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.

iii

To My Family

For All Their Support

iv

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

v

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

vi

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

ix

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

xii

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

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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