Lift Force Determination in Bio-Inspired Flapping wings

Author: Sam Knight

Aerospace Engineering MSc

Brunel University

Uxbridge

Abstract: This report details the design and construction of a Test rig flor flapping wings and compares the results measured from its subsequent use against some predicted values from numerical modelling. The test rig uses Servo motors mounted in the wings in order to replace the flexibility of natural wings for the twisting of the wing during operation. The results conclusively show that an increase in the frequency of flapping not only applies more force within a set period of time, but also raises the force achieved per wing beat.

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ContentsTitle Page

1. Acknowledgements 4

2. Notation 5

3. Abbreviations 6

4. Introduction4.1. Context4.2. Objectives4.3. Limitations4.4. Summary of Methods

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5. Literature Review5.1. Notable Projects

5.1.1. Festo Smartbird5.1.2. Clear Flight Solutions: Robirds

5.2. Bird Wing Profiles5.3. Bird Wing Anatomy5.4. Models For Flapping Wings

5.4.1. Leading Edge Vortex (LEV)5.4.2. Rapid Pitch Up5.4.3. Wake Capture5.4.4. Clap And Fling Mechanism

5.5. Useful Equations5.6. Flexibility In Flapping Wings

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6. Chapter 1: Methods And Design6.1. Numerical Modelling

6.1.1. Aerofoil Selection6.1.2. Determining Reynolds Number Of The Flow Regime6.1.3. Predictions Of Flow Velocity Induced By Flapping6.1.4. Equations Of Wing Flapping Motion6.1.5. XFLR5 Analysis

6.2. Design6.2.1. CAD Modelling6.2.2. Materials6.2.3. Weight Estimation6.2.4. Control6.2.5. Electronics6.2.6. Measurement Of Results

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7. Chapter 2: Results7.1. Results Of Numerical Analysis

7.1.1. Theoretical Relationship of Flap Angle and α7.1.2. Component Flow Analysis7.1.3. Lift Predictions Using Calculated CL Values7.1.4. Lift Force Predictions For The wing Using XFLR57.1.5. XFLR5 Lift Force Predictions Across A Period Of

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Flapping7.2. Experimental Results

7.2.1. Symmetrical Positive And Negative α Study With Increasing Frequency

7.2.2. High Positive α Study With Increasing Frequency7.2.3. Increasing α Sweep Study At Constant Frequency

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8. Chapter 3: Analysis8.1. The Design8.2. Flap Angle, φ And Angle Of Attack, α8.3. Comparisons Between The Lift Force Calculated And Lift

Force Determined Experimentally8.4. The Relationship Of Lift Force And Frequency8.5. The Relationship Of Lift Force And α

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9. Conclusion 92

10.References 95

11.Project Management 97

12.Appendix: Dissertation Proposal: Bio-Inspired Flying Machines 99

13.Appendix 103

1. Acknowledgements3

I would like to thank my tutor Dr Farbod Khoshnoud for the support, help and inspiration he gave me for this project. His enthusiasm for the project and the subject

area ensured I stayed motivated throughout the whole period of work.

Recognition must also go to my family who were also very supportive of my work and helped in whichever way they could.

Others who inspired my ideas and solutions as well as helped me with my work such as the university technicians also must get a large amount of recognition as without their expertise and knowledge of equipment obtaining the results I needed would

have been far more challenging.

2. Notation RE – Reynolds Number

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V – Velocity V ∞ - Freestream Velocity V RES – Resultant Flow Velocity V CGMAX

– Maximum Wing centre of Gravity Velocity V GMAX- Maximum velocity of wing Centre of Gravity mph – Miles Per Hour m/s – Metres per Second cm/s – Centimetres per second ωw – Wing Angular Velocity ωG – Gear Angular Velocity αRES – Angle of Attack of the Resultant Flow ° - Degrees (Angle) kg – Kilograms g – Grams m – Metres cm – Centimetres mm – Millimetres l – Chord x – Rate of Change of Distance rG- Gear Radius rhinge – The Inboard Length of the Spar from push rod linkage to Hinge rCG – Distance from the Hinge to the wing Centre of Gravity AW – Wing Surface Area s - Second f - Frequency T - Period CL – Coefficient of Lift CD – Coefficient of Drag α – Angle of Attack φ – Flap Angle φ – Rate of Change of Flap Angle ρ – Air Density (1.225 kg/m^3 μ – Dynamic Viscosity ν – Kinematic Viscosity (1.5*10^-5 kgm^2/s) L – Lift Force N - Newton

3. Abbreviations

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MAV – Micro Air Vehicle LEV – Leading Edge Vortex CAD – Computer Aided Design ESC – Electronic Speed Controller BPM - Beats per Minute CG – Centre of Gravity

4. Introduction

4.1. Context

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Humans have been taking inspiration for the design of aerospace vehicles from

nature centuries before the wright brothers made their first flight in 1903. However

until quite recently, efforts to fly as a bird or insect under the power of flapping wings

have been largely unsuccessful. Within the past two decades or so, new

manufacturing techniques, leaps forward in control and electronics, and experience

gained using strong lightweight materials have brought about some successful

examples of flapping wing flight. Such aircraft are often referred to as MAV’s (Micro

air vehicles) were the aircraft is usually the size of a bird or remote control plane.

Commercially, even though unsuitable for manned flight there is a large amount of

scope for a Flapping wing MAV, though methods used for their flight and control are

still much under development with a variety of theories on how a successful project

would be best achieved.

A successful flapping wing MAV vehicle has scope to be sold and operated in a

variety of sectors. These span through military, intelligence, agricultural, surveying

and search and rescue organisations who all have use for Bio-Inspired air vehicles.

The attraction for such a vehicle comes from its similarities to birds and how they

overcome some fundamental flaws with current aircraft and helicopter systems. A

birds control through flapping wings allows them to be very manoeuvrable and

access areas that an aircraft could not, such as flying in tight spaces within rock

formations, a particular advantage in the search and rescue application. However, a

bird is also able to cover a lot of ground in a short space of time which a MAV

helicopter system could not. It is this versatility which makes a viable Bio-Inspired

flapping wing vehicle a desirable asset for many applications.

4.2. Objectives

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The main focus of the project will be the measurement of Lift Force exerted by a pair

of flapping wings. Where natural examples use passive wing flexibility [1], which

provides the necessary characteristics to a birds wings relative to the conditions they

experience. The design of the test rig however will seek to use servo motors in built

to the wing to replace the need for wing flexibility and its complex design problems.

As much as possible, inspiration will be taken from biological examples with regard

to the shape of aerofoil used and wing geometry. Analysis of the wings will be

carried out numerically to obtain predicted values for Lift Force in the planned

studies for the increase in frequency and stroke Angle of Attack (α).

With results predicted for the test rig, the design will then be finalised and

constructed. This will seek to use, if possible the same material that would be used

should the design be applied to a flight vehicle. The design of the test rig will

incorporate a pair of wings each with an internally mounted servo in order to twist the

wing, as well as a frame which will hold the wings, motor and mechanism necessary

for their flapping motion. Control will be achieved with the use of an Arduino board,

this was selected due to the ease of controlling servos and a brushless motor.

The measurement of the results experimentally will be achieved by the use of a load

cell. This decision was made through the experience of the inadequacy of strain

gauges mounted on a stand holding the test rig. This would allow force to be

measured in a single direction with the direct output relationship to force being

extremely attractive with regard to the processing time of results. The load cell would

be mounted between a base plate clamped to a desk, and the test rig, in a vertical

position to exclusively measure the forces created in a vertical direction. Once the

measurements had been taken these would then be compared to those calculated

and the differences and similarities discussed.

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4.3. Limitations

As there is a timescale for the project, this will be a large factor into completing the

work as planned. Provisions have been made in order to ensure that the project

remains active throughout its duration, and delay’s due to the delivery and machining

of parts will not be responsible for the projects failure. For ease of construction, the

test rig must be built to have a wing span of around 70cm. Although this allows or

easier construction and sourcing of parts, there are drawbacks to the relatively large

wingspan. All tests will have to be carried out in static airflow with the test rig being

too large for the wind tunnels available. This may cause some difference between

the predicted and measured results due to the inability to calculate values of Lift

Force with a velocity of 0m/s. Lastly, a potential limitation in the materials used could

be the difficulty of machining carbon fibre. This would be the material of choice for

the test rig structure, however it is costly to machine and requires specialised tooling

which cannot be provided in house. In the event of this not being possible, the

carbon fibre parts can be machined from plywood.

4.4. Summary of Methods

The numerical analysis will be challenging, due to the 3-dimensional nature of a

flapping wing problem. This will be done using two approaches, the first will be in

XFLR5. This provides a visual representation of the design wing which will aid in the

design of the structure for the test rig, allowing dimensions to be clearly seen

alongside the wing geometry. XFLR5 can then analyse the wing using data from an

aerofoil analysis, which is also conducted in the software, to produce values for CL.

The second method of obtaining Lift Force will be using equations and methods used

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in previous work and applying these to the predicted changes in the parameters of

Flap Angle (φ) and α.

The measurement of experimental data will be done over two studies. The first will

be the increase in frequency over two different Angle of Attack configurations. One

with a symmetrical movement between identical values of positive and negative α.

The other with a high positive Angle of Attack with the aim of creating a more

efficient pattern of movement. The second study will be into the Angle of Attack

achieved at the peak velocity point of the downstroke, this will aim to determine if Lift

Force is increased with a larger negative α or to find its optimal value. The result of

each set case for testing will be analysed using the same method as used by Sane

S.P. (2001) [2] where multiple wing strokes are taken and averaged into a dataset for

a single wing stroke.

5. Literature Review

5.1. Notable Projects

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5.1.1. Festo Smartbird

Perhaps the most successful attempt at recreating bird flight, this example uses a

lightweight carbon structure, weighing only 450grams with a wingspan of nearly

2meters. A high gearing ratio between the motor and the mechanism ensures that a

relatively small motor can drive its wings. The key feature of the Smartbird is the

active torsion designed into its wings. This consists of a servo mounted towards the

wing tip, on the outer most wing rib. This is connected to a microcontroller to

calculate the input from information drawn from an array of sensors for acceleration,

torsional force on the hand wing, and motor position. Data acquired from testing,

provides the relevant information in order to position the hand wings to twist into an

optimised position for the current flight conditions and phase of wing motion [3]. This

approach brings this design closer to its natural inspiration than any other design;

with it not only mechanically replicating the movement and motion of the bird’s

skeleton and muscles, but also replicating the bird’s sensory system by the various

on-board sensors. Festo has also undertaken other projects with flapping wings

drawing inspiration from dragonflies and butterflies in some of its other notable

Bionic Learning Network projects, known as the BionicOpter [4] and

eMotionButerflies [5].

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Figure 1: The Festo Smart bird [6] Figure 2: A CAD image of the Dragonfly inspired BionicOpter [7]

5.1.2. Clear Flight Solutions: Robirds

Designed as a deterrent for nuisance birds around airports, waste and agricultural

sites [8], their manufacturer claims significant reductions in numbers of smaller birds

from repeated use in a given area [9]. However, they are not currently commercially

available and are still undergoing development. Unlike the Smartbird, the wings are

not articulated and do not contain servos to optimise twisting. They are however of a

flexible foam construction. A front and rear spar move to twist the chord of the wing

which provides lift and thrust. With regard to control, the Robirds do not have the

same aerodynamic turning effects with the tail and head moving together, however

enough manoeuvrability is still achieved for operation within an outdoor space.

Currently two types are being developed to replicate a peregrine falcon and an

eagle, which are still in the testing phase with an aim to make their flight completely

autonomous with an autopilot system. Perhaps not as technologically advanced as

the Smartbird, the Robirds do however have the speed to match their natural

equivalents, with a manufacturer’s claim of a 50mph top speed in the Falcon model

[10].

5.2. Bird Wing Profiles

Various attempts have been made to model bird wing profiles, however this proves

challenging in practice. A number of approaches have been tried, but due to the

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Figure 3: The Clear flight solutions Falcon model. The wing shape plays a large part in its success as a bird deterrent which when flapping looks similar to the real bird. [8]

nature of avian wings and their unique flexibility to suit a range of flight profiles, great

effort is required in order to obtain a profile for even one flight state. One initial

approach was to take measurements from museum specimens [11] and treat these

as fixed aerofoils rather than a highly deformable bird wing. However this method is

inaccurate due to the necessary process of preservation. Recently deceased

specimens [12] also experience problems in the uncertainty in what flight conditions

the wing was last set for. Even without these effects, errors would still occur as when

a bird is in flight, its sensory system is constantly optimising the wing through

differing flight stages [13]. Therefore the variables the wing experienced most

recently would be unidentifiable. Through this, the optimum method utilised is to

measure the wing whilst in flight. One such method by the Oxford department of

Zoology used a trained bird and photogrammetric techniques in order to pin

coordinates to points on the wing to model the inner surface. This was done by

setting up a series of six cameras around a known control volume containing a perch

on which the trained steppe eagle would land [14]. This meant measurements were

taken in a rapid pitch up manoeuvre from a shallow glide into a stall to land. Similar

work to this had already been undertaken, however this involved smaller birds in

wind tunnels with sparrow [15] and starling [16] test subjects. The use of smaller

birds provides little insight into Reynolds number regimes that would be experienced

by MAV’s built with current technology, as it is unlikely that a smaller bird species

could be replicated.

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5.3. Bird Wing Anatomy

Although in many ways very different, the avian wing demonstrates numerous

similarities to the human arm [17]. Both in bone structure and the associated

muscles to drive movement. There are recognisable shoulder, arm and hand

sections to the bone structure, with the hand wing forming the significantly larger

area towards the tip of the wing containing the primaries [17] (primary feather group-

the largest feathers on the wing). The feathers attached to the arm wing are known

as the secondaries [17]. Unlike in a human arm, the arm wing in a bird accounts for

less than half of the total wing span. Other feather groups are known as the coverts

and the scapulars, with the coverts forming the feather covering of the leading edge

and the centre of the wing surface. Other notable similarities between birds and

humans is the presence of pectoral muscles used for flapping the wings down [18],

humans have similar muscles in the chest used to move their arms forward and

together.

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Figure 4: The profiles that resulted from the photogrammetric study undertaken by the Oxford department of zoology of a Male steppe eagle in a high pitch up manoeuvre. [14]

5.4. Models For Flapping Wings

In order to design an optimised flapping wing MAV with the flight characteristics of a

real bird, the problem has to be numerically understood. Considerable work has

been done on the angle of attack, flap angle, and wing beat frequency, as well as

four unsteady mechanisms that frequently occur, and various other variables

associated with not only airflow but also a constant movement of the wings. Four

unsteady mechanisms cited frequently in literature are leading edge vortices, rapid

pitch up, wake capture and clap and fling [20]. These mechanisms are typical of

problems faced as they clearly aid in lift production in insects and birds but are

difficult to predict for variations with current methods of analysis. In further detail,

these models are described as follows:

5.4.1. Leading Edge vortex (LEV)

A flow of air created around the front of the wing which rolls over the leading edge

during the downstroke. The low pressure at the centre of the vortex creates a suction

force that attaches it to the wing during the stroke and increases the possible angle

of attack before stall is induced. This creates higher lift than is normally obtainable by

the same wing and enhances the performance of the wing over its capabilities in

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Figure 5: the labelled arrangement of feathers on a bird wing. [19]

steady state flow. The vortex has been found by studies to be conical in shape,

having a smaller radius towards the root of the wing and much larger diameter at the

wing tip. This is due to the increases in the wings tangential flow velocity along the

span. This mechanism has been identified as the most significant in flapping wing

flight to increase the lift, however observations vary as to the LEV’s behaviour on

different wings. In some cases it is seen to be permanently attached, whereas in

other cases it sheds and reforms with each beat.

5.4.2. Rapid Pitch Up

A quick rotation at the end of each stroke, where the wing moves from a low to high

angle of attack, generating much higher lift coefficients than the steady state stall

value [20].

5.4.3. Wake Capture

Occurs as a wing travels through the wake it created on a previous wingbeat.

Research has shown peaks in aerodynamic force when the wake of a previous wing

beat is captured with correct phasing and twist of the wing [20].

5.4.4. Clap And Fling Mechanism

This refers to the way the set of wings are moved during the wingbeat. The majority

of birds do not use this type of motion in normal flight, however some, such as the

hummingbird could be described to use a clap and fling motion. More applicable to

insect flight, this model for wing movement describes the upward motion (the clap),

where the wing leading edges are clapped together at the end of the upstroke. The

downstroke consists of the leading edges moving apart whilst the trailing edge

remains stationary, therefore the wing rotates around the trailing edge. This is known

as the ‘fling’ [19].

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5.5. Useful Equations

For the Numerical Analysis of the project there are some papers for work previously done

that provide good methods and equations that could be applied. These studies carried out

are notably those by Whitney J.P (2001) [22], and Dickinson M.H. (1999) [23]. Both provide

good relationships to be followed and good approximations of CL and CD to be applied to

flapping wings.

The Study by Whitney [22] focuses on conceptual design of MAV’s with no practical work

undertaken. A large focus of the paper is on the hovering energetics and predicting the flight

performance such as the range and speed of the vehicle. However, of interest to this project

is the work undertaken to predict the damping force and the relationship produced between

φ and α (Figure 7). This would be useful to predict the timing of the parameters of the test rig

wings and apply further calculations to obtain the wings lifting force as a function of the

theoretical angle of attack.

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Figure 6: The clap and fling mechanism, here the diagrams are shown as if looking from above the insect/ bird and the circular ends represent the leading edge of the aerofoil. [21]

The second study by Dickinson [23] produces approximations for CL and CD in flapping

wing applications (Figure 8). More importantly these are a function of α which due to the

planned servos in the wings, is easy to control. To obtain a theoretical lift force, these

equations can be applied to the predicted or actual α to find an approximation. The CL value

could then be used in conjunction with the lift equation in order to provide a predicted or

theoretical Lift Force.

CL=0.225+1.58 sin (2.13α−7.2 )

CD=1.92−1.55 cos (2.04α−9.82 )

L=CL ρV 2

2A

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Figure 7: Top: J.P. Whitney projects the theoretical relationship between φ and α n his design. More of interest is the phasing of both sets of motion which follow a sinusoidal relationship. This timing would be good to replicate in the experimental section of the project.

Bottom: The plot of damping force with α, this is the force that acts against the driving mechanism. [22]

Figure 8: The approximations made by Dickinson in his work with the Lift equation presented below. With a way of measuring Density and velocity aswell as the angle of attack, these equations could be applied as in work by Sane S.P. [2] to the physical data gathered from the test rig and compared to actual values.

5.6. Flexibility In Flapping Wings

When comparing wings of aircraft to those found in the natural world, one of the

main differences is the flexibility of bird and insect wings. Insects are typically

characterised with very thin transparent wings with an intricate vein structure to add

rigidity. Whereas bird’s wings consist mostly of feathers with a minority of the wing

surface area being taken up by the bone structure and muscular makeup necessary

for flapping. Feathers typically have a stiff spine to them however this is still not

completely rigid, which allows for a flexible wing. Although studies into natural flyers

initially focussed on defining wings as rigid, studies have now been undertaken to

determine the effects of flexibility.

It has been found that trailing edge flexibility has a considerable effect on the wing

aerodynamics. When a rigid wing translates at a high angle of attack, the leading

and trailing edge vortices periodically generate and shed as found in the results of

(Zhao, et al, 2010) [24]. A wing that has an optimised flexible trailing edge, however

can generate a smaller but much more stable leading edge vortex, with some

parameters out performing rigid wings when used in flapping configurations [24].

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6. Chapter 1: Methods and Design

6.1. Numerical Modelling

Before designing a test rig and wing structure, a numerical analysis of the problem

had to be made. This would provide an indication of the forces acting on the wing. It

was necessary to make calculations, as a critical element to designing a vehicle with

flapping wings would be the lift and thrust achieved, compared to the weight. An

initial estimate for a vehicle weight of 400g was made based on weights of the

notable projects studied in the literature review, most specifically the Festo Smartbird

was considered due to a wealth of information available [3]. With this estimation in

place, the task was to produce a wing and carry out appropriate sizing to produce

adequate lift to support the vehicle in flight. Initial work involved research into

aerofoils, which led into a determination of the Reynolds flow regime the wing would

operate in, this would then be used in XFLR5 to provide results with greater

relevance to a vehicle of the design size. Further theoretical work then required

calculations for resultant flow velocities to find the velocity of induced flow due by

flapping of the wings. This could then be used in XFLR5 to attempt to estimate for lift

force achieved by the test rig at a specific flapping frequency and Angle of Attack

during strokes.

6.1.1. Aerofoil Selection

When selecting a profile for the wing, several considerations had to be made. Firstly

as the project would draw inspiration from biological applications, the profile of the

wing should reflect that of those found in the natural world. Secondly, there would

not be the time or the need for developing a profile unique to the project as a large

variety of aerofoil shapes are readily available for public use. Another consideration

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would be the strength of material the sections would be constructed from and

tolerances involved with cutting the wing ribs to that profile. These limitations and

criteria required considerable research in order to ensure the right profile was

chosen.

To better understand the characteristics of a bird wing aerofoil, the literature review

aimed to investigate papers where work had been done to obtain a cross section of a

bird wing in flight. The oxford department of zoology [14] achieved this successfully

using a series of cameras around a control volume to obtain an accurate model for

the inner wing of a trained eagle. The result of this study is shown below in Figure 9.

With these findings it was realised that the profile needed to be highly cambered and

have a large leading edge radius and thin trailing edge to correctly replicate the

natural wing. It would also be desirable for the aerofoil to be designed for Low

Reynolds number flow, as based on the vehicles dimensions, it would be expected to

operate somewhere between ℜ1×105 and ℜ2×105.

After a search to find a selection of profiles that fitted the already mentioned criteria,

possible candidates were those shown in Figure 10. All aerofoils in this selection are

for Low Reynolds flow, and are highly cambered. The high camber is essential as

the vehicle is operating at low speeds in comparison to conventional aircraft, an

aerofoil with low camber would likely not generate enough lift. As the Reynolds

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Figure 9: Aerofoil profiles obtained by the oxford department of zoology. This provided a good foundation for the characteristics to look for in bird-like aerofoils. [14]

number of the flow is low, as well as speed, the amount of drag that a high camber

foil would produce is not nearly as significant as it would be if the same profile was

applied to an air vehicle designed for carrying people.

After reviewing the profiles, two were identified as appropriate for the main wing. The

GOE358 and the Selig 1210 both offered a high camber whilst having enough

thickness to be accurately cut and remain robust in a range of materials. More

importantly this offered the possibility to be laser cut out of wood if desired, which

would be important for rapid production of parts. It was finally decided that the

GOE358 would be more suitable as it has a thicker trailing edge, this would more

conducive to laser cutting if required. The thickness in the aerofoil would be needed

in order to provide enough space for the necessary structure and a servo mounted in

the wing for twisting.

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6.1.2. Determining Reynolds Number of The Flow Regime

For varying sizes of airborne vehicles, the flow regime that they experience changes.

This is measured by the Reynolds number of the flow. Commercial jets fly in the

regime of ℜ1×107 which is considered as high, birds and insects on the other hand

operate at ℜ1×103−ℜ1×105, with insects towards the bottom of the scale and large

birds at the top (Figure 11). Major work in the lower Reynolds regimes has come

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Figure 10: The aerofoil profiles considered for the design. (1. FX60-100 10%, 2. GM15, 3. GOE368, 4. GOE63, 5. GOE358, 6. Selig 1210 12%, 7. GOE500) [25]

about in recent times with the interest in Micro-Air Vehicles, small unmanned aircraft

similar in size to large birds do not experience the same effects as a large aircraft

and must be designed differently.

The flow regime can be determined by using the equation stated below which takes

into account the chord of the wing, and velocity of flight.

ℜ= ρVlμ

=Vlv

Where:

ℜ=Reynoldsnumber

V=velocity

l=chord

ρ=Air Density (1.225 kgm3 )

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Figure 11: A plot showing the Reynolds number against the speed of airborne body. This shows how various applications compare [26].

μ=Dynamic viscosity

v=Kinematic viscosity (1.5 x10−5 kgm2

s)

The assumption was made that Air density and Kinematic viscosity were the

international standard values for air as stated above. The velocity was assumed as

the flight speed of the vehicle at 10m/s. This was then applied to the root of the wing

and the tip of the wing using the different chord lengths to obtain an idea of the

regime change with variation in wing geometry.

For the Root (250mmchord )=(10m /s)×(250mm)

1.5 x10−5 kgm2

s

=166666.67≈ℜ1.7×105

For the Tip (150mmchord )=(10m /s )×(150mm)

1.5x 10−5 kgm2

s

=100000≈ℜ1×105

These resulting values show that the vehicle would operate in the top end of the

regime of birds and indicate that analysis should be done in XFLR5 taking into

account that the flow regime must be between ℜ1×105 and ℜ2×105.

6.1.3. Prediction of Flow Velocity Induced By Flapping

To predict the effects of the increase in flow velocity over the wing due to the

flapping motion, relations of trigonometry and angular velocity were used to find an

average at the wing Centre of gravity (CG). This method, used in analysis of

propeller’s (Blade Element Theory), would be the best way to approximate flow

velocity for the entire wing, as naturally a larger velocity or rate of change of flap

angle, φ, would be experienced at the tip than at the root. Though the wing features

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a reduction in chord towards the tip, the Centre of gravity position would provide a

suitable representation of the entire wing. An explanation of the approach taken is

given below with variables explained in Figure 12.

The initial calculation was to obtain an angular velocity of the gear for a given value

of frequency, f (Rotations of the gear that drives the wing per minute). This would be

simply:

ωG= f 2π

Following on the vertical velocity induced by the linkage between the gear and wing

was found, using the known angular velocity and radius of the gear, rG:

V GMAX=rGωG

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Gear

Wing CGWing Hinge

Wing Spar

φωG

x

ωw

Figure 12: A diagram of the major components to detail important angular and linear velocities for finding the velocity.

From this point, to model the rate of change of flap angle through one period, a good

result could be obtained by using trigonometry to derive the rate of change of vertical

displacement at the gear linkage, x (Vertical velocity of the push rod) as the gear

rotates. The top position of the push rod on the gear was taken as 0°, bottom as 180°

and the left and right as 90° and 270° these values map the position of the gear to the

sinusoidal period of flapping experienced by the wing. Positions as shown in Figure

13.

With a value of velocity induced by the linkage to the wing, the instantaneous

angular velocity of the wing spar could be obtained by:

ωw=V GMAX

rhinge

Where rhinge is the distance between the spar connection to the linkage, and the

centre of the hinge.

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270°

180°

90°

0°

Figure 13: Angular positions shown on the gear.

Applying this angular motion of the wing spar, the vertical velocity of the wing could

be found:

φMAX= ωwrCG

Where rCG is the distance of the wing span from the hinge to the wing CG.

With the values calculated it is possible to calculate the peak resultant flow velocity

over the wing by using the components of the downward or upward movement of the

wing CG and the free stream flow velocity. These calculations are identical to those

carried out for Blade element theory on aircraft propellers [27], this relies on the

simple trigonometry of an aerofoil moving at a constant velocity, perpendicular to a

freestream velocity generated by the flight speed on the vehicle. This in turn would

produce a resultant effective velocity acting at an angle offset to the freestream.

Although some previous studies have omitted these calculations, many were for

smaller insect like wings. Due to the span of the test rig wings it was felt that the

velocity induced by the wings through their fastest point at the horizontal position

may be significant. This peak velocity could have an effect on the peak lifting force

generated by the wings. This is of interest in this study as the peak force achieved

would give an indication into the feasibility of the concept being adapted to a flying

vehicle. In Figure 14 the components of the resultant velocity are shown.

28

In order to obtain the resultant flow velocity over the wing and its resultant angle, it

was simply a matter of applying Pythagoras, using a given velocity of the freestream,

and trigonometry to find its angle. Below calculations would provide the final inputs

for XFLR5.

V RES=√V ∞2+ φMAX

2

And

αRES=sin−1( φ

V RES ) 6.1.4. Equations Of Wing Flapping Motion

Having calculated some important elements of flow over the wing, it was also

necessary to determine and plot further characteristics. Using work done by Whitney

and Wood (2011) [22], the relationship between flap angle and alpha through one

period of flapping was calculated for various cases. Particularly the relationship

between flap angle and alpha would be useful as this would need to be recreated in

the control of the flapping motor and the servos for wing twist. The damping force

29

Figure 14: A diagram to show the relative direction of flow velocities acting on the wing [28].

αRES

Where:

V ∞: Free Stream Velocity

V CGMAX: Vertical Velocity of Wing CG

V RES: Resultant Velocity

αRES: Angle of the Resultant velocity from the free stream

V RES

V CGMAX

V CGMAX

Wing CG

V ∞

would also be important as if this was too great, the mechanism and motor would not

be able to withstand and overcome it to drive the wings. Flapping angle when

considered in the context of this study, is the angle of displacement of the wing from

the central datum of its range of movement.

Predominantly used were the equations derived in Whitney and Wood’s conceptual

model for instantaneous lift and damping force. Plots were also created for the

calculated change in flap angle, found by taking the V CGMAX discussed in the previous

section. The relative movement of φ, the flap angle from a datum is shown in Figure

15.

Flap angle was mapped to increments of 10° throughout one period of flapping,

corresponding φ values were then found. α increments were also calculated at the

same points taking the maximum positive and negative positions as 0° and the

30

−φMAX=21.5

+φMAX=21.5

−φ

+φFigure 15: The relation of positive and negative flap angle on the wing.

resultant angle into account. Below is the equation that maps the α incrementally at a

given frequency.

α=7cos (T incr¿)+3¿

The T incr represents the increment of a period of flapping, the 7 is determined by the

best lift to drag ratio and should provide the aerofoil the best α for efficiency. The

addition of 3 to the end of the calculation is the zero lift angle of the aerofoil, this is

necessary so that the wing has a higher α on the upstroke and less on the down

stroke to provide more upwards lift. Without this the forces between strokes would be

close to equilibrium. These calculations resulted in a plot to represent the relation of

flap angle φ and angle of attack α during a period of wing movement. This

relationship is shown in figure 16.

0 0.15 0.3 0.45 0.6 0.75 0.9 1.05 1.2 1.35 1.5

-25

-20

-15

-10

-5

0

5

10

15

20

25

Change in flap angle, φ at 40 Beats per minute

φα

Time, (s)

Angle

, (°)

This analysis of flapping angle and angle of attack allowed for further calculations

and analysis of lift force generated by the wing. This would allow predictions of the

31

Figure 16: The relation between φ and α . Notice that there is a 0.5 phase difference as the maximum of each must occur at the end of a stroke for φ and halfway through a stroke for α .

lift force for cases run on the test rig for varying frequency’s and angles of attack.

These further calculations would be made in XFLR5 and would obtain values for

comparison with those obtained experimentally by the load cell on the test rig.

6.1.5. XFLR5 Analysis

XFLR5 was good platform for some analysis of the wing, as it is optimised for

smaller aircraft and could give good estimates of CL and lift force. Having

predetermined the Reynolds number range of flow over the wing and aerofoil profile

to be used, these could be entered into the program. The initial stage of design

would be to analyse the aerofoil to obtain plots and a set of results for its

characteristics. These results could then be used by the program and extrapolated

out to a wing when the geometry was specified at a later stage. Results of both the

aerofoil analysis and the ultimate analysis of the wing could be used in estimating

the best twist on the wing for up strokes and down strokes, as well as the lifting force

induced by the airflow.

The aerofoil analysis gave a set of plots that show various properties of the profile.

Predominantly relationships between CL, CD and alpha, these plots (Figure 17, 18

and 19) enabled the values of important aerofoil properties such as the alpha value

at CL=0 (Figure 18), and the angle of attack (Alpha) for the best Lift/Drag ratio

(Figure 19). From this it follows that if the best Lift/Drag ratio was known, the wing

twist could be optimised to give the most efficient flight of the vehicle. This could be

achieved with the wing at the correct Alpha to the resultant flow in both the upstroke

32

and the down stroke. The same applies for the upstroke in specific flight regimes

where a CL=0 condition may be required, this would also be possible with a known

value allowing the wing twist to achieve the required alpha.

Finally with the data generated about the aerofoil profile, the program could apply

this to the wing geometry. This could provide a value for CL to be used in lift force

calculations for the whole wing. This was achieved by the equation:

L=CLρ∞V

2

2AW

As XFLR5 provides the option for specifying the density, freestream velocity and the

wing area being determined by the design. All values in this equation were known

leading to just a single run for each case in the program being needed to find the lift.

This was useful when compared to the predicted weight of the vehicle to find out if lift

generated by the wings would be sufficient. The 3-Dimensional plots generated

would also aid in structural design as they would detail the panel forces across the

mesh, this would reveal the areas of the highest force (Figure 20). Other plots that

were of interest were also available such as those of coefficient of pressure, surface

velocity and streamlines of flow in the wings wake. However these were not essential

to the project as they would be inaccurate for the instantaneous cases that were run

for various data points.

33

34

Figure 17: The CL vs CD plot for the aerofoil profile used on the wing.

Figure 18: CL vs Alpha, this is useful to determine the maximum effective angle of attack of the wing before it begins to stall.

35

Figure 19: Perhaps the most useful plot generated, the CL/CD vs α, this shows the most efficient angle of attack of the wing before the relationship between lift and drag deteriorates.

Figure 20: A plot of the panel forces across the wing at the top of the upstroke. Notice the information given including data about the geometry of the wing, results of the analysis and a key for interpretation of the 3D plot.

Before Analysis could be made on the wing model, a mesh analysis had to be

carried out comparing CL to the amount of panels used to build the wing model.

There would be a relationship between results for CL and the amount of panels

used, with results eventually converging to a value as the number of panels was

made greater. This point had to be determined as it would indicate the optimum

mesh configuration for providing accurate results with the least computing power

needed. The final mesh and the results of the mesh analysis are shown in Figure 24.

36

Figure 21: A plot for CP (Coefficient of pressure) Figure 22: Surface velocity plot

Figure 23: The streamline plot for the wing, showing the wingtip vortices.

0 500 1000 1500 20000.49

0.5

0.51

0.52

0.53

0.54

0.55

0.56

Mesh Analysis

Number of Panels

CL

6.2. Design

The basic concept for the design of the test rig was taken from findings in the

literature review, and how best to achieve the fundamental aims of the project. Most

examples of previous work use a simple straight set of wings directly connected to

the internal mechanism. This configuration was decided on for the design of the test

rig, not only as a result of these findings, but also for obtaining a symmetrical lifting

force and for simplicity of design. An articulated wing has many more moving parts

which would need to be fitted correctly, as well as the distances of the pushrods in

the wing refined to a very high precision.

37

Figure 24:

Left: The XFLR5 model of the wings with the final mesh.

Below: The results of the mesh analysis of number of Panels vs CL. Note the plot converges to a value of 0.556. This determines the number of panels as 1820.

6.2.1. CAD Modelling

The overall configuration of the testing rig would consist of a mechanism driven by a

motor to flap the wings, with servo motors to twist the wings accordingly. This would

simplify the control of the wings, but still enable control of the frequency and the twist

for angle of attack. With this in mind, work on the design for the test rig began first

and foremost with research into components that could not accurately be made in

house. Largely, this meant the gears for transmission of the rotary motion of the

motor, to the wings. Once the size of gears was known, other components could be

sized appropriately.

With the aerofoil profile and wing geometry being decided by previous work, design

of the structure took place within Solidworks. This approach had a number of

benefits, including the ability to visualise and check the design before fabrication, as

well as providing accurate part files for precise machining of components. A further

benefit of the software, was the capability to animate the model and simulate motor

motion on parts. This allowed motion to be checked and refined thoroughly as well

as close inspection for any interference between moving parts. The final assembly

model is shown in Figure 25.

38

When designing the individual parts for the structure, some parts would be used as

they were purchased, needing either a very basic level of machining or none at all.

An example of this was the carbon rods used as spars in the wings, these were

simply purchased and cut to size. To avoid issues with fitting these parts with others,

they were reproduced in the CAD software so they could be placed in an assembly

file with all the other components. This allowed the tolerancing of the parts as cutting

would not be completely accurate, such as the wing ribs, where holes for the spars

would be made 0.2mm larger than the carbon rod to ensure a proper fit (Figure 26).

This approach needed to be taken for almost all areas where parts would fit together,

as even though the 3D printing and laser cutting machines used are very precise,

they still have a limited accuracy meaning parts may come out slightly larger or

smaller than designed.

39

Figure 25: The CAD model of the final assembly of the test rig. This model was animated and had the possibility of moving constrained parts by dragging them. This proved extremely valuable to the design process.

The use of the CAD model was invaluable to machining the wooden parts of the

design and 3D printing the hinges. These components have complex geometries

which may have been hard to achieve using traditional machining and cutting

techniques (Figure 27). The Ribs have an aerofoil shape that is highly cambered with

a thin trailing edge, this would be almost impossible to do accurately by hand. As

well requiring precision for their basic shape, the ribs and frames also involved some

intricate cut outs which were only made possible by the laser cutting machine. The

shape of the ribs and frames are shown in Figure 28.

40

Figure 26: The tolerance in the CAD model on the front spar of the wing is shown with a very obvious gap between the spar and edges of the hole. This accounts for error in the spar diameter and the cutting of the wooden parts.

Figure 27: The separate assembly of the wing made the final assembly of the whole test rig much easier to produce. This also shows the complexity of the rib shapes.

6.2.2. Materials

The selection of materials is an essential phase to any design and is subject to many

considerations. Parameters such as cost, machinability, structural strength,

availability and density were all considered in the selection of materials for the wings

and frames. Considerations were made for each part as to what the loads and

stresses might be, which allowed the qualities of the material to be prioritised. This

can be seen in the final design and prototype by the use of carbon, plywood and

balsawood for different elements in the structure.

The ribs of the wing are primarily responsible for maintaining the profile of the wing.

This requires them to be good at holding their shape under load. The loads

experienced by the ribs however, are relatively much lower than those found in the

spars, therefore it was decided that the ribs could be constructed from lightweight

birch plywood. This has good strength for the requirements of the wing ribs and

could easily and accurately be laser-cut to size straight from the CAD model in

house (Figure 28). As the model was to be a one off prototype, purely for testing, it

41

Figure 28: The laser cut parts for the Ribs and Frames with the highly cambered aerofoil profile and complex cut outs.

would not be necessary to use Carbon fibre due to the much higher cost of buying

and cutting the material, as well as the difficulty in machining the parts.

The frames were constructed from the same birch plywood. Laser cutting was also

the easiest method for cutting these components due to the accuracy required for

distances between holes as well as the irregularly sized cut-outs.

For the spars, carbon tubes were selected as these offered good strength against

the loads experienced by a flapping wing. Although the flapping wing would be

considerably smaller and therefore subject to much smaller loads than conventional

full size aircraft, the wings motion might induce loads that were beyond the

capabilities of plywood. The carbon rods due to their cylindrical geometry, would also

provide good stiffness which would be important for the wing to maintain its shape

and strength throughout a flap cycle.

Balsawood was also used in the design, however no major structural components

were made from balsa. The use of this material is simply to support the wing

covering at the leading and trailing edge and enable the covering to be attached

securely.

6.2.3. Weight Estimation

A calculation of the weight was essential for several aspects of the project. As the

majority of parts had been designed in Solidworks, it was easy to use the data

available from the programme in order to determine the physical properties of the

individual parts. This would allow for an accurate estimation of the overall weight of

the entire structure. The volume of the parts would be used with the known average

density of its material, in Solidworks it was also possible to obtain data on the

42

centroid of a part or structure which would be useful when calculating moments of

the centre of mass.

First and foremost the weight estimation would be used when determining the

capacity of load cell required for testing. This was necessary to ensure that the setup

was optimised to achieve the best results. Using a load cell with a capacity too large

would lead to inaccurate measurements, whereas using a capacity that is too small

could damage the measuring equipment or lead to obtaining an incomplete set of

results.

A second purpose of the weight estimation would be in the calculation for its

feasibility. If the lift results found in testing were to show that enough force was

produced to lift the weight of the test rig, it is feasible that it could be converted into a

flight vehicle. Optimisation could then take place to investigate for any improvements

to be made. If the test rig was found to be too heavy, a successful flight vehicle

would require the material and geometry of the parts to be changed, or the structure

redesigned.

The estimation of the individual component weights is included below in Figure 29.

The estimated assembly weights are in Figure 30 with comparison to the actual

weight. Note that the wings came out lighter than predicted, this was due to the

difficulty in predicting the exact density of the wood and the loss of material from the

cut outs in the ribs. The frame however came out heavier than expected, this is

partially due to the extra wooden spacers needed to give the frame rigidity, and

minor design changes that were made to the assembly to give the gears a more

functional arrangement.

43

Component Weight Estimation

Wing

Rib 1 14.1 g

Rib 2 9.7 g

Rib 3 11.6 g

Rib 4 7.9 g

Rib 5 6.6 g

Rib 6 5 g

Front Spar 7.1 g

Centre Spar 37.6 g

Servo 53 g

Frame

Frame 1 31.7 g

Frame 2 31.7 g

Motor 53 g

Carbon rods 10.7 g

Gears 25 g

Assembly Estimation Actual

Left Wing 76.3 65 g

Right Wing 76.3 65 g

Frame 152.1 177 g

44

Figure 29: Table of component weight estimation

Figure 30: Table of Assembly weight estimations

6.2.4. Control

In order to conduct the testing accurately and precisely, a good degree of control

was needed over the test rig. Previously mentioned was the motor and two servos

included in the design which were to control wing flapping frequency, and the angle

of attack of the aerofoil respectively. In order to obtain good results that could be

compared to the theoretical cases predicted in the numerical modelling, the

frequency needed to be kept as a constant and the angle of attack consistently

changing between pre-set values.

The solution to control was the use of an Arduino board which could be programmed

to run the tests autonomously. The Digital outputs were capable of operating the

motor and servos by the use of the ‘write()’ command. This command was important

as once an object had been specified as a servo, and the servo library imported, it

would simply use a value representing degrees of servo movement to operate the

wings. Therefore, for the servo motors, this was as simple as specifying the

movement in degrees, with ‘write(90)’ being the zero angle of attack position of the

wings. The ESC (Electronic Speed Controller) and Motor also had function similar to

the Servos, with a simple calibration allowing the number of degrees specified to

equate to a percentage of the motor speed. This was achieved via the digital outputs

on the board which would generate the signal to be interpreted by the components.

The programmable nature of the board allowed for a function to be written for the

sweeping of the servos back and forth. This meant that they would not have to be

manually controlled and greatly aided the repeatability of each case as the speed of

the sweep and its magnitude could easily be set.

45

An example of a test case to be programmed into the board is shown below in

Appendix 3.

The code shown in Appendix 3 has 3 main lines of code that control the motor and

the servo motors. These 3 lines are the most important with regard to test cases

being run with the flapping and wing twisting in synchronisation, as they control

motor and servo speed, along with the minimum and maximum values of the servos.

The line controlling motor speed is shown below:

escmot.write(43);

In this line, the motor has been related to the servo library with the name ‘escmot’

and associated to a digital output pin of the Arduino. The write command then

specifies the angle that would be signalled to the motor which acts as a servo, in this

case 43. From testing it was found that different angles written to the motor would

give varying motor speeds and these were appropriately calibrated to give a list of

‘write()’ values for corresponding frequency in wingbeats per minute, for the example

above, 43 gives a frequency of 60 beats per minute.

The other lines of importance were as follows:

for(pos = 70; pos < 170; pos +=3.5)

for(pos = 170; pos >= 70; pos -=3.2)

These parts of the code determine the change of the variable ‘pos’, this variable

changes depending on the current position of the servo, and adds or subtracts the

end value depending on the instantaneous state of the servo. This variable is then

used to input back into the servo and creates and autonomous sweep back and forth

of the servo arms. In the case of the examples given, the addition and subtraction

values for degrees of the servo is 3.5 and 3.2 respectively. This essentially specifies

46

how many degrees the servo arm moves every loop of the code. A 15 millisecond

delay is included to allow the servo time to act accordingly. The 70 and 170 define

the limits in degrees the servo may sweep, in this case the wing can achieve up to

30° negative angle of attack and 70° positive, this occurs as for the servos mounted

in the wings, a 0° angle of attack is achieved at pos=100. It follows that the first line

specifies an increase in increments of 3.5° from a servo position of 70° to 169°, and

the second line a decrease of 3.2° for the wing servo moving back from 170° to 70°.

The difference in what is effectively the speed of the servos movement, is a result of

the wing travelling faster in one direction than the other as it has gravity to aid it in

the down stroke.

6.2.5. Electronics

Once a program had been written to control the test rig, the final stage was to wire

up the motors and breadboard accordingly. This was important as improper wiring

could cause the servos to move in the wrong direction, or could potentially damage

the Arduino should the power supply to the ESC be connected wrong. As it was

found that the 5 volt power supply of the Arduino board was enough to power the

servos, this only left the ESC and motor needing to be powered by an alternative

source.

It was important that the brushless motor received a consistent power supply from

the power source via the ESC. The power supply from the Arduino although

sufficient to power the servo motors, could not power all three motors, therefore an

alternative source was needed. Initially a 9V battery was used, which proved

adequate to power the motor, however it was quickly drained and did not provide a

consistent current and voltage. For this reason a power supply was used with a

47

variable current and voltage, this was the perfect solution providing a uniform voltage

and current as well as enabling changes to be made with ease. It was important that

this power source did not come into contact with the Arduino board as it could easily

damage it, either with excessive voltage or current. For this reason the power supply

was connected straight to the ESC rather than going through the breadboard which

took away the risk from an error in the connections.

Another issue in terms of electronics was the load cell used for measurement of

results. This required a nominal voltage of 10 volts to function and was therefore

connected to a separate power supply that would feed a consistently. This would

keep results as accurate as possible as it avoided any potential variation in the

voltage which could be picked up by the oscilloscope measuring the output. The load

cell also had two wires for output voltage, it was these wires that were connected to

the oscilloscope to obtain a readable signal. With one wire being for positive and the

other wire for negative, this allowed the load cell to measure both compressive and

tensile forces. These output wires had a capacitor between them, this was necessary

as the signal was initially found to be quite ‘noisy’. The capacitor served the purpose

of smoothing out the signal, reducing the amplitude of oscillations and making the

detectable frequency limit considerably lower.

Figure 31 shows a diagram of the circuit for the test rig. The associated power

supply connections for the ESC and brushless motor are also shown. All the

connections were kept as simple as possible and arranged neatly to avoid mistakes

when connecting the circuit to set up the test rig. Also of importance was the correct

motor being connected to the correct digital output pin, this was important as if the

motor was to receive a signal for one of the servo motors it would have potentially

48

caused damage to the test rig by too many revolutions per minute inducing

excessive frequency to the wings.

6.2.6. Measurement Of Results

It was decided early in the beginning of the project that measurement would be

undertaken by use of a load cell. A load cell could be used in the place of strain

gauges mounted on a support of the test rig, this would have the effect of removing

the complications of properly installing strain gauges as well as providing a more

accurate measurement of vertical forces exerted by the flapping wings. This would

come as a result of the load cells specific measurement of force exerted in a single

direction rather than the strain in a material as a result of that force.

49

Figure 31: The diagram of the circuit required for the control of the test rig with the code in Appendix 3. (Yellow and orange wires represent signal wires, red is positive, black or brown are ground wires)

The load cell required some initial set up. In order to amplify the voltage from the

output, a circuit was constructed that increased the strength of the signal by a

thousand times through a series of resistors, a H-bridge and an alternative power

supply. This took the signal received on the oscilloscope from the order of millivolts

to volts which, in conjunction with a capacitor, greatly reduced noise in the signal and

provided a more accurate reading. With this circuit providing a good signal from the

load cell, it was then calibrated using known masses and measuring the output

voltage (Figure 32). As the limit of the load cell was 20N (2kg) increments of weight

were added up to a maximum of 17N (1.7kg.), to avoid reaching the load cell limit.

This calibration was to confirm that the equipment specification was correct and the

relationship between output voltage and force exerted was linear.

0 2 4 6 8 10 12 14 16 180

0.5

1

1.5

2

2.5

3

3.5

4

Volts/Newtons

Volts/Newtons

Force (N)

Volts

(V)

50

Figure 32: The Load cell calibration showing the relationship between voltages received from the output of the device and the forces applied.

7. Chapter 2: Results

7.1. Results Of Numerical Analysis

7.1.1. Theoretical Relationship of Flap Angle and α

To optimise the Lift Force achieved by the test rig, it was essential that there was a

good synchronisation between change in Flap Angle and change in Angle of Attack.

To do this, a correct configuration for the Angle of Attack was calculated for various

points throughout one period and an appropriate sinusoidal function was generated

to model the sweeping motion replicated by the servo. By thinking about the flow

over the wing and the Angle of Attack induced by the wings vertical reciprocating

motion, it follows that the best configuration for the upstroke would be a steep

positive Angle of Attack to minimise negative air resistance forces. The down stroke

would require a negative Angle of Attack due to the vertical component of velocity

and the resulting angle of effective flow. Both the top and bottom of the strokes

would require an Angle of Attack of 0°. For this reason, the sinusoidal functions of

both the Flap Angle φ, and Angle of Attack α, would need to be exactly one half of a

period out of phase. This is shown in the following figures of results from the

numerical analysis.

Due to the challenge of obtaining results for a wide range of configurations

experimentally, the number of cases run would be limited. The solution was two

studies, one for the effect of increasing Angle of Attack, the other which would be for

rate of change of Flap Angle (frequency). The frequency study would be repeated

over four different frequencies with two different servo programmes. One of these

would be a symmetrical sweep of Angle of Attack between +30° and -30° (In

programming the servo, 0° for the wing was at 90° rotation for the servo making this

51

case 60° - 120°). The other would be a larger sweep with a steep Angle of Attack

during the upstroke between +70° and -30° (For the same reason as before, the

angle felt by the servo this would be 60° – 160°). In real terms, the first case would

be more similar to a bird in a cruising phase of sustained flight, the second would be

more similar to take off, with more lift required and less resistance on the upstroke.

These tests would be run in a static condition with an effective freestream velocity of

0 m/s suggesting that the second pattern of movement might yield better lift results,

being more similar to technique used by birds in a similar condition.

Below (Figure 33) is an example of the relationship between φ and α when the wings

are at a frequency of 64 Beats per minute. It can clearly be seen from the plot of the

results that the function for α is exactly half a period out of phase with φ. The

symmetrical sweep on the servos applied in this model means the positive and

negative amplitude of α are the same. This configuration as mentioned before is

more similar to a bird in a sustained period of flight, with a constant airflow forming a

horizontal component over the chord of the wings. For this case, the sinusoidal

relation to Flap Angle for the Angle of Attack is as follows:

α=30cos (φ )

52

0 0.15 0.3 0.45 0.6 0.75 0.9

-40

-30

-20

-10

0

10

20

30

40

Change in φ and α (64BPM-Sweep:60-120)

φα

Time, (s)

Angle

, (°)

Figure 34 shows a different configuration of Angle of Attack during one cycle of

flapping (A full wing beat through the upstroke and downstroke). The input angles to

the servo in this case were 60-160, creating a sweep of the wing through from +70°

to -90° α. This greater amplitude in Angle of Attack is more similar to that seen in

bird wings during take-off and climb at low velocity. When reproduced experimentally

a better Lift Force was expected, as the test rig would operate in stationary flow

conditions. Notice in Figure 34 that the phasing of both parameters is identical to that

of Figure 33, but here the function of α has been altered to give a larger positive

amplitude. The function was altered as below:

α=50cos (φ )+20

53

Figure 33: Plot of Flap Angle and angle of attack for the test rig at 64 beats per minute with a symmetrical servo sweep for angle of attack.

0 0.15 0.3 0.45 0.6

-40

-30

-20

-10

0

10

20

30

40

50

60

70

80

Change in φ and α (96 BPM-Sweep:60-160)

φα

Time, (s)

Angle

, (°)

Calculations were also made to provide a representation for φ with an increasing

value of α. For this study into increasing Angle of Attack, the sweep of α was kept

symmetrical from the centre of the servo range. These cases would be kept to the

same frequency to allow the measurement of change with a single parameter, this

meant the motor speed was to be kept constant through all the tests at 88BPM. The

measurements taken would confirm the amount of twist to be applied to the wing for

the best lift production with the induced airflow over the wing. Figure 35 shows the

theoretical relationship of the two parameters for the study into Angle of Attack

variation.

0 0.1 0.2 0.3 0.4 0.5 0.6

-60

-40

-20

0

20

40

60

Flap Angle and Increasing α sweep against Time

Flap angleα=10α=20α=30α=40α=50

Time, s

Angl

e, °

54

Figure 34: Plot of Flap Angle and angle of attack for the test rig at 96 beats per minute with an asymmetrical servo sweep creating a greater α on the upstroke.

Figure 35: Flap Angle against the increasing steps of α. Note that the plots of alpha show a symmetrical.

The other parameter that would be investigated would be the rate of change of Flap

Angleφ. This is directly linked to the frequency of the flapping which is mostly

referred to as Beats per Minute (BPM) of the wings in this paper. The theory behind

φis that when the wings beat faster, the cumulative force they exert over the space of

a minute would be greater due to a higher number of cycles. This is similar to a

higher number of revolutions in an engine. However, with a higher frequency the

wings also move faster through the air vertically, which would have the effect of

slightly increasing the force generated by each flap. Figure 36 shows the modelling

of higher frequency flapping, it can be seen from the plots for the increasing BPM,

that 96BPM will lead to almost a whole extra period in the sinusoidal motion of the

wing over 64 BPM. It follows that in theory the wings could generate twice the force

at 96 BPM, with an increased airflow velocity and the wings beating double the

amount of times within the same time period. The frequencies plotted here were

determined by the inputs to the motor from the Arduino. This was done as if entering

angles to a servo, and to avoid over stressing the mechanism of the test rig, the

inputs were kept below a certain value as its loss would have been fatal to the limited

timescale for the project.

55

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-25

-20

-15

-10

-5

0

5

10

15

20

25

Comparison of change in φ  

64 BPM76 BPM88 BPM96 BPM

Time, t (s)

Flap

Ang

le, φ

(°)

Similar to the Flap Angle, the α change was also plotted for comparison. Figure 37

presents the results for the prediction of the same frequencies as in Figure 36 with

identical colours used for ease of understanding. It shows the sweep of the wings

Angle of Attack for the symmetrical configuration with both the positive and negative

amplitude being 30°. This calculation of Angle of Attack was not only used to predict

and model the motion for analysis, but also used for setting up the experimental rig.

As the rig would rely heavily on the timing of each servo and the motor, these plots

were used to work out the starting position of the wings to provide a good timing

between φ and α. For example, the comparison of these plots would show what Flap

Angle the wings would need to be set at for a predetermined initial condition of the

servos.

56

Figure 36: A comparison of increasing frequencies of flapping. The Blue plot for 64 BPM shows one period of the wings motion, the other frequencies can be seen in relation. One flap is classed as a complete cycle through the maximum positive and negative values of the plot.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

-40

-30

-20

-10

0

10

20

30

40

Comparison of change in α for Servo Sweep: 60°-120°

64 BPM76 BPM88 BPM96 BPM

Time, (s)

α, (°

)

The last representation to be generated was the combined plot for φ and α (Figure

38). This enabled the above two figures (Figures 36 and 37) to be seen as one.

Although somewhat busy, it does show how quickly the change in α could become

out of phase with φ, as viewing a mismatching frequency for Flap Angle and α

reveals. This plot shows the amplitude of the large range of servo sweep from 60° to

160°, where the amplitude on the upstroke was to give the wing a very high positive

Angle of Attack at 70°. The twist of the wing to achieve this condition had to happen

at a considerably increased rate, in order to do this the lines of code referred to in

the methods chapter, had to be altered to allow a faster sweep of the servo arm.

Typically this involved increasing the degree increments from in the region of 3.0 to

around 4.5-5.0. This meant the servo arm would move further every time the code

loop was executed and therefore the sweep was faster.

57

Figure 37: The comparison of frequencies for change in α, or the sweep of the servo.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-40

-20

0

20

40

60

80

Relation between and φ and α for varying frequency (60-160)

64 BPM (Flap angle)64 BPM (Alpha)76 BPM (Flap angle)76 BPM (Alpha)88 BPM (Flap Angle)88 BPM (Alpha)96 BPM (Flap Angle)96 BPM (Alpha)

Time, s

An

gle

(°)

7.1.2. Component Flow Analysis

Applying the basic trigonometry for blade element theory, it was possible to predict

the effective angle of the flow felt by the wing [27]. Presented here in the results is

simply this resultant angle. It was found that as the free stream flow increased, the

angle of the resultant becomes increasingly smaller as can be seen in Figure 39.

These results prove the theory that in ‘zero’ velocity conditions, the test rig high

Angle of Attack on the upstroke would be important, especially at higher frequency.

Due to the low velocity which can be seen as the 1m/s line in Figure 39, we can see

the movement of the wing creates a large angle between the datum for the

freestream and the effective flow compared to faster flight speeds. This result would

also suggest that the test rig might benefit from further studies being carried out in a

wind tunnel, or some other form of freestream flow if future studies were to be made.

58

Figure 38: A combined plot of φ and α for a range of -30° to +70° of wing twist.

5 15 25 35 45 55 65 75 850

10

20

30

40

50

60

Beats per minute vs Resultant component of flow over wing.

@ 1 m/s@ 2 m/s@ 3 m/s@ 4 m/s@ 5 m/s@ 6 m/s@ 7 m/s@ 8 m/s@ 9 m/s@ 10 m/s

Beats per Minute BPM

Degr

ees °

7.1.3. Lift Predictions Using Calculated CL Values

Using the method outlined by Sane and Dickinson (2001) [2] for their experimental

results, the same approach was taken with the calculated theoretical values obtained

for φ and α. This involved using equations derived by Dickinson et al (1999) [23] for

the approximation of CL and CD in flapping wings. Using this method, a separate

estimate of lifting force could be obtained to those found in XFLR5. Both approaches

would have their short comings, however both would provide results for comparison

to test results achieved. Figure 40 details the values found for both CL and CD for

both cases of the symmetrical ±30° α wing sweep, and the case of the wing having a

high α on the upstroke. These values would remain constant for any frequency (Also

the timescale plotted) over one period of the wings sinusoidal motion, due to the

59

Figure 39: The plot of the resultant flow angle study. Here the resultant α is shown on the y axis against the beats per minute frequency of the wings for varying speeds of freestream flow.

nature of the CL as value (Velocity of the air has no effect on CL, it is directly related

to Lift Force)

The equations derived by Dickinson et al (1999) used to predict CL and CD values

for the following results are as follows:

CL=0.225+1.58 sin(2.13 α−7.2)

¿

CD=1.92−1.55cos (2.04α−9.82)

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1

0

1

2

3

4

Predicted CL and CD Values for sweep of 60-120

CLCD

Time, s

CL-

CD

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1

0

1

2

3

4

Predicted CL and CD Values for sweep of 60-160

CLCD

Time, s

CL-C

D

60

Figure 40: Top-CL and CD predicted for the case of symmetrical servo sweep.

Bottom: The CL and CD for the servo case of large upstroke α.

Having found the CL of the wing, Lift Force could then be calculated using the lift equation.

This would produce a Lift Force plot for any wing case providing the velocity over the wing

was known. Figure 41 shows both Lift Force plots of the symmetrical and large upstroke α

cases at 96BPM as the CL is plotted in Figure 40.

0 0.1 0.2 0.3 0.4 0.5 0.6

-1.5

-1

-0.5

0

0.5

1

1.5

2

Predicted Lift Force for servo sweep: 60-120

Lift Force

Time s

Forc

e N

0 0.1 0.2 0.3 0.4 0.5 0.6

-1.5

-1

-0.5

0

0.5

1

1.5

2

Predicted Lift Force for Servo Sweep: 60-160

Lift Force

Time, s

Forc

e N

7.1.4. Lift Force Predictions For The Wing Using XFLR5

By using XFLR5 it was possible to obtain a prediction of the wings CL throughout a

series of flight conditions. These CL values could then be used in the equation for

Lift Force to find the equivalent force produced by the wings. There were some

61

Figure 41: Top- Lift Force predictions for symmetrical α sweep.

Bottom- Lift Force predictions for high α upstroke.

limitations to carrying out this in XFLR5 as the software is primarily used for the

evaluation of fixed wing model aircraft, with no capacity to go into turbulent flow

conditions. This means it only has an accuracy at smaller angles of attack. It was not

practical to use different software or attempt to take this study any further, as trying

to model the wing Lift Force at higher angles of attack and in flapping conditions,

would be more than sufficient as work for a completely different project. This is due

to unsteady aerodynamic mechanisms being present around the wing during its

flapping motion that allow wings to stay effective beyond the normal point of stall. For

static conditions however, Figure 42 predicts the Lift Force that can be obtained with

change in Angle of Attack at varying freestream velocities. This would still be useful

as it enables an insight into the force that could be obtained by the wings if the twist

for Angle of Attack could be optimised. In the production of a flying vehicle this could

be invaluable when positioning the wing for both thrust and lift to keep the vehicle in

the air at constant velocity.

-20 -15 -10 -5 0 5 10 15 20

-6

-4

-2

0

2

4

6

8

10

12

Lift Force generated vs AOA across a range of freestream velocities

1 m/s2 m/s3 m/s4 m/s5 m/s6 m/s7 m/s8 m/s9 m/s10 m/s

Angle of Attack (°)

Lift F

orce

N

62

Figure 42: The plot of the results for Angle of attack, α vs Lift Force obtained from the wings. The force obtained by the rig was expected to be in the lower region of Lift Force due to the static nature of the testing, however it was quite possible that more force might be obtained due to the unsteady mechanisms that may form on the flapping wings.

7.1.5. XFLR5 Lift Force Predictions Across A Period Of Flapping

With all previous calculations made concerning Flap Angle and Angle of Attack,

Values of φ and α could be picked at time intervals through one period of flapping to

find the CL and Lift Force produced by the wings. This approach would allow a plot

for Lift Force of which values could be directly compared to the force obtained

experimentally from the load cell. There would be some limitations in doing this with

accuracy due to the previously mentioned downfalls of XFLR5. However along with

the plot of Lift Force against Angle of Attack, this provided the best approximation of

the performance expected.

The limitations of XFLR5 meant that the program could not model the CL of the wing

to a high Angle of Attack, however due to the resultant flow this was not completely

necessary. As the resultant flow direction could be far from an α of 0°, this meant

that in reality the Angle of Attack of the flow experienced by the wing may not be as

great as the wing twist and could therefore be calculated by XFLR5. Because of this,

a reduction in α was assumed and the values scaled to be within the range of

XFLR5. Although not completely accurate, this would at least enable a prediction at

a flow velocity for incremental stages of a flapping cycle. All the values used for φ, α,

ρ and V were all taken from the previous stages of calculation.

Figure 43 shows an example of the initial prediction for Lift Force throughout a flap

cycle of the wings. This was made at a low frequency, as it was originally not known

how fast the mechanism would be capable of moving the wings without causing

damage. In reality this estimate was to low and the motor could not function properly

with the low revolutions required to flap the wings at 40 beats per minute. The Angle

63

of Attack was calculated as if the wings were flying at 3m/s freestream velocity to be

at an Angle of Attack of 7° for the best Lift/Drag ratio.

0 0.15 0.3 0.45 0.6 0.75 0.9 1.05 1.2 1.35 1.50

1

2

3

4

5

6

7

8

9

Lift Force vs Time @40 BPM (Sweep: -4°to 10°)

1m/s2m/s3m/s4m/s5m/s6m/s7m/s8m/s9m/s10m/s

Time (s)

Lift F

orce

(N)

The same process to obtain results was undertaken for some specific cases of

flapping configuration. One of these cases was for the wing at a frequency of

96BPM, with a wing twist for an α of -30° to 70°. This Angle of Attack was not

possible in XFLR5, however as previously mentioned, due to resultant flow, in reality

the wing would not be achieving the high value of 70° due to the resultant angle of

the velocity component. Instead the maximum possible values for the aerofoil were

used at +30° and -20°. These were then mapped and scaled to the range of the wing

twist that would be applied for the experimental test. This should provide a result that

although was not directly comparable, did give an indication of a calculated force.

The plot in Figure 44 shows that for the low velocity cases, a lifting force of 1N or

less was to be expected from the wings. This estimate seemed a reasonable value

to expect from physical testing, as once the test rig had built up to speed, and the

wings were flapping, it would be reasonable to assume that there would be some

64

Figure 43: A plot of Lift Force over a flap cycle for 40 Beats per minute with a sweep of the wing twist between -4° and 10°.

airflow around them. For an idea of the numerical value of the forces calculated from

this same example, the table of values used for the plot of the 1, 2 and 3m/s cases is

shown in Figure 45.

0 0.15 0.3 0.45 0.6

-10

-5

0

5

10

15

20

Lift Force vs Time @96BPM (Sweep: -20°to 30°)

1 m/s2 m/s3m/s4m/s5 m/s6 m/s7 m/s8 m/s9 m/s10 m/s

Time (s)

Lift Fo

rce (

N)

65

Figure 44: The Lift Force vs time plot for the calculated numerical analysis with the largest possible angle of attack possible in XFLR5 applied.

Figure 45: The table of numerical values showing the predicted forces for figure 10. Values of 1.3N at peak lifting force would be good to obtain experimentally and show that the design of the test rig could be feasible.

Time φ α CL Force @1 m/s (N)

Force @2 m/s

(N)

Force 3m/s (N)

0 0 30 1.69 0.144918 0.579671.30425

8

0.0694 13.81 22.98 1.4623 0.1253920.50156

9 1.12853

0.104 19.26 15 1.2976 0.1112690.44507

71.00142

3

0.16 21.17 0 0.3493 0.029952 0.119810.26957

2

0.226 16.5-

19.28 -0.77 -0.06603 -0.26411 -0.594250.3125 0 -30 -0.834 -0.07152 -0.28606 -0.64364

0.43 -21.17-

10.26 -0.0014 -0.00012 -0.00048 -0.00108

0.469 -21.5 0 0.3483 0.0298670.11946

70.26880

1

0.556 -13.82 23 1.4608 0.1252640.50105

41.12737

2

0.59 -10.5 28.19 1.6763 0.1437430.57497

11.29368

5

7.2. Experimental Results

The results obtained from the load cell on the test rig were the product of a snapshot

taken from the oscilloscope screen. This meant that the results initially covered a

series of flap cycles and still contained some noise, even though capacitors had

been added to the circuit across the output leads to quieten the signal. An example

of a screen shot from the oscilloscope can be seen in Figure 46 with Figure 47 being

a plot of the force obtained after initial averaging and manipulation of the raw

numerical data. It would not be useful to analyse the results of multiple wing flaps as

some inconsistency could be found, it would also be hard to compare the large

amount of data generated over two cases. Because of this it was decided that the

best approach was that of Sane and Dickinson (2001) [2], where the average of

multiple wing strokes was taken to provide data for just a single wingbeat. This would

lead to any anomalies being lost into a data set for a single wing beat of averages.

To remove the small amount of noise still recognised by the oscilloscope, an array

average was used similar to the technique used for a noisy analogue input with an

Arduino board, in order to create a smoother output. This also had the effect of

slightly reducing the value of the inertial forces of the wing.

For the purposes of looking at the Lift Force obtained in this study, the inertial forces

that are a product of the change in direction at the end of the down stroke will be

ignored. Lift Force will be the main interest in this study, with the positive force

obtained on the plots from the load cell being the main focus. It is also important to

remember that as the wings are tethered to the desk, airflow over the wings is

negligible, therefore there will always be negative force induced as the wings are on

the upstroke due to inertial forces and air resistance as it was not possible to twist

the wings on the rig to a full 90° Angle of Attack.

66

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

76 BPM (Sweep: 60-120)

76 BPM (Sweep: 60-120)

Time s

Forc

e N

7.2.1. Symmetrical Positive And Negative α Study With Increasing Frequency

The following four figures (Figure 48, 49, 50 and 51) are of plots from the

symmetrical servo sweep study at increasing increments of frequency. This would

67

Figure 46: The screenshot of data obtained from the oscilloscope. Even with capacitors added to the circuit with the load cell there is still noise in the signal output from the load cell.

Figure 47: A plot of the data once initial processing had taken place with a conversion of the output voltage from the load cell into Force in Newtons.

allow the measurement of the effect of the increased airflow over the wing induced

by higher φ.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Average Stroke 64 BPM (60°-120°)

Average stroke

Time s

Forc

e N

0 0.1 0.2 0.3 0.4 0.5 0.6

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Average Stroke 76 BPM (Sweep: 60°-120°)

Average Stroke

Time s

Forc

e N

0 0.1 0.2 0.3 0.4 0.5 0.6

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Average Stroke 88BPM (60°-120°)

Average Stroke

Time s

Forc

e N

68

Figure 48: Symmetrical servo sweep configuration at 64 Beats per minute

Figure 49: Symmetrical servo sweep configuration at 76 Beats per minute

Figure 50: Symmetrical servo sweep configuration at 88 Beats per minute

0 0.1 0.2 0.3 0.4 0.5 0.6

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Average Stroke 96 BPM (Sweep: 60°-120°)

Average Stroke

Time s

Forc

e N

7.2.2. High Positive α Study With Increasing Frequency

The next study made was again into the increasing frequency of flapping, but with

the variation of a much higher Angle of Attack on the upstroke. As mentioned by

Anderson (2001), the rapid pitch up at the end of the stroke allows higher CL to be

achieved towards the end of the lift stroke [20]. The higher α in the upstroke should

also produce less negative force due to the reduced surface area perpendicular to

the velocity of the wings centre of mass. The results for this study are plotted in

Figures 52, 53, 54 and 55. All increments in the increase in frequency have been

kept the same as for the symmetrical servo sweep study.

69

Figure 51: Symmetrical servo sweep configuration at 96 Beats per minute

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Average Stroke 64 BPM (Sweep:60°-160°)

Average Stroke

Time s

Forc

e N

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Average Stroke 76 BPM (Sweep:60°-160°)

Average Stroke

Time s

Forc

e N

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Average Stroke 88BPM (Sweep:60°-160°)

Average Stroke

Time s

Forc

e N

70

Figure 52: The Force plot for the high positive α study at 64 beats per minute

Figure 53: The Force plot for the high positive α study at 76 beats per minute

Figure 54: The Force plot for the high positive α study at 88 beats per minute

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Average Stroke 96BPM (Sweep:60°-160°)

Average Stroke

Time s

Fo

rce N

7.2.3. Increasing α Sweep Study At Constant Frequency

The final set of results obtained experimentally was a study into the effect of Angle of

Attack increase. As with the study into symmetrical servo sweep, the positive Lift

Force generated was the main focus, with the large spikes of inertial force, and other

negative forces generated being ignored. This study would be useful as calculations

into the best Angle of Attack were not accurate, due to the ability to only find

solutions to a static wing in two dimensional flow. The case of flapping would present

a far more difficult problem and for the purposes of this project would be better

analysed experimentally. The symmetrical servo sweep analysed, ranged from ±10°

through to ±50° in increments of 10°. These results are shown in Figure 56 to 60.

The same procedure was used as for the previous results by applying Sane and

Dickinson’s method [2] of averaging all strokes measured into a single wing beat.

This would keep all results obtained consistent.

71

Figure 55: The Force plot for the high positive α study at 88 beats per minute

0 0.1 0.2 0.3 0.4 0.5 0.6

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±10° Flap force

Flap cycle average

Time s

Forc

e N

0 0.1 0.2 0.3 0.4 0.5 0.6

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±20° Flap force

Average Flap cycle force

Time s

Forc

e N

72

Figure 56: The result of a servo sweep of ±10°

Figure 57: The result of a servo sweep of ±20°

0 0.1 0.2 0.3 0.4 0.5 0.6

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±30° Flap force

Flap cycle average

Time s

Forc

e N

0 0.1 0.2 0.3 0.4 0.5 0.6

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±40° Flap force

Flap Cycle Average

Time s

Forc

e N

73

Figure 58: The result of a servo sweep of ±30°

Figure 59: The result of a servo sweep of ±40°

0 0.1 0.2 0.3 0.4 0.5 0.6

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±50° Flap force

Flap Cycle Average

Time s

Forc

e N

8. Chapter 3: Analysis

The results for the numerical modelling and the experimental studies allowed a

comparison between the theoretical calculations and reality. Not only would these

comparisons provide answers, but the differences between the experimental results

and the theory proved to be just as revealing as the similarities as to the challenges

of flapping wing flight. As well as considerations that would need to be made or

addressed in the design of an MAV. These answers or new challenges would not

only come from the results but also from the design and operation of the test rig,

74

Figure 60: The result of a servo sweep of ±50°

revealing design faults that may have already been addressed by the designers of

previous successful projects such as the Festo Smartbird[3].

8.1. The Design

The selection of wood as the predominant material was chosen because of the

speed in producing parts by laser cutting. However this added unnecessary weight to

the test rig. The 3mm and 5mm thick plywood used is the same as that used in

remote control model aeroplanes. However these thicknesses were more than

required as the structure proved plenty strong enough. As to the loads induced on

the wood, the design played well to the material strengths, adding to the case for the

potential of thinner wood. Alternatively, the ribs could have been made from much

lighter balsa wood due to the loads being quite low and the structure more than

adequate.

Looking at the results of experimental testing, the most noticeable characteristic is

the large peak of negative force. This is created by the large inertial forces produced

by the wings, as their momentum is rapidly damped at the end of each downstroke.

This is amplified by the motion of the mechanism quickly lifting the wings for the

upstroke. The use of carbon fibre in the Festo Smartbird, allows for a lightweight,

tough design that can withstand harder landings. Furthermore, the Smartbird’s two

part wing may have corrected the problem of large negative inertial forces. The out

of phase movement of the wings in the Smartbird could reduce momentum by

always having one of both panels of the wing moving while the other is stationary. In

comparison to the test rig, which has an aggressive flapping style, this provides a

much smoother flap cycle.

75

The second design point of interest was the use of the servos for wing twist. On the

Smartbird, these are located towards the tip of the wing, in line with the spar that the

wing rotates around. Although the connection of the servo arm to a sliding pin in the

wing hinge did prove effective, in an improved version of the test rig, this would be a

point for a major redesign. In testing the end of the pin would be jammed by the test

rig frame at the extremes of φ, the distance between the servo arm and the sliding

pin track also proved problematic with moments causing some bending. The

configuration of the servo connected directly to the spar instantly overcomes these

problems, and although space is limited at the tip of the test rig wings, there is no

reason why the solution could not be implemented at the centre of the wing (Figure

61). If the current mechanism was kept in an improved version, it is likely a metal

servo arm would be needed for strength with a better fixing to the pin. A different

material would also be needed for the sliding pin track, as the 3D printed plastic was

quick to wear.

76

Figure 61: The Dashed red box shows the potential location of the servo in a redesign.

Another key area of improvement was the fixing of the push rod gears to the frame. These

gears were constantly brought out of line by the load of the wings through the push rod, this

was improved by gluing the washers that held them in place closer to the frame. However

the issue still remained (Figure 62). In all other projects, similar mechanisms are used with

pushrods on circular gears, with gears remaining in the correct plane. An improved version

would seek to learn more from previous projects, and how the gears were fixed. This may be

that the tolerances are much finer for a tighter fit of the axel to the frame, or potentially an

improved version may use the method of keeping the axel fixed in position with the gear

rotating around it.

8.2. Flap Angle, φ And Angle Of Attack, α

The flap angle and alpha calculations in the numerical analysis proved hard to

implement in the physical model of the test rig. Without a feedback or sensor

77

Figure 62: The two red gears side by side had problems with alignment. This was mainly down to the large tolerance of the holes in the frame for their axels. Fixing the axels to the frame and allowing the gears to rotate around them may have been a better configuration for the load carrying gears.

connected to the Arduino to measure the rate of change of φ, it was hard to properly

synchronise the twist of the servos. This meant that considerable calibration had to

be done before the running of any test in order to find values that produced the

correct amount of cycles per minute, from both the servos and motor individually.

Once inputs were found to give an approximate timing, the servos and motor were

run together and fine-tuned to be synchronised. This however was still not a

complete solution, as it would be impossible to know the precise φ in order to induce

an appropriate twist for the desired α.

With further work on the project, the addition of sensors would be the most practical

and useful modification. A sensor could easily be positioned on the frame to register

the movement of one of the gears or the wing spar. This could be used as a trigger

to activate a twist of the servo with regard to its current position. This addition would

alleviate the need for calibration and the correct starting position of the test rig,

allowing the parameters affecting beats per minute to be changed exclusively with

the speed of the motor.

8.3. Comparisons Between The Lift Force Calculated And Lift

Force Determined Experimentally.

Due to the nature of the numerical analysis, it was possible to use two different

methods for calculating the Lift Force produced by the wings. One method would

apply the calculation of sinusoidal functions of φ and α as by Whitney and Wood

(2012) [22], to then apply equations for the approximation of CL and CD as by

Dickinson et al (1999) [23] to finally produce a force prediction from the lift equation.

The second method for theoretically determining the lift would again use calculation

of φ and α to then run an analysis on increments of the flap cycle in XFLR5 to find a

78

CL, this would then as before, be used in the lift equation. Both methods would have

their advantages and disadvantages but when comparing the two methods over a

single case with identical values of φ, α, V ∞ and ρ, there is a strong correlation

between the results obtained. A comparison is shown in Figure 63 with a comparison

between the methods for a case of 96BPM, an Angle of Attack sweep of -30° to

+70°, and a freestream velocity of 3m/s.

-0.4 0.1 0.6

-1.5

-1

-0.5

0

0.5

1

1.5

2

XFLR5 prediction vs Calculated values

XFLR5 pre-diction

Calculated prediction

Time, s

Lift F

orce

, N

Figure 63 shows a good correlation between the peak Lift Force values predicted by

both methods. The Lift Force peak in the middle of the downstroke has less than a

0.1N difference. However, in the upstroke of the wing, the negative Lift Force values

have less similarity. This highlights one of the problems in using XFLR5 to predict Lift

Force in flapping wings. Whereas the approximations will take into account

assumptions and previous data gathered on the subject, XFLR5’s use is exclusively

to small fixed wing aircraft. This means that especially in the extreme α values

79

Figure 63: A representation of the two different methods used in the numerical analysis of the project. The plot of results of the XFLR5 prediction is much less continuous, however it is composed of much less data points, if the capability to analyse more data points quickly was there, the results may show an even stronger correlation between 0.3 and 0.45 seconds.

experienced by a flapping wing, XFLR5 is unable to predict conditions which the

equations developed by Dickinson allow for.

The other downfall of the XFLR5 analysis which is remarkably clear is the inability to

analyse and obtain results for more than one case at a time. The software which is

primarily for the remote control hobbyist wishing to design their own aircraft, is not

set up for full analysis of changes taking place in a flapping wing. Although possible

to analyse Angle of Attack in a sweep between two values, the range of angles may

only span across a maximum of 40° at a time. The software is also able to do the

same with freestream velocity. However in the example of a flapping wing vehicle,

the software cannot sweep through more than one set of parameters at a time, and

in the case of wing dihedral which is constantly changing in flapping flight, this must

be altered manually every time. To this end, the plot of the XFLR5 results is

composed of only 10 data points, with plots for the calculated values containing

some 37 data points. This becomes obvious when viewing them side by side, as the

plot for the XFLR5 values is far less continuous in profile due to a far less regular

spacing of values. This is not to say however, that an XFLR5 analysis with more data

points could provide a much more coherent analysis.

80

0 10 20 30 40 50 60 70 80 90 1000

0.5

1

1.5

2

2.5

3

3.5

Low Speed resultant velocity induced by flapping

@ 1 m/s@ 2 m/s@ 3 m/s

Frequency BPM

Velo

city,

m/s

Figure 64 shows the predicted increase in the freestream flow over its value due to

the added component of the wings velocity in the downstroke. From the results of the

application of blade element theory, which treats the wing as a propeller blade

moving at a constant velocity perpendicular to an oncoming flow, it can be seen that

the increase becomes less with increasing horizontal airspeed. An airspeed of 1m/s

sees an increase of almost 100% with a frequency of 90BPM. However at the same

frequency, a freestream flow of 3m/s experiences only around a 33% increase.

Interestingly, when it comes to the experimental setup, these theoretical calculations

would suggest that the test rig experiences a significant induced horizontal flow from

its own motion. The force calculations made at 3m/s produce peak Lift Force values

similar in magnitude to those seen from the experimental results, most notably those

in Figure 54 and 55 (In Chapter 2) for 88BPM and 96 BPM with large servo sweep. A

comparison of theoretical against the experimental results for the same case is seen

in Figure 65. This would suggest that either the flow experienced by the wings after

run up to the correct speed was considerably higher than predicted, or that in reality

81

Figure 64: The predictions for low velocity resultant flow over the wings using Blade element theory [27].

the unsteady aerodynamic mechanisms present in flapping wings are responsible for

a large portion of lift generated at stationary conditions. However it is also possible

that the flow associated with the vortices is created by the unsteady mechanisms

responsible for the increase, as is the possibility of the wake of previous wing strokes

having an effect of airflow.

The solution to the increased Lift Force over that expected is not entirely certain. The

lack of flow visualisation, control over horizontal flow and local air conditions, or any

sensors to determine pressure around the wing make finding the solution to this very

difficult. In further work, these criteria would make for an interesting investigation and

help to further validate experimental results. Some indications however prove that

flows were certainly created by the running test rig, such as movement of small loose

debris on the desk.

-0.4 0.1 0.6

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Calculation vs XFLR5 vs Experimental Results

Lift Force Calcu-lation

Lift Force XFLR5

Experimental

Time, s

Forc

e, N

82

Figure 65: A comparison of the two theoretical approaches against the experimental results. All plots show a frequency of 96 BPM. The two theoretical approaches are both modelled with a horizontal flow of 3m/s which are the closest match of the predicted values to those obtained experimentally. It is hard to know the exact airflow and the degree of the effect of the wake capture and vortices generated by the flapping motion of the test rig during the experimentation.

The important characteristic to consider in Figure 65 is the peak Lift Force obtained

by each set of results. The exact values of this peak force are shown in Figure 66 to

allow for further comparison. The peak force resulting from the calculations made

with the relationships derived by Sane (2001) and Dickinson (1999) is the highest,

with the experimentally generated value as the lowest. The value from the XFLR5

analysis comfortably sits midway between the two. All results however are relatively

close in magnitude, being all within a 0.2N range. This is quite a good relationship

between the method and the experiment which is still followed for the increase in

frequency which uses the relationship shown if Figure 64, for the relationship

between resultant velocity and frequency. This is shown in Figure 67 where resultant

velocity predicted for the experimental frequency is used to calculate the Lift Force

failing a method to experimentally determine velocity.

8.4. The Relationship Of Lift Force And Frequency

83

Peak ForceCalculate

dXFLR

5Experiment

al

1.39 1.30

1.19

Figure 66: The Raw values of Peak Lifting force for the theoretical and experimental results.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-2

-1.5

-1

-0.5

0

0.5

1

1.5

64 BPM Servo sweep: 60°-160°

64 BPM

64 BPM

Time, s

Force

, N 0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

76 BPM Servo sweep: 60°-160°

76 BPM

76 BPM

Time, s

Force

, N

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

88 BPM Servo sweep: 60°-160°

88 BPM

88 BPM

Time, s

Force

, N 0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

96 BPM Servo sweep: 60°-160°

96 BPM

96 BPM

Time, s

Force

, N

The general trend discovered for increasing frequency was more or less as predicted

by the numerical analysis. The increased φ had the effect of increasing the velocity

of flow over the wings allowing them to produce more lift with higher frequency. This

trend is well demonstrated by the progressive plots in Figure 7. The experimental

force is obtained using the predicted flow increase with frequency for a horizontal

component of 2m/s. This relationship can be found in Figure 64 and is used as a

representation of aerodynamic mechanisms that are likely to be in action around the

wing, as before measuring, the wings were run up to the frequency under

investigation.

84

Figure 67: The plots for increasing frequency with a servo sweep to high α

This trend was shown far more exaggerated in the study for increasing frequency

with symmetrical servo sweep. Looking at the experimental results for the peak

positive lifting force between Figure 48 and Figure 51(Chapter 2), there is a

difference of around 1N of lifting force. Here the maximum positive Lift Force

achieved by the test rig at 96BPM is 1.78N, considerably higher than that achieved

with the high α upstroke configuration of flapping. This is likely down to the time it

takes the wing servos to carry out their sweep for the change of the wings Angle of

Attack. The quicker movement of the servo arm needed for the high alpha upstroke

may cause one of two problems: the first may be that the faster travel of the servo

leaves the wing with less time in the downstroke close to its optimum Angle of

Attack. The second may be that the asymmetrical wing twist between positive and

negative leaves the wing at an undesirable α for a larger portion of the stroke.

A good way to assess directly the effect of increasing frequency and therefore φ on

the wing is to compare the maximum Lift Force measured against the maximum

predicted Lift Force. This gives a direct relationship that may be instantly recognised

of both theoretical and measured values increasing with the frequency (Figure 68

and Figure 69). The Angle of Attack however does have the same effect on both the

predicted values and the experimental values in the studies made. The symmetrical

sweep for the Angle of Attack predicts quite low values of Lift Force, however the

measured values actually turned out to be similar to those achieved, as would be

expected with the same downstroke alpha in the configuration of the 60° to 160°

servo sweep. This is interesting as the equations are a product of α rather thanφ. It is

likely that the peak force predicted for the high α configuration on the upstroke is

being displayed rather than the value achieved on the downstroke. On the other

85

hand the predictions proved to be accurate, as the high upstroke alpha configuration

has a good correlation with the results.

64 69 74 79 84 89 940

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Predicted Lift Force vs Experimentally Obtained Lift Force (60-120)

TheoreticalPredicted

Frequency, BPM

Forc

e, N

64 69 74 79 84 89 940

0.2

0.4

0.6

0.8

1

1.2

1.4

Maximum Predicted Lift Force vs Experimentally Obtained Lift Force

TheoreticalExperimental

Frequency, BPM

Forc

e, N

Although peak Lift Force is close to theoretical values, the profile of Lift Force

variation is vastly different. The theoretical Lift Force demonstrates a profile close to

a sinusoidal function with a small plateau at the peak for positive Lift Force and a

slight positive jump in the trend at peak negative Lift Force. On the other hand, the

86

Figure 68: The Comparison of predicted and measured values for the symmetrical servo sweep configuration. Here the predicted is far lower than the measured.

Figure 69: The comparison between the predicted and measured values for the high α configuration. The results here show far better correlation, with predicted values being far more accurate.

experimental data obtained shows a roughly exponential increase in Lift Force to the

maximum value, with a sharp drop following to the maximum negative value. This is

likely due to two factors, firstly there is no consistent horizontal airflow. This would

serve to create a more sinusoidal profile, as it would provide a steady Lift Force on

the wings, rather than the wings movement having to disturb the stationary air they

are operating in. The predicted values for Lift Force however even if not completely

correct will follow the more sinusoidal relationship, as they are the result of nothing

but the product of a relation with α which does have such a variation.

The trend seen in the force obtained experimentally, is a result of the relationship

between the mechanism in the test rig and its power application to the wings. The

equations used to predict the Lift Force do not take into account inertial forces,

gravity and frictional loses between the gears, all of which play a part in the results

gained from the test rig. Inertial forces of the wings are responsible for the much

larger negative force than predicted as previously mentioned, however they are also

the reason for the peak force being pushed to later in the cycle than predicted. This

comes as the mechanism must overcome the wings inertia to bring them up on the

upstroke, due to the use of a small motor similar to the one used in the Smartbird.

The motor was not able to fully enforce its motion continuously to the wings through

the mechanism. An added load on the motor was the gravitational acceleration

acting on the wings which aided the sharp acceleration on the downstroke. Also as

previously discussed, the added volume of the wings being made from 3mm thick

plywood added to their weight. All this together meant that rather than experiencing a

velocity peak mid stroke, the wings were moving at their fastest as they came to the

lower part of the downstroke. Reflected by the late peak seen in the result plots.

87

Fluctuations may also be seen as a characteristic in all graphical representations of

the results. These are a result of the frictional forces in the mechanism which

hindered the movement of the rig. The rapid nature of having to produce and build

the test rig led to inevitable faults which affected the smoothness of operation, this

was a result of mostly minor faults such as the wing spars being improperly fixed

against rotation and frictional contact between the rough finish of the plywood and

the 3D printed hinges.

8.5. The Relationship Of Lift Force And α

In fixed wing applications, an increase in α will to a point yield an increase in lift. The

test rig was built to be in configuration to test both change in Angle of Attack and

change in frequency. It was decided that the study into the wing α would be a sweep

symmetrical about the chordwise datum of 0° α. Both wings would be swept to and

from the same positive and negative value for ease of programming and to keep

consistency in the testing, as programming asymmetrical cases might have led to

varying servo speeds that might induce unwanted forces in the rig. All cases were

carried out at a frequency of 88 BPM, as it was decided from the results and

observations made in previous tests that it would provide a good rate of flap angle

change that would neither be too slow to obtain meaningful lift values or fast enough

to induce large inertial forces.

As before with the increasing frequency studies, the theoretical lift was calculated

using sinusoidal relationships for φ and α. The α values would then in turn be used

to find CL and then Lift Force which could be plotted alongside that obtained

experimentally for comparison. The Lift Force obtained from the load cell was

averaged over six wing beats in order to give an average set of values for a single

88

flap cycle. This approach to the theoretical calculations from the work of both

Whitney, J.P. (2012) [22] and Dickinson, M.H. (1999) [23] proved the most

straightforward way of processing the large amount of data generated in testing. This

coupled with the method of presenting experimental results by Sane, S.P. (2001) [2]

provided the best way of presenting both the predicted and actual values for a

specific combination of the frequency and amplitude of α applied to the test rig

wings.

Figure 70 shows the plots of theoretical and experimental results for the testing of

increasing Angle of Attack. As much as possible, parameters were kept constant

across all testing with the same frequency, same conditions and the servos moving

the wings between positive and negative α at a uniform speed. Again as in previous

discussion over the theoretical results, the velocity applied in the equation for Lift

Force is not 0m/s which would be the true horizontal component of velocity on the

test rig wings. The freestream speed was again treated as 2m/s with the increase

induced by the wings flapping at 88 beats per minute. This allowed the aerodynamic

mechanisms and the motion of the wings to be accounted for in force calculations.

89

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±10° Flap force

Flap cycle average

Theoretical LIft

Time s

Force N

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±20° Flap force

Average Flap cycle force

Theoretical Lift

Time s

Force N

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±30° Flap force

Flap cycle average

Theoretical Lift

Time s

Force

N 0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±40° Flap force

Flap Cycle Average

Theoretical Lift

Time s

Force

N

0 0.1 0.2 0.3 0.4 0.5 0.6

-2

-1.5

-1

-0.5

0

0.5

1

1.5

±50° Flap force

Flap Cycle AverageTheoretical Lift

Time s

Forc

e N

The results of this study of comparison of the theoretical and experimental are hard

to draw from. At a glance, the theoretical force suggests that an increasing trend

90

Figure 70: The representations for the increase in symmetrical α sweep. Theoretical and experimental values are displayed.

should be seen in the peak Lift Force achieved, however it seems to remain more or

less constant for all cases but 40° α, which drops as an anomaly. This result was

unexpected as it was assumed that an increasing value of Angle of Attack in the

downstroke would allow for better performance into the effective on coming flow and

provide better lifting capabilities.

The lack of a trend in the results could be the product of a number of factors. The

first possibility could be that in fact the 88 beats per minute was not high enough to

produce the force needed for a good analysis. As was found in the frequency study,

the increase in frequency would have induced an increase in forces measured.

Another factor could be the lack of oncoming flow over the wing. The incremental

changes in peak Lift Force predicted with increase in α do suggest that forces would

be as high as those found in the frequency study, with no prediction being 1N of

force or more. An oncoming flow of 2m/s may have produced better results. The final

factor, could be as previously mentioned; the lack of sensors or a feedback loop in

the control. As it is hard to judge the timing of the flapping and Angle of Attack, it

may be that a change in α was not correctly timed in any of the tests.

In order to directly compare the difference between the predicted and theoretical

forces it is useful to look at the peak forces achieved. Figure 71 shows the peak

forces plotted against the sweep angle for α. Here we can see that the experimental

results, although showing a slight increase, are fairly inconsistent with the lowest

value seen at 30°α. The predicted results on the other hand show the expected

upward trend.

91

10 15 20 25 30 35 40 45 50

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Peak Lift Force Predicted vs Peak Lift Force Measured

Predicted ForceMeasured Peak Force

Angle of Sweep, °

Forc

e, N

92

Figure 71: The peak force values show the extent of the discrepancy between the experimental and predicted results. Further work would seek to provide a conclusive study in this area.

9. ConclusionThe results of this project bring forward a number of conclusions which may be

backed up by the data collected and the work undertaken. The theoretical study and

application of blade element theory to the flapping wings determines that flow must

increase with an increase in frequency. From this it follows that an increase in lift is

to be expected which is confirmed by both experimental studies into the variation of

frequency, with both Figures 68 and 69 (Chapter 3) showing an upward trend in Lift

force measured.

The second point worth mentioning is the difficulty in predicting the Lift that can be

generated by a set of flapping wings in ‘Zero’ Velocity conditions. Any calculation

made to predict lift force will not be entirely accurate for the conditions experienced,

to this end, the velocity of flow over the wings must to some extent be assumed by

the application of velocity induced by the flapping motion, determined by the use of

blade element theory. This difficulty led to the disparities seen in the theoretical and

experimental values for the angle of attack variation study, and the symmetrical α

sweep increase in frequency.

It is extremely obvious in the measurements from the load cell that the inertial forces

present during the motion of the wings is considerably higher in magnitude than the

forces under investigation. These forces could have the effect of obscuring some

results as they are clearly the dominant force at work within the test rig. In order to

conduct some more conclusive testing, these would have to be addressed.

As a result of the data collected in this study it is obvious that the main parameter

investigated essential to generating a suitable Lifting Force, was the flapping

frequency. The results show conclusive evidence that the lift force is increased per

93

stroke with higher frequency. It goes without saying that with higher frequency, the

force generated is applied more regularly per minute than the lesser force at a lower

amount of beats per minute. In the design of a flapping wing air vehicle, possibly the

most essential factor in its success would be to match the frequency with the

characteristics of the wings to ensure enough lift for the required performance. Angle

of Attack of the wings in the stroke, although important to some degree is thought

would be more essential in generating thrust which was not a subject of this project.

In further work there are many more alterations and measurements that would be of

use to the development of flapping wing flight. However as a result of this project and

specifically the work done in testing the concept of the flapping wings, with internal

servos providing wing twist, the main additional investigation would be as follows:

Firstly the investigations carried out in the results of this project, would be carried out

in some form of airflow, or the test rig attached to a rotating arm of constant speed.

This would allow forces to be measured outside of the zero velocity condition and

would allow the exact parameters used in the theoretical calculations to be

controlled. A second study to be carried out would be into the propulsive force

generated by the wings and the effect of the Angle of Attack and frequency on the

thrust the wings generate. For work such as this, it may also be of interest to add

some form of flexible trailing edge towards the tip of the wing, which could enhance

the thrust created significantly. Lastly the alteration off the design to the two panelled

wing configuration of the Festo Smartbird [3] would allow for a comparison of inertial

forces. The two panelled wing by its nature should provide a better conservation of

momentum in the flapping wings, due to the panels flapping out of phase. Forces at

the end of the down stroke would likely be far less in amplitude, with the entire flap

cycle being much smoother without the rapid change in direction of the wings seen

94

with this apparatus. That is not to say however that with some design alterations, the

concept here could not be developed into a fully functioning MAV where the servos

used for wing twist could be used as a good substitute for the flexibility seen in

natural wings.

95

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25. Images availiable at: http://m-selig.ae.illinois.edu/ads/coord_database.html26. Image availiable at: http://www.wfis.uni.lodz.pl/edu/Proposal.htm27. Robert S. Merrill (2011) Nonlinear Aerodynamic Corrections to Blade Element

Momentum Modul with Validation Experiments, Logan, Utah : Utah State University, (p5-p11)

28. D.J. Auld, K. Srinivas (1995-2006) Aerodynamics for Students - Blade element propeller analysis, Available at: http://www-mdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/propeller/prop1.html(Accessed: 8th July 2015).

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11. Project Management

Shown in Figure 1 is the original plan proposed for the project, however this was

subject to some change in the duration of the project for various reasons. The first

difference one can notice in the actual timescale shown in Figure 2, Is the changes

in some of the tasks to be carried out. The main differences occur at the bottom of

the task list where original work proposed was slightly over ambitious with not

enough time being left to test the propulsive force of the test rig. This would have

required considerably more time with a considerable amount of change needed in

order to change the plane of the load cell by 90°, and not to mention a new way of

supporting the frame.

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Figure 1: The Original Gantt Chart plan for the project

Figure 2 has another difference in that the experimental work is pushed much further

towards the end of the project. This came as a result of an unexpected amount of

time needed to order and obtain specific parts for the project, such as the load cell

and the hinges. This situation of parts not being always available at the planned time

pushed back the construction of the wings and mechanism and delayed the test rig

calibration and set-up. Had these unexpected circumstances not been present

however, it is likely the last part of the project would have run much closer to

schedule.

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Figure 2: This shows the actual timings of the project and the changes in the steps to be taken are included with minor changes made to the task list.

12. Appendix: Dissertation Proposal: Bio-inspired

Flying Machines

1. Introduction and Background to the Project

There is currently a fast increasing interest in bird and insect flight and how this

could be interpreted into a mechanical flying machine, more specifically in the form

of a UAV (unmanned air vehicle). Potential for such vehicles has been identified in a

number of sectors, most notably in the military market. With development of stealth

technology and radar being in a constant battle of development, a new form of

stealth is being considered, in the form of ‘bird or insect like’ vehicles. These would

be small and disguised to look as their counterparts in the natural world making them

very hard to detect visually and by radar. Lessons have already been learn for the

current generation of small UAV’s as birds and insects have naturally evolved to

operate in similar Reynolds number regimes [1].

Many attempts have been made to achieve flapping wing flight as it has been a

dream of man-kind for century’s to fly like a bird resulting in many ornithopter

attempts and to this day models are still being produced for hobbyists, some

powered by elastic bands, others powered by electric motors. However perhaps

the most significant step forward in bird like flight is the FESTO Smartbird, based

on a gull (Figure 1). This uses flapping with a servo to actively twist the wing

based on sensor readings for torsion of the wing, load on the motor and motor

position. Other vehicles have also been produced drawing inspiration from other

areas such as hummingbirds, dragonflies and other insects, however most of

these are much smaller and the end result is not as convincingly real.

Nonetheless, some of these have also provided major leaps forward in

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understanding aerodynamics, control and flight characteristics of flapping wing

flight.

2. Aims and objectives

Listed below is what the project will aim to achieve in order to ensure that the

project has a direction and a plan for development of ideas.

Build upon work carried out in the group project using similar wing

configuration

Experimentally develop the aerodynamics of the wing in order to obtain

greater force.

Test the wing using a load cell to obtain lifting force from flapping

Further testing to investigate the propulsive force.

Develop a configuration that could be used in the construction of a flapping

wing vehicle.

3. Summary of Methodology

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Figure 1: The Festo smartbird

Review literature and summarise the findings with a specific focus on wing

profiles, shapes. Look also at models and equations for lift generated by

wing flapping relating to angle of attack to the oncoming flow

Learn how to program an Arduino board, this will be useful when it comes

to testing as the correct motors and servos will be able to set up in order to

control the test and gain accurate results.

Produce CAD models of wing designs for both preliminary analysis and for

ease of producing accurate components in experimental testing.

Design and build prototype wings and test rig. It is essential that the

different test subjects may be interchanged easily without lengthy

adaptions or having to largely disassemble the experimental set-up.

Produce a programmed electronic system using the Arduino set to be

applied to flap and twist the wings whilst being experimented on.

Run a series of tests using a load cell mounted with the motors for the

electronic flapping in order to determine differences between test subjects.

Test for propulsive force obtained from the wing using a similar load cell

configuration in the horizontal axis, rather than vertical.

Attempt to apply results to build a full model for the configuration of a

flapping wing vehicle, this would follow work done in the group project

using a similar concept.

4. Project Plan

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References

1. Carruthers A.C.∗, Walker S.M., Thomas A.L.R., Taylor G.K. (2009) 'Aerodynamics of aerofoil sections measured on a free-flying bird', Part G: J. Aerospace Engineering,224(AERO737), pp. 855-864.

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13. Appendix

1- The outline of the frames for Laser Cutting

2-The File of the wing ribs to be laser cut.

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#include <Servo.h>

Servo escmot;

Servo myservo1;

Servo myservo2;

int pos = 0;

void setup() {

3. The Arduino Code

4. Pictures of the completed Wing Structure

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#include <Servo.h>

Servo escmot;

Servo myservo1;

Servo myservo2;

int pos = 0;

void setup() {

5. Picture of the Test Rig and Experimental Set-up

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