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Design and Analysis of Morphing Wing
for Unmanned Aerial Vehicles
by
Vlad Paul Galantai
A thesis submitted in conformity with the requirements
for the degree of Masters of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
Copyright by Vlad Paul Galantai 2010
Design and Analysis of Morphing Wing
for Unmanned Aerial Vehicles
Vlad Paul Galantai
Masters of Applied Science
Department of Mechanical and Industrial Engineering
University of Toronto
2010
Abstract
This study is concerned with the design and development of a novel wing for UAVs that
morphs seamlessly without the use of complex hydraulics, servo motors and controllers. The
selected novel design is characterized by a high degree of ight adaptability and improved
performance with a limited added weight. These characteristics were attained through the
use of shape memory actuators in an antagonistic fashion. Unlike compliant actuators, the
antagonistic setup requires the thermal energy to deform the wing but not to maintain its
deformed shape. Structural analysis based upon safety factors specied by FAR23 standards
and aerodynamic analysis using FLUENT were conducted on the novel design to validate
its suitability as a viable wing for UAVs. In addition, thermal conditioning of the shape
memory actuators was conducted using a specially designed programmable controller. This
thesis does not concern itself with the design of a skin that accommodates the shape changes.
ii
Acknowledgments
The author is grateful for the nancial support provided by Defence Science Organization
National Laboratories of Singapore, under contract number DSOCO07212. The author also
wishes to thank Professor Meguid for the kind supervision, the careful guidance and all the
help he provided in the past two years, while working on this project. Finally, he wishes to
thank Dr. Soa for all the support and for a very pleasant collaboration.
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To My Family
For All Their Support
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Contents
1 Introduction and Justication 1
1.1 Unmanned Aerial Vehicles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Morphing and Shape Adaptation in Aircraft . . . . . . . . . . . . . . . . . . 3
1.3 Morphing using Shape Memory Alloys . . . . . . . . . . . . . . . . . . . . . 4
1.4 Objectives of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Method of Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Literature Review 8
2.1 Unmanned Aerial Vehicles - Historical Overview . . . . . . . . . . . . . . . . 8
2.2 A Brief History of Morphing Wings . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Existing Adaptive Wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Current State of the Art of Morphing . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Wing Planform Morphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.1 Wing Span Resizing . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.5.2 Chord Length Change . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5.3 Sweep Angle Variation . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6 Out-of-plane Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6.1 Airfoil Camber Change . . . . . . . . . . . . . . . . . . . . . . . . . . 18
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2.6.2 Lateral Wing Bending . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6.3 Wing Twisting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.6.4 Airfoil Prole Adjustment . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Conceptual Design of Morphing Wings for Unmanned Aerial Vehicles 24
3.1 Design Specication of UAV . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Preliminary Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 Adaptive Airfoil Concept . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.2 Airfoil Tracer Concept . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.3 Variable Morphing Wing Concept . . . . . . . . . . . . . . . . . . . . 30
3.2.4 Adaptive Octahedron Concept . . . . . . . . . . . . . . . . . . . . . . 32
3.3 The Selected Design: The Adaptive Octahedron Concept . . . . . . . . . . . 37
3.4 Development of Prototype . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5 Conditioning of Shape Memory Alloys . . . . . . . . . . . . . . . . . . . . . 39
4 Aerodynamic and Load Analysis of Morphing Wing 41
4.1 CFD Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.1 Discretization of Morphed Wing . . . . . . . . . . . . . . . . . . . . . 41
4.1.2 Details of Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Analysis of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 Analytical Verication of Results . . . . . . . . . . . . . . . . . . . . . . . . 50
4.4 Performance Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.5 Load Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 Conclusions and Future Work 61
5.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
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5.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.4 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Bibliography 64
vii
List of Figures
1.1 AAI Shadow 200 (After [1]) . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Comparison of mission proles for a generic commercial airliner vs. a genericsurveillance UAV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 UAV funding prole (After [2]) . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Comparison of Manned vs. Unmanned Funding (After [2]) . . . . . . . . . . 3
1.5 Compliant vs. Antagonistic implementation of SMAs . . . . . . . . . . . . . 5
1.6 Detailed Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Diagram showing the change in eective airfoil thickness-to-chord length ratio 12
2.2 Classication for shape morphing of a wing . . . . . . . . . . . . . . . . . . . 14
2.3 The inatable telescopic spar concept . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Reed's concept of interpenetrating partial ribs (After [3]) . . . . . . . . . . . 17
2.5 Span-wise camber variation of Fowler aps (After [4, 5]) . . . . . . . . . . . 18
2.6 The antagonistic exural unit cell (After [6]) . . . . . . . . . . . . . . . . . . 20
2.7 Lockheed Martin morphing UAV (After [7]) . . . . . . . . . . . . . . . . . . 21
2.8 Morphing wing using the eccentuator concept (After [8]) . . . . . . . . . . . 22
3.1 Detailed Morphing Wing Design Methodology . . . . . . . . . . . . . . . . . 25
3.2 Adaptive Airfoil Concept: Span-wise section of the wing . . . . . . . . . . . 27
3.3 Airfoil change as a result of chord length variation . . . . . . . . . . . . . . . 27
viii
3.4 Top view - Four planform congurations . . . . . . . . . . . . . . . . . . . . 28
3.5 Section showing the exible beam deected by the 4 actuators, the corrugatedmaterial and exible skin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.6 Sample wing congurations . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.7 Octahedral unit cells forming a spar, coupled to ribs via ball-joints . . . . . . 33
3.8 Top view showing the two spars. Left - straight wing; Right - backwardcurved wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.9 Straight wing in unmorphed and morphed states . . . . . . . . . . . . . . . . 35
3.10 Three spar structure used for the airfoil prole variation along the span-wisedirection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.11 Prototype of an AOC spar . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.12 Prototype showing the exibility of the unit cells . . . . . . . . . . . . . . . 38
3.13 Shape memory alloy degradation (After [9]) . . . . . . . . . . . . . . . . . . 39
3.14 Automated antagonistic setup for SMA conditioning . . . . . . . . . . . . . . 40
4.1 Sample structured mesh for curved wing. Units of airfoil chord length (c) . . 43
4.2 Straight wing in-plane morphing . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3 Drag and lift coecients for in-plane morphing of straight wing . . . . . . . 46
4.4 Span-wise components of ow. Note: the curved wing experiences a strongerspan-wise component which develops closer to the root of the wing. . . . . . 47
4.5 Swept wing in-plane morphing . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.6 Drag and lift coecients for swept, morphed wing . . . . . . . . . . . . . . . 48
4.7 Straight wing, partial in-plane morphing . . . . . . . . . . . . . . . . . . . . 48
4.8 Drag and lift coecients for straight, partially morphed wing . . . . . . . . . 48
4.9 Drag and lift coecients for wing bending . . . . . . . . . . . . . . . . . . . 49
4.10 Drag and lift coecients for wing twisting . . . . . . . . . . . . . . . . . . . 50
4.11 Power requirement for steady level ight for straight, morphed wing . . . . . 53
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4.12 Aerodynamic performance of baseline straight wing, and of morphed wings . 54
4.13 Elliptical lift distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.14 Elliptical lift distributions for the three in-plane morphed cases . . . . . . . . 56
4.15 Span-wise shear force distribution . . . . . . . . . . . . . . . . . . . . . . . . 57
4.16 Bending moment about the roll axis . . . . . . . . . . . . . . . . . . . . . . . 57
4.17 Wing twisting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.18 Twisting moment as a result of the wing curvature . . . . . . . . . . . . . . . 58
4.19 Shear force on spars as a result of twisting . . . . . . . . . . . . . . . . . . . 59
4.20 Bending moment about the roll axis as a result of twisting . . . . . . . . . . 59
x
List of Tables
2.1 Modern UAV classication (After [10]) . . . . . . . . . . . . . . . . . . . . . 10
3.1 UAV specications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Actuator selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Design selection matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1 Parasitic and induced drag coecients for straight, morphed wing . . . . . . 52
5.1 Lift, drag coecients and L/D ratios for backward-curved wings . . . . . . . 71
5.2 Lift, drag coecients and L/D ratios for bent wings . . . . . . . . . . . . . . 72
5.3 Lift, drag coecients and L/D ratios for twisted wings . . . . . . . . . . . . 73
5.4 Lift, drag coecients and L/D ratios for morphed, swept wings . . . . . . . . 74
5.5 Lift, drag coecients and L/D ratios for straight, partially morphed wings . 75
xi
Symbols and Abbreviations
CA- axial force coecient on wing
CN - normal force coecient on wing
CD- drag coecient
CL- lift force coecient
CLα- lift line slope
e- span eciency factor
AR- aspect ratio
D- drag force
P - propulsive power
V - ight speed
A- wing area
W - UAV weight
NBC- nuclear, biological and chemical weapons
EW - usage of electromagnetic waves
RSTA- reconnaissance, surveillance and target acquisition
BDA- battle damage assessment
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Chapter 1
Introduction and Justication
1.1 Unmanned Aerial Vehicles
Unmanned aerial vehicles are dened as being aircraft that do not require an on-board
human crew in order to y. UAVs can y fully autonomously or they can be remotely
controlled by a human pilot. This makes them a great candidate for missions involving
a high degree of risk. In addition to this, their airborne endurance is not limited by the
endurance of a pilot. Their size can range from something comparable to an average radio
controlled hobby plane to very large ones such as the Global Hawk, which is comparable in
size to some commercial airliners. An example of a mid-size UAV is the AAI Shadow 200,
as shown in Figure 1.1.
Figure 1.1: AAI Shadow 200 (After [1])
The use of UAVs as a test platform for wing morphing technology can be attributed to
their complex ight mission proles, as well as their requirement to dynamically change
their mission proles during ight. For comparison, a commercial airliner can spend 90%
or more of its ight mission cruising. As a result, their xed wings are designed to achieve
1
optimal performance during cruising - highest lift to drag ratio. Even if the wings are slightly
inecient during the remainder of the ight mission prole, the overall mission eciency
will not be greatly decreased. Most UAVs have mission proles that require them to cycle
between loitering, cruising, fast ascents and fast descents.
As shown in Figure 1.2, each of these stages of the mission prole becomes a bigger compo-
nent of the overall mission, so it would make sense to try to design a wing which will oer
optimal ight performance over the entire mission prole.
Figure 1.2: Comparison of mission proles for a generic commercial airliner vs. a genericsurveillance UAV
Although their development began as early as 1950s, in the last two decades signicant
improvements have been made in their design, endurance and image recognition, as evi-
dence by their success in surveillance missions, scientic data gathering and for military
applications. According to Ref. [2], the future of aircraft will shift focus from manned to
unmanned aerial vehicles as shown by the following Figure 1.3. It is believed that funding
for UAVs will be tripled, reaching over 10 billions dollars in the current decade.
2
Figure 1.3: UAV funding prole (After [2])
In addition to this, the shift towards UAV technology is shown in Figure 1.4 by the manned
vs. unmanned funding ratio, which shows a large jump from 4% in 2000 to 31% in 2010.
Figure 1.4: Comparison of Manned vs. Unmanned Funding (After [2])
1.2 Morphing and Shape Adaptation in Aircraft
The term morphing originates from the eld of biomimetics. Research in the eld of
biomimetics has the goal of observing and replicating concepts seen in nature and mak-
3
ing use of nature's tendency to reach optimal functionality in new designs.
In the eld of aeronautics, we link the term morphing to shape adaptation and are commonly
used when talking about morphing wings. One could dene morphing wings as the ability
of the wing to change its shape seamlessly in order to provide optimal performance to suit
dierent ight conditions and mission proles. Clearly, the seamless change in the geometry
of the wing should not involve highly complex technologies and/or weight penalty.
It is known that the ow characteristics over an airfoil can dramatically change the value
of lift and drag. In current xed wings, these changes can be achieved with the use of the
control surfaces, which aid in the control and stability of an aircraft.
The problem with current technology is that all control surfaces are discrete. Depending
on their conguration, the airfoil shape can be discontinuous. Such abrupt changes in the
wing surface can decrease the aerodynamic eciency of the wing. By morphing a wing, we
are trying to achieve seamless shape changes of signicant magnitude in order to allow the
UAV to dynamically adapt to dierent ight scenarios. We are expecting that a successful
morphing platform will yield aircraft with a high degree of adaptability, increased ight
eciency and improved maneuverability.
1.3 Morphing using Shape Memory Alloys
Let us consider a rigid wing with a standard rib and spar conguration. If we to add morph-
ing to this wing using hydraulic actuators, pumps and other auxiliary support systems, this
would result in higher degree of complexity and weight penalty. The most ecient approach
to add morphing capability to an aircraft is to add multifunctionality to its ribs and spars,
so as to enhance the degree of freedom of these structures. This multifunctionality is the
new trend in aircraft design and would ensure reduced complexity and weight penalty.
Recent developments in smart materials and adaptive structures would help in adding mul-
tifunctionality to many engineering structures, such as those used in aircraft industry. Ma-
terials such as shape memory alloys, shape memory polymers and piezo crystals are just
some of the materials that can be used as actuators in smart structures. They each posses
a dierent blend of actuation stress, strain and speed, and depending on the application
some will be more suited than others.
4
For instance, piezo crystals typically provide very fast high stress actuation, but at the cost
of limited displacement. Shape memory polymers provide high actuation strains, but at the
cost of very small stress. As stated earlier, wing morphing requires the shape changes to
be both seamless and a signicant magnitude. Shape memory alloys, such as NiTi, possess
a good combination of actuation stress and strain needed for wing morphing. Therefore,
SMAs can be used to functionalize wing spars so as to allow shape changes, as well as
contribute to load sharing without signicantly adding weight to the overall system.
Shape memory alloys (SMA) can be implemented in a structure following a compliant or
an antagonistic setup. Compliant structures make use of the elastic potential energy stored
in one or more members as means of bringing the system to initial shape. As a result, the
simplest compliant structure only requires one SMA actuator. Figure 1.5 shows an actuator
connected to an elastic member, while being constrained at the tips. At the initial position,
the actuator is pre-strained and its microstructure is 100% martensitic. When heated, it
undergoes phase transformation from martensite to austenite, and as a result, it contracts.
In order to bring the system to its initial shape, the SMA actuator must be cooled such
that it will undergo the reverse phase transformation, from austenite back to martensite.
At this point, the elastic potential energy, previously stored in the elastic member, would
stretch the SMA.
Figure 1.5: Compliant vs. Antagonistic implementation of SMAs
In an antagonistic setup, at least two SMA actuators are required. They are arranged in
such a way that while one actuator contracts, the other actuators are strained. By varying
the order in which the actuators are cooled and heated, a two-way motion can be achieved.
5
While compliant systems have the benet of requiring fewer SMA actuators, one of their
biggest shortfalls is the continuous requirement of heating in order to maintain their de-
formed shape. Antagonistic structures, on the other hand, do not suer from this problem,
as they only require energy to change shape and not to maintain it. In situations where
both deformed and non-deformed shapes are to be kept for extended periods of time, the
antagonistic setup has a net advantage.
1.4 Objectives of Research
The objective of this study is to use shape memory alloys in the design of a morphing wing
structure, in an unmanned aerial vehicle. Specically, the aims of this work are to:
1. develop a new conceptual design in wing morphing using shape memory alloys so as
to ensure mechanical integrity, reduced weight penalty and improved performance,
2. carry out structural and aerodynamic analysis for the newly adopted morphing wing
design,
3. build a prototype to demonstrate the viability of the devised concepts accounting for
conditioning of the SMA used,
4. design and develop a programmable controller to actuate the SMA to induce necessary
deformation in wing spars.
1.5 Method of Approach
In this study, several concepts using mechanical, hydraulic and smart material based ac-
tuators were investigated. The results clearly pointed out that smart materials were good
candidates for morphing actuators. Given below, is the method of approach used in the
design process, as shown in Figure 1.6.
6
Figure 1.6: Detailed Design Process
The selected morphing concept must satisfy a number functional requirements. These in-
clude: ight performance, structural integrity, morphing response, added weight, reliability
and cost eectiveness.
Both structural and aerodynamics analysis were performed. Structural analysis was per-
formed analytically assuming loading factors specied by the FAR23 standards used in
aircraft design. Elliptical wing lift distribution was assumed and preliminary analysis was
performed under the rigid body assumption. Aerodynamic analysis was performed with
the help of the ANSYS Fluent package and validated whenever analytical solutions were
available for simple geometries.
Scale down prototypes were built to test the functionality of the morphing scheme. The
reliability and degradation of the actuators was tested experimentally. Wind tunnel testing
was scheduled but is currently re-scheduled for a later stage of the project.
7
Chapter 2
Literature Review
2.1 Unmanned Aerial Vehicles - Historical Overview
The rst radio-controlled UAV was built in 1917 by Cooper and Sperry [11]. They converted
a U.S. Navy Curtiss N-9 aircraft by implementing Sperry's previously invented gyroscopic
stabilizer. The result was the Sperry Aerial Torpedo, a UAV that was successfully ight
tested over a distance of 50 miles with a 300-pound bomb on board. Early UAVs were
developed as expendable, inexpensive aircraft whose survivability was not important, as
stated in Ref. [12]. The Queen Bee was the rst UAV that had the ability to land, making
them reusable for future missions. The Queen Bees were used by the Royal Navy between
1935 and 1947 as targets for anti-aircraft gunners. The remotely controlled Queen Bee had
a biplane conguration and the ability to reach speeds of 100 mph, travel up to 300 miles
and a service ceiling of 17000 feet.
The U.S. Air Force used the OQ UAVs as targets that aided the training of anti-aircraft
gunners. They were developed by the Radioplane Company (currently Northrop Grumman).
The OQ UAVs were radio-controlled, and made use of a large slingshot in order to take-o.
The OQs landed with the help of a parachute.
The AQM-34 Ryan Firebee was based on a Q-2C Firebee, with the added feature of low
radar signature as a result of the radar-absorbing blankets placed on the fuselage, and a
screen over the intake. The UAVs relied on a parachute to land safely. Between 1964
and 1975 more than 1000 AQM-34 Ryan Firebee UAVs ew more than 34000 surveillance
8
missions. They proved to be very reliable with a survival rate of 83% during the Vietnam
War.
In 1964, as a result of the Cold War, Lockheed Martin tested the D-21 UAV [13] for the
rst time. The D-21 still remains the fastest UAV, as a result of its ability to reach speeds
of Mach 4 [11]. It had a range of 3000 miles, with a service ceiling of 90000 feet. It had
stealth capability as a result of an anti-radar coating. The only D-21 built ew 4 missions,
crashing during the last one.
In 1978, Israel developed and built the Scout surveillance UAV. Its low radar signature was
the result of a small size berglass frame, which made the Scout a target very hard to detect
and destroy. In 1982 they were used in combat, searching for Syrian missile sites.
The Pioneer UAV was the rst inexpensive, small UAV used by the U.S. Army [11]. The
Pioneer was a surveillance UAV that was successfully used in the Golf War and the conict
in Bosnia. The U.S. Air Force currently makes use of the RQ-1 Predator UAV. Its various
on-board equipment, such as the synthetic aperture radar (SAR), visible spectrum and
Infrared cameras give it the ability to send back a clear and detailed picture of the battle
eld. The on-board technology coupled with a range of 450 miles, which translates in 14 to
16 hours of ight time, make the Predator an excellent surveillance UAV.
The RQ-4 Global Hawk, produced by Northrop Grumman [14] is one of the largest UAVs
ever built. It is oered in many congurations, such as Block 10, 20 30 and 40. Its on-
board equipment is customized with mission-specic sensors that can provide intelligence,
surveillance and reconnaissance (ISR) information back to the control base. Depending on
the conguration, the Global Hawk can have a range of 22780 km, with a service ceiling
of 19800 meters. Although used by the military, it can be adapted for civil missions such
as border patrol, hurricane monitoring and scientic research. More information about the
use of UAVs in border patrol and for scientic purposes can be found in Ref. [15], and
respectively, in Ref. [16] .
The Pathnder UAV was developed by AeroVironment Corporation. It is an ultra-lightweight,
solar-powered UAV intended for research missions. In 1997, it set a new world altitude
record for solar aircraft, reaching 67350 feet. The Pathnder's main tasks are to take high
resolution pictures as well as to gather wind and weather data. More information about the
chronological evolution of UAVs as discussed in this section is presented in Ref. [11]. Table
2.1 provides a classication of current UAVs.
9
UAV Class Category Range
(km)
Sample Missions Current Systems
Micro/Mini Micro (MAV) <10 Scouting, NBC sampling,
surveillance inside buildings
Black Widow, MicroStar, Microbat,
FanCopter, QuattroCopter, Mosquito,
Hornet, Mite
Mini <10 Film and broadcast industries,
agriculture, pollution
measurements, surveillance
inside buildings, communications
relay and EW
Mikado, Aladin, Tracker, DragonEye,
Raven, Pointer II, Carolo C40/P50,
Skorpio, R-Max, R-50, Robocopter,
YH-300SL
Tactical Close Range
(CR)
10-30 RSTA, mine detection, search
and rescue, EW
Observer I, Phantom, Copter 4, Mikado,
RoboCopter 300, Pointer, Camcopter,
Aerial and Agricultural RMax
Short Range
(SR)
30-70 BDA, RSTA, EW, mine
detection
Scorpi 6/30, Luna, SilverFox, EyeView,
Firebird, R-Max Agri/Photo, Hornet,
Raven, Phantom, GoldenEye 100, Flyrt,
Neptune
Medium Range
(MR)
70-200 BDA, RSTA, EW, mine
detection, NBC sampling
Hunter B, Mucke, Aerostar, Sniper,
Falco, Armor X7, Smart UAV, UCAR,
Eagle Eye+, Alice, Extender, Shadow
200/400
Long Range
(LR)
200-500 RSTA, BDA, communications
relay
Hunter, Vigilante 502
Endurance (EN) >500 BDA, RSTA, EW,
communications relay, NBC
sampling
Aerosonde, Vulture II Exp, Shadow 600,
Searcher II, Hermes 450S/450T/700
Medium
Altitude, Long
Endurance
(MALE)
>500 BDA, RSTA, EW weapons
delivery, communications realy,
NBC sampling
Skyforce, Hermes 1500, Heron TP, MQ-1
Predator, Predator-IT, Eagle-1/2,
Darkstar, E-Hunter, Dominator
Strategic High Altitude,
Long Endurance
(HALE)
>2000 BDA, RSTA, EW,
communications relay, boost
phase intercept launch vehicle,
airport security
Global Hawk, Raptor, Condor, Theseus,
Helios, Predator B/C, Libellule,
EuroHawk, Mercator, SensoCraft,
Global Observer, Pathnder Plus
Special
Task
Lethal (LET) 300 Anti-radar, anti-ship,
anti-aircraft, anti-infrastructure
MALI, Harpy, Lark, Marula
Decoys (DEC) 0-500 Aerial and naval deception Flyrt, MALD, Nulka, ITALD, Chukar
Stratospheric
(Strato)
>2000 - Pegasus
Exo-
stratospheric
(EXO)
TBD - MarsFlyer, MAC-1
Table 2.1: Modern UAV classication (After [10])
10
2.2 A Brief History of Morphing Wings
The study of bird ight led to the development of the rst functional wing. Sir Charles
Cayley, in the late 1700s, realized that the lift function and the thrust function of bird
wings were distinct. Furthermore, they could be emulated by dierent systems on a xed-
wing aircraft. A century later, in 1891, German engineer Otto Lilienthal, [17] began his
work on heavier-than-air ying machines. He focused his eorts on a xed-wing glider.
Birds are able to adapt their wings to the conditions that need be met at a given time far
better than current aircraft. They can fold their wings tightly when they are going to dive
for a prey, or extend their wings completely when they want to glide to save energy.
Studies have also shown that Swifts are some of the most ecient birds when it comes to
active ying. Researchers have proved how these birds change the shape of their wings to
improve performance. The results of the analysis provided clues as to how aircraft wings
can be improved. By carrying out wind tunnel testing on dead swifts, [18] researchers found
out that low speed ight with extended wings gives swifts maximum ight eciency. But
swept wings deliver a better aerodynamic performance at higher ight speeds. Swept wings
increase maneuverability as a result of a smaller aspect ratio which translates into a smaller
rolling inertia. They also found that these birds are able to adjust the shape of their wings
to increase the eciency of their glide and/or to make faster turns.
One might argue that the concept of morphing wing began on December 17, 1903 by the
Wright Brothers. They ew the Wright Flyer from Kitty Hawk, North Carolina for 12
seconds and covered a distance of 120 ft. Details of the inventions of the Wright Brothers is
provided in their patents [19, 20, 21, 22, 23, 24]. The Wright Brothers twisted the surface
of each wing separately and succeeded in changing its orientation with respect to oncoming
airow. Such changes in position led to changes in ight direction. Their theory was initially
tested by ying a kite, and later was used to control the Wright Flyer.
2.3 Existing Adaptive Wings
Morphing can involve a change in the shape of the wing, the sweep of the wing, the camber
of the airfoil, the skin roughness and any other wing parameter. All these can contribute
signicantly to aircraft ight performance. Currently, there are several modern airplanes
11
that take advantage of variable geometry wings. The F-14 Tomcat and B-1B Lancer wings,
along with several modern military ghter jets, are designed with a variable sweep, specif-
ically using swing wing technology. During supersonic ight, the wings are swept back
by pivoting them around a point located in the fuselage in order to change the eective
thickness-to-chord ratio of the wing, as shown in Figure 2.1. By decreasing this ratio the
critical Mach number of the wing can be delayed, and as a result the wave drag is decreased.
Furthermore, by sweeping a wing the span is decreased, which also makes the aircraft more
maneuverable as a result of the rolling inertia being decreased.
Figure 2.1: Diagram showing the change in eective airfoil thickness-to-chord length ratio
The B1 Lancer bomber went into operation in October 1986. It has a wing-body that can
change its span from 79 ft to 137 ft by changing the sweep of its wing. In the unswept
conguration, the B1 can take o in a shorter distances and increase its range. In the swept
position, it can achieve supersonic speeds. The morphing aspect of this bomber has made
the B1-B famous for its ability to carry large payloads at high speed over large distances.
The F-14 utilizes swing wing technology. In this case, the wing pivot structure spans the
entire center of the airplane. Unfortunately this translates into a signicant weight penalty.
The normal sweep range is 20 degrees to 68 degrees, with the possibility of undergoing
oversweep for hangar stowage. The sweep speed is 7.5 degrees per second [25]. In this
case, the unswept morphing helps short take o and landing as well as storage in the carrier.
12
In the swept position, the F-14 can reach speeds in excess of Mach 2. The system relies
on hydraulic actuators and linkages, to activate the wing deformation at enormous weight
penalty, and high point loads.
In the past, great measures were taken to ensure greater torsional stiness so as to ensure
wing rigidity. This resulted in heavy and more rigid mission specic structures. The current
approach is to make use of torsional exibility, as previously implemented by the Wright
Brothers. In this case, use will be made of natural warping of the wing to control the
aircraft. The AFTI/F-111 [26] Mission Adaptive Wing and the F/A-18A Hornet [27] with
active aeroelastic wing are designed with a seamless camber. The camber prole changes
in response to increased aerodynamic loads, increasing ight performance. Actually, the
F/A-18A Hornet was chosen for this application because it was originally thought that the
wing torsional stiness was underestimated. These wings were taken out of storage and
used for the same mission they were originally designed for with more exible wings. The
amount of twist is only 4 degrees maximum. This resulted in reduced drag, increased range,
and more ecient fuel consumption.
2.4 Current State of the Art of Morphing
Current research in the area of wing morphing is focused on overcoming the major challenges
imposed by wing morphing as outlined by Reich and Sanders [28]:
• the requirement for high-power density actuators
• structural mechanization
• exible skins
• control law development
As stated previously in this thesis, the idea behind wing morphing is to signicantly change
the in-ight behavior of a wing as a result of signicant seamless shape changes. In the
design of their morphing UAV , Lockheed Martin [29] has derived the requirements for
loiter, cruise and low altitude dash [30] and proved that the wetted area is the common
variable in all three cases, as outlined below:
13
• Loiter:
Endurance =(
1SFC
) (LD
)ln(W0
W1
)=
f(LD
)= f
(b√Swet
)• Cruise:
Range =(
VSFC
) (LD
)ln(W0
W1
)=
f(M · L
D
)= f
(b√Swet
)• Low Altitude Dash:
CD = CD0,0 +C2L
ρ·e·AR = CD0,0 = f (Swet)
SFC = Specic Fuel Consumption
L/D = Lift to Drag Ratio
W0= Initial Weight
W1= Final Weight
M = Mach Number
b = Span
Swet= Vehicle Wetted Area
e = Span Eciency Factor
AR = Aspect Ratio
V = Velocity
CD= Drag Coecient
CD0,0= Drag Coecient - Zero Lift, Zero
Camber
CL= Lift Coecient
Recently, Soa and Meguid [31] have written a review concerning the classication of the
dierent shape morphing techniques available. This classication for shape morphing is
outlined in Figure 2.2. The review shows that the three main changes that help in wing
morphing are (1 - in-plane deformation, 2 - airfoil prole changes and 3 - out-of-plane
deformation).
Figure 2.2: Classication for shape morphing of a wing
14
2.5 Wing Planform Morphing
Planform changes of the wing include: span change, chord length change and the changing
of the sweep angle. Span and chord length changes result in the change of the aspect ratio
of the wings. A high aspect ratio is associated with a low induced drag and a higher span
eciency factor, but will decrease the maneuverability of the aircraft. The case involving
very high aspect ratio present designers with a challenge in creating a morphed structure
that can sustain high bending moments at its root. Small aspect ratios have the benet
of improved maneuverability, which is the reason why modern jet ghters employ such a
conguration, but at the expense of reduced cruising ability.
2.5.1 Wing Span Resizing
One way of modifying the span of a wing is by using telescopic actuators as spars. In such a
conguration, the structure of the wing is divided in segments with a reduced cross sectional
area towards the tip of the wing, such that they can each slide into the adjacent segment in
order to decrease the span.
Neal et al. [32] proposed a concept of achieving such shape changes using a thin-walled
stainless steel pneumatic cylinder actuator with a carbon steel rod. It was reported that
the wing managed to achieve a 38% span change. Blondeau et al. [33] also made use of
pneumatic actuators to alter the span of the wing. The wing was divided into three sections;
each of them could be retracted inside the adjacent section closer to the root. In order to
achieve a large span change - reported as being 114% - 3 segment telescopic actuators were
used, controlling each of the wing sections, as shown in Figure 2.3.
15
Figure 2.3: The inatable telescopic spar concept
The experimental results were obtained by Supekar [34] and showed that the lift to drag
ratio of their wing in extended conguration was 25% lower than the equivalent xed wing.
Wind tunnel experiments have indicated that the aerodynamic performance of the wing is
deteriorated as a result of the lumpiness of the skin.
Another technique to induce morphing by altering the span made use of scissor mechanisms.
Bharti et al. [35] tested a platform using scissor mechanisms actuated by a DC motor and
screw. The concept was devoted to the change in the span and the sweep angle of the wing,
and it was reported that a span change of 55% was achieved. Joo et al. [36] performed
an optimization analysis vis-a-vis the ideal location of actuators inside the structure. da
Costa Aleixo [37] also created a wing that could change the chord length and span indepen-
dently, but the weight penalty was high due to the usage of servo motors and transmission
components.
2.5.2 Chord Length Change
Chord length changes are one option to increase the wing planform area and are commonly
used in xed wing aircraft where these changes are performed via the extension of the leading
and trailing edge aps.
Reed et al. [3] used partial ribs to form a structure similar to two interpenetrating combs,
16
as shown in Figure 2.4.
Figure 2.4: Reed's concept of interpenetrating partial ribs (After [3])
Actuation was performed by DC motors and lead screws. While in the compressed state,
there are little gaps between the ribs, in fully extended state these gaps become signicant.
This became a problem, since the skin of the wing must be supported at all times in order to
maintain its airfoil shape. Reed et al. have researched the use of lled honeycomb structures
that have high stiness in one plane, but are easily deformed on the perpendicular plane.
2.5.3 Sweep Angle Variation
The variation in sweep angle is commonly seen in birds during fast descents. This inspired
aircraft designers to sweep the wings of airplanes. The simplest way to imagine a swept-back
wing is to imagine a xed wing being pivoted backwards about its root. The wing being at
an angle to the direction of ight, the streamlines are subjected to a thinner airfoil prole,
as discussed in detail in Ref. [38]. Actively changing the sweep angle has been successfully
implemented in many military aircraft, such as the F-14, F-111 and the B-1. The pivoting
mechanism brings a few challenges: it is typically heavy as a result of its complexity, it
experiences high point loads about the pivoting points and requires elaborate maintenance.
Neat et al. [32] designed his prototype to be able to achieve sweep changes via two electrome-
chanical actuators as part of a 3 bar mechanism. Another attempt in achieving variable
wing sweep was done by Mattioni et al. [39] who made use of bi-stable composite spars.
The spars were designed to snap into a second stable position if a bending moment was to
be applied. The area which they were to snap about was to act as a hinge. However, this
raised the problem of fatigue occurring at the snapping point.
17
2.6 Out-of-plane Transformations
2.6.1 Airfoil Camber Change
It is known that dierent airfoil proles provide dierent amounts of lift and drag. As well,
the angle of attack further changes the lift and drag coecients. It is of no surprise to
see a lot of research being performed in the area of airfoil camber change. Monner et al.
[4, 5] designed a system composed of plate-like elements connected by revolute joints. The
concept is shown in Figure 2.5. What is interesting about this design is that all linkages
were actuated by a single mechanical actuator. Monner et al. also presented a variation of
the initial kinematic system; in the redesigned concept he made use of an additional lever.
The result was that the loading on the large joint was reduced by 90%. This concept allows
the camber to be varied along the span of the wing as to vary the lift distribution on the
wing. It was reported that the root bending moment can decrease by 12-15% as a result of
the lift distribution reconguration.
Figure 2.5: Span-wise camber variation of Fowler aps (After [4, 5])
Poonsong [40] also designed and built a wing making use of hinged rib segments. This
wing has low twist stiness, as only one spar was used. As a result of the pneumatics
and the heavy rib elements, there is a high weight penalty associated to the design. The
model was covered in latex skin, which caused a drag rise as a result of its low stiness.
Saggere and Kota [41, 42] designed a wing that could achieve camber change as a result of
the actuation of the leading and trailing edges. The change in geometry was performed by
18
shape memory alloys and piezoelectric actuators, and the motion was further amplied by
an internal mechanism.
Another concept called the belt-rib was proposed by Campanile and Sachau [43]. They
proposed a type of rib containing inner spokes joining the top and bottom surfaces of the
airfoil. The camber change was performed by the contraction of these. The constructed
prototype proved to be light and sti, and as a result promising to be a good candidate
for a future morphing wing. Diaconu et. al [44] made use of bi-stable plates to create a
morphing wing via camber change. The bi-stable polymer is connected to the rear spar and
hinged to the airfoil surface. By actuating the bi-stable plates the airfoil shape goes into
a second stable position. A clear disadvantage of this system is the fact that it only oers
two discrete shapes, rather than a smooth continuous shape change.
Wang et al. [45] proposed a concept using piezoelectric actuators to achieve camber alter-
ation. The piezoelectric actuators were placed between the two exure block vertebrae
which converted the small induced strain of the piezo actuators to local movement of the
trailing edge of the airfoil. It was concluded that the small strain of the piezo actuators
was insucient to induce a large enough deformation of the airfoil and a second approach
was considered. In their second approach, the use of mechanical ampliers was considered
in order to provide higher strains. This, however, had to be discarded as a result of the
high stresses in the amplication mechanism. Shape memory alloys were also tested in the
DARPA Smart Wing program [45]. Two SMA linear actuators were placed in an antago-
nistic setup: on one side to the top and bottom of the rear spar, and the tips were joined
together close to the trailing edge. It was reported that the system could not provide a
sucient deformation of the trailing edge as a result of the center sheet compression.
Soa et al. [6, 9, 46, 47, 48] proposed a design based on the antagonistic exural unit cell
(AFC) to minimize the energy loss as a result of the center sheet compression. The concept
made use of two corrugated sheets placed between the SMA ribbons and the center sheet,
as depicted in Figure 2.6. The result was a highly exible beam in-plane with the actuators,
yet very sti in the out-of-plane direction. With respect to the slow cooling of the SMA
actuators, Soa recommends this design to be used in order to change the overall shape of
the wing but not for actuation of control surfaces, where speed is of high importance.
19
Figure 2.6: The antagonistic exural unit cell (After [6])
Berton [49] made use of SMA wire to actuate the trailing edge close to the wing tip. The
result was that a section of the trailing edge could be moved towards the back of the aircraft,
essentially resulting in an in-plane shape of a raked wingtip. The problem with this system
is the associated weight penalty as a result of the complexity of the mechanism.
2.6.2 Lateral Wing Bending
NASA [50] performed a study on hyper-elliptical wings, which are representative of shapes
seen in many bird wings. All except one variation of the HECS wing achieved higher lift-to-
drag ratios as compared to the baseline wing, which had an elliptical planform and a raked
tip. It was concluded that the HECS wings making use of various wingtip congurations
promise a high aerodynamic eciency.
By simplifying the problem, we could look at straight wings with an out of plane bending
in the span-wise direction. Wiggins et al. [51] conceptualized a scissor mechanism that
could induce an out-of-plane curving of the wing in the span-wise direction by using only
one actuator. Another attempt was done by Manzo and Garcia [52] who tried morphing a
wing in a similar fashion but this time, using a nger-type mechanism and making use of
SMA tendons and DC motors as actuators.
A highly detailed analysis of out of plane morphing was performed by Lockheed Martin
[53], as shown in Figure 2.7. Their concept made use of a folding mechanism to reduce
20
the wing span and eectively the wetted area of the wings. The actuation was performed
by electrical motors and intensive research was performed on the seamless skin material in
order to allow for a high degree of folding, which was reported to be 130 degrees. Initially,
an elastomeric sock made out of fabric reinforced silicone material, was proposed. This
material would have covered the entire wing. In the end, to simplify the manufacturing
process it was decided that only the folding areas and the leading edge should be covered
with the elastomeric material. Lockheed Martin have performed wind tunnel testing as well
as successfully ight tested their prototype.
Figure 2.7: Lockheed Martin morphing UAV (After [7])
2.6.3 Wing Twisting
From a structural point of view, by moving the loading closer to the root a smaller bending
moment about the roll axis could be achieved. Wing twisting can be carried out in two
ways:
1. geometric twisting uses the same airfoil prole along the span, but the local angle of
attack is varied
2. aerodynamic twisting varies the airfoil prole along the span of the wing
During the DARPA Smart Wing 2 project [8], a concept using an eccentuator was investi-
gated, as shown in Figure 2.8. The eccentuator originates in the 70s [54] and is a curved
21
beam that can be rotated at the root to determine the direction in which it is curving
(up/down/forward/backwards as well as combinations of them). The actuation of choice
was an ultrasonic motor coupled to a 5.5:1 gearbox. Eectively, the two eccentuators in the
wing form the two spars which the ribs sit onto. By independently rotating the eccentuators,
each rib changes its local angle of attack, and results in a wing with a geometric twist.
Figure 2.8: Morphing wing using the eccentuator concept (After [8])
Majji [55] constructed a wing which made use of four concentric tubes independently at-
tached at dierent points along the span in order to provide the twisting action to the four
wing sections. This wing made use of an elastomeric skin. Stanford et al. [56] used wing
twisting to control the roll of a small size UAV. The actuation was performed by torque
rods that ran along the span of the wing. They were connected to the wing with bushings to
allow them to rotate. The tips of the torque rods were bent at a 90 degree angle backwards
forming an L-shape rod which was connected to a exible membrane similar to what we see
in xed wing control surfaces. Their numerical analysis showed that the concept suered
from a severe drag penalty.
Soa et al. [47] and Elzey et al. [48] induced wing twist by controlling the various vertebrae-
based ribs along the span of the wing. By having dierent ribs undergo camber change, a
twist of the wing was developed.
22
2.6.4 Airfoil Prole Adjustment
Changing the airfoil prole is another way of changing the lift and drag characteristics of
a wing. Airfoil shape morphing requires the main camber line to not be changed. Austin
et al. [57] designed a truss-like structure composed of mechanical ball-screw actuators to
induce airfoil shape changes. They performed theoretical investigation of the concept by
determining the optimal airfoil shape under various ight conditions as well as built an
adaptive rib with 14 actuators. A dierent approach was taken by Joo and Sanders [58]
who created a system that was relying on both internal actuators as well as a compliant
wing skin for a 2 way actuation.
With regards to the implementation of shape memory alloys in airfoil adjustable systems,
Strelec [59] has successfully demonstrated a working model which made use of internally
connected SMA wires. They carried out an optimization study in order to determine the
optimal positioning of their smart actuators. Dong et al. [60] used SMA springs to modify
the airfoil prole. The springs were placed between the wing box and each of the top and
bottom surfaces. By changing the length of the springs, they managed to locally adjust the
distance between the wing box and the top/bottom surfaces.
23
Chapter 3
Conceptual Design of Morphing Wings
for Unmanned Aerial Vehicles
3.1 Design Specication of UAV
Design specications of the baseline UAV are provided in Table 3.1. The specications are
similar to a Shadow 200 UAV. They were selected accordingly, as to facilitate the comparison
of the results from the performance analysis, to a currently produced UAV. In this chapter,
we make use of these design characteristics to develop a novel morphing scheme to enhance
the performance of the considered UAV. The detailed geometry of the UAV will not be
disclosed because of condentiality issues. The loading analysis section and Section 3.5, do,
however, contain some information about the span and weight of the UAV, as specied by
Defence Science Organization National Laboratories of Singapore.
Length [m] 3.40
Wingspan [m] 3.89Aspect Ratio 7.07
Airfoil NACA 4415Weight [kg] Empty: 75 kg / Max: 150 kgSpeed [m/s] Loiter: 30.6 / Cruise: 46.1 / Max:
60.5
Table 3.1: UAV specications
24
3.2 Preliminary Concepts
The approach adopted in the current morphing wing design is depicted in Figure 3.1 (and
Figure 1.6).
Figure 3.1: Detailed Morphing Wing Design Methodology
Table 3.2 presents an assessment of the current available actuators. The table was compiled
using an evaluation scheme from 0 to 5, 5 being the highest (best) rating. It is based on
previous implementation eorts and observations, as stated in the literature. It is worth
noting that the table was contructed based on experience, and knowledge of these systems.
In aerospace applications, it is necessary to ensure reduced weight, fast response and reduced
complexity. These will be typically weighted in the design selection matrix. However, the
table shows clearly that shape memory alloys, without any weighting parameters, are by far
the most appropriate for morphing wing structures in small UAVs travelling at maximum
speeds of approximately 200 km/h. In cases involving high speed UAVs it may not be
possible to actuate the wing using shape memory alloys. This is because of the large loads
excerted on the aircraft. In the following, we provide conceptual designs for both low and
25
high speed UAVs.
ActuationForce
Displacement Response SystemWeight
SystemComplexity
Total
Mechanical 5 4 3 0 3 15Hydraulic 5 4 3 0 2 14Pneumatic 5 3 3 0 2 13Piezoelectric 5 0 5 1 3 14
SMA 3 3 3 5 5 19
SMP 0 3 1 2 5 11
Table 3.2: Actuator selection
3.2.1 Adaptive Airfoil Concept
The rst concept was developed out of familiarity with linkages and mechanism design. The
concept was intended for use in large scale UAVs. In the actuator selection, priority was
given to hydraulic actuators, as these have been successfully implemented in many of the
current aircraft control systems. The idea behind this concept revolved around the concept
of planform area variation. This variation was the result of an airfoil prole change. The
airfoil prole can be changed as a result of the extension of the hydraulic actuators, which
cause both the leading and trailing edges to move away from the wing spar, as shown in
Figure 3.2, 3.3 and 3.4. If all actuators are extended, the surface area of the wing increases,
while the aspect ratio decreases.
26
Figure 3.2: Adaptive Airfoil Concept: Span-wise section of the wing
Figure 3.3: Airfoil change as a result of chord length variation
If the actuators closer to the root are extended more than the ones closer to the tip of the
wing, a tapered wing can be obtained. If we keep the leading edge xed to this swept back
shape and make the trailing edge parallel to it, a swept-back wing is obtained.
27
Figure 3.4: Top view - Four planform congurations
There are several problems associated with this concept. The main one is the large weight
penalty as a result of heavy actuators, and a high density of the wing as a result of many
overlapping surfaces. The system is limited to the use of a single spar. Dividing the leading
edge morphing mechanism to one spar and the trailing edge morphing mechanism to the
second spar, would generate twisting of the spars. As a result, the entire load must be
carried by one spar. Even so, in order to minimize the twisting moment it is recommended
that the leading and trailing edge actuators be extended in such a manner that the lift
distribution will not cause excessive twisting of the spar. In addition, the surface of the
wing is of concern, as it may aect the aerodynamic performance. Without a skin covering
the wing, the discontinuities of the surfaces could perturb the airow leading to increased
drag, and even early stalling as a result of premature ow separation. If the wing were to
be covered with an elastomeric skin, there is the risk of pinching the skin by two adjacent
surfaces, which could damage the wing.
28
The above design suered from the following shortcomings:
1. large weight penalty,
2. limited to one spar per wing; this could become a problem for high loading scenarios,
as the load could not be distributed on multiple spars,
3. leading and trailing edge mechanisms not fully independent. The localized centers of
pressure of all wing sections should always be aligned with the spar's neutral axis,
such that the twisting moment would be kept to a minimum,
4. discontinuities in the airfoil prole which could perturb the airow,
5. problematic implementation of skin.
3.2.2 Airfoil Tracer Concept
Continuing with the idea of airfoil change, the second concept emerged. The idea behind
it was to adjust the curvature of the upper and lower surfaces in order to achieve optimal
performance at dierent speeds. Adjusting the curvature of the two surfaces would change
the air ow pattern around the airfoil. By making use of a thick airfoil, high lift could be
generated at low speeds, while thin airfoils would be preferred for high speed ight.
The wing followed the classical rib and spar topology, and had the actuators mounted on
each spar. Each of the top and bottom surfaces were to be constructed out of a exible beam
connected at both ends to the leading and the trailing edges of the wing. The actuators
would move the rollers at dierent positions in the plane of the airfoil, pushing against the
beam and causing it to bend. One can imagine the shape of the bent beam to resemble a
spline having 4 points placed on it, as shown in Figure 3.5.
29
Figure 3.5: Section showing the exible beam deected by the 4 actuators, the corrugatedmaterial and exible skin
This system requires a skin to be wrapped around it. The challenge is to use a exible skin
around the airfoil prole, but it must be sti enough between the ribs to prevent sagging.
The solution was to place corrugated material between the ribs and the exible skin. This
concept allows for dierent airfoil shapes to be obtained and it may be feasible to obtain a
change in airfoil proles along the span direction.
The main problems with this concept are that the changes are limited to the airfoil prole
change. In addition to this, the positions of the two rollers are not fully independent. If one
imagines just one roller to push against the beam, one must realize that the second roller
must be raised to just reach the beam. If the rst roller was to bend the beam more, the
second roller would have to move as well. Perhaps the main problem, however is the weight
penalty from the hydraulic actuators and the auxiliary hydraulic system.
Due to all of the above mentioned problems and the relatively small benets, this concept
was discarded.
3.2.3 Variable Morphing Wing Concept
The Delta Morphing Concept marked the point where airfoil changes were abandoned in
favor of planform changes. As previously stated in Chapter 2, the wetted area does have a
signicant impact on the performance of a wing. This concept was designed to allow a UAV
30
to take on very dierent mission proles, allowing it to be fast and maneuverable, while
beneting from ecient ight.
The concept is based on a 5 bar chain. For high speed conguration, the wing would be
similar to a delta wing, as shown by Figure 3.6 (a). This conguration provides the UAV
with a large surface area required to generate lift at high altitudes, as well as have the
typical benets of a delta wing at high speeds.
The next conguration depicted in Figure 3.6 (b) is intended for ecient cruising at lower
altitudes. In this conguration, the tip of the wing is moved forward such that the trailing
edge becomes perpendicular to the moving direction, while the leading edge does maintain
a certain sweep angle. The reasons for this selection are:
• it promises a high aerodynamic eciency, as a taper ratio of approximately 0.3 oers
an aerodynamic advantage as discussed by Ref. [38, 61],
• it allows for a streak to be formed in order to further increase the lift closer to the
root. Strakes have been successfully been implemented in aircraft, such as the F-16
[62, 63],
• it provides a higher lift distribution closer to the root of the wing, and decreasing to-
wards the tip. The advantage is that the bending moment about the root is decreased.
Since this conguration is similar to a straight wing, we are expecting that the L/D ratio
to be high, making the wing suitable for cruising, but less agile and maneuverable. Moving
the tips farther towards the forward direction, the streak is retracted inside the fuselage,
while both the leading and trailing edges become tilted towards the front of the aircraft,
forming a forward swept wing with a reduced area, as depicted in Figure 3.6 (c). Forward
swept wings are known to provide high L/D ratios, and allow for high maneuverability as
a result of their aerodynamic instability. More information about this topic is available in
Ref. [64].
31
Figure 3.6: Sample wing congurations
One of the the main reasons why forward swept wings are not commonly used is that the
airow tends to lift the tips of the wing. As the tips are lifted, their local angle of attack
is increased, which further increases the lift distribution towards the tips. As a result, an
excessive wing twisting moment in generated, which could lead to wing breakage. This can
be avoided with the use of a torsionally sti wing box together with a wing twist in order
to decrease the lift distribution at the tips.
One of the problems of this concept is the potentially high loads generated at the pivoting
points, especially at the ones close to the root. A diculty with this concept is the de-
ployment of a light and sti structure which allows for the surfaces to accommodate large
displacements with dierent congurations. This would most likely require extensive use
of composite, cellular materials and cellular materials. As far as the weight penalty is con-
cerned, a single actuator could be used and implicitly not carry a large weight penalty.
Pending a detailed analysis, although the system carries a weight penalty, it is a feasible
alternative for a morphing wing.
3.2.4 Adaptive Octahedron Concept
The selected concept is a novel idea that makes use of the Adaptive Octahedron Cell (AOC)
in order to provide a wide selection of possible shape changes. It diers from all the other
ones proposed by this thesis. It is fully actuated by SMAs and it combines both planform
and airfoil prole changes. Furthermore, it provides a large number of independent shape
changes. The system relies on the AOC unit cell which, is repeatably used in order to create
32
the wing spars.
The idea behind the concept is to have two adjacent unit cells share a common point about
which they can pivot in two directions independently. The actuation is ensured by the
4 SMA wires which connect the 8 points, that reside on the mid-plane of each unit cell.
By simultaneously heating two adjacent SMAs, the structure pivots as it is pulled by the
contracting SMAs. In the selection of the joint, two options were considered: U-joint and
ball joint. By using a ball joint, we allow the structure to pivot in both directions, but
more importantly it is free to rotate. Rotation can occur as a result of a slight actuation
mismatch between the SMA wires. Should this happen, the adjacent cells would twist,
risking an entanglement of the wires. A U-joint solves the problem of accidental twisting
by constraining the system and not allowing it to rotate about the spar's neutral axis. A
ball joint was chosen to connect the ribs to the deformable spars. This joint allows the rib
to rotate about the joint, but constraints any other movement, as shown in Figure 3.7.
Figure 3.7: Octahedral unit cells forming a spar, coupled to ribs via ball-joints
Let us imagine a cantilever beam that is formed by connecting several unit cells together.
If the bottom SMA wires are heated, they would contract. The pivoting motion about the
common point, would strain the top wires and cause the beam to bend downwards. Similarly,
should the top actuators be heated, the beam would curve upwards. The same holds for
the actuators on the sides. They would cause the beam to bend forwards/backwards. Now,
let us imagine having 2 cantilever beams of this sort and use them as spars. If both are
33
simultaneously bent in plane, a sweeping motion of the wing is attained, as shown in Figure
3.8.
Figure 3.8: Top view showing the two spars. Left - straight wing; Right - backward curvedwing
The area of a straight wing in morphed state, S, can simply be calculated as being:
S =b · c2
· cos (β) (3.1)
where b is the aircraft wing span, c is the airfoil chord length and β is the sweep angle, as
shown in Figure 3.9.
34
Figure 3.9: Straight wing in unmorphed and morphed states
To deform the wings upwards, both beams need to be deformed upwards as well. The same
applies for the downwards deformation direction. A more interesting shape occurs when one
beam is curved upwards, while the other one is curved downwards. Such a conguration
would yield a wing with a geometric twist capability. If more than 2 spars are to be used,
an aerodynamic twist can also be achieved, as shown in Figure 3.10.
35
Figure 3.10: Three spar structure used for the airfoil prole variation along the span-wisedirection
At each location along the span, the airfoil mean camber line would change as a result of
the varied deection of the three spars. Eectively, the mean camber line is an interpolated
spline of the three unit cell centers at each location along the span. By varying the degree
with which the spars are bent, even combinations of geometric and aerodynamic twists can
be obtained together with in-plane and out-of-plane shape changes.
To summarize, this concept allows the following basic shape changes:
• in-plane curving of the wing as a result of heating the forward or backward mounted
SMAs
• out-of-plane bending as a result of heating all the top mounted, or all bottom mounted
SMAs
• geometric twist as a result of one spar curving upwards while the other one is curved
downwards
36
• aerodynamic twist for systems with at least 3 spars as a result of independently curving
the beams in the upwards and downwards direction
In addition to these, combinations of the previously mentioned basic shape changes can be
made in order to obtain complex wing surfaces.
3.3 The Selected Design: The Adaptive Octahedron Con-
cept
In the above sections we have discussed four dierent designs. These designs are evaluated
in Table 3.3 on a 0 - 5 scale, with regards to functionality, aerodynamic performance, added
weight penalty, degree of complexity and reliability. Based on the results of the table, it is
clear that for the selected UAV, the AOC concept is the most suitable concept.
Functionality AerodynamicPerformance
WeightPenalty
Degree ofComplexity
Reliability TOTAL
AdaptiveAirfoil
1 2 0 1 2 6
AirfoilTracer
0 1 1 1 1 4
VariableMorphingWing
3 3 2 1 3 12
AdaptiveOctahedron
4 5 5 1 4 19
Table 3.3: Design selection matrix
3.4 Development of Prototype
Figures 3.11 and 3.12 show a prototype of an AOC spar with 3 unit cells. The prototype
was created to test the basic functionality of the structure as well as to observe the weight.
The prototype was built using 3 mm diameter brass bars, each with a length of 8 cm. The
U-joints are stainless steel, and were brazed to the octahedral unit cells.
37
Figure 3.11: Prototype of an AOC spar
Figure 3.12: Prototype showing the exibility of the unit cells
The morphing structure based on the AOC promises a low weight penalty as its overall
structure follows the conventional spar-rib structure. It relies of the use of lightweight
SMA for actuation. The mass of the prototype was only 241 grams, giving a ratio of
602.5 grams/meter of spar, even with the use of relatively heavy stainless-steel U-joints.
For a span of 2.9 meters, the mass of the 2 spars should be less than 3.5 kg. The initial
requirements were that the wing should not exceed 4.4 kg; this leaves 900 grams for the
SMA actuators, the composite ribs, and the skin. With a detailed design, better materials
choice and optimization, the mass of the system can be reduced signicantly. For instance,
a CAD model based on 4 mm diameter Al-6061 bars, with a span of 38.8 cm, and 2 mm
actuators reported a mass of only 180 grams for each spar. For a span of 2.9 m, the result
is a structure of only 2.7 kg. In this case, the composite ribs and skin should not exceed 1.7
kg. Based on this weight analysis, the concept is considered feasible.
38
The biggest problem is related to the cyclic degradation of the shape memory alloys. Should
this happen, the wings will start curving upwards in-ight, as well as the degree of actuation
will be decreased. Pending the development of a new class of SMAs with improved resistance
to degradation, it is believed that this system is a good choice for wing morphing as it oers
a vast variety of independent shape changes.
3.5 Conditioning of Shape Memory Alloys
Shape memory alloys suer from degradation as a result of cyclic loading. The recoverable
strain decreases, and it has been proven that it reaches a plateau after approximately 120
cycles, as shown in Figure 3.13.
Figure 3.13: Shape memory alloy degradation (After [9])
A raw SMA actuator used in a smart structure as part of a morphing wing would cause
the wing to lose its ability to morph when degraded. This should be avoided, since the
degree with which the wing is morphed changes with time resulting in a system with a low
predictability. In order to avoid this from happening, SMA actuators must be conditioned
prior to their implementation in the structure.
The conditioning of the SMA actuators was carried out with a specially designed pro-
grammable controller for an antagonistic setup, as shown in Figure 3.14. Two SMA ribbons
were connected head-to-head with their ends constrained to a rigid support. One of the
ribbons was previously pre-strained. The ribbons were heated by means of custom made
39
Teon-coated nichrome wire heaters that were wrapped around the ribbons. Each ribbon
was heated as soon as the other one cooled down to room temperature. By repeating this
cycle, the SMA ribbons reached the plateau, where the recoverable strain remains approxi-
mately constant.
A programmable controller was built that could deliver up to 1.25 KW of power to each of
the heaters. The logic side of the circuit made use of the Atmega 168 processor, while the
power controller contained IRF530 MOSFET transistors to control the high power relays.
Figure 3.14: Automated antagonistic setup for SMA conditioning
This circuit was designed by the author to deliver AC power from a variable voltage trans-
former. An earlier version of the controller was designed to provide DC heating. Although
it performed well in testing other SMA-based structures, it could not be used in the present
setup as it would have required an expensive DC power supply. The automated setup proved
to be a time saver as it handled the conditioning of the SMAs. Each full cycle lasted 3-5
minutes and the SMA actuators were conditioned with up to 400 cycles. In addition to
this, its versatility allowed it to control the morphing of other prototypes; the only changes
required were the reprogramming of the micro-controller, and a voltage adjustment of the
transformer.
40
Chapter 4
Aerodynamic and Load Analysis of
Morphing Wing
The aerodynamic analysis focused on the in-plane morphing of the selected concept. How-
ever, the study of out-of-plane twisting and bending was also performed, and the results are
presented in the following sections. The in-plane sweeping action can further be split into
3 categories:
• Case 1 - morphing of a straight wing
• Case 2 - morphing of an initially swept wing
• Case 3 - partial morphing of 1/3, 1/2 and 2/3 of the wing
4.1 CFD Modeling
4.1.1 Discretization of Morphed Wing
The grid generation was performed in GAMBIT. In order to keep the errors due to dis-
cretization consistent, a structured mesh was selected. Previous tests were performed on
meshed wings using tetrahedral elements rened around the volume of the wing via sizing
functions. This method was believed to provide good renement all around the wings and
41
a smooth transition from the rened region toward the course one. After analyzing the re-
sults of the simulations, it was agreed that the boundary layer can be better approximated
by hexahedral elements. In addition to this, tetrahedral elements are known to be highly
sensitive to the aspect ratio. Since the X and Y directions (the airfoil prole is in the XY
plane) need to be highly rened to provide good approximation of the airfoil prole and of
the boundary layer, the span-wise renement would have to be similarly rened in order to
maintain the low aspect ratio of the tetrahedral cells.
According to Ref. [65], the advantage of triangular/tetrahedral elements over the quadri-
lateral/hexahedral elements is that when the length scale of the ow is large, a mesh with
fewer cells can be created because triangular/tetrahedral elements allow easy adaptation
from a rened region into a coarse region, while quadrilateral/hexahedral elements would
be placed in regions where added accuracy would not aect the overall outcome of the
problem. Quadrilateral/hexahedral elements do however have an important advantage over
the triangular/tetrahedral elements. It appears that for simple geometries, where quadri-
lateral/hexahedral elements can suciently approximate the geometry, they do oer a more
stable solution.This is due to the fact that triangular/tetrahedral elements are sensitive to
skew angles caused by high aspect ratios.
Quadrilateral/Hexahedral elements are capable of being stable even at high aspect ratios.
For problems with simple geometries, they are desirable because a few high aspect ratio
quadrilateral/hexahedral elements would be capable of replacing a much higher number of
triangular/tetrahedral elements.
The wings in this analysis have a taper ratio equal to 1, no aerodynamic twist and no
geometric twist. We are expecting the span-wise component of the ow to be considerably
smaller than the ow components in-plane with the airfoil. As a result, less renement is
required in the span-wise direction. Since hexahedral elements can be stable even at high
aspect ratios, they were selected for our mesh. The resulting mesh contained 720835 cells.
More detailed information on the subject of modeling and meshing an airfoil in GAMBIT
can be found in Ref. [66].
In order to minimize the boundary eects on the airow near the wing, the control volume
was sized accordingly, as shown in Figure 4.1.
42
Figure 4.1: Sample structured mesh for curved wing. Units of airfoil chord length (c)
A brief summary of the meshing procedure is presented below:
• The support plate is split into 6 faces. All resulting edges are meshed. Radially all
edges are split into 50 sections with nodes distributed according to a geometric series
with a growth ratio of 1.2. The top and bottom sections of the leading edge are split
into 30 intervals with a growth ratio of 1.06. The upper and lower edges behind the
leading edge are split into 30 equal sections.
• The rst volume region was created by sweeping the 6 previously meshed faces along
the leading edge of the wing.
• The 7 resulting faces on the wingtip plane are meshed and swept in the span direction,
up to Z = 3.89 m, to create the second volume.
The wings in cases 1 and 2 were split in 3 surfaces: upper, lower and wingtip. The partially
morphed wing from, case 3, had both the upper and lower surfaces divided in two: the root
section which is xed, and the tip section which allows shape morphing.
43
4.1.2 Details of Model
All the surfaces lying on the wing and on the support plate were meshed as wall regions. All
other faces bounding the control volume were used as pressure far eld. The simulations were
performed in Fluent 6.3.26 using the double precision 3D solver. The results were obtained
from running steady-state simulations at constant free stream velocity and iterating through
angles of attack between 4 and 12 degrees in steps of 4 degrees.
One of the most important decisions before running the simulations was to select the right
turbulence model. The Spalart Allmaras is a one equation turbulence model that was
developed for the use in the aerospace industry in problems involving wall-bounded ows,
such as airfoils and wings. Being a 1-equation model, it oers at least a theoretical advantage
in computational speed [67], as compared to the k − ε and k − Ω 2-equation models [68].
The Spalart Allmaras [69] was designed to solve a modeled transport equation for the
kinematic eddy viscosity. From Ref. [69] we nd important information about how the
Spalart Allmaras model was applied in Fluent. While the original model presented in Ref.
[70, 71, 72] was designed as a low Reynolds number model that required the viscous region
of the boundary layer to be solved, the way it is used in Fluent diers from that used in
the previous references. The Fluent application uses wall functions, making it capable of
working with coarse meshes.
Another advantage is that the gradients close to walls are much smaller than in the case of
the generic model. This advantage implies that the model is less sensitive to numerical error
[69]. As a warning, Ref. [69] indicates that this model is still new and 1-equation models
are often criticized for not being able to quickly accommodate changes from wall-bounded
ow into free ow. Ref. [67] presents a comparison between the Spalart Allmaras model
and the k − ε model. The conclusion is that the Spalart Allmaras model requires the least
computational time, while the k− ε model is slower; depending on the variation (standard,
realizable, RNG), an additional small variation of 10-15% is expected. The Reynolds Stress
Model [73], while being the most advanced model oered in Fluent and desirable for compli-
cated problems, requires about 50-60% more computing time per iteration than the models.
In addition, the memory requirement increases by about 15-20%. As far as the convergence
is concerned, the RNG model comes with the warning that it is more sensitive to time
dependent eects, which can make it less stable. However, if the convergence is achieved,
this model is capable of modeling vertex shading more accurately, as a result of its increased
sensitivity. The Reynolds Stress Model [67] converges slower because of the strong relation-
44
ship between the Reynolds stresses and the mean ow. We performed simulations using the
above-mentioned models before selecting the nal turbulence model. While results varied,
the Spalart Allmaras seemed to be very stable yet model the turbulent eddies well. The
verication of this model is presented in the section of this report that is concerned with
the analytical verication of our simulations. The air stream was assumed to be an ideal
gas with a constant Cp, thermal conductivity, and molecular weight. The viscosity was
assumed to follow Sutherland's Law [74]. As stated by Fluent Inc. in their tutorial entitled
Modeling Compressible Flow over an Airfoil [75], when dealing with compressible ows it
is recommended that the operating pressure to be set to 0 Pa in order to minimize the errors
caused by pressure uctuations. The air speed was considered to be equal to approximately
42.7 m/s, which translates into a Reynolds number of 1.55x106.
4.2 Analysis of Results
The simulations were used to measure the axial forces on the wing. In order to compute
the drag and lift forces, the following transformations were used:
CD = CAcos (α) + CNsin (α) (4.1)
CL = CNcos (α) − CAsin (α) (4.2)
The in-plane morphing of a straight wing is shown in Figure 4.2. The decrease in planform
area, as a result of morphing, is accompanied by a decrease in lift and drag coecients, as
shown in Figure 4.3 and Table 5.1. This decrease was observed when comparing wings at
identical angles of attack. At low angles of attack, the lift-to-drag ratio of curved wings
is higher when using the CL value as reference. Even based on the angle of attack as a
reference, the ratio does not decrease signicantly as a result of the wing curvature. The
L/D ratio drops by 7.8% when comparing the case of the straight wing and the wing being
curved by 30 degrees at 4o angle of attack. Considering that the accuracy of the simulations
is approximately 4.5%, a clear conclusion cannot be drawn, as the numerical error is close
to the L/D ratio change. However, considering that there is a consistent trend of decreasing
L/D as the wing is curved more, one can see that there is a very small decrease in L/D. This,
45
however, is predicted by theory and there is a simple explanation as to why this happens.
In the case of a straight wing, the ow over the wing has almost zero span-wise component;
the only area where a span-wise component exists is close to the wingtips.
Figure 4.2: Straight wing in-plane morphing
Figure 4.3: Drag and lift coecients for in-plane morphing of straight wing
In the case of a curved wing, the ow encounters the out-of-plane curvature of the airfoil
together with the in-plane curvature as a result of morphing. The result is a higher span-
wise component of the ow, as shown in Figure 4.4. We must realize that only the free-
stream component around the airfoil is responsible for the generation of lift. By having
it decomposed into a smaller free-stream component around the airfoil and a span-wise
component, the lift decreases. It is believed that the small decrease in L/D ratio can be
further reduced with the addition of fences, especially on the top surface of the wing. Fences
impede the formation of the span-wise component of the ow [76].
46
Figure 4.4: Span-wise components of ow. Note: the curved wing experiences a strongerspan-wise component which develops closer to the root of the wing.
Figures 4.5 and 4.7 shown the morphing of a swept wing, as well as the partial morphing of
a straight wing. The results are presented in Figure 4.6 and 4.8, as well as in Table 5.4 and
5.5
Figure 4.5: Swept wing in-plane morphing
47
Figure 4.6: Drag and lift coecients for swept, morphed wing
Figure 4.7: Straight wing, partial in-plane morphing
Figure 4.8: Drag and lift coecients for straight, partially morphed wing
48
It is a well known fact that the formation of wingtip vortices decreases the aerodynamic
performance of a wing. Wingtip vortices are formed as a result of the air circulation between
the high pressure bottom surface of the wing, and the low pressure top surface. One could
only imagine that by impeding this span-wise air circulation, the aerodynamic performance
of the wing would increase. One attempt in achieving this is by testing the eects of
wing bending. This was evaluated over 4 angles: upward/downward at 10 and 20 degrees.
The plots depicted in Figure 4.9 show that the highest lift coecient is obtained from a
straight wing, while the lift coecient decreases as the bending angle increases, with higher
coecients reported for upward curvature. An interesting observation is that the L/D ratio
of bent wings is higher that the ones of a straight wing especially at higher angles of attack,
as shown in Table 5.2.
Figure 4.9: Drag and lift coecients for wing bending
Wing twisting was also considered as it was thought to decrease the formation of the wingtip
vortices and as a method to change the load distribution of the wing. In addition to this,
wing twisting can also be used as a method to control the roll of an aircraft. The results are
presented in Figure 4.10 and Table 5.3, where the eective angle of attack is the mid-span
angle of attack.
49
Figure 4.10: Drag and lift coecients for wing twisting
It can be seen that simply based on the eective angle of attack, the lift and drag coecients
are very similar to the ones of a straight wing. Even with the same L/D ratios of a straight
wing, the wing twisting causes the lift distribution to be modied. The result is a decrease
in the bending and twisting moments at the root, which in terms translates into a lighter
wing. In addition to this, it oers the ability to decrease the eective angle of attack of
the wing tip, which will decrease the tendency of wingtip stall, an advantage especially in
swept-back wings.
4.3 Analytical Verication of Results
In order to validate the CFD results, the analytical solution for a straight, unmorphed wing
was used. The lift coecient for an innite wing can be calculated using the following
formula:
CL = CLα (α− αL=0) (4.3)
where the lift line slope is given by:
CLα =Clα
1 +57.3·Clαπ·e·AR
(4.4)
50
and Oswald's eciency factor (e) is:
e =1
1 + κD(4.5)
For the assumed NACA 4415 airfoil with aspect ratio AR = 7.07, the lift slope Clα = 0.10
and the κD = 0.058, giving a span eciency factor e = 0.945.
In order to calculate the drag of the nite wing we must take into consideration the induced
drag:
CD = Cd + kC2L (4.6)
where
k =1
π · e · AR(4.7)
The airfoil drag coecient was found to be equal to 0.0078 according to the chart in Ref.
[77]. The analytical results are presented in Figure 4.3. The CL shows a deviation of 4.5%
as compared to the CFD results. The CL vs CD plot shows the identical trend in both
the CFD and analytical cases. The slight vertical shift in believed to be as a result of the
analytical solution not including the wing materials properties, and implicitly, the eect of
the skin drag which are taken into consideration in the CFD analysis; the result is a slight
underestimation of the CD.
4.4 Performance Analysis
The ultimate goal of a morphing wing is to increase ight eciency. This goal of this
section is to prove how the planform changes in the selected concept can achieve this goal.
The analysis was performed under the assumption of steady level ight and used the fuel
savings as a measure of eciency. The assumption was that fuel consumption is directly
proportional to the power required to maintain steady level ight. From basic principles we
know that
51
P = DV 2 (4.8)
where the drag force is
D =1
2CDρAV
2 (4.9)
This gives us that the power
P =1
2CDρAV
3 (4.10)
Knowing that the aircraft is in level ight, we always know the required lift required to keep
the aircraft at the same altitude. We can express CD as a function of CL, as follows
CD = CD0 + CD0,LCL + CD0,L2C
2L (4.11)
where the parasitic drag coecient CD0 is the sum of the parasitic drag coecient of the
wings plus the parasitic drag caused by the fuselage, tail, landing gear and power plant.
CD0 = CD0wings + CD0other (4.12)
According to Ref. [78], a good estimate for CD0other is about 0.025. All other coecients
were determined by tting a second order polynomial over the CLvs. CD plot. The tting
yielded the coecients presented in Table 4.1.
β CD0wings CD0,LCD0,L2
0o 0.0127 -0.006 0.057410o 0.0126 -0.0054 0.058520o 0.0123 -0.0056 0.062830o 0.0118 -0.0072 0.0725
Table 4.1: Parasitic and induced drag coecients for straight, morphed wing
Rewriting the power formula, we obtain:
52
P =1
2
CD0other + CD0wings + CD0,L
(2W
ρA2
)+ CD0,L2
(2W
ρA2
)2 ρAV 3 (4.13)
The performance based on the power requirement is presented in Figure 4.11.
Figure 4.11: Power requirement for steady level ight for straight, morphed wing
Another way of quantifying the aerodynamic performance of a wing is to look at the variation
of the L/D ratio with respect to the lift coecient, as presented in Figure 4.12.
53
Figure 4.12: Aerodynamic performance of baseline straight wing, and of morphed wings
From the above diagrams, we can see that swept-back curved wings promise higher eciency
54
at lower lift coecients. The maximum improvement in L/D ratio was observed at CL = 0.15
and was approximately 8.9% higher than the one obtained by a straight wing. This is of
great importance as this translates into small angles of attack, which are typically used by
aircraft in level ight. Bent wings also seem to yield a higher aerodynamic performance at
low angles of attack. Wing twisting does not promise a higher aerodynamic performance,
but still needs to be considered because of the previously mentioned benets. As a note, in
many simulations the wings morphed by bending or twisting did report a higher L/D ratio
than of the baseline straight wing at the same angles of attack. However, this was at the
expense of lower lift generated at the corresponding angle of attack.
4.5 Load Analysis
The loading analysis on the unmorphed and morphed wings was carried out analytically. In
the case of an unmorphed straight wing, the loading is similar to a simple cantilever beam.
As such, the lift distribution on the wing produces a bending moment about the rolling axis
and an upward shear force. In the case of a backward-curved wing, the lift distribution adds
a twisting moment about the pitch axis, which results in additional shear force on the two
wing spars.
An ideal elliptical lift distribution was used in the analysis. All calculations include a factor
of 3.8 G, as specied by the FAR23 standards. A sample UAV was assumed to have a mass
of 15 kg, with a wing span of 2.9 meters. In the analysis, the mass of the wings was assumed
to be equal to 4 kg. As such, the maximum loading on the wing will be as a result of the
wings lifting the 11 kg of the fuselage and the auxiliary components inside the fuselage. As
a result, each wing would have to carry a load of 205 N.
The circulation distribution on the wing is shown in Figure 4.13, and is given by [38]:
Γ (y) = Γ0
√1 −
(2y
b
)2
(4.14)
55
Figure 4.13: Elliptical lift distribution
The total lift generated by the wing is the integral of the lift/span distribution:
L′ (y) = ρV∞Γ (y) (4.15)
L =
ˆ b/2
−b/2L′ (y) dy =
ˆ b/2
−b/2ρV∞Γ0
√1 −
(2y
b
)2
dy =π
4ρV∞Γ0b (4.16)
The resultant lift distributions for the three morphed wing cases are presented in Figure
4.14:
Figure 4.14: Elliptical lift distributions for the three in-plane morphed cases
The lift is responsible for the span-wise shear force distribution, as shown in Figure 4.15:
56
Figure 4.15: Span-wise shear force distribution
This results in the bending moment about the roll axis, as shown in Figure 4.16, and dened
as:
M =
ˆ b/2
0
L′ (y) · ydy (4.17)
Figure 4.16: Bending moment about the roll axis
The maximum bending moment decreases as the wing morphs to a higher sweep angle. The
reason is that the span of the wing decreases at higher sweep angles. The twisting moment
occurs as the lift distribution creates a torque arm between the wing's center of pressure and
57
the neutral pitching axis as shown in Figures 4.17 and 4.18. The calculations do not take
into consideration the airfoil pitching moment as it was found to be negligible compared to
the twisting moment generated by the lift.
Figure 4.17: Wing twisting
Figure 4.18: Twisting moment as a result of the wing curvature
The twisting moment creates additional shear force loading on the two spars, as shown
by Figure 4.19. The calculations were performed under the assumption that the spacing
between the two wing spars is 12 cm, and that they equally oppose the twisting moment.
58
Figure 4.19: Shear force on spars as a result of twisting
The shear force distribution can be integrated with respect to the distance to the roll axis
over the length of the spar to provide the bending moment about the roll axis, as shown in
Figure 4.20.
Figure 4.20: Bending moment about the roll axis as a result of twisting
As a result of the high shear force generated by the twisting of the wing, the bending moment
about the roll axis is higher than the bending moment generated by the lift distribution,
excluding the eects of wing twisting. Once again, we can see the eects of the shear force
as a result of twisting. In designing a curved wing such as the one we are dealing with, the
distance between the two spars should be as large as possible in order to decrease the shear
force acting on the spars.
59
In real-life scenario, the eect of wing twisting will in fact add to the loading of one of the
spars, but in the same time unload the other one. In addition to this, the location of the
spars with respect to the center of pressure will dictate the loading on each of them.
60
Chapter 5
Conclusions and Future Work
5.1 Statement of the Problem
This study is concerned with the design and development of a novel morphing wing for a
specic UAV. The design specications for the UAV were provided by the DSO Singapore,
under contract DSOCO07212. The new morphed wing design should posses a high degree
of ight adaptability, and improved performance with a limited added weight. It is believed
that these characteristics can be obtained via the use of shape memory actuators in an an-
tagonistic fashion. Aerodynamic, structural and performance analysis should be conducted
on the novel design to validate its suitability as a viable UAV wing.
5.2 Conclusions
A novel design was proposed, using the Adaptive Octahedron Cell concept. It was selected
from three other new proposed concepts. The main feature of the selected design is its
ability to provide a wide range of shape changes, coupled with a low weight penalty. The
aerodynamic, load and performance analyses were carried out to evaluate the response of
the concept to the applied loads. Use was made of shape memory wires in an antagonistic
fashion, so that the thermal energy required is used to deform the wing, but not to maintain
its deformed shape. In addition, we carried out thermal conditioning of SMAs using a
specially designed circuitry and programmable controller. This is essential since shape
61
memory alloys degrade with cyclic loading, and the conditioning of these shape memory
wires will stabilize their actuation ability. The functionality and adaptability of the newly
devised Adaptive Octahedron Cell were emphasized through the construction and operation
of a prototype.
5.3 Thesis Contributions
The thesis contribution is manifest in four main areas:
1. development of a new conceptual design using the Adaptive Octahedron Cell that
makes use of shape memory alloys in an antagonistic fashion,
2. development of an aerodynamic model using Fluent 6.3.26 to examine the performance
of the newly developed morphed wing design, as well as evaluate its structural integrity
using the FAR23 standards,
3. development of a special designed circuitry with its associated programmable controller
to allow the conditioning of shape memory ribbons in an antagonistic setup,
4. building a prototype of the Adaptive Octahedron Cell assembly to demonstrate the
adaptability of the new morphing wing concept.
5.4 Future Work
1. This work did not consider the wing skin. This will have a major eect on the
performance of the UAV. It is necessary to employ an elastomeric exible skin that
will accommodate the morphed wing deformations in a reliable manner. However, it
is expected that some challenges will be faced in terms of their aeroelastic behaviour.
2. In typical morphing wing applications, shape memory alloys will be subjected to
combined low cycle-high cycle fatigue loading. To the author's knowledge, this has
not been investigated. The integrity of the shape memory alloys are essential for
actuating the morphed wing structure. Accordingly, future work that examines the
combined eect of low cycle-high cycle fatigue behaviour of shape memory alloys will
be highly benecial for the morphing wing studies.
62
3. A second level aerodynamic analysis may be necessary to treat the highly coupled
deformation patterns resulting from morphing deformation.
4. The structural integrity analysis were performed using traditional solid mechanics
techniques which did not allow for localized deformations at the applied loads. Future
work should examine the eect of these using nite element analysis.
5. The work focused on a small weight and low speed UAV. The work could be extended
to account for higher cruising speeds M = 0.8 with greater lift and drag loads that
can be used for more varied applications.
63
Bibliography
[1] AAI Corporation. Shadow 200 brochure, 2009.
[2] Bolkcom C. Bone E. Unmanned aerial vehicles: Background and issues for congress.
Technical report, Congressional Research Service, 2003.
[3] Pelley B. M. Havens E. Reed Jr. J. L., Hemmelgarn C. D. Adaptive wing structures.
In: Smart structures and materials 2005: Industrial and commercial applications of
smart structures technologies. Proc SPIE, 5762:132-42, 2005.
[4] Breitbacha E. Monner H. P., Hanselkaa H. Development and design of exible fowler
aps for an adaptive wing. In: Smart structures and materials 1998: industrial and
commercial applications of smart structures technologies. Proc SPIE, 3326:60-70, 1998.
[5] Monner H.P. Realization of an optimized wing camber by using formvariable ap
structures. Aerosp. Sci. Technol., 5:445455, 2001.
[6] Wadley H. N. G. Elzey D. M., Soa A. Y. N. A shape memory-based multifunctional
structural actuator panel. Inter J Solids Struct, 42:1943-55, 2005.
[7] Maja V. http://gravityloss.wordpress.com/2009/12/15/rq-170-sentinel-a-morph-wing-
aircraft/.
[8] Martin C. A. Kudva J. N. West M. N. Bartley-Cho J. D., Wang D. P. Development
of high-rate, adaptive trailing edge control surface for the smart wing phase 2 wind
tunnel model. J Intel Mater Syst Struct 2004, 15:279-91.
[9] Wadley H. N. G. Soa A. Y. N., Elzey D. M. Cyclic degradation of antagonistic shape
memory actuated structures. Smart Mater Struct, 17:025014:6p, 2008.
[10] De Fatima Bento M. Unmanned aerial vehicles: An overview. InsideGNSS, 2008.
64
[11] Krock L. Time line of uavs. http://www.pbs.org/wgbh/nova/spiesy/uavs.html,
November 2002.
[12] Bartolomeo P. Survivability initiatives for unmanned aerial vehicles (uavs). Aircraft
Survivability, 2005.
[13] Museum of Aviation. Lockheed d-21b unmanned aerial vehicle (uav). Museum of
Aviation - D-21B fact sheet.
[14] Northrop Grumman. Rq-4 hale enterprise. http://www.as.northropgrumman.com/products/globalhawk/index.html.
Global Hawk UAV manufacturer specications.
[15] Gertler J. Haddal C. C. Homeland security: Unmanned aerial vehicles and border
surveillance. Technical report, Congressional Research Service, 2010.
[16] Francis J. A. Wegener S. S. Bierly E. W., Delnore V. E. Review of the u.s. department of
energy's atmospheric radiation measurement (arm) unmanned aerospace vehicle (uav)
program. Technical report, Biological and Environmental Research Advisory Commit-
tee, 2002.
[17] Bowers A. The wright brothers and the future of bio-inspired ight, 2007.
[18] Stamhuis E. J. de Kat R. van Gestel W. Veldhuis L. L. M. Henningsson P. Hedenstrom
A. Videler J. J. van Leeuwen J.L. Lentink D., Muller U. K. How swifts control their
glide performance with morphing wings. Nature, 446:10821085, 2007.
[19] Wright O. Wright W. Flying machine construction and design of 1902 glider, 1906.
[20] Wright O. Wright W. Flying machine automatic stabilizer, 1913.
[21] Wright O. Wright W. Flying machine yaw control, 1911.
[22] Wright O. Wright W. Flying machine vertical rudders, 1914.
[23] Wright O. Wright W. Mechanism for exing the rudder of a ying machine, horizontal
rudder, 1909.
[24] Jacobs J. W. Wright O. Airplane split ap, 1924.
[25] GlobalSecurity.org. http://www.globalsecurity.org/military/systems/aircraft/f-14-
design.htm, 2006.
65
[26] Larson R. R. Afti/f-111 maw ight control system and redundancy management dis-
cription. Technical report, NASA, 1987.
[27] Reichenbach E. Y. Olney C. D., Hillebrandt H. An evaluation technique for an f/a-18
aircraft loads model using f/a-18 systems research aircraft ight data. Technical report,
NASA, 2000.
[28] Sanders B. Reich G. Introduction to morphing aircraft research. J Aircraft, 44:1059,
2007.
[29] Demonstration of Morphing Technology through Ground and Wing Tunnel Tests, April
2007. 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Ma-
terials Conference, Honolulu, Hawaii.
[30] Design of a Morphing Vehicle, April 2007. 48th AIAA/ASME/ASCE/AHS/ASC Struc-
tures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii.
[31] Tan K.T. Yeo W.K. Soa A.Y.N, Meguid S.A. Shape morphing of aircraft wing: Status
and challenges. Materials and Design, 31:12841292, 2010.
[32] Johnston C. O. Robertshaw H. H. Mason W. H. Inman D. J. Neal D. A., Good M. G.
Design and wind-tunnel analysis of a fully adaptive aircraft conguration. In: Pro-
ceeding of 45th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics and
materials conference, Palm Springs, California, page 1727, 2004.
[33] Pines D. J. Blondeau J., Richeson J. Design, development and testing of a mor-
phing aspect ratio wing using an inatable telescopic spar. In: Proceeding of 44th
AIAA/ASME/ASCE/AHS structures, structural dynamics, and materials conference,
Norfolk, Virginia, page 1718, 2003.
[34] Supekar A. H. Design, analysis and development of a morphable wing structure for
unmanned aerial vehicle performance augmentation. Master's thesis, The University of
Texas at Arlington, 2007.
[35] Lesieutre G. Browne J. Bharti S., Frecker M. I. Tendon actuated cellular mechanisms
for morphing aircraft wing. In: Modeling, signal processing, and control for smart
structures. Proc SPIE, 6523:652307-1, 2007.
[36] Johnson T. Frecker M. I. Joo J. J., Sanders B. Optimal actuator location within a
morphing wing scissor mechanism conguration. In: Smart structures and materials:
modeling, signal processing, and control. Proc SPIE, 6166:616603-1, 2006.
66
[37] da Costa Aleixo P. M. M. Morphing aircraft structures design and testing an ex-
perimental uav. Master's thesis, Instituto Superior Tecnico, Universidade Tecnica de
Lisboa, 2007.
[38] Anderson J. D. Jr. Fundamentals of Aerdynamics 4e. McGraw Hill, 2007.
[39] Potter K. D. Friswell M. I. Mattioni F., Weaver P. M. The application of thermally
induced multistable composites to morphing aircraft structures. In: Industrial and
commercial applications of smart structures technologies. Proc SPIE, 6930:693012-1,
2008.
[40] Poonsong P. Design and analysis of a multi-section variable camber wing. Master's
thesis, University of Maryland, 2004.
[41] Kota S. Compliant systems using monolithic mechanisms. Smart Mater Bull, 3:7-10,
2001.
[42] Kota S. Saggere L. Static shape control of smart structures using compliant mecha-
nisms. AIAA J, 37:572-8, 1999.
[43] Sachau D. Campanile L. F. The belt-rib concept: a structronic approach to variable
camber. J Intel Mater Syst Struct, 11:215-24, 2000.
[44] Mattioni F. Diaconu C. G., Weaver P.M. Concepts for morphing airfoil sections using
bi-stable laminated composite structures. Thin-Walled Struct, 46:689-701, 2008.
[45] Martin C. A. Hallam B. Wang D. P., Bartley-Cho J. D. Development of high-rate, large
deection, hingeless trailing edge control surface for the smart wing wind tunnel model.
In: Smart structures and materials 2001: industrial and commercial applications of
smart structures technologies. Proc SPIE, 4332, 2001.
[46] Wadley H. N. G. Soa A. Y. N., Elzey D. M. An antagonistic exural unit cell for
design of shape morphing structures. In: Proceedings of the ASME aerospace division:
adaptive materials and systems, aerospace materials and structures, Anaheim, CA,
pages 2619, 2004.
[47] Wadley H. N. G. Soa A. Y. N., Elzey D. M. Two-way antagonistic shape actuation
based on the one-way shape memory eect. J Intel Mater Syst Struct, 19:1017-27, 2008.
67
[48] Wadley H. N. G. Elzey D. M., Soa A. Y. N. A bio-inspired, high-authority actuator for
shape morphing structures. In: Smart structures and materials 2003: active materials:
behavior and mechanics. Proceedings of SPIE 2003; 5053.
[49] Berton B. Shape memory alloys application: trailing edge shape control. NATO OTAN
RTO-MP-AVT-141, 2006.
[50] Lazos B. S. Biologically inspired xed-wing conguration studies. J Aircraft, 42:1089-
98, 2005.
[51] Johnson C. O. Robertshaw H. H. Reinholtz C. F. Inman D. J. Wiggins L. D.,
Stubbs M.D. A design and analysis of a morphing hyper-elliptic cambered span (hecs)
wing. In: Proceeding of 45th AIAA/ASME/ASCE/AHS/ASC structures, structural
dynamics & materials conference, Palm Springs, California, 2004.
[52] Manzo J. E. Analysis and design of a hyper-elliptical cambered span morphing aircraft.
Master's thesis, Cornell University, 2006.
[53] Crossley W. A. Skillen M. D. Modeling and optimization for morphing wing con-
cept generation ii, part i: morphing wing modeling and structural sizing techniques.
NASA/CR-2008-214902.
[54] Musgrove R. G. The eccentuator: a new concept in actuation. In: Proceedings of the
14th aerospace mechanical symposium, US, pages 5767, 1980.
[55] Majji M. Robust control of redundantly actuated dynamical systems. Master's thesis,
Texas A&M University, 2006.
[56] Lind R. Ifju P. Stanford B., Abdulrahim M. Investigation of membrane actuation for
roll control of a micro air vehicle. J Aircraft, 44:741-9, 2007.
[57] Nostrand W. V. Knowles G. Austin F., Rossi M. J. Static shape control for adaptive
wings. AIAA J, 32:1895-901, 1994.
[58] Sanders B. Joo J. J. Optimal location of distributed actuators within an in-plane
multi-cell morphing mechanism. J Intel Mater Syst Struct, 20:481-92, 2009.
[59] Khan M. A. Yen J. Strelec J. K., Lagoudas D. C. Design and implementation of a shape
memory alloy actuated recongurable airfoil. J Intel Mater Syst Struct, 14:257-73, 2003.
68
[60] Jun L. Dong Y., Boming Z. A changeable aerofoil actuated by shape memory alloy
springs. Mater Sci Eng A, 485:243-50, 2008.
[61] Philips W. F. Mechanics of Flight. Wiley, John Wiley & Sons, 2004.
[62] Bertin J. J. Whitford R. Brandt S. A., Stiles R. J. Introduction to Aeronautics: Design
Perspective 2e. AIAA Education Series, 2004.
[63] Raymer D. P. Aircraft Design: Conceptual Approach 4e. AIAA Education Series, 2006.
[64] Hicks J. W. Saltzman E. J. In-ight lift-drag characteristics for a forward-swept wing
aircraft (and comparisions with contemporary aircraft). Technical report, NASA, 1994.
[65] Fluent Inc. Choosing the appropriate grid type. Technical report, Fluent Inc., 1999.
[66] Sibley School of Mechanical Cornell University and Aerospace Engineering. Fluent
Tutorials - Flow over an Airfoil, 2002.
[67] Fluent Inc. Computational eort: Cpu time and solution behavior. Technical report,
Fluent Inc., 1999.
[68] Wilcox D. C. Turbulence Modeling for CFD 3e. DCW Industries, 2006.
[69] Fluent Inc. The spallart-allmaras model. Technical report, Fluent Inc., 1999.
[70] Chow J. S. Bradshaw P. Dacles-Mariani J., Ziliac G. G. Numerical/experimental study
of a wingtip vortex in the near eld. AIAA, 33 (9):15611568, 1995.
[71] Allmaras S. R. Spalart P. R. A one-equation turbulence model for aerodynamic ows.
AIAA, 92-0439, 1992.
[72] Allmaras S. R. Spalart P. R. A one-equation turbulence model for aerodynamic ows.
La Recherche Aerospatiale, pages 521, 1994.
[73] Fluent Inc. The reynolds stress model. Technical report, Fluent Inc., 1999.
[74] Sutherland W. The viscosity of gases and molecular force. Philosophical Magazine
Series 5, 36:507531, 1893.
[75] Fluent Inc. Modeling compressible ow over an airfoil. Technical report, Fluent Inc.,
2007.
69
[76] Eisenmann W. W. Vorrichtung zum verhindern der ausbreitung von stroemu-
ngsstoerungen an ugzeuguegeln, 1940.
[77] Von Doenho A. E. Abbott I. H. Theory of wing sections. Courier Dover Publications,
1959.
[78] Boschetti P. Reducción de resistencia aerodinámica en el avión no tripulada de conser-
vación ecológica. Master's thesis, Univ. Simón Bolívar, Caracas, Venezuela, 2006.
70
Angleof
Attack
Straight
100Morphed
200Morphed
300Morphed
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
-40.012
-0.006
-0.479
0.012
-0.009
-0.712
0.012
-0.010
-0.836
0.012
-0.012
-1.083
00.016
0.296
17.994
0.016
0.292
17.799
0.016
0.276
17.356
0.015
0.251
16.695
40.030
0.606
19.985
0.030
0.599
19.675
0.029
0.568
19.255
0.029
0.529
18.427
80.054
0.911
16.826
0.054
0.898
16.544
0.053
0.851
16.190
0.049
0.781
15.905
120.087
1.191
13.638
0.087
1.171
13.491
0.084
1.110
13.258
0.080
1.018
12.706
Table5.1:
Lift,dragcoe
cients
andL/D
ratios
forbackward-curved
wings
71
Angleof
Attack
Straight
200Dow
nwards
100Dow
nwards
100Upwards
200Upwards
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
-40.012
-0.006
-0.479
0.012
-0.014
-1.101
0.012
-0.10
-0.782
0.012
0.002
0.145
0.008
0.0002
0.029
00.016
0.296
17.994
0.015
0.260
17.072
0.016
0.277
17.577
0.016
0.291
17.901
0.015
0.260
17.073
40.030
0.606
19.985
0.027
0.535
19.998
0.028
0.569
20.012
0.030
0.592
19.862
0.028
0.549
19.636
80.054
0.911
16.826
0.047
0.800
17.163
0.050
0.853
16.975
0.053
0.889
16.750
0.049
0.823
16.871
120.087
1.191
13.638
0.074
1.044
14.074
0.080
1.114
13.840
0.085
1.163
13.660
0.077
1.076
13.902
Table5.2:
Lift,dragcoe
cients
andL/D
ratios
forbentwings
72
Angleof
Attack(at
root)
Straight
20Twist
40Twist
60Twist
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
00.016
0.296
17.994
0.017
0.232
13.966
0.016
0.166
10.355
0.016
0.098
6.029
20.021
0.380
18.508
0.019
0.311
16.775
0.017
0.244
13.923
40.030
0.606
19.985
0.027
0.531
19.704
0.024
0.460
19.398
0.021
0.390
18.334
60.036
0.683
18.929
0.031
0.611
19.469
0.028
0.539
19.455
80.054
0.911
16.826
0.048
0.833
17.447
0.042
0.761
18.266
0.037
0.690
18.843
100.062
0.977
15.795
0.054
0.907
16.662
0.048
0.837
17.431
120.087
1.191
13.638
0.078
1.112
14.230
0.069
1.045
15.048
0.062
0.978
15.836
140.097
1.232
12.766
0.087
1.170
13.515
0.078
1.108
14.253
Table5.3:
Lift,dragcoe
cients
andL/D
ratios
fortwistedwings
73
Angleof
Attack
Λ=
00,β
=20
0Λ
=10
0,β
=20
0Λ
=20
0,β
=20
0
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
-40.012
-0.010
-0.836
0.011
-0.013
-1.171
0.010
-0.005
-0.460
00.016
0.276
17.356
0.014
0.239
16.594
0.013
0.226
16.761
40.029
0.568
19.255
0.026
0.495
18.753
0.028
0.473
17.049
80.053
0.851
16.190
0.047
0.743
15.889
0.046
0.681
14.711
120.084
1.110
13.258
0.074
0.966
13.044
0.072
0.884
12.194
Table5.4:
Lift,dragcoe
cients
andL/D
ratios
formorphed,sweptwings
74
Angleof
Attack
a/b=
1/3
a/b=
1/2
a/b=
2/3
CD
CL
L/D
CD
CL
L/D
CD
CL
L/D
-40.012
-0.011
-0.910
0.012
-0.007
-0.615
0.012
-0.006
-0.485
00.016
0.273
17.503
0.016
0.274
17.590
0.016
0.291
17.959
40.029
0.561
19.156
0.029
0.561
19.090
0.030
0.594
19.525
80.053
0.841
15.994
0.053
0.840
15.895
0.055
0.890
16.279
120.085
1.108
13.077
0.085
1.097
12.904
0.088
1.160
13.199
Table5.5:
Lift,dragcoe
cients
andL/D
ratios
forstraight,partially
morphed
wings
75