Conceptual Design for a
Laminar-Flying-Wing Aircraft
Tariq Issam Saeed
Trinity Hall
University of Cambridge
A thesis submitted for the degree of
Doctor of Philosophy
February 2012

Declaration
Described in this dissertation is worked performed in the Department of Engineer-
ing at the University of Cambridge between October 2008 and February 2012. I
hereby declare that no part of this work has been submitted as an exercise for a
degree at this or any other university. This dissertation is entirely the result of
my own work and includes nothing which is the outcome of collaboration. This
dissertation contains approximately 122 figures and 48,500 words.
Signature:
Date:

This thesis is dedicated to my father, for his guidance and encouragement
throughout my life, and my mother.

Acknowledgements
Firstly, I would like to express my gratitude toward my supervisor Dr Will Gra-
ham, for sharing his knowledge of aerodynamics, and his unwavering support
throughout. It has been a honour to work with him.
I would like to thank Prof Holger Babinsky for the useful discussions on the
pressure drop across a porous skin, and his general advice. I must acknowledge
Dr Chez Hall’s contribution to this research through his derivation of the pump
power; I am also indebted to him for the many useful discussions on aircraft
jet propulsion. Thanks also go to Dr Keith Seffen for the useful discussions on
structural design and Dr Jerome Jarrett for his general advice. Finally, I would
like to acknowledge Jeremy Eastwood, Mudassir Lone, Charles Ni and Ian Vigrass
for their contributions to the undergraduate ‘Green Aircraft Design’ project; I am
especially grateful to Jeremy Eastwood for sharing with me his knowledge of shell
scripting.
I must thank the UK Engineering and Physical Sciences Research Council for
its financial support via its Doctoral Training scheme. In addition, I extend my
gratitude to Trinity Hall for its financial assistance, which has helped facilitate
my attendance at international conferences.

Abstract
The laminar-flying-wing aircraft appears to be an attractive long-term prospect
for reducing the environmental impact of commercial aviation. In assessing its
potential, a relatively straightforward initial step is the conceptual design of a
version with restricted sweep angle. Such a design is the topic of this thesis.
In addition to boundary layer laminarisation (utilising distributed suction) and
limited sweep, a standing-height passenger cabin and subcritical aerofoil flow are
imposed as requirements. Subject to these constraints, this research aims to:
provide insight into the parameters affecting practical laminar-flow-control suction
power requirements; identify a viable basic design specification; and, on the basis
of this, an assessment of the fuel efficiency through a detailed conceptual design
study.
It is shown that there is a minimum power requirement independent of the suc-
tion system design, associated with the stagnation pressure loss in the boundary
layer. This requirement increases with aerofoil section thickness, but depends
only weakly on Mach number and (for a thick, lightly-loaded laminar flying wing)
lift coefficient. Deviation from the optimal suction distribution, due to a practi-
cal chamber-based architecture, is found to have very little effect on the overall
suction coefficient. In the spanwise direction, through suitable choice of chamber
depth, the pressure drop due to frictional and inertial effects may be rendered
negligible. Finally, it is found that the pressure drop from the aerofoil surface to
the pump collector ducts determines the power penalty; suggesting there is little
benefit in trying to maintain an optimal suction distribution through increased
subsurface-chamber complexity. For representative parameter values, the mini-
mum power associated with boundary-layer losses alone contributes some 80% –
90% of the total power requirement.
To identify the viable basic design specification, a high-level exploration of the
laminar-flying-wing design space is performed, with an emphasis above all on
aerodynamic efficiency. The characteristics of the design are assessed as a func-
tion of three parameters: thickness-to-chord ratio, wingspan, and unit Reynolds
number. A feasible specification, with 20% thickness-to-chord, 80 m span and a
unit Reynolds number of 8× 106 m−1, is identified; it corresponds to a 187 tonne
aircraft which cruises at Mach 0.67 and altitude 22,500 ft, with lift coefficient
0.14. The benefit of laminarisation is manifested in a high lift-to-drag ratio, but
the wing loading is low, and the structural efficiency and gust response are thus
likely to be relatively poor.
On the basis of this specification, a detailed conceptual design is undertaken. A
220-passenger laminar-flying-wing concept, propelled by three turboprop engines,
with a cruise range of 9000 km is developed. The estimated fuel burn is 13.9
g/pax.km. For comparison, a conventional aircraft, propelled by four turboprop
engines, with a high-mounted, unswept, wing is designed for the same mission
specification and propulsion characteristics, and is shown to have a fuel burn of
15.0 g/pax.km. Despite significant aerodynamic efficiency gains, the fuel burn
of the laminar flying wing is only marginally better as it suffers from a poor
cruise engine efficiency, due to extreme differences between takeoff and cruising
requirements, and is much heavier.
The laminar flying wing proposed in this thesis falls short of the performance im-
provements expected of the concept, and is not worth the development effort. It is
therefore proposed that research efforts either be focussed on improving the engine
efficiency, or switching to a low aspect ratio, high sweep, design configuration.
Publications
1. Saeed, T.I., Graham, W.R., Babinsky, H., Eastwood, J.P., Hall, C.A., Jar-
rett, J.P, Lone, M. and Seffen, K.A., Conceptual Design for a Laminar Flying
Wing Aircraft, 27th AIAA Applied Aerodynamics Conference, San Antonio,
Texas, June 22-25, 2009, AIAA-2009-3616.
2. Saeed, T.I., Graham, W.R., Babinsky, H. and Hall, C.A., Boundary Layer
Suction System Design for Application to Laminar Flying Wing Aircraft,
28th AIAA Applied Aerodynamics Conference, Chicago, Illinois, June 28-1,
2010, AIAA-2010-4379.
3. Saeed, T.I., Graham, W.R. and Hall, C.A., Boundary-Layer Suction System
Design for Laminar-Flying-Wing Aircraft, Journal of Aircraft, Vol. 48, No.
4, 2011, pp. 1368 – 1379.
4. Saeed, T.I. and Graham, W.R., Conceptual Design for a Laminar-Flying-
Wing Aircraft, 50th AIAA Aerospace Sciences and New Horizons Meeting,
Nashville, Tennessee, January 9-12, 2012, AIAA-2012-0868.

Contents
Contents xiii
List of Figures xix
List of Tables xxvii
Nomenclature xxix
1 Introduction 1
2 Literature Review 7
2.1 Laminar Flow Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Profile Drag Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 Flow Control Design Methodology . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Boundary Layer Stability . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.3.1 Tollmien-Schlichting Waves . . . . . . . . . . . . . . . . . . . 14
2.1.3.2 Taylor-Go¨rtler Vortices . . . . . . . . . . . . . . . . . . . . . 14
2.1.3.3 Crossflow Instabilities . . . . . . . . . . . . . . . . . . . . . . 14
2.1.3.4 Attachment-Line Instabilities . . . . . . . . . . . . . . . . . . 16
2.1.3.5 Shock Wave / Laminar Boundary Layer Interactions . . . . . 17
2.1.3.6 Example Suction Distributions . . . . . . . . . . . . . . . . . 17
2.1.4 LFC System Design Considerations . . . . . . . . . . . . . . . . . . . . 19
2.2 The Flying Wing Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.1 Structural Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.2 Cabin Arrangement and Operational aspects . . . . . . . . . . . . . . 25
2.2.3 Stability and Control Considerations . . . . . . . . . . . . . . . . . . . 27
2.2.3.1 Longitudinal Stability . . . . . . . . . . . . . . . . . . . . . . 27
2.2.3.2 Lateral-Directional Stability . . . . . . . . . . . . . . . . . . 29
2.2.3.3 Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
xiii
CONTENTS
2.2.3.4 Effects of Wing and Planform Geometry on Stability and Con-
trol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.2.4 Flying and Handling Qualities . . . . . . . . . . . . . . . . . . . . . . 35
2.2.4.1 Civil and Military Specifications . . . . . . . . . . . . . . . . 35
2.2.4.2 Behaviour of Tailless Aircraft . . . . . . . . . . . . . . . . . . 36
2.2.5 Aeroelastic Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.3 Laminar-Flying-Wing Design Concepts . . . . . . . . . . . . . . . . . . . . . . 37
2.3.1 Greener by Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.2 Delta-Wing Aircraft with Suction . . . . . . . . . . . . . . . . . . . . . 38
2.3.3 The Handley Page HP117 Proposal . . . . . . . . . . . . . . . . . . . . 40
2.4 Summary and Research Proposal . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 Design Methodology 45
3.1 General Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2 Technical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1 3-D Airframe Generation and Aircraft Performance . . . . . . . . . . . 47
3.2.1.1 Computational Tools . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1.2 Aircraft Profile Drag Estimation Method . . . . . . . . . . . 50
3.2.2 Propulsion System Design . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2.2.1 Design Cycle Parameters . . . . . . . . . . . . . . . . . . . . 57
3.2.2.2 GasTurb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.3 Structures and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.3.2 Loading Conditions . . . . . . . . . . . . . . . . . . . . . . . 65
3.2.3.3 Fuselage Structure . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2.3.4 Wing Structure . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.3.5 Validity of Design Methodology . . . . . . . . . . . . . . . . 85
3.2.4 Mission Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4 Boundary-Layer Suction System Design 91
4.1 Boundary-Layer Suction Calculation Method . . . . . . . . . . . . . . . . . . 91
4.1.1 Boundary Layer Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.1.2 Suction Algorithm and Validation . . . . . . . . . . . . . . . . . . . . 94
4.2 Pump Power Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.3 Minimum Suction Requirements . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.3.1 Typical Suction and Power Distributions . . . . . . . . . . . . . . . . . 98
xiv
CONTENTS
4.3.2 Parameter Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.4 Suction Hardware Design and Power Consumption . . . . . . . . . . . . . . . 104
4.4.1 Suction Chamber Layout . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.4.2 Skin Losses and Chamber Discretisation . . . . . . . . . . . . . . . . . 105
4.4.2.1 Pressure Drop Across a Porous Skin . . . . . . . . . . . . . . 106
4.4.2.2 Chamber Specification Algorithm . . . . . . . . . . . . . . . 107
4.4.2.3 Chamber Constraint Trade-Off Study . . . . . . . . . . . . . 109
4.4.3 Spanwise Chamber Losses . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.4.4 Collector Duct Trade-Off Study . . . . . . . . . . . . . . . . . . . . . . 116
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5 LFW Aircraft and Mission Specification 121
5.1 Design Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.1.1 Aircraft Configuration and Geometric Constraints . . . . . . . . . . . 122
5.1.2 Aerodynamic Constraints . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.1.2.1 Unit Reynolds Number . . . . . . . . . . . . . . . . . . . . . 123
5.1.2.2 Planform Sweep . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.1.2.3 Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.1.3 Design Specification Algorithm . . . . . . . . . . . . . . . . . . . . . . 124
5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2.1 Drag Polar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.2.2 Cruise Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.2.3 Lift and Drag Calculations . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3 Aircraft and Mission Parametric Study . . . . . . . . . . . . . . . . . . . . . . 128
5.3.1 Aspect Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.2 Sweep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.3 Profile Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
5.3.4 Cruise Lift Coefficient and Aerodynamic Efficiency . . . . . . . . . . . 129
5.3.5 Cruise Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.6 Cruise Altitude and Velocity . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.7 Wing Loading and Maximum Lift Coefficient . . . . . . . . . . . . . . 134
5.3.8 Maximum Cruise Weight and Structural Weight Fraction . . . . . . . 135
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
5.4.1 Mission Parameter Conflicts . . . . . . . . . . . . . . . . . . . . . . . . 138
5.4.2 Synthesis of Parameter Considerations . . . . . . . . . . . . . . . . . . 139
5.4.3 Sensitivity to Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
xv
CONTENTS
5.4.4 Comparison with Conventional Aircraft . . . . . . . . . . . . . . . . . 141
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
6 Conceptual Design Study 145
6.1 Laminar-Flying-Wing Design Concept . . . . . . . . . . . . . . . . . . . . . . 145
6.1.1 Three-Dimensional Airframe Generation . . . . . . . . . . . . . . . . . 145
6.1.1.1 Flying and Handling Qualities Requirement . . . . . . . . . . 146
6.1.1.2 Planform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
6.1.1.3 Wing and Cabin Design . . . . . . . . . . . . . . . . . . . . . 152
6.1.2 Aircraft Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.1.2.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
6.1.2.2 Cruise Performance . . . . . . . . . . . . . . . . . . . . . . . 159
6.1.2.3 Low-Speed Performance . . . . . . . . . . . . . . . . . . . . . 161
6.1.3 Suction-System Technology Integration . . . . . . . . . . . . . . . . . 163
6.1.3.1 System Architecture . . . . . . . . . . . . . . . . . . . . . . . 164
6.1.3.2 System Specification . . . . . . . . . . . . . . . . . . . . . . . 165
6.1.3.3 Power Requirement and Weight Penalty . . . . . . . . . . . . 169
6.1.4 Propulsion System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.1.4.1 Thrust and Power Requirements . . . . . . . . . . . . . . . . 170
6.1.4.2 Power-Plant Scoping Study . . . . . . . . . . . . . . . . . . . 171
6.1.4.3 LFW Engine Performance . . . . . . . . . . . . . . . . . . . . 178
6.1.4.4 Sensitivity Study . . . . . . . . . . . . . . . . . . . . . . . . . 182
6.1.5 Structures and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . 182
6.1.5.1 Structural Configuration . . . . . . . . . . . . . . . . . . . . 183
6.1.5.2 System Loads Distribution . . . . . . . . . . . . . . . . . . . 185
6.1.5.3 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . 185
6.1.5.4 Weight Breakdown . . . . . . . . . . . . . . . . . . . . . . . . 189
6.1.5.5 Centre-of-Gravity Buildup and Landing Gear Arrangement . 189
6.1.6 Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
6.2 Competitor Aircraft Design Concept . . . . . . . . . . . . . . . . . . . . . . . 193
6.2.1 Target Gross Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.2.2 Cruise Lift Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6.2.3 Aircraft Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
6.2.3.1 Fuselage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
6.2.3.2 Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.2.3.3 Tailplane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
xvi
CONTENTS
6.2.4 Aircraft Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.2.4.1 Cruise Performance . . . . . . . . . . . . . . . . . . . . . . . 198
6.2.4.2 Low-Speed Performance . . . . . . . . . . . . . . . . . . . . . 199
6.2.5 Propulsion System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
6.2.6 Structures and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . 201
6.2.6.1 Structural Weight . . . . . . . . . . . . . . . . . . . . . . . . 201
6.2.6.2 Fuel Weight . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
6.2.6.3 Aircraft Weight Buildup and Centre-of-Gravity Travel . . . . 203
6.3 Comparison of LFW and Competitor Aircraft . . . . . . . . . . . . . . . . . . 204
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
7 Conclusions and Future Work 207
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
7.1.1 Motivation for the Study . . . . . . . . . . . . . . . . . . . . . . . . . 207
7.1.2 Conclusions of the Study . . . . . . . . . . . . . . . . . . . . . . . . . 207
7.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . . . . . . 210
References 213
xvii
CONTENTS
xviii
List of Figures
1.1 Conventional aircraft layout — the Boeing 787 Dreamliner. . . . . . . . . . . 1
1.2 Engine fuel consumption and fuel burn per seat over a 1000 nm mission (from
Birch (2000)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 D8 aircraft series (from Greitzer et al. (2010)). . . . . . . . . . . . . . . . . . 2
1.4 Boeing X-48B blended wing body. . . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 Northrop YRB-49 bomber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 Stable and unstable velocity profiles in a flat-plate laminar boundary layer —
flat plate corresponds to zero-pressure gradient. (Taken from Green (2006).) . 8
2.2 Boundary layer development with suction (from Lachmann (1955)). . . . . . 9
2.3 Wake profile for an integrated propulsion and suction system (from Lee (1961)). 11
2.4 Variation in wing drag coefficient with chord Reynolds number for laminar
boundary layers (from Denning et al. (1997)). . . . . . . . . . . . . . . . . . . 12
2.5 Block diagram of LFC design cycle (from Harris et al. (1988)). . . . . . . . . 13
2.6 Schematic diagram of Taylor-Go¨rtler vortices (from Joslin (1998b)). . . . . . 14
2.7 Schematic diagram of the crossflow instability and velocity profile. . . . . . . 15
2.8 Schematic diagram of attachment-line flow (from Joslin (1998b)). . . . . . . . 16
2.9 Example suction flow velocity distribution for the 30◦ (quarter-chord) sweep
X-21A aircraft (Joslin (1998a)). . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.10 Example suction flow velocity distribution for the 10◦ (quarter-chord) sweep
Vampire aircraft (from Head (1955)). . . . . . . . . . . . . . . . . . . . . . . . 18
2.11 Outline for a laminar flow control system (from Edwards (1977)). . . . . . . . 19
2.12 Typical suction surface (from Edwards (1977)). . . . . . . . . . . . . . . . . . 20
2.13 Various pressure loss components making up pump power (from Lachmann
(1955)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.14 X-21A laminar flow pumping system (from Kosin (1965)). . . . . . . . . . . . 22
2.15 Structural concepts for the centrebody pressure vessel (from Liebeck (2004)). 24
2.16 Cabin seating arrangement (from Martinez-Val (2007)). . . . . . . . . . . . . 25
xix
LIST OF FIGURES
2.17 Differential elevon control for a pure aileron deflection to the right without any
elevator effect (from Nickel and Wohlfart (1994)). . . . . . . . . . . . . . . . . 30
2.18 B-2 split flap rudders. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.19 The lift distributions of two rectangular wings with an aspect ratio of 5 and
sweep angles of φ = 0◦ and φ = 45◦. The lift distribution of the swept wing
has been plotted for equal lift (solid line) and for the same angle of attack
(dashed line). (Taken from Nickel and Wohlfart (1994)). . . . . . . . . . . . . 33
2.20 Laminarised aircraft — relative range performance — fixed integrated delta
planforms. Assumptions: optimum L/D cruise (no allowances), cruise Mach
number of 0.8, datum CD0 = 0.010 (no suction treatment), and CQ = 0.0005.
(Taken from Denning et al. (1997)). . . . . . . . . . . . . . . . . . . . . . . . 39
2.21 Handley Page HP117 LFW configuration (from Green (2006)). . . . . . . . . 40
3.1 Schematic diagram of the design process envisaged for the LFW. . . . . . . . 46
3.2 Wake streamline contraction due to fuselage thickness, carrying wing circula-
tion into the wake (from Greitzer et al. (2010)). . . . . . . . . . . . . . . . . . 48
3.3 Example distribution of bound and trailing vortices (output from AVL). . . . 49
3.4 Schematic diagram of friction and pressure drag forces on an infinite swept-
wing (Greitzer et al. (2010)). . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.5 Derivation of fuselage cross-flow drag (from Torenbeek (1976)). . . . . . . . . 53
3.6 Estimated fuselage profile drag increment due to angle of attack and rear fuse-
lage upsweep (from Torenbeek (1976)). (α′f demarcates the fuselage incidence
at which the extra drag is a minimum for a given β value.) . . . . . . . . . . 54
3.7 Profile drag increment due to surface roughness (from Torenbeek (1976)). . . 57
3.8 45◦ swept eight-bladed propeller map at M∞ = 0.70 (from Rohrbach et al.
(1982)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.9 Compressor map scaling parameters (from GasTurb manual). . . . . . . . . . 63
3.10 Schematic of structural design methodology. . . . . . . . . . . . . . . . . . . . 66
3.11 Multi-bubble geometric parameters (perpendicular to the spanwise axis). . . . 68
3.12 Cabin cross section (perpendicular to the chordwise axis). . . . . . . . . . . . 69
3.13 Variation of the ratio of axial-to-hoopwise stress with θf,vb and N for θf,1 =
θf,2 = pi/2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.14 Vertical bulkhead force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.15 Conventional fuselage geometry and applied loads (from Greitzer et al. (2010)). 73
3.16 Wing construction (from Howe (2004)). . . . . . . . . . . . . . . . . . . . . . 74
3.17 Wing (or tail) planform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
xx
LIST OF FIGURES
3.18 Wing (or tail) aerofoil and wing-box cross section (perpendicular to the refer-
ence axis). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.19 Schematic diagram of rib flange and spar construction. . . . . . . . . . . . . . 79
3.20 Schematic diagram of rib arrangement and forces at hinge attachment point. 80
3.21 Schematic diagram of control surface structural arrangement and forces. . . . 81
3.22 Outboard surface Cp for a trailing edge flap deflection of 10◦ over the last 10%
of chord (output from XFoil). . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.23 Structural force discretisation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.24 Resolution of moment and torque couples across a wing-sweep discontinuity. . 84
3.25 Assumed Boeing 737-200 configuration. . . . . . . . . . . . . . . . . . . . . . 86
3.26 Wing shear force, bending moment and torque diagrams — initial estimate
(solid x-marked line) and final estimate (solid line). . . . . . . . . . . . . . . . 87
4.1 NACA 654 − 021 incompressible surface velocity distribution — Cl = 0. . . . 95
4.2 Comparison of calculated suction distribution — NACA 654 − 021 aerofoil,
Cl = 0 and Rec = 20× 106. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.3 Comparison of calculated momentum thickness distribution — NACA 654−021
aerofoil, Cl = 0 and Rec = 20× 106. . . . . . . . . . . . . . . . . . . . . . . . 96
4.4 Section pressure (solid) and suction velocity distribution (dashed) for the upper
surface of a NACA0028 aerofoil — M∞ = 0.56, Rec = 40× 106 and Cl = 0.15. 99
4.5 Distribution of dynamic pressure loss through boundary layer (solid), and
suction velocity (dashed) for the upper surface of a NACA0028 aerofoil —
M∞ = 0.56, Rec = 40× 106 and Cl = 0.15. . . . . . . . . . . . . . . . . . . . 99
4.6 Distribution of (area-distributed) power to overcome losses through boundary
layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.7 Variation of CQ and W˜p with Rec: NACA0028, Cl = 0.15 and M∞ = 0.56.
Both variables are scaled by
√
Rec, so that a constant level implies propor-
tionality to Re−1/2c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.8 Dependence of distributed suction on section thickness for a range of symmet-
rical 4-digit NACA aerofoils at Cl = 0.15, M∞ = 0.5 and Rec = 40 × 106:
solid line – 10%; dashed line – 20%; and dashed-dotted line – 30%; ‘x’ markers
detail Cp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.9 Variation of (a) CQ and (b) W˜p with maximum thickness-to-chord ratio and
section lift coefficient — symmetrical 4-digit NACA aerofoil series, M∞ = 0.5
and Rec = 40× 106. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
xxi
LIST OF FIGURES
4.10 Variation of CQ (solid line) and W˜p (dashed line) with free-stream Mach num-
ber and maximum thickness-to-chord ratio — symmetrical 4-digit NACA aero-
foil series, Cl = 0.15 and Rec = 40× 106. . . . . . . . . . . . . . . . . . . . . . 104
4.11 Suction hardware layout for an untapered wing of span b and chord c. . . . . 105
4.12 Schematic diagram of surface pressure variation over a single chamber width
(downstream of the suction peak). . . . . . . . . . . . . . . . . . . . . . . . . 109
4.13 Chordwise distribution of differential pressure across the porous skin with the
critical pressure superimposed. . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.14 Variation of the total number of chambers with ∆P˜s,av and r˜c. . . . . . . . . 111
4.15 Dependence of CQ on ∆P˜s,av and r˜c. The optimal value calculated by the
algorithm of Sec. 4.1.2 is CQ = 2.24× 10−4. . . . . . . . . . . . . . . . . . . . 111
4.16 Variation of chordwise distribution of suction with r˜c and ∆P˜s,av. . . . . . . . 112
4.17 Variation of actual (solid lines) and approximate (‘x’ markers) W˜p with ∆P˜s,av
and r˜c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.18 Notation for chamber flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.19 Spanwise-chamber pressure drop dependence on b/h and wc/h with h = 10 cm. 115
4.20 Schematic diagram of an alternative chamber-collector-duct arrangement. . . 116
4.21 Comparison of surface, chamber and collector static pressures — ∆P˜s,av = 0.15
and r˜c = 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.22 Variation of W˜p with the number of collectors and r˜c, with ∆P˜s,av = 0.15. . . 118
5.1 Altitude against velocity with contours of Mach number and unit Reynolds
number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.2 Schematic diagram of a simplified laminar-flying-wing planform layout. . . . . 123
5.3 Wing sweep angle dependence on thickness-to-chord ratio and unit Reynolds
number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.4 Zero-lift drag breakdown and its dependence on thickness-to-chord ratio and
unit Reynolds number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.5 The dependence of cruise lift coefficient and lift-to-drag ratio on thickness-to-
chord ratio for: (a) a range of spans and a fixed Reu of 8× 106 m−1 and, (b)
a range of unit Reynolds numbers and a fixed span of 80 m. . . . . . . . . . . 131
5.6 Cruise Mach number dependence on thickness-to-chord ratio, span and unit
Reynolds number. (Top figure corresponds to a Reu = 8 × 106 m−1, and the
bottom to a span of 80 m.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
xxii
LIST OF FIGURES
5.7 The dependence of cruise altitude and cruise velocity on thickness-to-chord
ratio for: (a) a range of spans and a fixed Reu of 8× 106 m−1 and, (b) a range
of unit Reynolds numbers and a fixed span of 80 m. . . . . . . . . . . . . . . 133
5.8 Variation of aircraft wing loading with thickness-to-chord ratio, span and unit
Reynolds number. (Top figure corresponds to Reu = 8 × 106 m−1, and the
bottom to a span of 80 m.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.9 Variation of required maximum lift coefficient with thickness-to-chord ratio,
span and unit Reynolds number. (Top figure corresponds to a Reu = 8× 106
m−1, and the bottom to a span of 80 m.) . . . . . . . . . . . . . . . . . . . . 136
5.10 Variation of aircraft allowable weight with thickness-to-chord ratio, span and
unit Reynolds number. (Top figure corresponds to a Reu = 8× 106 m−1, and
the bottom to a span of 80 m.) . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.11 Variation of wing-weight fraction with thickness-to-chord ratio, span and unit
Reynolds number. (Top figure corresponds to a Reu = 8 × 106 m−1, and the
bottom to a span of 80 m.) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.1 Variation of cabin half-width with roll-mode time constant for a range of ver-
tical accelerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
6.2 Schematic diagram of aircraft planform geometry: (a) TR = 0.1 and Hw = 5
m and (b) TR = 1 and Hw = 2 m. . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.3 Variation in longitudinal NP position over a range of outboard wing taper
ratios and wingtip-fin heights . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.4 Variation in lateral NP position over a range of outboard wing taper ratios
and wingtip-fin heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.5 Change in (a) yawing moment coefficient and (b) side force with sideslip angle
over a range of outboard wing taper ratios and wingtip-fin heights. . . . . . . 153
6.6 Aerofoil section generator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
6.7 Schematic diagram of the multi-bubble cabin embedded within an aerofoil
section — vertical spar locations are represented by the dash-dot lines, whilst
the minimum spacings between the cabin and wing surface are indicated by
the ‘x’ markers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.8 Three dimensional view of wing half-span, spanwise variations of aerofoil sec-
tion geometry, multi-bubble cabin arrangement, and Cp distribution at the
cruise (with suction) condition: centrebody M⊥ = 0.63, outboard M⊥ = 0.61,
wingtip-fin M⊥ = 0.67; see Fig. 6.9 for Cl⊥ values. . . . . . . . . . . . . . . . 157
xxiii
LIST OF FIGURES
6.9 Spanwise variation in section lift coefficient in the free-stream and wing normal
directions — CL = 0.14 and M∞ = 0.67. . . . . . . . . . . . . . . . . . . . . . 160
6.10 Variation in viscous drag coefficient along the wing half-span — Reu = 8×106
m−1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.11 Force diagram at takeoff rotation. . . . . . . . . . . . . . . . . . . . . . . . . . 161
6.12 Spanwise lift distribution corresponding to a clockwise roll at take off with:
δa = +/− 12.2◦ and δE = −2.5◦: M∞ = 0.21 and CL = 0.61. . . . . . . . . . 163
6.13 Typical inboard suction-system architecture. . . . . . . . . . . . . . . . . . . . 165
6.14 Distribution of inboard chamber and surface (non-dimensional) pressures across
regions B and C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
6.15 Critical (non-dimensional) differential pressures across porous skin along the
centrebody region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
6.16 Outboard (non-dimensional) chamber pressure drop. . . . . . . . . . . . . . . 169
6.17 Variation in overall suction coefficient and pump drag coefficient along the
wing half-span. CQ is 3.10 × 10−4 and W˜p is 6.27 × 10−4 — Reu = 8 × 106
m−1, ηp = 0.85. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
6.18 Two engine turbofan HPC operating map, detailing the TOC design point
(white circle), and takeoff off-design point for increasing engine mass flow rate
(yellow squares). The non-dimensional spool speed (N) is represented by the
solid black contours, and the compressor efficiency by the red contours. . . . 172
6.19 Net thrust, HPC exit temperature and burner exit temperature variation with
engine mass flow rate at TO conditions for a two-engine turbofan designed for
TOC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
6.20 Two engine turbofan HPC operating map, detailing the TO design point (white
circle), and various off-design points (yellow squares). The non-dimensional
spool speed (N) is represented by the solid black contours, and the compressor
efficiency by the red contours. The design point has been rescaled with β = 0.3
and N = 1.05. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
6.21 Three engine turbofan HPC operating map, detailing the cruise-without-suction
design point (white circle), and various off-design points (yellow squares). The
non-dimensional spool speed (N) is represented by the solid black contours,
and the compressor efficiency by the red contours. The design point has been
rescaled with β = 0.3 and N = 1.05. . . . . . . . . . . . . . . . . . . . . . . . 175
6.22 Propeller map for a three-engine turboprop with TO as the design point. (Solid
black lines represent contours of propeller efficiency.) . . . . . . . . . . . . . . 176
xxiv
LIST OF FIGURES
6.23 Three engine turboprop HPC operating map, detailing the TO design point
(white circle), and various off-design points (yellow squares). The non-dimensional
spool speed (N) is represented by the solid black contours, and the compressor
efficiency by the red contours. The design point has been rescaled with β = 0.2
and N = 1.05. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.24 HPC operating map detailing the takeoff design point, various off-design points,
non-dimensional spool speed (N) contours (solid black), and efficiency contours
(red). The design point has been rescaled with β = 0.2 and N = 1.05. . . . . 179
6.25 Variation of cruise (with suction) engine sfc with thrust. . . . . . . . . . . . 182
6.26 Schematic diagram of LFW fuselage structural arrangement. . . . . . . . . . 183
6.27 Wing structural geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
6.28 The distribution of weights and point loads over the planform is shown in a),
whilst in b) and c) the root cantilever model is illustrated for the in-flight and
on-ground load cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6.29 Shear force, bending moment and torque diagrams for critical load cases —
initial estimate for in-flight (solid line), final estimate including self weight for
in-flight (dashed line) and final estimate for ground (solid-star line). . . . . . 187
6.30 Tricycle landing gear geometric arrangement. . . . . . . . . . . . . . . . . . . 190
6.31 Tipback geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
6.32 Overturn geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
6.33 Aft tail positioning (from Raymer (1999)). . . . . . . . . . . . . . . . . . . . . 195
6.34 Competitor aircraft configuration. . . . . . . . . . . . . . . . . . . . . . . . . 197
6.35 Spanwise loading distributions for CL = 0.48 and M∞ = 0.67 — Cl (dashed)
and Clc/cref (solid). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
6.36 Surface Cp distribution for an RAE2822 aerfoil, with the critical Cp superposed
— Cl = 0.52 and M∞ = 0.67. . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
6.37 Comparison of LFW and competitor aircraft MTOW breakdowns. . . . . . . 204
xxv
LIST OF FIGURES
xxvi
List of Tables
2.1 Aerofoil drag comparisons on the F-94A upper surface, all for Rec ≈ 30× 106
(from Green (2006)). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 HP117 aircraft design specification (from Lee (1961)). . . . . . . . . . . . . . 41
3.1 Summary of two-spool turboprop iteration variables and errors. . . . . . . . . 64
3.2 Summary of two-spool, unmixed flow, turbofan iteration variables and errors. 65
3.3 Estimated wing structural weight breakdown for the B737-200. . . . . . . . . 88
3.4 Estimated fuselage structural weight breakdown for the B737-200. . . . . . . 88
3.5 Structural weight breakdown for the B737-200. . . . . . . . . . . . . . . . . . 89
3.6 Operating empty weight breakdown for the B737-200. . . . . . . . . . . . . . 90
5.1 Laminar-flying-wing aircraft design specification. . . . . . . . . . . . . . . . . 140
6.1 Static stability — C.G. locations (see Sec. 6.1.5.5): 11.38 m (start of cruise
and climb out) and 11.44 m (end of cruise). . . . . . . . . . . . . . . . . . . . 152
6.2 LFW section geometry variables specification. . . . . . . . . . . . . . . . . . . 156
6.3 LFW lift and drag coefficient breakdown. . . . . . . . . . . . . . . . . . . . . 163
6.4 LFW aerodynamic performance parameters for climb-out and takeoff with one
engine inoperative, and cruise, with C.G. at 11.38 m. . . . . . . . . . . . . . . 164
6.5 Chamber specifications for the inboard section. . . . . . . . . . . . . . . . . . 166
6.6 Chamber specifications for the outboard section. . . . . . . . . . . . . . . . . 168
6.7 Thrust and suction power requirements (per engine) at various flight conditions
for two/three engines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.8 Thrust and suction power requirements (per engine) at various flight conditions.179
6.9 LFW engine performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.10 LFW structural weight breakdown . . . . . . . . . . . . . . . . . . . . . . . . 189
6.11 LFW aircraft weight buildup . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
6.12 LFW mission-fuel weight buildup . . . . . . . . . . . . . . . . . . . . . . . . . 192
6.13 Competitor aircraft geometric parameters. . . . . . . . . . . . . . . . . . . . . 196
xxvii
LIST OF TABLES
6.14 Competitor aircraft cruise lift and drag coefficient breakdown. . . . . . . . . . 200
6.15 Competitor aircraft engine design variables. . . . . . . . . . . . . . . . . . . . 200
6.16 Competitor aircraft engine performance summary. . . . . . . . . . . . . . . . 201
6.17 Competitor aircraft wing structural weight buildup. . . . . . . . . . . . . . . 202
6.18 Competitor aircraft fuselage structural weight breakdown. . . . . . . . . . . . 202
6.19 Competitor aircraft structural weight breakdown. . . . . . . . . . . . . . . . . 203
6.20 Competitor fuel weight breakdown. . . . . . . . . . . . . . . . . . . . . . . . . 203
6.21 Competitor aircraft weight buildup. . . . . . . . . . . . . . . . . . . . . . . . 204
xxviii
Chapter 0
Nomenclature
AR = aspect ratio
b = span
c = chord
d = suction hole diameter
Cd = dissipation coefficient
CD = drag coefficient
Cf = wall skin friction coefficient
Cl = rolling-moment coefficient,
and section lift coefficient
CL = lift coefficient
Cm = pitching-moment coefficient
CM0 = zero-lift pitching-moment
coefficient
Cn = yawing-moment coefficient
cp = specific heat capacity of air
at constant pressure
Cp = Pe−P∞1
2
ρ∞U2∞
, surface pressure
coefficient
CQ =
∮
V0
U∞d (s/c), suction flow
coefficient
D∗ = dissipation function for a
laminar boundary layer
Deq = 2h
wc/h
1+wc/h
, equivalent
diameter for rectangular conduits
D = diameter
e = Oswald efficiency
f = friction factor
g = 9.81 m/s2, gravitational
acceleration
h = chamber height
Hw = wingtip-fin height
H12 = δ1/δ2, shape factor
H32 = δ3/δ2, energy shape factor
k = P˜∞ − P˜c, non-dimensional
pressure difference constant
Ks = skin resistance
m˙ = mass flow rate per unit width
along spanwise chamber
m˙f = fuel mass flow rate
m˙s = area-distributed suction mass
flow rate
M = Mach number
N = rotational speed
p = roll rate
q = pitch rate
P , P˜ = pressure; P1
2
ρ∞U2∞
,
non-dimensional pressure
r = yaw rate
xxix
CHAPTER 0. NOMENCLATURE
r˜c =
∆ ePs,max
∆ ePs,min , ratio
of non-dimensional pressure
difference across skin over a
single chamber width
ReDeq =
2m˙
µ
wc/h
1+wc/h
, spanwise-chamber
Reynolds number
Reh = Vhd/ν, suction hole
Reynolds number
Reδ2 = ueδ2/ν, momentum
Reynolds number
s = intrinsic distance along aerofoil
S = area
t = maximum aerofoil thickness,
and time
ts = porous skin thickness
T = temperature
TR = outboard wing taper ratio
T02 = compressor exit temperature
T04 = burner exit temperature
u = streamwise velocity inside
boundary layer
ue = local velocity outside boundary
layer
U = velocity
V0 = area-distributed suction
velocity
Vh = hole suction velocity
w = normal velocity
wc = chamber width
wL = wing loading
w˜p, W˜p = area-distributed, and total,
power coefficient
W = weight
x = chordwise distance
y = lateral coordinate
Y = side force
z, z˜ = spanwise distance, z/b
Z = normal force
Cnβ = dCn/dβ
CYβ = dCY /dβ
Clβ = dCl/dβ
Clr =
∂Cl
∂(rb/2U∞)
Cnr =
∂Cn
∂(rb/2U∞)
Cmq =
∂Cm
∂(qc/2U∞)
Symbols
α = angle of attack
β = sideslip angle
δ = control surface deflection; boundary
layer thickness
δ1, δ2, δ3 = Boundary layer displacement,
momentum and kinetic energy
thickness
∆P , ∆P˜ = Pressure difference; ∆P1
2
ρ∞U2∞
,
non-dimensional pressure difference
∗ = skin-friction function for a
laminar boundary layer
Λ = wing sweep angle
ν = kinematic viscosity
φ = bank angle
ρ = density
σ = stress
τR = roll-subsidence time constant
Subscripts
a = aileron
av = average
c = chord, and chamber
C = compressor
d = duct
xxx
e = engine, and boundary-layer edge
ex = pump exit
E = elevator
h = hole
i = induced
in = pump inlet
j = jet
max = maximum
PR = propeller
r = rudder
ref = reference
s = skin
sp = suction pump
te = trailing edge
th = thermal
u = unit
uc = undercarriage
UTS = ultimate tensile strength
v = viscous
w = wall
wet = wetted
0 = zero lift, and stagnation
quantity
∞ = free stream
⊥ = perpendicular
Abbreviations
APU = auxiliary power unit
BPR = bypass ratio
CG = centre of gravity
CF = crossflow
FW = flying wing
HPC = high pressure compressor
LCV = low calorific value
LFC = laminar flow control
LFW = laminar flying wing
MTOW = maximum takeoff weight
OEW = operating empty weight
PPR = pump pressure ratio
sfc = specific fuel consumption
T-S = Tollmien-Schlichting
xxxi
CHAPTER 0. NOMENCLATURE
xxxii
Chapter 1
Introduction
With the continued growth in air travel, focus is being increasingly drawn to the environmen-
tal impact of engine combustion products. The technology sub-group of Greener by Design,
led by Green (2002), considers that, amongst the various environmental issues, the reduction
of CO2 emissions is likely to emerge as the most important. For kerosene-fuelled aircraft, this
translates directly to a requirement to reduce fuel burn, i.e. the amount of fuel consumed
per unit passenger-range measured over a whole journey.
Over the last five decades aircraft have changed little in their appearance and operating
conditions. They are characterised by a high-aspect-ratio wing joined to a slender fuselage,
with a tailplane located at the rear and pod-mounted engines, as shown in Fig. 1.1. Fur-
thermore, they operate with turbulent boundary layers at cruise altitudes between 30,000 –
40,000 ft in a high-subsonic Mach number range of 0.8 – 0.85.
Figure 1.1: Conventional aircraft layout — the Boeing 787 Dreamliner.
Despite significant improvements in efficiency since its introduction, Fig. 1.2 shows that
the performance of this configuration appears to be approaching an asymptote. The trends in
engine fuel consumption suggests that these improvements have largely been due to advance-
1
CHAPTER 1. INTRODUCTION
ments in engine technology. Furthermore, Denning et al. (1997) comment that improved
materials and further drag reductions for swept-wing turbulent aircraft are likely to have
limited benefit. For this reason, researchers, such as Green (2002) and Greitzer et al. (2010),
have considered a number of alternatives.
Figure 1.2: Engine fuel consumption and fuel burn per seat over a 1000 nm mission (from
Birch (2000)).
One such alternative solution, still based on the tube and wing concept, has been proposed
by Greitzer et al. (2010) with the D8 series aircraft. The arrangement, shown in Fig. 1.3,
consists of a double-bubble fuselage with a lifting nose, embedded aft engines, pi tail arrange-
ment, and reduced Mach number operations. The overall estimated reduction in fuel burn,
with the B737-800 as a baseline and assuming current technology levels, is given at 49%.
(This improvement is projected to increase to 71% on incorporation of advanced technologies
such as: ultra high bypass ratio engines, advanced structural materials and natural laminar
flow.) The benefits from flying slower are an aircraft with: an increased aspect ratio, permit-
ted by unsweeping the wing; a reduced empty weight; and, a lower minimum static margin,
which reduces trim drag. Due to these changes alone, the fuel burn reduction is estimated at
8%.
Figure 1.3: D8 aircraft series (from Greitzer et al. (2010)).
2
Blended wing-body (BWB) aircraft with turbulent boundary layers have received much
attention in recent years. The concept is shown in Fig. 1.4. It consists of swept outer wing
regions with a ‘wing-cum-fuselage’ centrebody. The configuration benefits from the absence
of fuselage and tail drag, at the cost of greater difficulty in achieving satisfactory longitudinal
stability and control characteristics (Nickel and Wohlfart (1994)). Furthermore, the study of
Bolsunovsky et al. (2001) has shown that, with the distribution of payload and low aspect
ratio configuration, takeoff weight is likely to be lower than an equivalent swept wing aircraft.
Based on the concept of Bolsunovsky et al. (2001), Green (2002) estimates a 23% reduction
in fuel burn on a baseline swept-wing aircraft design for the same mission specification.
Figure 1.4: Boeing X-48B blended wing body.
Assuming present day technology, Green (2002) identifies the ‘laminar flying wing’ (LFW)
as having the greatest potential for fuel-burn reduction. The concept consists of a flying-
wing (FW) arrangement, which utilises distributed suction through porous wing surfaces as a
means of laminar flow control (LFC). The flying wing has had proponents since the early days
of powered flight, and has been physically realised in a number of designs over the intervening
years; one such example is the Northrop YRB-49 bomber shown in Fig. 1.5, developed in
the 1950’s. The configuration differs from that of a BWB as the entire FW consists of a
single lifting surface, whilst the BWB’s centrebody and wing are still distinguishable from
one another with their markedly different shapes.
The flying wing has traditionally been viewed as unsuitable for passenger aircraft, because
of accommodation issues. Nonetheless, Martinez-Val et al. (2006) have argued that an 80m-
span flying wing with a passenger capacity of 300 and a fuel burn of 19.8 g/pax.km is a
practical possibility. Such a vehicle would be approximately 16% more efficient than a Boeing
777 aircraft, which has a fuel burn of 23.5 g/pax.km (Martinez-Val et al. (2006)). Torenbeek
(1991) has also considered the potential of the flying wing for passenger transport, as one of
3
CHAPTER 1. INTRODUCTION
Figure 1.5: Northrop YRB-49 bomber.
a range of wing-body configurations, all having the same useful volume. His conclusions are
less optimistic (because the increased wetted area of a flying wing offsets the drag benefit of
eliminating the fuselage), and suggest that a pure flying wing does not necessarily represent
the optimum allocation of usable volume between a body and a wing.
The flying-wing configuration is, however, unambiguously superior once LFC is envisaged.
Laminar flow control reduces skin-friction drag by suppressing boundary-layer transition,
usually via surface suction. On a conventional aircraft, Green (2006) considers the application
of LFC to the wing, fin, tail and nacelle surfaces (arguing that it cannot practically be applied
to the fuselage, whilst Denning et al. (2003) add that problems also arise towards the rear
of wings with flaps and spoilers), and estimates a fuel burn reduction of just 16% on a
baseline turbulent aircraft for the same mission. However, on a flying wing it can lead to a
very significant drag reduction. The LFW proposed by Greener by Design is a flying-wing
aircraft with LFC over (almost) all its surface. On the basis of the Breguet range equation,
and estimates for its component parameters (assuming 2001 technology levels), Green (2006)
suggests that a turbofan powered LFW with the same payload (86 mt) and range (12,500 km)
has a fuel burn that is around 50% below that of a baseline-turbulent aircraft. Alternatively,
Green (2002) considers an unducted-fan configuration, at the same technology level, and this
figure is expected to increase to around 60%. Finally, at 2050 technology levels, a fuel-burn
reduction of 70% is anticipated (Green (2002)).
This thesis begins in Chap. 2 with a review of the open literature on laminar flow control,
flying wing aircraft, and studies which combine the two technologies. Chapter 3 gives an
overview of the design methodology and numerical design tools used in the conceptual design
evaluation. Chapter 4 then provides insight into the parameters affecting practical LFC
4
suction power requirements for a commercial LFW transport aircraft. In Chap. 5 a viable
basic aircraft design specification is given. Then, in Chap. 6, the detailed design of a LFW and
a baseline, conventional, aircraft is undertaken. The thesis culminates with some conclusions
and suggestions for future work in Chap. 7.
5
CHAPTER 1. INTRODUCTION
6
Chapter 2
Literature Review
In this chapter, the open literature is surveyed. First, the well researched area of laminar flow
control is discussed. Then the flying wing configuration is explored. Finally, the integration
of these two technologies is examined.
2.1 Laminar Flow Control
The boundary layer was first discovered by Prandtl in 1904 (Anderson (1997)). It is a thin
layer of fluid close to the surface of a body, over which the velocity reduces from its free-
stream value at the edge of the boundary layer to zero at the wall. The boundary layer can
be categorised as either: laminar, where the flow is in smooth streamlines parallel to the
surface; or turbulent, where the flow consists of irregular fluctions in velocity superposed on
the mean flow, and roughly parallel to the surface (Young (1989)). The process of change
between these two states is known as transition. The velocity fluctuations within a turbulent
boundary layer provide a powerful mechanism for mixing, and lead to a higher rate of strain,
and hence wall shear stress, relative to laminar boundary layers. Consequently, laminar skin
friction can be as much as 90% less than turbulent skin friction at the same Reynolds number
(Joslin (1998a)). The concept of applying surface suction to stabilise a laminar boundary
layer and limit its growth, thereby reducing drag, is not new. Much of the work on full-chord
LFC with permeable surfaces took place in the 1940s through the mid-1960s, pioneered by
Lachmann in the UK and Pfenninger in the USA. More contemporary laminar flow control
studies have mainly been concerned with hybrid laminar flow control (HLFC) systems, which
integrate the ideas of natural laminar flow with surface suction (Denning et al. (1997)).
This section begins with an exploration of the basic concept of boundary layer stability
and its control through the application of suction. Then the design of LFC suction systems
is discussed.
7
CHAPTER 2. LITERATURE REVIEW
2.1.1 Profile Drag Reduction
Two dimensional boundary layers are characterised by their velocity profile, as shown in
Fig. 2.1. In the absence of flow control, the shape of the velocity profile depends solely on
the streamwise pressure gradient. A favourable pressure gradient leads to a fuller velocity
profile with a negative curvature (∂2u/∂y2). In contrast, an adverse pressure gradient leads
to a less full profile with a region of positive curvature, and the consequent existence of an
inflection point.
Figure 2.1: Stable and unstable velocity profiles in a flat-plate laminar boundary layer — flat
plate corresponds to zero-pressure gradient. (Taken from Green (2006).)
The realm of stability theory is beyond the scope of this thesis; however, Green (2006)
notes that for flows in which the velocity profile has an inflection point, transition occurs at
much lower Reynolds numbers compared to the zero pressure-gradient case. In contrast, the
opposite applies for a more convex velocity profile.
The change of boundary layer thickness and velocity profile due to suction is detailed
schematically by Lachmann (1955) in Fig. 2.2. The effect of suction is two-fold: 1) the
boundary layer profile is made more convex, and 2) the boundary layer thickness (and hence
8
2.1. LAMINAR FLOW CONTROL
local Reynolds number) is reduced. This combination leads to a more stable boundary layer.
Figure 2.2: Boundary layer development with suction (from Lachmann (1955)).
These observations can be understood through consideration of the incompressible bound-
ary layer momentum equation with surface suction at the wall, which Green (2006) gives to
be
µ
∂2u
∂y2
=
dp
dx
− ρV0
(
∂u
∂y
)
w
. (2.1)
This expression shows that, as expected, flow acceleration and suction through the wall both
promote a convex velocity profile.
The boundary layer is characterised by two integral parameters: the displacement and
momentum thickness. Displacement thickness (δ1) is a measure of the displacement of the
free stream away from the surface due to boundary-layer growth, whilst momentum thickness
(δ2) is a measure of the momentum deficit. These definitions are retained downstream of the
aircraft and, for two-dimensional shock-free flow, δ2 far downstream is directly proportional
to the drag of the body.
δ1 =
∫ ∞
0
(
1− u
ue
)
dy (2.2)
δ2 =
∫ ∞
0
(
u
ue
(
1− u
ue
))
dy (2.3)
On integration of Eq. 2.1, combined with the continuity equation and Eqs. 2.2 and 2.3,
von Ka´rma´n derived the momentum integral equation
dδ2
dx
+ (2 +H12)
1
ue
due
dx
δ2 = Cf − V0
ue
, (2.4)
9
CHAPTER 2. LITERATURE REVIEW
where the shape factor
H12 =
δ1
δ2
. (2.5)
Equation 2.4 can be re-written in a form that shows the influence of suction on the rate of
boundary layer growth
ρ
d
dx
(
u2eδ2
)
= δ1
dP
dx
+ τw − Vo
ue
. (2.6)
Green (2006) highlights that the term on the left is the rate of growth of momentum deficit
in the boundary layer, whilst the first and second terms on the right are the contributions to
local pressure and friction drag. He explains that when dP/dx is large in comparison to the
skin friction term, the increase in momentum deficit, and hence drag, is proportional to the
local thickness.
Drawing largely from a paper by Edwards (1961), Lee (1961) attempts to clarify some
common misconceptions of how a reduction in profile drag through surface suction is actually
manifested. He explains that, as expected of a laminar boundary layer, the pressure and
skin friction drags are low. However, there is a limit to this: excessive suction will produce
a boundary layer that is extremely thin, with an associated skin friction coefficient that can
approach, or even exceed, that of a thick turbulent boundary layer. (Note, though, that a
turbulent boundary layer would result in a larger wake with a larger amount of unrecovered
energy left behind in the atmosphere.) Lee (1961) concludes that the application of suction
should be such that the boundary layer remains on the verge of transition.
Lachmann (1955) highlights that the need to re-energise the sucked air was investigated by
Pfenninger. Early experiments demonstrated an additional 40% reduction in effective drag
if the (stagnant) sucked flow is accelerated to free-stream velocity. Therefore, the sucked
low momentum fluid, which would otherwise need to be cancelled by an equal and opposite
momentum increase in the propulsion wake, does not appear as a deficit in the wake, as
illustrated in Fig. 2.3. To summarise, the actual drag reduction effects are: 1) a reduction of
wake drag to a practically insignificant magnitude, and 2) a recovery with high mechanical
efficiency of the kinetic energy of the air which has been sucked from the lower, almost
stagnant, strata of the boundary layer.
In contrast to natural laminar flow, Lachmann (1955) observes that the critical parameter
for laminar flow with distributed suction is Reynolds number per unit chord. Denning et al.
(1997) interpret this result as there being no upper limit to wing chord size because the
boundary layer is continually ‘regenerating itself’.
The maximum possible unit Reynolds number depends on the surface finish and at-
mospheric turbulence levels (Lachmann (1955)); these effects become less significant with
10
2.1. LAMINAR FLOW CONTROL
Figure 2.3: Wake profile for an integrated propulsion and suction system (from Lee (1961)).
increasing cruise altitude as a result of the increase in kinematic viscosity (Green (2006)).
The F94-A aeroplane maintained full-chord laminar flow for unit Reynolds numbers of over
13×106 m−1; therefore, based on the state-of-the-art at the time, Lachmann (1955) proposes
that unit Reynolds numbers of up to 16× 106 m−1 may realistically achievable.
With the growth rate of a boundary layer with suction independent of chord length,
the boundary layer thickness relative to the wing chord is reduced. This result implies
a reduction in drag coefficient with Rec. This is shown in Fig. 2.4. Furthermore, at high
Reynolds numbers, e.g. 100×106, complete laminar flow aerofoils produce drag levels around
one tenth of turbulent values.
There is a drawback with suction, however. Power is needed to energise the suction
system, in order to develop a sufficient pressure ratio to maintain the desired flow rate. This
is commonly referred to as an equivalent ‘pump drag’.
Green (2006) provides illustrative profile and pump drag coefficients taken from the upper
surface suction glove, flight-tested by Northrop, on the F-94A; these are repeated in Tab. 2.1.
Green (2006) comments that the fully laminar values are conservative, as the suction flow
rates are 10% higher than for minimum drag; added to this, they have been obtained by
doubling the upper surface values (as no data for the lower surface was available). The
profile drag for the fully laminar flow is approximately a fiftieth of the turbulent case, whilst
the pump drag for the fully laminar aerofoil is more than 80% of the total drag. The total drag
reduction is 89%: confirming the potential of laminarised surfaces. Green (2006) comments
11
CHAPTER 2. LITERATURE REVIEW
Figure 2.4: Variation in wing drag coefficient with chord Reynolds number for laminar bound-
ary layers (from Denning et al. (1997)).
that the same result is likely to apply for a fully laminar aircraft. Lachmann (1955) even
goes to the extent of suggesting that, to a first approximation, the profile drag of laminarised
surfaces may be neglected altogether.
Table 2.1: Aerofoil drag comparisons on the F-94A upper surface, all for Rec ≈ 30 × 106
(from Green (2006)).
Fully turbulent Fully laminar
Profile drag 0.00912 0.00018
Pump drag 0 0.00078
Total drag 0.00912 0.00096
12
2.1. LAMINAR FLOW CONTROL
2.1.2 Flow Control Design Methodology
The basic approach to the design of LFC wings is illustrated in Fig. 2.5. It is first necessary
to design the basic aerofoil section to meet any aircraft stability requirements and geometric
constraints. With the baseline wing design, the wing pressures and velocities, calculated using
transonic wing theory or computational fluid dynamics, can then be used in a boundary-
layer stability calculation to determine the minimum suction requirements for laminar flow
maintenance to the desired transition location. If suction requirements are unacceptably
high then, depending on the most dominant instability mode and its region, the aerofoil wing
section is adjusted accordingly, whilst still being capable of meeting other design constraints.
The process is iterative and ultimately there will be a trade-off between aerofoil section
characteristics and required suction flow rates.
With the desired suction flow rate determined, it is possible to proceed with the LFC
system design. Joslin (1998a) outlines that the pressure drop through the skin must be set
to a obtain a reasonable subsurface compartmentation and perforation spacing distribution
for the desired suction distribution; furthermore, the ducts must be arranged and sized to
minimise pressure losses. Finally, the compressor requirements can be used to estimate the
demanded suction power.
Figure 2.5: Block diagram of LFC design cycle (from Harris et al. (1988)).
13
CHAPTER 2. LITERATURE REVIEW
2.1.3 Boundary Layer Stability
2.1.3.1 Tollmien-Schlichting Waves
In two-dimensional boundary layers, Tollmien-Schlichting (T-S) waves are the primary insta-
bility mechanism. Saric and Reed (2006) describe these as essentially two-dimensional convec-
tive travelling wave disturbances generating streamwise instabilities that are slow growing.
This instability is influenced by the shape of the non-dimensional boundary-layer velocity
profile, which Hall et al. (1984) explain is due to the associated effects on the distribution of
vorticity within the layer and viscous effects due to the change in Reynolds number. Green
(2006) explains that, for high Reynolds number flows, these disturbances can be amplified
even for profiles which do not have an inflection point; whilst for low Reynolds number flows
small disturbances can be damped out.
2.1.3.2 Taylor-Go¨rtler Vortices
Over the concave section of the lower surface of a cambered aerofoil, Taylor-Go¨rtler vortex-
induced instabilities dominate. These are stationary, streamwise oriented, counter-rotating
vortices, as shown schematically in Fig. 2.6. Saric and Reed (2006) comment that this
mechanism can easily be controlled through the use of convex curvature, whereby vortices of
the opposite sign are generated, and are more stabilising than those produced by the concave
curvature are destabilising; furthermore, they become less significant the larger the sweep
angle is.
Figure 2.6: Schematic diagram of Taylor-Go¨rtler vortices (from Joslin (1998b)).
2.1.3.3 Crossflow Instabilities
The crossflow (CF) instability appears as co-rotating vortices, which all rotate in the same
direction and whose axes are aligned to within a few degrees of the inviscid streamlines,
as shown in Fig. 2.7(a). They dominate in regions where the flow is either accelerating or
14
2.1. LAMINAR FLOW CONTROL
decelerating, as both the surface and flow streamlines are highly curved. The combination
of wing sweep and pressure gradient deflect the inviscid-streamlines inboard (in a manner
shown in Fig. 2.7(a)), which, when combined with the low momentum fluid in the boundary
layer, makes the deflection even larger (Reed and Saric (1989)).
Figure 2.7(b) shows that there is an inflection point in the crossflow velocity profile: at
the wall the no-slip condition is satisfied, whilst the crossflow velocity component in the
free stream is zero. This causes a strong primary instability which depends on the crossflow
Reynolds number, defined as ReCF = Wmaxδ10/ν — the boundary layer thickness δ10 corre-
sponds to the point where the the crossflow velocity is at 10% of its maximum value (Reed
and Saric (1989)).
(a) Crossflow instabilities (from Joslin (1998a))
(b) Velocity components within a swept boundary layer
(from Reed and Saric (1989)).
Figure 2.7: Schematic diagram of the crossflow instability and velocity profile.
15
CHAPTER 2. LITERATURE REVIEW
2.1.3.4 Attachment-Line Instabilities
A further issue in swept-wing transition is the stability of the ‘attachment-line’ boundary
layer. This instability develops along the ‘stagnation line’ and causes transition in the leading
edge region. It is shown schematically in Fig. 2.8.
Figure 2.8: Schematic diagram of attachment-line flow (from Joslin (1998b)).
By considering an infinite swept-wing attachment-line boundary layer in a low turbulence
free stream, Poll (1979) derived a governing Reynolds number dependent upon edge conditions
and a characteristic length (which in turn depends on the chordwise velocity gradient), given
by
Rea.l =
(
V 2e c
νeU∞U⊥
) 1
2
, (2.7)
where U⊥ = cU∞
(
due
ds
)
s=0
. The critical value of this attachment-line Reynolds number beyond
which transition occurs was experimentally determined by Poll (1979) to be in the range 600
– 700.
Taking Eq. 2.7, and considering the potential-flow solution for a cylinder, Poll (1979)
showed that, for this case,
Rea.l =
(
U∞r
ν
× sin Λ tan Λ
2
) 1
2
. (2.8)
In Eq. 2.8 we see that there is an explicit dependence on unit Reynolds number, leading-edge
radius and wing sweep. Saric and Reed (2006) add that, for most applications, reduction of
the nose radius for a specific sweep angle is a practical form of control. (This also has the
compounded benefit of decreasing the chordwise extent of the crossflow region and providing
a more rapid acceleration of the flow over the wing.)
16
2.1. LAMINAR FLOW CONTROL
2.1.3.5 Shock Wave / Laminar Boundary Layer Interactions
During flight testing of the F-94A a new potential problem appeared. As the aircraft speed
was increased to the point where the local Mach number on the wing surface exceeded about
1.10, full-chord laminar flow was lost with the slot configuration tested (Braslow (1999)).
The problem was attributed to the steep pressure rise through the shock waves that formed.
In more recent experiments performed by Harris et al. (1988), much effort was put into
obtaining a shock-free supercritical aerofoil with a large supersonic zone of over 80% of the
upper surface. The maximum local Mach number was recorded to have reached about 1.11
— greater in both extent and magnitude than those measured on the F-94A. A problem with
the aerofoil, however, was that it had a very narrow off-design operating range.
Harris et al. (1988) reviewed some of the earlier work on this and found that suction
laminarisation only appears practicable in regions of weak shocks on transonic aerofoils;
moreover, the pressure rise that a laminar boundary layer can negotiate in the region of an
incident shock-wave decreases with increasing Reynolds number, unless the thickness of the
upstream boundary layer can be reduced in some manner, for example, by suction. However,
Harris et al. (1988) conclude that quantification for boundary layer control in such shock-
interaction regions still requires experimentation.
2.1.3.6 Example Suction Distributions
As we have seen, the presence of T-S and CF disturbances in the boundary layer are primarily
dependent on the pressure gradient and wing sweep angle. However, Joslin (1998b) comments
that for wings with sweeps between 0◦ and 25◦, T-S wave instabilities dominate; whilst for
wing sweeps greater than 25◦ both T-S and CF disturbances are present; and for even greater
wing sweeps of above 30◦ to 35◦, CF disturbances alone dominate near the wing leading edge.
An example chordwise suction distribution necessary for laminarisation of the 30◦ swept
X-21A aircraft is shown in Fig. 2.9. (The stability calculations were performed assuming
incompressible laminar boundary layers for flow over an infinitely swept wing. The calculated
suction distribution is compared against that measured during flight tests in the figure, and
agrees reasonably well.) The pronounced suction over the leading edge is due to a combination
of strong crossflow instabilities in the favourable pressure gradient region and attachment-line
instabilities. (In order to prevent attachment-line contamination from the turbulent fuselage,
a number of control techniques were employed: a fence, vertical slots, and a gutter.) Over
the mid-chord, where there is a mild adverse pressure gradient, T-S waves dominate and
these require a lower degree of surface suction for stabilisation. Toward the trailing edge, the
increased adverse pressure gradient results in a higher requirement, due to a combination of
17
CHAPTER 2. LITERATURE REVIEW
T-S and CF instabilities.
Figure 2.9: Example suction flow velocity distribution for the 30◦ (quarter-chord) sweep
X-21A aircraft (Joslin (1998a)).
In contrast, we can see in Fig. 2.10 that the shape of the suction distribution calculated
for the Vampire, with a quater-chord sweep of 10◦, differs considerably. Suction stabilisation
against crossflow instabilities over the front of the aerofoil is absent given the reduced wing
sweep, whilst the requirement increase over the rear of the aerofoil, due to the adverse pressure
gradient, is much further downstream.
Figure 2.10: Example suction flow velocity distribution for the 10◦ (quarter-chord) sweep
Vampire aircraft (from Head (1955)).
In a review of the historical aspects of LFC, Denning et al. (1997) quote Lachmann, who
comments that only 5 – 10% extra suction flow is required on a swept planform relative to an
unswept one. Quantification for a specific case confirming this does not seem to be available
in the open literature.
18
2.1. LAMINAR FLOW CONTROL
2.1.4 LFC System Design Considerations
Figure 2.11 shows, schematically, the key elements of a LFC suction system. The boundary
layer flow, with a total pressure equal to the local static pressure, is sucked across a porous
skin into a set of corrugations and transported along a set of ducts, through which additional
losses are incurred; it is then fed into a set of suction pumps, which are required to increase
the total pressure of the flow and discharge it rearwards.
Figure 2.11: Outline for a laminar flow control system (from Edwards (1977)).
Pearce (1983) comments that a practical suction system implementation must be light
weight and should minimise the fuel consumed by the LFC system; highlighting the pressure
loss in the system as the critical parameter. For this reason, previous studies of the required
power have mainly focussed on trying to minimise the suction-system losses. In summarising
research conducted at Northrop, Pfenninger (1977) considers throttling and mixing losses,
flow separation, duct-wall friction and secondary-flow losses, and proposes a number of novel
solutions to minimise them. However, compared to the losses associated with the deceleration
of the flow in the boundary layer, the additional contributions through the suction system
seem fairly small. Lachmann (1955) and Gregory (1961) both state that the main effort
should be in overcoming boundary-layer losses. Gregory (1961) also notes that low additional
suction power demands a porous surface whose resistance to flow varies over the chord, in
order to minimise unwanted variations; Head (1955) and Lachmann (1955) incorporated
19
CHAPTER 2. LITERATURE REVIEW
such a resistance into throttle holes situated in a cellular subsurface structure, as shown in
Fig. 2.12. A final strategy for minimising the additional power is suggested by Pearce (1983):
in regions where the suction requirements are high, triangular chambers of full aerofoil section
depth may be implemented to minimise losses in transporting the flow along the wing to the
suction pumps. He also adds that higher losses can be tolerated over the rear of the aerofoil
as the surface pressure is higher.
Figure 2.12: Typical suction surface (from Edwards (1977)).
Green (2006) explains that the pump power required to energise the suction system can-
not be expressed as a simple function of the total suction quantity (as it can for inviscid
flow, whereby the sucked flow is treated as sink drag), but has to be estimated carefully
for each individual case. The pressure losses incurred through a typical suction system are
detailed in Fig. 2.13. The loss in free-stream dynamic pressure and external losses due to the
surface supervelocity distribution dominate the losses through the surface and ducting. The
pump inlet total pressure is set at the lowest pressure in the system; however this leads to
unneccessary additional losses for the flow over the rear of the aerofoil. Instead, Lachmann
(1955) proposes that a multi-stage pump be utilised in order to grade the suction pressure.
Edwards (1961) proposes three schemes through which power may be delivered to the
suction system. The first consists of a primary propulsion system delivering the power via a
drive shaft. The second is an auxiliary engine, separate from the propulsion system, used to
drive the suction pump via a drive shaft. The third is direct boundary layer ingestion by the
20
2.1. LAMINAR FLOW CONTROL
Figure 2.13: Various pressure loss components making up pump power (from Lachmann
(1955)).
main propulsive units. Edwards (1961) comments that the second scheme should be applied
to research aircraft, as it is only slightly less efficient than the first, and would not require
the same extensive modifications to the primary propulsion system, whereas the third scheme
simply has lower thermal and overall efficiencies.
Kosin (1965) provides some information with regard to the suction/propulsion system
integration for the X-21A flight test programme. The main turbojet propulsion engines were
suspended on pylons at the rear of the fuselage to reduce noise and the ensuing turbulence
level on the wing. The suction pumps for the LFC experiments were located in nacelles
underneath the wing, and installed at about one-third half-span to keep the collector ducts
short and duct velocities low. The suction pumps were driven by compressor bleed from the
main propulsion engines — this combination effectively converts the turbojet into a turbofan
engine, whereby the pumps act as fans increasing the bypass ratio. A schematic diagram
of the system is provided in Fig. 2.14. In agreement with Edwards (1961), Kosin (1965)
comments that if the pumping compressor were driven by its own independent powerplant a
lower total efficiency would result.
Two suction pumps were utilised in the X-21A study: a small pump with a pressure ratio
of 1.2, and a large pump with a pressure ratio of 1.65. The smaller pump sucks boundary
21
CHAPTER 2. LITERATURE REVIEW
Figure 2.14: X-21A laminar flow pumping system (from Kosin (1965)).
layer fluid from the low-pressure region of the wing, and the flow is then discharged together
with the remaining boundary layer fluid into a mixing chamber in front of the large pump.
The total sucked airflow is then ejected through a nozzle at the end of the suction nacelle.
(Lachmann (1955) comments that for most suction applications, the pumps will need to
produce a pressure ratio no more than the order of 2.5 – 3.0.)
Pfenninger (1987) explains that background disturbances coming from the engine can
have a great affect on the stability of a laminar boundary layer. However, in a more recent
technology assessment, Wilson (1997) concludes that the influence of wing mounted engines is
minor, and is only an issue for the maintenance of laminar flow over the nacelles themselves,
given the proximity of the noise source.
On the integration of the propulsion system with a suction-laminarised aircraft, Lachmann
(1955) says: “The more cruising drag and thrust are reduced by progressive laminarisation,
the more the ratio take-off to cruising thrust reaches uncomfortably large values, and the
endeavour to substitute existing power plants by boundary layer propulsion must be tem-
pered by take-off and climb considerations”. He then goes on: “ It is obviously uneconomical
to carry an over-sized power plant over the whole range to the detriment of payload, the
function of part of this power plant being restricted to relatively short duration”. Conse-
quently, Lachmann (1955) proposes that the engines be tailored to meet cruise conditions,
but supported by another engine specifically designed to bolster the thrust at takeoff, in an
effort to minimise the overall propulsion system weight.
2.2 The Flying Wing Configuration
The flying-wing configuration is an attractive concept in terms of its aerodynamics and struc-
tural weight, which arise due to a lower wetted area and span loading effects, respectively.
22
2.2. THE FLYING WING CONFIGURATION
Furthermore, Martinez-Val (2007) explains that there is the potential for a quieter aeroplane,
as engines may be located above the wing, whilst high-lift devices in the low-speed config-
uration are not required. It is mainly for these reasons that there has been a great deal of
activity, at a conceptual level, in recent years.
However, research into the flying wing concept began over 60 years ago with the Horten
brothers’ sailplanes in Germany during the 1930’s and 1940’s. The Hortens were followed by
John Northrop with the YRB-49 in the USA post-world war two. However, we are yet to see
such an aircraft in service in the commercial aviation market. Weishaar and Ashley (1973)
highlight two of the most prominent reasons for the failure of the early flying wings to evolve
as operational aircraft:
1) a difficulty to achieve satisfactory unaugmented handling qualities, particularly in the
lateral-directional modes;
2) and that the early FW’s tested were simply not big enough.
This section begins with an overview of the structural architecture of the flying wing and
various operational design considerations. Then the influence of key configuration parameters
on the aircraft’s stability and control characteristics are discussed. Finally, the flying wing’s
handling qualities and aeroelastic behaviour are reviewed.
2.2.1 Structural Architecture
The structural architecture of the FW is two-fold: the centrebody must accommodate pas-
sengers, whilst the outer wing has a more conventional structure providing volume for fuel
tanks and cargo holds (Martinez-Val (2007)). In order to enable efficient use of the inner
space for application to civil transport, aerofoils with large thickness-to-chord ratios are nec-
essary as passengers must be capable of standing upright; otherwise, very long chord lengths
are necessary; for example, Liebeck (2004) and Martinez-Val (2007) consider 17 percent thick
aerofoils. Although aerodynamically challenging, Bolsunovsky et al. (2001) comment that
the increased structural depth makes it possible to increase the wing span with less weight
penalty compared to conventional aircraft.
With the payload located inside the wing, the centrebody structure must resist pressuri-
sation in addition to ordinary bending and torque moments induced by external aerodynamic
and inertial loads in its function as a wing. Martinez-Val (2007) comments that the loads
combine in a nonlinear manner, which under extreme maneouvres or gusts can produce sig-
nificant stresses and deformations.
Liebeck (2004) considers two structural concepts for the centrebody pressure vessel in
which the skin would be capable of resisting all prescribed loads: 1) a separate pressure
23
CHAPTER 2. LITERATURE REVIEW
shell; and 2), an integrated skin and shell structure. These are illustrated schematically in
Fig. 2.15.
Figure 2.15: Structural concepts for the centrebody pressure vessel (from Liebeck (2004)).
Having a separate pressure shell divides the load carrying responsibility of the two major
structures. The arched pressure vessels are used to react the pressurisation loads in tension,
and the conventional outer skin bears the additional loads. Liebeck (2004) comments that a
potential safety issue with this concept is that if a rupture were to occur in the thin arched
skin, the cabin pressure would have to be borne by the wing skin, and therefore must be sized
accordingly with a corresponding increase in structural weight. However, as Martinez-Val
(2007) comments, the inner vaulted skin effectively takes the equivalent responsibility as the
fuselage structure in conventional aeroplanes, which are sized to resist quite large ruptures.
A problem with the second configuration is that the outer skins are made up of quasi-planar
panels, which are very inefficient in resisting internal pressure loads. With both concepts,
ribs are necessary to carry concentrated shear forces, contribute to the torsional stiffness of
the structure and maintain the external aerodynamic shape (Martinez-Val (2007)). As far
as the passengers are concerned, i.e. headroom and passages, there are no major differences.
Bolsunovsky et al. (2001) comment that a separate pressure shell would allow the placement
of various items, such as the LFC hardware, in between the inner and outer skins. Other
concept selection criteria may include direct operating costs, which are mainly influenced
by manufacturing and maintenance issues. However, according to Martinez-Val (2007), no
studies have been carried out on the influence of such considerations.
For conceptual and preliminary design studies, initial weight estimates are commonly
24
2.2. THE FLYING WING CONFIGURATION
attained using correlations based on historical data of existing aircraft. The applicability
of such approaches to aircraft of an unconventional configuration is somewhat suspect. To
take full account of aircraft geometry and attain greater accuracy (at the cost of complex-
ity), finite-element methods are available, but are usually reserved for the detailed design
phase. A third, intermediate, option is to size primary structural elements by treating them
as simple geometric shapes subject to the necessary loading conditions, using standard an-
alytical methods. The TASOPT and PDCYL aircraft structural design modules discussed
by Greitzer et al. (2010) and Ardema et al. (1996), respectively, employ the latter technique;
both modules have been developed for the analysis of new aircraft configurations that assume
non-conventional materials, but still retain the ‘tube and wing’ layout.
2.2.2 Cabin Arrangement and Operational aspects
Figure 2.16 shows a cabin arrangement that takes the form of a set of parallel bays. Martinez-
Val (2007) argues that this arrangement allows seats to be classed according to comfort
levels in rough flights, because those seats further outboard are more likely to experience ride
comfort troubles with regard to lateral and vertical g-loads about the roll axis. (However,
he comments that unpleasant rolling accelerations could be balanced by smooth manoeuvres
and multimedia equipment.)
Figure 2.16: Cabin seating arrangement (from Martinez-Val (2007)).
Aeroplane operation concerns on-ground manoeuvres and servicing, and emergency evac-
uation. In the FW design study of Bolsunovsky et al. (2001), great attention is paid to the
following operational aspects:
• structure and logistics of emergency exits;
25
CHAPTER 2. LITERATURE REVIEW
• service compartment arrangement e.g. galleys etc.;
• cabin floor inclination at cruise;
• waterline ditching and provision of ramp slides;
• landing gear and wheel base track;
• tip-over on taxiing;
• centre-of-gravity build-up — loading sequence, positioning, fuel tank capacity and usage
sequence.
In respect of runway/taxiway movements or airport terminal operations, Martinez-Val (2007)
argues that there are no significant differences between FW and conventional aircraft.
The locations of doors/emergency exits depend on a number of factors, and are discussed
by Martinez-Val (2007). For example, placement along the leading edge demands additional
structural reinforcement to ensure integrity during a crash or object strike, whilst also re-
quiring provisions to avoid cabin flooding in the event of a ditch. In contrast, the placement
of exits through the rear poses fewer problems. Alternatively, Lee (1961) proposes passenger
entry to the cabin via the landing gear hatches on the underside of the aircraft, with pas-
senger escape hatches located on the top surface. Another consideration is that the doors
must also be arranged to allow access to the aircraft independently for galley servicing and
cleaning.
Emergency evacuation is another important consideration. However, Martinez-Val (2007)
concludes that, although the flying wing does suffer from having an extra wide body, it does
not pose any serious problems in respect of passenger flow rate and total evacuation time.
Maximising on ground servicing access is important as it enables a shorter turn-around
time, which, for current aircraft, is typically around 45 minutes (Martinez-Val (2007)). With
galleys often located at the rear for aesthetic and evacuation purposes, the front doors may be
used for cabin cleaning and servicing access. Martinez-Val (2007) adds that in this situation
passenger services, cargo/baggage handling, and aeroplane servicing can be done simultane-
ously with an overlap of activities. Another consideration is the loading and unloading of
passengers in airport piers, which requires the floor to be positioned a certain height above
ground level — for current aircraft this is around 5 m.
Martinez-Val (2007) comments that with regard to airport infrastructure, there is no real
justification for having an aircraft of span greater than 80 m even for entry in the mid-term
future, as all major airports have recently made major modifications to aircraft boxes to
26
2.2. THE FLYING WING CONFIGURATION
accommodate the A380 and other potential ultra high capacity aeroplanes. Furthermore,
runway widths are currently at 14 m.
The provision of windows is restricted to the leading edge, and this has been highlighted
as a potential concern by aircraft manufacturers. With LFW aircraft, the positioning of
windows is even more restrictive as they cannot be laminarised. On this point, Lee (1961)
proposes the use of multi-media equipment to reduce feelings of claustrophobia.
2.2.3 Stability and Control Considerations
In steady flight, an aircraft is said to be in a trimmed state if there are no resulting turning
moments about any of the aircraft’s axes. An aircraft has six degrees of freedom that lead to
the following three stability criteria about each of the three axes:
• Longitudinal stability : Cmα < 0 — a form of pitching stability about the lateral axis
whereby the aircraft tends to pitch down after an increase in α.
• Directional stability : Cnβ > 0 — also known as ‘weathercock stability’, refers to the
yawing stability about the vertical axis.
• Lateral stability : Clβ < 0 — refers to the rolling stability about the longitudinal axis.
Lateral and directional stability are closely interconnected, with the generation of an adverse
yaw during a roll manoeuvre. Therefore, these two areas will be discussed simultaneously.
A measure of longitudinal static stability is given by the static margin σL, defined as:
σL =
xNP − xCG
c
, (2.9)
where xNP is the neutral point (NP). The NP is the chordwise location at which the aerofoil
section only sees a change in lift coefficient with angle of attack whilst the pitching moment
coefficient remains constant, and equal to the zero-lift pitching moment coefficient CM0. If
the NP lies aft of the C.G., σL > 0 and the aircraft exhibits longitudinal static stability.
In addition to static stability, inertial and time-dependent effects govern an aircraft’s
dynamic stability. This characterises any unsteady motions whereby after a disturbance, the
aircraft may first return back to its original state and is therefore statically stable, but then
progressively larger oscillations may build up around that state of equilibrium.
2.2.3.1 Longitudinal Stability
As for conventional aircraft, Donlan (1944) concludes that the longitudinal static stability of
a FW is assured if the C.G. lies ahead of the NP. However, once the C.G. is allowed to shift
27
CHAPTER 2. LITERATURE REVIEW
to a position behind the NP, Jones (1941) highlights that the rate of divergence of a tailless
aeroplane is more rapid, and may become uncontrollable even at small distances.
Although a positive static stability margin is desired, Donlan (1944) explains that it should
not be too great as excessive elevator control power might be required during take-off, whilst
the resulting large deflection of the elevator would impair the aerodynamic performance of
the wing. Bolsunovsky et al. (2001) investigated the limits of fly-by-wire control systems
technology and found that during the landing and takeoff regimes a static margin close to
zero was possible, whilst in cruise flight dCm/dCL ≤ 0.03 should not be exceeded.
An important stability characteristic of tailless aircraft relative to conventional aircraft
arises due to a reduced kinematic damping of the pitching motion, Cmq . Jones (1941) explains
that this phenomenon is mainly because of the absence of the tail surface, with the effect of
the fuselage shown to be unimportant. Jones (1941) comments that if the FW also has a
short static margin, it is likely to be more sensitive to pitch control giving a much increased
manoeuvrability.
Nevertheless, for a statically stable tailless aircraft, free rotations in pitch are coupled
with motions normal to the chord. Consequently, additional damping is obtained through
this coupling, as the vertical damping parameter CZw absorbs most of the energy of the
oscillation. The lack of direct damping appears to alter the sequence of the motions in such
a way as to make this coupling more effective in the case of a tailless aeroplane. Therefore,
in spite of the low direct pitch damping, Donlan (1944) and Northrop (1957) found the
short period oscillation (SPO) instability to be highly damped for tailless configurations
and as great as that for conventional aircraft. Finally, Northrop (1957) comments that any
differences in the phugoid damping with respect to conventional aircraft are insignificant as
it is a slow motion that can easily be controlled.
Both Nickel and Wohlfart (1994) and Donlan (1944) describe a form of dynamic instability
known as tumbling, which is observed with tailless aircraft but is not a particular issue for
conventional aircraft. Tumbling manifests itself as a continuous automatic rotation about the
pitch axis. The only occurrence of tumbling as noted by Donlan (1944) was that simulated
in a free-spinning tunnel. A large static margin helps prevent it arising. If the static margin
does become negative, then there is a danger of either encountering a divergence in pitch
attitude from straight flight or tumbling. However, Donlan (1944) contends that tumbling
would never arise during a normal flight condition, whether it be as a result of a stall or a
spin.
28
2.2. THE FLYING WING CONFIGURATION
2.2.3.2 Lateral-Directional Stability
The provision of sufficient weathercock stability and damping in yaw proves to be the main
difficulty, due to the short available moment arm for control. Northrop (1957) comments
that the swept-back wing has inherent directional stability, which increases with CL, but is
alone not sufficient for satisfactory flight characteristics under all circumstances, thus requires
wingtip fins.
A consequence of the FW’s inherent weak damping in yaw and corresponding poor direc-
tional stability is the increased resulting strength of the adverse yaw associated with a roll
manoeuvre. If coupled with a positive skid-roll moment, Nickel and Wohlfart (1994) high-
light that the effectiveness of the ailerons for lateral control may be destroyed. It is therefore
important to eliminate this strong adverse yaw. Jones (1941) suggests that an autopilot,
used to provide directional control, could be linked with the aileron control to minimise the
effects of adverse aileron yaw; however, the problem may also be countered through geometric
considerations.
Particularly at low speeds, high weight and high altitude, Dutch roll is comparatively
bad for tailless aircraft because of the combination of a large effective dihedral, Clβ , and low
weathercock stability Cnβ (Northrop (1957)). Furthermore, if the rudder is particularly weak,
the time of response to rudder control may be of the same order as the period of the Dutch
roll. This makes directional control especially difficult in landing conditions, where the roll
controls are not usable for changing heading. Another factor adding to the weak damping of
the Dutch roll is the low value of yaw damping Cnr . However, as was the case for damping
in pitch, both Jones (1941) and Donlan (1944) found that, in general, the damping of the
lateral oscillations is greater than indicated from the damping due to yawing velocity alone.
Thus the small value of Cnr is not detrimental to the flying qualities, provided that adequate
directional stability is provided; furthermore, Dutch roll is of a rather long period, therefore
it is typically not necessary to have a high rate of damping as control is usually easy.
Associated with the low values of Cnr is some concern over large angles of sideslip devel-
oping when the aircraft is subjected to an asymmetric loss in thrust. However, referring to
wind-tunnel tests, Donlan (1944) comments that the effects of Cnr are “probably secondary to
other parameters”. Furthermore, Donlan (1944) explains that the maximum amplitude of the
sideslip oscillation is markedly influenced by the rolling moment due to sideslip Clβ and the
yawing moment due to sideslip Cnβ . On this point Donlan (1944) concludes that increasing
either the directional stability or the dihedral reduces the magnitude of the sideslip generated
by a yawing moment; however, observes that the former gives the greater reduction.
Donlan (1944) and Northrop (1957) both point out that the steady-spin characteristics
29
CHAPTER 2. LITERATURE REVIEW
are comparable to those of conventional aircraft. However, Nickel and Wohlfart (1994) add
that, in fact, tailless aircraft are probably less spin prone because the primary forces which
influence spinning are gyroscopic, therefore a distribution of masses lying far away from the
CG, as for flying wings, increases the rotational resistance of the aircraft.
On the spiral mode stability, Northrop (1957) comments that tailless aircraft have readily
acceptable characteristics in this mode.
2.2.3.3 Control
The longitudinal and lateral controls are combined into elevons, which operate together for
pitch control and differentially for roll control. To realise the advantages of a differential
aileron system, a two control surface combination is required, as illustrated in Fig. 2.17.
Nickel and Wohlfart (1994) explain that the outer surfaces work differentially as ailerons,
whilst the inner surfaces not only support the aileron effect, but also take care of the balance
of pitching moments about the lateral axis. For the example here, the inner surface on the
left is more deflected than the outer surface on the right because it has to balance the pitching
moments at a shorter lever arm due to the sweep back.
Figure 2.17: Differential elevon control for a pure aileron deflection to the right without any
elevator effect (from Nickel and Wohlfart (1994)).
Trim control is achieved on tailless aircraft with the aid of elevator control surfaces located
30
2.2. THE FLYING WING CONFIGURATION
at the trailing edge of the wing. To produce the same change in Cm, the elevator of a tailless
aircraft must be deflected more than that of a conventional aircraft of the same static margin.
With aircraft generally having an overall nose-down pitching moment, upward deflection of
these surfaces generates down-lift over the trailing edge, increasing the profile moment of the
wing section. This not only reduces the local section Cl but also CL,max, worsening as the
static margin increases (Nickel and Wohlfart (1994)). However, Northrop (1957) comments
that the required elevator trim will be less for tailless aircraft with close to neutral static
stability.
Northrop (1957) chose to eliminate vertical fin and rudder control surfaces, firstly because
they violate the all-wing principle and add drag to the basic aerofoil; whilst secondly, for
designs incorporating a moderate amount of sweepback, the moment arm of a conventional
rudder about the CG is small and an excessively large rudder would result when aiming to
achieve conventional yaw control moments. However, Nickel and Wohlfart (1994) comment
that wingtip fins are not only useful for steering but also increase directional stability, whilst
decreasing induced drag. Nevertheless, Northrop (1957) concentrated on trying to find a type
of drag-producing device at the wing tips that would give adequate yawing forces, without
affecting pitch or roll. The drag needed is not very large since it works over quite a long lever
arm, about half-span.
A double-split flap at the wing tip was found to have the most satisfactory all-round char-
acteristics, whilst allowing for the combination of a trim flap and rudder in the same portion
of wing trailing edge; however, it does suffer from low effectiveness at low angles of rudder
deflection, and in addition Nickel and Wohlfart (1994) comment that besides increased con-
struction complexities, the departing vortices associated with double-split flaps often induce
vibrations on the flaps. Nevertheless, the double-split flap was adopted by Northrop on the
B-2 bomber, as illustrated in Fig. 2.18. 1.
Spin recovery is generally accomplished by deflecting the ailerons such that a rolling
moment is generated to counter the spin. However, Donlan (1944) explains that wingtip fins
are also effective for spin recovery, especially if the rudder extends below the wing in order to
overcome/reduce the blanketing effects of the wing. In contrast, drag rudders were not found
to be very successful due to the varying nature of performance of those located in stalled and
unstalled regions — in some cases they were even found to produce pro-spin rolling moments.
Rudder control is not only necessary to counter the effects of adverse yaw, but also to
trim the aircraft directionally under asymmetric power conditions. Donlan (1944) proposes
that, to reduce the rudder control requirements, the thrust lines should be located as close as
1http://upload.wikimedia.org/wikipedia/commons/thumb/b/be/USAF B-2 Spirit.jpg/600px-USAF B-
2 Spirit.jpg
31
CHAPTER 2. LITERATURE REVIEW
Figure 2.18: B-2 split flap rudders.
possible to the centreline and ailerons that create favourable yawing moments when deflected
should be adopted. Bolsunovsky et al. (2001) also suggest the use of split flap elevons in
addition to vertical rudder control surfaces in order to provide extra yaw control.
2.2.3.4 Effects of Wing and Planform Geometry on Stability and Control
Sweep
Figure 2.19 shows that sweeping the wing significantly changes the lift distribution. A ‘lift
valley’ results toward the centreline, whilst a ‘lift mountain’ develops toward the wing tips,
becoming more pronounced as the angle of sweepback increases. (Sweeping the wings forward
has the opposite effect; however, this is not practical from the perspective of attaining lon-
gitudinal static stability on (Donlan (1944), Northrop (1957), Nickel and Wohlfart (1994)).)
For an unswept wing of normal aspect ratio, the NP is located at around quarter-chord.
However, as the aspect ratio is reduced to very low values, Jones (1941) states that the NP
moves ahead and upward, making the attainment of stability and balance more difficult.
With the majority of the payload accommodated toward the centreline of the aircraft, an
increase in positive static margin will result with increased sweepback, producing favourable
conditions for longitudinal static stability (Nickel and Wohlfart (1994)). The increased effec-
tive lever arm gives good trim characteristics; however, although the moment produced for
32
2.2. THE FLYING WING CONFIGURATION
Figure 2.19: The lift distributions of two rectangular wings with an aspect ratio of 5 and
sweep angles of φ = 0◦ and φ = 45◦. The lift distribution of the swept wing has been plotted
for equal lift (solid line) and for the same angle of attack (dashed line). (Taken from Nickel
and Wohlfart (1994)).
a given control surface deflection increases with sweep, the overall response of the aircraft
is also affected by the increased moment of inertia about the lateral axis. Sweep also con-
tributes to the effectiveness of wingtip fins (see below), producing more directional stability
and rudder control or, alternatively, allowing them to be made smaller. There is the possi-
bility of using centre spanwise surfaces as high-lift devices, whereby lift increments produce
only minor changes in pitching moment. Jones (1941) explains that sweepback increases the
effective dihedral, and that this effect is strongly dependent on angle of attack (increasing
with lift coefficient). He adds that the lateral stability and control characteristics of tailless
aircraft should be able to approach those of conventional aircraft, and concludes that weath-
ercock stability can be secured provided sweepback is combined with either negative dihedral
or wingtip fins. Sweepback helps prevent the occurrence of α-oscillations (also known as
pecking) — an oscillatory motion about the lateral axis — which can become problematic
in gusty weather conditions (Donlan (1944)). Although tumbling has been shown not to be
particularly troublesome, an increased amount of sweep helps prevent its occurrence (Nickel
and Wohlfart (1994)).
Swept-back wings have an inherent tendency to undergo premature tip stall, especially
during high-lift flight conditions such as take-off and landing. This is a very serious condition,
as the aircraft will tend to “roll-off” around the longitudinal axis, and as it is a self-amplifying
process (Nickel and Wohlfart (1994)). Tip stall also has an increased tendency to arise when
the aircraft is yawing. Donlan (1944) shows that it first occurs over the rear portion of the
33
CHAPTER 2. LITERATURE REVIEW
wing where the control surfaces are located; hence, it is likely that aileron control will be
ineffective. Furthermore, the tip stall also manifests as a pitching instability, as the loss of lift
often occurs behind the CG. Ground clearance issues may therefore become of importance,
necessitating dihedral (though this in turn increases the skid-roll moment). Finally, flying
wings with large sweepback have a stronger tendency to Dutch roll.
Taper
Taper is the other main parameter which influences both the aerodynamic performance of
the FW and its construction. One specific advantage of taper is that the volume of material
decreases outboard, with the largest amount of usable spar height in the wing centre (where
the highest spar bending moments occur). Therefore the spar can be built smaller overall,
resulting in a reduction in aircraft weight. In addition, there is a reduction in the intensity
of the span loading moving outboards. Thus the outer spar sections can be built lighter,
which means a concentration of weight closer to the centreline, which in combination with
sweep favours a positive static margin and increased directional stability. Strong tapering
does however increase the danger of wingtip stall with higher local values of Cl outboard.
Aerofoil Section
On tailless aircraft, a nose-down aerofoil pitching moment cannot be compensated for by a
horizontal stabiliser, therefore the aerofoil section CM0 is important. Although sweep and
washout can be used to an extent for balance, alone they are unable to counter very large
pitching moments. Therefore, tailless aircraft having small, or even zero, zero-lift pitching
moments are preferable. This may be obtained either with a symmetrical aerofoil or a reflexed
aerofoil, whereby a convex leading edge generates most of the lift whilst the concave rear part
provides stability. A disadvantage with symmetric sections is that they have their minimum
drag at zero lift, therefore a lifting wing would have more drag than could be achieved with
a properly cambered wing to match the cruise lift coefficient.
In general, the aerofoil section only has a slight affect on the NP (Nickel and Wohlfart
(1994)). However, Jones (1941) notes that an extreme reduction in thickness toward the
trailing edge can slightly shift the NP rearwards.
Washout
The required washout distribution depends on the lift coefficient at which the aircraft flies
with neutral elevators. Nickel and Wohlfart (1994) explain that with a low degree of washout,
the elevators are neutral at high speed but are permanently deflected at low speeds. The
34
2.2. THE FLYING WING CONFIGURATION
opposite is true for a large degree of washout. The latter condition is less desirable as there
is a drag penalty over a much longer flight time. For a fixed design CL, static margin and low
CM0, the required amount of washout increases with a drop in planform sweep and aspect
ratio. Washout may be used to mitigate the effects of wingtip stall by reducing local Cl, but
at the cost of a reduced overall CL. Nickel and Wohlfart (1994) add that the NP position is
also independent of washout.
Wingtip Fins
Nickel and Wohlfart (1994) explain that the overall influence of wingtip fins on the local lift
density is a reduction over the wing centre, and an increase towards the tips of the basic
wing. This effect: shifts the neutral point of a sweptback wing further aft, increasing the
longitudinal static margin; improves aileron effectiveness; and contributes to a reduction in
induced drag below the ‘optimum’ elliptic case for a plane wing — also noted by Lee (1961);
gives the wing an effective dihedral by generating a skid-roll moment; finally, helps reduce,
even eliminate, unwanted adverse yaw effects, due to the strong vortex generated by an aileron
deflection which combines with the wingtip fin to produce an opposing side force.
As the lift density is approximately equal on both sides of the wing bend, Nickel and
Wohlfart (1994) suggest that it is appropriate to give the wingtip fins the exact same aerofoil
shape installed at the tips of the basic wing. However, there does not seem to be an optimum
wingtip fin planform, i.e. sweep, taper and aspect ratio.
2.2.4 Flying and Handling Qualities
The flying and handling qualities of an aircraft describe the ease and effectiveness with which
it responds to pilot commands in the execution of some flight task. Cook (1997) explains that
the pilot’s perception of flying qualities is considered to comprise a qualitative description of
how well the aeroplane carries out the commanded task ; whilst handling qualities describe
the adequacy of the short term dynamic response to controls in the execution of the flight
task. The quantification of flying and handling qualities directly is difficult; nevertheless,
quantifiable parameters include: the stability, control and dynamic characteristics of the
airframe; flight control system dynamics; and response to atmospheric disturbances.
2.2.4.1 Civil and Military Specifications
With the significant advances in flight control systems since fly-by-wire technology was first
used on the A320 aircraft, excellent flying qualities are now possible over all flight phases
(Cook (1997)). The primary purpose of current civil aviation requirements, such as the
35
CHAPTER 2. LITERATURE REVIEW
European JAR-25 1 and the North American FAR-25, is to ensure safety of operation covering
all aspects of aircraft design; specific requirements relating to stability, control and handling
are relatively less detailed. Moreover, these specifications have been compiled for conventional
aircraft with limited stability augmentation. In contrast, military specifications, the main one
being MIL-F-8785C, do quantify requirements in terms of stability and control parameters.
On this issue, Cook (1997) comments that an aeroplane designed to meet the military flying
and handling requirements would undoubtedly also meet the civil requirements.
Since the publication of MIL-F-8785C, new technologies developed for flight control sys-
tems have enabled the exploitation of capabilities such as relaxed static stability, manoeuvre
load alleviation, structural mode suppression and gust load alleviation. A more recent mili-
tary specification, MIL-STD-1787B, was issued to take into account the use of high gain and
high authority augmentation (Cook (1997)).
2.2.4.2 Behaviour of Tailless Aircraft
Northrop (1957) explains that the response to an abrupt vertical gust is the only form of
longitudinal motion where significant differences between tailed and tailless aircraft arise.
He attributes the reduced accelerations experienced by the FW to a relatively larger wing
chord, increasing the time for the transient lift to build up, and a shorter effective tail
length, decreasing the time interval between the disturbing impulse at the lift surface and
the correcting impulse at the effective tail, so that the aeroplane tends to pitch into the gust.
With regard to the dynamic lateral response, Northrop (1957) observed that, due to the
reduced wing loading of tailless aircraft and the added effect of a high effective dihedral
and low weathercock stability, flight in turbulent air is somewhat rougher than conventional
aircraft of similar weight. Northrop (1957) comments that although weathercock stability
has a slight effect on damping rates, it reduces the amplitude of response to gusts materially.
He continues that increasing the side-force derivative CYβ improves Dutch roll damping very
materially but has virtually no effect on the amplitude of response to gusts.
2.2.5 Aeroelastic Behaviour
The aeroelastic behaviour of aircraft is characterised by flutter, which manifests itself as a
periodic movement of the aircraft structure in response to the interaction of the structure with
the (steady) airflow during flight. Flutter is a potentially destructive phenomenon because,
once excited, it grows in amplitude inducing large mechanical stresses, which can often result
1Joint Aviation Requirements - developed through the cooperation of a group of European countries.
http://www.mp.haw-hamburg.de/pers/Scholz/vorschriften/JAR-25.html
36
2.3. LAMINAR-FLYING-WING DESIGN CONCEPTS
in the break-up of an aircraft. It cannot be easily suppressed by a pilot control input, as
oscillations typically occur at frequencies above 1 Hz (Nickel and Wohlfart (1994)).
For flutter to arise during subsonic flight there needs to be a coupling between at least
two degrees of freedom, for example, spar-bending and wing torsion. Both tailed and tailless
aircraft have many degrees of freedom, which means that both types are prone to flutter.
However, with the absence of a tailplane, Nickel and Wohlfart (1994) comment that tailless
aircraft may actually be slightly more flutter resistant. In fact, in the early FW aircraft
flight tests by Northrop, Northrop (1957) does not comment on any aeroelastically induced
problems. However, Weishaar and Ashley (1973) suggest that the main reason for this may
be due to the conservative structural design of the early FW’s.
Weishaar and Ashley (1973) carried out elementary aeroelastic studies to compare the
behaviour of FW arrangements relative to conventional aircraft. In the idealised analysis,
the FW was treated as a free-free beam-rod, with the conventional aircraft modelled as an
equally stiff and massive cantilever beam-rod of half the span. On comparing these two
simple models, in the absence of bending and torsion coupling, the analysis showed equal
low torsional frequencies and pairs of higher harmonics. The analysis therefore suggests that
it is unlikely for any new aeroelastic phenomena to present themselves with the FW layout.
Moreover, the overall conclusion after assessing the limitations of the various models is that
flutter effects for FW aircraft seem more favourable.
As the lift and inertial distributions along the span of a tailless aircraft are approximately
proportional to one another, Weishaar and Ashley (1973) expect the contribution to the
overall internal structural load from payload and fuel-load, e.g. during a pull-up manoeuvre
or gust encounter, to be mild. Therefore, on consideration of stiffness and aeroelasticity
effects, Weishaar and Ashley (1973) expect that a higher structural weight fraction will
result in order to attain acceptable flutter margins, compared to that estimated from static
structural design loads alone.
2.3 Laminar-Flying-Wing Design Concepts
2.3.1 Greener by Design
In arriving at the performance estimates for a LFW, Green (2002) bases his evaluation on a
number of parameters from the detailed conceptual BWB study of Bolsunovsky et al. (2001).
However, attempts are incorporated to allow for differences between the two configurations.
The additional weight and volume requirement of an integrated suction system is thought
to favour a lower aspect ratio wing, and is consequently set at a value of 5. With a more
37
CHAPTER 2. LITERATURE REVIEW
integrated flying wing, it is argued that the vortex induced drag factor should be lower, and
closer to unity, therefore a value of 1.1 is assumed. The profile drag coefficient is taken as a
quarter of that estimated for the the BWB, CD0 = 0.0026 — Green (2002) deems this value
to be conservative based on the F-94A flight test results (see Sec. 2.1.1).
An overall propulsive efficiency typical of modern high bypass ratio turbofan engines is
assumed at 37%. Green (2002) proposes that if the cruise Mach number is dropped from 0.85
to 0.80, and an unducted fan is utilised, an overall engine efficiency of 42% is achievable.
The LFW is taken to have a takeoff weight and span equal to that for the BWB. However,
the wing loading is adjusted to account for a reduced aspect ratio and lower optimum cruise
altitude.
The aircraft’s mission fuel is estimated using empirical correlations based on conventional
aircraft, but modified to incorporate an increase of 7.5% takeoff weight to allow for suction
hardware installation (based on an empirical correlation provided by Gregory (1961)), and a
10% reduction in structural weight associated with payload; however, potential weight savings
with a lower aspect ratio are not accounted for.
At 2001 technology levels, Green (2002) estimates, for a LFW utilising turbofan technol-
ogy, a reduction of around 50% on a baseline turbulent aircraft. Utilising UDF engines, this
figure is projected to increase to around 60%. Allowing for 2050 technology improvements,
this value further increases to around 70%.
2.3.2 Delta-Wing Aircraft with Suction
Denning et al. (1997) argue that an integrated delta-wing aircraft, with aspect ratio in the
range 3 – 4, benefits from a low structural weight that can be traded off against a lower L/D.
They add that it also permits a higher wing sweep, and hence a larger chord length for a
given wing thickness (i.e. lower thickness-to-chord ratio), which then enables higher critical
Mach numbers, better aeroelastic performance, and larger permissible internal volumes.
Denning et al. (1997) draw upon Lanchester’s minimum drag condition to show that:
CL ∝
√
CD0. This expression implies that a reduction in profile drag consequently leads to a
reduction in cruise altitude and higher critical Mach numbers via a reduced CL; nevertheless,
the aerodynamic efficiency will increase as L/D ∝ √1/CD0. In contrast, Denning et al.
(1997) comment that the current aircraft design philosophy is to decrease induced drag by
increasing aspect ratio as this permits higher values of CL, requiring an increase in optimum
cruise altitude and higher speeds for a given Mach number.
For a fixed aircraft geometry, and assuming: a constant cruise Mach number, optimum
L/D, cruise-climb-datum cruise altitude, at fixed wing loading, of 40,000 ft, Denning et al.
38
2.3. LAMINAR-FLYING-WING DESIGN CONCEPTS
(1997) investigate the effect of an arbitrary profile drag reduction on altitude and non-
dimensional engine thrust FN/δ (where δ is the ambient static pressure relative to that
at sea level). They found that a 50% reduction in profile drag gives a 41% increase in L/D,
an increase in ambient pressure by 41% (i.e. a reduction in cruise altitude to 33,000 ft), and
a 50% reduction in non-dimensional engine thrust requirement. Denning et al. (1997) also
document the impact that additional suction penalties, in terms of the suction coefficient,
have on range performance. In Fig. 2.20 we see that the overall range performance is rather
insensitive to the suction assumptions.
Figure 2.20: Laminarised aircraft — relative range performance — fixed integrated delta
planforms. Assumptions: optimum L/D cruise (no allowances), cruise Mach number of 0.8,
datum CD0 = 0.010 (no suction treatment), and CQ = 0.0005. (Taken from Denning et al.
(1997)).
39
CHAPTER 2. LITERATURE REVIEW
2.3.3 The Handley Page HP117 Proposal
The basic design philosophy of the HP117 proposal, documented by Lee (1961), is focussed
on the minimisation of direct operating costs. This parameter acts as a performance index
for both transport efficiency and first cost. Economy of operation is achieved through the
combination of LFC with the all-wing arrangement and a high cruise speed. However, some
loss in aerodynamic/engine efficiency is accepted to reduce design/development expenses.
Four constraints are imposed on the design: 1) low cruise drag, 2) large internal volume,
3) high critical Mach number, and 4) good low-speed behaviour. The mission specification
consists of: transatlantic flight at a cruise Mach number of 0.8, with a payload of 300 pas-
sengers and 4500 kg of freight. (Lee (1961) comments that the true benefits of the LFW can
only be realised with over 200 passengers and a range greater than 2000 nm.) The proposed
configuration is shown in Fig. 2.21, and the design specification is summarised in Tab. 2.2.
Figure 2.21: Handley Page HP117 LFW configuration (from Green (2006)).
The design features a high degree of sweepback from the perspective of yielding a rea-
sonable value for thickness-to-chord ratio to permit satisfactory passenger accommodation,
whilst, combined with a low cruise CL, allowing for a high cruise Mach number; however, Lee
(1961) highlights that this is limited to 50◦ for fear of tip stall issues, and problems with the
undercarriage design and adverse lateral stability characteristics.
40
2.3. LAMINAR-FLYING-WING DESIGN CONCEPTS
For a given payload, and hence cabin geometry, the wing area is minimised to reduce
structural weight. It is argued that smaller wing areas also have the added benefit of higher
wing loadings, lower cruise altitudes and, consequently, smaller engines. However, the upper
value for wing loading is limited by low speed performance, unit Reynolds number, and the
desire for a high critical Mach number.
Taper ratio is selected on the basis of passenger accommodation volume. However, the
need for wingtip fins, which provide the necessary directional control, prevents the adoption
of a triangular planform, whilst structural efficiency and passenger comfort considerations
limit the feasibility of an untapered planform. The final taper ratio leads to a cabin volume
10 – 15% lower volume than the maximum possible.
Cabin volume reduces with aspect ratio; however, direct operating costs, assessed on the
basis of structural and powerplant considerations, also reduce with aspect ratio. Therefore,
a compromised aspect ratio is selected.
Table 2.2: HP117 aircraft design specification (from Lee (1961)).
Maximum thickness (m) 2.9
Root thickness-to-chord ratio 0.13
Outboard thickness-to-chord ratio 0.20
Tip thickness-to-chord ratio 0.15
Span (m) 40
Unit Reynolds number (m−1) 7.5× 106
Sweep (degrees) 50
Mean chord (m) 14.5
Planform area (m2) 581
Aspect ratio 2.7
Taper ratio 0.33
Cruise lift coefficient 0.17
Mach number 0.80
Altitude (ft) 30,000
Velocity (m/s) 243
Allowable weight (kg) 140× 103
Wing loading (N/m2) 2340
The cabin is integrated with the outer wing structure: the upper and lower panels are
supported by the front and rear spars, and ribs. The suction surface is integrated within the
structure. The structural elements are sized based on load conditions, and include: the skins;
the spars, including curved cabin pressure walls; and the floors. The rest of the aircraft is sized
using standard weight estimation techniques available at the time for a conventional metal
41
CHAPTER 2. LITERATURE REVIEW
alloy. In contrast to conventional aircraft, the report suggests that ground loads would be a
more critical design condition than in flight, due to the distribution of structural and payload
weight across the wing span. A structural weight fraction of 27% MTOW is estimated;
however, Lee (1961) comments that the cabin weight estimate may be optimistic.
A low cruise drag is achieved using slit suction: the resulting low profile drag permits a
large wing area without a parasite drag penalty, and hence low span loading and induced drag.
Laminarised tip fins increase the effective aspect ratio, without any costs in terms of parasite
drag. Consequently, a vortex induced drag factor of 0.943 is assumed. To avoid turbulence
contamination downstream of areas not available for laminarisation, such as the cockpit
windshield and doors, ‘clean-up’ slots are utilised, which enable a new laminar boundary
layer to begin downstream.
The powerplant installation consists of six (very) low bypass-ratio Rolls-Royce RB.163
engines. One group of engines receive sucked boundary layer flow, whilst another group
receive air from the clean-up slots, supplemented with contributions from ram intake. This
scheme was selected as it had an advantage in terms of first cost benefit over a separate suction
pump system. As prefigured by Lachmann (1955), Lee (1961) identifies takeoff thrust as the
most significant engine design feature.
Lee (1961) gives the overall, effective, cruise L/D at 33. With a cruise lift coefficient
of 0.17, a vortex-induced drag factor of 0.943, and an aspect ratio of 2.7, the induced drag
coefficient CD,i is 0.0032, and therefore the profile drag coefficient (including pump drag)
CD0 is 0.0020. Consequently, the low value for aspect ratio has compromised the aircraft’s
aerodynamic efficiency. On the basis of the Handley Page cruise and climb performance
studies, which assume suction availability for altitudes above 15,000 ft, the estimated fuel
burn of the HP117 is around 18 g/pax.km.
2.4 Summary and Research Proposal
Green (2002) projects that a UDF-powered laminar-flying-wing aircraft with 2001 technology
can potentially achieve up to a 60% reduction in specific fuel burn on a baseline-turbulent
aircraft, increasing up to 70% if 2050 technology levels are also factored in. Such potential
clearly warrants further examination.
Unfortunately, there is little useful information in the open literature on laminar-flying-
wing aircraft. Denning et al. (1997) present a largely qualitative discussion of the benefits of
low-aspect-ratio, integrated delta-wing planforms, including consideration of drag reduction
via LFC, but do not define in detail an optimum aircraft layout nor provide a quantitative
fuel-burn estimate. It is necessary to go back 50 years, to the Handley Page HP117 aircraft,
42
2.4. SUMMARY AND RESEARCH PROPOSAL
documented by Lee (1961), to find a reasonably detailed conceptual design study with this
information. The HP117 has an estimated specific fuel burn of around 18.0 g/pax.km. This
figure is only marginally better than that for the forthcoming B787 aircraft, which is forecast
to consume 19.6 g/pax.km 1. In other words, although the Handley Page design would have
been a major improvement on aircraft of the 1960s, it falls short of the performance suggested
by Greener by Design. New studies, assuming present-day technology, are therefore required
to substantiate (or challenge) the Greener by Design estimate. The overall objective of this
thesis is to produce one such study.
We have seen that the basic architecture of a practical LFC suction system is well es-
tablished. However, there is still little general guidance available on the important design
parameters and their interactions. Furthermore, the requirements imposed on the system by
a passenger-carrying LFW are likely to differ significantly from the conventional context, as
revealed by the Handley Page study. As a consequence of the viscous drag reduction, the
induced drag was also small, which in turn required a wing with low span loading, operat-
ing at a lift coefficient below conventional values. Finally, the freedom to optimise section
geometry was restricted by passenger accommodation requirements, which in turn lead to
thick aerofoil sections, and moment balance constraints. These changes therefore reduce the
applicability of the past LFC studies to the configuration of interest here.
The HP117 study started from a perceived market need, which then defined a mission (i.e.
range, speed, payload) and, eventually, the aircraft itself (as is normal in aircraft design). In
contrast, it is more productive to reverse this approach for our LFW; specifically, start from
the premise that an LFW is to be designed, with an emphasis above all on fuel efficiency, and
then assess its capabilities once the design is complete. This means that the approach departs
in some respects from a conventional methodology; by so doing, it ensures that the resulting
LFW will not be unnecessarily constrained by current practice. With this philosophy, a
high-level exploration of the design space can be performed to identify a specification for
the key configuration and mission parameters of the proposed LFW. On the basis of this
specification, a detailed conceptual design study can be undertaken. To quantify the direct
benefits associated with a flying-wing configuration utilising LFC, it is necessary to compare
against the performance of a conventional baseline-turbulent aircraft with the same mission
and propulsion characteristics.
It should be acknowledged that, while LFC is proven in principle, its operational use
remains subject to practical difficulties. Surface finish requirements are demanding, and en-
vironmental contamination is a major concern. Of interest here, however, is the fuel-efficiency
potential of the LFW. This can be assessed independently of operational issues. Indeed, con-
1http://www.greencarcongress.com/2007/07/boeing-rolls-ou.html, January 2012
43
CHAPTER 2. LITERATURE REVIEW
cern over the latter seems unnecessary until it is clear that the LFW holds sufficient promise
to justify its radical nature.
There is obvious merit in performing simpler studies ahead of more complex ones. There-
fore, extensive and systematic optimisation procedures shall be eschewed in favour of reasoned
design choices, and a configuration that is amenable to analysis by simplified methods shall
be insisted upon. It is thus unlikely that the resulting concept aircraft will represent the
best possible LFW, but it will provide a useful first indication of what may be expected of
the type. Equally, any critical restrictions in the design tools will become apparent, allowing
future development efforts to be efficiently targeted.
44
Chapter 3
Design Methodology
In this chapter, an overview of the conceptual design approach for conventional aircraft is
given, and compared against that envisaged for a LFW aircraft. Then, the numerical tools
and design methodologies employed in this study are discussed.
3.1 General Approach
The conventional approach to an aircraft conceptual design problem begins with the definition
of a mission specification. Then, a suitable donor aircraft is usually identified, and is used
to base initial estimates of target weight, surface areas, etc. The design approach, following
e.g. Raymer (1999), is then as follows:
(1) target gross weight specified;
(2) cruise CL estimated, thereby fixing cruise altitude;
(3) tailplane geometry defined for balance and stability;
(4) detailed drag assessment in the en-route configuration provides an estimate of the lift-
to-drag ratio;
(5) aircraft structural weight estimated;
(6) engine sized and fuel weight to complete mission estimated;
(7) MTOW evaluated and, if higher than initial target specification, process repeated from
(2) with revised MTOW.
In contrast, with an emphasis above all on fuel efficiency, the design process for the LFW
is reversed. The design methodology, shown schematically in Fig. 3.1, is broken down into five
45
CHAPTER 3. DESIGN METHODOLOGY
main parts: 1) 3-D airframe generation, 2) aircraft performance analysis, 3) suction-system
technology integration, 4) propulsion system design, and 5) structures and weights. (However,
as is evident from the figure, the design process is not linear.) Once a viable aircraft has
been identified, the mission can be specified. For each design area, it is helpful to consider
what are the main inputs and outputs, what are the constraints, and what must initially be
assumed. These shall be discussed further as the conceptual design evolves in Chaps. 5 and
6. Before this, an overview of the technical approach is provided in the following section;
note, the suction-system design approach is presented in Chap. 4.
Aircraft 
Performance
Propulsion
Planform
Low-speed
Suction-System 
Technology 
Integration
Range
Fuel burn 
Pax
Cabin
Thrust
SFC
Mission fuel
Spars
3-D Airframe
Generation
Structures 
and Weights
Loading 
Cruise 
C.G. travel 
Power
Volume
Engine weight
Suction pump weight
Wing
Aerofoil section
Airframe
geometry Lift distribution
Suction
distribution
Control surface area
Aero.
efficiency
Allowable weight
Pax
Mission
Unit Re, CL, 
Mach No.
Max. thickness, chord, 
span, sweep
Unit Re, Mach 
No.
Mach No., altitude, 
allowable weight
Cabin width
Figure 3.1: Schematic diagram of the design process envisaged for the LFW.
46
3.2. TECHNICAL APPROACH
3.2 Technical Approach
3.2.1 3-D Airframe Generation and Aircraft Performance
A quasi-3D approach is employed to evaluate the aircraft aerodynamics, as a full 3-D analysis
is too costly to fully explore the design space. AVL 3.27 1, a numerical design tool that imple-
ments a (2-D) vortex lattice method, is used to evaluate the spanwise lift distribution, aircraft
stability derivatives and induced drag coefficient. This is combined with a sectional inviscid
aerofoil analysis in VGK (Ashill et al. (1987)) to evaluate the surface pressure distribution.
(Note, a viscous analysis is performed in XFoil to check for flow separation on evaluation
of control surface deflections.) The Eppler and Somers (1980) boundary-layer solver is then
used in conjunction with a suction-system design algorithm, developed in Chap. 4, to evaluate
the suction requirements for the maintenance of laminar flow, and the corresponding section
viscous drag coefficients with and without suction. Additional aircraft drag contributions are
accounted for using empirical correlations in Torenbeek (1976) and Raymer (1999).
3.2.1.1 Computational Tools
AVL
AVL implements a vortex-lattice model suited for aerodynamic configurations mainly con-
sisting of thin lifting surfaces at small angles of attack and sideslip. Furthermore, it assumes
quasi-steady flow, and therefore neglects the shedding of unsteady vorticity; consequently,
the period of oscillatory motions should be much longer than the time it takes for the flow
to traverse the wing chord.
To better represent the characteristics of thick aerofoils, the lift-curve is scaled by CLα,
which from 2D potential flow theory, is
CLα = 1 + 0.77
t
c
. (3.1)
The effect is a chordwise shift of the control point relative to the bound vortex on each
element. However, the AVL user-primer notes that viscous effects will reduce the 0.77 factor.
Finally, slender bodies, such as fuselages, are modelled as lines of distributed source/sink
elements.
The mathematical analysis of transonic flow regimes, where there are regions of subsonic
and supersonic flow, involves the solution of a set of non-linear differential equations that
require advanced computational techniques. However, assuming small perturbations to the
1http://web.mit.edu/drela/Public/web/avl/
47
CHAPTER 3. DESIGN METHODOLOGY
(inviscid) free-stream flow conditions, linearised theories can be applied. AVL employs one
such method: the classical Prandtl-Glauert equation of motion in the compressible plane is
transformed to the Laplace equation, which is then solved by incompressible methods (see,
e.g., Houghton and Carpenter (1993) for further details). The forces are then computed by
applying the Kutta-Joukowsky relation to each vortex, which remains valid for compressible
flow.
The AVL user-primer details that surfaces and wakes are represented as a single-layer of
vortex sheets, which are discretised into horseshoe vortex filaments whose trailing legs are
parallel to the x-axis (as depicted in Fig. 3.3). By continuity, the streamlines downstream of
an aircraft fuselage, and hence wake, contract; this is depicted in Fig. 3.2, whereby the annular
streamtubes are mapped to a different spanwise position in the Trefftz Plane. Similarly, the
wing annular streamtube contracts to another annular streamtube in the wake, but with the
same cross-sectional area. (Due to fuselage viscous-wake effects, Greitzer et al. (2010) explain
that the centre wake radius is taken to be non-zero and the circulation in this region is not
evaluated; therefore, as highlighted in the AVL user-primer, the approach is only valid for
cases where the fuselage is expected to have a negligible influence.)
Figure 3.2: Wake streamline contraction due to fuselage thickness, carrying wing circulation
into the wake (from Greitzer et al. (2010)).
The perturbation velocities in the horizontal and vertical directions in the Trefftz Plane
are calculated from the circulation distribution immediately behind the trailing edge which
is convected into the wake. These are used to evaluate the overall lift and induced drag.
A resolution study was performed to investigate the necessary balance between the desired
accuracy levels and computational efficiency. It revealed that this balance is achieved with 20
48
3.2. TECHNICAL APPROACH
chordwise and 40 spanwise vortices, with a distribution such that a higher density of panels
are concentrated toward the tips, as shown in Fig. 3.3.
Figure 3.3: Example distribution of bound and trailing vortices (output from AVL).
XFoil
XFoil implements a linear-vorticity streamfunction formulation that solves the incompressible
potential flow equations. The aerofoil contour is discretised into flat panels, with the two-
dimensional inviscid flowfield constructed by superposition of a free-stream flow, a vortex
sheet on the aerofoil surface, and a source sheet on the surface and in the wake. A panel
of uniform source and vortex strength is placed across the trailing-edge if there is a finite
thickness. The vortex sheet strengths are determined by invoking the Kutta condition and
requiring that the streamfunction at each node on the surface be equal to a constant. For
viscous flows, the source strengths are determined by invoking the boundary-layer momentum
and energy integral equations. The eN method is employed to determine the transition
location. Much like AVL, XFoil uses a correction to determine the surface Cp on an aerofoil
in compressible flow: the Karman-Tsien formulation. Further details can be found in Drela
(1989).
VGK
VGK (Viscous Garabedian-Korn) developed by Qinetiq, formerly RAE, is a two-dimensional
viscous-inviscid interaction type solver. In contrast to AVL and XFoil, VGK solves the full
steady potential flow equations for a compressible gas. These equations are exact in the case
of shock-free flow. The potential equations are solved on a mesh by means of an iterative finite
difference scheme with a relaxation method. A conformal mapping function generates the
49
CHAPTER 3. DESIGN METHODOLOGY
mesh in the external region of the aerofoil. First, a small number of iterations are performed
on a coarse mesh to speed up the procedure, then a large number of iterations are performed
using a fine mesh to achieve a converged and accurate solution. With the Eppler and Somers
(1980) method employed in this study (see Chap. 4), the reader is referred to ESDU 96028
(2004) for further details of the viscous solver, and drag calculation methods utilised by VGK.
3.2.1.2 Aircraft Profile Drag Estimation Method
Torenbeek (1976) explains that aircraft profile drag can be subdivided into five groups: wing,
fin and stabiliser; fuselage; engine nacelles; viscous interference; and protuberances, surface
imperfections, gaps, etc. The methods used to determine these contributions are presented
in this section.
Wing Profile Drag
Determination of the drag coefficient for a swept wing requires careful consideration. In
Fig. 3.4 a schematic diagram of an infinite swept wing, with the direction of the potential
flow streamline detailed, along with the pressure and friction drags, is provided. The friction
drag is shown to act mostly in the free-stream direction, whilst pressure drag, which in
shock-free flow is due to the viscous displacement of the boundary layer, acts normal to the
wing-spanwise axis (i.e. normal to the isobars, which for quasi 2-D flow are aligned parallel
to the wing-spanwise axis).
Figure 3.4: Schematic diagram of friction and pressure drag forces on an infinite swept-wing
(Greitzer et al. (2010)).
50
3.2. TECHNICAL APPROACH
In principle, the friction and pressure drag have to be calculated independently, but this
is not straightforward via purely 2-D calculations. Two noteworthy approaches have been
developed by Ashill et al. (1988) and Greitzer et al. (2010), and are discussed here.
Ashill et al. (1988) first take the perpendicular-plane pressure drag and resolve it into the
free-stream direction. This is then combined with the skin-friction drag. Hence,
CDv = CDp⊥ cos
3 Λ + CDf , (3.2)
where CDf =
Df
1/2ρ∞U2∞c
. The skin friction drag is also calculated in the wing-normal direc-
tion, using an equivalent Reynolds number. It is then assumed that the flow in a turbulent
boundary layer is aligned parallel to the free stream, provided the wing is sheared; they
conclude then that, the skin-friction drag coefficient is independent of sweep angle
CDf (Re,Λ) = CDf (Re, 0) . (3.3)
(A power law for turbulent flows is used to allow for Reynolds scaling effects.)
Greitzer et al. (2010) adopt a similar approach. The skin-friction and pressure drag
coefficients are also calculated in the perpendicular plane, but are then scaled by a “Re-
scaling exponent”, appropriate for a fully turbulent flow, to obtain CDf and CDp . It is
then assumed that CDf acts mostly in the free-stream direction and scales with the dynamic
pressure in this direction, whilst the pressure drag scales with the wing-normal dynamic
pressure and acts in this direction.
Both methods are approximate as the potential-flow streamline is not aligned in either
the wing-normal or streamwise direction across the entire chord length, so the use of one-
dimensional integral equations for the boundary layer introduces errors. Therefore, the skin
friction drag estimate is strictly not correct; in contrast, the perpendicular-plane pressure drag
estimate is correct, if determined by integrating the surface pressure distribution normal to the
isobars. Moreover, both methods rely on a Reynolds number scaling applicable to turbulent
boundary layers. Furthermore, the infinite swept-wing model breaks down near the wing
root, where the potential flow streamline is necessarily aligned in the free-stream direction.
The approach employed in this study is to estimate the profile drag coefficient from
a boundary-layer calculation in the free-stream direction, assuming that the error in the
pressure drag term is negligible. The surface velocity distribution in the normal plane, u⊥,
is evaluated through an inviscid calculation using, for example, XFoil or VGK. The external
velocity ‘seen’ by the boundary layer consists of the u⊥ component and the component due
51
CHAPTER 3. DESIGN METHODOLOGY
to sweep, U∞ sin Λ. When resolved and added, they give a streamwise external velocity
ue = U∞ sin2 Λ + u⊥ cos Λ. (3.4)
This external flow velocity is then used as an input to the boundary-layer calculation described
in Chap. 4. For a sharp trailing edge aerofoil, the Squire-Young formulation (Young (1989)),
which is based on a ‘far-field’ approach for shock-free flow, is then used to evaluate the viscous
drag coefficient,
CDv = 2
δ2,∞
c
= 2δte
(
ue
U∞
)Hte12+5
2
. (3.5)
Component Profile Drag Contributions
Torenbeek (1976) explains that in pre-design applications, where the aeroplane shape is not
fully defined, the ‘flat plate analogy’ may be used. This method assumes that the component
shapes can be treated as smooth streamline bodies, and therefore the body profile drag can
be related to that of a flat plate. The skin-friction drag coefficient of a flat plate, including
Mach number effects (Eq. 12.27, pp. 282 in Raymer (1999)), is
CF =
0.455
(log10Re)2.58 (1 + 0.144M2)
0.65 , (3.6)
assuming transition at the leading edge.
This is related to the profile drag of the object through a shape correction factor φf via
(Eq. F-27, pp. 498 in Torenbeek (1976))
CD0basic = CF (1 + φf )
Swet
Sref
, (3.7)
which accounts for the difference in skin friction due to different boundary-layer flow de-
velopment around an object, variation in boundary-layer edge velocity due to the object’s
thickness, and pressure drag.
Fuselage
For a streamlined fuselage (without a blunt nose or short-afterbody tail section), the fuselage
drag consists of a basic contribution (corresponding to an uncambered, smooth, streamline
body at zero incidence, and no jet efflux), and a correction for angle of attack and up-sweep
52
3.2. TECHNICAL APPROACH
effects (Eq. F-37 pp. 502 in Torenbeek (1976))
CD0f = CD0basic + ∆αβCD0f . (3.8)
The basic drag contribution is evaluated using Eqs. 3.6 and 3.7. The Reynolds number is
based on the fuselage length lf . The shape factor (φf ) is evaluated using Eq. 3.9 (Eq. F-41,
pp. 502 in Torenbeek (1976)), which is a function of the slenderness ratio (λeff ) given by
Eq. 3.10 (Eq. F-40, pp.502 in Torenbeek (1976))
φf =
2.2
λ1.5eff
+
3.8
λ3eff
for
lA
Dfeff
≥ 2. (3.9)
λeff =
lf
Dfeff
or λeff =
lN + lA
Dfeff
+ 2 (3.10)
whichever is less; Dfeff =
√
4
piAc, where Ac is the (mean) fuselage cross-sectional area; lN
and lA denote the length of the nose and afterbody regions, respectively.
According to Torenbeek (1976), a reasonable approximation of the fuselage profile drag
increment due to angle of attack and fuselage upsweep can be made on the basis of the
‘cross-flow concept’. The drag on an element, as shown in Fig. 3.5, with a circular cross
section (equal to the local fuselage cross section) perpendicular to the airflow, for an isolated,
infinitely long, cylindrical fuselage in uniform flow, is integrated along the length of the
fuselage. The result is plotted in Fig. 3.6 for typical values of slenderness ratio and ratio of
planform areas in sections I and II. For fuselage incidence, αf , and upsweep angle, β, values
in excess of 5◦, the extra drag starts to become a significant proportion of the basic drag.
Figure 3.5: Derivation of fuselage cross-flow drag (from Torenbeek (1976)).
53
CHAPTER 3. DESIGN METHODOLOGY
Figure 3.6: Estimated fuselage profile drag increment due to angle of attack and rear fuselage
upsweep (from Torenbeek (1976)). (α′f demarcates the fuselage incidence at which the extra
drag is a minimum for a given β value.)
Wing/Fuselage Viscous Interference
Lift effects result in a thickening of the boundary layer flow near the wing/fuselage inter-
sections, and an increase in local flow velocity. At small angles of attack, Torenbeek (1976)
(Eq. F-66, pp. 509) gives the drag increment to be approximately
∆i (CDS)p = 1.5CF trCci cos
2 Λ1/2, (3.11)
where: Cci is the total circumferential length for both wing halves of the wing/fuselage
intersection line, tr is the thickness of the wing section at the root, Λ1/2 is the mid-chord-line
sweep, and CF is evaluated near the wing/body interconnection.
Torenbeek (1976) adds that the pressure gradients and section forces increase on the upper
side of the wing, and decrease on the lower side. The lower side effects may be mitigated
by suitable filleting, whilst, on a high-mounted wing, the fuselage drag on the upper side
is reduced at high lift coefficients. A simple correction is provided by Torenbeek (1976)
(Eq. F-67 pp. 510)
∆i (CDS)p
CFCLcrDfeff
= −0.81, (3.12)
54
3.2. TECHNICAL APPROACH
where cr is the root-chord length.
Finally, as a consequence of the wing circulation, the cross flow effects on fuselage drag are
affected. Torenbeek (1976) suggests that this form of interference may be taken into account
by reducing the value for α′f (detailed in Fig. 3.6). However, for low values of β and αf the
effects are negligible.
Tailplane and Tailplane/Airframe Viscous Interference
Torenbeek (1976) comments that tailplane viscous interference effects account for a small
proportion of the tailplane profile drag. He adds that this it is justifiable to assume that no
extra drag need be accounted for.
Nacelle and Pylon
Nacelle and pylon drag is estimated following Raymer (1999). A modified version of Eq. 3.7
is used to account for interference effects Q (Eq. 12.21, pp. 281 in Raymer (1999))
CD0 = CF (1 + φc)Q
Swet
Sref
, (3.13)
where φc is the component shape factor. For components mounted directly on the wing
Q = 1.5, otherwise if they are mounted less than one engine diameter Q = 1.3.
• The pylon shape factor (Eq. 12.30, pp. 283 in Raymer (1999)) is:
φpylon =
[
1 +
0.6
(x/c)m
(
t
c
)
+ 100
(
t
c
)4] [
1.34M0.18 (cos Λm)
0.28
]
− 1, (3.14)
where Λm refers to the sweep of the maximum-thickness line, and (x/c)m is the chord-
wise location of the aerofoil at the maximum thickness point.
• The nacelle shape factor (Eq. 12.32, pp. 283 in Raymer (1999)) is:
φnacelle = 0.35/f (3.15)
where f (Eq. 12.33, pp. 283 in Raymer (1999)) is:
f =
l
d
=
l√
(4/pi)Amax
(3.16)
where Amax refers to the maximum cross-sectional area.
55
CHAPTER 3. DESIGN METHODOLOGY
For an estimate of the drag contributions from these two components, the following ge-
ometries are assumed: a nacelle diameter of 2 m and length of 3.5 m; and pylon having a
chord of 3.5 m, span of 2 m, zero sweep, t/c = 0.1 and maximum thickness at x/c = 0.3.
Interference effects are based on the assumption that the engines are mounted less than one
diameter away.
In the event of an engine failure, not only is there a reduction in available thrust, but
there is also a drag increment associated with a stopped propeller or windmilling engine. A
conservative estimate of this drag contribution is provided by assuming the latter condition
(Eq.12.41, pp. 290 in Raymer (1999)).
CD0engine failure = 0.3
Aengine front face
Sref
. (3.17)
Miscellaneous Contributions
The miscellaneous drag contributions considered in this study arise from the cockpit wind-
shield, gaps where there are retracted flaps and control surfaces, and surface roughness.
1. Cockpit Wind-Shield
Torenbeek (1976) gives a value of 0.02 for the drag coefficient based on window frontal area.
This translates to roughly 2 – 3% of the total fuselage drag.
2. Gaps due to Retracted Flaps and Control Surfaces
A drag coefficient of 0.0002 based on the projected area of the surface of interest (i.e. wing,
fin and stabiliser) is assumed achievable for the control surfaces (Torenbeek (1976)).
3. Surface Roughness
If the size of the roughness element is less than a critical value, the surface is treated as smooth
with no drag penalty. This critical roughness is given by (Eq. F-82, pp. 517 in Torenbeek
(1976)): (
k
l
)
crit
=
39.5
Re0.94
, (3.18)
where: k is the equivalent sand grain roughness thickness, which Raymer (1999) gives, for
smooth paint, a value of 6.3 × 10−6 m; l is the body or chord length; and Re is based on l.
Otherwise, the profile drag increment is evaluated using Fig. 3.7.
56
3.2. TECHNICAL APPROACH
Figure 3.7: Profile drag increment due to surface roughness (from Torenbeek (1976)).
3.2.2 Propulsion System Design
The propulsion system design is conducted using GasTurb 1: a commercial package that
performs a thermodynamic analysis to specify the engine at the chosen design point, and
then assess off-design performance. To aid an understanding of the design approach adopted,
an elementary description of the gas turbine provided by Cumpsty (1997) follows.
3.2.2.1 Design Cycle Parameters
The overall efficiency, which relates the work done on the aircraft to energy released from the
fuel, is given by
η0 = ηpηth. (3.19)
The propulsive efficiency is, approximately, given by Eq. 3.20, and compares the rate of work
done on the aircraft to the rate of increase of energy of the flow through the engine.
ηp =
2
1 + Uj/U∞
(3.20)
Whilst the thermal efficiency is given by
ηth =
W˙net
m˙fLCV
, (3.21)
and relates the rate of increase of energy of the flow through the engine to the thermal
energy made available by burning the fuel. Cumpsty (1997) shows that it has a functional
1http://www.gasturb.de
57
CHAPTER 3. DESIGN METHODOLOGY
dependence on the following parameters
ηth = fn
(
T02,
T04
T02
, r, ηcomp, ηturb
)
, (3.22)
where r is the overall pressure ratio.
To obtain a high thermal efficiency, it is essential to operate at high values of T04/T02 and
pressure ratios for the core. However, this invariably leads to a high power output, which, if
used to accelerate the core flow, would lead to a high jet velocity ratio Uj/U∞ and, therefore,
a poor propulsive efficiency. This may be circumvented through the utilisation of a fan or
propeller, which supplies a relatively small increment in kinetic energy to a large bypass
stream.
Turboprop (i.e. gas-turbine-powered propeller engines) offer the best combination of
propulsive and thermal efficiency; Mair and Birdsall (1992) suggest up to a 25% lower specific
fuel consumption relative to a high-bypass-ratio turbofan. However, these types of engines
are limited by compressibility issues at high-subsonic flight Mach numbers.
The propeller efficiency is defined as the ratio of the useful thrust power to the shaft
power:
ηPR =
FpU∞
Ps
. (3.23)
This is the single most important measure of propeller performance, as high efficiency is
desired over all important phases of flight (Torenbeek (1976)). The thrust and power are
expressed as non-dimensional coefficients
CT =
Fp
ρ∞N2PRD
4
PR
(3.24)
and
Cp =
Ps
ρ∞N3PRD
5
PR
. (3.25)
These three coefficients can be related through the advance ratio
J =
U∞
NPRDPR
(3.26)
= ηPR
Cp
CT
.
J is low when the rotational speed is high relative to the flight velocity, e.g, at takeoff, whilst
is higher in cruise.
58
3.2. TECHNICAL APPROACH
Mair and Birdsall (1992) explain that for propellers of fixed geometry
(CT , CP , ηPR) = fn (J,Re,M) . (3.27)
The influence of Reynolds number may usually be taken as negligible, but the effects of Mach
number are important. Neglecting the components of induced velocity, the helical tip Mach
number is a function of advance ratio
MT = M∞
[(pi
J
)2
+ 1
]1/2
. (3.28)
High tip Mach numbers lead to the formation of shockwaves, and rapid increases in associated
drag. The same shockwaves also produce noise, and it is mainly for this reason turboprops
have not been utilised by high-subsonic speed aircraft (Mair and Birdsall (1992)).
Rohrbach et al. (1982) performed wind tunnel tests on a 45◦ swept eight-bladed propeller
at free-stream Mach numbers between 0.45 – 0.85. The propeller map obtained for the
M∞ = 0.70 case is provided in Fig. 3.8. It details propeller efficiency contours as a function
of the power coefficient and advance ratio, and the tip Mach number variation with advance
ratio. Tip Mach numbers in the range 0.8 – 1.1 are achieved through varying blade angle,
which is also detailed in the figure. The propeller map shows that propeller efficiencies of up
to 82% have been demonstrated for this case.
One final, interesting, point is discussed by Mair and Birdsall (1992). If the increase of
velocity (Uj − U∞) across a propeller of area A is uniform, the propeller thrust is
Fp =
1
2
ρ∞A
(
U2j − U2∞
)
(3.29)
⇒ 2Fp
1/2ρ∞AU2∞
=
(
Uj
U∞
)2
− 1.
This tells us that propulsive efficiency, as given by Eq. 3.20, is related directly to the propeller
loading Fp/A. The higher the loading, the lower the propulsive efficiency (as more power is
lost to the increasing kinetic energy of the flow). Furthermore, for a constant propeller thrust,
it shows that increasing diameter will lead to better efficiency.
Raymer (1999) points out that the limitation on this is the propeller tip speed — large
diameter blades require low rotational speeds to avoid compressibility issues, as discussed
earlier. However, the propeller is driven by a low pressure turbine, which generally operate
at high rotational speeds (as the power output is proportional to the square of the blade
speed). Therefore, as the LPT drives the propeller, a gearbox is required. Consequently, the
lower the rotational speed, the heavier the reduction gearbox will be.
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CHAPTER 3. DESIGN METHODOLOGY
Figure 3.8: 45◦ swept eight-bladed propeller map at M∞ = 0.70 (from Rohrbach et al.
(1982)).
3.2.2.2 GasTurb
GasTurb 1 is used for the analysis of the thermodynamics of gas turbines. It covers important
aspects such as design cycle selection and off-design behaviour. Real compressor, turbine and
propeller maps are used to yield representative results. For off-design calculations, iterative
methods are implemented.
Design Cycle
The design cycle calculation determines the mass flows, total pressures and temperatures at
the inlet and exit of all components, and the exhaust flow area. Furthermore, when the flow
Mach number at the component boundaries is selected, the dimensions of the gas turbine are
fixed. The design approach for turbofan and turboprop engines is discussed in the following.
First, a number of assumptions are applied to both engine types considered:
• kerosene fuelled, the fuel having a calorific value of 43.1 MJ/kg;
• isentropic component efficiencies, for simplicity;
1www.gasturb.de
60
3.2. TECHNICAL APPROACH
• compressor and burner exit temperatures restricted (by current technology levels) to
900 K and 1800 K, respectively (Cumpsty (1997));
• auxiliary power off-take of 50 kW per engine (default value in GasTurb for turbofan
engines).
The temperature limits are most likely to be breached at takeoff; therefore, design-point
values will be reduced to the maximum allowable, in order to yield the highest thermal
efficiencies possible. Note, in GasTurb, auxiliary power off-takes, including the power to
drive the suction pumps, are supplied by the high pressure turbine.
Turbofan
A two-spool engine is assumed, as opposed to a three-spool engine, for simplicity. Default
values of 2.5 for the inner fan and 1.8 for the outer fan pressure ratios are also assumed. The
approach to the turbofan design problem is as follows:
a) required power off-take is specified;
b) engine mass flow rate and high-pressure compressor (HPC) pressure ratio are iterated
until the thrust requirement and limit on compressor exit temperature are reached,
respectively;
c) the design bypass ratio (BPR) is set to avoid significant departures from the ideal jet
velocity ratio;
d) off-design performance is evaluated through specification of the thrust and power off-
take requirements;
e) compressor map is rescaled (discussed below), if necessary, to: 1) improve efficiency
at cruise and 2), negate issues pertaining to close proximity of off-design points to the
surge/stall line.
Turboprop
A two-spool turboprop engine is chosen over a single spool. The main difference between the
two types is the transmission of power: with two spools, the propeller is driven by a dedicated
turbine, the low pressure turbine. There are no obvious advantages of choosing three spools
over two, unless the compressor pressure ratios are excessive. The design approach is similar
to that for the turbofan, however differs in that there is a propeller. Therefore, step c), above,
is replaced by
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CHAPTER 3. DESIGN METHODOLOGY
• blade diameter and rotational speed are chosen to ensure that the power loading and
thrust coefficients are not excessive, whilst avoiding compressibility issues;
• propeller efficiency in cruise is maximised by rescaling the design point advance ratio
and power coefficient in the propeller map (provided by GasTurb), assuming that the
blade angle, pitch etc can be varied to obtain a realistic propeller efficiency.
Compressor, Turbine and Propeller Maps
Before proceeding with the off-design calculations, the design point must be correlated with
the compressor and turbine maps. Standard maps are used in this study. These are supplied
by GasTurb, and are taken from open literature. In the GasTurb user manual, it is explained
that the maps may be scaled, e.g. to increase the surge margin, provided the compressor
design pressure ratio does not deviate significantly from the original map. However, a conse-
quence of this is that the efficiency contours are also rescaled; as the design cycle efficiency
must remain the same, there is a tradeoff between high compressor surge margin and good
efficiency off-design.
There are two scaling parameters: a non-dimensional speed N/
√
T and an auxiliary
coordinate β. These lie in the pressure-ratio – corrected-flow plane, and are shown in Fig. 3.9.
β-lines are defined in GasTurb as “lines of pressure ratio versus mass flow which result in
unique intersections with the speed lines”, with values between 0 – 1, as indicated in the
figure.
The turbine scaling parameters are defined in an identical manner to those for the com-
pressor. However, map rescaling is unlikely to be necessary, as the turbine blades operate
under a favourable pressure gradient, and therefore do not posit a constraint.
Finally, GasTurb also provides a standard propeller map defined in the Cp− J plane. To
match this propeller map with that provided in Fig. 3.8, Cp and J are rescaled such that the
maximum efficiency contours are at approximately the same values.
62
3.2. TECHNICAL APPROACH
Figure 3.9: Compressor map scaling parameters (from GasTurb manual).
Off-Design
Once an engine has been sized based on the design cycle calculation, the analysis for each
off-design point requires iteration. GasTurb does this by estimating several input iteration
variables for the thermodynamic cycle. After each iteration, the imperfect estimates for the
variables yield a set of inconsistencies in the thermodynamic analysis, which are referred
to as iteration errors. With the total number of errors equal to the number of variables,
GasTurb implements a Newton-Raphson solver to determine the change in the iteration
variable required to drive the error to zero. A brief outline is provided here for the two
engine types considered in this study.
Turboprop
The iteration variables and errors for a two-spool turboprop are summarised in Tab. 3.1. The
first three iteration variables: βC , NC and βHPT , are combined with the inlet conditions, and
compressor and turbine maps, to determine the compressor flow rate, burner inlet conditions,
HPT flow rate and HPT work. The difference between the burner exit flow rate and HPT
flow rate gives the first error; furthermore, as the HPT and compressor work (plus any power
off-take) must be equal, any difference leads to the second error. With NLPT as an input
variable (equal to a default value in GasTurb), the fourth iteration variable βLPT is combined
63
CHAPTER 3. DESIGN METHODOLOGY
with the LPT map to determine the flow rate through the LPT. This is also derived from
a second source, and the difference between two approaches gives the third error. With the
nozzle inlet conditions now fixed, the total pressure in the core nozzle P08 can be determined;
however, for a choked nozzle of a certain area, the total pressure P08,required to drive the flow
gives a difference that sets up the fourth error. Finally, a fifth iteration variable is required,
T04, to achieve the required thrust specification.
Table 3.1: Summary of two-spool turboprop iteration variables and errors.
Iteration variable Error
βC HPT flow
NC HPT work
βHPT
βLPT LPT flow
P08 − P08,required
T04 Thrust requirement
Turbofan
Table 3.2 summarises the iteration variables and errors for a two-spool, unmixed flow, tur-
bofan engine. The compressor inlet conditions are combined with the LPC map, which is
read through the first two iteration variables βLPC and NLPC , to determine the LPC exit
conditions. Furthermore, the total mass flow rate is derived from the map — the split be-
tween the bypass and core streams are defined by the third iteration variable m˙c/m˙b. With
the rotational speed of the HPC, NHPC , assumed to be an input (equal to a default value
in GasTurb), the HPC map is read with the fourth iteration variable βHPC . There is now
enough information to determine the first error: the difference between the LPC and HPC
flow rates. With the burner inlet conditions known, the burner exit temperature T04 is the
fifth iteration variable; this is combined with the sixth iteration variable βHPT , which now
sets the HPT map (as NHPC known), to determine the HPT work — the difference between
the HPC (plus any power-off take) and HPT work is the third error. With the LPT connected
to the LPC, the seventh iteration variable βLPC is now enough to read the LPC map, and
determine the remaining errors, which include differences between: the LPT flow rate from
the map and that from a second source; the LPC and LPT work; and P08 and P08,required
(see above); the bypass stream provides the final error, i.e. the difference between P18 and
P18,required, which is the total pressure required to force the flow through the nozzle of area
A18.
64
3.2. TECHNICAL APPROACH
Table 3.2: Summary of two-spool, unmixed flow, turbofan iteration variables and errors.
Iteration variable Error
βLPC HPC flow
NLPC
m˙c/m˙b
βHPC
T04 HPT flow
βHPT HPT work
βLPT LPT flow
LPT work
P08 − P08,required
P18 − P18,required
3.2.3 Structures and Weights
The structural weight is evaluated by sizing primary structural elements on the basis of their
loading, using standard analytic methods detailed by Howe (2004) and Greitzer et al. (2010).
In this section, an overview of the methods used for sizing conventional aircraft are discussed,
and then adapted for an analysis of the LFW aircraft. Finally, the approach is applied to a
conventional aircraft with a known weight breakdown for validation.
3.2.3.1 Methodology
The proposed structural design methodology is summarised in Fig. 3.10. First, external loads
are identified. The aerodynamic loadings resulting from a manoeuvre and a gust are then
assessed, and the critical case identified. The primary and secondary structural elements of
the fuselage, wing and tailplane are sized, assuming a conventional Aluminium Alloy 2024-
T3 and a safety factor Ns of 1.5. (There are potential benefits in using composite materials,
however to exploit these would require going beyond the initial sizing calculations presented
here.) A conservative first estimate of the structural weight follows. The structural elements
are resized to allow for inertial relief with the inclusion of self-weight, and the process is
iterated until convergence of the final weight estimate. Finally, the structural forces on
landing are assessed, and additional structural material is added if necessary.
3.2.3.2 Loading Conditions
A summary of the design airworthiness requirements is provided by Jenkinson et al. (1999).
The key elements considered in this study are:
65
CHAPTER 3. DESIGN METHODOLOGY
Identify external loads:
aero, passenger, baggage, 
fuel, fixments, engines and 
undercarriage
Size primary and 
secondary 
structural elements
Critical aero-load: 
manoeuvre vs. gust.
Safety factor, material 
properties
Estimate self-weight
1st iteration
Include self-weight in 
load analysis
Self-weight 
converged
Stop
Yes
No
Yes
Figure 3.10: Schematic of structural design methodology.
1. Flight manoeuvre, gust and ground loads;
2. Supplementary conditions (e.g. pressurisation, unsymmetrical loads);
3. Control surface and system loads.
A load factor of 3-g for landing conditions is stipulated in FAR regulations 1. Meanwhile,
the acceleration arising from a sharp manoeuvre is generally considered the most critical
aero-load scenario for conventional aircraft — Raymer (1999) gives a value of around 2.5-g.
However, gust loads, assumed uniform across the span and acting parallel to the vertical
1http://www.flightsimaviation.com/data/FARS/part 23-561.html
66
3.2. TECHNICAL APPROACH
axis of the aircraft can be higher, especially for lightly loaded aircraft. The load factor, ∆n,
experienced due to a vertical gust is given by
∆n =
∆L
W
=
ρUgU∞CLα
2W/S
, (3.30)
where the gust velocity Ug is determined from statistical data.
System loads include items such as: engines, suction hardware, fixed equipment, avionics,
auxiliary power units, and nose and main landing gears. A passenger weight of 80 kg plus 20
kg of luggage is specified, on the basis of the study of Hileman et al. (2007). The landing-
gear weight is estimated, following Hileman et al. (2007), at 4% MTOW, with 10% of this
allocated to the nose gear (Raymer (1999)). Fixed-equipment weight consists of items such as
avionics, APU, etc, and is assumed equal to the payload weight (see Hileman et al. (2007));
of this, 10% is allocated to the avionics and 3.5% to the APU.
The internal pressurisation of the fuselage is governed by FAR codes and is set at 0.75
bar for flight altitudes above 8000 ft (FAR Sec. 25.841). This in turn determines the pressure
difference across the cabin skin at the design altitude.
3.2.3.3 Fuselage Structure
In Chap. 2 we saw that the fuselage structure of a flying wing is quite different to a conven-
tional aircraft. The former utilises a multi-bubble shell configuration, whilst the latter has a
cylindrical pressure vessel. Both are subject to pressurisation and distributed loads; however,
additional horizontal and vertical loads must be considered for tube-and-wing aircraft.
Multi-Bubble Pressure Vessel
Geometry
Figure 3.11 shows a cross section of the multi-bubble pressure vessel perpendicular to the
spanwise axis. For N cylindrical bubbles, there are N-1 vertical bulkheads of height 2hf,vb
and thickness tf,vb. Each cylinder has a radius Rf and skin thickness tf,s, and the overall
section area is Af,s. The bubbles either terminate at wing spar locations, or are cylindrical.
The shell has the following geometric and section-area relations:
θf,vb = arcsin
√1− (hf,vb
Rf
)2 (3.31)
Af,s = 2(θf,1 + θf,2)Rf tf,s + (N − 1)4θf,vbRf tf,s (3.32)
Af,vb = 2(N − 1)hf,vbtf,vb + 2Rf tf,vb(cos θf,1 + cos θf,2) (3.33)
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CHAPTER 3. DESIGN METHODOLOGY
The total fuselage cross-sectional area and surface area of the cabin shell are denoted by Af
and Sf,mb, respectively:
Af =
(
θf,1 + θf,2 +
1
2
(sin 2θf,1 + sin 2θf,2)
)
R2f
+(N − 1)(2θf,vb + sin 2θf,vb)R2f (3.34)
Sf,mb = 2(θf,1 + θf,2)Rf lf,mb + 2(N − 1)lf,mbRfθf,vb (3.35)
where lf,mb is the spanwise length of the cabin (as shown in Fig. 3.12).
Figure 3.11: Multi-bubble geometric parameters (perpendicular to the spanwise axis).
Figure 3.12 shows a cross section of the fuselage perpendicular to the chordwise axis.
The multi-bubble cabin section is capped off from the unpressurised regions at the spanwise
extremes by domed bulkheads of radius Rf and thickness tf,db. Wing ribs (fuselage frames)
extend through the lower surface to support the floor.
The dome-bulkhead surface area Sf,db is an extension of the approximation for a spherical
bulkhead given by Greitzer et al. (2010):
Sf,db ' 2
(
(θf,1 + θf,2)R2f + (N − 1)4θf,vbR2f
)
. (3.36)
68
3.2. TECHNICAL APPROACH
Figure 3.12: Cabin cross section (perpendicular to the chordwise axis).
Shell
The skin resists internal pressurisation in hoop-wise tension provided vertical bulkheads are
placed at the ‘bubble’ joins. The axial and hoop-wise skin stresses are:
σxx = Ns∆P
Af
Af,s +Af,vb
(3.37)
σθθ = Ns∆P
Rf
tf,s
(3.38)
The ratio of these two stresses, as a function of the various geometric parameters that define
the multi-bubble pressure vessel, is:
σxx
σθθ
=
1
2
(
θf,1 + θf,2 + (N − 1)(2θf,vb + sin 2θf,vb)
θf,1 + θf,2 + (N − 1)(2θf,vb + cos θf,vb)
)
. (3.39)
The ratio σxxσθθ is plotted against θf,vb for extreme values of N in Fig. 3.13 for the case where
θf,1 = θf,2 = pi/2. The figure shows that for the cylindrical case, i.e. one bubble, σxx/σθθ =
1/2, as expected; in contrast, for a large number of bubbles (N = 20), the maximum value of
σxx/σθθ does not exceed around 0.6. Consequently, the skin thickness must be sized by the
larger, hoop-wise, stress to meet the allowable stress σf,s:
tf,s = Ns∆P
Rf
σf,s
. (3.40)
The hoop-wise membrane forces T make an angle φ with the vertical, and are reacted by
a tensile force F in the vertical bulkhead at the multi-bubble joins, as illustrated in Fig. 3.14.
69
CHAPTER 3. DESIGN METHODOLOGY
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
θf,vb (rad)
σ
xx
/σ
θθ
 
 
N=20
N=1
Figure 3.13: Variation of the ratio of axial-to-hoopwise stress with θf,vb and N for θf,1 =
θf,2 = pi/2.
Assuming both components have the same material properties, the vertical bulkhead thickness
T T
F
ϕϕ
Figure 3.14: Vertical bulkhead force.
is given by
tf,vb = 2tf,s cosφ (3.41)
where φ = pi/2− θf,vb.
For a cylindrical pressure vessel with a semi-hemispherical end-cap, the stress in the cap is
half the hoop-wise stress, and therefore the cap thickness is half the cylinder thickness. Such
70
3.2. TECHNICAL APPROACH
a discontinuity induces local bending moments, and a transition is required. Therefore, it is
conservatively assumed that the domed-bulkhead thickness (tf,db) is equal to the fuselage-skin
thickness (tf,s).
The volumes of material required for the domed bulkheads, multi-bubble cylinders and
vertical bulkheads are:
Vf,db = Sf,dbtf,s (3.42)
Vf,mb = Af,slf,mb (3.43)
Vf,vb = Af,vblf,mb (3.44)
A breakdown of the shell weight is therefore:
Wf,s = ρalg(Vf,mb + Vf,db) (3.45)
Wf,vb = ρalgVf,vb (3.46)
Wf,sh = Wf,s(1 + ff,st) +Wf,vb (3.47)
where ρal is the material density, and the weight fraction of the stringers is given by Howe
(2004) to be ff,st = 0.25.
Floor
Transverse floor beams are required to support the payload and additional weights (seats,
galleys, etc), which are assumed uniformly distributed, and have a weight per unit area
Wf,fl = NlNs
(Wpay +Wfix)
(lf,mb + 2Rf )wf,fl
. (3.48)
In sizing the floor beams, the emergency landing case (Nl = 3) is taken as critical.
Figure 3.12 shows that the floor joints are modelled as pinned, with a separation lf,fl
equal to the rib/frame pitch. This arrangement leads to a more conservative weight estimate
than a clamped model would. The load due to the floor self-weight is neglected, as it is
typically much smaller than the payload. The maximum shear force and bending moment
expressions are subsequently
Sf,fl =
1
2
wf,fllf,flWf,fl (3.49)
Mf,fl =
1
8
wf,fll
2
f,flWf,fl (3.50)
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CHAPTER 3. DESIGN METHODOLOGY
where the floor width
wf,fl = 2(N − 1)Rf sin θf,vb +Rf sin θf,1 +Rf sin θf,2. (3.51)
For a set of floor I-beams with height hf,fl, the total average cross-sectional area and
corresponding volume of beam material are given by Greitzer et al. (2010) as:
Af,fl =
2.0Mf,fl
σf,flhf,fl
+
1.5Sf,fl
τf,fl
(3.52)
Vf,fl = wf,flAf,fl (3.53)
(The coefficients of 2.0 and 1.5 assume no tapering of the cross section; the floor height hf,fl
is assumed to be 10 cm.) The floor weight is then
Wf,fl = ρalgVf,fl + wf,fl(lf,mb + 2Rf )Wf,fl−pl (3.54)
where Wf,fl−pl is a specified floor-plank weight density.
Cylindrical Pressure Vessel
The reader is referred to the study of Greitzer et al. (2010), as this is followed directly.
However, a short summary of the sizing method follows.
The model consists of a cylindrical pressure vessel with an ellipsoidal nose endcap and a
hemispherical tail endcap. The fuselage is subjected to internal pressurisation ∆P , vertical
(Mv) and horizontal (Mh) bending, and torsion (Qv) loads. These are depicted in Fig. 3.15.
(In this study, the added weight Wpadd and seat weight Wseat are not treated in the same
way. Instead, a fixed equipment weight is included Wfix.)
The skin thickness is sized based on the hoop-wise skin stress that results from cabin
internal pressurisation. Reinforcements such as frames and stringers are assumed to con-
tribute 25% each to the total shell weight (Howe (2004)). Additional vertical and horizontal
bending material is added wherever the resulting bending moments exceed the capability of
the pressure vessel’s thickness based on pressurisation considerations alone. The schematic
diagram in Fig. 3.15 (a) shows that the moments acting over the front and rear of the fuselage
match at the location xwing, which for simplicity is taken as the wing’s area centroid. The
distributed loading, weight of the tailplane NWtail and aerodynamic loading acting on the
horizontal tailplane rMhLh contribute to Mh. Two scenarios are considered: in-flight at the
maximum load factor, and an emergency landing impact. Meanwhile, Mv depends solely on
the vertical fin loading rMvLv. (The factors rMv and rMh account for inertial relief.)
72
3.2. TECHNICAL APPROACH
(a) Conventional fuselage layout, loads, and bending moment and inertia distributions.
(b) Fuselage cross-section, and torsion load from ver-
tical fin.
Figure 3.15: Conventional fuselage geometry and applied loads (from Greitzer et al. (2010)).
Secondary Structures
Secondary fuselage weights are given by empirical weight fractions:
1. Windows (conventional only): an area-distributed weight of 0.66 kg/m2, estimated from
the study of Greitzer et al. (2010).
2. Insulation: an area-distributed weight of 1.08 kg/m2, estimated from the study of
Greitzer et al. (2010).
73
CHAPTER 3. DESIGN METHODOLOGY
3. An area-distributed floor-plank weight of 5 kg/m2 (Torenbeek (1976)).
3.2.3.4 Wing Structure
The wing structure of the flying wing is sized following conventional methods given by Howe
(2004). Instances where the analysis differs for the conventional configuration are highlighted;
otherwise, the same methods are used to size that aircraft’s wing, horizontal tailplane and
vertical fin.
Overview of Structural Elements
Figure 3.16 shows the primary structural elements of the wing. The skin provides the required
aerodynamic shape whilst, structurally, the upper and lower surfaces act as the main carriers
of longitudinal bending; a proportion is also reacted by spanwise stringers. (Stringers also
serve to reduce the size of areas of unsupported skin, thereby reducing local buckling loads
and aiding restriction of potential deformations.) Spar webs are positioned at the extremities
of the wing-box section. In a two-spar construction, Howe (2004) advises that the front spar
should be as far forward as possible subject to there being enough wing depth to efficiently
carry vertical shear loads, whilst the rear spar should be as far aft as possible such that control
surfaces can be accommodated and also have sufficient depth. Chordwise ribs help maintain
the aerodynamic shape of the wing cross-section, transmit local loads chordwise across to the
spanwise beams (spars), and limit the length of the skin-stringer panel arrangement to an
efficient column compressive strength. Additional secondary components such as slats, flaps,
spoilers and control surfaces make up the remaining structural weight.
Figure 3.16: Wing construction (from Howe (2004)).
74
3.2. TECHNICAL APPROACH
Geometry
A schematic diagram of a typical wing and wingtip fin configuration is provided in Fig. 3.17.
To complement a discussion of the wing structural forces and stresses, four spanwise stations
and the reference axes, which coincide with the wing-box shear-centre locus, are detailed.
The reference axes are inclined at an angle Λ relative to the axis normal to the centreline,
and are of length Lw. The resolved chord length c⊥ is detailed, and lies perpendicular to the
reference axis. A structurally efficient layout would consist of a single spar-web construction
running along the span (i.e. Λ1−2 = Λ2−3); however, if geometric constraints do not permit
this, a kinked spar-web construction would follow.
Figure 3.17: Wing (or tail) planform.
A cross section of the wing-box construction in the plane perpendicular to the reference
axis is shown in Fig. 3.18. The wing-box depth hw,box and width ww,box at each spanwise
station are used to evaluate the stresses, and hence the required thicknesses of flange and
spar-web material tw,f and tw,w, respectively. (Note, the flange thickness combines both the
skin and effective stringer thickness.) The shear centre is located half-way between the front
and rear spars, which are a distance xlesp and xtesp, respectively, from the leading edge, as
illustrated. (The leading and trailing edge regions are not detailed as they do not contribute
to the wing-box structure analysis.)
75
CHAPTER 3. DESIGN METHODOLOGY
tw,f
tw,w
ww,box
h w,box
c
aerofoil cross section
spanwise-normal plane
distributed flange
spar web
x tesp
x lesp
w     /2w,box h     /2w,box
shear centre
Figure 3.18: Wing (or tail) aerofoil and wing-box cross section (perpendicular to the reference
axis).
Stress and Weight Formulation
In the following, an account of the analytical methods used to size the primary elements of
the wing structure is given. Note, an index superscipt (‘j’) is used to show explicitly that
forces, stresses and material thicknesses are evaluated at each spanwise station.
Skin and Stringer Panels
The wing skin is modelled as a distributed flange reinforced by Zed-stringer sections (Howe
(2004)). Its size depends on the bending moment M(j)w,s, or rather the equivalent axial force
P
(j)
w,s in the upper and lower surfaces
P(j)w,s =
M
(j)
w,s
h
(j)
w,box
. (3.55)
Howe (2004) explains that for preliminary design studies, it is sufficient to assume that
the skin reacts 65% of the bending load. Therefore, the wing-skin thickness is
t(j)w,s = 0.65
P
(j)
w,s
w
(j)
w,boxσ
(j)
w,s
, (3.56)
where σ(j)w,s is the maximum allowable stress.
The allowable working stress σ(j)w,s is dictated by buckling stability for the compression
surface and fatigue/crack avoidance for the tensile surface:
76
3.2. TECHNICAL APPROACH
a) The minimum stress under which buckling occurs σ(j)w,b in the compression surface for a
given applied load P(j)w,s is
σ
(j)
w,b = AFb
 P(j)w,s
w
(j)
w,boxp
(j)
w,r
 12 , (3.57)
where: for aluminium A is 138, and Fb is 0.96 for a Zed stringer configuration; the
loading intensity P
(j)
w,s
w
(j)
w,boxp
(j)
w,r
(unit MN/m2) is the main parameter determining the al-
lowable compression stress; p(j)w,r is the support spacing along the axis of the beam, i.e.
the rib/frame pitch. (Interestingly, by limiting the width of the wing box, a higher
structural efficiency may be attained as higher working stresses can carried by the dis-
tributed flanges, though this would require sacrificing potential cabin, cargo and fuel
volume.)
b) Ashby et al. (2001) give the number of cycles that the wing material must endure as
107 (under aviation regulations), resulting in a (fatigue) stress limit σw,f = 0.30 σuts
for the tension surface.
Accounting for geometric tapering of the wing, the wing skin volume is
V(j)w,s =
(
t(j),compw,s + t
(j),tens
w,s
)
w¯
(j)
w,boxL
(j)
w . (3.58)
where w¯(j)w,box =
(
w
(j)
w,box + w
(j+1)
w,box
)
/2. Hence the skin weight is given by
Ww,s = ρalg
∑
j
V(j)w,s. (3.59)
Stringers react the remaining 35% of the bending load, giving a ‘smeared’ area ratio for
the stringers-to-skin of
Aw,st
Aw,s
= 0.54. (3.60)
The weight of the stringer construction is
Ww,st = ρalg
∑
j
A
(j)
w,stL
(j)
w . (3.61)
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CHAPTER 3. DESIGN METHODOLOGY
Spar Webs
The spar-web thickness is sized to react vertical and torsional shear loads. The shear flow
due to torsion around the wing-box section is
QT
(j)
w
w,w =
T
(j)
w
2A(j)e
(3.62)
where A(j)e is the area enclosed by the wing-box section. For equal spar-web heights, the
vertical shear in each web is half the total vertical shear acting on the wing section S(j)w . The
vertical shear flow is therefore
QS
(j)
w,w =
S
(j)
w
2h(j)w,box
. (3.63)
The direction of the shear flows is important. For example, if the torsion couple acts in a
nose-up direction, the shear flows in the front spar will act to effectively cancel, whereas in
the rear spar they reinforce one another. For a worst case estimate, both spars are sized
according to the more critical condition.
The spar-web thickness is given by
t(j)w,w =
QT
(j)
w
w,w +Q
S(j)
w,w
σ
(j)
w,w
. (3.64)
(Assuming that the cover skins and internal webs do not buckle in shear, it is sufficient to
assume that at ultimate conditions the shear stress in the web σ(j)w,w = 0.5 σuts.)
The spar-web volume, allowing for geometric tapering of the wing, is
V(j)w,w = 2t
(j)
w,wh¯
(j)
w,boxL
(j)
w , (3.65)
where h¯(j)w,w =
(
h
(j)
w,box + h
(j+1)
w,box
)
/2. Therefore the weight of the spar-web construction is
Ww,w = ρalg
∑
j
V(j)w,w. (3.66)
Ribs
The rib construction depends on its function. Across all regions the rib consists of a web (i.e.
a thin metal sheet), serving to prevent buckling of the wing skin and withstanding dynamic
forces arising from fuel slosh. In regions where the ribs must support: control surfaces at
hinge attachment points, engines, and the landing gear, spars are required to react vertical
78
3.2. TECHNICAL APPROACH
shear loads, along with flanges to react torsional shear loads.
The rib flange and spar construction, with dimensions ww,rf and hw,rsp , respectively, are
illustrated in Fig. 3.19. It also shows the location of a point load Wp relative to the shear
centre.
Rib flange
Rib spar
Figure 3.19: Schematic diagram of rib flange and spar construction.
For initial calculations, Howe (2004) advises that a satisfactory estimate of the rib pitch
to prevent buckling of the wing skin may be estimated using the empirical correlation
p(j)w,r = 0.55(h
(j)
w,rsw)
1/2. (3.67)
Along the wing span, the section depth hw,rsw varies due to tapering of the wing. Therefore,
the required rib pitch to avoid buckling instability will subsequently change over each spanwise
section. The number of ribs required is therefore
N (j)w,r =
L
(j)
w
p
(j)
w,r
. (3.68)
The rib webs are assumed to have a thickness equal to the minimum used in industry to
withstand fuel slosh loads; Niu (1988) gives tw,rw = 1 mm. The ribs are aligned orthogonally
to the reference axis, and therefore have a length equal to the mean perpendicular chord
length over a spanwise region. The weight of the rib webs is consequently
Ww,rw = ρalg
∑
j
N (j)w,rtw,rw h¯
(j)
w,rsw c¯
(j)
⊥ , (3.69)
where c¯(j)⊥ = (c
(j)
⊥ + c
(j+1)
⊥ )/2.
The rib spars are sized following the same method detailed for the wing spar webs. The
79
CHAPTER 3. DESIGN METHODOLOGY
rib spar weight is
Ww,rsw = 2ρalg
(
Nw,ret
2
w,re h¯w,rsp +Nw,ruct
2
w,ruc h¯w,rsp
)
. (3.70)
where tw,re and tw,ruc denote the spar material thickness corresponding to the engine and
undercarriage, respectively, and are assumed to have square cross sections; Nw,re and Nw,ruc
refer to the number of engines and landing gears. (The front and rear spars are assumed to
have equal thickness, corresponding to the maximum calculated.)
The rib flanges are sized to support the control surfaces. Figure 3.20 illustrates the
transfer of control surface loads to the ribs at the hinge-attachment points. The weight of
the control surface Wcs induces a torsional moment, which is reacted by the rib flange as a
direct axial force Rcs. The rib-flange cross-sectional area is therefore
Aw,rf =
Rcs
σuts
. (3.71)
The weight depends on the number of hinge attachment points that connect the control
surfaces to the wing surface Ncs (discussed further in the control surface sizing section below)
Ww,rf = 2ρalg
∑
j
N (j)cs Aw,rf w¯
(j)
w,rf
. (3.72)
Control surface
Rib flange
Rib spar
Figure 3.20: Schematic diagram of rib arrangement and forces at hinge attachment point.
Control Surface
For a conventional aircraft layout, the empirical correlations provided by Torenbeek (1976) are
satisfactory to estimate the structural weight of flaps, slats, spoilers, ailerons, etc. In contrast,
for the LFW, these items must be sized through a detailed structural analysis. Note, without
80
3.2. TECHNICAL APPROACH
the need for high-lift devices (see Chap. 2), only control surfaces are considered.
Each control surface is supported by two hinge attachment points. A spanwise separation
of 55 % along the control surface span is assumed. (Howe (2004) comments that tapering of
the wing usually pushes the outer hinge further outboard, however this is neglected here).
With a triangular cross section, as detailed in Fig. 3.21, the structural loads are reacted by
a single I-beam spar boom.
Spar boom
Figure 3.21: Schematic diagram of control surface structural arrangement and forces.
The shear force (Scs) and bending moment (Mcs) acting at a hinge are calculated by
integrating the pressure distribution and the moment of the pressure force, respectively, for
a given surface deflection over, e.g, the last 10% of chord. An example pressure distribution
is provided in Fig. 3.22.
Figure 3.22: Outboard surface Cp for a trailing edge flap deflection of 10◦ over the last 10%
of chord (output from XFoil).
The I-beam flanges are sized to react Mcs. For simplicity, both the tensile and compres-
81
CHAPTER 3. DESIGN METHODOLOGY
sive flanges are sized based on the stress limit corresponding to fatigue/crack propagation
avoidance requirements. The shear web is sized to react vertical shear. (Torsional shear Tcs
is neglected.) The total cross-sectional area, per hinge, is therefore
A(j)w,cssb =
M
(j)
cs
0.30σuts
+
S
(j)
cs
0.5σuts
. (3.73)
The total weight of the control surface spar booms, Wcssb , is then
Wcssb = ρalg
∑
N (j)cssbkcsc¯
(j)
⊥ A
(j)
cs , (3.74)
where kcs is the proportion of chord dedicated to the control surfaces, and Ncssb denotes the
number of hinges over each spanwise region.
The cover skin thickness tw,scs is sized to withstand the distributed pressure forces. The
cover skin weight is subsequently
Wcss = ρalg
∑
j
2t(j)w,scsb
(j)
(h(j)w,rsw
2
)2
+
(
kcsc¯
(j)
⊥
)21/2 . (3.75)
Wing Structural Analysis
The wing structure is treated as a root-cantilever beam. The shear force, bending moment
and torsion couple are calculated along the spanwise reference axis by free-body analysis of
the wing region outboard of the cross-section of interest. The structural loads are evaluated
through numerical integration in the resolved coordinate system.
Figure 3.23 details the forces acting on panel faces ‘i’ and ‘i+1’, and the aerodynamic and
inertial forces acting over a panel with area Ai. The aerodynamic force Li is treated as a point
load acting at quarter chord and is offset from axis ‘i’ by a distance ∆i/2 = (yi+1−yi)/2; the
resolved aerodynamic pitching moment contributions MrTi,c/4 and T
r
Ti,c/4
also act here. The
distributed inertial loads, e.g., baggage, payload, wing structural mass, etc are denoted by
W (the combination of loads depends on which region of the wing is being analysed); they
have a chordwise centre of gravity, xi,cgW , and act a distance ∆i/2 from panel edge i. (For
the LFW, the fuselage structural mass also contributes to the distributed loading.) Point
loads such as the engine, undercarriage, ground reaction, etc, are represented by WP , and
are assumed to act at the location of panel face i, at a chordwise location xi,cgWP .
82
3.2. TECHNICAL APPROACH
Figure 3.23: Structural force discretisation.
The shear force, bending moment and torque couple acting on the panel face i are:
Si = −
∑
WP −WAi + Li,c/4 + Si+1 (3.76)
Mi = Mi+1 +MrTi,c/4 − Li,c/4 ×
∆i
2
+WAi × ∆i2 − Si+1 ×∆i (3.77)
Ti = Ti+1 + TrTi,c/4 + Li,c/4 × (xi,sc − xi,c/4)−
∑
WP ×
(
xi,sc − xi,cgWP
)
+WAi × (xi,sc − xi,cgW) (3.78)
The aerodynamic lift and pitching moment acting at the quarter-chord position are de-
83
CHAPTER 3. DESIGN METHODOLOGY
termined by AVL in the free-stream axes. The lift force requires no further consideration;
however, the pitching moment contribution results in an additional bending moment
MrTc/4 = Tc/4 sin Λ (3.79)
TrTc/4 = Tc/4 cos Λ. (3.80)
(For symmetrical aerofoil sections Cm0 = 0, and hence Tc/4 is zero.)
Consider the moments and torques acting about the sweep discontinuity at station 2 shown
in Fig. 3.24. The resolved moment and torque componentsMri+1 and T
r
i+1, respectively, acting
on the shaded element are given by
Mri+1 = Mi+1 cos (Λ2−3 − Λ1−2) + Ti+1 sin (Λ2−3 − Λ1−2) (3.81)
and
Tri+1 = Mi+1 sin (Λ2−3 − Λ1−2) + Ti+1 cos (Λ2−3 − Λ1−2) (3.82)
The actual moment at i is the sum of the resolved component plus the additional moment
that arises due to forces acting over the shaded region, Mi = Mri+1 + . . .. Consequently,
the moment couple is slightly over-estimated. Since the error is a conservative one, further
refinement is not attempted.
321
Figure 3.24: Resolution of moment and torque couples across a wing-sweep discontinuity.
84
3.2. TECHNICAL APPROACH
3.2.3.5 Validity of Design Methodology
In this section, the validity and accuracy of the design approach is investigated. A Boeing
737-200 aircraft 1, for which a structural weight breakdown is provided by Kroo 2, is sized.
The specified maximum takeoff weight is approximately 59 mt. Two Pratt & Whitney
JT8D turbofan engines weighing around 2.4 mt each power the B737-200. For 136 passengers,
the payload weight is 12,920 kg. (The wing structural forces are evaluated for zero fuel
weight.) The aircraft’s economy cruise speed occurs at an altitude of 9145 m and flight Mach
number 0.73 (Aboulafia (1996)).
Geometry
A simplified model of the aircraft is detailed schematically in Fig. 3.25. The fuselage is
modelled as a cylinder with a semi-hemispherical nose endcap and tapered tailcone. The
wings are low-mounted and have a constant quarter-chord sweep of 25◦. The horizontal
tailplane is mounted on the top-side of the fuselage with a quarter-chord sweep of 35◦. Finally,
the vertical fin has a quarter-chord sweep of 45◦. The wing aerofoil cross-section is provided
on the AVL website 3; it has a maximum thickness-to-chord ratio of 11%. Symmetrical
NACA-4-digit aerofoils with a maximum thickness-to-chord ratio of 10% are assumed for the
horizontal tailplane and vertical fin. The engines and undercarriage are assumed to act as
point loads located on the leading edge at 40% half-span, and 75% chord at 30% half-span,
respectively. The front and rear spars are assumed at 10% and 70% chord, respectively, for
all surfaces.
Wing and Tailplane Structures
A typical 2.5-g pull-up manoeuvre in cruise is assumed critical for sizing of the wing structure.
The structural forces that arise with and without self-weight included are shown in Fig. 3.26.
Overall, across the span, the shear force increases going inboards. There are two distinct
drops in shear force at the engine and undercarriage positions. The, negative, increase in
bending moment and slight kinks in the diagram may be attributed to the same factors as
those for the shear force; however, there is a positive increase at the root due to the resolved
torque component. The torque distribution shows a slight, overall, increase across the span;
there is an increase at the engine position, and a decrease at that of the undercarriage; at
the wing root, there is a sharp reduction due to the resolved moment component. This is
1www.aerospaceweb.org, September 2011.
2http://adg.stanford.edu/aa241/AircraftDesign.html
3http://web.mit.edu/drela/Public/web/avl/
85
CHAPTER 3. DESIGN METHODOLOGY
(a) Front view.
(b) Plan view.
(c) Side view.
Figure 3.25: Assumed Boeing 737-200 configuration.
86
3.2. TECHNICAL APPROACH
physically consistent as the wing is swept back, and therefore the overall lift lies aft of the
shear centre; whilst locally, the lift force acts forward of the shear centre. The inclusion of
self-weight acts to provide some bending relief, but does not affect the torque distribution,
as self-weight acts at the shear centre.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0
2
4
6
8
x 105
S 
(N
)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
−6
−4
−2
0
x 106
M
 (N
m)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
−20
−15
−10
−5
0
5
x 105
T 
(N
m)
y
e
 (m)
Figure 3.26: Wing shear force, bending moment and torque diagrams — initial estimate
(solid x-marked line) and final estimate (solid line).
Howe (2004) notes that, typically, a pull-out manoeuvre in a nose dive is critical for the
horizontal stabiliser; here, the lift distribution on the tailplane in trimmed cruise is scaled
to a maximum section Cl of 0.80 (Polentz (1949)). The vertical fin is sized to react loads
incurred during engine-out at takeoff and is scaled by a factor of 0.70 to account for inertial
effects (Greitzer et al. (2010)); the resulting yawing moment coefficient Cn is assumed to be
0.002; rudders are taken to occupy the full fin height beginning at 70% chord.
87
CHAPTER 3. DESIGN METHODOLOGY
The estimated wing structural weight breakdown is provided in Tab. 3.3. The total,
structural, weight of the tailplane is estimated to be 1,052 kg.
Table 3.3: Estimated wing structural weight breakdown for the B737-200.
Component Weight (kg) Percentage (%)
Skin and stringers 5,137 89
Spar webs 129 2
Flaps, slats, spoiler and control surfaces 415 7
Ribs 97 2
Total 5,778 100
Fuselage Structure
A breakdown of the fuselage weight is given in Tab. 3.4. The estimate here is 1,789 kg, which
is significantly lower than that quoted for the B737-200 (see Tab. 3.5).
Table 3.4: Estimated fuselage structural weight breakdown for the B737-200.
Component Weight (kg) Percentage (%)
Shell 971 60
Tail cone 6 ∼ 0
Additional side material 8 ∼ 0
Additional vertical material 0 0
Windows 251 20
Insulation 153 10
Floor 400 30
Total 1,789 100
Torenbeek (1976) presents a basic weight penalty method for fuselage structural weight
prediction, which is empirically based. (Hence this is not applicable to a multi-bubble shell.)
Aspects that have been neglected in this study thus far include:
• gross shell modifications such as doors, fasteners, rivets, etc;
• support structures for the wing/fuselage connection, tailplane, and nose landing gear;
• wing/fuselage fairings.
The first item is typically a factor of two above the gross shell weight, adding 1789 kg. For
low-wing aircraft with a continuous wing box, the wing/fuselage connection weight is 100 kg.
88
3.2. TECHNICAL APPROACH
The tailplane support structure adds 145 kg. The nose landing gear bay weight adds 166 kg.
Finally, wing/fuselage fairings add 300 kg. Therefore, the total added weight is estimated to
be around 2355 kg.
Structural Weight Breakdown
A breakdown of the estimated structural weight is summarised in Tab. 3.5, and compared
against those provided by Kroo 1. The wing and tailplane weights compare well, with a
percentage difference of 14% and 2%, respectively. The fuselage weight is 23% lower. The
total structural weight compares well, with a difference of just 5%. Given the approximate
nature of the calculated loadings and assumed geometries, the structural weight predictions
are deemed sufficiently close enough to support the structural design approach used here.
Table 3.5: Structural weight breakdown for the B737-200.
Component Weight (kg) Actual (kg)
Fuselage 4,144 5,412
Wing 5,778 5,068
Tailplane 1,052 1,074
Total 10,974 11,554
Operating Empty Weight Breakdown
The aircraft operating empty weight is created from estimates of structures, propulsion sys-
tem, landing gear and fixed equipment. A breakdown is provided in Tab. 3.6.
The structures weight compares very well. The landing gear weight estimate is conser-
vative, with a difference of 19%. The calculated fixed equipment weight is 57% greater.
The total estimated OEW is 16% greater, and is due mainly to the large difference in fixed
equipment weight.
1http://adg.stanford.edu/aa241/AircraftDesign.html
89
CHAPTER 3. DESIGN METHODOLOGY
Table 3.6: Operating empty weight breakdown for the B737-200.
Component Weight (kg) Actual (kg)
Structure 10,974 11,554
Landing gear 2,187 1,833
Propulsion 4,289 4,289
Fixed equipment 12,920 8,220
Total 30,370 26,083
3.2.4 Mission Analysis
The mission fuel consists of climb fuel and fuel needed to complete the mission. In addition,
the aircraft must carry reserve fuel in case of a diversion and make allowances for unusable
fuel.
The climb fuel is calculated using Eq. 3.83:
mclimbf =
∆(KE + PE)
ηovLCV
, (3.83)
where ∆(KE + PE) is the change in kinetic and potential energies between takeoff and
maximum altitude, and ηov is the overall engine efficiency: in cruise with suction for the
LFW, and at top-of-climb for the competitor aircraft.
The fuel to complete the mission is calculated by applying the Breguet range equation
over the entire distance (including climb and descent)
s = −V L/D
g.sfc
log
(
We
Ws
)
. (3.84)
For the LFW this must be broken down into climb/landing and cruise, as LFC is only
assumed available once the aircraft has reached an altitude above 15,000 ft. (The average
climb and descent angles are taken as 2◦.) Therefore, cruise (without suction) values for
lift-to-drag ratio, velocity, and sfc are assumed over the climb and landing flight phases up
to the ‘suction initiation’ altitude.
The reserve fuel must be sufficient to ensure, if necessary, the aircraft can fly 200 nm and
hold for a further 0.75 hrs at the cruise fuel-burn rate in the event of a diversion (Hileman
et al. (2007)). In the event of a suction system failure, it is assumed that the LFW will be
allowed to land immediately. Therefore, the more critical of the two methods sets the reserve
fuel weight for the LFW. The unusable fuel is taken as 1% of the sum of mission and reserve
fuel.
90
Chapter 4
Boundary-Layer Suction System
Design
The aim of this chapter is to provide insight into the parameters affecting practical LFC suc-
tion power requirements for a commercial LFW transport aircraft. Specifically, the objectives
are: to characterise the increased power requirement due to the individual system elements,
relative to the theoretical minimum associated with the unavoidable boundary-layer losses;
to investigate the trade-off between reduction of the additional power requirement and in-
creasing system complexity; and to formulate approximate calculation methods that may
be of use in overall LFW design and optimisation. The chapter begins by introducing the
boundary-layer stability code, which calculates the ‘optimal’ distribution of suction for the
maintenance of laminar flow. Then, the influences of a number of key design parameters on
the level of suction are investigated. Finally, the main contributors to the various pressure
drops through the suction system are discussed in turn.
4.1 Boundary-Layer Suction Calculation Method
In developing a suction system design, the required level and distribution of suction for the
maintenance of laminar flow must first be determined. In this section a boundary-layer solver
is implemented and validated, and a suction algorithm is developed and compared against
an example calculation by Head (1959).
4.1.1 Boundary Layer Solver
The current industry standard for transition prediction is the eN -method, which is based on
the growth rate of linear instabilities in the boundary-layer flow and empirically determined
91
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
criteria for the degree of growth necessary for transition to occur (Joslin (1998b)). In gen-
eral, there are several classes of instability that cause transition. However, restricting the
analysis here to wing-sweep angles below about 25◦, attention can be restricted to the influ-
ence of two-dimensional Tollmien-Schlichting instabilities (see Chap. 2). In this case simpler
methods, which are more computationally efficient, may be employed; here the Eppler and
Somers (1980) two-dimensional semi-empirical computational model, shown to give excellent
predictions of transition in wind tunnel experiments (Bowers and Sim (1984)), is employed.
The computational analysis is divided into inviscid and viscous steps. The aerofoil surface
is discretised into a number of panels. The inviscid calculation is performed using XFoil,
which calculates the aerofoil surface-pressure distribution via an incompressible vortex-panel
method combined with a compressibility correction (see Chap. 3). (The default number of
panels in XFoil is 160, with a maximum of 354. The accuracy in the final calculated suction
quantity was found to worsen with increases in maximum section thickness and free-stream
Mach number; Cl variation had no effect. For a NACA0030 aerofoil, with M∞ = 0.5 and
Cl = 0, there is an error of 1.3% between the default and maximum number of panels.) The
viscous analysis takes the pressure distribution and, for a specified chord Reynolds number,
calculates the development of the boundary layer using the Eppler and Somers (1980) method.
The Eppler and Somers (1980) method is based on a numerical solution of the (incom-
pressible) integral momentum and energy equations:
δ′2 + (2 +H12)
u′e
ue
δ2 = Cf − V0
ue
(4.1)
and
δ′3 + 3
u′e
ue
δ3 = Cd − V0
ue
, (4.2)
respectively, where: Cf = ∗/Rec ueU∞
δ2
c ; Cd = 2D
∗/Rec ueU∞
δ2
c ; and 
∗, D*, H12 are functions
of the energy shape factor H32.
The location of transition is based on a critical momentum thickness, which is a function
of H32 only:
ln (Reδ2) = 18.4H32 − 21.78. (4.3)
Previous boundary-layer stability studies — using the eN -method — have found that, in
the case of excessive suction, the critical amplification value (N) for the onset of transition
reduces i.e. the transition criteria for sucked and un-sucked flows are not identical (Ellis
et al. (2000)). Eppler (1978) comments that, because suction is normally combined with
finite disturbances, transition mostly occurs before the linear stability limit is reached. For
H32 > 1.62, which can only be reached by suction, the Eppler and Somers (1980) empirical
92
4.1. BOUNDARY-LAYER SUCTION CALCULATION METHOD
criterion predicts transition well before that corresponding to the linear stability limit.
At low local Mach numbers, the influence of compressibility on the stability of the bound-
ary layer may be taken as negligible; in fact, Berry (1989) points out that the well established
Orr-Sommerfeld equation has this as an underlying assumption. For subcritical flow regimes,
compressibility effects become increasingly important with Mach number, with the growth
rate of the Tollmien-Schlichting type instability reducing as a consequence. This highly sta-
bilising influence was exploited by Viken and Wagner (1991) in the design of high-speed
natural-laminar-flow aerofoils. Mack (1979), through a linear stability analysis, found that
incompressible codes over-predict the local amplification rates. Harris et al. (1988) performed
experimental investigations on a swept-supercritical aerofoil employing LFC and calculated
that, relative to incompressible predictions, compressibility effects reduced the amplification
values in the mid-chord Tollmien-Schlichting wave dominated regions by approximately 40%.
Harris et al. (1988) chose to base their final suction-system design on the incompressible
calculations, due to the increased conservatism of the estimated suction requirements that
follow. Further studies on the influence of compressibility can be found in the works of
Atkin (2004), Bushnell and Malik (1987) and Berry et al. (1987). However, the literature
does not provide a quantitative indication of the likely error in incompressible LFC suction
calculations.
Nonetheless, the simplicity and conservatism of an approach employing the incompressible
form of the integral equations make it attractive. Furthermore, surface roughness effects (see
Joslin (1998b)) are neglected in the present study, and a conservative calculation goes some
way in compensating for this. The integral boundary-layer equations are solved using a
standard 4th-order Runge-Kutta algorithm with adaptive spacing, with the relative error
tolerance set to 0.1%.
The laminar-boundary-layer solver was first validated by modelling a zero-pressure-gradient
flow over a flat plate: the δ2 variation was in agreement with Blasius’s prediction (Young
(1989)). Next, assuming a linearly retarded velocity profile, the code’s ability to predict lam-
inar separation was confirmed against Howarth’s boundary-layer calculation (Young (1989)).
Further checks, for pressure distributions corresponding to a range of symmetric aerofoil
thicknesses, lift coefficients and chord-based Reynolds numbers, were made against Thwaites’
method (Young (1989)) with excellent results.
Over certain regions of the aerofoil, suction may not be permissible. Therefore it is also
necessary to solve Eqs. 4.1 and 4.2 for a turbulent boundary layer. The only differences
that arise are the forms of Cf , Cd and the empirical relations depending on H32. Turbulent
separation is flagged when H32 drops below 1.46.
93
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
4.1.2 Suction Algorithm and Validation
A calculation method is required such that the power demanded to maintain laminar flow
is kept to a minimum. Head (1959) claimed that applying just enough suction to keep the
boundary layer in a condition of neutral stability would give a total power requirement which
approximates closely to that minimum. While not immediately evident, this claim can be
supported by a simple argument. On consideration of the minimum (incompressible) pump
power per unit span required to return the sucked flow to the free-stream stagnation pressure:∫ c
0
[P0,∞ − Pw]V0dx,
and assuming, as an approximation, that suction is only necessary in regions of adverse
pressure gradient, it is apparent that suction earlier, where Pw is lower, is penalised more
than suction later on. Therefore, in determining V0 the minimum allowable value is aimed
for, i.e., to maintain the boundary layer on the verge of transition. This can be achieved via
the following algorithm.
Consider the integral momentum and energy equations, Eqs. 4.1 and 4.2: assuming Cf
and Cd are not significantly affected by the application of surface suction, the energy shape
factor at the end of a panel of length ∆s may be estimated as:
H32 =
δ
(i+1)
3 − (V0/ue)∆s
δ
(i+1)
2 − (V0/ue)∆s
, (4.4)
where i+ 1 denotes the conditions at the end of the panel which would apply in the absence
of suction. To maintain the boundary layer on the verge of transition, V0 should be set such
that the stability criterion given by Eq. 4.3 is not flagged; a target energy shape factor H(t)32 is
thereby defined and set equal to the right-hand-side of Eq. 4.4. On rearrangement, an initial
estimate of the suction velocity required is obtained:
V0
ue
=
(
H
(t)
32 −H(i+1)32
)
δ
(i+1)
2(
H
(t)
32 − 1
)
∆s
. (4.5)
The initial suction estimate may deviate significantly from the minimum required, especially
in regions where Cp changes considerably. Therefore, the calculation is then iterated to find
the ‘optimised’ panel suction corresponding to Head’s criterion.
To assess the accuracy of the algorithm, the distribution of suction calculated for a NACA
654 − 021 aerofoil at zero incidence (with an incompressible surface velocity distribution as
94
4.1. BOUNDARY-LAYER SUCTION CALCULATION METHOD
shown in Fig. 4.1) and for a Rec of 20 million, is compared against the prediction of Head
(1959) in Fig. 4.2. NACA 6-series aerofoils were designed to maintain natural laminar flow
over a large percentage of chord by delaying the adverse pressure gradient. Ladson and Brooks
(1974) explain that the thickness envelope was developed using aerofoil theory; however,
no simple definition of the shape is available. The aerofoil required here was generated
using the Ladson and Brooks (1974) computational program, which provides a reasonable
approximation to the thickness distribution. The corresponding velocity distribution was
then generated using XFoil. It agrees closely with that given by Head (1959) (also shown in
Fig. 4.1).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.25
0.5
0.75
1
1.25
1.5
x/c
u
e/ 
U ∞
 
 
Head
NACA 654−021
approximation
Figure 4.1: NACA 654 − 021 incompressible surface velocity distribution — Cl = 0.
The calculated level of distributed suction compares very well with Head’s prediction
downstream of 40% chord. The obvious difference between the two distributions is the chord-
wise position at which suction is initiated; this is due to the difference between Lin’s transition
criterion (which Head uses in conjunction with the Thwaites solution for a laminar boundary
layer) and that of Eppler and Somers (1980). Both predict transition within the weakly-
favourable pressure-gradient region between 10% and 45% chord (as might be expected for
such a high Reynolds number), but Lin’s does so earlier. Head estimates (for the upper and
lower surface combined) CQ = 5.14 × 10−4; here, it is calculated that CQ = 5.18 × 10−4 —
the discrepancy, in terms of volumetric flow-rate, is negligible.
A final comparison is made against Head’s calculated momentum thickness distribution
95
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
in Fig. 4.3. There is excellent agreement between the two methods.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
1
2
3
4
5
6
7
8
x 10−4
x/c
V 0
/U
∞
 
 
Head
Eppler method
Figure 4.2: Comparison of calculated suction distribution — NACA 654−021 aerofoil, Cl = 0
and Rec = 20× 106.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
x 10−4
x/c
δ 2
/ c
 
 
Head
Eppler method
Figure 4.3: Comparison of calculated momentum thickness distribution — NACA 654 − 021
aerofoil, Cl = 0 and Rec = 20× 106.
96
4.2. PUMP POWER ANALYSIS
4.2 Pump Power Analysis
With the method of calculating the desired pattern of inflow to maintain laminar flow deter-
mined, it remains to estimate the power input necessary to drive the suction system. In this
section, a non-dimensional power coefficient is defined.
In addition to the stagnation pressure loss in the boundary layer, there is an associated
drop across each of the hardware components (detailed later in Fig. 4.11). The suction pumps
are required to raise the stagnation pressure of the sucked flow back to a value that allows it
to be discharged with some speed V at free-stream static pressure. Assuming adiabatic and
reversible flow across the pump, an area-distributed pump-power coefficient w˜p is:
w˜p =
ρV0(x, z)cpT0,in
(
PPR
γ−1
γ − 1
)
1
2ρ∞U
2∞.U∞
, (4.6)
where the pump pressure ratio PPR = P0,ex/P0,in(x, z). The total pump power coefficient
W˜p is subsequently:
W˜p =
1
bc
∫ b
0
∫ c
0
w˜pdxdz. (4.7)
(The coordinate axes ‘x’ and ‘z’ are defined in Fig. 4.11.) The principal variables affecting
these dimensionless coefficients are the distribution of suction flow rate (V0) and the increase
in total pressure (PPR) required across the pumps. The latter depends not only on the wing
pressure distribution, porous skin and ducting network, but also on the discharge velocity of
the sucked flow.
The works of Rioual et al. (1996), Head (1955) and Edwards (1961) have shown that,
based on a consideration of the total power required to overcome drag forces, it is optimal
to discharge at a velocity slightly above free-stream velocity, depending on the relative ef-
ficiencies of the suction pump and aircraft propulsion systems. However, the benefit of the
excess is typically small. Furthermore, Atkin (2004) comments that the effect of losses in
the system is to flatten the minimum in the pump-drag versus exhaust Mach number rela-
tionship. Finally, given that the engine sizing for an LFW aircraft is likely to be determined
by take-off requirements (see Chap. 2), increasing the discharge velocity above free-stream
could increase suction-pump weights without reducing propulsion system weight; therefore,
a free-stream exit velocity is unlikely to be far from optimal. In the absence of propulsion
system information it is assumed that V = U∞, and hence P0,ex = P0,∞.
97
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
4.3 Minimum Suction Requirements
Once the wing geometry and flight condition are set, the minimum suction and power require-
ments can be determined independently of any details of the LFC suction system design. The
aim of this section is to provide estimates of these requirements for the range of design pa-
rameters expected of a LFW aircraft, and to understand which parameters have the greatest
influence.
The LFW is likely to require a high aspect-ratio wing and low Cl. When combined
with a section height sufficient for passenger accommodation, and structural considerations,
this gives rise to a thick wing with low sweep. To keep the flow subcritical requires a low
cruise Mach number. Typical design parameter values are: Rec = 40 × 106, t/c = 28%,
Cl = 0.15 and M∞ = 0.56. As the section geometry will be significantly constrained by
non-aerodynamic considerations, NACA00 series aerofoils are selected for this study. First,
the suction requirements for the parameter values given above are characterised, and then
the variation with Cl, Rec, M∞ and maximum t/c is investigated.
4.3.1 Typical Suction and Power Distributions
The upper-surface Cp distribution for a NACA0028 aerofoil at the chosen design point is plot-
ted in Fig. 4.4, along with the ‘optimised’ distribution of suction required for laminarisation.
The suction requirement starts just upstream of the suction peak and remains reasonably
constant until the severe adverse-pressure-gradient region over the last 10% of chord. The
suction coefficient for the upper surface is CQ = 3.78× 10−4.
The loss in stagnation pressure associated with the boundary-layer flow is given by
∆PBL = P0,∞ − Pe (based on Prandtl’s assumption that the pressure across the bound-
ary layer is constant (Young (1989))), and is plotted in dimensionless form in Fig. 4.5, which
also repeats the suction velocity distribution. The (chordwise-distributed) minimum power
requirement is approximately the product of these two quantities. However, for the exact
minimum power calculation, Eqs. 4.6 and 4.7 are used. Here P0,in = Pe, P0,ex = P0,∞ and,
assuming adiabatic flow in the boundary layer, T0,in = T0,∞.
As discussed in Sec. 4.1, the greatest stagnation pressure loss in the boundary layer is
concentrated in regions of low pressure (for example, near the suction peak); consequently,
although the sucked velocity is low in comparison to that toward the trailing edge, it is
penalised heavily — this is evident from the distribution of w˜p in Fig. 4.6. The total pump
power coefficient for the upper surface is W˜p = 4.11× 10−4. At the other extreme from this
idealised minimum, one could envisage a suction system in which all the sucked flow enters
a single chamber, with the pressure maintained just below the value of Pe at the suction
98
4.3. MINIMUM SUCTION REQUIREMENTS
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−1.5
−1
−0.5
0
0.5
1
1.5
2
−
C p
x/c
 
 
0
0.5
1
1.5
2
2.5
3
3.5
x 10−3
V 0
/U
∞
V0/U∞
Cp
Figure 4.4: Section pressure (solid) and suction velocity distribution (dashed) for the upper
surface of a NACA0028 aerofoil — M∞ = 0.56, Rec = 40× 106 and Cl = 0.15.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
3
∆
P˜
B
L
x/c
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10−3
V 0
/U
∞
 
 
∆P
V0/U∞
Figure 4.5: Distribution of dynamic pressure loss through boundary layer (solid), and suction
velocity (dashed) for the upper surface of a NACA0028 aerofoil — M∞ = 0.56, Rec = 40×106
and Cl = 0.15.
99
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
peak, and with the suction velocity distribution achieved by varying the skin resistance.
This is the basis of the power requirement estimate of Pearce (1983); for this case it yields
W˜p = 11.0× 10−4, almost three times greater than the minimum.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.5
1
1.5
2
2.5
3
3.5
4
x 10−3
x/c
w˜
p
Figure 4.6: Distribution of (area-distributed) power to overcome losses through boundary
layer.
4.3.2 Parameter Study
The dependence of the overall suction coefficient (upper and lower surface combined) on
chord Reynolds number is well established as CQ ∝ Re−1/2c (see, for example, Pankhurst and
Gregory (1952)); this result is reproduced in Fig. 4.7 using the suction algorithm developed for
the present study. In Eq. 4.6, the power requirement depends directly on the distribution of
V0 and the pressure drop. The integrated area of V0
√
Rec/U∞ along the chord, i.e. CQ
√
Rec,
is almost exactly independent of Rec, as expected. However, as chord Reynolds number
is increased, the suction initiation point moves further upstream, and the mean level of
V0
√
Rec/U∞ over the suction region drops. Sucked flow near the surface pressure minimum
is penalised more in terms of power, so this redistribution leads to the gradual increase in
W˜p
√
Rec with Rec observed in Fig. 4.7.
The influence of t/c on suction is detailed in Fig. 4.8, for three NACA00 series aerofoils
with maximum thickness-to-chord ratios of 10%, 20% and 30%; the corresponding Cp distri-
butions are also shown, using ‘x’ markers. (A free-stream Mach number of 0.5 is assumed
100
4.3. MINIMUM SUCTION REQUIREMENTS
here, otherwise the flow becomes supercritical for the highest value of t/c.) Increasing t/c de-
lays transition, however, the overall suction magnitude increases as a result of the associated
rise in adverse pressure gradient over the rear of the aerofoil.
For the range of Cl and t/c relevant to the LFW aircraft, Fig. 4.9(a) shows that t/c has
a much greater effect on the overall suction requirement than Cl; the influence of the latter
only becomes evident as t/c is reduced below 15%. The effect on W˜p is slightly stronger,
as detailed in Fig. 4.9(b). However, for the high thickness-to-chord ratios of interest in
this study, the influence of Cl on the overall suction requirement is likely to be negligible;
consequently, variations in Cl along the span of a properly designed LFW aircraft could
possibly be neglected in initial calculations.
Although the boundary-layer calculation is incompressible, the Mach number has an ef-
fect via the aerofoil pressure distribution. The influence of free-stream Mach number and
maximum section t/c on CQ and W˜p is detailed in Fig. 4.10. Each line of constant t/c is
plotted up to the Mach number at which the flow over the aerofoil first reaches the critical
limit, in order to avoid shock waves (see Chap. 2). At the lower Mach numbers, the Cp
distribution for a given Cl is unlikely to vary significantly; hence the initial weak dependence
of CQ and W˜p on M∞ for a fixed t/c is relatively unsurprising. As t/c and M∞ increase, the
effect of M∞ becomes more noticeable, but not to the extent that it can be regarded as a
significant influence.
101
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
0 1 2 3 4 5 6 7 8 9 10
x 107
0
1
2
3
4
5
6
Re
c
C
Q
√ R
e
c
,
W˜
p
√ R
e
c
 
 
CQ
W˜p
Figure 4.7: Variation of CQ and W˜p with Rec: NACA0028, Cl = 0.15 and M∞ = 0.56. Both
variables are scaled by
√
Rec, so that a constant level implies proportionality to Re
−1/2
c .
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−1.5
−1
−0.5
0
0.5
1
1.5
2
−
C p
x/c
0
0.5
1
1.5
2
2.5
3
3.5
x 10−3
V 0
/U
∞
Figure 4.8: Dependence of distributed suction on section thickness for a range of symmetrical
4-digit NACA aerofoils at Cl = 0.15, M∞ = 0.5 and Rec = 40×106: solid line – 10%; dashed
line – 20%; and dashed-dotted line – 30%; ‘x’ markers detail Cp.
102
4.3. MINIMUM SUCTION REQUIREMENTS
5 10 15 20 25 30
0
1
2
3
4
5
6
7
8
x 10−4
t/c
C Q
Cl = 0, 0.1, 0.2, 0.3 and 0.4
(a)
5 10 15 20 25 30
0
1
2
3
4
5
6
x 10−4
t/c
W˜
p
Cl = 0, 0.1, 0.2, 0.3 and 0.4
(b)
Figure 4.9: Variation of (a) CQ and (b) W˜p with maximum thickness-to-chord ratio and
section lift coefficient — symmetrical 4-digit NACA aerofoil series, M∞ = 0.5 and Rec =
40× 106.
103
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x 10−3
M
∞
W˜
p
,
C
Q
 
 
t/c = 0.1, 0.2 and 0.3
Figure 4.10: Variation of CQ (solid line) and W˜p (dashed line) with free-stream Mach number
and maximum thickness-to-chord ratio — symmetrical 4-digit NACA aerofoil series, Cl = 0.15
and Rec = 40× 106.
4.4 Suction Hardware Design and Power Consumption
The power requirements associated with the inevitable loss in stagnation pressure through the
boundary layer have been explored thus far. It now remains to specify a system to implement
the LFC in practice. In this section a practical internal layout is proposed, consisting of
spanwise chambers and chordwise ducts. The additional power demands associated with
pressure drops across the porous skin, chambers and ducts are introduced in turn.
The typical LFW design parameter values and wing section geometry, specified in Sec. 4.3,
are utilised. However, at this point, for clarity, considerations are restricted to the upper
surface of the wing only. Spanwise variations in chord are also neglected.
4.4.1 Suction Chamber Layout
One possible internal pipework arrangement is a single collector duct receiving sucked air
from all over the wing. However, pressure recovery over the rear of the aerofoil means that
the driving pressure across the skin will increase significantly, making it difficult to attain
the desired suction distribution with a constant skin resistance. Gregory (1961), and others
104
4.4. SUCTION HARDWARE DESIGN AND POWER CONSUMPTION
such as Lachmann (1955), proposed that the ideal solution would be to have a number of
pumps, or several stages in one pump, so that the applied pressure difference can be varied
over the surface of the wing, thus keeping the flow rates across the skin to a minimum; or,
alternatively, to grade the skin resistance. The latter approach, however, is a less efficient
solution; although the correct flow rates are maintained, the pressure difference between the
surface and pump entry will be greater than necessary in the high resistance regions.
A plan view of the proposed suction hardware configuration is illustrated in Fig. 4.11 —
the LFW aircraft would consist of several such arrangements along its span. The boundary-
Figure 4.11: Suction hardware layout for an untapered wing of span b and chord c.
layer fluid is sucked through the porous skin and then transported along spanwise chambers
to a set of chordwise collector ducts; each duct feeds a pump, which ejects the sucked fluid
into the free stream. Spanwise chambers, instead of chordwise, are adopted because they are
structurally more efficient, allowing for integration with the main wing-box stiffeners (Pearce
(1983)); furthermore, this arrangement minimises variations in the difference between the
outer surface pressure and the (almost-constant) chamber pressure. Finally, given the space
constraints imposed by a sharp-trailing-edge aerofoil, laminarisation is assumed possible up
to 90% chord only.
4.4.2 Skin Losses and Chamber Discretisation
The chamber layout shown will provide a piecewise-constant subsurface pressure distribution.
In this section, an algorithm is developed to specify this distribution, along with a skin-
resistance gradation, and then calculate the resulting ‘real’ suction flow. First, the analytical
expression that relates the suction velocity across the porous skin to the applied pressure
difference is presented. Then the algorithm is described, and the effect of parameter variations
105
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
investigated. Finally, an approximate method for estimating the power associated with skin
losses is given.
4.4.2.1 Pressure Drop Across a Porous Skin
The flow physics associated with sucking boundary-layer flow through a hole (or slot) has
been well researched; here, in summarising the main features, reference is made to the works
by Gregory (1961) and Thomas and Cornelius (1982). Essentially, there are two flow regimes:
the external boundary-layer flow and the suction slot flow. For laminar flow applications, it
is the flow immediately adjacent to the surface that is of importance in the first regime.
Gregory (1961) stated that the flow in the hole, and hence the pressure drop across the
surface, is a function of three dimensionless groups: the hole Reynolds number, aspect ratio
(ts/d) and Mach number. However, Thomas and Cornelius (1982), and other researchers
such as Doerffer and Bohning (2000), have pointed out that the pressure drop also depends
on the cross-flow velocity. Thomas and Cornelius (1982) thus added a fourth independent
variable, characterising the boundary-layer flow immediately adjacent to the surface by a
non-dimensional wall-velocity gradient.
Gregory (1961) commented that, for very low flow rates, the pressure drop is roughly
proportional to the velocity through the hole — corresponding to the viscous type flow region
over which D’Arcy’s law holds; for larger flow rates, inertial effects become more important,
with the pressure drop becoming proportional to the square of the hole velocity until, for
large Reh, ∆Ps1
2
ρwV 2h
= fn(Reh) ∼ const. For LFC applications, Poll et al. (1992) concluded
that the flow through an individual hole is laminar, incompressible and pipe-flow-like, with
the pressure drop having a quadratic dependence on the mass flow rate.
In spite of this body of work, no universal formula for the hole pressure drop has been
agreed upon. Fortunately, for the present study, this obstacle can be circumvented as follows.
On the basis of the existing literature, it may be asserted that a hole diameter which corre-
sponds to a high-Reynolds-number and low-Mach-number flow regime can always be found.
Furthermore, the external cross-flow at a given location is fixed, so now ∆Ps1
2
ρwV 2h
∼ const. This
implies that the area-averaged suction velocity, in terms of the non-dimensional pressure
difference across the skin ∆P˜s, is given by
V0
U∞
= Ks
√
ρ∞
ρw
∆P˜s, (4.8)
where Ks depends on the chosen hole aspect-ratio and the skin porosity. The former is
constrained by the original assertion, but it may be assumed that the latter remains under
the control of the designer through the selection of a suitable value for Ks.
106
4.4. SUCTION HARDWARE DESIGN AND POWER CONSUMPTION
In principle, this would allow for an optimised suction distribution to be realised with any
chordwise ∆P˜s distribution. In reality, the associated continual porosity variation would be
impractical. Instead, a single value of porosity, and hence Ks, associated with each chamber
is suggested.
A final consideration is the flow temperature variation through an isolated hole in the
porous surface. Doerffer and Bohning (2000) assume that the flow across a perforated plate is
adiabatic. In contrast, Inger and Babinsky (2000) prefer to take it to be isothermal, although
they also note that the temperature change calculated from an adiabatic assumption would
be small (because the flow Mach numbers on entry and exit are likely to be similar). Neither
approach appears to have been directly substantiated; given the low-Mach-number constraint
here, both would give very similar results. However, the isothermal assumption prevents the
calculation of the stagnation temperature at hole exit. Therefore, in this study, it is assumed
that the flow is adiabatic. The stagnation temperature of the flow in the chamber is then
equal to the static temperature on the external side of the skin.
4.4.2.2 Chamber Specification Algorithm
In the chordwise direction of a suction chamber, the pressure drop across the porous surface
will change due to the surface pressure variation. As a result, the suction requirement to
maintain laminar flow may no longer be satisfied (Lachmann (1955)). Therefore, it is nec-
essary to determine a relationship between the suction required for laminarisation and that
which can actually be achieved for a specified porous surface, as a function of the aerofoil’s
surface pressure distribution. First, the former is considered.
Eliminating u′e/ue from the boundary-layer integral equations, 4.1 and 4.2, and assuming
suction maintains the boundary layer on the verge of transition such that δ′2 = δ′3 = 0:
(2 +H12)
δ2
3δ3
(
Cd − V0
ue
)
= Cf − V0
ue
. (4.9)
Under these assumptions, the shape factor H32 is constant, so both Cf and Cd vary only
with the external (potential) flow velocity ratio ue/U∞, as (ue/U∞)−1. For incompressible
flow the velocity ratio is related to Cp by:
ue
U∞
=
√
1− Cp. (4.10)
107
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
Hence the scaling for the required V0/ue is:(
V0
ue
)
required
∼ 1√
1− Cp
. (4.11)
For the practical, chamber-based, implementation here, the skin pressure drop is:
∆P˜s = Cp + P˜∞ − P˜c. (4.12)
Combining this with Eq. 4.8, the dependence of V0 on Cp is:
(
V0
ue
)
actual
∼
√
k + Cp
1− Cp , (4.13)
where k = P˜∞ − P˜c is a constant.
Combining Eqs. 4.11 and 4.13:(
V0
U∞
)
actual(
V0
U∞
)
required
∼
√
k − (−Cp). (4.14)
Equation 4.14 reveals that, as −Cp drops downstream of the suction peak, (V0/U∞)actual
increases at a faster rate than (V0/U∞)required; so choosingKs to meet the suction requirement
at the upstream edge of the chamber should ensure successful laminarisation across its entire
width. On the other hand, laminarisation issues may arise with the increasing −Cp upstream
of the suction peak. The former, more usual, case is considered first.
Figure 4.12 shows a schematic diagram of the internal and external pressures across a
single chamber. The minimum and maximum pressure differences, ∆P˜s,min and ∆P˜s,max,
are design parameters which implicitly define the chamber width wc. The required skin
constant Ks is evaluated from Eq. 4.8, using ∆P˜s(= ∆P˜s,min) and the optimal suction velocity
(V0/U∞)opt at the upstream end of the chamber. The calculation proceeds downstream,
calculating (V0/U∞)actual — continuously checking the laminar flow condition (since Eq. 4.14
is only an approximate guide) — until ∆P˜s > ∆P˜s,max. The optimal suction velocity at the
start of the next chamber is then calculated on the basis of the current boundary-layer state.
For large ∆P˜s,max, the boundary layer may be stabilised to such an extent that the
required (V0/U∞)opt at the start of the next chamber is negligible and, hence, the initial
estimate of Ks too small to maintain laminar flow over that chamber. If this issue arises, Ks
is increased iteratively until transition is avoided.
108
4.4. SUCTION HARDWARE DESIGN AND POWER CONSUMPTION
Figure 4.12: Schematic diagram of surface pressure variation over a single chamber width
(downstream of the suction peak).
Upstream of the suction peak, the locations of ∆P˜s,min and ∆P˜s,max switch, as does the
prediction of Eq. 4.14 for the most critical point. The skin constant is thus still set with
∆P˜s,min, but using an optimum suction velocity calculated at the downstream end of the
chamber. The actual suction distribution is then evaluated starting from the upstream end,
as usual.
In summary, a chamber’s pressure is set by specifying ∆P˜s,min: P˜c = P˜e −∆P˜s,min; and
its chordwise extent is determined by ∆P˜s,max. Both of these parameters are constrained by
the incompressible flow assumption implicit in the definition of the skin constant Ks. (The
practical benefit of this constraint is an avoidance of possible choking problems that might
otherwise arise.)
4.4.2.3 Chamber Constraint Trade-Off Study
To understand the influence of ∆P˜s,min and ∆P˜s,max on the suction power requirement, the
following parameters are introduced: ∆P˜s,av = 12
(
∆P˜s,min + ∆P˜s,max
)
and r˜c =
∆ ePs,max
∆ ePs,min .
The first term characterises the resistance of the porous surface, whilst the latter influences
the sensitivity of the suction distribution over a chamber. The maximum value of each
parameter is restricted by the incompressible flow assumption across the skin; a suitable range
is 0.05 ≤ ∆P˜s,av ≤ 0.27 and 2 ≤ r˜c ≤ 4. Figure 4.13 details the chordwise variation of ∆P˜s
corresponding to the upper limits specified, which give the greatest pressure difference; the
critical pressure differential, corresponding to a hole Mach number of 0.4 (Pc/P0,e = 0.8703),
is superimposed.
Before exploring the suction requirements, consider Fig. 4.14, which shows the number
109
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
x/c
∆
P˜
s
 
 
Critical
Actual
Figure 4.13: Chordwise distribution of differential pressure across the porous skin with the
critical pressure superimposed.
of chambers as a function of ∆P˜s,av and r˜c. Here we see that, for a given r˜c, the number
reduces significantly initially, and then more gradually, with increasing ∆P˜s,av. This is due
to the growing difference between ∆P˜s,min and ∆P˜s,max. The rate of reduction decreases for
higher values of r˜c; however, increasing r˜c for a given ∆P˜s,av results in fewer chambers.
The associated suction coefficient is plotted in Fig. 4.15. CQ is remarkably insensitive
to ∆P˜s,av and r˜c. The former dependence is unsurprising, given the varying skin resistance
used to meet suction targets. To understand the latter, consider Fig. 4.16, which details the
variation of the chordwise distribution of suction with ∆P˜s,av and r˜c for the combination of
extreme values. Increasing r˜c increases the fluctuation of the suction distribution, but the
average level of suction is insignificantly affected; oversuction towards the end of a chamber
is almost exactly compensated by a reduced requirement at the start of the next. Figure 4.16
also confirms that increasing ∆P˜s,av does not significantly affect the fluctuation, or overall
magnitude, of the suction.
The corresponding W˜p variations are plotted in Fig. 4.17, showing that this parameter
has a greater dependence on ∆P˜s,av compared to r˜c. This is unsurprising given the suction
velocity behaviour, which implies that the surface resistance correlates almost solely with
∆P˜s,av. The small increase in power with r˜c is attributed to the redistribution of suction,
nearer the suction peak, where the stagnation pressure loss through the boundary layer is
110
4.4. SUCTION HARDWARE DESIGN AND POWER CONSUMPTION
0 0.05 0.1 0.15 0.2 0.25 0.3
0
10
20
30
40
50
60
70
80
∆P˜s ,av
N
um
be
r o
f C
ha
m
be
rs
r˜ c= 2, 3, 4
Figure 4.14: Variation of the total number of chambers with ∆P˜s,av and r˜c.
0 0.05 0.1 0.15 0.2 0.25 0.3
0
0.5
1
1.5
2
2.5
x 10−4
∆P˜s ,av
C Q
r˜ c= 2, 3, 4
Figure 4.15: Dependence of CQ on ∆P˜s,av and r˜c. The optimal value calculated by the
algorithm of Sec. 4.1.2 is CQ = 2.24× 10−4.
greatest. This effect is most prominent at higher values of ∆P˜s,av, as can be deduced from
the chordwise distribution of suction detailed in Fig. 4.16.
111
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
1
2
3
4
5
x 10−4
x/c
V 0
/U
∞
 
 
Optimised
r˜ c = 2
r˜ c = 4
(a) ∆ ePs,av = 0.05 (for r˜c = 2 and 4, CQ = 2.25 × 10−4 and 2.26 × 10−4,
respectively).
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
1
2
3
4
5
x 10−4
x/c
V 0
/U
∞
 
 
Optimised
r˜ c = 2
r˜ c = 4
(b) ∆ ePs,av = 0.27 (for r˜c = 2 and 4, CQ = 2.28 × 10−4 and 2.33 × 10−4,
respectively).
Figure 4.16: Variation of chordwise distribution of suction with r˜c and ∆P˜s,av.
112
4.4. SUCTION HARDWARE DESIGN AND POWER CONSUMPTION
0 0.05 0.1 0.15 0.2 0.25 0.3
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10−4
∆P˜s ,av
W˜
p
r˜ c= 2, 3, 4
W˜p,min
Figure 4.17: Variation of actual (solid lines) and approximate (‘x’ markers) W˜p with ∆P˜s,av
and r˜c.
The almost-linear dependence of W˜p on ∆P˜s,av suggests that it may be possible to find a
simple approximate relationship between the two. First, note that due to the Mach-number
constraint, the hole flow will be not far from incompressible. If, additionally, variations in
the pressure difference are neglected, the power consumption associated with the skin is
W˜p,s ≈ CQ∆P˜s,av. (4.15)
Finally, the minimal dependence of CQ on the chamber design parameters means that it can
be approximated by its optimal value. Adding the minimum power requirement associated
with the optimised suction distribution to Eq. 4.15 gives an approximate estimate of the
total power, which is also plotted in Fig. 4.17. There is excellent agreement between the two
approaches; however, the incompressible flow assumption does begin to underestimate the
power requirement somewhat at higher pressure differences, due to the differences between
optimal and actual CQs, and the neglect of compressibility (accounted for in Eq. 4.6).
Given the dependencies of the total number of chambers and power requirement, a rea-
sonable choice of parameters might be ∆P˜s,av = 0.15 and r˜c = 3. The number of chambers is
then 13, CQ is 2.28× 10−4 and W˜p is 3.70× 10−4. A breakdown of W˜p into the losses across
the boundary layer and the skin is 3.32× 10−4 and 0.38× 10−4, respectively; in comparison,
the optimised suction distribution, with stagnation pressure loss through the boundary layer
113
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
alone, has W˜p = 3.23 × 10−4. Therefore the redistribution of suction has had little adverse
effect on the power requirement, and the increase due to the resistance of the porous skin is
small, contributing only 10% to the total power.
4.4.3 Spanwise Chamber Losses
With the chamber widths and baseline pressures now fixed, it is necessary to introduce the
influence of spanwise chamber losses. By discretising the chamber in the spanwise direction,
the pressure drop is calculated numerically. The sucked mass flow into the first element is
known from the chamber pressure set to pass the flow across the porous skin. However,
the chamber pressure then drops in the spanwise direction (due to inertial and wall-friction
effects), the differential pressure across the skin increases and, consequently, so does the
suction mass flow into the chamber. For each spanwise element, the pressure drop and
suction rate are calculated iteratively. The converged chamber pressure is then used to begin
the iteration over the next element. The laminar flow condition is also checked at each stage.
In analysing the flow along a chamber, it is assumed that the chamber velocities are
low enough to warrant the assumption of incompressible flow. By application of the 1D
momentum and mass continuity equations, and accounting for wall friction, the static pressure
gradient over an element of length δz, width wc and height h, as illustrated in Fig. 4.18, is:
dP
dz
= − 2m˙
2
ρch2
(
m˙s
m˙
+
f
Deq
)
. (4.16)
The friction factor f is a function of ReDeq and Deq — the latter influence is due to roughness
effects. The equivalent diameter Deq = 2h
wc/h
1+wc/h
must be used for rectangular conduits; and
subsequently, ReDeq =
2m˙
µ
wc/h
1+wc/h
. The friction factor is calculated using the standard relation
for laminar flow, whilst Churchill’s correlation is used for turbulent flow; furthermore, the
chambers are assumed to have the same roughness as drawn tubing (Menon (2004)).
Figure 4.18: Notation for chamber flow.
114
4.4. SUCTION HARDWARE DESIGN AND POWER CONSUMPTION
The relevant geometrical parameters affecting the pressure drop over a span b are b/h
and wc/h (through Deq). To understand the influence of these parameters, the pressure loss
along a single spanwise chamber is investigated, with external flow properties equivalent to
those at an altitude of 10900 m and M∞ = 0.56, and having: a constant external chordwise
suction distribution of V0/U∞ = 3.29× 10−4; a skin porosity Ks = 11.0× 10−4; and typical
surface and chamber pressures of P˜e = 4.58 and P˜c = 4.49, respectively.
Figure 4.19 details the variation of ∆P˜c with b/h and wc/h, for a constant chamber depth
h of 10 cm. As expected, there is a strong dependence on b/h. Initially, ∆P˜c decreases with
wc/h, and then becomes independent of this parameter for higher values. Plots for other
values of h are very similar, but not identical, due to Reynolds number dependence.
0 50 100 150 200 250 300 350 400 450 500
0
0.05
0.1
0.15
0.2
0.25
b/h
∆
P˜
c
w
c
/h = 1, 10, 100, 1000
Figure 4.19: Spanwise-chamber pressure drop dependence on b/h and wc/h with h = 10 cm.
In order to interpret these results, it is helpful to assume that the pressure drop is small
enough to warrant the approximation m˙s ≈ constant; and that the friction factor is constant
along the length of a chamber. Then, on integration of Eq. 4.16, the non-dimensional chamber
pressure drop becomes:
∆P˜c = − 2m˙
2
s
ρcρ∞U2∞
(
b
h
)2 [
1 +
f
3
(
b
h
)(
1 + wc/h
wc/h
)]
. (4.17)
Equation 4.17 suggests that the inertial term’s contribution to the pressure drop is approxi-
mately quadratic in b/h, and the friction term’s is cubic. The explicit dependence on wc/h is
115
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
restricted to the friction term, and disappears for wide, shallow chambers. These observations
are consistent with the results of Fig. 4.19.
From the design viewpoint, Eq. 4.17 shows that the spanwise extent of chambers must be
limited to avoid excessive losses. If the friction contribution is not to exceed the inertial, and
we take f w 0.01, then we require b/h . 300 (for shallow chambers). At a typical value of
m˙2s, m˙
2
s/ρwρ∞U2∞ w 10−7, giving ∆P˜c w 0.036 at the upper limit. Thus, for example, 10 cm
deep chambers could run for 30 m with negligible pressure drop, suggesting that the power
losses from this source should be avoidable in a practical design.
4.4.4 Collector Duct Trade-Off Study
The power calculations in Sec. 4.4.2 correspond to a system architecture having one collector
duct and pump per chamber. This, however, is likely to become impractical for a large
number of chambers. An alternative arrangement where the flow from multiple chambers
is collected by a single collector duct is detailed schematically in Fig. 4.20. As the required
static pressures of adjacent chambers (Pc,1, Pc,2, Pc,3 etc) differ, flow rate control devices
(e.g. orifice plates) are then needed. The collector duct stagnation pressure P0,d is set by
the lowest static pressure among the chambers which feed it. (It is assumed here that the
collector ducts are large enough for skin friction losses to be negligible.)
Figure 4.20: Schematic diagram of an alternative chamber-collector-duct arrangement.
It is necessary to understand the trade-off between the power requirement and the number
of chambers and collector ducts. The final number of ducts (and pumps) must be based on a
consideration of geometric constraints and power requirements. More ducts imply increased
complexity, but lower average pressure loss from chamber to pump.
The pressure losses associated with throttling the flows from the chambers can be min-
imised by having an approximately equal number of chambers per collector. If the total
chamber number is not an integer multiple of the collector number, the first residual cham-
ber is added to the last collector arrangement, and the remainder allocated to successive
arrangements starting from the first. Figure 4.21 provides an example illustration of the
116
4.4. SUCTION HARDWARE DESIGN AND POWER CONSUMPTION
pressure distribution corresponding to 13 chambers and four collectors — each collector has
a minimum of three chambers, with the last having four.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2.5
3
3.5
4
4.5
5
5.5
6
x/c
P˜
 
 
Surface
Chamber
Collector
Figure 4.21: Comparison of surface, chamber and collector static pressures — ∆P˜s,av = 0.15
and r˜c = 3.
The variation of W˜p with the total number of collector ducts, for different values of r˜c, is
detailed in Fig. 4.22. Consider the case where r˜c = 2 (which gives 19 chambers) first: one
collector duct, having a pressure offset from the suction peak pressure of ∆P˜s,av(= 0.15), gives
the greatest power requirement, but W˜p starts to asymptote very quickly; by five collectors
the power penalty is only 10%. As r˜c is increased, the number of chambers, and hence
the maximum number of collector ducts decreases; interestingly, this insignificantly affects
the power variation and its magnitude. Therefore, for a given number of collector ducts
and average skin pressure drop, there are no direct benefits to be had from increasing the
number of chambers and trying to maintain a near-optimal suction distribution. (There
may, nonetheless, be indirect benefits, specifically if the chamber sidewalls also have a role
as structural stiffeners.) This observation, should, in fact, be no great surprise: the overall
average pressure drop between the suction surface and the pumps is now set by the number of
collector ducts, and the only potential benefit in having more chambers is to ensure a suction
distribution closer to optimal. However, as we have seen, departures from the optimum have
very little effect on overall suction volumes, and hence also on power consumption.
117
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
0 5 10 15 20 25
0
1
2
3
4
5
6
7
x 10−4
Number of Collectors
W˜
p
 
 
r˜ c= 2
r˜ c= 3
r˜ c= 4
Figure 4.22: Variation of W˜p with the number of collectors and r˜c, with ∆P˜s,av = 0.15.
4.5 Summary
The Eppler and Somers (1980) semi-empirical boundary-layer stability algorithm has been
implemented to determine the optimal distribution of suction required to maintain laminar
flow over a desired region, for a specified aerofoil geometry, surface pressure distribution and
chord Reynolds number. To facilitate the design of a practical suction system, an automated
algorithm has been developed. It requires, only, the specification of the porous skin’s surface
resistance and the sensitivity of the suction distribution (represented by an average pressure
drop across the skin, ∆P˜s,av, and the maximum-to-minimum pressure difference ratio, r˜c,
across a chamber), to define a set of subsurface chamber widths and pressures. The method
assumes that, for a given chamber pressure distribution, the corresponding real suction distri-
bution and power calculation can be found without needing to calculate suction hole velocities
explicitly; however, the pressure difference across the skin should be such that flow remains
subsonic (and incompressible). The spanwise chamber pressure drop required to overcome
frictional and inertial effects has been investigated. Finally, the effects of collector ducts
(introduced to reduce system architecture complexity) on the power requirement have been
explored.
The study identified a minimum power requirement independent of the suction system
design; this is associated with the boundary-layer stagnation-pressure loss of the flow in an
118
4.5. SUMMARY
optimal suction distribution (one which maintains a neutrally stable laminar boundary-layer).
Deviations from the optimal suction distribution, due to a practical porous-skin and suction-
chamber architecture, have very little effect on the overall suction coefficient, but additional
power is required, due to the skin resistance. To a good approximation, this power penalty is
given by the product of the optimal suction flow-rate coefficient and the average skin pressure
drop. In the spanwise direction, the effect of the chamber pressure drop due to frictional and
inertial effects is two-fold: firstly, it gives rise to excess suction, and secondly, it combines
with the excess suction to increase the pressure losses. However, in practise, through suitable
choice of spanwise-length-to-chamber-depth, it should be possible to make this contribution
to the overall power requirement negligible. Finally, if there are fewer collector ducts (and
hence pumps) than chambers, it is the average pressure drop from the aerofoil surface to the
collector ducts, rather than to the chambers, that determines the power penalty.
With regard to the conceptual design of a LFW, a suction system consuming little more
power than the optimum value is a practical possibility. However, a representative aerofoil
pressure distribution and associated suction profile are necessary to obtain an accurate esti-
mate of this optimum. Once these are available, the system architecture may be specified by
the following algorithm:
(1) set the average skin pressure drop, ∆P˜s,av;
(2) decide the number of suction pumps;
(3) choose the pressure ratio parameter r˜c so that the number of chambers is equal to the
number of pumps;
(4) check suction hole Mach numbers and, if too high, iterate from (2);
(5) estimate skin resistance power penalty and, if necessary (either the penalty or the
number of pumps is too high) iterate from (1);
(6) set the chamber depth so that spanwise pressure losses are negligible (c.f. equation 4.17).
On the basis of the typical LFW design parameters used in this study, such an approach can
be expected to produce a design consuming at most 20%, and more likely around 10%, excess
power over the optimum value.
119
CHAPTER 4. BOUNDARY-LAYER SUCTION SYSTEM DESIGN
120
Chapter 5
LFW Aircraft and Mission
Specification
This chapter begins, in Sec. 5.1, by developing a high-level design approach. In particu-
lar, the approach starts from the conditions that the aircraft will be a LFW operating at
near-optimum aerodynamic efficiency, and that its suction requirements must be essentially
determinable from two-dimensional boundary-layer calculations. A discussion of the detailed
constraints which result from these conditions follows, and it is shown how they may be
combined to yield a combined aircraft/mission specification, given values for three principal
design variables: span, thickness-to-chord ratio and unit Reynolds number. In Sec. 5.2 the
methodology and analytical models used for the calculations are described. Then, in Sec. 5.3,
a parametric study is undertaken to investigate the effects of the principal design variables on
the aircraft/mission specification. Finally, the choice of design variables for a detailed study,
which will follow in Chap. 6, is discussed in Sec. 5.4.
5.1 Design Approach
The mission specification that will be defined here consists of the cruise speed and altitude
(the range of the LFW will be an output of the subsequent conceptual design work). This
immediately sets one parameter of fundamental importance for all aircraft — the Mach
number — and one that Lachmann (1955) highlights as crucial to LFC applications: the unit
Reynolds number, U∞/ν. Figure 5.1 shows how Mach number and unit Reynolds number
vary with altitude and speed, according to the American Standard Atmosphere (1976). Self-
evidently, the unit Reynolds number at a given altitude can be lowered by reducing the cruise
speed. Less obviously, for a given cruise speed, the Reynolds number decreases with altitude,
but with an associated increase in Mach number until the tropopause is reached at 11 km.
121
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
0.2
0.2
0.2
0.4
0.4
0.4
0.6
0.6
0.6
0.8
0.8
0.8
1
2
2
2
4
4
4
4
6
6
6
6
8
8
8
10
10
12
12
14
14
16
18
Velocity (m/s)
Al
tit
ud
e 
(m
)
 
 
0 50 100 150 200 250 300
0
2500
5000
7500
10000
12500
15000
Mach Number
Re/chord (x106)
Figure 5.1: Altitude against velocity with contours of Mach number and unit Reynolds
number.
In this section, the constraints and design variables that influence the choice of Mach
number and unit Reynolds number are identified, and an explanation of how they are com-
bined to produce a design specification is given. The constraints fall under two categories:
geometric and aerodynamic.
5.1.1 Aircraft Configuration and Geometric Constraints
The architecture of the flying-wing aircraft is two-fold: the centrebody accommodates pas-
sengers, whilst the outer wing has a more conventional structure, providing volume for fuel
tanks and cargo holds (see Chap. 2). For the sake of simplicity, a swept, untapered flying-wing
planform, having chord c and span b, is assumed here (see Fig. 5.2).
A cabin height of about 2 m must be provided for passengers to stand upright. A value
of 2.5 m is therefore imposed on the (maximum) wing section thickness; the extra 0.5 m
allows for the hardware necessary to suck and transport the air from the boundary layer, and
for the wing structural reinforcements. It is immediately apparent that thickness-to-chord
ratios comparable to current high-speed subsonic aircraft verge on the impractical — 10%,
for example, would require a chord of 25 m — and thicker sections may well be preferable.
122
5.1. DESIGN APPROACH
Therefore, the range 0.1 ≤ t/c ≤ 0.3 is considered. The aerofoil section geometry will be
dictated as much by passenger accommodation requirements as aerodynamic performance,
and should have minimal nose-down pitching moment at zero lift (for trim reasons (Nickel
and Wohlfart (1994), Donlan (1944), and Jones (1941))). Therefore, where section details
are needed, the family of symmetrical (00) NACA 4-digit aerofoils will be assumed.
The large chord associated with the passenger accommodation constraint implies a cor-
respondingly large wingspan. Existing airport ground-handling infrastructure requires that
the aircraft planform fit within an 80 m × 80 m box (Denning et al. (1997)). For possible
span values, we consider 60 m, 80 m and 100 m. The last is to quantify any advantages that
might ultimately lead to a re-evaluation of current airport facilities.
Finally, note that elements providing directional stability and yaw control are not shown
in Fig. 5.2. The use of ‘winglet rudders’ is envisaged, which are essentially vertical fins, with
control surfaces, placed at the wing tips (see Chap. 2).
Λ
c
b
Figure 5.2: Schematic diagram of a simplified laminar-flying-wing planform layout.
5.1.2 Aerodynamic Constraints
5.1.2.1 Unit Reynolds Number
As previously discussed in Chap. 2, the maximum possible unit Reynolds number depends
on the surface finish and atmospheric turbulence levels. Although a Reu up to 16× 106 m−1
is realistically achievable for a two-dimensional aerofoil flow, values this high compromise
the stability of the attachment-line boundary layer on swept wings (see below). Here, then,
values of 4, 8 and 12× 106 m−1 are considered.
5.1.2.2 Planform Sweep
This study is restricted to LFW configurations for which the suction requirements can be cal-
culated from consideration of two-dimensional, Tollmien-Schlichting instabilities only. Thus,
to avoid cross-flow instabilities, the wing sweep angle must be limited. The dependence of
123
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
cross-flow instability on pressure distribution, discussed in Chap. 2, means that this limit is a
function of the aerofoil section geometry. However, in light of Joslin (1998b) (see Chap. 2), a
uniform value of 25◦ should ensure that the suction flow is dominated by the need to stabilise
Tollmien-Schlichting waves.
A further issue in swept-wing transition is the stability of the ‘attachment-line’ boundary
layer on the leading edge (see Chap. 2). For the LFW, attention is restricted to natural tran-
sition on the attachment line. As the nose radius of NACA 4-digit aerofoils has a functional
dependence on the maximum section thickness-to-chord ratio (Abbott and Von Doenhoff
(1959)), Eq. 2.8 (repeated below) allows for evaluation of the maximum planform sweep an-
gle consistent with a laminar attachment-line boundary layer. In this calculation, Rea.l is set
to 650, at the centre of Poll’s critical-value range.
Rea.l =
(
U∞r
ν
× sin Λ tan Λ
2
) 1
2
.
5.1.2.3 Mach Number
In Chap. 2 problems arising due to a steep pressure rise through a shock wave associated
with supercritical flow, and its adverse effect on the stability of the boundary layer, were
discussed. Consequently, in this study, the design is restricted to the subcritical flow regime;
i.e. the cruise Mach number is chosen to be equal to the critical Mach number, for a given
wing sweep angle, section thickness-to-chord ratio and lift coefficient.
5.1.3 Design Specification Algorithm
An approach is developed whereby the aircraft/mission specification is defined on the basis
of three key variables: unit Reynolds number, span and thickness-to-chord ratio. With the
thickness already fixed, the chord length, planform aspect ratio and planform area follow
directly from the span and thickness-to-chord ratio. The algorithm then proceeds as follows:
(a) the wing sweep is maximised, subject to the cross-flow limit and the attachment-line
transition criterion;
(b) the aircraft drag polar is estimated;
(c) the requirement that the aircraft cruises at high efficiency is used to set the lift and
drag coefficients;
(d) with lift coefficient and section geometry known, the critical Mach number is calculated;
124
5.2. METHODOLOGY
(e) the cruise Mach number and unit Reynolds number now set the cruise altitude and
speed (c.f. Fig. 5.1). The allowable cruise weight, wing loading and lift-to-drag ratio
follow directly from the cruise lift coefficient, drag coefficient and aircraft geometrical
parameters, combined with the free-stream conditions.
The algorithm outlined above is performed over a range of thickness-to-chord ratios: first
for the three specified spans and a fixed unit Reynolds number, and then three specified unit
Reynolds numbers and a fixed span. Results from this process are presented in Sec 5.3. First,
in the following section, details of the aerodynamic calculation methodology are given.
5.2 Methodology
5.2.1 Drag Polar
A drag polar of the form given in Eq. 5.1 is assumed, where the first and second terms are
the zero-lift and lift-dependent drag respectively (Katz and Plotkin (2001)). (Martinez-Val
and Perez (1991) comment that the errors involved in Eq. 5.1 are very small, since drag
divergence is not an issue in long-range cruise.)
CD = CD0 +KC2L (5.1)
On a conventional aircraft, the lift-dependent drag parameter, K, is typically slightly
greater than the ‘ideal’, elliptical-lift-distribution value, (piAR)−1. In part, the excess is due
to ‘trim drag’, which may, depending on the longitudinal stability margin, be more significant
for a flying wing. On the other hand, the end-plate effect of winglet rudders will tend to reduce
K. Therefore, in the absence of detailed quantitative information on these competing factors,
it is taken equal to (piAR)−1.
An estimate for the zero-lift drag coefficient, CD0, is obtained by performing a drag
calculation for the aerofoil section with zero lift and wing-normal Mach number 0.5. (This
Mach number is close enough to the final expected cruise condition to avoid significant errors,
whilst, in addition, guaranteeing subcritical flow for the full range of thickness-to-chord ratios
considered.) Details of the calculation are given below.
It should be recognised that this approach falls some way short of a detailed drag build-up.
In particular, contributions from the winglet rudders, the engine pylons, and the other sources
classified by Torenbeek (1976) (and detailed in Chap. 3) as ‘miscellaneous’ are neglected. For
this reason, sensitivity to errors in the estimated drag polar should be considered; this issue
will be addressed in Sec. 5.4.3.
125
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
5.2.2 Cruise Condition
At the optimum cruise condition, an aircraft’s fuel consumption per unit distance is min-
imised. This requirement corresponds to maximising the range parameter (U∞/sfc) (L/D),
where sfc (the specific fuel consumption) is, in general, a function of cruise speed and alti-
tude, and depends on the type of powerplant used (Martinez-Val and Perez (1991)).
For an aircraft utilising suction, the thermal energy from the fuel is determined by the
thrust power requirement and the power off-take necessary to energise the suction system:
m˙fLCV =
TU∞
η0
+
DpumpU∞
ηpumpηth
. (5.2)
Adding the assumption that ηpump u ηp then, since η0 = 1sfc
U∞
LCV , Eq. 5.2 becomes
m˙f
U∞
=
W
L/D
× sfc
U∞
, (5.3)
where D = Daero + Dpump. This corresponds to the standard result, and suggests that it is
robust to the inclusion of pump drag in CD0.
Martinez-Val and Perez (1991) note that the performance of turbofan engines lies between
two theoretical idealisations: sfc = constant (in which case one should maximise U∞L/D)
and sfc ∝ U∞ (maximise L/D). To avoid assuming specific propulsion characteristics at this
stage, one of these conditions is chosen, accepting that it will probably be somewhat sub-
optimal. Given that either will imply unusually low wing loading (as will become apparent),
with adverse implications for structural efficiency, the condition which mitigates this issue is
opted for. This is the one corresponding to a higher lift coefficient, i.e. that of maximum
L/D. The associated lift and drag coefficients follow from Eq. 5.1; they are:
CL =
√
piCD0AR and CD = 2CD0. (5.4)
5.2.3 Lift and Drag Calculations
Sweep introduces three-dimensionality into the wing flow, as already discussed. For reason-
ably high aspect ratios, the flow over most of the wing is similar to that over a swept wing of
infinite span (Houghton and Carpenter (1993)). Hileman et al. (2007) use infinite swept wing
theory, as it greatly simplifies the aerodynamic calculations: it allows 3-D aircraft coefficients
to be related to simple perpendicular 2-D aerofoil coefficients. However, its use here should
be qualified by the observation that its predictions at the lowest aspect ratios considered in
the parameter study that will follow are unlikely to be reliable.
126
5.2. METHODOLOGY
The flow in the plane normal to the spanwise axis has a reduced Mach number
M⊥ = M∞ cos Λ; (5.5)
however the effective thickness-to-chord ratio increases to
(t/c)⊥ =
(t/c)
cos Λ
. (5.6)
If the 2-D lift coefficient for the normal-plane flow geometry is Cl⊥ , then the local lift coeffi-
cient (based on the free-stream velocity) is Cl⊥ cos
2 Λ. For a well designed aircraft, this local
lift coefficient will be closely representative of the overall, aircraft, lift coefficient, so
CL = Cl⊥ cos
2 Λ. (5.7)
The drag coefficient is determined following the considerations presented in Chap. 3 for
a swept wing, which requires evaluation of the surface pressure, and hence velocity, distribu-
tion. For the present investigation XFoil is used. The other stage at which the wing pressure
distribution is required, is for determining the critical Mach number at the cruise lift coef-
ficient. Here the section lift coefficient is found via Eqs. 5.4 and 5.7; XFoil calculations at
this lift coefficient are iterated numerically to find the Mach number at which Cp,min is equal
to the sonic value. (Note that this approach does not guarantee fully subcritical flow on
the centre-line, where the infinite swept-wing theory breaks down. On the other hand, the
calculation is conservative in the sense that the NACA 4-digit geometry is not optimised for
transonic flow; therefore, it may be argued that subcritical centre-line flow will be attainable
with a suitable, bespoke, aerofoil section.)
Contributions to the zero-lift drag are two-fold: there is a viscous profile drag, which
can be determined based on the momentum thickness at the trailing edge using the Squire-
Young formula, given by Eq. 3.5; and a ‘pump drag’, due to the additional power that must
be supplied by the engines to re-energise the sucked boundary layer fluid. In estimating
the pump-drag contribution, reference is made to Chap. 4, wherein a minimum pump-power
requirement independent of the suction system design was identified. It is associated with
the boundary-layer stagnation pressure loss of the flow in an optimal suction distribution,
and accounts for 80% – 90% of the total power requirement; therefore, in this study, the
pump drag is estimated based on the minimum power requirement alone. Furthermore,
the Mach number and lift coefficient were found to have a negligible effect on the pump
power requirement, compared to the influence of thickness-to-chord ratio, and are thus also
discounted here. Finally, as full-chord laminarisation is realistically unachievable, given the
127
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
space requirements of the suction hardware and the presence of trailing-edge control surfaces,
suction is assumed to be available over the first 90% of chord only. (Note, however, that it will
typically not be required until some distance aft of the leading edge, as detailed in Chap. 4.)
5.3 Aircraft and Mission Parametric Study
The planform layout and architecture of the LFW, along with the key design constraints, have
been identified. Moreover, three principal design variables have been proposed: maximum
section thickness-to-chord ratio (0.1 ≤ t/c ≤ 0.3), wing span (60 m, 80 m and 100 m) and
unit Reynolds number (4× 106, 8× 106 and 12× 106 m−1). Once these variables have been
set, the aircraft/mission specification follows from the algorithm of Sec. 5.1.3. At this stage,
enough information is available to investigate further parameters, namely: lift-to-drag ratio,
wing loading, take-off lift coefficient, and allowable weight.
5.3.1 Aspect Ratio
For the untapered swept-wing model assumed, the aspect ratio is simply given by AR = b/c.
Aspect ratio increases linearly with thickness-to-chord ratio, for a given span, because of the
fixed thickness constraint. Over the range of spans and thickness-to-chord ratios considered,
the aspect ratio varies from low values of around two, to much higher values near twelve.
5.3.2 Sweep
Figure 5.3 shows the variation of wing sweep with thickness-to-chord ratio and unit Reynolds
number. (Equation 2.8 is independent of wing span.) For low unit Reynolds numbers, the
assumed cross-flow limit of 25◦ applies. As unit Reynolds number is increased, the influence
of thickness-to-chord ratio on attachment-line stability becomes more important. For the
highest value of unit Reynolds number, the reduction in sweep at the maximum thickness-
to-chord ratio considered is approximately 8◦.
5.3.3 Profile Drag
Figure 5.4 details the zero-lift drag breakdown over a range of maximum thickness-to-chord
ratios and unit Reynolds numbers. As thickness-to-chord ratio is increased, the viscous drag
shows a small reduction. (This is because the momentum thickness at the trailing-edge
is almost independent of t/c, while the Squire-Young correction factor decreases slightly.)
However, the effect of thickness on pump drag is far more significant, due to greater losses in
dynamic pressure through the boundary layer, and increases in the required suction flow (see
128
5.3. AIRCRAFT AND MISSION PARAMETRIC STUDY
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
5
10
15
20
25
30
t/c
Λ 
(de
g)
Re
u
 = 4, 8 and 12 × 106 m−1
Figure 5.3: Wing sweep angle dependence on thickness-to-chord ratio and unit Reynolds
number.
Chap. 4). The influence of unit Reynolds number is important for both components of drag:
the momentum thickness at the trailing-edge reduces; whilst, for the pump drag, it is well
established that the suction flow rate depends on chord Reynolds number as CQ ∝ Re−1/2c .
In Chap. 4 it was found that the pump power coefficient, or equivalently the pump drag
coefficient, is found to have a similar, albeit slightly weaker, dependence.
5.3.4 Cruise Lift Coefficient and Aerodynamic Efficiency
With the zero-lift drag known, the cruise lift coefficient can be evaluated; moreover, the
variation of lift-to-drag ratio, L/D, can be determined. The results are detailed in Fig. 5.5.
The cruise lift coefficient lies between approximately 0.1 and 0.2 across the entire parameter
range. Such low values result directly from the small zero-lift drag contribution, which in
turn requires a low induced drag for cruise at maximum L/D. The increase in lift coefficient
with thickness-to-chord ratio is due to the rise in both zero-lift drag coefficient and aspect
ratio (see Eq. 5.4). For a given thickness-to-chord ratio, increasing span, and hence aspect
ratio, increases the lift coefficient. For fixed span and thickness-to-chord ratio, lift coefficient
drops with unit Reynolds number, due solely to the reduction in the zero-lift drag coefficient;
however, the influence is weak as, from Eq. 5.4, CL ∝
√
CD0, and the CD0 dependence itself
is less than Re−1/2.
129
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.25
0.5
0.75
1
1.25
1.5
x 10−3
t/c
C D
0
 
 
Pump
Viscous
Total
Re
u
 = 4, 8 and 12 × 106 m−1
Figure 5.4: Zero-lift drag breakdown and its dependence on thickness-to-chord ratio and unit
Reynolds number.
Due to the low zero-lift drag expected for LFW aircraft, we see from Fig. 5.5 that a
lift-to-drag ratio of around 50 – 90 is predicted. Again from Eq. 5.4, L/D ∝ √AR/CD0.
Consequently, the increase in L/D with t/c arises because the aspect ratio rises faster than
CD0. Furthermore, for fixed t/c, increases in span improve L/D via the aspect ratio term.
Finally, the lift-to-drag ratio also improves with unit Reynolds number, but this time due to
the reduction in the zero-lift drag coefficient.
130
5.3. AIRCRAFT AND MISSION PARAMETRIC STUDY
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.1
0.2
0.3
C L
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
20
40
60
80
100
t/c
L/
D
b = 60 m, 80 m and 100 m
b = 60 m, 80 m and 100 m
(a)
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.1
0.2
0.3
C L
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
20
40
60
80
100
t/c
L/
D
Re
u
 = 4, 8 and 12 × 10 m−1
Re
u
 = 4, 8 and 12 × 10 m−1
(b)
Figure 5.5: The dependence of cruise lift coefficient and lift-to-drag ratio on thickness-to-
chord ratio for: (a) a range of spans and a fixed Reu of 8× 106 m−1 and, (b) a range of unit
Reynolds numbers and a fixed span of 80 m.
131
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
5.3.5 Cruise Mach Number
With the dependence of lift coefficient on the three design variables evaluated, the critical
Mach number, and hence cruise Mach number, can be calculated via the approach outlined in
Sec. 5.2.3. The cruise Mach number is shown as a function of thickness-to-chord ratio, span
and unit Reynolds number in Fig. 5.6. Although inviscid flow is assumed in the calculation, a
small unit Reynolds number dependence arises due to the influence of zero-lift drag on cruise
lift coefficient. As expected, cruise Mach number reduces with increasing thickness-to-chord
ratio; span and unit Reynolds number variations have very little effect because the maximum
local Mach number is insensitive to lift coefficient changes at the low values found here. (The
same observation was made by Lee (1961) in the HP117 proposal.)
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.2
0.4
0.6
0.8
1
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.2
0.4
0.6
0.8
1
t/c
M
∞
b = 60 m, 80 m and 100 m
Re
u
 = 4, 8 and 12 × 106 m−1
Figure 5.6: Cruise Mach number dependence on thickness-to-chord ratio, span and unit
Reynolds number. (Top figure corresponds to a Reu = 8 × 106 m−1, and the bottom to a
span of 80 m.)
5.3.6 Cruise Altitude and Velocity
The calculations needed to specify the cruising altitude and speed are now complete. Fig-
ure 5.7 details the variation of these two parameters with thickness-to-chord, span and unit
Reynolds number.
We see in Fig. 5.7 (a) that, as thickness-to-chord ratio increases for a fixed unit Reynolds
132
5.3. AIRCRAFT AND MISSION PARAMETRIC STUDY
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
100
200
300
t/c
U ∞
 
(m
/s)
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
4000
8000
12000
16000
Al
tit
ud
e 
(m
)
b = 60 m, 80 m and 100 m
b = 60 m, 80 m and 100 m
(a)
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
4000
8000
12000
16000
Al
tit
ud
e 
(m
)
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
50
100
150
200
250
300
U ∞
 
(m
/s)
t/c
Re
u
 = 4, 8 and 12 × 106 m−1
Re
u
 = 4, 8 and 12 × 106 m−1
(b)
Figure 5.7: The dependence of cruise altitude and cruise velocity on thickness-to-chord ratio
for: (a) a range of spans and a fixed Reu of 8 × 106 m−1 and, (b) a range of unit Reynolds
numbers and a fixed span of 80 m.
133
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
number, the cruise Mach number drops and, hence, so do cruise altitude and velocity. At
fixed t/c (and Reu), span has a negligible influence on cruise Mach number, and hence also
altitude and velocity. Unsurprisingly, the influence of Reu is far more significant, as shown in
Fig. 5.7 (b). With the dependence of cruise Mach number on unit Reynolds number already
seen to be negligible, increases in the latter lead directly to reductions in cruise altitude (c.f.
Fig. 5.1). The associated increases in ambient temperature result in slightly higher cruise
velocities.
5.3.7 Wing Loading and Maximum Lift Coefficient
For conventional aircraft designs, Jenkinson et al. (1999) comment that, typically, takeoff
and landing requirements ultimately dictate the planform area, and hence wing loading. In
contrast, here, the requirement to cruise at maximum L/D, and the need to maintain laminar
flow, fixes the cruise altitude, velocity and lift coefficient, which in turn set the cruise wing
loading, as:
wL =
1
2
ρ∞U2∞CL. (5.8)
In Fig. 5.8, wing loading is shown to increase with thickness-to-chord ratio; despite the
associated reduction in cruise velocity, the drop in altitude (and hence increase in atmospheric
density) and increase in lift coefficient dominate. A slight dependence on span follows directly
from the influence of lift coefficient. In contrast, we can see that unit Reynolds number has a
far greater impact. Due to the significant reduction in altitude associated with an increase in
unit Reynolds number, the increments in wing loading are substantial. Nonetheless, even the
highest values in Fig. 5.8 barely exceed half of a conventional aircraft’s wing loading. Such
low figures raise the prospect of an unacceptably high structural-weight fraction; this issue
is therefore explored further in the following section.
For conventional aircraft, high-lift devices are necessary to achieve the lift coefficients
needed for takeoff and landing (Jenkinson et al. (1999)). The maximum lift coefficient is
related to wing loading by
CL,max =
wL
1
2ρseaU
2
stall
, (5.9)
where Ustall is the stalling speed. Despite the low wing loading expected of a LFW aircraft,
the maximum lift coefficient is of concern as high-lift devices cannot be utilised (Martinez-Val
et al. (2006)); therefore, it is necessary to check that the design does not implicitly assume
one that is too great.
To evaluate Eq. 5.9, an initial estimate of the stall velocity is based on that of a conven-
134
5.3. AIRCRAFT AND MISSION PARAMETRIC STUDY
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
1000
2000
3000
4000
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
1000
2000
3000
4000W
L 
(N
/m
2 )
t/c
b = 60 m, 80 m and 100 m
Re
u
 = 4, 8 and 12 × 106 m−1
Figure 5.8: Variation of aircraft wing loading with thickness-to-chord ratio, span and unit
Reynolds number. (Top figure corresponds to Reu = 8× 106 m−1, and the bottom to a span
of 80 m.)
tional aircraft. For a Boeing 737-200 in takeoff configuration, with1 CL,max = 2.07 and wL =
5040 N/m2, the stalling speed is 63.7 m/s. The LFW maximum lift coefficient corresponding
to this value is shown in Fig. 5.9. As expected from Eq. 5.9, CL,max has the same dependence
on the three design variables as wing loading. It lies below 1.4, a value attainable without
high-lift devices, over the entire range of parameters considered. Therefore, in conclusion,
CL,max is unlikely to constrain a LFW design in the way it does for conventional aircraft.
5.3.8 Maximum Cruise Weight and Structural Weight Fraction
In a conventional design process, the gross aircraft weight is estimated on the basis of a
detailed mission specification. In contrast, here the allowable weight of the aircraft in cruise
may simply be found from the cruise lift coefficient, as 12ρ∞U
2∞bcCL. This value then becomes
one of the constraints which will be passed to the conceptual design study in Chap. 6.
Figure 5.10 shows that, for the range of parameters considered here, the proposed LFW
could sustain a gross weight anywhere between 75 and 460 tonnes (mt). The figure shows
a reduction in allowable weight with thickness-to-chord ratio. This is because U2∞c drops at
a faster rate than ρ∞CL increases. As span increases for a given t/c, the allowable weight
1www.b737.org.uk/techspecsdetailed.htm, October 2011
135
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.5
1
1.5
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.5
1
1.5
t/c
C L
,m
ax
Re
u
 = 4, 8 and 12 × 106 m−1
b = 60 m, 80 m and 100 m
Figure 5.9: Variation of required maximum lift coefficient with thickness-to-chord ratio, span
and unit Reynolds number. (Top figure corresponds to a Reu = 8×106 m−1, and the bottom
to a span of 80 m.)
rises, as expected, given the increase in planform area. Note, however, that the improvement
in wing loading evident in Fig. 5.8 also has a significant effect. As for the influence of unit
Reynolds number, we see that the increased density and cruise velocity associated with the
reduction in cruise altitude vastly outweigh the effect of a slightly lower lift coefficient.
Perhaps more important than the overall weight is the structural-weight fraction, as it
gives an indication of the aircraft’s payload capability. The structure of the centrebody
pressure vessel will be of an unconventional nature (see Chap. 2), and an estimate of its
weight is beyond the scope of the present investigation. Nevertheless, the wing weight serves
as a useful indicator of the overall structural weight.
Since the wing structure of a LFW aircraft can be designed using conventional methods,
Raymer (1999) provides some guidance as to its weight through an empirical correlation for
cargo/transport aircraft (American units):
Ww = 0.0051 (WNz)
0.557 S0.649w A
0.5
R (t/c)
−0.4 (1 + λ)0.1 (cos Λ)−1 S0.1cs . (5.10)
Here the ultimate load factor Nz = 1.5 × limit load factor (the limit load factor is taken as
2.5), the control surface area Scs is assumed to be 10% of the total wing area Sw, and the
taper ratio λ = 1.
136
5.3. AIRCRAFT AND MISSION PARAMETRIC STUDY
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
100
200
300
400
500
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
100
200
300
400
500
t/c
W
 (m
t)
b = 60 m, 80 m and 100 m
Re
u
 = 4, 8 and 12 × 106 m−1
Figure 5.10: Variation of aircraft allowable weight with thickness-to-chord ratio, span and
unit Reynolds number. (Top figure corresponds to a Reu = 8× 106 m−1, and the bottom to
a span of 80 m.)
Further insight is provided through rearrangement of Eq. 5.10 into a form that gives the
wing-weight fraction for a given thickness and sweep as a function of wing loading, span and
maximum thickness-to-chord ratio,
Ww
W
∝ w−0.443L b0.806 (t/c)−0.206 . (5.11)
Equation 5.11 reveals that the wing-weight fraction has an inverse relationship with both
wing loading and thickness-to-chord ratio, whilst it increases with span. Recall that, from
Fig. 5.8, wL increases with t/c, b and Reu.
Figure 5.11 details the calculated variation of the wing-weight fraction with thickness-to-
chord ratio, span and unit Reynolds number. Here we see first the expected reduction with
t/c. Furthermore, as a consequence of increased wing loading, the wing-weight fraction drops
when unit Reynolds number rises (at fixed t/c). However, although the dependence of wL on
b tends to reduce Ww/W , Fig. 5.11 shows that there is an overall increase with span as the
direct dependence is stronger — this is confirmed by Eq. 5.11.
Finally, note that the absolute values of wing-weight fraction shown in Fig. 5.11 are
unlikely to be strictly accurate; although designable with conventional methods, the LFW
will be subject to a different loading distribution than its conventional counterpart. However,
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CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.2
0.4
0.6
0.8
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26 0.28 0.3
0
0.2
0.4
0.6
0.8
t/c
W
w
/W
Re
u
 = 4, 8 and 12 × 106 m−1
b = 60 m, 80 m and 100 m
Figure 5.11: Variation of wing-weight fraction with thickness-to-chord ratio, span and unit
Reynolds number. (Top figure corresponds to a Reu = 8 × 106 m−1, and the bottom to a
span of 80 m.)
the qualitative trends noted here will remain.
5.4 Discussion
In this section a feasible LFW design specification is determined by assessing trade-offs in
the aircraft and mission parameters introduced in Sec. 5.3. The sensitivity of the chosen
specification to potential errors in parameter estimates is discussed. Finally, key differences
between the proposed LFW specification and conventional aircraft are highlighted.
5.4.1 Mission Parameter Conflicts
First consider the influence of increasing thickness-to-chord ratio. Depending on the value
of the unit Reynolds number, there is a reduction in the allowable wing sweep; this conflicts
with balance and stability requirements, which, as we learned in Chap. 2, are likely to require
as much sweep as possible. There is a beneficial influence on the aerodynamic efficiency. The
cruise speed reduces, which may reduce the LFW’s attractiveness to airlines and passengers.
The cruise altitude decreases, which not only avoids the undesirable emission of combustion
products at high altitudes, but will also lead to a lighter cabin pressure vessel. The gust
138
5.4. DISCUSSION
performance will improve with the associated increase in wing loading (Jenkinson et al.
(1999)). Although the gross allowable weight decreases, so does the wing-weight fraction.
However, as passenger-comfort requirements constrain the outboard extent of the cabin, the
shorter chord at higher values of t/c may limit passenger capacity.
Now consider the influence of increasing unit Reynolds number. The wing sweep may
have to be reduced appreciably, again raising the prospect of balance and stability problems.
The aerodynamic efficiency increases. The cruise altitude reduces sharply which, although
generally beneficial (see above), could lead to adverse weather issues at the lower extremes.
Two further gains are an increase in wing loading and a reduction in wing-weight fraction.
Finally, the benefits of an increase in span are two-fold: the aerodynamic efficiency and
wing loading increase. However, we must bear in mind the penalty incurred in wing-weight
fraction.
5.4.2 Synthesis of Parameter Considerations
To synthesise the parameter considerations discussed above, it is helpful to consider what
combination of design variables leads to a high aerodynamic efficiency, without regard for
other factors. The attainment of optimum aerodynamic efficiency is achieved through spec-
ification of the highest values of thickness-to-chord ratio, unit Reynolds number and span.
This approach would also maximise wing loading, and hence minimise gust response issues.
The parameter conflicts discussed above reveal that high t/c and Reu limit the degree of
allowable sweep-back, and give rise to balance and stability issues; whilst the cruise speed
is limited by high thickness-to-chord ratios. Other potential problems include: the wing-
weight fraction, which is driven to higher values with b (though high t/c and Reu have a
favourable influence); impractically low cruise altitudes at the highest value of Reu; and
passenger capacity, which may be compromised at higher thickness-to-chord ratios.
These considerations lead to the conclusion that, to attain a viable design, values below
maximum for all three parameters must be chosen. Therefore unit Reynolds number and span
are fixed at 8 × 106 m−1 and 80 m, respectively, as these give rise to a reasonable range of
cruise altitudes and wing-weight fractions over the entire thickness-to-chord range considered
here. At this value of unit Reynolds number, thickness-to-chord ratio is fixed at 20%, because
for higher values the allowable wing-sweep angle begins to fall sharply. The resulting aircraft
and mission parameters are summarised in Tab. 5.1.
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CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
Table 5.1: Laminar-flying-wing aircraft design specification.
Maximum thickness (m) 2.5
Thickness-to-chord ratio 0.20
Span (m) 80
Unit Reynolds number (m−1) 8× 106
Sweep (degrees) 25
Chord (m) 12.5
Planform area (m2) 1000
Aspect ratio 6.4
Cruise lift coefficient 0.14
Mach number 0.67
Altitude (ft) 22500
Velocity (m/s) 209
Allowable weight (kg) 187× 103
Wing loading (N/m2) 1835
5.4.3 Sensitivity to Error
Having chosen a design specification, its robustness can now be considered. The potentially
contentious aspects of the approach in this study are the estimates of the drag polar param-
eters, CD0 and K (c.f. Eq. 5.1). Of these, K is the more reliable; uncertainties over the
competing influences of a non-ideal lift distribution and winglet end-plate effects are unlikely
to cause errors significantly in excess of 10%. In contrast, the pump-drag contribution to CD0
is heavily dependent on the neglect of suction requirements for the suppression of cross-flow
instabilities, and the overall zero-lift drag value (below 0.001) is so low that it could be signif-
icantly increased by excrescence drag contributions. Consider, then, the effect of a doubling
in this parameter on the design specification at given values of b, t/c and Reu. The cruise
lift coefficient will increase by a factor
√
2, and the drag coefficient by a factor 2. However,
given the extremely weak dependence of cruise Mach number on CL, the cruise speed and
altitude will be essentially unchanged. The parameters which will alter significantly are the
wing loading, allowable weight and structural efficiency, all of which will improve, and the
aerodynamic efficiency, which will deteriorate (the lift-to-drag ratio drops to 51). The effect
on appropriate values of b, t/c and Reu will be only to make the largest span more attrac-
tive than previously. However, the associated trade-off between aerodynamic and structural
efficiency would remain unclear, whereas there is a concrete argument (on existing airport
infrastructure grounds) against increasing b beyond 80m.
Alternatively, consider the effect of the same change in CD0 if all the parameters in
140
5.4. DISCUSSION
Tab. 5.1 are held constant. (This corresponds to moving the cruise condition away from
maximum L/D, and towards maximum U∞L/D.) The lift-to-drag ratio then drops by a
factor 2/3 to 48, just 6% below its (new) maximum value.
In conclusion, the key features of the proposed specification remain justifiable in the face
of potential errors in the zero-lift drag coefficient. The elements of Tab. 5.1 which may change
as a result of an improved CD0 estimate are the cruise lift coefficient, allowable weight and
wing loading; however, the level of uncertainty over their values does not undermine the
usefulness of this specification as a basis for a conceptual design study.
5.4.4 Comparison with Conventional Aircraft
The initial constraints of laminar flow, limited sweep and 2.5 m thickness imply a design
space that differs considerably from that inhabited by conventional aircraft. To attain the
full benefit from the viscous drag reduction associated with laminarisation, the induced drag
must also be small, which in turn leads to operation at a lift coefficient of 0.14, with a
correspondingly low wing loading of 1835 N/m2. (To put these values into perspective, the
Boeing 737-200 aircraft has a wing loading of 5040 N/m2, and current aircraft typically cruise
at a CL of around 0.5 (Cumpsty (1997)).) Under these conditions, the lift-to-drag ratio could
be as high as 72, well above values for current, fully turbulent, jet transports, which are
around 15 – 20 (Cumpsty (1997)). Gust response, however, is a potential concern.
In spite of the low cruise CL, the gross allowable weight is of the same order as conventional
aircraft, at around 187 mt. (In comparison, the small-to-medium range Boeing 737-200
and the long-range Boeing 747-100 have gross weights of approximately 45 mt and 322 mt,
respectively (Torenbeek (1976)).) This is due to the large planform area expected of the
LFW, and the reduced cruise altitude of 22,500 ft, relative to a current typical level around
35,000 ft.
Compared to conventional aircraft, the LFW is likely to have a high structural-weight
fraction. Although the value for wing weight given by Eq. 5.10, around 40% of total weight,
is unlikely to be very accurate, it hugely exceeds the 11% and 12% of the Boeing 737-200
and 747-100 respectively (Torenbeek (1976)). Furthermore, it must be borne in mind that
the flying-wing planform cannot accommodate a conventional cylindrical pressure vessel.
Instead, non-cylindrical pressure vessels have been proposed; however, due to additional
bending moment stresses, their weights may be excessive. Recall from Chap. 2 that, for this
reason, other authors have suggested that multi-bubble configurations are preferable. On
the positive side, the reduced cruise altitude should go some way towards alleviating this
additional weight contribution.
141
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
Assuming take-off speeds similar to conventional aircraft, as done in this study, the take-
off lift coefficient is likely to be well below the maximum section lift coefficient. This may
be exploitable to reduce the required airport runway length (which is often an issue for
conventional long-range aircraft), by increasing the take-off CL and reducing the take-off
speed. It also differentiates the LFW from the conventional design, whose wing area is largely
determined by the maximum achievable lift coefficient, and which thus requires sophisticated
high-lift devices.
Due to the imposed limitations on sweep angle, the requirement to maintain subcritical
flow, and the fixed cabin height (which results in thick aerofoil sections), the cruise Mach num-
ber is reduced (relative to current long-range aircraft values of 0.8 – 0.85) to 0.67. However,
an obvious advantage of cruising at a lower Mach number is that more efficient, open-rotor
engine designs become an option (Martinez-Val et al. (2006)). It should also be noted that
the proportionate drop in cruising speed is not as great as that in Mach number, due to the
lower cruising altitude; the LFW here flies at 209 m/s, compared to 237 m/s for a Mach 0.8
aircraft at 35,000 ft. The 16% Mach number reduction thus translates into a loss of only 12%
in speed.
Finally, flying-wing aircraft differ from their conventional counterparts in the absence of
a tail, and their longitudinal static stability margin is thus crucially dependent on sweep
(see Chap. 2). As a result, while the value of 25◦ specified here is not especially low by
conventional standards, it may imply a need for artificial stabilisation via the flight control
system.
5.5 Summary
In this chapter, the configuration and mission specification for a laminar-flying-wing aircraft
with limited sweep have been studied. It has been assumed that the restriction on sweep (25◦)
allows suction requirements for the suppression of cross-flow instabilities to be neglected. Two
further fundamental constraints have been imposed: it must be possible to stand in the cabin,
and the flow must remain subcritical.
By treating the aircraft as an untapered wing, the design space is defined via three
principal variables: span, thickness-to-chord ratio and unit Reynolds number. Suitable values
for these parameters were found to be: b = 80 m, t/c = 0.20 and Reu = 8 × 106 m−1. The
key elements of the design are: a planform with area 1000 m2, chord 12.5 m and sweep 25◦; a
gross allowable weight of 187 mt, with a cruise Mach number of 0.67 at an altitude of 22,500
ft; a provisional lift-to-drag ratio estimate in the range 48 – 72, assuming laminar flow is
maintained over 90% of the wetted area.
142
5.5. SUMMARY
To attain the full benefit of the viscous drag reduction, the induced drag must also be
reduced, which in turn drives the LFW to a low cruise lift coefficient of 0.14 and low wing
loading of 1835 N/m2. Consequences of the low wing loading condition include potential
gust response problems and a higher than conventional structural weight fraction; however,
it implies that take-off does not constrain the aerodynamic design (in contrast to conventional
aircraft). The combination of reduced sweep and high thickness-to-chord ratio is the cause of
the lower than conventional cruise Mach number; taking altitude reduction into account, the
LFW would fly about 12% slower than conventional aircraft. While potentially detrimental
for passenger acceptance, this reduction opens up the prospect of using more efficient, open
rotor, engines instead of standard turbofans. In addition, the low cruise altitude has beneficial
implications for the impact of the aircraft’s non-CO2 emissions.
A robust calculation of the fuel efficiency will follow from the conceptual design study, in
Chap. 6, on the basis of this specification. However, a conservative initial estimate can be
obtained as follows. Suppose that the empty weight of the aircraft is so high that it can carry
only just over 10% of its gross weight (20 mt) as flight fuel, and the same amount as payload
(say 200 passengers, with baggage, at 100 kg each). Then, for a lift-to-drag ratio of 50, the
overall propulsion system efficiency, η0, need only be 27% for the Breguet range equation,
given by Eq. 3.84, to yield a flight distance of 6700 km, corresponding to a fuel burn of 15
g/pax.km. This figure compares favourably with the value of 23.5 g/pax.km quoted for the
Boeing 777, confirming (subject to a number of fundamental assumptions) the potential of
the laminar-flying-wing configuration proposed here.
143
CHAPTER 5. LFW AIRCRAFT AND MISSION SPECIFICATION
144
Chapter 6
Conceptual Design Study
On the basis of the design specification given in Chap. 5, a detailed conceptual design of the
LFW is developed in this chapter, following the design methodology formulated in Chap. 3,
to assess the potential fuel-burn advantage over conventional aircraft. The specific objectives
are to: generate a three-dimensional airframe on the basis of attaining satisfactory stability
and control characteristics, and passenger accommodation; assess the cruise and low-speed
performance of the aircraft; integrate the suction-system technology; design an engine that
is capable of providing both the required thrust and suction power off-take; carry out an
evaluation of the structure and its weight; and finally, determine the aircraft mission, and
its fuel burn. For a fair comparison, the conceptual design of a baseline-turbulent aircraft
for the same mission (range, payload, Mach number) and propulsion characteristics is also
undertaken.
6.1 Laminar-Flying-Wing Design Concept
In Chap. 3 the overall design process for a LFW aircraft was outlined. In this section, the
five design areas identified are covered in the following order: 1) 3-D airframe generation, 2)
aircraft performance analysis, 3) suction-system technology integration, 4) propulsion system
design, and 5) structures and weights. An overview of the key design constraints, inputs
and outputs is provided for each area. Design methodologies specific to the LFW are also
detailed. On attainment of a viable design, the aircraft’s mission and fuel-burn performance
are determined.
6.1.1 Three-Dimensional Airframe Generation
Figure 3.1 shows that the airframe influences four aspects of the design: the suction system
via the aerofoil section geometry, the structure and its weight, the aircraft’s performance,
145
CHAPTER 6. CONCEPTUAL DESIGN STUDY
and the payload capacity. It consists of three main parts: the planform layout, and wing
and cabin geometry. The planform and wing section geometries are constrained by the
maximum thickness, chord, span and sweep values specified in the basic design specification.
However, passenger accommodation, static stability, and structural considerations affect the
final configuration. First, the flying and handling qualities required for this type of aircraft
are outlined.
6.1.1.1 Flying and Handling Qualities Requirement
Under MIL-F-8785C (Cook (1997)) a passenger carrying LFW is a Class III aircraft, as it
is large, heavy, and will demand low to medium manoeuvrability. The appropriate flight
phases are categories B (climb, cruise and loiter) and C (takeoff, approach, overshoot and
landing). Level 3 flying qualities are required, as the aircraft should be safely controllable,
with Category B and C Flight Phases completable.
6.1.1.2 Planform
Planform geometry primarily affects the aircraft’s stability characteristics, passenger-payload
capacity, and vortex drag. With the latter dominated by span, which is already fixed, atten-
tion is restricted to the first two aspects.
Centrebody Width
The cabin/centrebody width is constrained by passenger comfort requirements. Consider the
solution to a pure-rolling motion for a step aileron input (Nelson (1998))
dφ
dt
= pss
(
1− e−t/τR
)
. (6.1)
Equation 6.1 describes how bank angle varies with time for a given roll-mode time constant,
where pss is the steady-state roll rate. On integrating Eq. 6.1, with the initial boundary
condition that φ = 0 at t = 0,
pss =
φtg
ttg − τR
(
1− e−ttg/τR) . (6.2)
Here we see that pss depends partly on the time-constant (τR), and partly on the bank angle
(φtg) and time (ttg) within which a manoeuvre should be executed — MIL-F-8785C specifies
30◦ and 5 s, respectively.
146
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
The roll-induced acceleration a is
a = r
d2φ
dt2
= rpss
1
τR
e−t/τR (6.3)
where r is the cabin half-width. The maximum roll acceleration (at t = 0), amax, and
outboard distance, r, from the roll axis are thus related via
r =
amax(
d2φ
dt2
)
t=0
= amax
τR
pss
. (6.4)
Figure 6.1 shows the variation of cabin half-width with the time constant τR for a range of
maximum roll accelerations. Half-widths in the range of 5 – 30 m are expected over the range
of vertical accelerations detailed. Furthermore, we see that, as τR becomes very large, the
cabin half-width tends to a constant value. This is confirmed by considering the asymptotic
solution to Eq. 6.2 and combining it with Eq. 6.4, showing that r → amax t
2
tg
2φtg
.
0 2 4 6 8 10 12 14 16 18 20
0
5
10
15
20
25
30
35
τR
r 
(m
)
0.15g
0.05g
0.10g
Figure 6.1: Variation of cabin half-width with roll-mode time constant for a range of vertical
accelerations.
For a cabin half-width of 10 m, roll-mode time constants in excess of 8 s are necessary
to reduce the maximum vertical acceleration to a level recommended by Pratt (2000) of
147
CHAPTER 6. CONCEPTUAL DESIGN STUDY
0.05-g, at the cost of compromised flying qualities. Assuming a ‘flying plank’ geometry with
the allowable weight uniformly distributed gives a roll moment of inertia (Ixx) of 59.8× 106
kg.m2, which, combined with Clp = −0.481 rad−1 (see Sec. 6.1.2.3), provides an approximate
estimate for τR of 0.62 s through Eq. 6.5 (provided by Nelson (1998)).
lp = Clp
b
2U∞
QSrefb
Ixx
(6.5)
τR = − 1
lp
where Q = 1/2ρ∞U2∞. This leads to a roll acceleration of 0.20-g. Therefore, the roll-mode
time constant must be artificially increased. As a compromise, a slightly higher than recom-
mended vertical acceleration of 0.06-g is accepted, with τR = 4.5 s.
To achieve an acceptable payload capacity the centrebody region is given a straight trailing
edge. With the leading-edge sweep and cabin width now set, and chord length at the spanwise
extremes specified by t/c = 0.20, the centrebody planform geometry is fully defined.
Stability Characteristics
In Chap. 2 it was revealed that, provided the C.G. lies ahead of the neutral point (NP),
satisfactory longitudinal stability characteristics can be achieved; furthermore, despite large
differences in the lateral stability derivatives relative to conventional aircraft, flying wings
still exhibit satisfactory lateral-directional stability characteristics. Therefore, work here is
restricted to investigating how the planform parameters affect static stability. Zero wing-twist
and symmetrical aerofoil sections are assumed.
The C.G. position is not yet known. Therefore, given the low sweepback and hence danger
of the NP being ahead of the C.G., a neutral point that is as far aft as possible is targeted.
For directional static stability, the lateral NP must also lie aft of the C.G. Furthermore, for
lateral-directional stability, Clβ < 0 is a necessary condition.
To avoid adverse boundary-layer stability effects, the leading edge-sweep is fixed at 25◦.
With the centrebody region defined, two geometric parameters remain: outboard wing taper
ratio and wingtip-fin height (assuming the fins are untapered and aligned perpendicular to
the flow direction). Outboard wing taper ratios between 0.1 to 1, and wingtip-fin heights of
2 m to 5 m are considered. Figure 6.2 provides an illustration of the planform geometry for
extreme combinations of these two parameters — notice that for higher outboard wing taper
ratios the centrebody becomes more distinguishable.
148
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
(a)
(b)
Figure 6.2: Schematic diagram of aircraft planform geometry: (a) TR = 0.1 and Hw = 5 m
and (b) TR = 1 and Hw = 2 m.
149
CHAPTER 6. CONCEPTUAL DESIGN STUDY
Longitudinal Neutral Point
Figure 6.3 shows the variation in longitudinal NP position over a range of outboard wing
taper ratios and wingtip-fin heights. The neutral point has a strong dependence on taper
ratio, moving further aft as TR increases. For low taper ratios, wingtip-fin height has a weak
effect, but becomes increasingly influential at higher taper ratios.
TR
H w
 
(m
)
xNP (m)
 
 
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
2.5
3
3.5
4
4.5
5
10
10.5
11
11.5
Figure 6.3: Variation in longitudinal NP position over a range of outboard wing taper ratios
and wingtip-fin heights
For the geometric constraints imposed here, there is an increase in quarter-chord sweep
angle associated with a high taper ratio, and hence the neutral point is further aft. At low
taper ratios the effect of fin height is weak due to the reduced moment arm, despite the
increase in tip loading with fin-tip height. To summarise, an aft longitudinal NP is favoured
by a high taper ratio (higher quarter-chord sweepback) and large wingtip-fin height (increased
tip loading).
Lateral Neutral Point
The lateral NP is defined as the location at which the sideforce due to sideslip effectively acts.
Equation 6.6 shows that it depends on the weathercock and sideforce stability derivatives,
150
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
and wing span
xlat,NP − xref = −b
Cnβ
CYβ
, (6.6)
where xref is the point about which the stability derivatives are evaluated.
The effects of taper ratio and wingtip-fin height on the position of the lateral NP are shown
in Fig. 6.4. The lateral NP moves further aft with increasing taper ratio due to the associated
increase in sweepback; interestingly, this effect is strongest at low wingtip-fin heights. As
for the longitudinal NP, wingtip-fin height effects become more apparent at higher taper
ratios; however, somewhat counter-intuitively, the lateral NP moves further aft as wingtip-fin
height decreases. For mid-range values of TR, Xlat,NP travels forward then aftward with
increasing Hw. Further examination of the dependence of the weathercock and sideforce
stability derivatives on these parameters is required to understand these observations.
TR
H w
 
(m
)
xlat,NP (m)
 
 
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
2.5
3
3.5
4
4.5
5
18
18.2
18.4
18.6
18.8
19
19.2
19.4
19.6
19.8
20
Figure 6.4: Variation in lateral NP position over a range of outboard wing taper ratios and
wingtip-fin heights
Figure 6.5(a) shows how Cnβ varies with TR and Hw. The yawing moment coefficient
increases with wingtip-fin height due to the increased pressure force associated with a larger
surface area. For a constant wingtip-fin height, Cnβ initially increases with taper ratio due to
the increased sweepback and chord length (and hence area) combination; however, this ap-
proaches a maximum for mid-range values of TR and subsequently, though rather mildly, drops
with further increases in TR — this effect becomes weaker as Hw is reduced. Figure 6.5(b)
151
CHAPTER 6. CONCEPTUAL DESIGN STUDY
shows that the magnitude of the side-force stability derivative increases with tip-fin height,
whilst it increases to a maximum and then drops with TR for a given Hw. Similar arguments
for the effects on weathercock stability can also be applied to the side force. Therefore, it
is because the sideforce stability derivative decreases at a faster rate than the weathercock
stability derivative that, the lateral neutral point moves further aft with decreasing tip-fin
height.
Planform Summary
With values for the longitudinal NP and lateral NP between 10 – 11.5 m and 18 – 20 m,
respectively, the longitudinal NP position is more critical. Furthermore, Clβ < 0 is satisfied
for all combinations of taper ratio and fin height. Values for taper ratio and wingtip-fin height
below the maximum considered are selected for structural efficiency, therefore: TR = 0.9 and
Hw = 3.5 m.
The final planform design is summarised in Fig. 6.8. The reference area and span are
1087.9 m2 and 80 m, respectively. The aspect ratio is 5.9. The centrebody has a half-span of
10 m and a quarter-chord sweep of 18.9◦. The outboard quarter-chord sweep angle is 24.5◦.
The cruise and climb-out static margins, and longitudinal neutral points are detailed in
Tab. 6.1. The aircraft exhibits close to neutral static stability characterisitcs over all flight
phases of interest. Furthermore, the condition for spiral mode stability is ClβCnr/ClrCnβ > 1:
the LFW has values in the range 0.44 – 0.86. A flight control system is therefore required to
provide neutral spiral stability characteristics.
Table 6.1: Static stability — C.G. locations (see Sec. 6.1.5.5): 11.38 m (start of cruise and
climb out) and 11.44 m (end of cruise).
Parameter Cruise (with suction) Cruise (no suction) Climb out
M∞ 0.67 0.39 0.21
XNP 11.38 11.41 11.43
Static margin (%) 0/-0.5 0.2/-0.2 0.4/-0.1
ClβCnr/ClrCnβ 0.86 0.60 0.44
6.1.1.3 Wing and Cabin Design
The planform layout, along with the need for structural efficiency, dictates the wing spar
locations; this, combined with the need to maximise internal cabin volume, whilst observing
the subcritical flow constraint, defines the wing cross-section across the aircraft centrebody.
However, the outer wing regions are not subject to the same volumetric constraints.
152
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
TR
H w
 
(m
)
C
nβ
 
 
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
2.5
3
3.5
4
4.5
5
0.01
0.015
0.02
0.025
0.03
(a)
TR
H w
 
(m
)
CYβ
 
 
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
2.5
3
3.5
4
4.5
5
−0.14
−0.12
−0.1
−0.08
−0.06
−0.04
(b)
Figure 6.5: Change in (a) yawing moment coefficient and (b) side force with sideslip angle
over a range of outboard wing taper ratios and wingtip-fin heights.
153
CHAPTER 6. CONCEPTUAL DESIGN STUDY
The need for an aerofoil section exhibiting minimal nose-down pitching moment at zero-
lift was used, as an aerodynamic balance condition, to justify the selection of a NACA
4-digit section in Chap. 5. These are low-speed aerofoils, with a maximum thickness close to
the leading edge (Abbott and Von Doenhoff (1959)). A more sophisticated approach, that
maximises internal volume and improves transonic performance, is required here.
Methodology
Figure 6.6 shows a bespoke section generator (developed by Eastwood (2008)), which requires
six variables to define an aerofoil section geometry. The section generator first takes the
suction surface of the leading edge of a RAE2822 supercritical section, whose extent is marked
by the first control point CP0, to ensure good performance in this aerodynamically critical
region (Drela and Giles (1987)); the remaining surface is fitted by a cubic Be´zier curve to the
trailing edge, set by the control point CP3 whose vertical location lies along x/c = 1 (y/c > 0
leads to a blunt trailing-edge section). To ensure continuity between the adjoining sections,
the second control point CP1 is constrained to move along ‘Track 1’, which is tangential to
the surface at the join. By defining a trailing-edge wedge angle θte, the third control point
CP2 is constrained to move along ‘Track 2’, which is tangential to the surface at the trailing
edge. The curve is then mirrored to form a symmetric section, and expanded to the required
thickness.
Figure 6.6: Aerofoil section generator.
To simplify the structural design task: a multi-bubble geometry comprising intersecting
transverse cylinders is chosen for the pressurised cabin (see Sec. 6.1.5). The bubble overlap
is chosen to: a) give a minimum height of 1.9 m, based on the statistic, in Torenbeek (1976),
that 99% of passenger heights are below this value, and b) have a seat pitch of 80 cm to
154
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
90 cm, which Torenbeek (1976) cites as typical of conventional-type passenger carriers. A
bubble diameter of 2.14 m is chosen, leading to a bubble pitch of 1 m. Each seat row is
assumed to lie on a bubble axis; consequently, the number of bubbles sets the number of
rows. The number of seats abreast is determined by assuming one aisle every three seats;
Torenbeek (1976) quotes values for seat and aisle widths of 42.5 cm and 50.8 cm, respectively,
which give an effective seat width of 59.4 cm. The aerofoil section and number of bubbles
are determined via trial and error:
a) multi-bubble arrangement arbitrarily defined between, and ahead, of the front and rear
vertical spar positions (see Sec. 6.1.5);
b) aerofoil cross-section fitted to meet the various geometric constraints;
c) inviscid calculation using VGK in the perpendicular plane to ensure the flow is subcrit-
ical, and viscous calculation to ensure attached flow in cruise and takeoff; if not, iterate
from b).
Figure 6.7 shows a cross-section of a representative multi-bubble cabin embedded within
a centrebody wing section. Markers are placed at the front and rear bubble locations to
denote minimum clearance requirements for the placement of suction hardware components
and structural elements. At the spar locations, the bubbles intersect at the same height
to prevent localised bending moments. To reduce surface curvature over the rear, a blunt
trailing edge geometry is utilised. In contrast, sharp trailing-edge wing sections are employed
outboard of the cabin.
Figure 6.7: Schematic diagram of the multi-bubble cabin embedded within an aerofoil section
— vertical spar locations are represented by the dash-dot lines, whilst the minimum spacings
between the cabin and wing surface are indicated by the ‘x’ markers.
155
CHAPTER 6. CONCEPTUAL DESIGN STUDY
Specification
Figure 6.8 details the final aerofoil and multi-bubble section geometries, and associated Cp
distributions calculated at the local section Cl values (see Sec. 6.1.2). Specific details of the
aerofoil sections are provided in Tab. 6.2.
Table 6.2: LFW section geometry variables specification.
Parameter y = 0.84 m y = 4.20 m y = 9.18 m y = 10 - 40 m z = 0 - 3.5 m
(t/c)max 0.149 0.164 0.194 0.20 0.10
CP0X 0.03 0.03 0.08 0.10 0.10
CP1X 0.15 0.15 0.26 0.40 0.40
CP2X 0.91 0.90 0.80 0.85 0.85
CP3Y 0.012 0.008 0.002 0 0
θte (deg) 28 26 17 5 5
Along the central axis, the reduced maximum thickness-to-chord ratio permits the place-
ment of bubbles ahead of the front spar, whilst a blunt trailing edge is required to alleviate
flow conditions over the rear. Moving out across the centrebody, the (non-dimensional) rear
spar location effectively moves forwards as the chord drops. This permits a lower trailing-
edge wedge angle and thickness. With the leading edge swept, the distance between the front
spar and nose drops, therefore the number of bubbles ahead of the front spar decreases. To
allow for a smooth transition to the outboard region, the outer centrebody section is scaled
to the required t/c, and a sharp trailing-edge is enforced. The fin sections are scaled down
versions of the outer sections with t/c = 0.10.
The total cabin floor area is around 138 m2, but approximately 7 m2 is required for items
such as: wardrobes, toilets, etc., for a 200-passenger aircraft (Torenbeek (1976)). Therefore,
the passenger specification for the LFW is 220 persons.
156
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
F
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157
CHAPTER 6. CONCEPTUAL DESIGN STUDY
6.1.2 Aircraft Performance
The aircraft performance is already broadly defined by the cruise CL, wing loading, cruise
Mach number and unit Reynolds number. However, in this section, it is further broken down
into cruise and low-speed performance. In Fig. 3.1, aircraft performance is shown to be
central to the overall design integration. For example, the cruise lift distribution affects the
suction-system design and the wing section geometry; furthermore, the loading distribution is
necessary for a structures and weights analysis, which in turn provides the C.G. position. The
minimisation of non-LFC surface areas constrains control surface sizes; however, satisfactory
control characteristics must be ensured at low-speed conditions. The lift-to-drag ratio for
both flight conditions affects engine performance and is essential for evaluating aircraft range.
Before proceeding with an assessment of cruise and low-speed performance, an exposition of
the methods used to assess pitch trim and calculate viscous drag is provided.
6.1.2.1 Methodology
Pitch Trim
In contrast to traditional definitions given in Chap. 2, the whole elevon is called the elevator,
whilst the outer elevons are referred to as ailerons. The elevator is assumed to occupy 67% of
the wing half-span (starting from the wingtip fin) and the last 10% of chord. The associated
pitching moment has to balance contributions (about the centre of gravity) from the engine
thrust and the wing in flight; whilst on the ground there are additional reaction and friction
forces acting through the main undercarriage (assumed to be located at 75% chord at the
outboard extremes of the aircraft centrebody). (The thrust line is taken to be 3.325 m above
the aerofoil’s axis of symmetry, which corresponds to half an engine diameter (see Sec. 6.1.4)
above the point of maximum aerofoil section height.)
The required elevator deflection and aircraft angle of attack are found through the solution
of Eq. 6.7. [
CLtarget
Cmtarget − Cm0
]
=
[
CLα CLδE
Cmα CmδE
][
α
δE
]
(6.7)
With symmetrical aerofoil sections and zero twist, Cm0 = 0; CLtarget and Cmtarget correspond
to the flight phase of interest. These, in addition to the stability derivatives, are summarised
in Tab. 6.4.
158
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
Viscous Drag
The wing viscous drag for a swept wing is calculated following the method detailed in Chap. 3.
However, the Squire-Young formulation of Eq. 3.5 is not applicable to blunt-trailing-edge
aerofoils. Therefore, conservatively, the above-ambient trailing-edge pressure is neglected,
and the momentum deficit at the trailing edge used directly, i.e.,
CDv = 2
δ2,te
c
. (6.8)
For small trailing-edge thicknesses, Eq. 6.8 gives a conservative estimate of the viscous drag,
as it fails to account for pressure recovery effects in the wake. The overall wing viscous-
drag coefficient CwingDv is estimated by averaging the section-viscous drag coefficients over the
planform area. For the low section Cls here, it is assumed that the zero-lift viscous drag
CwingD0 ' CwingDv . Additional viscous drag contributions are determined following the methods
detailed in Chap. 3.
6.1.2.2 Cruise Performance
The combination of Cm0 = 0, near-neutral static stability, and low thrust requirement in
cruise (with suction) translates to a negligible elevator deflection of −0.1◦ for aircraft trim.
The wing incidence α is 1.5◦ — this is below a value of 3◦, which Hileman et al. (2007)
provide as a recommended fuselage maximum.
The lift coefficient distribution is shown in Fig. 6.9. With a linear decrease in chord
across the centrebody, section Cl⊥ increases from around 0.15 to a maximum of 0.20, but
then decreases to 0.10 at the wingtip fins. The streamwise and section-normal curves coincide
at y > 40 m as the wingtip fin is unswept. The calculated Oswald efficiency e is 1.08. This
favourable value is attained thanks to the efficient all-lifting wing surface and wingtip-fin
combination, and is not compromised by the trim requirements here.
A drag breakdown is provided in Tab. 6.3. Figure 6.10 details the variation in wing viscous
drag coefficient (based on local chord length) across the inboard and outboard regions. The
sharp reduction in viscous drag at the centrebody/outboard junction and increase between
y = 4.2−5.8 m are associated with changes in trailing-edge thickness. With a negligible influ-
ence of Cl at these low values, it is the reduction in chord Reynolds number that contributes
to an overall increase across the centrebody; whilst the negligible change in Rec outboard
leads to an almost constant coefficient.
The calculated lift-to-drag ratio is 60.9. This figure is significantly higher than current,
turbulent, jet aircraft with values of 15 – 20 (cited by Cumpsty (1997)).
159
CHAPTER 6. CONCEPTUAL DESIGN STUDY
0 5 10 15 20 25 30 35 40 45
0
0.05
0.1
0.15
0.2
0.25
y (m)
Se
ct
io
n 
lift
 c
oe
ffi
cie
nt
 
 
Cl
Cl⊥
Figure 6.9: Spanwise variation in section lift coefficient in the free-stream and wing normal
directions — CL = 0.14 and M∞ = 0.67.
0 1 2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10−3
y (m)
C D
0
w
in
g
(a) Inboard
10 15 20 25 30 35 40 45
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10−3
y (m)
C D
0
w
in
g
(b) Outboard
Figure 6.10: Variation in viscous drag coefficient along the wing half-span — Reu = 8× 106
m−1.
In the event of a suction-system failure, the loss of laminar flow results in a significant
increase in total viscous drag. Continuing to fly at a lift coefficient optimised for minimum
fuel consumption with suction on is far from optimum, as CL ∝
√
CD0 (see Chap. 5). The
160
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
revised cruise CL and flight Mach number are 0.38 and 0.39, respectively, assuming constant
cruise altitude. With a higher thrust requirement, an elevator deflection of −0.8◦ is required
to trim the aircraft, whilst the wing incidence increases to 4.8◦. The Oswald efficiency
remains unchanged at around 1.08. The lift-to-drag ratio is significantly degraded at 24.4
(see Tab. 6.3).
6.1.2.3 Low-Speed Performance
Takeoff CL
The stalling speed and corresponding maximum lift coefficient for a B737-200 aircraft are 63.7
m/s and 2.07, respectively (see Chap. 5). Assuming a takeoff speed of 70 m/s, the takeoff CL
and Mach number are 0.61 and 0.21, respectively. Therefore, CL,max is unlikely to constrain
the design here.
Pitch Trim and Elevator Performance
During climb out, the elevators are required to trim the aerodynamic (L and MC.G.) and
thrust (FN ) forces acting on the aircraft by generating a force (LE), at the demanded takeoff
CL. However, for rotation at takeoff, with the nose wheel off the ground, the reaction force
(R) due to the weight of the aircraft and associated friction force (Fµ) — Raymer (1999) gives
a typical rolling friction coefficient of 0.03 — through the main undercarriage, contribute to
an additional nose down moment, as detailed schematically in Fig. 6.11.
W
R
Fμ
MC.G.
FN
L
EL
Flight direction
Figure 6.11: Force diagram at takeoff rotation.
The speed of the aircraft at rotation is estimated to be approximately 66.8 m/s, following
Torenbeek (1976). With all engines operating, the demanded elevator deflection for rotation
at takeoff is found to be more critical, with a δE of −20.2◦ and an α of 11.3◦. (Note, Raymer
161
CHAPTER 6. CONCEPTUAL DESIGN STUDY
(1999) comments that ground effect typically increases the lift-curve slope by up to 10% for
conventional aircraft; however, this has been neglected here.)
With one engine out on climb-out, an elevator deflection δE of −2.5◦ and wing incidence
α of 8.3◦ are required to trim the aircraft. The upwards elevator deflection has a beneficial
influence on Oswald efficiency which increases to 1.09 from 1.08 (corresponding to zero ele-
vator deflection). Note, the lift-to-drag ratio corresponding to this flight condition is used to
evaluate the required engine thrust in Sec. 6.1.4: it has a value of 22.4.
Rudder Performance
Rudders are located on the trailing edge of the wingtip fins for directional control. The
rudders are sized to provide sufficient yaw authority at engine-out upon takeoff for maxi-
mum available thrust (see Sec. 6.1.4). At the critical C.G location (xC.G. = 11.38 m — see
Sec. 6.1.5.5), ∂Cn∂δr = 0.00688. With a single engine located along the central axis, an offset of
7 m for the remaining two engines yields a Cn of 0.00174. For rudders that occupy the last
10% of chord and extend across the full height of the wingtip fin, an asymmetric deflection of
δr = 14.5◦ is demanded of both rudders. A viscous XFoil calculation, with a chord Reynolds
number of 53.8 million and required maximum section Cl of around 0.5, reveals that the flow
remains attached.
Aileron Performance
The classical steady-state solution to the equation of motion for a pure rolling motion, as
given by Nelson (1998), is
pssb
2U∞
= −Clδa
Clp
∆δa. (6.9)
The change in Clδa/Clp over the various flight phases is found to be negligible in comparison
to the change in flight speed. Therefore, maximum aileron deflection is expected to occur
during a banked motion on climb out.
For ailerons that occupy the outer 50% of the the elevon’s span, the roll-moment coefficient
due to aileron deflection Clδa is 0.114 rad
−1, whilst the roll-damping moment coefficient Clp
is -0.481 rad−1. A minimum 30◦ bank angle change within 5 seconds and τR = 4.5 s, i.e.,
pss = 0.149 rad/s (see Sec. 6.1.1), is achieved with an average deflection δa of 12.2◦. At
takeoff, the trim requirement in pitch means that there is already a -2.5◦ elevator deflection;
therefore, the required left and right aileron deflections for a clockwise roll would be 9.7◦
and −14.7◦, respectively. Figure 6.12 shows that the critical values for section Cl over these
surfaces are 0.83 and 0.2, respectively. A viscous XFoil calculation with Rec = 60 × 106
162
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
reveals that the flow remains attached for both cases.
Figure 6.12: Spanwise lift distribution corresponding to a clockwise roll at take off with:
δa = +/− 12.2◦ and δE = −2.5◦: M∞ = 0.21 and CL = 0.61.
Table 6.3: LFW lift and drag coefficient breakdown.
Coefficient Cruise (suction) Cruise (no suction) Climb out
CL 0.14 0.38 0.61
CD 0.0023 0.01535 0.02721
CDi 0.00098 0.0072 0.01838
CDv,wing 0.00067 0.0075 0.0080
CDv,misc 0.00065 0.00065 0.00083
L/D 60.9 24.8 22.4
6.1.3 Suction-System Technology Integration
In Fig. 3.1 we saw that suction-system technology integration is influenced by the airframe,
and aircraft performance. The extent of laminarised wetted area is limited by the need for
satisfactory control authority at low speeds. The wing cross section not only influences the
extent of laminarisation through geometric constraints at the trailing edge but, when com-
bined with the lift distribution in cruise (for a given planform, cruise CL and Mach number),
determines the surface pressure distribution, which in turn sets the level of distributed suc-
tion, and hence suction-pump power. The suction system in turn affects cruise performance,
163
CHAPTER 6. CONCEPTUAL DESIGN STUDY
Table 6.4: LFW aerodynamic performance parameters for climb-out and takeoff with one
engine inoperative, and cruise, with C.G. at 11.38 m.
Derivative Cruise (suction) Cruise (no suction) Climb out / Takeoff rotation
CL 0.14 0.38 0.61
M∞ 0.67 0.39 0.21
CLα (rad−1) 5.239 4.629 4.417
CLδE (rad
−1) 0.834 0.762 0.742
Cmα (rad−1) 0.00115 -0.0100 -0.0163
CmδE (rad
−1) -0.490 -0.433 -0.424
Cm,target 0.00056 0.0049 0.0161/0.146
α (deg) 1.5 4.8 8.3 / 11.3
δE (deg) -0.1 -0.8 -2.5 / -20.2
whilst extraction of the required suction power affects engine performance, and the associated
hardware weight affects the structure and its weight.
In arriving at the aircraft design specification in Chap. 5, the optimum suction distribution
for maintenance of laminar flow was combined with the aerofoil surface pressure distribution
to obtain the optimum pump and viscous drag. However, for a detailed conceptual design
study it is necessary to include the effects of a practical system architecture. The approach
here is to take the basic arrangement proposed in Chap. 4 and apply it to the aircraft
configuration shown in Fig. 6.8.
6.1.3.1 System Architecture
An illustration of the hardware arrangement for the centrebody region is detailed in Fig. 6.13.
Ideally, the spanwise chambers should be continuous across the span. This is made difficult
by large variations in surface Cp associated with an increasing thickness-to-chord ratio (see
Fig. 6.8), which would lead to violation of the incompressible flow assumption described
in Chap. 4. By tailoring the chamber sets and corresponding pressures to each surface
pressure distribution, high differential pressures are avoided. Therefore, the spanwise chamber
arrangement is divided across three regions (with the dash-dot lines corresponding to changes
in wing-section geometry). Flow rate controllers throttle the flow between chambers, which
is then ducted into a set of chordwise ducts (each attached to a suction pump) located along
the centrebody/outboard junction, and ejected at flight speed along the trailing edge of the
centrebody. The grey areas correspond to regions where suction is not applied: over the
leading edge suction is not required until some distance aft (see Chap. 4), whilst hardware
space requirements and the presence of trailing-edge control surfaces limit its extent to the
164
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
first 90% of chord.
Duct entry
No suction
regions
Pumps
Spanwise chambers
y
x
C1
C2
C3
C4
C5
B1
B2
B3
B4
A1
A2
A3
A4
Throttle valves
Chordwise duct
Chamber pressure:
point 1
Chamber pressure:
point 2
Chamber pressure:
point 3
Figure 6.13: Typical inboard suction-system architecture.
With no variation in wing section across the outboard and wingtip-fin regions, the ar-
rangement consists of (separate) continuous chamber sets over each region. However, the
sucked flow from the wingtip fins is throttled to match the chamber pressures of the out-
board wings. The flow is subsequently transported to the collector ducts and pumps at the
centrebody/outboard junction.
6.1.3.2 System Specification
The system architecture over each region is specified via the algorithm provided in Chap. 4.
However, ensuring that each region has a similar number of spanwise chambers introduces
a further constraint on the ratio of non-dimensional pressure difference across the skin over
165
CHAPTER 6. CONCEPTUAL DESIGN STUDY
a single chamber width (r˜c). With reference to Fig. 6.13, an outline of the LFW system
architecture specification algorithm is given below:
a) a boundary layer calculation at the inboard extreme of a region, where Rec is highest
(leading to earlier transition prediction and suction initiation), sets the chamber layout
and pressure, surface porosity distribution, and hence suction velocity distribution;
b) as Rec reduces outboards, for a constant distribution of skin porosity and chamber
pressure, the associated level of distributed suction is insufficient to maintain laminar
flow; therefore, the skin porosity coefficient, Ks, is increased uniformly across the region
of interest until the suction level is sufficient at the outboard extreme of a region;
b) chamber depths are set such that inertial and frictional effects are small relative to the
differential pressure across the skin, using Eq. 4.17;
c) the chamber pressures in region B are set higher than those in C, and those in A higher
than in B, to attain the desired flow direction;
d) the ‘real’ suction distribution calculated over each region is combined with the chamber
pressure distribution over region C, which sets the pump inlet pressures, to provide an
estimate of the suction power.
For low values of Cl, it was shown in Chap. 4 that this parameter has a negligible effect on
the suction requirements; therefore, spanwise variations in Cl across a region are neglected.
However, the highest values of Cl, shown in Fig. 6.9, over a spanwise region, are used to
evaluate the suction requirements: these correspond to the surface Cp distributions shown in
Fig. 6.8.
Table 6.5 summarises the chamber properties for the inboard region. The maximum num-
ber of chambers on the upper and lower surfaces is five and four, respectively; the minimum
being two and four, respectively. Fewer chambers are required on the lower surface given the
reasonably flat surface Cp distribution (see Fig. 6.8).
Table 6.5: Chamber specifications for the inboard section.
Parameter y <= 0.84 m y <= 4.20 m y <= 10 m
∆P˜s,av 0.15 0.15 0.15
r˜c 4 4 6
k = Ks,actual/Ks,ideal 1.1 1.1 1.1
No. Chambers (upper / lower) 4 / 2 4 / 2 5 / 4
166
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
The distributions of surface pressure and chamber pressure (provided spanwise chamber
losses are small) are detailed in Fig. 6.14 for region B (0.84 < y <= 4.20 m) and region C
(4.20 < y <= 9.18 m). The solid line is the chamber pressure distribution across region B,
and is determined based on consideration of the surface pressure distribution, indicated by
the dash-dot line. Region B has one small chamber upstream of the suction peak, and three
downstream. The chamber pressures in region C are lower than those over region B, and
hence ensure the desired flow direction. (Note, that the last chamber of region C is isolated
and not connected to region B.)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
x/c
 
 
P˜
Surface: y = 4.20 m
Chamber: y = 4.20 m
Chamber: y = 9.18 m
Figure 6.14: Distribution of inboard chamber and surface (non-dimensional) pressures across
regions B and C.
The critical differential pressures, corresponding to a flow Mach number of 0.4 across
the porous skin, for the three regions considered are detailed in Fig. 6.15. The maximum
∆P˜s across the skin is below critical, and therefore the assumption of incompressible flow is
satisfactory. A maximum chamber depth of around 3 cm is required to keep chamber pressure
losses small.
The chamber specifications for the outboard and wingtip fin regions are summarised in
Tab. 6.6. The sharp trailing-edge constraint results in a steep pressure gradient over the rear
of the outboard aerofoil, leading to a greater number of spanwise chambers relative to the
inboard regions. However, relative to the outboard region, fewer chambers are required over
167
CHAPTER 6. CONCEPTUAL DESIGN STUDY
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.1
0.2
0.3
0.4
0.5
0.6
x/c
∆
P˜
s
 
 
y = 0.84 m
y = 4.20 m
y = 9.18 m
Figure 6.15: Critical (non-dimensional) differential pressures across porous skin along the
centrebody region.
the wingtip fins because of the reduction in maximum thickness-to-chord ratio. As with the
inboard region, the flow across the porous skin may be treated as incompressible.
Table 6.6: Chamber specifications for the outboard section.
Parameter y <= 40 m z <= 3.5 m
∆P˜s,av 0.15 0.15
r˜c 6 3
k = Ks,actual/Ks,ideal 1.1 1
No. Chambers (upper / lower) 8 / 6 6 / 4
However, with a span of 33 m, the outboard spanwise chambers are prone to high chamber
pressure losses. Ignoring effects of wing taper and additional suction flow entering from the
wingtip fins, Fig. 6.16 details the pressure drop for three chamber depths: 0.05 m, 0.10 m
and 0.15 m, determined using Eq. 4.17. It reveals that chamber depths greater than 0.10 m
are necessary to ensure that chamber pressure losses remain small relative to the pressure
drop across the skin.
168
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
x/c
∆
P˜
c
 
 
0.15 m
0.10 m
0.05 m
Figure 6.16: Outboard (non-dimensional) chamber pressure drop.
6.1.3.3 Power Requirement and Weight Penalty
Figure 6.17 details the spanwise variation in suction coefficient CQ and pump power coefficient
W˜p. The (dimensionless) suction requirements increase across the centrebody due to the
increase in section thickness-to-chord ratio and reduction in chord Reynolds number. A
reduction in trailing-edge thickness and increase in t/c lead to a sharp increase between y =
4.2 − 5.8 m and at the centrebody/outboard intersection. Wingtip-fin suction requirements
are lower, given the reduced t/c.
The overall CQ is 3.10× 10−4 and, assuming a suction pump efficiency ηp of 85%, W˜p is
6.3 × 10−4. With a planform area of 1088 m2, U∞ = 209 m/s and ρ∞ = 0.599: the total
suction mass flow is 43.5 kg/s and the power to energise the suction system is 1.87 MW.
The suction pump weight is estimated to be 895 kg, assuming a pump weight of 0.48 kg per
kW (estimated by Wilson (1997)). The spanwise chambers are integrated within the aircraft
structure, and are therefore not included in the weight estimate here — see Sec. 6.1.5.
6.1.4 Propulsion System
Recall, Fig. 3.1 shows that the propulsion units are required to power the suction system,
generate enough thrust at takeoff, and have a satisfactory level of fuel consumption. Also,
169
CHAPTER 6. CONCEPTUAL DESIGN STUDY
0 1 2 3 4 5 6 7 8 9 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x 10ï3
y (m)
W˜
p
,
C
Q
 
 
CQ
W˜p
(a) Inboard
10 15 20 25 30 35 40 45
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x 10ï3
y (m)
W˜
p
,
C
Q
 
 
W˜p
CQ
(b) Outboard
Figure 6.17: Variation in overall suction coefficient and pump drag coefficient along the wing
half-span. CQ is 3.10× 10−4 and W˜p is 6.27× 10−4 — Reu = 8× 106 m−1, ηp = 0.85.
for an evaluation of the mission performance, a detailed assessment of the propulsion system
characteristics is necessary.
Cumpsty (1997) explains that engines are typically sized for conditions at top-of-climb
and, under normal conditions, provide ample thrust at takeoff. In contrast, the open litera-
ture (see Chap. 2) suggests that takeoff is a more critical condition for laminarised aircraft.
Furthermore, with a cruise Mach number of 0.67, the prospect of turboprop engine propul-
sion is a possibility. Therefore, in this chapter, a power-plant scoping study is undertaken to
compare the relative performances of turbofan and turboprop engines, over a range of design
points, following the design methodology proposed in Chap. 3. Configurations that provide
satisfactory operation are compared on the basis of specific fuel consumption in cruise with
suction.
6.1.4.1 Thrust and Power Requirements
For an aircraft with a flight path angle γ and mass M , the thrust required to react the weight
and drag forces is
FN = Mg
(
sin γ +
cos γ
L/D
)
. (6.10)
Mair and Birdsall (1992) specify that the most demanding takeoff flight segment for the
engines is at an altitude of around 120 m, with the undercarriage retracted, and making
allowance for the failure of one engine. In this study, two and three-engine configurations are
170
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
considered; the corresponding minimum climb-out angles are 1.38◦ and 1.55◦, respectively
(Mair and Birdsall, 1992). At cruising altitude, the minimum rate of climb is usually taken
as 300 feet per minute, which translates to a flight-path angle of around 0.5◦. In cruise, the
flight-path angle is taken as zero.
For the purposes of the power-plant scoping study, four operating conditions are consid-
ered: top-of-climb (with suction), takeoff (without suction) with one engine inoperative, and
beginning of cruise with/without suction. (End of cruise is considered in Sec. 6.1.4.3 once an
appropriate power plant has been identified.)
6.1.4.2 Power-Plant Scoping Study
Table 6.7 summarises the requirements, per engine, over the range of operating conditions for
both two and three-engined configurations. (Note, the thrust requirement for two engines is
evaluated based on the calculated L/D for three engines.) At takeoff, the required thrust is
strongly dependent on the weight of the aircraft, rather than its aerodynamic performance.
Therefore, the obvious design challenge is that around a ninth of the takeoff thrust is needed
in laminarised cruise for a two-engined aircraft, though this is slightly higher, at around a
seventh, for a three-engined aircraft.
Table 6.7: Thrust and suction power requirements (per engine) at various flight conditions
for two/three engines.
Parameter Suction No suction
TOC Begin cruise Begin cruise Takeoff (engine out)
Altitude (m) 6858 6858 6858 120
M∞ 0.67 0.67 0.39 0.21
FN (kN) 23.1/15.4 15.0/10.0 37.1/24.7 126.1/65.7
PWX (kW) 983/672 983/672 — —
Turbofan
Two engines
Taking the design point at TOC, an engine with a BPR of four gives satisfactory jet velocity
ratios for all operating conditions. In an attempt to alleviate conditions off-design, the
compressor and burner exit temperatures are reduced with T03 = 700 K and T04 = 1500 K.
The HPC map, detailing the design point and the operating line for increasing engine speed
at takeoff (TO) conditions, is shown in Fig. 6.18. The HPC pressure ratio at the design
point is around nine. The overall pressure ratio (OPR) is around 40, which is comparable to
171
CHAPTER 6. CONCEPTUAL DESIGN STUDY
typical OPRs detailed in Cumpsty (1997). In contrast, much higher HPC pressure ratios are
expected at TO.
Figure 6.18: Two engine turbofan HPC operating map, detailing the TOC design point (white
circle), and takeoff off-design point for increasing engine mass flow rate (yellow squares).
The non-dimensional spool speed (N) is represented by the solid black contours, and the
compressor efficiency by the red contours.
Figure 6.19 details the net thrust, HPC exit temperature and burner exit temperature
variation with engine mass flow rate at TO conditions (with the design point at TOC). The
maximum available thrust is below 72 kN, whilst both T03 and T04 breach the limits imposed
in this study. This typically critical design condition therefore falls short of providing the
required thrust at TO.
Consider now the HPC operating map shown in Fig. 6.20 with takeoff as the design
condition, for an engine with a bypass ratio of six. Clearly takeoff is the most demanding
operating condition of the three detailed. (Note, TOC is not an extreme operating condition,
and consequently is not shown.) To maximise engine efficiency in cruise, T03 and T04 at
TO are set to the maximum values, i.e. 900 K and 1800 K, respectively. Due to the large
172
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
Figure 6.19: Net thrust, HPC exit temperature and burner exit temperature variation with
engine mass flow rate at TO conditions for a two-engine turbofan designed for TOC.
variation in thrust requirement across the flight envelope, the HPC map reveals that the
operating points are much more widely spaced than is typical, with cruise efficiency reduced
below typical values. Moreover, in an attempt to improve cruise efficiency and move this
point away from the surge/stall line, the design point on the operating map, at the cost
of a lower compressor efficiency, has been rescaled — an insignificant compromise, given it
represents a small fraction of the total flight time. The resulting sfc for cruise with suction
is 23.0 g/kN.s
In an attempt to improve cruise efficiency, taking cruise without suction as the design
point was considered. The engine sfc for laminarised cruise was found to improve, but at
the cost of high burner exit temperatures and high relative HPC/LPC non-dimensional spool
speeds at takeoff.
173
CHAPTER 6. CONCEPTUAL DESIGN STUDY
Figure 6.20: Two engine turbofan HPC operating map, detailing the TO design point (white
circle), and various off-design points (yellow squares). The non-dimensional spool speed (N)
is represented by the solid black contours, and the compressor efficiency by the red contours.
The design point has been rescaled with β = 0.3 and N = 1.05.
Three engines
As for the two engine case, attempts to maximise efficiency in cruise with suction by taking
the design point at TOC were faced with a lack of available thrust at takeoff. Therefore,
alternative design points are considered below.
Figure 6.21 shows the HPC operating map for an engine with a BPR of five and cruise
without suction as the design point. Despite TO and the design point being very closely
spaced, compromised values for T03 and T04 of 700 K and 1500 K, respectively, were necessary
to alleviate conditions for the former. As for the two-engine case, the compressor efficiency
at TO was compromised by rescaling the map, primarily to better improve the efficiency at
cruise with suction. Similarly, the takeoff and cruise points are widely spaced. The estimated
sfc for cruise with suction is 23.0 g/kN.s.
174
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
Figure 6.21: Three engine turbofan HPC operating map, detailing the cruise-without-
suction design point (white circle), and various off-design points (yellow squares). The
non-dimensional spool speed (N) is represented by the solid black contours, and the com-
pressor efficiency by the red contours. The design point has been rescaled with β = 0.3 and
N = 1.05.
Turboprop
Two engines
As for the two engine turbofan, preliminary investigations showed that the turboprop suf-
fers from a lack of available thrust at takeoff when taking the design point at top-of-climb.
However, a different problem arises with TO as the design point : the turboprop suffers from
a high thrust coefficient. GasTurb has a threshold of CT = 0.5: a 5.6 m diameter blade
rotating at a speed of 853 RPM, corresponding to a blade tip speed of 250 m/s, puts the
thrust coefficient at this limit. Such a low rotational speed posits various problems, whilst
GasTurb places an upper limit of 5 m on blade diameter. Despite accepting slightly higher
blade tip speeds, satisfactory thrust coefficient values remained difficult to obtain.
175
CHAPTER 6. CONCEPTUAL DESIGN STUDY
Three engines
With three engines the thrust requirement at takeoff per engine is reduced. Consequently, a
blade diameter of 4.15 m rotating at 1150 RPM (blade tip speed of 250 m/s) is permissible
without encountering high thrust coefficients. The propeller map over the range of operating
conditions is detailed in Fig. 6.22.
Figure 6.22: Propeller map for a three-engine turboprop with TO as the design point. (Solid
black lines represent contours of propeller efficiency.)
The compressor operating map shown in Fig. 6.23 corresponds to an engine designed at
TO. The map has been rescaled to alleviate conditions in cruise with suction, whilst also
improve efficiency. Cruise without suction operates at the highest non-dimensional spool
speed, and as a consequence, design point values for T03 and T04 of 700 K and 1600 K
were selected in order to avoid compromising the viability of the design. The maximum
compressor pressure ratios are also encountered at this condition, with a value of around 18.
(Saravanamuttoo (1987) notes that turboprop engines typically operate between a value of
16 – 25.) The calculated sfc for cruise with suction is 21.5 g/kN.s.
Further consideration of alternative design points is not pursued. This is because taking
176
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
Figure 6.23: Three engine turboprop HPC operating map, detailing the TO design point
(white circle), and various off-design points (yellow squares). The non-dimensional spool
speed (N) is represented by the solid black contours, and the compressor efficiency by the red
contours. The design point has been rescaled with β = 0.2 and N = 1.05.
cruise-without-suction as the design point will severely compromise compressor efficiency in
laminarised cruise, whilst TOC as the design point will compromise the viability of the design
at takeoff and cruise-without-suction.
Discussion
The power-plant scoping study has examined the application of turboprop and turbofan
engines to the LFW aircraft for the following operating conditions: top-of-climb with suction,
takeoff, and cruise with/without suction. The investigation revealed that the engine operating
characteristics differ significantly from those utilised by conventional aircraft, primarily due
to the large difference in thrust requirement between takeoff and laminarised cruise.
First two turbofan engines were investigated. Taking TOC as the design point, to max-
177
CHAPTER 6. CONCEPTUAL DESIGN STUDY
imise efficiency in cruise with suction, the thrust generated at takeoff was found to be insuffi-
cient. Designing for TO gave a viable engine design with a sfc of 23.0 g/kN.s for cruise with
suction. Finally, designing for cruise without suction to improve sfc resulted in extreme con-
ditions at takeoff. With three turbofan engines, the thrust requirement at takeoff per engine
reduced; however, fixing the engine size at TOC still resulted in a design that was incapable
of generating the required thrust at takeoff. Designing for cruise without suction gave the
best sfc for this configuration, 23.0 g/kN.s. There appear, therefore, to be no benefits from
adopting a three-engine turbofan configuration over a two-engine one.
Next turboprops were considered. A configuration based on two engines with the design
condition at TOC with suction, like the turbofan, suffered from inadequate thrust generation
at TO. Takeoff as the design point was then investigated. Due to the high thrust requirement,
overly high thrust coefficients were unavoidable. Therefore, three engines were considered. A
blade diameter of 4.15 m with a rotational speed of 1150 RPM avoided an excessively high
thrust coefficient. Like the turbofan, TOC as the design point produced an engine incapable
of achieving the TO thrust required. Design at takeoff gave the best cruise-with-suction sfc
of 21.5 g/kN.s, which is 7% lower than the best turbofan design.
6.1.4.3 LFW Engine Performance
On the basis of the power-plant scoping study, a three-engine turboprop offers the best
solution for the laminar flying wing. Table 6.8 summarises the requirements per engine
over the full range of flight conditions needed for estimation of the aircraft’s mission range.
Start and end of cruise conditions are calculated based on a cruise-climb flight path. The
change in L/D is assumed to be negligible. However, a change in altitude and flight speed
affects the unit Reynolds number, and hence suction power requirement. For constant values
of: thickness-to-chord ratio, Mach number and CL, the increase in Reynolds number, here,
translates to just under a 7% increase in power (evaluated based on the parametric study
presented in Chap. 4). Should suction not be available at top-of-climb, the mission would be
aborted; therefore, only cruise is considered for the suction-failure case.
The HPC map with takeoff as the design point is shown in Fig. 6.24. It reveals that in the
event of suction failure, cruise is the more critical condition with a pressure ratio of around
20. However, designing for this condition would further compromise engine efficiency when
suction is employed. Note, as in the scoping study, the design point has been rescaled to
ensure operation with suction does not result in an engine surge/stall, and also to improve
the efficiency at this condition without encountering problems for cruise without suction.
The engine design specification is summarised in Tab. 6.9. A propeller diameter of 4.15
178
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
Table 6.8: Thrust and suction power requirements (per engine) at various flight conditions.
Parameter Suction No suction
TOC Begin cruise End
cruise
Begin cruise End
cruise
Takeoff (e/o)
Altitude (m) 6858 6858 8717 6858 8137 120
M∞ 0.67 0.67 0.67 0.39 0.39 0.21
FN (kN) 15.4 10 8.4 24.7 20.7 65.7
PWX (kW) 672 672 715 — — —
Figure 6.24: HPC operating map detailing the takeoff design point, various off-design points,
non-dimensional spool speed (N) contours (solid black), and efficiency contours (red). The
design point has been rescaled with β = 0.2 and N = 1.05.
m and rotational speed of 1150 RPM avoids excessive thrust coefficients and power loadings
at takeoff, with values of 0.49 and 351 kW/m2, respectively. Furthermore, the advance ratio
and power coefficients operate within a range of 0.90 – 2.64 and 0.51 – 0.80, respectively.
The compressor and burner exit temperatures at the design point are 700 K and 1500 K
— the latter reduced, c.f. 1600 K in the scoping study, to alleviate values at end of cruise
179
CHAPTER 6. CONCEPTUAL DESIGN STUDY
with suction. A propeller shaft power of around 6045 kW is required at takeoff. The overall
efficiency in cruise ranges between 20 – 22%. The calculated sfc at start of cruise with
suction is 22.0 g/kN.s, increasing to 23.2 g/kN.s at end of cruise.
To put the engine specification into perspective, consider the Europrop TP400 1 used to
power the Airbus A400M. This engine delivers a shaft power of 8203 kW on takeoff, which is
37% more than that for the LFW. The propeller consists of eight blades having a diameter of
5.3 m, compared to only 4.15 m for the LFW; its power loading is 17% lower at 292 kW/m2.
It has a higher overall pressure ratio of 25, which, however, is split between an intermediate
and a high pressure compressor, with ratios of 3.5 and 7.2, respectively.
GasTurb predicts a total mass of around 300 kg. However, many details of a real engine
are not modelled explicitly by GasTurb, and therefore the calculated mass is on the low side
2. The TP400 and NK-12 (see Saravanamuttoo (1987)) turboprop engines have dry-weight-
to-takeoff-power ratios of 0.23 kg/kW and 0.26 kg/kW, respectively. Therefore, assuming
the dry engine weight scales directly with shaft power delivered at takeoff, the estimated dry
weight per engine is around 1500 kg here.
1Information taken from www.roll-royce.com and www.europrop-int.com, October 2011
2Detailed in the GasTurb manual - www.gasturb.de.
180
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
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181
CHAPTER 6. CONCEPTUAL DESIGN STUDY
6.1.4.4 Sensitivity Study
With a large difference in thrust requirement between laminarised cruise and takeoff, the
engine sfc is compromised. Figure 6.25 details the variation of engine sfc in cruise (with
suction) as the engine speed, and hence thrust, is increased. It shows that, with a 36%
increase in thrust, i.e. a 26% reduction in lift-to-drag ratio, the reduction in sfc is about
14% (an increase in ηov from 22% to 25%). Further improvements in sfc begin to decay
above 13.6 kN. Using the Breguet-range equation, a 26% reduction in L/D thus translates
to around a 14% reduction in range (for a fixed fuel weight and flight speed).
Figure 6.25: Variation of cruise (with suction) engine sfc with thrust.
6.1.5 Structures and Weights
The structures and weights analysis consists of sizing primary structural elements for a given
loading distribution and airframe geometry. Amongst other system loads (introduced later),
the weights and locations of the passengers, suction pumps and engines are needed. The
weight buildup and C.G. location are necessary for the airframe generation (Sec. 6.1.1),
aircraft performance (Sec. 6.1.2), and determination of available fuel weight.
The structural components are sized using simple theory detailed in Chap. 3. The main
construction material is assumed to be an aluminium alloy, 2024-T3 (Niu (1988)).
182
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
6.1.5.1 Structural Configuration
The fuselage structure is modelled as a multi-bubble arrangement. It consists of several
circular cylinders combined together and joined by vertical bulkheads to make an extended
structure. The vertical bulkheads have cut-outs incorporated into them to allow access be-
tween adjoining cylinders, and passage throughout the cabin. Both frames and stringers
stabilise against potential local buckling and provide extra structural rigidity (e.g. in the
event of a low speed collision); frames also serve to transmit local shear loads to the wing
structure. However, it is proposed that wing ribs also double-up as frames. A cabin floor
is required to support the payload and seats etc. Pressure bulkheads cap off the spanwise
extremes of the cabin from the unpressurised regions. A portion of the fuselage is detailed in
Fig. 6.26 — the fuselage would consist of several such arrangements in the spanwise direction.
Chordwise
rib-frames
Spanwise
stringers
Vertical bulkheads
Upper surface:
rib-frame / lower suction 
surface attachment
Multi-bubble
pressure vessel
Figure 6.26: Schematic diagram of LFW fuselage structural arrangement.
Geuskens et al. (2008) propose that segregation of the cabin from the wing structure elim-
inates the appearance of large stresses in the wing structure. Furthermore, with the pressure
vessel supported by wing ribs, and the connections assumed pinned, negligible bending mo-
ments are likely to be incurred due to self weight. For preliminary design purposes, the cabin
and wing structures are assumed to be effectively decoupled. Therefore, the cabin shell is
analysed subject to pressure loads alone.
The LFW is assumed to have a conventional wing structure, consisting of four main
elements: the wing skin, stringers, ribs and spar-webs. The chambers are integrated into
183
CHAPTER 6. CONCEPTUAL DESIGN STUDY
the distributed flange construction by allowing the top of the chamber (the wing skin) and
its bottom plate to resist bending loads, whilst the chamber walls act as stiffeners/stringers.
Note, the wing skin thickness is set at 1 mm, regardless of loading, to avoid manufacturing
issues with a porous skin (Inger and Babinsky (2000)).
A schematic diagram of the wing and wingtip-fin geometries is provided in Fig. 6.27. Four
spanwise reference stations are highlighted: 1) wing root, 2) cabin boundary, 3) outboard
wing/wingtip-fin intersection, and 4) wingtip fin edge. The front and rear spars of the
wing-box are positioned at 10% and 70% chord along the outboard regions; however, across
the centrebody they have a fixed distance from the nose of the aircraft. The reference axis
coincides with the locus of the shear centre of the wing box. The outboard axis has a non-zero
sweep angle. With the front and rear spars aligned parallel to the centrebody trailing edge, a
kink in the wing-box construction results at station 2. A rectangular wing-box construction
is assumed, as detailed by Howe (2004), with depths, selected on the basis of providing
accommodation for the placement of suction equipment and structural reinforcements, of: 1)
2.3 m, 2) 2.2 m, and 3) 1.0 m.
Figure 6.27: Wing structural geometry.
184
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
6.1.5.2 System Loads Distribution
Figure 6.28 illustrates: a) the regions over which the imposed loads act, and the critical
load combinations for b) in-flight and c) on ground. Structural, payload, baggage and fuel
weight are distributed between the front and rear spars; payload occupies the centrebody
regions, whilst baggage and fuel are placed outboard with their spanwise extent limited by
minimum volume requirements. (A volume per bag of 0.3 m3 and a factor of 1.5 applied to
the total number of passengers gives a total baggage volume requirement of 99 m3; jet fuel
has a density of around 750 kg/m3, translating to a fuel tank volume requirement of 40 m3.
1) Baggage storage is placed further inboard relative to the fuel tank for passenger safety.
The aero-loading is shown as a distributed pressure force p(y) (see Sec. 6.1.2). The engine,
auxiliary power units (APU), suction hardware, avionics, nose wheel and undercarriage are
modelled as point loads. The ground reaction force R acts as a point load through the main
undercarriage, which is arbitrarily positioned at 75% chord at the spanwise extremes of the
centrebody (the landing gear arrangement is discussed further in Sec. 6.1.5.5). With three
engines having a blade diameter of 4.15 m, the spacing is set at 7 m. A minimum distance
of 1 m is reserved either side of the cabin for suction ducting.
The maximum takeoff weight (MTOW) consists of the design payload, the operating
empty weight (OEW), and the fuel weight. The design payload is defined as 220 persons in
Sec. 6.1.1, each with a total weight allotment of 100 kg (including 20 kg for baggage). The
OEW is created from estimates of structures, propulsion system, suction system, landing
gear, and fixed equipment.
6.1.5.3 Structural Analysis
Structural Forces and Moments
The aero-loading is calculated at the cruise flight condition (CL = 0.14 and M∞ = 0.67) with
zero control surface deflection. It is scaled by the gust load factor for the low wing loading
LFW, which is found to be more critical than a typical 2.5-g pull-up manoeuvre, at around
3.5-g.
The structural forces that arise when the (initially unknown) self-weight is excluded are
indicated by the solid lines in Fig. 6.29. Overall, along the span, the shear force increases
going inboards. There is a distinct reduction in the slope over the centrebody region, due
to the action of the system loads. The overall, negative, increase in bending moment and
reduction in slope over the centrebody region may be attributed to the same factors as those
1www.bp.com - Air BP, handbook of products.
185
CHAPTER 6. CONCEPTUAL DESIGN STUDY
We
R
p(y)
p(y)
wfix
w fix w bag w fuel
321
baggage
fuel
engine, APU
17.2 m
undercarriage
winglet
a)
b)
c)
l.e spar
t.e spar
We
fixments, 
payload
nose
wheel
self-weight
suction pumps
Wsp,Wuc
Wsp,WucWe
We
14 m
7 m
10 m 1 m
1.6 m 0.7 m
40 m
Figure 6.28: The distribution of weights and point loads over the planform is shown in a),
whilst in b) and c) the root cantilever model is illustrated for the in-flight and on-ground
load cases.
186
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
for the shear force; the distinct jump is due to the resolution of moments across the sweep
discontinuity. The increase in torque is physically consistent as the local lift acts forward
of the shear centre of the outboard wing; whilst the distinct reduction across the sweep
discontinuity, due to the resolution of forces, arises as the overall lift on the swept outboard
section lies aft of the shear centre of the inboard section.
0 5 10 15 20 25 30 35 40 45
−5
0
5
10
15
x 106
S 
(N
)
0 5 10 15 20 25 30 35 40 45
−15
−10
−5
0
5
x 107
M
 (N
m)
0 5 10 15 20 25 30 35 40 45
−5
0
5
10
x 107
T 
(N
m)
y
e
 (m)
Figure 6.29: Shear force, bending moment and torque diagrams for critical load cases — initial
estimate for in-flight (solid line), final estimate including self weight for in-flight (dashed line)
and final estimate for ground (solid-star line).
The converged structural forces for the in-flight and ground regimes are indicated by
the dashed and solid-star lines in Fig. 6.29, respectively. The in-flight loading calculation
with self-weight included shows some bending relief, but the torque on the outboard section
187
CHAPTER 6. CONCEPTUAL DESIGN STUDY
is unaffected due to the coincidence of centre of mass and shear centre. The reduction in
the change in torque across the sweep discontinuity is due to the reduced bending moment.
The ground forces reveal hogging on the outboard section, whilst sagging occurs over the
centrebody region due to the action of the reaction force via the undercarriage. There is no
torque over the outboard span as the baggage, fuel and structural weight C.G.s are taken
to coincide with the wing shear centre. A negative torque arises on resolution of moments
and torques across the sweep discontinuity due to the bending moment contribution; the step
reduction in torque at 10 m is due to the eccentricity of the undercarriage force.
On comparing the ground and in-flight structural forces: the in-flight shear force at the
inboard/outboard intersection is most critical outboard, in contrast to the ground shear
force at the inboard/outboard intersection for the centrebody region; the in-flight bending
moments and torque couples are most critical for sizing the structural elements.
Material Thickness
The fuselage skin and vertical/domed bulkheads each have thicknesses of 1.5 mm. The cabin
floor consists of a plank supported by 10 cm deep I-beams. The wing structure consists of: a
main-wing skin with a mean effective thickness of 7 mm and 14 mm for the compressive and
tensile surfaces, respectively; the mean wingtip-fin skin thickness is 2 mm; the main-wing spar
webs have a mean thickness of 12 mm, whilst those corresponding to the wingtip-fins are 4
mm; the rib webs have a thickness of 1 mm, whilst only the ribs supporting the undercarriage
have a significant spar thickness of around 12 mm — buckling requirements demand a rib
pitch over the outboard and wingtip fin regions of 0.82 m and 0.55 m, respectively, whilst
the spacing over the cabin region is dictated by fuselage buckling requirements; the control
surfaces have a mean spar-boom flange thickness of 4 mm, with negligible shear-web and
cover-skin thicknesses. Though not required for an estimate of stringer weight, the stringer
pitch is important given they also serve as suction chambers. Empirical correlations given
by Howe (2004) for stringer pitch correlate directly with the flange thickness; the pitch is
estimated at around 0.5 m over the main wing, and 10 cm over the wing-tip fins. As the suc-
tion chambers are typically much wider, additional partitions are unnecessary. Furthermore,
despite the low stringer pitch over the wingtip-fins, chamber losses are unlikely to pose any
serious problems: there is freedom to vary chamber depth, whilst the suction flow rates are
small.
188
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
6.1.5.4 Weight Breakdown
A breakdown of the aircraft structural weight is provided in Tab. 6.10. The total weight is
around 74.7 mt, with the wing weight being 15 times greater than that of the fuselage. As
a fraction of MTOW, the structural weight is around 40%, whilst the wing weight alone is
37%.
Table 6.10: LFW structural weight breakdown
Component Wing Component Cabin
Flange (kg) 36,790 Skin (kg) 1,921
Stringers (kg) 19,866 Stringers (kg) 480
Shear webs (kg) 9,184 Vertical bulkheads (kg) 922
Ribs (kg) 3,899 Cabin floor (kg) 794
Control surface (kg) 108 Insulation (kg) 276
Total (kg) 69,847 Total (kg) 4,393
The aircraft weight buildup is presented in Tab. 6.11. The OEW constitutes 58% MTOW,
however this may be higher once aeroelastic effects (Weishaar and Ashley (1973)), and ad-
ditional items such as rivets, screws, etc, have been accounted for. Therefore, the available
weight is reserved for additional structural items. The fuel weight with reserves is 29.9 mt
(see Sec. 6.1.6), around 16% MTOW
Table 6.11: LFW aircraft weight buildup
Component Weight (kg)
MTOW 187,000
Available weight 26,351
Design payload 22,000
Fuel with reserves 29,534
OEW 109,112
Structures 74,240
Landing gear 7,480
Fixed equipment 22,000
Propulsion 4,500
Suction pumps 895
6.1.5.5 Centre-of-Gravity Buildup and Landing Gear Arrangement
Whilst the aircraft is on the ground, a number of important design criteria must be adhered
to. These are detailed by Raymer (1999). The first concerns the location of the main landing
189
CHAPTER 6. CONCEPTUAL DESIGN STUDY
gear and hence the elevation of the aircraft, i.e. how high the centre of gravity is above ground
level, and the need to avoid wingtip contact with the ground during takeoff or landing. A
second requirement concerns the load bearing capacity of the nose wheel. Finally, when
taxiing around a sharp corner, the aircraft must not overturn. The key geometric parameters
for the tricycle gear arrangement adopted in this study are shown in Fig. 6.30.
Figure 6.30: Tricycle landing gear geometric arrangement.
When the aircraft is at OEW, the C.G is at its maximum aft position of 11.9 m. The
maximum fore position is at 11.38 m when the aircraft is at MTOW. The main landing gear,
positioned at 14 m from the nose, lies aft of the maximum rearwards C.G position; therefore,
the aircraft is not in danger of tipping over whilst stationary.
To prevent “tipback” on takeoff, the angle between the main gear, C.G and the vertical,
β, should be at least 15◦. The calculated maximum takeoff rotation in Sec. 6.1.2.3 is 11.3◦;
therefore, a value for α, at which the tips touch the ground, of 12◦ is assumed. From Fig. 6.31
we can deduce that
hC.G. <=
d
tan (α+ β)
. (6.11)
For d = 2.62 m, this gives a maximum centre of gravity height of 5.14 m. With a wing
thickness of 2.5 m, this translates, approximately, to a maximum landing gear height of 3.89
m. With current airport infrastructures, boarding finger floors are positioned at a height of 5
m. Therefore, a landing gear height of 3.75 m can meet this requirement whilst also satisfying
tipback considerations.
The nose force borne by the wheel must not exceed 20% of the aircraft weight, but should
be greater than 5% to ensure adequate wheel traction for taxiing. Vertical and moment
equilibrium about the leading edge gives the proportion of weight knose reacted by the nose
190
6.1. LAMINAR-FLYING-WING DESIGN CONCEPT
Figure 6.31: Tipback geometry.
wheel:
knose = 1− dC.G
dbase
. (6.12)
For knose to be reasonably small, dC.G needs to be around the same size as dbase, i.e. the C.G
needs to lie close to the main landing gear. With the nose wheel at the apex of the aircraft,
it bears between 15 – 19% of the aircraft’s weight.
The overturn angle ζ, as illustrated in Fig. 6.30, is the angle from the C.G to the main
wheel looking from the main wheel to the nose wheel, at a location where the main wheel
is aligned with the nose wheel. On consideration of the geometric parameters detailed in
Fig. 6.32, it can be shown that
ζ = arctan
(
hC.G
√
(dtrack/2)2 + (L+ dC.G)2
dC.Gdtrack/2
)
. (6.13)
Raymer (1999) gives a range for ζ between 50◦ – 60◦, below which an aircraft has a reduced
tendency to overturn. With a wheel track of 30 m, at the maximum aft C.G position ζ =
17.5◦, which is comfortably in the safe region.
191
CHAPTER 6. CONCEPTUAL DESIGN STUDY
Figure 6.32: Overturn geometry.
6.1.6 Mission
The mission, reserve and unusable fuel weights are calculated following the methods outlined
in Chap. 3. The fuel weight breakdown is summarised in Tab. 6.12. For a range of 9000 km,
the mission fuel weight is 27.4 mt, of which 1.8 mt (1% MTOW) is required to provide the
takeoff and climb-out potential and kinetic energy gains. Combined with a passenger-payload
of 220 pax, the estimated fuel burn is 13.9 g/pax.km.
Table 6.12: LFW mission-fuel weight buildup
Component Weight (kg)
Total 29,534
Mission 27,434
Reserve 1,808
Unusable 292
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6.2. COMPETITOR AIRCRAFT DESIGN CONCEPT
6.2 Competitor Aircraft Design Concept
In this section, a conventional turboprop aircraft is designed (following the methodology
outlined in Chap. 3) for the same mission specification as the LFW (passenger-payload of 220
persons, range of 9000 km, and cruise Mach number of 0.67). This allows the performance
benefits associated with the adoption of a flying-wing configuration and the utilisation of
laminar flow control to be quantified directly.
With a similar passenger-payload and range, the Boeing 757-200 serves as an ideal donor.
Where necessary, representative dimensions, areas, weights, and loadings are obtained from
this aircraft 1.
6.2.1 Target Gross Weight
In a single class cabin arrangement, the B757-200 has a passenger-payload of 228 persons and
an MTOW of 115,680 kg. Scaling the donor aircraft to a passenger-payload of 220 persons,
the target MTOW for the competitor aircraft is 111,621 kg. Hileman et al. (2007) assume
that 2% MTOW fuel is burned by conventional aircraft in climb. This puts the estimated
start of cruise weight at 109,388 kg.
6.2.2 Cruise Lift Coefficient
The lift coefficient is given by
CL = βLFW
√
CD0piARe. (6.14)
For a fair comparison against the LFW, both aircraft must have the same propulsion char-
acteristics, i.e., βLFW = 0.736. It is initially assumed that an Oswald efficiency, e, of 0.85 is
achievable (Torenbeek (1976)). It therefore remains to evaluate AR and CD0.
A lower flight Mach number permits a reduced wing sweep angle relative to high-subsonic
aircraft. Wing weight correlations provided by Raymer (1999) for transport aircraft show
that, at some hypothetical wing weight, wing sweep may be traded for aspect ratio
AR ∝ 1√cos Λ1/4 . (6.15)
The B757-200 has a wing aspect ratio of 7.8 and quarter-chord sweep of 25◦; unsweeping the
wing gives a 22% increase in aspect ratio to a value of 9.5.
1www.aerospaceweb.org, November 2011
193
CHAPTER 6. CONCEPTUAL DESIGN STUDY
van Es (2002) provides a method for estimating the zero-lift drag coefficient based on
the principle of equivalent skin friction, which are linked via Eq. 6.16. The equivalent skin-
friction coefficient is related to a Reynolds number, which depends on the reference length
Swet/b, via an empirical correlation given by Eq. 6.17. A first estimate of the wetted area is
given by assuming a value for Swet/Sref of 5.6, and a wing loading equal to that of the B757-
200 estimated at 6003 N/m2 (this also helps in achieving satisfactory takeoff and landing
performance). Evaluation of the zero-lift drag coefficient is iterative as it depends on altitude
and velocity. The final, converged, value is 0.0166. This compares well with the typical range
for high-subsonic-speed jets, provided by Torenbeek (1976), of 0.014 – 0.020.
CD0 = Cfe (Swet/Sref ) (6.16)
with
Cfe = 0.00258 + 0.00102 exp
(−6.28× 10−9Re)+ 0.00295 exp (−2.01× 10−8Re) (6.17)
and
Re = (Swet/b)V/ν (6.18)
The final estimate of CL is 0.48, compared to around 0.58 for the B757-200. Furthermore,
the cruise altitude is 11,450 ft lower at 23,550 ft. To maintain a constant CL and M∞ between
start and end of cruise, the aircraft must climb to 30,928 ft, whilst the cruise speed must drop
from 207 m/s to 202 m/s (assuming end of cruise weight is equal to OEW plus payload —
see Sec. 6.2.6 for further details of the aircraft weight breakdown). With a reduction of 9%
in unit Reynolds number, the change in skin-friction coefficient (see Chap.3) for a turbulent
boundary layer along the wing is less than 2%; therefore, the expected change in L/D is
negligible.
6.2.3 Aircraft Geometry
In this section, the methods used to define the fuselage, wing, vertical fin and horizontal
tailplane are summarised. Figure 6.34 shows the aircraft geometry in plan, side and front
view. Table 6.13 details key geometric parameters.
6.2.3.1 Fuselage
A narrow-body aircraft is desired. With a single-aisle cabin, and six passengers per row,
the fuselage width is 3.55 m (based on the value of 0.592 m per passenger introduced in
Sec. 6.1.1). With a 1 m seat pitch (as assumed for the LFW), and galleys, toilets, wardrobes,
194
6.2. COMPETITOR AIRCRAFT DESIGN CONCEPT
etc, which require a floor area of around 7 m2 (as assumed in Sec. 6.1.1.3), the minimum
cabin length is 38.7 m. The fuselage length is scaled with the cabin length of the B757-200.
For simplicity, the fuselage is modelled as a cylinder with a tapered tail and elliptic nose.
6.2.3.2 Wing
Structural efficiency is compromised for better aerodynamic efficiency with a wing-taper ratio
of 0.50. The wing quarter-chord is positioned at 48% of the fuselage length. (In Sec. 6.2.4 it is
shown that this gives satisfactory balance and stability characteristics.) A high-mounted wing
is selected to accommodate the large propeller-blade-diameter turboprops (see Sec. 6.2.5). A
RAE2822 aerofoil section with a maximum thickness-to-chord ratio of 0.12 is chosen for the
unswept wing, as it has been shown to exhibit satisfactory aerodynamic characteristics at
transonic cruise Mach numbers (Drela and Giles (1987)).
6.2.3.3 Tailplane
Figure 6.33 is used to determine the vertical fin height. It shows that the stabiliser must
lie outside regions of influence of the main wing when stalled. A T-tail plane is adopted to
avoid the interaction of the engine efflux with the horizontal stabiliser. For the assumed wing
position, a fin height of 8.7 m is required.
Figure 6.33: Aft tail positioning (from Raymer (1999)).
195
CHAPTER 6. CONCEPTUAL DESIGN STUDY
The surface areas are determined using an empirical correlation given by Raymer (1999).
That for the horizontal tailplane is given by
SHT = cHT cSref/LHT , (6.19)
where the horizontal tailplane volume coefficient has a value cHT of 1.0; LHT is the distance
from the wing and stabiliser quarter chords — Raymer (1999) indicates that this is roughly
equal to 50% of the fuselage length. Similarly, the vertical fin area is given by
SV T = cV T bSref/LV T , (6.20)
where cV T = 0.09 (accounting for end-plate effects associated with a T-tail arrangement), and
LV T ' LHT . A typical taper ratio of 0.60 is selected for the vertical fin. Sweep of the vertical
fin is not essential here given the low cruise Mach number; however, the fin has a leading-
edge sweep of 9◦ due to the combination of a straight trailing edge and fin taper. In contrast,
the stabiliser is untapered with the chord length chosen to match the fin-tip chord length.
A sweep of 5◦ is chosen on the recommendation of Raymer (1999) to avoid the stabiliser
stalling simultaneously with the main wing at high angles of attack. Symmetrical NACA-
4-digit aerofoils are selected for both surfaces. For satisfactory structural performance, the
maximum thickness-to-chord ratio is 10%.
Table 6.13: Competitor aircraft geometric parameters.
Parameter Value
Wing area (m2) 178.75
Wing span (m) 41.2
Wing AR 9.5
Mean wing chord (m) 4.3
Fin area (m2) 29.3
Stabiliser height (m) 8.7
Stabiliser area (m2) 25
Stabiliser span (m) 13.55
Stabiliser AR 6.3
196
6.2. COMPETITOR AIRCRAFT DESIGN CONCEPT
(a) Front view.
(b) Plan view.
(c) Side view.
Figure 6.34: Competitor aircraft configuration.
197
CHAPTER 6. CONCEPTUAL DESIGN STUDY
6.2.4 Aircraft Performance
In assessing the aerodynamic performance, the cruise and low-speed flight conditions are
studied (with more emphasis on the former).
6.2.4.1 Cruise Performance
The longitudinal NP is 25.4 m from the nose. With the C.G. initially unknown, a 5% static
margin is assumed, which puts its location at 24.1 m from the nose. (On evaluation of C.G.
travel in Sec. 6.2.6, the final estimate does not warrant further iteration.) Pitch trim is
achieved with a stabiliser incidence of −1.05◦ and zero elevator deflection. With no wing
twist, the fuselage incidence is 2.1◦, which is 0.9◦ below the recommended maximum.
Figure 6.35 details the spanwise loading and Cl distributions. With a high-mounted wing
configuration, the lift distribution is not significantly affected by the presence of the fuselage.
The lift coefficient increases outboard due to wing taper. The increased spanwise loading,
ClC/Cref , going inboard is structurally favourable. The local Cl on the tailplane is negative,
corresponding to the download required for pitch trim. The Oswald efficiency is 0.98: 15%
better than that assumed in Sec. 6.2.2.
Figure 6.35: Spanwise loading distributions for CL = 0.48 and M∞ = 0.67 — Cl (dashed)
and Clc/cref (solid).
198
6.2. COMPETITOR AIRCRAFT DESIGN CONCEPT
Figure 6.36 shows a cross section of the RAE2822 aerofoil and surface Cp distribution
at the maximum calculated Cl and Mach number. The critical pressure coefficient C∗p is
superposed, and reveals that the flow remains subcritical throughout. Example surface Cp
distributions at the Cls corresponding to the stabiliser can be found in Chap. 4.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
−1
−0.5
0
0.5
1
1.5
x/c
 
 
−
C p
−0.1
0
0.1
y/
c
−Cp
*
Figure 6.36: Surface Cp distribution for an RAE2822 aerfoil, with the critical Cp superposed
— Cl = 0.52 and M∞ = 0.67.
The aeroplane profile drag in the en-route configuration is evaluated following the methods
detailed in Chap. 3. A breakdown is provided in Tab. 6.14. The estimated lift-to-drag ratio is
19.3, which is at the upper end of typical conventional configuration values (Cumpsty (1997)).
6.2.4.2 Low-Speed Performance
Torenbeek (1976) provides a useful first-order approximation to the drag polar on initial
climb-out after take-off
CDV2 = C0 +
C2LV2
piARE
. (6.21)
For a takeoff speed V2 of 70 m/s, CLV2 = 2.04. E, with flaps extended and one engine
inoperative, is taken as 0.672, and C0 = 0.018; evaluating Eq. 6.21, CDV2 = 0.225. The
lift-to-drag ratio is therefore around 9.
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CHAPTER 6. CONCEPTUAL DESIGN STUDY
Table 6.14: Competitor aircraft cruise lift and drag coefficient breakdown.
Coefficient Value
CL 0.48
CD 0.0249
CD,i 0.0072
CD wing 0.0066
CD vertical fin 0.0011
CD stabiliser 0.0012
CD fuselage 0.0068
CD engine nacelles 0.0014
CD interference effects 0.0002
CD protuberances, surface imperfections, etc 0.0004
6.2.5 Propulsion System
The engine design approach detailed in Chap. 3 is followed. As top-of-climb is generally
taken to be the design point for conventional aircraft, this is assumed here without further
justification. Note, a design burner exit temperature of 1600 K is assumed.
Two turboprop engines sized to meet conditions at top-of-climb are unable to meet takeoff
thrust requirements without encountering a high thrust coefficient. Therefore, a four engine
configuration is adopted. Takeoff thrust is based on a minimum climb-out angle of 1.72◦ with
one engine inoperative (following Mair and Birdsall (1992)); the top-of-climb and cruise angles
are 0.5◦ and 0◦, respectively (as in Sec. 6.1.4). The requirements per engine are summarised
in Tab. 6.15; in addition, there is an auxiliary power off-take of 50 kW. To avoid problems
with high thrust coefficient values, a rotational speed of 1100 RPM and blade diameter of
4.3 m are selected.
Table 6.15: Competitor aircraft engine design variables.
Description T.O.C. Start of Cr. End of Cr. T/O
Altitude (m) 7178 7178 9427 120
Mach number 0.67 0.67 0.67 0.21
Thrust (kN) 16.2 13.9 10.1 51.3
A summary of the engine performance at top-of-climb, start and end of cruise, and takeoff,
is provided in Tab. 6.16. The engine has satisfactory values for compressor and burner exit
temperature over the range of operating conditions. The maximum compressor ratio occurs at
top-of-climb and has a value of 21.4, which, as explained in Sec. 6.1.4, is within the capabilities
of modern turboprop engines. The engine operates well away from the surge/stall line, with
surge margins between 20 – 30%. The range of values of advance ratio, thrust and power
200
6.2. COMPETITOR AIRCRAFT DESIGN CONCEPT
coefficients are typical of current turboprop blades. The propeller efficiency is maximised for
cruise with a value of around 90%. Overall efficiency is maximum at top-of-climb, but is of
a similar order at start of cruise. The average overall efficiency in cruise is around 35%. The
maximum shaft power occurs at takeoff, and has a value of 5345 kW. Scaling the dry engine
weight based on this parameter (see Sec. 6.1.4), the weight per engine is 1.26 mt. Finally,
the thrust specific fuel consumption for cruise has an average value of 13.6 g/kN.s.
Table 6.16: Competitor aircraft engine performance summary.
Parameter T.O.C. Start of Cr. End of Cr. T/O
Compressor exit temperature (K) 700 677 634 719
Burner exit temperature (K) 1600 1534 1472 1605
Compressor pressure ratio 21.4 19.4 19.4 17.9
Surge margin (%) 22.5 25.7 24.7 29.4
Advance ratio 2.62 2.62 2.54 0.90
Thrust coefficient 0.247 0.214 0.202 0.354
Power coefficient 0.723 0.622 0.572 0.465
Propeller efficiency 0.897 0.901 0.900 0.682
Shaft power delivered 3964 3414 2403 5345
Propulsive efficiency 0.885 0.885 0.885 0.683
Thermal efficiency 0.418 0.412 0.412 0.359
Overall efficiency 0.358 0.352 0.355 0.245
Thrust spec. fuel cons. (g/kN.s) 13.56 13.81 13.40 6.74
6.2.6 Structures and Weights
6.2.6.1 Structural Weight
The aircraft structural weight is determined following the sizing methods outlined in Chap. 3.
As for the LFW, the construction material is aluminium 2024-T3.
A 2.5-g pull-up manoeuvre in cruise flight is taken as the critical loading condition for
the wing. System loads acting on the wing half-span consist of two engines mounted on the
leading edge at 24% and 66% half-span. (In Sec. 6.2.5 the weight per engine is estimated at
1.26 mt.) The main landing gear is attached to the fuselage at 57% of its length. Fuel weight
acts to provide bending relief, and is therefore not included in the calculation. The total
estimated wing structural weight is approximately 15.3 mt, which is around 14% MTOW; a
breakdown is provided in Tab. 6.17.
Howe (2004) notes that, typically, a pull-out manoeuvre in a nose dive is critical for the
horizontal stabiliser; here, the lift distribution on the tailplane in trimmed cruise is scaled
to a maximum section Cl of 0.80 (Polentz (1949)). The vertical fin is sized to react loads
201
CHAPTER 6. CONCEPTUAL DESIGN STUDY
Table 6.17: Competitor aircraft wing structural weight buildup.
Component Mass (kg)
Skin & stringers 14,010
Spar webs 448
Ribs 370
Flaps, slats, etc 459
Total 15,287
incurred during engine-out at takeoff and is scaled by a factor of 0.70 to account for inertial
effects (Greitzer et al. (2010)). The total tailplane weight is 1.6 mt, which is less than 2%
MTOW.
Table 6.18 shows a breakdown of the fuselage structural weight. The fuselage shell, tail
cone, floor and added bending material are sized to withstand applied loadings which include:
differential pressure, horizontal and vertical bending moments in flight and on landing, and
torsional shear (Greitzer et al. (2010)). The remainder of the fuselage weights are estimated
using empirical correlations provided by Torenbeek (1976) for: shell modifications, consisting
of added weights including rivets, fasteners, local reinforcements, etc; and the support struc-
tures of the wing, tailplane and fuselage mounted landing gear. The total estimated fuselage
weight is 10 mt, around 9% MTOW.
Table 6.18: Competitor aircraft fuselage structural weight breakdown.
Component Mass (kg)
Shell 1,891
Tail cone 9
Floor 803
Additional horizontal bending material 46
Windows 509
Insulation 311
Shell modifications 1891
Support structures 4564
Total 10,024
The total structural weight is estimated at around 26.9 mt. A breakdown is given in
Tab. 6.19. For comparison, the wing, tail and body structures of the B737-200 comprise
43%, 11% and 46%, respectively, of the total structural weight 1.
1http://adg.stanford.edu/aa241/AircraftDesign.html, December 2011
202
6.2. COMPETITOR AIRCRAFT DESIGN CONCEPT
Table 6.19: Competitor aircraft structural weight breakdown.
Component Mass (kg)
Wing 15,287
Tailplane 1597
Fuselage 10,024
Total 26,908
6.2.6.2 Fuel Weight
The mission, reserve and unusable fuel weights are calculated following the methods outlined
in Chap. 3. The fuel weight breakdown is summarised in Tab. 6.20. For a range of 9000 km,
the mission fuel required is 29.6 mt, of which 0.7 mt (0.6% MTOW) is to raise the potential
and kinetic energies between takeoff and cruise. With a passenger-payload of 220 persons,
the estimated fuel burn is 15.0 g/pax.km.
Table 6.20: Competitor fuel weight breakdown.
Fuel Mass (kg)
Total 30,942
Mission 29,608
Reserve 1,028
Unusable 306
6.2.6.3 Aircraft Weight Buildup and Centre-of-Gravity Travel
The aircraft weight buildup is presented in Tab. 6.21. The OEW contributes 52% MTOW,
which compares well with conventional aircraft configurations. For comparison, the Boeing
757-200 has an empty-weight fraction of 0.55 (Aboulafia (1996)). Fuel with reserves represents
28% MTOW.
The maximum aft C.G. location is at 25.1 m when the aircraft is loaded with fuel only.
In contrast, the maximum fore location corresponds to the aircraft loaded with payload only
at 23.9 m. The mean C.G. position during cruise is 24.35 m, which is approximately 2%
further aft of that assumed for the pitch trim analysis in Sec. 6.2.4.1. Furthermore, there is
no danger of tipback, with the landing located at 28.4 m (see Sec. 6.2.6.1).
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CHAPTER 6. CONCEPTUAL DESIGN STUDY
Table 6.21: Competitor aircraft weight buildup.
Component Mass (kg)
MTOW 111,621
OEW 58,397
Available weight 282
Design payload 22,000
Fuel with reserves 30,942
Structure 26,908
Fixed equipment 22,000
Landing gear 4,465
Propulsion 5,024
6.3 Comparison of LFW and Competitor Aircraft
A comparison of the MTOW breakdown for each aircraft is detailed in Fig. 6.37. The LFW
has a MTOW of 187 mt relative to around 112 mt for the competitor aircraft. With a 69%
lower wing loading, the LFW has a significantly higher structural weight fraction of 40%,
compared to just 22% for the competitor. The LFW has an OEW which is 58% of MTOW,
higher than that for the competitor at around 52%. The LFW values may also increase on
inclusion of aeroelastic effects and additional item weights; therefore, the available weight is
reserved for this purpose, allowing the OEW potentially to increase to 72% of MTOW.
(a) LFW — MTOW of 187 mt. (b) Competitor aircraft — MTOW of 111.6 mt.
Figure 6.37: Comparison of LFW and competitor aircraft MTOW breakdowns.
The cruise lift-to-drag ratios of the LFW and competitor aircraft are 60.9 and 19.3,
respectively. The value for the competitor aircraft is comparable to current advanced aircraft.
204
6.4. SUMMARY
For the LFW, an all-lifting surface with wingtip fins contributes to a 10% better Oswald
efficiency, whilst the utilisation of suction over 90% of the wetted area leads to a 93% lower
viscous drag coefficient.
However, the superior lift-to-drag ratio comes at a cost: the overall engine efficiency is
significantly compromised, with a value of 21%. In contrast, the competitor aircraft has an
efficiency of 35%. This corresponds to a lower competitor engine sfc of 13.6 g/kN.s relative
to 22.6 g/kN.s for the LFW. The poor performance of the LFW engine is due to the large
difference in thrust requirement between takeoff and cruise. Despite a higher takeoff L/D
of 22.4 relative to a value of 9, the LFW has a takeoff thrust per engine comparable to the
competitor aircraft, due to the aircraft weight contribution. As a consequence, the engine
design point is at takeoff, which leads to the degraded performance in cruise. In contrast, the
competitor aircraft engine is designed at top-of-climb, as is typical, and maximises efficiency
in cruise.
Despite a lift-to-drag ratio that is over three times higher for the LFW, the higher sfc
and higher aircraft weight compromise fuel burn. The LFW has an estimated fuel burn of
13.9 g/pax.km, which is just 7% lower than the competitor aircraft at 15.0 g/pax.km.
6.4 Summary
This chapter has described the conceptual design for a laminar-flying-wing aircraft, based on
the design specification presented in Chap. 5. It is found that a laminar flying wing with:
satisfactory stability and control characteristics, accommodation for 220 pax at adequate
passenger comfort levels, distributed suction over 90% of the wetted area for the maintenance
of laminar flow, and powered by three turboprop engines, is capable of flying a distance of
9000 km at a Mach number of 0.67 with a fuel burn of 13.9 g/pax.km. This figure compares
favourably with the value of 23.5 g/pax.km quoted for the Boeing 777 (Martinez-Val (2007)).
However, it falls short of the 60% reduction suggested by Greener by Design, due to low
values of engine efficiency and payload weight fraction.
To put the LFW estimate in context, a conventional, turbulent-flow, aircraft was designed
for the same mission specification. A high wing configuration was selected to accommodate
four, large diameter, turboprop engines, which in turn required a T-tailplane configuration.
The reduced cruise Mach number permitted an unswept wing configuration, which led to
a lift-to-drag ratio comparable to current advanced aircraft. In contrast to the LFW, the
competitor aircraft’s engines had favourably high efficiencies in cruise and the payload weight
fraction was typical, leading, despite a lower lift-to-drag ratio, to a comparable fuel burn
estimate just 7% higher at 15 g/pax.km.
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CHAPTER 6. CONCEPTUAL DESIGN STUDY
In summary, the exceptional aerodynamic efficiency of the laminar flying wing design
presented here is associated with penalties in aircraft weight and propulsion efficiency, to the
extent that a conventional turboprop aircraft flying at the same speed might be almost as
efficient. Unless these penalties can be significantly mitigated, the LFW will fall short of the
potential suggested by considering its lift-to-drag ratio in isolation.
206
Chapter 7
Conclusions and Future Work
7.1 Conclusions
7.1.1 Motivation for the Study
Growing air travel and its environmental impact is increasingly becoming a public concern.
The laminar flying wing, which utilises boundary-layer suction as a means of laminar flow
control, has been proposed by Greener by Design as a potential solution. On the basis of
the Breguet range equation, and estimates for various component parameters, Green (2002)
proposes that a laminar flying wing, with 2001 technology levels and powered by UDF engines,
would consume 60% less fuel relative to a conventional aircraft. It is necessary to go back 50
years, to the Handley Page HP117, to find a conceptual design that provides a quantitative
fuel burn estimate. However, the estimated fuel burn is only marginally better than that
of the B787, and therefore falls short of the gains expected of it. New studies, assuming
present-day technology, are therefore required to substantiate (or challenge) the Greener by
Design proposal. In this thesis, one such study has been produced.
7.1.2 Conclusions of the Study
I. The basic architecture of practical laminar flow control systems is well established.
However, little guidance on the important design parameters and their interactions is
available. This study has aimed to provide such insight for a commercial laminar-flying-
wing transport aircraft.
It has identified a minimum power requirement, independent of the suction system
design, associated with the boundary layer stagnation pressure loss of the flow in an
optimal suction distribution. Furthermore, an automated algorithm has been developed
to facilitate the design of a practical suction system, requiring only the specification
207
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
of the skin’s surface resistance and the sensitivity of the suction distribution, to de-
fine the subsurface chamber width and pressure. Deviations from the optimal suction
distribution have been found to have little effect on the overall suction coefficient, but
additional power is required due to the skin’s surface resistance. In the spanwise direc-
tion, through suitable choice of spanwise-length-to-chamber-depth, inertial and friction
losses may be made negligibly small. Combined with the pressure drop from the aero-
foil surface to the collector ducts, rather than to the chamber, which determines the
power penalty, it is proposed that the number of collectors and (hence) pumps should
equal the number of chambers. Furthermore, there should be few chambers, as in-
creasing chamber architecture complexity does not reduce the power penalty. Finally,
the study revealed that the additional power requirement associated with a practical
suction-system implementation for a laminar flying wing is likely to consume at most
20%, and more likely around 10%, excess power above the minimum value.
II. The basic philosophy adopted was that the laminar flying wing would be designed with
an emphasis, above all, on aerodynamic efficiency. A high-level exploration of the design
space was performed to identify the key configuration and mission parameters, with the
following constraints: wing sweep is restricted to 25◦, to justify the neglect of additional
suction requirements for the suppression of cross-flow instabilities; it must be possible to
stand in the cabin; and the flow must remain subcritical. Furthermore, a configuration
that could be analysed on the basis of simple methods was insisted upon. Therefore, the
aircraft was treated as a swept, untapered, wing utilising distributed suction, without
any regard for a practical suction-system implementation (on the basis of conclusion
I.) Furthermore, the design was defined by three principal variables: thickness-to-chord
ratio, unit Reynolds number, and span.
It was determined that optimum aerodynamic efficiency would be achieved by spec-
ifying the highest possible values for all three variables, which would also maximise
wing loading, and hence minimise gust response issues. However, the combination of
high thickness-to-chord ratio and unit Reynolds number was found to limit the degree
of allowable sweepback due to attachment-line instability, hence raising the prospect
of balance and stability issues, whilst high thickness-to-chord ratios also significantly
compromised the cruise speed. Other potential problems identified included: the wing
weight fraction, which was driven to higher values by the span length; unfavourably
low cruise altitudes at higher unit Reynolds numbers; and passenger volume restrictions
at higher thickness-to-chord ratios. These considerations drove the design towards a
compromise specification: a 187 tonne, 80 m span, aircraft, with an aspect ratio of 6.4,
208
7.1. CONCLUSIONS
cruising at Mach 0.67 and an altitude of 22,500 ft, with lift coefficient 0.14.
III. On the basis of this specification, a detailed conceptual design was performed. Five
areas were assessed: 1) 3-D airframe generation, 2) aircraft performance, 3) suction-
system technology integration, 4) propulsion system, and 5) structures and weights.
In contrast to a conventional methodology, the approach for the laminar flying wing
was essentially reversed, with the mission (i.e. range, Mach number, payload) being an
output, once a viable aircraft specification had been identified. To quantify the benefits
associated with the flying wing configuration utilising laminar flow control, the design
was compared against a competitor, turbulent flow, aircraft with a conventional layout,
designed for the same mission, the same propulsion characteristics, and following the
same technical approach.
The key aspects of the laminar flying wing studied here are as follows:
– On consideration of passenger-roll comfort requirements, the outboard extent of
the centrebody cabin limits the passenger capacity to 220 persons (i.e. a payload-
weight fraction of 12% MTOW), and reduces the (80 m span) wing aspect ratio
to 5.9 (from 6.4).
– Satisfactory stability and control characteristics are obtained with the utilisation
of: wingtip fins, wing sweepback, symmetrical wing sections; but flight control
systems may be required to artificially stabilise dynamic stability modes.
– Distributed suction over 90% of the wetted area significantly reduces the aircraft
profile drag. When this is combined with a low induced drag (via a low cruise CL,
high-aspect-ratio wing, and a ‘better than elliptic’ lifting surface) the estimated
cruise lift-to-drag ratio is 60.9; however, a practical suction-system implementation
requires 1.87 MW of power to drive the suction pumps.
– A low cruise Mach number enables the utilisation of more efficient turboprop, over
turbofan, engines. However, the performance of both engine types is significantly
degraded by the large difference in thrust requirement between takeoff and lami-
narised cruise. For this reason, and to avoid high thrust coefficients, three engines
are required; furthermore, in contrast to conventional aircraft, the engine design
point is taken to be at takeoff, which compromises the overall engine efficiency at
21%, and engine sfc at 22.6 g/kN.s.
– The combination of a low wing loading, high-aspect-ratio wing, and the limit on
outboard extent of the passenger payload, leads to a high structural weight of 40%
MTOW, with an allowance to increase to 54% MTOW.
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CHAPTER 7. CONCLUSIONS AND FUTURE WORK
– On the basis of the mission fuel available, the range is 9000 km.
The key aspects of the competitor aircraft are as follows:
– With a low cruise Mach number, wing sweep is traded for aspect ratio. The result
is a zero-sweep wing with an aspect ratio of 9.5 and a span of 41.2 m. The effect
is a cruise lift-to-drag of 19.3, comparable to current advanced aircraft.
– Four large-blade-diameter turboprop engines are utilised to avoid excessive thrust
coefficients at takeoff. The overall engine efficiency is 35%, which results in an
engine sfc of 13.6 g/kN.s.
– The MTOW is 112 mt, with a payload weight fraction of 20%.
The laminar flying wing has an estimated fuel burn of 13.9 g/pax.km, whilst the com-
petitor aircraft is just 7% higher at 15.0 g/pax.km. In conclusion: despite a superior
lift-to-drag ratio, the high-aspect-ratio laminar flying wing proposed in this study suf-
fers from a low payload-weight fraction and poor propulsion efficiency, and hence falls
short of the potential expected of it by Greener by Design.
7.2 Recommendations for Future Work
If the high aspect ratio, low sweep and low wing loading aircraft presented in this study is to
realise the substantial reduction in fuel efficiency anticipated by consideration of aerodynamic
efficiency alone, the overall engine efficiency, which is compromised by the large difference
in thrust requirement between takeoff and laminarised cruise, must be improved upon. This
could either be through optimisation of the turboprop considered here, or by consideration of
alternative, novel, design solutions. If this issue can be successfully addressed, then further
design refinement would be required; considerations may include: an analysis of aeroelastic
effects, which could lead to a higher structural weight than that calculated based on a static
analysis alone; and design of the flight control system, in order to estimate the required
control power.
If these issues cannot be overcome, then, on the basis of the design considerations pre-
sented in this study, relationships between the relevant parameters and their functional depen-
dence on one another could be established to facilitate an optimisation study. The outcome
of such a study may be the compromise of aerodynamic efficiency via a low-aspect-ratio wing.
This configuration could potentially lead to an improvement in the overall engine efficiency,
and reduce the structural weight fraction (whilst avoiding flutter issues). However, this would
210
7.2. RECOMMENDATIONS FOR FUTURE WORK
demand an increased amount of wing sweepback, which would have the compounded benefit
of a higher payload volume, but would increase the complexity of the aerodynamic analysis.
211
CHAPTER 7. CONCLUSIONS AND FUTURE WORK
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