. . . . . . . . . . . . . . . . . . . . 29
3.11 An illustration of the airfoil C
p
parameterization with important pres
sure features labeled. . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.12 The inverse deisgn C
p
parametrization with the pressure variables la
beled in blue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.13 Example wing section pressure distributions at selected spanwise loca
tions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.14 Example wing section geometry at selected spanwise locations. . . . . 35
4.1 The wing control surfaces are deﬁned by the wing break sections. . . 39
4.2 The wing static and dynamic stress design constraints are collocated
with yposition of the aerodynamic control points. . . . . . . . . . . . 41
4.3 The 1–Cosine gust. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.4 Positive 1–Cosine vertical gust ﬁelds at dierent gust gradient lengths H. 44
4.5 Positive 1–Cosine vertical gust ﬁelds at dierent gust encounter alti
tudes z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.6 Aircraft dynamics through gust encounters. . . . . . . . . . . . . . . 47
4.7 Control surface deﬂection time history for each trailing edge channel. 48
4.8 Control deﬂection rate laminar MLA+GLA design. . . . . . . . . . . 48
4.9 Dynamic wing stresse constraints. . . . . . . . . . . . . . . . . . . . . 53
5.1 Examples of the highsweep turbulent and lowsweep NLF aircraft
families. The transition fronts are shown in green. . . . . . . . . . . . 55
xiv
6.1 The optimized Mach 0.78 turbulent aircraft with dierent levels of
active load alleviation. . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.2 A comparison of the optimized turbulent aircraft. The performance
metrics and conﬁguration parameters are normalized against the corre
sponding values of the Mach 0.78 turbulent baseline. . . . . . . . . . 63
6.3 A comparison of the optimized turbulent wing planforms. All parame
ters are normalized by their values in the Mach 0.78 turbulent baseline. 65
6.4 Turbulent wing and skin thickness distributions. . . . . . . . . . . . . 65
6.5 Comparisons of the turbulent maneuver C
l
(solid lines) and C
lmax
(dashed lines) distributions. . . . . . . . . . . . . . . . . . . . . . . . 66
6.6 Maneuver and gust bending stresses for the optimized turbulent designs
at Mach 0.78. The wing bending stresses ‡ are normalized by the
allowable stress ‡
a
. The gust stresses represent the maximum values
encounter by each wing section at all gust gradient lengths. . . . . . . 67
6.7 A plot of the relative operating cost of optimized turbulent designs as
functions of Mach number. Each point represents an optimized aircraft.
The performance metrics are normalized to the Mach 0.78 baseline. . 69
6.8 A plot of the relative fuel burn of optimized turbulent designs as func
tions of Mach number. Each point represents an optimized aircraft.
The performance metrics are normalized to the Mach 0.78 baseline. . 70
6.9 The optimized Mach 0.78 turbulent aircraft with dierent levels of
active load alleviation. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.10 A comparison of the optimized laminar aircraft. The performance
metrics and conﬁguration parameters are normalized by those of the
Mach 0.78 turbulent baseline. . . . . . . . . . . . . . . . . . . . . . . 72
6.11 A comparison of the optimized laminar wing planforms. All parameters
are normalized by their values in the Mach 0.78 turbulent baseline. . 74
6.12 Laminar wing and skin thickness distributions. . . . . . . . . . . . . . 74
6.13 Laminar wing C
l
and C
lmax
distributions. . . . . . . . . . . . . . . . . 75
xv
6.14 Maneuver and gust bending stresses for the optimized laminar designs
at Mach 0.78. The wing bending stresses ‡ are normalized by the
allowable stress ‡
a
. The gust stresses represent the maximum values
encounter by each wing section at all gust gradient lengths. . . . . . . 76
6.15 A plot of the relative cost of optimized laminar designs as functions
of Mach number. Each point represents an optimized aircraft. The
performance metrics are normalized to the Mach 0.78 baseline. . . . . 77
6.16 A plot of the relative fuel burn of optimized laminar designs as functions
of Mach number. Each point represents an optimized aircraft. The
performance metrics are normalized to the Mach 0.78 baseline. . . . . 78
6.17 A comparison of the optimized MLA+GLA aircraft parameters. The
displayed parameters are normalized by the value of the Mach 0.78
turbulent baseline. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.18 Relative cost of turbulent and laminar designs as functions of Mach
number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.19 Relative fuel burn of turbulent and laminar designs as functions of
Mach number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
7.1 Optimized highsweep NLF design at Mach 0.78. . . . . . . . . . . . . 82
7.2 Comparison of highsweep laminar25 aircraft. . . . . . . . . . . . . . 83
7.3 Comparison of highsweep laminar25 MLA+GLA aircraft. . . . . . . 84
7.4 Optimized aircraft cost as functions of Mach number. . . . . . . . . . 84
7.5 Optimized aircraft fuel burn as functions of Mach number. . . . . . . 85
7.6 Optimized MLA+GLA aircraft costs as functions of maximum load
alleviation control surface deﬂections. . . . . . . . . . . . . . . . . . . 86
7.7 Optimized MLA+GLA aircraft fuel burns as functions of maximum
load alleviation control surface deﬂections. . . . . . . . . . . . . . . . 86
7.8 MLA+GLA aircraft cost trends as functions of maximum allowable
load alleviation control surface deﬂection rates. . . . . . . . . . . . . 87
7.9 MLA+GLA aircraft fuel burn trends as functions of maximum allowable
load alleviation control surface deﬂection rates. . . . . . . . . . . . . 88
xvi
7.10 GLA using only outboard control surfaces. . . . . . . . . . . . . . . . 89
7.11 Laminar MLA+GLA aircraft cost trends with dierent GLA control
allocations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.12 Laminar MLA+GLA aircraft fuel burn trends with dierent GLA con
trol allocations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
7.13 Comparison of the MLA+GLA aircraft designed with turbulent and
laminar bottom surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.14 Comparison of the MLA+GLA aircraft designed with turbulent and
laminar bottom surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.15 Cost trends for the Laminar MLA+GLA aircraft with turbulent and
laminar bottom surfaces. The results of the Turbulent MLA+GLA are
included for reference. . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.16 Duel burn trends for the Laminar MLA+GLA aircraft with turbulent
and laminar bottom surfaces. The results of the Turbulent MLA+GLA
are included for reference. . . . . . . . . . . . . . . . . . . . . . . . . 92
7.17 A comparison of gateconstrained aircraft.(b<120 ft) . . . . . . . . . 93
7.18 A comparison of the turbulent aircraft designed with and without gate
constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.19 A comparison of the Turbulent MLA+GLA aircraft designed with and
without gate constraints. . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.20 A comparison of the Laminar MLA+GLA aircraft designed with and
without gate constraints. . . . . . . . . . . . . . . . . . . . . . . . . . 96
A.1 Example airfoil optimization geometry, C
p
and boundary layer momen
tum thickness results. . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
A.2 Optimized airfoil transition and C
dp
as a function of C
l
and Mach
Œ
.
The section t/c and Re
c
are ﬁxed at 9% and 20 million respectively. . 103
A.3 Optimized airfoil transition and drag as a function of t/c and Mach
Œ
.
The C
l
and Re
c
are ﬁxed at 0.4 and 20 million respectively. . . . . . . 104
A.4 Optimized airfoil transition and drag as a function of Re
c
and Mach
Œ
.
The C
l
and t/c are ﬁxed at 0.4 and 9% respectively. . . . . . . . . . . 104
xvii
Nomenclature
x
aircraft
Aircraft design variables
x
CG
Vector of longitudinal centerofgravity positions for all ﬂight conditions
x
GLA
GLA design variables
x
mission
Mission variables
x
MLA
MLA design variables
x
pressure
Pressure design variables
x
transition
Transition design variables
x
wing
Wing design variables
¯
C Modal damping matrix
¯
K Modal stiness matrix
¯
M Modal mass matrix
¯
Q Orthonormal basis for modal decomposition
C Global damping matrix
K Global stiness matrix
L Triangular Cholesky factorization matrix
M
e
Element mass matrix
M Global mass matrix
u Generalized displacement
dCp
dx l
Lower surface airfoil pressure gradient
dCp
dx u
Upper surface airfoil pressure gradient
D
T
Dragtothrust ratio
Ÿ
if
Inﬂation index
1
2
‹ Kinematic viscosity
c Mean aerodynamic chord
C
p
Canonical pressure coecient
˜
C
p
l
Airfoil lower surface C
p
in sweeptaper system
˜
C
p
u
Airfoil upper surface C
p
in sweeptaper system
˜ u
l
Airfoil lower surface velocity in sweeptaper system
˜ u
u
Airfoil upper surface velocity in sweeptaper system
A Element cross section area
AR Trapezoidal wing aspect ratio
c
a
Airplane cost (excluding engines)
c
a
The airplane cost
c
e
Engine cost
c
ce
engine material cost per ﬂight hour
c
he
engine material cost per ﬂight cycle
c
tic
Estimated ticket cost
D
a
Depreciation period (years)
E Young’s modulus
F Generalized forces
f Modal forcing
F
g
Gust alleviation factor
H Boundary layer shape factor
h Gust gradient length
h
c
Second segment climb gradient
H
te
Shape factor at trailing edge
I Crosssection inertia
I
ra
Insurance rate
K
e
Element stiness matrix
k
d
GLA derivative gain
k
p
GLA proportional gain
L Element length
l
land
Landing ﬁeld length
3
l
to
Balanced takeo ﬁeld length
LF Load factor)
M
dd
Airfoil drag divergence Mach number
M
land
Landing Mach number
M
to
Takeo Mach number
n Load factor
N
e
Number of engines
N
pax
Passenger count
p
fuel
Price of aviation fuel ($/gal)
p
oil
Price of lubrication oil ($/lb)
R Aircraft mission range
R
req
Required mission range
RF Range factor
S Stratford concavity parameter
s Airfoil surface coordinate
S
h
Horizontal tail area
S
u
Upper surface Stratford concavity parameter
S
ref
Trapezoidal wing reference area
t(x) Airfoil thickness distribution
T
0
Sealevel static engine thrust
T
m
Air and ground maneuver time
t
s
Wing box skin gauge thickness
t
w
Wing box web gauge thickness
t
ce
Labor manhours per ﬂight hour
T
cl
Climb time
t
he
Labor manhours per ﬂight cycle
t
inv
Airfoil thickness distribution from the inverse solution
TSFC Thrust speciﬁc fuel consumption
U
a
Annual utilization
u
e
External velocity
u
r
Velocity at the start of recovery
4
U
ds
1–Cosine design gust amplitude
U
ref
Gust reference vertical design velocity
u
te
Velocity at trailing edge
V Cruise velocity
V
block
Block speed
W
e
Engine dry weight
W
f
Final cruise weight
w
g
Gust vertical velocity
W
i
Initial cruise weight
W
MLW
Maximum landing weight (lb)
W
MTOW
Maximum takeo weight
W
MZFW
Maximum zerofuel weight
x Eective boundary layer length
x
a
Longitudinal position of aft spar in the airfoil system
x
e
Longitudinal position of elastic axis in the airfoil system
x
f
Longitudinal position of forward spar in the airfoil system
x
t
Longitudinal location of transition in aircraft system
x
mg
Longitudinal position of main landing gear
x
ng
Longitudinal position of the nose gear
x
root
Longitudinal position of wing root
x
TE
Airfoil trailing edge
z(x) Airfoil camber distribution
z
f
Final cruise altitude
z
i
Initial cruise altitude
z
max
Maximum operational altitude (ft)
Re
x
Eective local Reynolds number
◊
te
Momentum thickness at trailing edge
C
Lh
Horizontal tail lift coecient
C
linv
Airfoil C
l
from the inverse
C
lmax
Section maximum lift coecient
C
Mac
Pitching moment about aerodynamic center
5
L
e”
4
Elastic wing pitch moment due to aileron deﬂection
L
r”
4
Rigid wing pitch moment due to aileron deﬂection
Re
x
Local Reynolds number
Re
exp 9
Local transition Reynolds number as predicted by e
9
ﬁts
Re
e
9 Transition Re
x
as predicted by e
9
ﬁts.
RF
f
Final cruise range factor
RF
i
Initial cruise range factor
R
L
Labor rate $/hr
t
ha
Labor manhours per ﬂight hour
C
Lhmax
Maximum horizontal tail lift coecient
C
p
LEl
Lower surface airfoil leading edge C
p
C
p
LEu
Upper surface airfoil leading edge C
p
AIC Aerodynamic inﬂuence coecient matrix
TSFC
0
Sealevel static TSFC
–
0
Zerolift angle of attack
–
i
Local angle of attack at panel i
— PrandtlGlauert correction factor
” Flap deﬂections in between breakpoints
”
i
Control surface deﬂection for channel i
c Wing trailing edge extension ratio
”
s
Slat deﬂection
÷ Dimensionless span ÷ = y/(b/2)
d”
i
dt
Control surface deﬂection rate for channel i
i
Circulation at panel i
⁄ Trapezoidal wing taper ratio
1/4
Trapezoidal wing quarterchord sweep
‹ Kinematic viscosity
Ê Wing natural frequency
ﬂ Element mass density
‡ Bending stress
· Shear stress
6
◊ Wing jig twist
˜ ·
”
4
Wing torque due to aileron deﬂection
’ Damping ratio
”
land
Landing ﬂap deﬂection
”
to
Takeo ﬂap deﬂection
‡
a
Allowable bending stress
·
a
Allowable shear stress
Chapter 1
Introduction
1.1 Motivation
The classical Breguet Range equation decomposes aircraft range and hence, cruise
eciency into propulsive (TSFC), structural (W
i
/W
f
) and aerodynamic (L/D) com
ponents:
R =
3
L
D
4
V
TSFC
ln
A
W
i
W
f
B
(1.1)
One can certainly improve the individual terms in the range equation: Historically, the
most signiﬁcant improvements in jet aircraft eciency have come from improvements
in the propulsive term associated with the development of highbypass turbofan
engines. The expanding use of highstrength composites can increase the weight
fraction. And conﬁguration changes such as increased wingspan can lead to improved
L/D. However, the integrated nature of the aircraft design means that few substantive
conﬁguration changes can be made without incurring some multidisciplinary tradeos.
Increasing the wingspan for example also increases the wing weight.
Yet the same integrated nature of aircraft design is also an opportunity: signiﬁcant
improvements can come from conﬁgurations that can simultaneously exploit aerody
namic, control and structural advances to improve eciency. The Boeing/NASA Sugar
7
CHAPTER 1. INTRODUCTION 8
Volt pictured in ﬁg. 1.1 is one such multidisciplinary design concept. Developed as part
of the NASA N+3 studies to envision future airliners, the Sugar Volt deploy a slew of
advanced technologies from hybridelectric open rotor engines to trussbraced wings
(TBW) to greatly improve cruise eciency and enviromental performance.
1
Figure 1.1. The Boeing Sugar Volt – part of the NASA N+3 advanced subsonic
transport study.
1
The focus of this thesis is on the Sugar Volt’s combination of extreme span and
extensive natural laminar ﬂow (NLF) – all made possible by the aggressive application
of maneuver (MLA) and gust load alleviation (GLA). The combination of these
technologies holds the potential to greatly improve both the weight and aerodynamic
terms in the Breguet equation. However, the potential gains from a complex and highly
coupled design like the Sugar Volt can be dicult to quantify. Conceptual design
tools typically reduce laminar ﬂow and active load alleviation to empirical technology
factors applied on weight and drag.
1,3,4
The Sugar Volt design for example assumes
that a properly designed active load alleviation system can reduce the wing weight
by 25%. It also assumes that the wing transition Reynolds number lies somewhere
between 15 to 17 million irrespective of the pressure distribution over the wing.
1
An empirical approach however can miss important tradeos and constraints that
drive the design: the eectiveness of load alleviation systems can be constrained by
maximum lift, wing aeroelastic response and control power. And the design of a
transonic NLF wing is driven by a balancing act to control proﬁle drag, structural
CHAPTER 1. INTRODUCTION 9
weight and compressibility eects.
The objective of this research is to develop a new design framework that leverage
physicbased methods to incorporate active load alleviation and natural laminar ﬂow
into conceptual design.
1.2 Natural Laminar Flow
Viscous drag accounts for upwards of half of the total aircraft drag in cruise. Achieving
extensive laminar ﬂow over the wings net signiﬁcant drag reductions. One way to
maintain laminar ﬂow at high Reynolds numbers is to employ active laminar ﬂow
control (LFC) to reshape the pressure distribution, reenergize the boundary layer and
delay ﬂow transition. The notional geometry and pressure distribution of an active
laminar ﬂow control airfoil is shown in ﬁg. 1.2. Active ﬂow control systems however
can incur signiﬁcant weight, maintenance and power penalties.
An alternative to active LFC is to design the wing pressure distribution to passively
stabilize the boundary layer, which gives rise to natural laminar ﬂow (NLF). There
is a substantial body of literature that aims to solve the NLF wing design problem
using high ﬁdelity tools.
5–9
However, these methods often require detailed deﬁnitions
of the wing geometry, which may not be practical in the early stages of design. This
has led aircraft designers to use empirical, designoriented ﬁts of ﬂow transition in
aircraft design problems.
4,10
Yet the impact of laminar ﬂow can be fundamental. And laminar ﬂow wing design
should be formally integrated into conceptual design. The potential fuel savings from
airliners designed with NLF wings have been variously quoted as somewhere between
512%.
11–13
The extent of the fuel savings is subject to complex multidisciplinary
tradeos. The most important of which involves wing sweep.
In two dimensions an NLF airfoil can be designed with extended regions of ﬂow
acceleration to suppress streamwise TollmienSchlichting (TS) instabilities. In the
CHAPTER 1. INTRODUCTION 10
(a) Turbulent
C
p
Suclion
x
l
x
l
(b) Active laminar ﬂow control
(c) Natural laminar ﬂow (NLF)
Figure 1.2. Representative airfoil geometries and C
p
distributions.
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 35
S
w
e
e
p
(
D
e
g
)
Transition Reynolds Number (Million)
NLF Region
Figure 1.3. A plot of NLF transition as a function of wing sweep based on the results
of historical laminar ﬂow experiments.
2
CHAPTER 1. INTRODUCTION 11
case of swept wings there exists a fundamental tradeo between the need to stabilize
the streamwise and crossﬂow (CF) boundary layers: while ﬂow acceleration stabilizes
the streamwise boundary layer, it has the opposite, destabilizing eect on crossﬂow.
The implication is that extensive natural laminar ﬂow becomes progressively more
dicult to maintain at higher wing sweep. Indeed ﬂight tests demonstrate that at
a sweep of 10
¶
laminar ﬂow can be reasonably achieved over 50% of a NLF wing.
However, if sweep is increased to 25
¶
then the laminar region is reduced to just
20% of the wing area.
11
The trend of reduced laminar ﬂow with increasing sweep is
also demonstrated by the complication of four decades of NLF ﬂight test results in
ﬁg. 1.3.
2
0.06 0.07 0.08 0.09 0.1
0
5
10
15
20
Mach=0.78, C
l
=0.4
Airfoil t/c
C
o
m
p
r
e
s
s
i
b
i
l
i
t
y
D
r
a
g
(
C
o
u
n
t
s
)
Λ = 25 deg
Λ = 10 deg
Figure 1.4. An illustration of typical compressibility drag rise trend as a function
of streamwise t/c and wing sweep.
One could certainly reduce the sweep to render wings more compatible with NLF.
However, unsweeping the wing at transonic speed carries steep penalties.
14–16
A typical
plot of transonic drag rise as a function of sweep and thickness in ﬁg. 1.4 shows that
an unswept wing has to be made much thinner than its swept counterpart to prevent
drag divergence. The structural consequences of reducing wing sweep and thickness
CHAPTER 1. INTRODUCTION 12
can be illustrated with the simple wing weight relationship of Cleveland:
17
W
wing
s
Ã
⁄
M
x
t
dy Ã
b
3
(t/c) cos
2
S
ref
The equation shows that although unsweeping the wing may have a small, positive
eect on structural eciency, the eect of the cos
2
() term is easily overshadowed by
the linear weight increase with reduced t/c. A thin, unswept NLF wing can therefore
weigh substantially more than its turbulent counterpart. And the weight penalties
can wipe out the drag savings.
One way to cope with the aerostructural consequences of unsweep is to simply slow
down. Indeed, most NLF design concepts are designed to cruise at Mach 0.70 to
0.75. The Sugar Volt for example is designed to cruise at Mach 0.71. However, in
the absence of variable cycle technology, reduced cruise speed can negatively impact
engine eciency. And at today’s fuel prices, slowing down can incur utilization and
cost penalties. Moreover, air trac control (ATC) could also be complicated by the
presence of slower aircraft.
The alternative to slowing down is to reduce the weight penalties from a thin wing.
Active load alleviation is one such technology that can tilt the balance of the Mach
sweepthickness (MT) trade in favor of lowsweep NLF wings.
1.3 Maneuver Load Alleviation
Maneuver load alleviation systems respond to pseudostatic maneuvers commanded by
the pilot. Figure 1.5 shows two aircraft undergoing symmetric maneuver at the same
load factor. The dierence is that the MLAequipped aircraft can use coordinated
control deﬂections to concentrate lift inboard and reduce the wing bending moment.
This allows the wing of the MLAequipped aircraft to be made lighter, or longer and
thinner at the same weight.
CHAPTER 1. INTRODUCTION 13
(a) Conventional (b) MLA
Figure 1.5. Lift distribution for conventional and MLA aircraft at the same maneu
ver load factor.
MLA has been the subject of numerous studies. Results suggest that MLA can
achieve span increases of 1015% and drag savings of 813% at ﬁxed wing weight.
3,18–21
Experimental MLA systems have been ﬂight tested under the NASA Mission Adaptive
Wing (MAW) and Active Flexible Wing (AFW) programs. And production MLA
systems have been integrated into commercial aircraft like the Airbus A320, A330.
22,23
However, the full beneﬁt from load control can only be realized by incorporating the
technology early on in the design process. The goal of the present research is to
formally incorporate MLA into conceptual design.
1.4 Gust Load Alleviation
As MLA relaxes the structural design constraints imposed by maneuver loads, dynamic
gust loads can becomes critical design conditions.
24
The implications are twofold: 1)
gust loads should be considered when evaluating the eectiveness of MLA systems
and 2) a gust load alleviation system is likely needed to realize the full beneﬁts of
MLA.
GLA responds to dynamic, unanticipated atmospheric turbulence. Unlike the MLA
system, eectiveness of GLA systems may be fundamentally constrained by sensor and
actuator bandwidths. The close interdependence between aircraft conﬁguration and
gust response complicates the process of GLA control law design. Previous studies
have sought to address components of the integrated GLA design problem: 1) how to
CHAPTER 1. INTRODUCTION 14
ﬁnd the worstcase gust for a given airplane,
25–29
2) how to design aircraft structure
to sustain a given gust
30–33
and 3) how to design a GLA control systems for a given
airplane.
34–36
The more recent work of Fidkowski et al.
37
surveys stochastic gust
design criteria and assesses the sensitivities of gust load to modeling assumptions.
The present work extends these previous research and address the integrated problem
of how to simultaneously design an aircraft with its GLA control system.
1.5 Organization
In chapter 2 we introduce the design framework, which extends our previous work on
MLA and gust load alleviation.
38
In chapters 3 and 4 we develop new aerodynamic
and structure analysis tools to incorporate laminar ﬂow and active load alleviation
into conceptual design. Next, the aeroservoelastic design framework is applied to a
series of design studies in chapter 5. This is followed by a discussion of the results in
chapter 6. Finally, we examine the performance sensitivities of the optimized aircraft
to changes in critical design assumptions in chapter 7.
Chapter 2
Design Framework
The aeroservoelastic design framework developed in this thesis is based on the Program
for Aircraft Synthesis Studies (PASS).
39
PASS in its basic form leverages fast, semi
empirical models to capture aircraft performance sensitivities to conﬁguration and
mission variables. In this chapter we introduce the components of the PASS mission
analysis framework that are most relevant to load alleviation and NLF design. A
more detailed discussion of the basic PASS framework can be found in Kroo.
39
2.1 Aircraft Parameterization
The design framework is geared toward the analysis of "conventional" aircraft conﬁgu
rations characterized discrete fuselage, empennage and wing components. The wing
parameterization and design are detailed in the next chapter.
The aircraft fuselage dimensions are dictated by the seating arrangement and passenger
count, which are ﬁxed for a given optimization. The horizontal tail is parameterized
by its area ratio relative to the wing S
h
/S
ref
. The longitudinal position of the wing
root x
root
is an important parameter for trim, stability and landing gear integration.
15
CHAPTER 2. DESIGN FRAMEWORK 16
The set of aircraft optimization variables can be summarized as:
x
aircraft
=
C
S
h
S
ref
, x
root
, W
MTOW
, W
MZFW
, T
0
, x
mg
D
The engine weight and dimensions are sized by the sea level static thrust variable
T
0
. The thrust and fuel consumption at a given ﬂight condition are computed using a
rubberized PW2037 engine deck.
39
The sealevel static thrusttoweight ratio and fuel
consumption (TSFC) are scaled to match the more modern CFM567B27 turbofan
used on the comparable Boeing 737800. The characteristics of the reference PW
2037 engine and the CFM567B27 used in the engine scaling are summarized in
table 2.1.
Engine TSFC
0
(lb/lbhr) W
e
(lb) T
0
(lb)
PW2037 0.326 7,160 34,250
CFM567B27 0.380 5,216 24,000
Table 2.1. Engine parameters for the PW2037 (reference engine deck) and CFM
567B27 turbofans.
A number of aircraft parameters are included as design variables to eliminate internal
iterations. For example, the values of the maximum takeo and zero fuel weights
W
MOTW
and W
MZFW
are both needed before they can be evaluated in the analysis.
Rather than relying on iterations to converge the weights, we simply include W
MOTW
and W
MZFW
as design variables and use compatibility constraints to enforce conver
gence. Similarly, the longitudinal placement of the landing gear x
mg
is a function of the
aircraft centerofgravity (CG), which is itself dependent on the landing gear position.
The aircraftlevel compatibility constraints can be summarized as follows:
x
mg
=
max (x
CG
) ≠0.08x
ng
0.92
W
MTOW
= W
MZWF
+W
fuel
+W
res
Z
_
_
^
_
_
\
Aircraft Compatibility Constraints
The weight constraint ensures that the sum of the empty weight, fuel weight and fuel
reserves W
res
adds up to the takeo weight. The landing gear compatibility constraint
CHAPTER 2. DESIGN FRAMEWORK 17
ensures that the nose carries at least 8% of the aircraft weight for traction.
2.2 Mission Analysis
We evaluate aircraft performance in the context of the representative shorthaul
mission proﬁle illustrated in ﬁg. 2.1. The mission includes takeo, climb, cruise and
approach segments. Not shown is a standard diversion reserve. The mission also
includes representative gust encounters and limit maneuvers that combine to size the
wing structure. The choice of the maneuver and gust ﬂight conditions are detailed
in chapter 4. The important mission parameters such as the initial and ﬁnal cruise
altitudes and the takeo and landing Mach numbers and ﬂap schedules are optimized
concurrently with the aircraft:
x
mission
= [z
i
, z
f
, M
to
, M
land
, ”
to
, ”
land
]
The aircraft is designed to meet the range, ﬁeld length, engineout climb gradient
and cruise thrust margin constraints summarized in eq. (2.1). The ﬁeld performance
requirements are based on published payloadrange diagrams for the Boeing 737800.
The climb gradient constraint follows from the Federal Aviation Regulations (FAR).
The cruise stage dragtothrust constraints ensure that the aircraft has sucient thrust
at altitude to sustain operational climb.
l
to
< 7,900ft, l
land
< 5,500ft, h
c
> 0.024
D
T i
< 0.88,
D
T f
< 0.88, R > 2,000nm
Z
_
_
^
_
_
\
Performance Constraints (2.1)
The computation of the climb gradient, cruise stage dragtothrust ratios and cruise
range require the aircraft drag and thrust at dierent ﬂight conditions. The available
thrust comes from the rubberized engine deck discussed in section 2.1.
39
We compute
CHAPTER 2. DESIGN FRAMEWORK 18
Finul Ciuiso, h
f
, V
f
2.óg Munouvoi
20,000 fl, V
c
Socono Sognonl ClinL
400 fl, 1.2V
s
1ukool Iolulion
S.L. V
i
Appiouch
S.L. ,1.8V
s
Iniliul Ciuiso, h
i
, V
i
1.8g Munouvoi
40,000 fl, V
c
2,000nn nission plus slunouio iosoivos
Gusl Lncounloi
10,000 fl, V
c
Gusl Lncounloi, h
i
, V
c
Gusl Lncounloi, h
f
, V
c
Figure 2.1. The design mission proﬁle and ﬂight conditions.
the fuselage and empennage parasite drag using equivalent plate area methods and
empirical shape factors.
39
We assume that the wave drag of the fuselage and tail are
negligible compared to the wing. The more wing drag buildup is discussed in detail
in chapter 3.
To approximate the eects of stepclimbs we assume a linear variation in aircraft
weight, drag and TSFC from an initial to a ﬁnal cruise state.The aircraft range R
can then be integrated as follows:
R = RF
i
≠RF
f
+
A
RF
f
≠W
f
RF
f
≠RF
i
W
f
≠W
i
B
ln
A
W
i
W
f
B
(2.2)
The aerodynamic and propulsion contributions to range are captured in the range
factor:
RF =
v
TSFC
3
L
D
4
The aircraft is subject to trim, stability and maximum lift constraints at each of the
ﬂight conditions in ﬁg. 2.1. The trim constraints consists of lift matching and tail
maximum lift components:
C
Lh
< C
Lhmax
, nW =
ﬂv
2
S
ref
C
L
2
<
Trim Constraints
CHAPTER 2. DESIGN FRAMEWORK 19
A conservative static stability margin of 10% is imposed at all ﬂight conditions to
account for aeroelastic washout in cruise, which tends to move the aerodynamic center
forward and thereby diminish the stability margin:
≠
dC
Mac
dC
L
> 0.10c
J
Stability Constraints
In addition to the ﬂight conditions outlined in the mission proﬁle we also include a
stability constraint for cruise at operational empty weight (OEW). For conventional
conﬁgurations the empty aircraft typically has the aftmost center of gravity and
is critical in stability. The liftmatching constraint enforces force balance in each
equilibrium ﬂight condition. The tail maximum lift coecient prevents tail stall.
The wing C
L
and the horizontal tail C
Lh
needed to trim the aircraft are solved from
the force and moment balance:
C
mac
≠
C
Lw
c
(x
acw
≠x
cg
) ≠
C
Lh
c
(x
ach
≠x
cg
)
S
h
S
w
= 0
C
L
= C
Lw
+C
Lh
S
h
S
w
The wing aerodynamic center x
ac
and stability derivatives such as the pitch moment
coecient C
mac
are evaluated using the Weissinger panel method. The pitch moment
includes contributions from wing twist, control surface deﬂections and the zerolift
airfoil pitch moment, which is integrated from the inverse airfoil design discussed in
more detail in section 3.5.1. Also included are the aeroelastic wing twist induced by
control surface deﬂection.
Chapter 3
Wing Design
The multitude of new design sensitivities and constraints introduced by load alleviation
and NLF call for physicsbased wing design tools. The analysis is grounded on a
detailed parameterization of the wing and structure box. A Weissinger panel method
with compressibility corrections is used to solve the aerodynamic loads and stability
derivatives. Finally, we develop a hybridinverse viscous design tool to incorporate
NLF into aircraft design.
3.1 Geometry
The wing parametrization begins with the deﬁnition of the trapezoidal planform. The
reference area S
ref
, aspect ratio AR, taper ratio ⁄ and quarterchord sweep
1/4
are all design variables. The vector of wing jig twists ◊ at the exposed breakpoints
are also subject to optimization. The trapezoidal wing is modiﬁed by trailing edge
extensions deﬁned at wing breakpoints. The extensions c are deﬁned as fractions
of the trapezoidal chord. All intermediate planform geometries and twists are linearly
interpolated.
While the design framework can accommodate an arbitrary number of wing breaks, we
20
CHAPTER 3. WING DESIGN 21
choose the six sections highlighted in ﬁg. 3.1 to deﬁne the planform. The breakpoint
positions as fractions of the semispan are held constant in the optimization.
y=y](b]2)
Fuselage WidLh
y=0.3
y=0.5
y=0.1
y=0.7
y=0
y=1
Figure 3.1. The wing break sections that deﬁne the planform and twist. The inner
most section (÷ = 0) corresponds to the wing root. The next section
deﬁnes the wingfuselage intersection.
Figure 3.2. The wing structure box conﬁguration.
The wing structural box in ﬁg. 3.2 extends from 20 to 65% of the chord. The
hexagonal wing box geometry is deﬁned by the elastic axis and forward and aft spar
heights at each breakpoint section. The skin and web thicknesses t
s
and t
w
at the
breakpoints are also optimization variables. The intermediate wing box geometries are
again interpolated. The wing loadbearing weight follows directly from the wing box
geometry and material density. However, the weight of the spars and webs represents
only a portion of the total wing weight. We establish the relationship between wing
loadbearing and total weight using the empirical ﬁt developed by Gallman,
40
which
accounts for minimum gauge eects and nonstructural weight. The wing geometry
CHAPTER 3. WING DESIGN 22
Figure 3.3. The parameterization of the wing box cross section.
design variables x
wing
can be summarized as follows:
x
wing
=
Ë
S
ref
, AR, ⁄,
1/4
, c, ◊, t(x
e
), t(x
f
), t(x
a
), t
s
, t
w
È
The wingbox geometry is fully deﬁned by the optimization variables. The winbox
is sized by the spanwise static and dynamic stress constraints in the optimization.
The resolution of the aerodynamic loads are discussed in detail in chapter 4.
3.2 Aerodynamics
We compute the wing lift distribution and stability derivatives using a modiﬁed
Weissinger method, which is a vortex lattice method (VLM) with only one chordwise
panel.
41
Each semispan is modeled using 31 skewed bound vortices centered along the
quarter chord line. The ﬂow tangency boundary conditions are enforced at control
points along the threequarterchord line. The control point arrangement is illustrated
in ﬁg. 3.4.
The linear system for the vortex strengths
i
can be written in terms of the aerody
namic inﬂuence coecient matrix and the local angle of attack –
i
:
[AIC]
i
= U
Œ
–
i
Where element AIC
ij
relates the induced downwash at control point i to the vortex
CHAPTER 3. WING DESIGN 23
C
l
(y) 0.525
The required aileron eciency of 53% at V
c
is rather conservative. The aileron
reversal limit is an operational parameter and should be investigated in more detail.
The rigid wing roll moment due to a unit aileron deﬂection can be readily solved using
the Weissinger method. To obtain the elastic wing roll moment we add the aeroelastic
twist ◊
e
to the panel method boundary conditions. The aileroninduced twist about
the elastic axis can be integrated as follows:
˜ ·
”
4
= q
⁄
b/2
˜ y
cos
3
e
c(›)
2
C
m”
4
(›)d›
˜
◊
e
=
⁄
˜ y
0
˜ ·
”
4
(›)
GJ(›)
d›
We transform the twist into the spanwise direction to obtain the modiﬁcations to
the aerodynamic boundary conditions.
CHAPTER 3. WING DESIGN 29
3.5 Inverse Design
The extent of attainable wing natural laminar ﬂow is a strong function of the pressure
distribution. We develop a hybridinverse viscous design tool to link ﬂow transition
and proﬁle drag to the wing geometry and lift distribution. In the inverse approach,
we ﬁrst deﬁne the pressure distribution and then solve for the corresponding geometry.
The pressure distribution and geometry are then combined with integral methods
to solve for the boundary layer development, transition location and ultimately, the
proﬁle drag. The method is inspired by the work of Liebeck.
45
It can also be
understood as a smooth, 2D analogue of the more involved 3D viscous design system
of Allison el. al.
13
3.5.1 Pressure Distribution
The pressure variables deﬁne the compressible streamwise C
p
distributions at the ex
posed wing stations highlighted in ﬁg. 3.10. The wingfuselage intersection highlighted
in red is always assumed to be turbulent to reﬂect the dominant eects of attachment
line instabilities at the intersection.
Fuselage WidLh
y=0.3
y=0.5
y=0.1
y=0.7
y=0
y=1
Figure 3.10. The wing breakpoints with inverse design sections highlighted. The
blue sections can be designed for NLF while the red wingfuselage inter
section is always assumed to be turbulent to account for the dominant
role of attachment line instabilities.
CHAPTER 3. WING DESIGN 30
Slialfoiolypo
iocovoiy
Linoai iooflop
Slail of Iocovoiy
Figure 3.11. An illustration of the airfoil C
p
parameterization with important pres
sure features labeled.
x
i
oC
p
,ox(u)
M
i
(u)
C
I
LL
(u)
C
I
LL
(l)
oC
p
,ox(l)
S(u)
M
i
(l)
Figure 3.12. The inverse deisgn C
p
parametrization with the pressure variables
labeled in blue.
CHAPTER 3. WING DESIGN 31
The motivation for an inverse approach stems chieﬂy from the commonality of NLF
airfoil pressure distributions. Figure 3.11 illustrates the features of a representative
NLF pressure distribution: 1) an extended region of accelerating, 2) a short transition
ramp, 3) a weak shock and 4) a rapid recovery to the trailing edge. The pressure
features can be even more succinctly described using the parameterization illustrated
in ﬁg. 3.12. Here the C
p
distribution is parameterized by a linear ramp followed by a
Stratfordtype recovery.
46
The pressure variables are deﬁned in eq. (3.3).
x
pressure
=
C
x
r
, C
p
LEl
, C
p
LEu
,
A
dC
p
dx
B
u
,
A
dC
p
dx
B
l
, S
u
D
(3.3)
The most important variable for laminar ﬂow is the rooftop pressure gradient
dCp
dx
– a "favorable" pressure gradient can stabilize the streamwise boundary layer. The
start of recovery x
r
determines both the extent of the rooftop and the balance of
aft loading. In the present analysis the value of x
r
controls the start of recovery on
both the upper and lower airfoil surfaces. This is done to reduce discretization and
numerical integration errors.
The Stratford criteria in section 3.5.1 deﬁnes a rapid recovery that is everywhere on
the verge of separation. By minimizing the recovery distance the Stratford recovery
can maximize the length of the laminar rooftop. An added computational beneﬁt of
the Stratford recovery is its simplicity: the shape of the recovery can be deﬁned using
only the ﬂow conditions at x
r
and the concavity parameter S:
S =
C
p
Ú
x
dCp
dx
(10
≠6
Re
x
)
0.1
Here the canonical pressure coecient C
p
and eective Reynolds number Re
x
are
deﬁned in terms of the ﬂow properties at the start of recovery:
Re
x
=
xu
r
‹
C
p
= 1 ≠
3
u
u
r
4
2
CHAPTER 3. WING DESIGN 32
The classical Stratford criteria is formulated with a concave recovery at S = 0.39.
However, a ﬂow that is everywhere on the edge of separation cannot be used for
practical design. We derive therefore the solution to the Stratford criteria for an
arbitrary S in section 3.5.1 and use a more conservative S of 0.35 to deﬁne the
recovery.
C
p
=
Y
_
_
]
_
_
[
5
C
p
m
3
+ 0.1893Re
x
1/5
ln
1
x
xm
2
S
2
6
1/3
C
p
< 4/7
1 ≠
ka
Ô
k
b
+
x
xm
C
p
Ø 4/7
Here the free parameters k
a
and k
b
are solved numerically to match the canonical
pressure C
p
and its derivative at the inﬂection point where C
p
exceeds 4/7.
Pressure Constraints
The pressure distribution generated using the current parameterization scheme are
not guaranteed to be realistic. We use constraints to ensure that the design pressure
distributions are consistent with the spanwise lift distribution and produce acceptable
highspeed performance:
⁄
c
0
Ë
C
p
l
(x) ≠C
p
u
(x)
È
dx > C
l
(÷)
M
ru‹
< 1.1, M
rl‹
< 0.95
Z
_
^
_
\
Pressure Constraints (3.4)
The section lift coecient integrated from the chordwise pressure distribution must
match the spanwise C
l
from the Weissinger solution. We specify the liftmatching
constraint as an inequality because the optimized pressure distribution should always
reach the C
l
upper bound.
A useful design heuristic for supercritical airfoils is to limit the preshock Mach number
on the suction side M
ru‹
to less than 1.1. Stronger shocks may lead to drag divergence
and ﬂow separation. We apply the sweeptaper transformation of Lock
47
to obtain
M
ru‹
from the design pressure distribution.
For a given C
l
and thickness the pressure gradient is restricted only by the preshock
CHAPTER 3. WING DESIGN 33
Mach number. The inverse design method captures therefore a fundamental tradeo
between high speed performance and natural laminar ﬂow. The restriction on the
shock Mach number is conservative. Indeed, a recent study by Jameson, Vassberg
and Shankaran
48
suggests that low sweep transonic wings may be attainable with
modern CFD design tools. This would a signiﬁcant eect on the extent of realizable
laminar ﬂow. Sensitivity studies show that even an increase from a limit preshock
Mach number of 1.1 to 1.15 can lead to signiﬁcant increases in the laminar run.
The compressibility drag is estimated using an assumed quartic drag rise proﬁle. We
assume 15 counts of compressibility drag for a top wing surface shock Mach number
of 1.1. This is in line with the performance of welldesigned supercritical sections.
A singleparameter empirical model of C
dc
is admittedly quite limited. However,
by restricting the maximum recovery Mach number above and below the airfoil we
ensure that the airfoil designs are reasonable. And by making the compressibility
drag sensitive to the peak Mach number, we link the compressibility drag evaluation
to NLF and structural design: the optimizer can trade C
dc
against C
dp
and structural
eciency. The compressibility drag is referenced to the sweep of the xposition of
the start of pressure recovery (x
r
) to better match the isobar ahead of the moderate
shock. Implicit is the assumption that the compressible aerodynamics of the section
is better related to the wing sweep incident of the shock.
C
dc‹
Ã M
xr ‹
C
dc
= C
dc‹
cos
3
(
xr
)
3.5.2 Airfoil Geometry
We use thin airfoil theory to map a deﬁned pressure distribution to its associated airfoil
geometry. Classical thin airfoil theory holds for incompressible ﬂow. It is necessary
then to apply both the sweeptaper and inverse KármánTsien transformations to
convert the compressible streamwise C
p
to the equivelent incompressible pressure
distribution
˜
C
p
normal to the local isobars. We map the incompressible pressure
CHAPTER 3. WING DESIGN 34
distribution to airfoil thickness t(x) and camber z(x) distributions using the following
integral equations:
˜ u
u
(x) + ˜ u
l
(x)
2
=
1
ﬁ
⁄
c
0
dt(›)
d›
d›
x ≠›
– ≠
dz
dx
=
1
4ﬁ
⁄
c
0
Ë
˜
C
p
l
(›) ≠
˜
C
p
u
(›)
È
d›
› ≠x
The induced velocity at the chord line are speciﬁed by the pressure distribution:
˜ u(x) =
Ò
1 ≠
˜
C
p
(x)
We discretize the airfoil and solve the integral equations using a panel method. Thick
ness constraints deﬁned in the chordwise direction ensure that the inverse airfoil
geometry can accommodate the previously deﬁned wing box:
t
inv
(x
e
) > t
e
, t
inv
(x
f
) > t
f
t
inv
(x
a
) > t
a
, t
inv
(x
te
) = 0
Z
_
^
_
\
Wing Box Compatibility Constraints
The inverse thicknesses solution at the forward spar, elastic axis and aft spar must
match the wingbox geometry deﬁned in x
wing
. The trailing edge thickness is con
strained to close the airfoil. An example of optimized wing section C
p
distributions
and their corresponding geometries can be found in ﬁgs. 3.13 and 3.14. The ﬁrst
section at ÷ = 0.1 corresponds to the wing root. The root section is forced to be
turbulent to reﬂect the impact of attachment line boundary layer instabilities. The
optimizer sees little incentive to design a favorable pressure gradient in that case.
The outboard sections are designed for NLF and all show various degrees of favorable
pressure gradient.
CHAPTER 3. WING DESIGN 35
0 0.5 1
−0.5
0
0.5
−
C
p
(a) ÷ = 0.1
0 0.5 1
−0.5
0
0.5
−
C
p
(b) ÷ = 0.3
0 0.5 1
−0.5
0
0.5
−
C
p
(c) ÷ = 0.5
0 0.5 1
−0.5
0
0.5
−
C
p
(d) ÷ = 0.7
Figure 3.13. Example wing section pressure distributions at selected spanwise loca
tions.
0 0.5 1
−0.1
0
0.1
x/c
z
/
c
(a) ÷ = 0.1
0 0.5 1
−0.1
0
0.1
x/c
z
/
c
(b) ÷ = 0.3
0 0.5 1
−0.1
0
0.1
x/c
z
/
c
(c) ÷ = 0.5
0 0.5 1
−0.1
0
0.1
x/c
z
/
c
(d) ÷ = 0.7
Figure 3.14. Example wing section geometry at selected spanwise locations.
3.5.3 Boundary Layer Solution
We employ the integral methods of Thwaites and Head to solve the laminar and
turbulent boundary layers.
49
Compressible boundary layer solutions can certainly
increase accuracy. However, since compressibility tends to stabilize the streamwise
boundary layer,
14,50,51
an incompressible analysis is at least conservative. We do
however, apply compressibility corrections to the turbulent surface friction coecient
C
f
.
14
Laminar Boundary Layer
The Thwaites solution for the laminar momentum thickness ◊ is given by equation
section 3.5.3. The equation can be exactly integrated if the pressure distribution is
analytic with respect to the surface coordinate s. However, the laminar ramp in the
CHAPTER 3. WING DESIGN 36
present analysis is only linear in x; a numerical solution is still required.
◊
2
=
0.45‹
u
e
6
⁄
s
0
u
e
5
ds
Transition
To simulate turbulent sections we force ﬂow transition near 3% chord. For NLF
sections we allow the ﬂow to transition freely.
Transition prediction remains an area of active research. An often used engineering
transition criteria is the method of Michel.
49
Michel’s method is simple to use but
does not direct account for the eects of the pressure gradient. More importantly,
the method is not smooth and therefore incompatible with gradientbased optimiza
tion.
The e
9
transition envelope ﬁts of Drela and Giles
52
and those of Arnal, Habiballah
and Delcourt
53
are smooth and are sensitive to the pressure gradient. However,
these methods also require the numerical solution of both a point of critical stability
and a point of transition. The twopoint solution presents diculties for surface
discretization and numerical integration. To minimize numerical error we use the
simpler, singlestep H ≠R
x
transition criteria:
54
log[Re
e
9] = ≠40.4557 + 64.8066H ≠26.7538H
2
+ 3.3819H
3
The H≠R
x
criteria deﬁnes the transition Reynolds number at all points on the airfoil
as a function of the local shape factor of the boundary layer. Re
e
9 is the local Reynolds
number Re
x
where the ﬁts to the e
9
envelope predict ﬂow transition. Transition occurs
when the local Reynolds number exceeds the local transition Reynolds number:
Re
x
(x) > Re
e
9(x)
CHAPTER 3. WING DESIGN 37
At this point one could use interpolation on iterative solvers to solve the H ≠ R
x
criteria. However, while an interpolation scheme may be suciently accurate for
purposes of boundary layer analysis, it is not accurate enough for gradientbased
optimization. The numerical problems becomes intractable at high Reynolds numbers
where the transition location x
t
is sensitive to even small changes in the pressure
gradient. One way around this numerical problem is specify x
t
as an optimization
variable:
x
transition
= x
t
Of course the optimizer cannot be allowed to freely pick a transition point. That
would be too easy. It is necessary to further apply a compatibility constraint to
enforce laminar ﬂow before x
t
:
Re
x
(x
t
) < Re
e
9(x
t
)
The application of optimizerbased decomposition leverages the nonlinear solver
already present in the optimizer to converge the transition location. This eliminates
the costly internal iterations that would otherwise be needed to solve the transition
problem. The decomposition also reduces the laminar boundary layer evaluation to
just one point at x
t
.
Turbulent Boundary Layer
We solve the turbulent boundary layer using the Heads method. The boundary layer
solution is advanced to the trailing edge using the fourthorder RungeKutta scheme.
The section proﬁle drag of each surface is solved using the SquireYoung momentum
equation:
C
dp
= 2
◊
te
c
3
u
te
u
Œ
4
H
te
+5
2
The total wing proﬁle drag in cruise is integrated from the C
dp
solutions at the break
sections.
Chapter 4
Active Load Alleviation
An important goal of this thesis is to ﬁnd a way to develop the aircraft load control
system concurrently with the conﬁguration. The design framework includes therefore
detailed parameterization of the MLA control schedule and the GLA control law. The
dynamic loads in gust encounters are resolved using a combination of aircraft dynamics
simulations and modal solutions of the wing structural response. The individual
components of the structural dynamics solver are validated against standard beam
test cases.
4.1 MLA and GLA Parameterization
Active load alleviation systems use coordinated control surface deﬂections to minimize
wing stress. In principle any combination of control surfaces can be utilized. For
simplicity we restrict the MLA and GLA control surfaces to the ailerons and ﬂaps. This
includes all of the trailing edge control surfaces in shown in ﬁg. 4.1. The sensitivity of
the aircraft design to control allocation is examined in more detail in chapter 7.
Figure 4.1 illustrates the trailing edge control surface arrangement and parameteri
zation. Each exposed trailing edge section bounded by successive wing breakpoints
38
CHAPTER 4. ACTIVE LOAD ALLEVIATION 39
Figure 4.1. The wing control surfaces are deﬁned by the wing break sections.
represents an independent control surface. The inboard sections simulate ﬂap de
ﬂections; outboard sections simulate ailerons. Both the aileron and ﬂap surfaces are
assumed to extend over 25% of the chord. The chord ratio is somewhat lower than
the typical extended chord of ﬂaps. A conservative parameterization of the ﬂap chord
is however consistent with the need for lightweight, highbandwidth control surfaces
to achieve eective dynamic load alleviation. The control surface deﬂection schedules
and dynamic gains are optimized with the aircraft.
4.2 Maneuver Load Alleviation
A ﬁrstorder question in the design of the MLA system is the deﬁnition of the limit
maneuvers. The aircraft should ideally be designed for the entire V–n envelope.
An exhaustive search for the worst loads may not, however, be practical or indeed
necessary for conceptual design. An alternative is to identify representative maneuvers
that can eciently capture the key aerostructural tradeos and inform design.
The Federal Aviation Regulations (FAR) require commercial aircraft structures to be
designed to withstand a 2.5g maneuver at a structural safety factor of 1.5. For a
conventional aircraft the speed and altitude of the limit maneuver ﬂight condition
are not particularly important – the stress is determined by the load factor. Deﬁning
representative maneuvers becomes more complicated for aircraft designed with MLA.
CHAPTER 4. ACTIVE LOAD ALLEVIATION 40
Here the wing stress state is fundamentally dependent on the eectiveness of load
alleviation, which can in turn be dictated by aerodynamic constraints such as the
wing maximum lift.
We design the aircraft for a 2.5g symmetric pullup at an altitude of 30,000 feet
and the structural design velocity V
c
. The maneuver altitude is justiﬁed by two
observations. First, drastic maneuvers at altitudes higher than 30,000 feet are likely
constrained by available engine thrust and maximum lift. The ﬂight control system
of commercial aircraft typically restrict the maneuver envelope at altitude to prevent
stall.
22,23
Second, drastic maneuvers for obstacle avoidance and stall recovery are far
more likely at lower altitudes. We also design the aircraft for a 1.3g pullup at 40,000
feet and the cruise velocity. The maximumlift constraints help to ensure that the
wing remains buetfree in cruisestage maneuvers at high altitude.
The MLA design variables are the vector of trailing edge control deﬂections ” for each
of the design maneuver conditions:
x
MLA
= ”
The range of trailing edge deﬂections are limited by hinge moment, control reversal
and ﬂow separation considerations. We impose a generous absolute MLA deﬂection
limit of 10
¶
on each of the control surface:
≠10
¶
< ”
i
< 10
¶
The deﬂection limit is consistent with the published parameters of the load allevia
tion systems on the Airbus A320, A330 and A340, which share a maximum control
deﬂection of 11
¶
.
22,23
The limit is further supported by experiments, which show
that highspeed trailing edge deﬂections on the order of 8
¶
can be sustained without
signiﬁcant ﬂow separation.
18
And since limit maneuvers need not be performed at
constant altitude, drag penalties from the control surface deﬂections do not mean
ingfully impact the design. The sensitivity of the optimized aircraft to the allowable
range of control surface deﬂections is examined in more detail in chapter 7.
CHAPTER 4. ACTIVE LOAD ALLEVIATION 41
4.3 Gust Load Alleviation
The wing structure is also sized by timedependent gust load constraints in eq. (4.1).
The gust load constraints are imposed at the three dierent gust encounter ﬂight
conditions discussed in section 2.2: at 10,000 ft and the initial and ﬁnal cruise alti
tudes. The ypositions of the gustinduced stress constraints are collocated with the
aerodynamic control points.
{‡(÷, t)} < ‡
a
, {·(÷, t)} < ·
a
Ô
Dynamic Stress Constraints (4.1)
o(y,L) 0.024
D
T i
< 0.88,
D
T f
< 0.88, R > 2,000nm
Trim
C
Lh
< C
Lhmax
, nW =
ﬂv
2
S
ref
C
L
2
Stability
≠
dC
Mac
dC
L
> 0.10c
Maximum Lift
C
l
(÷) <
I
C
lmax
(÷) if ÷ < 0.75
C
lmax
(÷) ≠0.2 otherwise
Pressure
⁄
c
0
#
C
p
l
(x) ≠C
p
u
(x)
$
dx > C
l
(÷)
M
ru‹
< 1.1, M
rl‹
< 0.95
Wing Box
t
inv
(x
e
) > t
e
, t
inv
(x
f
) > t
f
t
inv
(x
a
) > t
a
, t
inv
(x
te
) = 0
Transition
Re
x
(x
t
) < Re
e
9(x
t
)
Static Stress
{‡(÷)} < ‡
a
, {·(÷)} < ·
a
Dynamic Stress
{‡(÷, t)} < ‡
a
, {·(÷, t)} < ·
a
Aileron Reversal
L
e”4
L
r”4




Vc
> 0.525
Table 5.3. Summary of all optimization constraints.
Chapter 6
Results
This chapter details the results of a number of design studies meant to demonstrate the
workings of the aeroservoelastic conceptual design framework. We ﬁrst present a series
of optimized turbulent aircraft with varying degrees of active load alleviation: no load
alleviation, MLAonly, GLAonly and ﬁnally both MLA and GLA (MLA+GLA). This
is followed by an analogous series of laminar aircraft with dierent load alleviation
systems. Finally, we compare the turbulent and laminar MLA+GLA designs in detail
to highlight the potential synergy between active load alleviation and laminar ﬂow.
The results include both "point optimizations" at a cruise Mach number of 0.78 and
optimization sweeps with cruise Mach numbers ranging from 0.70 to 0.82. We treat
the Mach 0.78 turbulent aircraft designed without load alleviation as the baseline
against which all other data are normalized.
60
CHAPTER 6. RESULTS 61
6.1 Turbulent Designs
6.1.1 Point Optimizations
The four optimized turbulent aircraft are compared in ﬁg. 6.1. In each design we force
ﬂow transition near the leading edge to ensure turbulent ﬂow over the wing. The
transition lines are highlighted in green.
(a) Turbulent (b) Turbulent MLA
(c) Turbulent GLA (d) Turbulent MLA+GLA
Figure 6.1. The optimized Mach 0.78 turbulent aircraft with dierent levels of active
load alleviation.
The details of the aircraft and wing conﬁguration are tabulated in table 6.1.
The optimized Mach 0.78 turbulent aircraft in ﬁg. 6.1a represents a conventional
CHAPTER 6. RESULTS 62
Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA
W
MTOW
(lb) 158,065 153,146 158,547 148,139
W
fuel
(lb) 25,916 25,030 25,779 23,520
W
wing
(lb) 19,200 16,582 19,720 14,637
T
0
(lb) 21,367 20,607 21,267 18,963
S
ref
(ft
2
) 1,652 1,512 1,678 1,497
b (ft) 136 140 137 151
AR 11.2 13.0 11.2 15.3
1/4
(Deg) 26.6 21.7 26.6 17.6
t/c 0.096 0.089 0.096 0.091
L/D 18.2 18.3 18.4 19.0
z
i
30,095 30,535 30,178 30,951
z
f
41,514 41,496 41,554 41,190
Table 6.1. Summary of optimized Mach 0.78 turbulent aircraft design parameters.
shorthaul design in the same class as the Boeing 737 and the Airbus A320. In fact,
the optimized maximum takeo weight matches well with the published ﬁgure of the
Boeing 737800 at 155,500 lb. The wing sweep of 26.6
¶
and average cruise L/D of
18 are also in line with the 737. The optimized span at 136 feet is on the other
hand substantially greater than the span of both the 737800 at 117 feet and the
Airbus A320 at 111 feet. The dierence is in part attributable to the absence of
gate compatibility constraints in the optimization. We examine the sensitivity of the
aircraft design to gate constraints in the next chapter.
Compared with the baseline, the Turbulent MLA aircraft in ﬁg. 6.1b shows a modest
increase in span from 136 to 140 feet. The introduction of MLA decreases the optimum
wing sweep by 5
¶
. A simultaneous decrease in the areaweighted average thicknessto
chord t/c from 9.6 to 8.9% compensates for the compressibility penalties of reduced
sweep.
The MLA wing is both thinner and longer than the baseline wing but still manages to
be some 3,000 lb lighter. Load alleviation clearly leads to tangible gains in structural
eciency. The eectiveness of the MLA system acting alone also suggests that
maneuver loads likely size a substantial portion of the baseline wing.
CHAPTER 6. RESULTS 63
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Turbulent
Turbulent MLA
Turbulent GLA
Turbulent MLA+GLA
Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA
Wing Weight 1.000 0.864 1.027 0.762
Fuel Weight 1.000 0.966 0.995 0.908
Sea Level Thrust 1.000 0.964 0.995 0.888
L/D 1.000 1.006 1.011 1.045
Cost 1.000 0.987 0.999 0.966
Figure 6.2. A comparison of the optimized turbulent aircraft. The performance
metrics and conﬁguration parameters are normalized against the corre
sponding values of the Mach 0.78 turbulent baseline.
CHAPTER 6. RESULTS 64
The GLA design shown in ﬁg. 6.1c on the other hand, is nearly identical to the baseline.
The only dierence is the formers slightly larger wing. The other planform parameters
are all within 1% of their baseline values. Gust loads then are clearly not sizing the
baseline wing in any signiﬁcant way. This result is not surprising because high wing
sweep leads to signiﬁcant aerodynamic stiness and damping in gust encounters.
Figure 6.1d shows that the application of both MLA and GLA signiﬁcantly alters the
optimized conﬁguration. Compared to the baseline the MLA+GLA wing is not only
15 feet longer but also 25% lighter. The sweep is reduced to 18
¶
. The gain in L/D is
modest in part because the ATA cost model used in the present analysis scales the
aircraft manufacturing cost against the zerofuel weight. Under this model the light
aircraft is not only more ecient in lift but also costs less. It should be emphasized
that the results in this chapter are all based on a fuel price of $2.5/gal. The balance
between weight and fuel savings is fundamentally dependent on fuel prices.
In certain cases it is convenient to examine the relative changes in performance
metrics and design parameters. The parameters in ﬁg. 6.2 are normalized to their
baseline values in the Mach 0.78 turbulent design. We observe that the independent
application of MLA has led to a modest but tangible 3.4% reduction in fuel burn
and 1.3% reduction in cost. The independent application of GLA on the other hand
produces only negligible gains. The combination of MLA and GLA has led to a
signiﬁcant 10% reduction in fuel burn and 3.4% reduction in cost.
The exposed wing planforms of the turbulent aircraft are compared in ﬁg. 6.3. Once
again we normalize the relevant parameters by their baseline values. The ﬁgure
highlight visually the similarity between the baseline and GLA wing and a clear trend
towards increased span and decreased wing sweep with the successive addition of load
alleviation technologies.
Figure 6.4 compares the turbulent wing and skin thickness distributions. The in
creased structural eciency of the MLA and MLA+GLA aircraft leads to reduced
wing and skin thicknesses. As load alleviation reduces the stress constraints, aeroe
lasticity can become dominant considerations. The optimizer chooses therefore to
CHAPTER 6. RESULTS 65
Turbulent
Turbulent MLA
Turbulent GLA
Turbulent MLA+GLA
Turbulent Turbulent MLA Turbulent GLA Turbulent MLA+GLA
S
ref
1.00 0.92 1.02 0.91
b 1.00 1.03 1.01 1.11
1.00 0.82 1.00 0.66
t/c 1.00 0.93 1.00 0.95
AR 1.00 1.16 1.00 1.36
Figure 6.3. A comparison of the optimized turbulent wing planforms. All parameters
are normalized by their values in the Mach 0.78 turbulent baseline.
0 0.5 1
0
0.05
0.1
0.15
0.2
Spanwise Position η
t
/
c
Turbulent
Turbulent MLA
Turbulent GLA
Turbulent MLA+GLA
(a) Wing t/c
0 0.5 1
0
0.5
1
1.5
Spanwise Position η
t
s
(
i
n
c
h
)
Turbulent
Turbulent MLA
Turbulent GLA
Turbulent MLA+GLA
(b) Skin Thickness (inch)
Figure 6.4. Turbulent wing and skin thickness distributions.
CHAPTER 6. RESULTS 66
increase the outboard stiness to prevent aileron reversal and increase MLA control
authority.
0 0.5 1
0
0.5
1
1.5
2
2.5
Spanwise Position η
C
l
a
n
d
C
l
m
a
x
Turbulent
Turbulent MLA
Turbulent GLA
Turbulent MLA+GLA
(a) 2.5g at 30,000 ft
0 0.5 1
0
0.5
1
1.5
2
2.5
Spanwise Position η
C
l
a
n
d
C
l
m
a
x
Turbulent
Turbulent MLA
Turbulent GLA
Turbulent MLA+GLA
(b) 1.3g at 40,000 ft
Figure 6.5. Comparisons of the turbulent maneuver C
l
(solid lines) and C
lmax
(dashed lines) distributions.
We compare the maneuver C
l
distributions of the turbulent aircraft in ﬁg. 6.5. The
C
l
distributions show that the MLA system has concentrated load inboard to reduce
bending and shear stresses. In the MLA design for example the wing tips are actually
negatively loaded in the 2.5g maneuvers. In this case the lift penalties are more than
oset by the greatly increased load alleviation inboard. The drag penalties from the
negatively loaded tips do not directly aect the design because the maneuvers do not
have to be performed at constant altitude.
The dashed lines in ﬁg. 6.5 corresponds to the section C
lmax
. A discontinuous change
in the section maximum lift indicates a change in the trailing edge controls surface
deﬂection. The actions of the MLA system on the turbulent designs, which gave
relatively thick wings enabled by sweep, are not constrained by the lift limit.
We examine the structure design in more detail in ﬁg. 6.6, which overlays the maneuver
and gustinduced wing stresses to highlight which load is sizing each section of the
CHAPTER 6. RESULTS 67
0 0.5 1
−1
−0.5
0
0.5
1
B
e
n
d
i
n
g
S
t
r
e
s
s
σ
/
σ
a
Spanwise Position η
2.5−g (30,000 ft)
1.3−g (40,000 ft)
gust (initial cruise)
gust (final cruise)
gust (10,000 ft)
(a) Turbulent
0 0.5 1
−1
−0.5
0
0.5
1
B
e
n
d
i
n
g
S
t
r
e
s
s
σ
/
σ
a
Spanwise Position η
2.5−g (30,000 ft)
1.3−g (40,000 ft)
gust (initial cruise)
gust (final cruise)
gust (10,000 ft)
(b) MLA
0 0.5 1
−1
−0.5
0
0.5
1
B
e
n
d
i
n
g
S
t
r
e
s
s
σ
/
σ
a
Spanwise Position η
2.5−g (30,000 ft)
1.3−g (40,000 ft)
gust (initial cruise)
gust (final cruise)
gust (10,000 ft)
(c) GLA
0 0.5 1
−1
−0.5
0
0.5
1
B
e
n
d
i
n
g
S
t
r
e
s
s
σ
/
σ
a
Spanwise Position η
2.5−g (30,000 ft)
1.3−g (40,000 ft)
gust (initial cruise)
gust (final cruise)
gust (10,000 ft)
(d) MLA+GLA
Figure 6.6. Maneuver and gust bending stresses for the optimized turbulent designs
at Mach 0.78. The wing bending stresses ‡ are normalized by the
allowable stress ‡
a
. The gust stresses represent the maximum values
encounter by each wing section at all gust gradient lengths.
CHAPTER 6. RESULTS 68
wing. The maneuver loads at 1.3 and 2.5g are shown as solid lines. The dashed lines
are formed by the maximum stresses at each wing section for all of the timedomain
gust simulations at a given altitude. The maximum stresses are normalized by the
allowable stresses ‡
a
. ﬁg. 6.6 is therefore a visual representation of both the optimized
state of the static and dynamic stress constraints discussed in chapter 4. A wing
section is deemed stresscritical if the local stress ratio ‡/‡
a
reaches their limit values
of 1 or 1.
The plot of stress constraints conﬁrms that the turbulent baseline wing structure is
essentially sized by maneuver loads. Much of the inboard wing is fullystressed in
maneuver. The outboard sections are designed by minimum gauge. The MLA system
signiﬁcantly reduces the maneuver load but leaves the wing to be designed by gust.
Figure 6.6b shows that the Turbulent MLA wing is designed by lowaltitude gusts
inboard and cruise stage gusts outboard. So while the MLA system has diminished
the role of maneuver loads in structural sizing, the gust loads remain to undercut
the potential structural savings. The opposite is true in the case of the GLA wing
stresses shown in ﬁg. 6.6b. Here the wing is designed almost exclusively by maneuver
loads.
Finally, ﬁg. 6.6d demonstrates that the MLA+GLA wing is designed by both maneuver
and gust loads. We also observe that the outboard portions of the wing are far from
being fullystressed; they are instead sized by the aforementioned aeroelastic and
minimum gauge considerations.
6.1.2 Mach Number Sweeps
The aircraft presented thus far are all designed to cruise at Mach 0.78. We now
present the cost and fuel burn trends of the four turbulent aircraft as functions of the
cruise Mach number. The cost and fuel burn metrics shown in ﬁgs. 6.7 and 6.8 are
normalized by the cost and fuel weight of the baseline design at Mach 0.78.
The results in Figure 6.7 demonstrate that at a fuel price of $2.5 per gallon the
CHAPTER 6. RESULTS 69
0.7 0.72 0.74 0.76 0.78 0.8
0.92
0.94
0.96
0.98
1
1.02
1.04
Cruise Mach Number
R
e
l
a
t
i
v
e
C
o
s
t
Turbulent
Turbulent MLA
Turbulent GLA
Turbulent MLA+GLA
Figure 6.7. A plot of the relative operating cost of optimized turbulent designs as
functions of Mach number. Each point represents an optimized aircraft.
The performance metrics are normalized to the Mach 0.78 baseline.
minimumcost objective continues to favor speed over fuel savings. Cost continues to
fall with increasing Mach number. Only the MLA+GLA design ﬂatlines near Mach
0.82. So while the turbulent designs can slow down to reduce fuel burn, they can only
do so at higher costs.
Figures 6.7 and 6.8 show that the relative savings from the independent application
of MLA and GLA are constant across the range of Mach numbers. The savings from
the MLA+GLA are however dependent on the Mach number. We reason that aileron
reversal constraints, which become more critical with increased speed, diminish the
savings from load alleviation.
CHAPTER 6. RESULTS 70
0.7 0.72 0.74 0.76 0.78 0.8
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Cruise Mach Number
R
e
l
a
t
i
v
e
F
u
e
l
B
u
r
n
Turbulent
Turbulent MLA
Turbulent GLA
Turbulent MLA+GLA
Figure 6.8. A plot of the relative fuel burn of optimized turbulent designs as func
tions of Mach number. Each point represents an optimized aircraft. The
performance metrics are normalized to the Mach 0.78 baseline.
6.2 Laminar Designs
6.2.1 Point Optimizations
The optimized NLF aircraft with dierent levels of load alleviation are compared in
ﬁg. 6.9. The wing sweeps of the NLF designs are restricted to less than 10
¶
– a limit
that is inevitably reached. The upper wing surfaces are designed for laminar ﬂow
while the lower surfaces are assumed to be turbulent.
We observe that in all but the MLA+GLA aircraft, the region of extensive laminar
ﬂow is restricted to the outboard portions of the wings. This result underscores the
severe structural penalties faced by a lowsweep NLF design at transonic speed. The
optimizer favors weight savings from improved structural eciency than aerodynamic
beneﬁts from extensive laminar ﬂow. The data in table 6.2 show that all of the laminar
designs reach their maximum wing sweep of 10
¶
. This result is also consistent with the
strong aerodynamic and aeroelastic incentives to increase wing sweep. Moreover, since
the boundary layer analysis does not include crossﬂow, there is no viscous penalty
against high wing sweep.
CHAPTER 6. RESULTS 71
(a) Laminar (b) Laminar MLA
(c) Laminar GLA (d) Laminar MLA+GLA
Figure 6.9. The optimized Mach 0.78 turbulent aircraft with dierent levels of active
load alleviation.
CHAPTER 6. RESULTS 72
Laminar Laminar MLA Laminar GLA Laminar MLA+GLA
W
MTOW
(lb) 160,904 157,382 158,961 148,897
W
fuel
(lb) 25,780 25,036 25,032 21,833
W
wing
(lb) 21,701 20,295 20,783 17,437
T
0
(lb) 21,569 20,756 20,638 17,845
S
ref
(ft
2
) 1,503 1,376 1,647 1,489
b (ft) 145 155 141 169
AR 14.0 17.4 12.0 19.1
1/4
(Deg) 10.0 10.0 10.0 10.0
t/c 0.088 0.091 0.091 0.090
L/D 18.7 18.9 19.1 20.9
z
i
29,531 30,310 30,191 30,019
z
f
41,998 41,784 41,604 42,000
Table 6.2. Summary of Mach 0.78 high sweep NLF aircraft parameters.
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Laminar
Laminar MLA
Laminar GLA
Laminar MLA+GLA
Laminar Laminar MLA Laminar GLA Laminar MLA+GLA
Wing Weight 1.130 1.057 1.082 0.908
Fuel Weight 0.995 0.966 0.966 0.842
Sea Level Thrust 1.009 0.971 0.966 0.835
L/D 1.027 1.039 1.052 1.148
Cost 1.002 0.991 0.993 0.951
Figure 6.10. A comparison of the optimized laminar aircraft. The performance
metrics and conﬁguration parameters are normalized by those of the
Mach 0.78 turbulent baseline.
CHAPTER 6. RESULTS 73
Figure 6.10 compares the key design parameters of the dierent laminar aircraft.
The thrust, L/D, weight and costs are all normalized by the corresponding turbulent
baseline values. The NLF aircraft achieves only a negligible 0.5% gain in fuel savings
and also costs more to operate. The thin, NLF wing contributes to a 2% improvement
in aircraft L/D but weighs 13% more than the baseline. The lackluster performance
of the NLF design is therefore directly attributable to the penalties associated with
unsweep.
The results from the independent application of MLA and GLA to the NLF wing
are comparable: both produce less than 1% improvements in cost and more than 3%
improvements in fuel burn. While the turbulent designs beneﬁt more from MLA than
GLA. The laminar design with its gustsensitive lowsweep wing stands to beneﬁt
more from GLA.
As in the case of the turbulent designs, the greatest performance gains come from the
coordinated application of both MLA and GLA. The Laminar MLA+GLA aircraft
sees an impressive 15% reduction in fuel burn and a 5% reduction in cost relative
to the baseline. The improvement comes from both aerodynamics and structural
improvements: a 15% increase in average cruise L/D coupled with a 5% reduction in
wing weight.
The planforms of the optimized NLF laminar aircraft are overlaid in ﬁg. 6.11. The
combination of MLA and GLA leads to a 24% increase optimized wingspan. Aircraft
designed without GLA have smaller wing areas. This is expected as gust load intensity
scales linearly with wing area. In the absence of GLA the optimum wing loading
increases.
The wing thickness and t/c distributions are compared in ﬁg. 6.12. The signiﬁcant
increases in the outboard t/c in the MLA+GLA wing are once again motivated by
the need to increase wing torsional rigidity and improve control authority.
Figure 6.13 shows the wing C
l
and C
lmax
distributions in maneuver. Unlike its turbu
lent counterpart the laminar MLA+GLA aircraft is liftcritical in a 2.5g maneuver.
CHAPTER 6. RESULTS 74
Laminar
Laminar MLA
Laminar GLA
Laminar MLA+GLA
Laminar Laminar MLA Laminar GLA Laminar MLA+GLA
S
ref
0.91 0.83 1.00 0.90
b 1.06 1.14 1.03 1.24
0.38 0.38 0.38 0.38
t/c 0.92 0.95 0.94 0.94
AR 1.25 1.55 1.07 1.70
Figure 6.11. A comparison of the optimized laminar wing planforms. All parameters
are normalized by their values in the Mach 0.78 turbulent baseline.
0 0.5 1
0
0.05
0.1
0.15
0.2
Spanwise Position η
t
/
c
Laminar
Laminar MLA
Laminar GLA
Laminar MLA+GLA
(a) Wing t/c
0 0.5 1
0
0.5
1
1.5
Spanwise Position η
t
s
(
i
n
c
h
)
Laminar
Laminar MLA
Laminar GLA
Laminar MLA+GLA
(b) Skin Thickness
Figure 6.12. Laminar wing and skin thickness distributions.
CHAPTER 6. RESULTS 75
0 0.5 1
0
0.5
1
1.5
2
2.5
Spanwise Position η
C
l
a
n
d
C
l
m
a
x
Laminar
Laminar MLA
Laminar GLA
Laminar MLA+GLA
(a) 2.5g Maneuver
0 0.5 1
0
0.5
1
1.5
2
2.5
Spanwise Position η
C
l
a
n
d
C
l
m
a
x
Laminar
Laminar MLA
Laminar GLA
Laminar MLA+GLA
(b) 1.3g Maneuver
Figure 6.13. Laminar wing C
l
and C
lmax
distributions.
The maximum lift constraints limit then the eectiveness of the MLA system. Al
though the reduction in wing sweep has a small, positive eect on maximum lift,
the thinner wings need to cope with increased compressibility drag produce a more
signiﬁcant reduction in C
Lmax
The normalized maneuver and gustinduced wing stresses are overlaid in ﬁg. 6.14.
Solid lines correspond to maneuver loads; dashed lines to the maximum gust loads.
Figure 6.14a shows that absent any load alleviation the wing of the laminar aircraft
is designed by gust loads inboard and by maneuver loads outboard. When comparing
the laminar wing stress distribution to its turbulent counterpart in ﬁg. 6.6a it is clear
that a greater portion of the laminar wing is sized by gust. The result is attributable
to the low aerodynamic damping associated with the nearly unswept wing.
The stress distributions in ﬁg. 6.14b show that while the MLA system is successfully
suppresses the maneuver stresses, gusts continue to size the wing. Similarly, while
the GLA system can eliminate the eects of intermediate and longwave gusts, the
maneuvers emerge to become critical design conditions. The simultaneous application
CHAPTER 6. RESULTS 76
0 0.5 1
−1
−0.5
0
0.5
1
B
e
n
d
i
n
g
S
t
r
e
s
s
σ
/
σ
a
Spanwise Position η
2.5−g (30,000 ft)
1.3−g (40,000 ft)
gust (initial cruise)
gust (final cruise)
gust (10,000 ft)
(a) Laminar
0 0.5 1
−1
−0.5
0
0.5
1
B
e
n
d
i
n
g
S
t
r
e
s
s
σ
/
σ
a
Spanwise Position η
2.5−g (30,000 ft)
1.3−g (40,000 ft)
gust (initial cruise)
gust (final cruise)
gust (10,000 ft)
(b) Laminar MLA
0 0.5 1
−1
−0.5
0
0.5
1
B
e
n
d
i
n
g
S
t
r
e
s
s
σ
/
σ
a
Spanwise Position η
2.5−g (30,000 ft)
1.3−g (40,000 ft)
gust (initial cruise)
gust (final cruise)
gust (10,000 ft)
(c) Laminar GLA
0 0.5 1
−1
−0.5
0
0.5
1
B
e
n
d
i
n
g
S
t
r
e
s
s
σ
/
σ
a
Spanwise Position η
2.5−g (30,000 ft)
1.3−g (40,000 ft)
gust (initial cruise)
gust (final cruise)
gust (10,000 ft)
(d) Laminar MLA+GLA
Figure 6.14. Maneuver and gust bending stresses for the optimized laminar designs
at Mach 0.78. The wing bending stresses ‡ are normalized by the
allowable stress ‡
a
. The gust stresses represent the maximum values
encounter by each wing section at all gust gradient lengths.
CHAPTER 6. RESULTS 77
of both load alleviation systems lead to a MLA+GLA design that balances the need
to suppress both gust and maneuver loads. The outboard portions of the MLA+GLA
wing are once again designed by elastic constraints.
6.2.2 Mach Number Sweeps
The variation in cost and fuel burn performance for the laminar aircraft as a function
of the cruise Mach number are shown in ﬁgs. 6.15 and 6.16. We observe that the perfor
mance of the MLA aircraft is progressively diminished by the need to sustain stronger
gust loads at high speed. The more important observation is that the combination of
the two load alleviations has unlocked much of the potential of NLF.
0.7 0.72 0.74 0.76 0.78 0.8
0.92
0.94
0.96
0.98
1
1.02
1.04
Cruise Mach Number
R
e
l
a
t
i
v
e
C
o
s
t
Laminar
Laminar MLA
Laminar GLA
Laminar MLA+GLA
Figure 6.15. A plot of the relative cost of optimized laminar designs as functions
of Mach number. Each point represents an optimized aircraft. The
performance metrics are normalized to the Mach 0.78 baseline.
CHAPTER 6. RESULTS 78
0.7 0.72 0.74 0.76 0.78 0.8
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Cruise Mach Number
R
e
l
a
t
i
v
e
F
u
e
l
B
u
r
n
Laminar
Laminar MLA
Laminar GLA
Laminar MLA+GLA
Figure 6.16. A plot of the relative fuel burn of optimized laminar designs as functions
of Mach number. Each point represents an optimized aircraft. The
performance metrics are normalized to the Mach 0.78 baseline.
6.3 Turbulent and Laminar Comparison
We compare the turbulent and laminar MLA+GLA designs sidebyside in ﬁg. 6.17.
In the turbulent design the eciency gains come primarily from increased structural
eciency though active control. The Laminar MLA+GLA design on the other hand
invests a portion of the weight savings from load alleviation to enable extensive laminar
ﬂow. So while the Turbulent MLA+GLA wing manages to be 24% lighter than the
baseline, the corresponding wing weight reduction in the laminar wing is only 9.2%.
But the addition of laminar ﬂow has led to a 14.8% improvement in aircraft L/D
relative to the baseline while the improvement in the turbulent aircraft L/D is limited
to 4.5%. An inspection of the Laminar MLA+GLA design shows extensive laminar
ﬂow even in the inboard portions of the wing.
Figures 6.18 and 6.19 show the trends in cost and fuel burn as we change the cruise
Mach number. We compare the aircraft designed without any load alleviation with the
respective MLA+GLA designs. The results demonstrate that active load alleviation
increases the Mach number at which NLF can be eciently exploited. Without load
alleviation, the NLF aircraft has to be designed to cruise at Mach 0.74 or less to realize
CHAPTER 6. RESULTS 79
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Turbulent MLA+GLA
Laminar MLA+GLA
Turbulent MLA+GLA Laminar MLA+GLA
Wing Weight 0.762 0.908
Fuel Weight 0.908 0.842
Sea Level Thrust 0.888 0.835
L/D 1.045 1.148
Cost 0.966 0.951
Figure 6.17. A comparison of the optimized MLA+GLA aircraft parameters. The
displayed parameters are normalized by the value of the Mach 0.78
turbulent baseline.
0.7 0.72 0.74 0.76 0.78 0.8
0.92
0.94
0.96
0.98
1
1.02
1.04
Cruise Mach Number
R
e
l
a
t
i
v
e
C
o
s
t
Turbulent
Turbulent MLA+GLA
Laminar
Laminar MLA+GLA
Figure 6.18. Relative cost of turbulent and laminar designs as functions of Mach
number.
CHAPTER 6. RESULTS 80
0.7 0.72 0.74 0.76 0.78 0.8
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Cruise Mach Number
R
e
l
a
t
i
v
e
F
u
e
l
B
u
r
n
Turbulent
Turbulent MLA+GLA
Laminar
Laminar MLA+GLA
Figure 6.19. Relative fuel burn of turbulent and laminar designs as functions of
Mach number.
tangible fuel and cost savings over the turbulent baseline. The Laminar MLA+GLA
aircraft on the other hand can achieve savings over turbulent MLA+GLA counterpart
at up to Mach 0.80, which match the cruise Mach number of typical airliners. The
combination of MLA and GLA therefore alters the terms of the transonic MT
trade in favor of a lowsweep, natural laminar ﬂow wing. The results presented in
this chapter assume conventional aluminum structures and inservice engines. The
gains in eciency are realized through laminar ﬂow, active control and conﬁguration
changes. The incorporation of advanced engines and composites would compound the
savings.
Chapter 7
Sensitivity Studies
The results presented in chapter 6 are based on a number of important assumptions:
1) the NLF wing sweep are less than 10
¶
, 2) the bottom surface of NLF wings are
turbulent, 3) all trailing edge control surfaces are available for load alleviation, 4) the
maximum load alleviation control surface deﬂections and rates are restricted to 10
¶
and 25
¶
/s respectively and 5) there are no gate compatibility constraints on wingspan.
Many of these assumptions are operational and dicult to set in conceptual design.
Yet changes in these assumptions can have profound impacts on the optimized design.
It is instructive therefore to examine the sensitivities of the design studies to changes
in our assumptions.
7.1 NLF Wing Sweep
A number of recent studies
11,13
suggest that the 10
¶
limit on the maximum NLF wing
sweep is likely conservative. It is not surprising then that the NLF aircraft without
load alleviation should compare unfavorably against its turbulent counterpart. The
results in the previous chapter demonstrate that a lowsweep transonic NLF wing
only becomes viable after the introduction of aggressive load alleviation technologies.
81
CHAPTER 7. SENSITIVITY STUDIES 82
But unsweeping the wing is not the only way to maintain laminar ﬂow. One can
certainly tailor the 3D wing pressure distribution to suppress both TS and crossﬂow
instabilities.
12,13
For completeness, the performance of a lowsweep NLF wing should
be compared to its highsweep counterpart.
However, the design of a 3D NLF wing is a nontrivial problem that requires so
phisticated ﬂow solvers and transition prediction tools. In this section we use the
2D inverse design tools at hand to give an optimistic estimate of 3D NLF wing
performance. We design the Laminar25 and Laminar25 MLA+GLA aircraft in
ﬁg. 7.1 with a maximum wing sweep of up to 25
¶
. We assume that the wings of
these aircraft are designed with tailored 3D pressure distributions and/or hybrid
laminar ﬂow control (HLFC) technologies to suppress crossﬂow instabilities without
compromising streamwise boundary layer stability. By neglecting alltogether the
design tradeos associated with stabilizing the crossﬂow, we arrive by deﬁnition at
an optimistic projection of what 3D boundary layer control can achieve.
(a) Laminar25 (b) Laminar25 MLA+GLA
Figure 7.1. Optimized highsweep NLF design at Mach 0.78.
Not surprisingly, ﬁg. 7.1a shows that the sweep of the optimized Laminar25 wing
reaches its upper bound of 25
¶
. Without the eect of crossﬂow the optimizer has every
incentive to increase sweep to moderate compressibility drag and increase aerodynamic
damping. The wing sweep of the Laminar25 MLA+GLA design is only 18
¶
– a
consequence of the increased eective structural eciency from load alleviation. The
CHAPTER 7. SENSITIVITY STUDIES 83
fact that the load alleviation drives the optimum sweep closer to the low sweep NLF
wing is important.
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Laminar
Laminar−25
Laminar Laminar25
Wing Weight 1.130 1.088
Fuel Weight 0.995 0.953
Sea Level Thrust 1.009 0.965
L/D 1.027 1.065
Cost 1.002 0.990
Figure 7.2. Comparison of highsweep laminar25 aircraft.
We compare the Laminar25 design with its lowsweep counterpart in ﬁg. 7.2. The
table shows that the high sweep NLF wing has a higher L/D and lower wing weight,
which combine to produce a 1% reduction in cost and a more than 4% reduction in
fuel burn. The Laminar25 MLA+GLA design in ﬁg. 7.3 on the other hand oers only
negligible beneﬁts over its low sweep counterpart. The cost is virtually unchanged
and the fuel burn savings amounts to less than 1%. The results conﬁrm that as the
load alleviation systems moderate the transonic MT trade, the lowsweep NLF wing
becomes more and more attractive.
This result is of course a function of the Mach number. The performance of the
unswept wing is still constrained at high Mach numbers. Figures 7.4 and 7.5 show the
variation of the optimized cost and fuel burn metrics as functions of the cruise Mach
numbers. As expected the Laminar25 designs outperform the lowsweep designs
at all Mach numbers. After all the additional wing sweep is "free". However, in
CHAPTER 7. SENSITIVITY STUDIES 84
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Laminar MLA+GLA
Laminar−25 MLA+GLA
Laminar MLA+GLA Laminar25 MLA+GLA
Wing Weight 0.908 0.832
Fuel Weight 0.842 0.833
Sea Level Thrust 0.835 0.835
L/D 1.148 1.156
Cost 0.951 0.948
Figure 7.3. Comparison of highsweep laminar25 MLA+GLA aircraft.
0.7 0.72 0.74 0.76 0.78 0.8
0.92
0.94
0.96
0.98
1
1.02
1.04
Cruise Mach Number
R
e
l
a
t
i
v
e
C
o
s
t
Laminar
Laminar−25
Laminar MLA+GLA
Laminar−25 MLA+GLA
Figure 7.4. Optimized aircraft cost as functions of Mach number.
CHAPTER 7. SENSITIVITY STUDIES 85
0.7 0.72 0.74 0.76 0.78 0.8
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Cruise Mach Number
R
e
l
a
t
i
v
e
F
u
e
l
B
u
r
n
Laminar
Laminar−25
Laminar MLA+GLA
Laminar−25 MLA+GLA
Figure 7.5. Optimized aircraft fuel burn as functions of Mach number.
the MLA+GLA designs the beneﬁts of increased wing sweep are negligible at Mach
numbers below 0.78. The results suggest that the combination of active load control
and lowsweep NLF wing can be a potential alternative to more sophisticated 3D
NLF wing design and complex active laminar ﬂow control systems.
7.2 MLA and GLA Control Surface Deﬂection
The eectiveness of the load alleviations systems can be a strong function of the
practical range of high speed control surface deﬂections max ”. Yet determining the
rational bounds on these control deﬂections is complex problem – one that involves
detailed considerations of hinge moment, reserve control authority, aeroelasticity and
actuator design and integration. It is instructive therefore to examine the aircraft
design sensitivities to changes in max ”.
Figures 7.6 and 7.7 show the variation in optimized MLA+GLA aircraft cost and fuel
burn as functions of the maximum allowable highspeed control surface deﬂections.
The cost and fuel burn trends both ﬂatten beyond a deﬂection of 10
¶
. The combina
tion of maximum lift constraints, elastic constraints and minimum gauge thickness
combine to eliminate further gains from increased deﬂection bounds. The results
CHAPTER 7. SENSITIVITY STUDIES 86
0 5 10 15
0.92
0.94
0.96
0.98
1
1.02
1.04
Allowable Load Control Deflection (Deg)
R
e
l
a
t
i
v
e
C
o
s
t
Turbulent MLA+GLA
Laminar MLA+GLA
Figure 7.6. Optimized MLA+GLA aircraft costs as functions of maximum load
alleviation control surface deﬂections.
0 5 10 15
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Allowable Load Control Deflection (Deg)
R
e
l
a
t
i
v
e
F
u
e
l
B
u
r
n
Turbulent MLA+GLA
Laminar MLA+GLA
Figure 7.7. Optimized MLA+GLA aircraft fuel burns as functions of maximum load
alleviation control surface deﬂections.
CHAPTER 7. SENSITIVITY STUDIES 87
also demonstrate that our assumed MLA and GLA control surface deﬂection ranges –
based on published parameters of existing load alleviation systems – are sucient to
achieve eective load control.
7.3 GLA Control Surface Bandwidth
The eectiveness of the GLA systems is a function of actuator bandwidth. In this
section we examine the sensitivity of the aircraft design to changes in actuator band
widths.
0 10 20 30 40
0.92
0.94
0.96
0.98
1
1.02
1.04
Load Control Deflection Rate (Deg/s)
R
e
l
a
t
i
v
e
C
o
s
t
Turbulent MLA+GLA
Laminar MLA+GLA
Figure 7.8. MLA+GLA aircraft cost trends as functions of maximum allowable load
alleviation control surface deﬂection rates.
Figures 7.8 and 7.9 show the variation in the optimized MLA+GLA aircraft cost and
fuel burn as functions of the maximum control surface deﬂection rate max (d”/dt).
The results conﬁrm that slow actuators can indeed restrict the eectiveness of the
GLA system. However, the trends for both the laminar and turbulent aircraft ﬂatten
out beyond a rate of 20
¶
/s – a rate that is well within the operating parameters of
commercial aircraft ailerons at 3540
¶
/s.
55
The diminishing returns can mean one of
two things: 1) typical aileron actuators are powerful enough to cope with the high
frequency gusts speciﬁed by the 1–Cosine criteria or 2) if a gust is fast enough to
saturate highspeed aileron actuators then it is also probably too fast to substantially
CHAPTER 7. SENSITIVITY STUDIES 88
0 10 20 30 40
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Load Control Deflection Rate (Deg/s)
R
e
l
a
t
i
v
e
F
u
e
l
B
u
r
n
Turbulent MLA+GLA
Laminar MLA+GLA
Figure 7.9. MLA+GLA aircraft fuel burn trends as functions of maximum allowable
load alleviation control surface deﬂection rates.
excite the wing structure modes. The consistent ratesaturation of the GLA actuators
in the dynamic simulations suggests that the second explanation is likely correct.
7.4 GLA with Only Ailerons
We assume that all trailing edge control surfaces can be used for both MLA and
GLA and that all control surfaces can sustain the same deﬂection rate. However,
aircraft ﬂaps are not typically sized as control surfaces. In fact, most ﬂap actuators
on commercial aircraft tend to be quite slow – a deﬂection rate of less than 2
¶
/s is
typical for complex, multislotted ﬂaps
55
. So while ﬂaps can be reasonably allocated
to the MLA system to work with anticipated, pseudostatic loads, their utilities in
gust encounters are questionable at best.
An conservative approach is to simply remove the ﬂaps from the GLA control system
and see how the design might change. To this end we set the two inboard GLA control
channel gains to 0. This leaves the outboard control surface deﬂections ”
3
and ”
4
shown in ﬁg. 7.10 for GLA. The MLA system remains unchanged and can schedule
all trailing edge control channels. The control arrangement represents a GLA system
CHAPTER 7. SENSITIVITY STUDIES 89
Figure 7.10. GLA using only outboard control surfaces.
that uses only ailerons.
0.7 0.72 0.74 0.76 0.78 0.8
0.92
0.94
0.96
0.98
1
1.02
1.04
Cruise Mach Number
R
e
l
a
t
i
v
e
C
o
s
t
Laminar MLA+GLA
GLA with aileron
Figure 7.11. Laminar MLA+GLA aircraft cost trends with dierent GLA control
allocations.
The results in ﬁgs. 7.11 and 7.12 demonstrate that most of the savings from the GLA
can be achieved with the outboard aileron control channels. This result suggests that
the control arrangements found on typical airliners should be adaquate for eective
GLA.
CHAPTER 7. SENSITIVITY STUDIES 90
0.7 0.72 0.74 0.76 0.78 0.8
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Cruise Mach Number
R
e
l
a
t
i
v
e
F
u
e
l
B
u
r
n
Laminar MLA+GLA
GLA with aileron
Figure 7.12. Laminar MLA+GLA aircraft fuel burn trends with dierent GLA
control allocations.
7.5 Lower Surface Laminar Flow
We study the sensitivities of the aircraft design to laminar ﬂow on the bottom surface.
We add the lower surface transition locations x
tl
as design variables and impose
compatibility constraints to ensure laminar ﬂow up to x
tl
:
Re
x
(x
tl
) < Re
e
9(x
tl
)
The optimized MLA+GLA aircraft with turbulent and laminar bottom surfaces are
compared in ﬁg. 7.13. The similarity between the two aircraft suggests that only
modest changes to the pressure distributions are needed to stabilize the lower surface
boundary layer.
The normalized aircraft parameters and performance metrics in ﬁg. 7.14 show that
maintaining laminar ﬂow on both the upper and lower surfaces nets a tangible 1%
improvement in cost and 5% improvement in fuel burn. The total fuel burn reduction
over the baseline turbulent design now stands at 20%.
The fuel and cost trends plotted in sections 7.5 and 7.5 conﬁrm that the improvement
from lower surface laminar ﬂow are consistent across a wide range of cruise Mach
CHAPTER 7. SENSITIVITY STUDIES 91
(a) Laminar MLA+GLA (b) Laminar Bottom Surface
Figure 7.13. Comparison of the MLA+GLA aircraft designed with turbulent and
laminar bottom surfaces.
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Laminar MLA+GLA
Bottom Surface NLF
Laminar MLA+GLA Bottom Surface NLF
Wing Weight 0.908 0.897
Fuel Weight 0.842 0.796
Sea Level Thrust 0.835 0.803
L/D 1.148 1.213
Cost 0.951 0.939
Figure 7.14. Comparison of the MLA+GLA aircraft designed with turbulent and
laminar bottom surfaces.
CHAPTER 7. SENSITIVITY STUDIES 92
0.7 0.72 0.74 0.76 0.78 0.8
0.92
0.94
0.96
0.98
1
1.02
1.04
Cruise Mach Number
R
e
l
a
t
i
v
e
C
o
s
t
Turbulent MLA+GLA
Laminar MLA+GLA
Laminar Bottom Surface
Figure 7.15. Cost trends for the Laminar MLA+GLA aircraft with turbulent and
laminar bottom surfaces. The results of the Turbulent MLA+GLA are
included for reference.
0.7 0.72 0.74 0.76 0.78 0.8
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
Cruise Mach Number
R
e
l
a
t
i
v
e
F
u
e
l
B
u
r
n
Turbulent MLA+GLA
Laminar MLA+GLA
Laminar Bottom Surface
Figure 7.16. Duel burn trends for the Laminar MLA+GLA aircraft with turbulent
and laminar bottom surfaces. The results of the Turbulent MLA+GLA
are included for reference.
CHAPTER 7. SENSITIVITY STUDIES 93
numbers. The plots also demonstrate that achieving laminar ﬂow on the upper surface
still accounts for the bulk of the fuel savings.
7.6 Gate Constraints
Active load alleviation systems can greatly increase the wingspan and reduce drag.
However, the wingspans of commercial aircraft are limited by more than just stress and
aeroelastic constraints. Gate and runway compatibility requirements can restrict the
wingspan and pose indirect operational constraints on MLA and GLA eectiveness.
Figure 7.17 shows the Mach 0.78 Turbulent, Turbulent MLA+GLA and Laminar
MLA+GLA aircraft designed with a 120 feet limit on wingspan.
(a) Turbulent (b) Turbulent MLA+GLA (c) Laminar MLA+GLA
Figure 7.17. A comparison of gateconstrained aircraft.(b<120 ft)
We ﬁrst ground the analysis with a comparison of the baseline turbulent aircraft
designed with and without gate constraints in ﬁg. 7.18. The results, not surprisingly,
demonstrate that the baseline is insensitive to the gate constraint.The span restrictions
produce only a negligible increase in cost and a modest 2% increase in fuel burn. While
the gate constraint reduces the span, the dierence is made up in part by reduced
wing weight.
The results in ﬁgs. 7.19 and 7.20 show that the addition of gate constraints halves
CHAPTER 7. SENSITIVITY STUDIES 94
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Turbulent
Gate−constrained
Turbulent Gateconstrained
Wing Weight 1.000 0.864
Fuel Weight 1.000 1.022
Sea Level Thrust 1.000 1.054
L/D 1.000 0.958
Cost 1.000 1.005
Figure 7.18. A comparison of the turbulent aircraft designed with and without gate
constraints.
CHAPTER 7. SENSITIVITY STUDIES 95
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Turbulent MLA+GLA
Gate−constrained
Turbulent MLA+GLA Gateconstrained
Wing Weight 0.762 0.616
Fuel Weight 0.908 0.957
Sea Level Thrust 0.888 0.978
L/D 1.045 0.968
Cost 0.966 0.979
Figure 7.19. A comparison of the Turbulent MLA+GLA aircraft designed with and
without gate constraints.
CHAPTER 7. SENSITIVITY STUDIES 96
Wing Weight Fuel Weight Sea Level Thrust L/D Cost
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
R
e
l
a
t
i
v
e
V
a
l
u
e
Laminar MLA+GLA
Gate−constrained
Laminar MLA+GLA Gateconstrained
Wing Weight 0.908 0.718
Fuel Weight 0.842 0.923
Sea Level Thrust 0.835 0.980
L/D 1.148 1.026
Cost 0.951 0.975
Figure 7.20. A comparison of the Laminar MLA+GLA aircraft designed with and
without gate constraints.
CHAPTER 7. SENSITIVITY STUDIES 97
the fuel savings in both the Turbulent and Laminar MLA+GLA aircraft. Unable to
increase the span, the optimizer reduces the wing weight to take advantage of load
alleviation. Hence gateconstrained wing is 40% lighter than the baseline. But the
weight savings cannot match the beneﬁts from increased span. An aggressive load
alleviation system may be hard to justify if aircraft remain constrained by existing
airport footprints. However, experience show that gate constraints can evolve with
new operational realities. The potentials of load alleviation and other new technologies
can motivate reevaluations of aircraft gate constraints.
Chapter 8
Conclusions and Future Work
In this thesis we develop a conceptual aircraft design framework that formally in
corporates active load alleviation and natural laminar ﬂow. We design the aircraft
concurrently with its load control system. The design framework incorporates both
aircraft dynamic simulations and modal solutions of the wing structural dynamics to
obtain gust loads. A hybridinverse viscous design tool is used to incorporate laminar
ﬂow into aircraft design. By directly operating on the wing pressure distribution, we
capture the tradeo between structure eciency, compressibility drag and natural
laminar ﬂow.
A series of design studies demonstrates two important results: ﬁrst, the gains from
the independent application of MLA and GLA control are modest. This is intuitive:
as MLA or GLA reduces one type of stress, other loads can emerge as critical design
conditions. Only by combining MLA and GLA can we realize signiﬁcant improvements
in eciency. Second, active load alleviation can tilt the balance of the transonic
aerostructural trade in favor of highspan, lowsweep laminar ﬂow wings. Without
load alleviation, a lowsweep NLF wing oers little real advantage over its turbulent
counterpart at high transonic speeds. Active load alleviation can increase the Mach
number at which NLF can be eciently exploited. The combination of MLA, GLA
and NLF represents therefore a potential alternative to the longestablished transonic
98
CHAPTER 8. CONCLUSIONS AND FUTURE WORK 99
paradigm of highsweep turbulent wing.
The results demonstrate that a minimum cost turbulent aircraft designed concurrently
with MLA and GLA control systems can a achieve a signiﬁcant 10% reduction in fuel
burn and 3.4% reduction in cost relative to a baseline design without load control.
The eciency gains come primarily from reduced weight and increased span though
active load control. The corresponding NLF aircraft invests the weight savings from
load alleviation to enable extensive laminar ﬂow and reduce drag. In this case the
fuel and cost savings grow to 15% and 5% respectively.
Sensitivity studies demonstrate that the control requirements for eective active
load control are within the parameters of today’s aircraft control actuators. We
demonstrate that a GLA system that utilizes only aileron to aect load control can
be eective. Comparisons with idealized highsweep NLF wing also suggest that the
combination of active load control and lowsweep NLF wing is a potential alternative
to more sophisticated 3D NLF wing design or complex active laminar ﬂow control
(LFC) systems.
The design framework developed in this thesis represents only the ﬁrst step toward
the design of more intelligent and responsive wings and their associated load control
systems. There is certainly room for improvement.
The development and integration of higher ﬁdelity boundary layer solvers that account
for compressibility and crossﬂow would complete the viscous design. Flutter and its
suppression are also important considerations for the high span, ﬂexible wings enabled
by load alleviation. Finally, while the application of quasisteady aerodynamics in the
gust simulations is likely conservative,
37
this assumption should be validated.
The most important area of improvement is in the GLA design process. In this thesis
we consider only reactive GLA control laws. Future research examine in more detail
the performance of dierent GLA control policies. Detailed exploration of controller
design also raises interesting questions of sensor selection and emplacement. Equally
important is the needs to account for measurement uncertainties and time delay in
CHAPTER 8. CONCLUSIONS AND FUTURE WORK 100
the dynamic simulations.
Sophisticated GLA controller design also requires a more physical description of the
gust. The 1–Cosine gust may be the FAR speciﬁed design criteria, but it does not
reﬂect the stochastic nature of atmospheric gust, nor does it produce the worstcase
gust.
37
And since the 1–Cosine gust is fully characterized by the gust gradient length,
it can be anticipated by a sophisticated controller.
The matched ﬁlter technique (MFT)
26
and statistical discrete gust (SDG)
28
represent
two attempts to address the shortfalls of the 1–Cosine gust in the context of controller
design. For linear systems the MFT method exploits superposition to directly solve
for the worstcase gust.
26,27,61
The SDG method on the other hand is an extension
of the 1–Cosine gust description with stochastic elements.
62
A logical next step is
to incorporate SDG or MFT gusts into the design framework and understand their
impact on total aircraft design. However, as the gust description becomes more
complex, the combinatorial growth in the number of possible gust waveforms may
require a completely dierent optimization strategy.
Finally, aerodynamic load alleviation is by no means the only way to increase the
wing structural eciency. Pfenninger ﬁrst proposed the strutbraced wing (SBW)
in the 1960s as a means to enable wings of very high span or thin wings that are
compatible with transonic laminar ﬂow.
63–66
SBW and aerodynamic load alleviation
represent therefore two dierent ways to exploit the same aerostructural synergy. The
current design framework can be readily extended to study the relative merits of the
dierent load alleviation schemes and their combined eect on natural laminar ﬂow
and aircraft design.
Appendix A
Airfoil Inverse Design
In this appendix we present the results of a series of airfoil optimizations to illustrate
the workings of the hybridinverse airfoil design tool. The objective in each case is
to minimize the sum of the section proﬁle and compressibility drag with respect to
the pressure variables. We ﬁrst presents the results of a point airfoil optimization
at a chord Reynolds number of 20 million, a wing sweep of 10
¶
and a freestream
Mach number of 0.75. The elastic axis x
e
is assumed to be at 43% of the chord. The
optimization is subject to pressure distribution, boundary layer and airfoil geometry
constraints:
Pressure Distribution
M
xm
< 1.1
C
l
> 0.4
C
m0
> ≠0.2
Transition
Re
x
(x
t
) < Re
E9
(x
t
)
101
APPENDIX A. AIRFOIL INVERSE DESIGN 102
Geometry
t
inv
(x
e
) > 0.09c
t
inv
(x
TE
) = 0
The optimized airfoil geometry, pressure distributions and boundary layer properties
are shown in ﬁg. A.1. The airfoil designed at the reference condition has 42 counts of
parasite drag with upper surface transition at 60% chord.
0 0.5 1
−0.1
0
0.1
z
/
c
x/c
(a) Airfoil
0 0.5 1
−1
−0.5
0
0.5
1
x/c
C
p
(b) C
p
0 0.2 0.4 0.6 0.8 1
0
1
2
3
4
x 10
−3
θ
/
c
x/c
(c) Momentum Thickness
Figure A.1. Example airfoil optimization geometry, C
p
and boundary layer momen
tum thickness results.
In the example optimization we force transition on the bottom surface near the leading
edge. There are two reasons for this simpliﬁcation: 1) the lower surface of an airfoil
is responsible for only about 1/3 of the total parasite drag
12
and 2) slat gaps, track
APPENDIX A. AIRFOIL INVERSE DESIGN 103
fairings and contaminants can lead to early transition on the bottom surface despite
the presence of favorable pressure gradients. Hence only the upper surface transition
x
tu
point is subject to optimization and the transition compatibility is also only
imposed on the upper surface. Finally, the constraint on C
m0
is added to impose a
trim penalty on severely aftloaded airfoil designs.
0.72 0.73 0.74 0.75 0.76
0
0.2
0.4
0.6
0.8
1
Mach
x
t
/
c
C
l
= 0.35
C
l
= 0.4
C
l
= 0.45
(a) x transition
0.72 0.73 0.74 0.75 0.76
0
20
40
60
80
100
Mach
C
d
p
(
c
o
u
n
t
s
)
C
l
= 0.35
C
l
= 0.4
C
l
= 0.45
(b) C
dp
Figure A.2. Optimized airfoil transition and C
dp
as a function of C
l
and Mach
Œ
.
The section t/c and Re
c
are ﬁxed at 9% and 20 million respectively.
Figures A.2 and A.3 show the optimized airfoil C
dp
and x
t
as a function of variations
in C
l
, t/c and M
Œ
. Each point corresponds to the results of an optimized airfoil. The
performance of the lowsweep NLF section is constrained by compressibility: once the
maximum M
xm
is reached, any increase in M
Œ
, C
l
or t/c has to be compensated by re
duced ﬂow acceleration. The result could well be earlier transition and increased drag.
The inverse method captures therefore the fundamental tradeo among structural
eciency, compressibility and laminar ﬂow.
APPENDIX A. AIRFOIL INVERSE DESIGN 104
0.72 0.73 0.74 0.75 0.76
0
0.2
0.4
0.6
0.8
1
Mach
x
t
/
c
t/c = 0.085
t/c = 0.09
t/c = 0.095
(a) x transition
0.72 0.73 0.74 0.75 0.76
0
20
40
60
80
100
Mach
C
d
p
(
c
o
u
n
t
s
)
t/c = 0.085
t/c = 0.09
t/c = 0.095
(b) C
dp
Figure A.3. Optimized airfoil transition and drag as a function of t/c and Mach
Œ
.
The C
l
and Re
c
are ﬁxed at 0.4 and 20 million respectively.
0.72 0.73 0.74 0.75 0.76
0
0.2
0.4
0.6
0.8
1
Mach
x
t
/
c
Re
c
= 20
Re
c
= 30
Re
c
= 40
(a) x transition
0.72 0.73 0.74 0.75 0.76
0
20
40
60
80
100
Mach
C
d
p
(
c
o
u
n
t
s
)
Re
c
= 20
Re
c
= 30
Re
c
= 40
(b) C
dp
Figure A.4. Optimized airfoil transition and drag as a function of Re
c
and Mach
Œ
.
The C
l
and t/c are ﬁxed at 0.4 and 9% respectively.
Appendix B
Numerical Solution of
SecondOrder ODEs
Modal decomposition can be used to decouple a system of ODEs into scalar inhomo
geneous secondorder ODEs:
¨ y
i
(t) + 2’
i
Ê
i
˙ y
i
(t) + Ê
i
2
y
i
(t) =
¯
f
i
(t)
The transient forced response of each mode i can be solved by the superposition of
piecewise impulse responses at discrete timesteps. The timemarching integration
105
APPENDIX B. NUMERICAL SOLUTION OF SECONDORDER ODES 106
scheme used in the structural dynamics solver is as follows:
59
A
0
=
a
Ê
i
2
≠
2’
i
b
Ê
i
3
A
1
=
b
Ê
i
2
A
2
= y
i
(t
0
) ≠A
0
A
3
=
˙ y
i
(t
0
) + Ê
i
’
i
A
2
≠A
1
Ê
di
B
1
= e
≠Ê
i
’
i
t
cos(Ê
di
t)
B
2
= e
≠Ê
i
’
i
t
sin(Ê
di
t)
y(t
1
) = A
0
+A
1
t +A
2
B
1
+A
3
B
2
˙ y(t
1
) = A
1
+ (Ê
di
A
3
≠Ê
i
’
i
A
2
)B
1
≠(Ê
di
A
2
+ Ê
i
’
i
A
3
)B
2
Here the solution y(t) is propagated from step 0 to 1. If the timestep t is constant
then only the A
2
and A
3
coecients need to be evaluated at every time step.
Appendix C
Cost Model
In this appendix we detail the methods contained in the extended Air Transport
Association (ATA) cost model.
60
The cost objective used in the analysis in the
previous chapters is the estimated ticket price c
tic
($/pax) in eq. (C.1). In chapters 6
and 7 the ticket price are presented in relative terms against the Mach 0.78 turbulent
baseline aircraft. The application reﬂects the fact that the simple cost model is at best
very approximate measure of relative economic performance. The methods detailed in
this section are heavy on empiricism. They represent a preliminary attempt to inject
costsensitivity into the design process.
c
tic
= 1.1
A
DOC
100
N
seat
N
pax
R +IOC
B
(C.1)
The distinction between N
seat
and N
pax
is that the former refers to the number of seats
in a oneclass conﬁguration while the latter is the number of passengers in the typical
3class arrangement. The ticket price can be decomposed into direct and indirect
operating component. The next section discusses the buildup of the aircraft direct
operating cost (DOC). This is followed by the discussion of the indirect operating
cost (IOC).
107
APPENDIX C. COST MODEL 108
C.1 Direct Operating Cost
The DOC includes all of the cost items that are associated with the ﬂight operations
of the aircraft. This includes the cost of fuel, the pilot (which is deemed essential for
ﬂight) and maintenance. Also included in the DOC estimates are the cost to insure
the aircraft and the cost of depreciation, which are strong functions of the acquisition
cost of the aircraft and the utilization rate. The DOC in cents per seatmile can be
written as:
DOC = (c
fuel
+c
pilot
+c
depreciation
+c
insurance
+c
maintenance
)
100
N
seat
C.1.1 Fuel Cost
We estimate the combined cost of fuel and lubrication oil as a function of thrust, the
price aviation fuel p
fuel
and the price of lubricants p
oil
:
c
fuel
=
1.02(p
fuel
W
fuel
+ 0.135p
oil
N
e
T
0
)
R
Unless otherwise speciﬁed, the assumed fuel and oil prices are $2.5/gal and $20/lb
respectively.
C.1.2 Pilot Cost
The pilot cost is correlated to the number and types of engines mounted on the aircraft.
For the twin turbofan conﬁguration in this study the following equation is used:
c
pilot
= Ÿ
if
0.05(W
MTOW
/1000) + 100
V
block
APPENDIX C. COST MODEL 109
Where the block speed – an important utilization parameter – is estimated as
follows:
V
block
=
R
T
m
+T
cl
+T
cr
Here the climb time T
cl
and ground and air maneuver time T
m
are based on historical
data. The cruise time in turn represents a small increase in the ﬂight time.
T
cr
=
1.02R + 20
V
The estimate of the block time is based on the assumption that the climb and descend
segments adds no additional distance to the mission. The descent is assumed to incur
no additional ﬂight time.
C.1.3 Depreciation and Insurance Costs
The depreciation of the capital value of an airplane is dependent to a large degree
on the individual airline and the world economic and competitive conditions as the
airplane is maintained in a fully airworthy condition throughout its life.
c
depr
=
c
t
+ 0.10(c
a
) + 0.40N
e
c
t
D
a
U
a
V
b
The insurance rate is roughly a function of the aircraft total cost and the utilization
rate. A typical insurance rate I
ra
is in the neighborhood of 0.2%. The insurance cost
is estimated using the following relationship:
c
insurance
=
I
ra
(c
t
)
U
a
V
b
APPENDIX C. COST MODEL 110
C.1.4 Maintenance Cost
The aircraft maintenance cost includes both labor and material components. The
airframe and engine maintenance costs are computed separately to reﬂect the dierent
operational cost sensitivities of the dierent aircraft components. The total aircraft
maintenance cost can be written as a sum of the engine and airframe maintenance
labor and material costs:
c
maintenance
= 1.8
Ë
c
(af,labor)
+c
(af,mat)
+c
(en,labor)
+c
(en,mat)
È
The material costs are dependent on the engine c
e
and the airframe costs c
a
. We
estimate the engine cost based on a ﬁt of published engine cost to engine T/W. The
total aircraft cost is estimated using the perlb cost of aircraft subsystem collected
in Thomas.
60
The weight data of the various components comes from historical data
and the PASS aircraft sizing modules. The total aircraft cost is as follows:
c
t
= (c
a
+c
e
n
e
)
Labor Cost
The aircraft maintenance labor costs is composed of perﬂightcycle (landing and
takeo) and perﬂighthour components. The labor manhours per ﬂight cycle t
ca
and
per ﬂight hour t
ha
are extrapolated using historical data:
c
(af,labor)
=
[t
ha
(t
block
≠0.25) +t
ca
] R
L
R
t
ca
= 0.05
W
a
≠W
e
1000
+ 6 ≠
630
Wa
1000
+ 120
t
ha
= 0.59l
ca
The labor rate R
L
is a user input and reﬂects the prevailing wage of aircraft mainte
nance personal. No inﬂation factor is applied to the labor cost if uptodate labor rates
APPENDIX C. COST MODEL 111
are used. W
a
refers to the aircraft empty weight excluding the engine weight. The
engine labor cost is also described by perﬂighthour and percycle components:
c
(en,labor)
=
(t
he
t
f
+t
ce
)R
L
R
t
ce
= (0.6 +
0.027T
0
10,000
)N
e
t
he
= (0.3 +
0.03T
0
10,000
)N
e
Material Cost
The aircraft material cost c
(af,mat)
is correlated to the estimated aircraft cost:
c
(af,mat)
= Ÿ
if
3.08c
a
t
f
+ 6.24c
a
10
6
R
The engine material cost c
(en,mat)
is broken down into per ﬂight hour and per ﬂight
cycle components:
c
(en,mat)
= Ÿ
if
c
he
t
f
+c
ce
R
c
he
=
2.5n
e
c
e
10
5
c
ce
=
2.0n
e
c
e
10
5
C.2 Indirect Operating Cost
Indirect operating costs (IOC) as the name may suggest include airlinespeciﬁc costs
that are not directly connected with the ﬂight of the aircraft. They can include the
cost of the cabin crew, landing fees, ground handling labor and even advertising.
Indirect costs are operational by nature and can be dicult to deﬁne. The IOC is
APPENDIX C. COST MODEL 112
coarsely estimated using a simple correlation of domestic ﬂight IOC to the maximum
takeo weight and the anticipated load factor LF:
IOC = Ÿ
if
5
≠0.04 + 0.00129
W
MTOW
1000
+ 0.00119n
p
+ 0.0127n
p
LF
6
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