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ResearchCite this article: Le TQ, Truong TV, Park SH,

Quang Truong T, Ko JH, Park HC, Byun D. 2013

Improvement of the aerodynamic performance

by wing flexibility and elytra – hind wing

interaction of a beetle during forward flight.

J R Soc Interface 10: 20130312.

http://dx.doi.org/10.1098/rsif.2013.0312

Received: 5 April 2013

Accepted: 13 May 2013

Subject Areas:biomimetics

Keywords:beetle, elytra, forward flight, wing interaction,

wing flexibility, computational fluid

dynamics simulation

Authors for correspondence:Jin Hwan Ko

e-mail: jhko@kiost.ac

Doyoung Byun

e-mail: dybyun@skku.edu

& 2013 The Author(s) Published by the Royal Society. All rights reserved.

Improvement of the aerodynamicperformance by wing flexibility andelytra – hind wing interaction of abeetle during forward flight

Tuyen Quang Le1, Tien Van Truong2, Soo Hyung Park2, Tri Quang Truong3,Jin Hwan Ko1, Hoon Cheol Park3 and Doyoung Byun4

1Korea Institute of Ocean Science and Technology, PO Box 29, Ansan 425-600, Korea2Department of Aerospace and Information Engineering, and 3Department of Advanced Technology Fusion,Konkuk University, Seoul, Korea4Department of Mechanical Engineering, Sungkyunkwan University, Suwon, Korea

In this work, the aerodynamic performance of beetle wing in free-forward

flight was explored by a three-dimensional computational fluid dynamics

(CFDs) simulation with measured wing kinematics. It is shown from the

CFD results that twist and camber variation, which represent the wing

flexibility, are most important when determining the aerodynamic perform-

ance. Twisting wing significantly increased the mean lift and camber

variation enhanced the mean thrust while the required power was lower

than the case when neither was considered. Thus, in a comparison of the

power economy among rigid, twisting and flexible models, the flexible

model showed the best performance. When the positive effect of wing inter-

action was added to that of wing flexibility, we found that the elytron

created enough lift to support its weight, and the total lift (48.4 mN) gener-

ated from the simulation exceeded the gravity force of the beetle (47.5 mN)

during forward flight.

1. IntroductionThe unsteady high force mechanism of a flapping wing including a leading edge

vortex (LEV), rotational motion, wake capture and clap-fling has been unveiled

[1,2]. Among them, the LEV is a crucial phenomenon; however, more studies

are required of the spiral LEV [3] as well as the momentum transfer between

the wing and the surrounding environment during three-dimensional flapping.

More recently, improving the aerodynamic performance of a flapping wing

mimicking a flying insect has attracted the interest of researchers. Wing inter-

action characteristics and flexibility during the flapping motion are primary

issues because they are believed to be the main reasons for the best aerodynamic

performance of a flying insect. A great improvement in the aerodynamic force

can be achieved from the interaction between two wings when they flap in appro-

priate parameters, including the gap between them, phase difference between

the motions of two wings, and the amplitudes of their plunge motions [4–6].

Meanwhile, more studies are necessary in order to explore the aerodynamic

performance caused by the interaction between flexible wings.

Wing flexibility is believed to be a key factor for improving the aerodynamic

performance of insect flight. The wing of hoverflies is known to be dramatically

deformed during the flapping period: the wing is positively cambered during

the downstroke by trailing edge tension compressing the radial veins and nega-

tively cambered with the tension released during the upstroke. The wing is also

strongly twisted along the spanwise direction [7]. Walker et al. [7,8] conducted a

detailed study of the deformable wing kinematics of hoverflies, including time-

varying wing camber, twist and angle of incidence. In addition, the wing

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deformation of a dragonfly was assessed using a compu-

tational fluid dynamic model [9] to explore the improvement

of its aerodynamic performance.

It is extremely difficult to build a numerical model to

analyse the interaction between a wing surface and its

surrounding air environment because the mechanics and

mutual interactions of both the solid and fluid continua

should be considered. Moreover, the solution should be

convergent at every iterative step in both the solid and

fluid domain. Alternative approaches are experimental

studies or numerical computations of a simplified model.

Recent research has shown that the twist angle indeed

plays more significant roles than the camber in determining

the aerodynamic forces during hovering flight by increasing

the lift coefficient and reducing the required aerodynamic

power [10]. When simplified wing-tip kinematics and

angles of attack in the models of insect flight are used, the

measured lift-to-drag ratio can be considerably reduced

compared with when the original kinematics are used [11].

An experimental study of the effects on the aerodynamic

force generation by wing flexibility showed that the net

force on a flexible wing can increase or decrease through

alternating sizing of the LEV by camber variation [12]

during forward flight. Spanwise flexibility was found to be

beneficial for thrust generation in a numerical study of flap-

ping wing propulsion. The spanwise flexibility yields a

small increase in the thrust coefficient and a small decrease

in the power-input requirement, which results in higher effi-

ciency [13]. Young et al. [14] analysed the aerodynamic forces

of wing deformation in the locust using a commercial compu-

tational fluid dynamic (CFD) code with pre-described wing

kinematics, later validating the numerical results through

particle image velocimetry and smoke wire visualization

methods. They found that a deformable wing achieved

greater power economy than an un-cambered twisted

model, which performed better than an untwisted model.

There are also attempts to build up a systematic fluid–struc-

ture interaction (FSI) for highly flexible flapping wing [15,16].

A systematic analysis of the aerodynamic performance of a

hovering hawkmoth, Manduca, was reported as the first suc-

cessful FSI of a flapping insect [17]. The hovering efficiency

of a flexible wing was found to be improved when twisting

is considered.

Here, the aerodynamic performance of a flexible wing

and elytra–hind wings interaction of a beetle are explored

by a three-dimensional numerical simulation. The aerody-

namics performance of the beetle owing to the previous

two factors is an interesting research topic because its size

is quite large compared with other insects, the hind wings

are highly flexible, and the elytra are hard wings whose

main function is the protection of the hind wing and the

body. The aerodynamics of flexible hind wings in beetle

flight is not fully known yet. Moreover, the aerodynamic

role of the elytra is not well elucidated owing to their small

size and great hardness. So far, the closing and opening

mechanism of elytra as well as their geometry have been

the main focus in previous studies [18,19]. The elevation of

the prothorax was speculated to be the main mechanism in

closing the elytra [20]. A simple method for analysing the

aerodynamic performance of elytra has been published

[21,22]. However, sophisticated studies of the aerodynamics

in both wings are still required. The role of elytra in aerody-

namics becomes more interesting when elytra–hind wing

interaction is considered because the beetle has one active

and one passive flapping wing, whereas other insects such

as dragonfly and desert locust have two active wings.

In this study, flexible wing kinematics including twist and

camber deformation is acquired through an experimental

study, with the results used as the input for a CFD analysis.

The kinematics of the elytra is captured in the study as well,

and a simulation considering the interaction between a

single elytron and the hind wing was then conducted in

order to investigate the aerodynamic role of the elytron

during flapping flight.

2. Materials and methods2.1. Wing kinematicsIn our work, measured kinematics is used instead of simplified

motions such as a sinusoidal function in order to investigate

the aerodynamics of a realistic wing considering its flexibility.

A male beetle is hung in the air inside a cubic chamber by a

hook that is attached to the head of the beetle with cyanoacrylate

glue. A cubic chamber of 50 � 50 � 50 cm is made of a transpar-

ent acrylic. Two high-speed cameras (Photron APX) are placed

outside the chamber. One captures the front view and the other

captures the side view. The camera is set to 2000 fps with a resol-

ution of 1024� 1024 pixels. Two halogen lamps of 1 KW power

are positioned to illuminate the region near the beetle. Fourteen

1 mm white dots are marked on the hind wing and four dots

are marked on the elytron as anatomical landmarks for digitiz-

ation purposes, as shown in figure 1. After several minutes of

suspension, the beetle initially flies freely, while two cameras

recorded its motion. A modified direct linear transformation

(DLT) method is used to merge two two-dimensional camera

recordings in a single three-dimensional coordinate space. Then,

the three-dimensional coordinate of each dot on the wings is ana-

lysed by the DLT method implemented in Matlab. The details of

the experimental study can be found in our previous work [23].

In the practical experiment, we repeated the pre-described pro-

cesses several times in order to obtain high-quality data. Finally,

we use averaged values in the six cycles of the flapping wing in

determining a stroke plane, a flapping angle, a stroke amplitude,

a deviation angle and an angle of attack (AOA) for the hind wing

and the elytron based on the dot’s coordinates (x, y and z values).

First of all, the stroke plane is defined as a plane which con-

tains a wing-tip path connecting the top, bottom and middle

positions during the cycle, which is called a representative tip

path, as shown in figure 1a. The stroke angle is defined as the

angle between the stroke plane and the horizontal plane

namely, the zx plane. The span line is defined as a line connect-

ing the selected dot near the wing tip and the selected dot near

the wing root (thick yellow line in figure 1a). The flapping

angle is defined as the angle between the span line and its pro-

jection on the horizontal plane. The stroke amplitude is defined

as the angle between the span line when the wing tip is at the

top position and the span line when the wing tip is the bottom

position. The deviation angle is the angle between the span

line and its projection onto the stroke plane (orange line in

figure 1a). The deviation angle is used as the measure that indi-

cates the difference of the instantaneous realistic tip path and the

representative tip path, namely it shows the out-of-plane motion

of the wing. The AOA is the angle between the chord line and the

stroke plane. Furthermore, the camber is defined as the ratio of

the mid-chord height (h) over the chord length (lc) at each sec-

tion. Similarly, the kinematics terminology of the elytron is

defined in figure 1b. The elytron is a rigid wing, so twist and

camber variations are negligible and the deviation angle is

almost 08. Hence, the kinematics of the elytron is described by

tip path

AOA

stroke planestroke amplitude

realistic tip path

representative tip path

stroke plane

angle of attack (AOA)

stroke plane

chord line

camber (h/lc)

dot on hind wing

lc

hdot on elytron

stroke amplitudedeviationangle

x

z y

(a) (b)

Figure 1. Definitions of terminologies in kinematics of (a) hind wing and (b) elytron. (Online version in colour.)

hind wingflexible

red grid: background mesh

green grid: body mesh

blue grid: wing surfacemesh

rigid

elytron

y

y

z x

x

z

y

y

x

x

z

y

x

z

z

(a) (b) (c)

Figure 2. (a) Structured grid for Chimera mesh, (b) difference between rigid (skyblue) and flexible (red) hind wing models at typical time steps during downstrokeand (c) kinematics of elytron and hind wing used in the simulation. (Online version in colour.)

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three parameters: the stroke angle, the flapping angle and the

AOA. The stroke plane of the elytron and the flapping angle

are defined by two dots at the tip and the root wing as shown

in figure 1b. The AOA is the angle of the chord line, which con-

nects two dots at the middle position along the spanwise

direction on leading and trailing edge, and the stroke plane.

2.2. Numerical methods2.2.1. Flow solverThe wing kinematics from pre-described experimental study was

used as the input condition of a CFD code in an effort to inves-

tigate the aerodynamic performance of a beetle. The in-house

code, termed KFLOW, is a parallelized multi-block-structured

Navier–Stokes solver; several turbulent models are available.

For the spatial discretization, the Roe flux difference slitting

scheme and third-order MUSCL are used with Van Albada lim-

iter to obtain secondary accuracy of inviscid flux. Meanwhile, the

simple central difference is used to obtain variable gradient of

viscous flux. The dual-time stepping with the diagonalized alter-

nate directional implicit method is used to advance the solution

in time. This allows not only the use of a large time increment

but also the maintenance of temporal accuracy. In addition,

dual-time stepping also eliminates factorization and lineariza-

tion errors by iterating the solutions along a pseudo-time. The

numerical detail has been described in previous works [24–27].

0

–0.2

0.2

0.4

lift (

N)

t/T

0.6

present studyDickinson et al. [2]Sun & Tang [36]Ramamurti & Sandberg [37]

0

0.2 0.4 0.6 0.8 1.0

Figure 3. Benchmarking of three-dimensional flapping simulation. (Online version in colour.)

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A Chimera mesh scheme was used to simulate a flapping wing

because of its advantage in handling the relative motion between

meshes [28]. In this Chimera overset method, a cut-paste algorithm

is applied to compose a cross section that exchanges informa-

tion between grids, which enables the generation of overlapping

grids with moderate mesh interface regions. The overlapped grid

method combines two major steps: hole cutting and donor

identification [29].

2.2.2. Wing and kinematics modellingThe morphologies of the hind wing and the elytron were measured

in order to rebuild realistic wing models used in the simulations.

Then, two block structure grids were created: one is the back-

ground mesh which covers the fluid domain in the simulation,

the other one is a body-fitted mesh that contains the wing surfaces

as shown in figure 2a. The no-slip boundary condition was applied

on the wing surface; meanwhile the far field condition was

imposed on the outer surface of the background mesh.

The numerical simulation was conducted in a standard air con-

dition in which the reference velocity (forward velocity) and

reference length (chord length) were 1.5 m s21 and 1.55 cm, respect-

ively. Hence, the non-dimensional parameters of the Reynolds

number (Re) and reduced frequency (k) were around 1500 and

1.25, respectively. The flapping motion of the wing was described

by the flapping angle, the AOA and the deviation angle while

the orientation of the motion was decided by the stroke plane.

The time variation of these three angles was digitally extracted

from the experimental study, and the approximate function with

time was then constructed for each angle by the following equation:

wðtÞ ¼Pn¼6

n¼0

�wcn cosðnktÞ þ wsn sinðnktÞ

�

bðtÞ ¼Pn¼6

n¼0

�bcn cosðnktÞ þ bsn sinðnktÞ

�

aðtÞ ¼Pn¼6

n¼0

�acn cosðnktÞ þ asn sinðnktÞ

�

9>>>>>>>>=>>>>>>>>;

; ð2:1Þ

where w(t), b(t) and a(t) are the flapping angle, the deviation angle

and the AOA, respectively. They are approximated by sixth order

series in order to match the experimental data well. The coefficients

of wcn;wsn; . . . ;acn;asn are determined by solving the approximate

matrix equation. In the case of the elytron, the deviation angle is too

small to be ignored, thus its motion is expressed through two

angles: the flapping angle and the AOA.

2.2.3. Wing flexibility and wing interactionFirst, the aerodynamic performance of the flexibility of the

hind wing was investigated through the following three

models. The first model is the rigid wing in which the AOA

along the spanwise direction was fixed as a measured value at

r/R ¼ 0.4. Here, r is the distance from the wing root to a refer-

ence point, meanwhile R is the hind wing’s length in the

spanwise direction, measured from the wing root to the wing

tip, namely, the AOA of all points on the wing at each time

step are equal to the measured AOA at r/R ¼ 0.4 at that time

step. In other words, AOA is not spatially varied in the rigid

wing model. The second model is a twisting wing in which the

AOA was varied along the spanwise direction, namely the

AOA becomes the function of time and space. The third model

is a flexible wing in which camber variation was added com-

pared with the twisting wing. So, both AOA and camber are

functions of time and space. Hence, the roles of spanwise twist-

ing and camber variation in aerodynamic performance in beetle

flight are expected to be clarified throughout the comparisons of

these wing models. The linear variation of the AOA along the

spanwise direction versus time are approximated by sixth

order series, which is similar to equation (2.1). Then, the vari-

ation of the AOA was automatically applied to each point of

the wing surface at each time step in the simulation of

the twisting wing. Similarly, the time and spatial variation

of the camber was also rebuilt as an approximate function,

which is applied to each point on wing surface at each time

step in the simulation of the flexible wing. Differences in the

(a) (b)

(c) (d )

angl

e (°

)ca

mbe

r (%

)

AO

A (

°)

30

60

90

120

150

180

r/R=0.2

r/R=0.2 r/R=0.8r/R=0.6r/R=0.4

r/R=0.4r/R=0.6r/R=0.8

rR

0 0.2 0.4 0.6 0.8 1.0t/T

r/R=0.2r/R=0.4r/R=0.6r/R=0.8

20

15

10

5

0

–5

–10

–15

–200 0.2 0.4 0.6 0.8 1.0

t/T

50

flapping angle

AOA

angl

e (°

)

40

30

20

10

0

0 0.25 0.50 0.75 1.0–10

flapping angledeviation angleAOA at r/R=0.4

0 0.25 0.50 0.75 1.0

180

135

90

45

0

–90

–45

Figure 4. Kinematics of (a) elytron and (b) hind wing, (c) angle of attack and (d ) camber deformation of the hind wing at different sections along the spanwisedirection. r is distance from wing root to reference point, meanwhile R is length from wing root to wing tip, in (c). (Online version in colour.)

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wing morphologies of the flexible and the rigid wings are rep-

resented at typical time steps: t/T ¼ 0, 0.25 and 0.5 which are

corresponding to beginning, middle and end positions of the

downstroke as shown in figure 2b.

Second, the simulation of the interaction between the elytron

and the hind wing was conducted in order to explore the aerody-

namic performance of the elytron. The wing interaction between

both sides and wing–body interaction in hovering hawkmoths

was studied in Aono et al. [30,31], which showed that the differ-

ence in the force on left and right wing is ignored owing to

symmetric flapping; also, the force generated by the body is

much smaller than that by the wing. The interaction between

the left and the right wing is expected to be significant only in

a small insect at low Reynolds number when the positions of

the two wings are closed enough [32]. The beetle is an insect

which has a large body and the gap between two wings is

quite large, hence the effect of the interaction is estimated to be

small. Thus, in this work, we just analysed the interaction

between the elytron and the hind wing on one side of the

beetle. Interaction simulation requires three blocks of structure

grid: one body-fitted mesh is for the elytron, the other is for

the hind wing and the background mesh is for the rest. Two

wings were controlled to flap simultaneously. The hind wing

was a flexible wing while the elytron was a rigid wing, where

no twist or camber was considered. The wing positions and

shapes at the typical time steps are shown in figure 2c.

2.2.4. Evaluation of force and validation of methodThe total aerodynamic force was calculated from the pressure

and the shear stress on the wing surface, which are obtained

from the solution of the Navier–Stokes equation. Between

them, the pressure is a critical factor in evaluating the force

in flapping motion. Hence, vortices, the pressure contour

around the wing and the pressure coefficient on the wing

surface were usually extracted for the quantitative analysis of

the aerodynamic performance. The vortices could describe

rotational flow structures and a considerable pressure drop

normally occurs near their core region. Here, the Q-criterion

is chosen among local vortex-identification criteria. Hunt

et al. [33] named Q after the second invariant of velocity

gradient tensor ru, which is calculated by

Q ¼ 12ð jVj jj

2 � jSj jj2Þ ¼ 12ðVijVij � SijSijÞ; ð2:2Þ

where Vij ¼ 1/2(@ui/@xj 2 @uj/@xi) and Sij ¼ 1/2(@ui/@xj þ @uj/@xi). Namely, Q is the balance between the rotational rate

jjVjj2 and the strain rate jjSjj2. Thus, iso-surfaces of positive

Q indicate areas where the strength of rotation overcomes

stroke plane

V•

forward velocity

flapping velocity, U

(c)

relative velocity, V

effectiveAOA

AOA

V•

stroke plane(d)

U

V

effectiveAOA

AOA

hind wing

elytronchord(0.2R)chord

(0.8R)leading edge

t/T=0.25

t/T=0.75

(a) (b)

Figure 5. Snapshots of the kinematics from (a) side view camera and (b) front view camera. A difference in orientation of chord line at r/R ¼ 0.2 ( pink line) andr/R ¼ 0.8 (yellow line) is clearly shown in (b). Correspondingly, AOA and effective AOA are defined at r/R ¼ 0.2 and r/R ¼ 0.8 in (c) and (d ), respectively, at themiddle position of the downstroke (t/T ¼ 0.25). (Online version in colour.)

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that of the strain. The pressure coefficient (CP) along a chord

line is plotted in order to show differences of pressure on

top and bottom surfaces. It is defined as

CP ¼P� P1

0:5r1V21

; ð2:3Þ

where P is the pressure at a reference point. P1, r1, and V1 are

pressure, fluid density and velocity under free-stream con-

ditions. Total aerodynamic force was resolved to horizontal

force, vertical force and side force in the x, y, and z directions,

respectively, in a global fixed coordinate (figure 2). The side

forces are cancelled out from left and right side wings owing

to symmetry in free-forward flight. The free-stream velocity is

parallel to the x direction, hence lift is the vertical force and

thrust is the negative horizontal force. The aerodynamic

torque (T ) in each direction of the flapping motion was also cal-

culated by the sum of the cross product of the force and the

position vector from the wing root to each cell centre located

on the wing surface as follows:

T ¼X

i

Fi � ri ð2:4Þ

where Fi and ri are force and position vectors at each cell. Then,

the aerodynamic power was calculated by the scalar products of

the angular velocity and the aerodynamic torque of the wing.

The accuracy of our flow solver in analysing a flapping wing

was validated in previous works [34,35]. Moreover, we performed

a simulation of a fruitfly model during hovering as the benchmark

for the three-dimensional flapping simulation. The flapping kin-

ematics were chosen from the experimental model described in

Dickinson et al. [2]. Then, the lifts from our results were compared

with the experimental results in Dickinson et al. [2] and other

numerical simulation results [36,37]. Figure 3 shows that our

results show good agreement with the previous data.

The convergence solution was obtained when the dependence

of the aerodynamic forces on the grid and time was minimized.

Two body meshes were used, grid 1 (260 � 40� 150) and grid 2

(350 � 50� 180), around the wing section in chordwise, normal

and spanwise directions. The difference of forces was less than

2.8 per cent between them. Hence, grid 1 was used to test the

effect of the number of time steps. The numbers of the time step

in a cycle were 100, 200 and 300 for case 1, 2 and 3, respectively.

The difference in force was less than 5 per cent between case 1

and case 2, and less than 3 per cent between case 2 and case 3.

Therefore, we chose grid 1 and case 2 for the present study.

3. Result3.1. Wing kinematics and morphologyThe wing morphology was obtained from the experimental

measurement. The lengths of the hind wing and elytron

were found to be around 48.20+1.38 and 24.14+1.25 mm,

respectively. The mean chord length of the hind wing and

the elytron were approximately 15.02+0.21 and 14.00+0.38 mm. Hence, the sizes of the hind wing and the elytron

were set to 50 � 15 and 25 � 14 mm, respectively, when the

grid system of both wings was generated.

The kinematics of the elytron is shown in figure 4a. Down-

stroke is the period from 0 to 0.5 non-dimensional time, t/Twhen the wing tip starts to move from the top position to

the bottom position, where T is total period. Meanwhile,

upstroke is the period from 0.5 to 1 t/T. Hence, the middle

positions of downstroke and upstroke are 0.25 and

0.75 t/T, respectively. There were 53 frames for a single stroke,

which means that the frequency ( f ) was 37.7+0.3 Hz. The

body angle is almost zero degrees with respect to the horizon-

tal plane. The free-forward velocity of the beetle was recorded

at 1.5 m s21 based on the tracking body position with the

frame at each time step. The stroke angle and the stroke ampli-

tude of the elytron are 78+4.68 and 32+4.48, respectively.

The AOA varies from 258 to 158. Regarding the hind wing,

figure 4b–d shows the wing kinematics as well as the variation

of the AOA and the camber deformation along the spanwise

direction at r/R ¼ 0.2, 0.4, 0.6 and 0.8. The stroke angle of

the hind wing was 72+2.38 during free-forward flight. The

stroke amplitude of the hind wing was recorded in a range

from 1608 to 1708 (averaging 164.4+5.68). The deviation

angle was less than 108. The variation of the AOA showed

that the hind wing twisted dramatically during the transla-

tional phase (0.1 � t/T � 0.4 and 0.6 � t/T � 0.9) in

downstroke and in upstroke, respectively. In the transition

phase (0.4 � t/T � 0.6 and 0.9 � t/T � 1.1), the AOA varied

largely towards the wing tip. For example, it varied from 468to 1268 and from 218 to 1718 at r/R ¼ 0.2 and 0.8, respectively.

In addition, the camber variation at each section of the hind

wing during the flapping stroke was determined; the maxi-

mum positive camber was recorded at around þ16% during

0

200

150

100

50

–50

–100

2000

1500

1000

500

0

t/T = 0.25 t/T = 0.35

t/T

t/T = 0.80

50

0

–50

–100

–150

hori

zont

al f

orce

(m

N)

vert

ical

for

ce (

mN

)po

wer

(m

W)

0

0

0 0.25 0.50 0.75 1.0

Figure 6. Effect of the flexibility of the hind wing on the aerodynamic force. (a-c) Dashed line, rigid wing; solid line with triangle, twisting wing; solid line, flexiblewing. (Online version in colour.)

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Table 1. Average values of the aerodynamic forces and required powerduring one cycle of flapping.

rigidwing

twistingwing

flexiblewing

thrust (mN) 32.2 26.7 38.9

vertical force (mN) 20.9 23.7 23.5

required power (mW) 709 496 535

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the downstroke, while the negative camber was 212% during

the upstroke [23].

The twist angle is defined as the difference of the AOA

between r/R ¼ 0.8 and 0.2. During the flapping cycle, the

AOA of the hind wing shows approximately linear decrement

in the downstroke and linear increment in the upstroke along

the spanwise direction as shown in figure 4c. Thus, the twist

angle was negative during the downstroke and positive during

the upstroke. For instance, the twist angle was 2258 and þ358at the middle positions of the downstroke (t/T ¼ 0.25) and the

upstroke (t/T¼ 0.75), respectively. Figure 5a,b shows the snap-

shots of wing kinematic and also represents the difference in

the orientation of the chord line at r/R ¼ 0.2 and 0.8. The

AOA was defined as the angle between the chord line and

the stroke plane; meanwhile, the effective AOA is the angle

between the chord line and the relative velocity (V ), which is

the resultant vector of the forward velocity (V1) and the local

flapping velocity (U¼ vr). For example, at t/T¼ 0.25, the

AOA is 60 and 35 on sections r/R ¼ 0.2 and 0.8, respectively.

The free-stream velocity is 1.5 m s21, whereas the local flapping

velocities are approximately 3 and 12 m s21 on these sections.

Thus, the effective AOA values are approximately 458 and 388on these sections. Similarly, the effective AOA values are

approximately 258 and 128 on sections r/R ¼ 0.2 and 0.8 at the

middle position during the upstroke (t/T¼ 0.75). Consequently,

the difference in the effective AOA between r/R ¼ 0.2 and 0.8

becomes smaller than that in the AOA as shown in figure 5c,dbecause the beetle instinctively changes its wing twist in order

to improve the efficiency of its flight.

3.2. Aerodynamic performance of a flexible hind wingThe aerodynamic forces and power required for the flapping

motion of three hind wing models are shown in figure 6. The

stroke plane angle was 728 with respect to the horizontal

plane, which indicates that the hind wing flapped with

nearly a vertical stroke; therefore, positive vertical force was

typically created during the downstroke and negative force

was formed during the upstroke. The magnitude of the

instantaneous vertical force of the twisting wing was smaller

than that of the rigid wing, as clearly shown in the middle

position of the stroke when the twist angle of the hind

wing was largest. The instantaneous vertical force of a flexible

wing with camber variation was similar to that of the rigid

wing during the downstroke; however, it was smaller

during the upstroke. Thrust was produced during both

strokes owing to the large variation of the AOA. The twisting

wing created less thrust than the other models. The thrust cre-

ated from the flexible wing was similar to that of the rigid

wing during the downstroke, while it was largest during

the upstroke. The required power for the translational

phase (0.1 � t/T � 0.4 and 0.6 � t/T � 0.9) was much

higher than that for the transition period in which the wing

rotates (0.4 � t/T � 0.6 and 0.9 � t/T � 1.1).

Specifically, the power required in the graph shows that

the rigid wing requires more energy for flapping in compari-

son with the other models. The average values of these

parameters are summarized in table 1. The advantage of

wing twist and camber variation was clearly shown in the

comparison of the power economy, which is defined as the

ratio of the total aerodynamic force to the required power.

The results indicate that the power economies were 0.054

and 0.071 N W21 for the rigid and twisting wing,

respectively. These values are 35 and 15 per cent lower com-

pared with that of the flexible wing (0.084 N W21).

To gain in-depth insight into the performance of all

wing models and for the comparisons among them, the

vortex and pressure around the wing must be analysed.

First, the aerodynamic performance at the middle position

of the downstroke, where the difference in the instant forces

and power required among these wing models is most sig-

nificant, was explored. Figure 7 shows the iso-surfaces of

the Q-criterion and pressure distribution on the hind wing

in the rigid (top) and the twisting (middle) and the flexible

(bottom) cases at t/T ¼ 0.25. The iso-surface of the Q-criterion

indicates the size of LEV and it is coloured by the pressure

magnitude in the figures. Corresponding to the vortices,

the pressure distributions on the wing surface as well as on

two cross-sections (r/R ¼ 0.3 and 0.75) are depicted in the

right column. In general, the vortex aspects in the three

cases were quite similar. However, vortex magnitudes dif-

fered. At the middle position of the downstroke, the

downward translational velocity of the hind wing reached

its maximum value and the spiral LEV occurred on the top

surface of the wing, and the spiral LEV near the wing tip

was inflected to form the tip vortex. Also, the root vortex

was connected to the tip vortex and round vortices formed.

In a comparison of the colour, the negative pressure in the

spiral LEV near the wing tip in the case of the twisting

wing was smaller than that of the rigid wing. This can be

explained by decrease in the effective AOA towards the

wing tip; at r/R ¼ 0.8, it was 388 for the twisting wing and

608 for the rigid wing. The instantaneous positive camber

enhanced the strength of the spiral LEV in the flexible wing

model. Consequently, the horizontal and vertical forces of

the flexible wing are more similar to those of the rigid wing

than to those of a twisting wing, as shown in figure 6. The

camber apparently improves the instant value of the lift as

well as the thrust of the flexible wing compared with the

twisting wing.

The negative pressure (blue) distribution indicated the

locations as well as the strength levels of the vortices. On

the top surface of the hind wing, the negative pressure

region was confined to the leading edge near the wing root

and was extended along the chordwise direction near the

wing tip; this phenomenon is caused by the spiral LEV.

Negative pressure on the cross-sections also shows the

strength of the LEV in the vicinity of the top surface of the

hind wing, while positive pressure (red) was observed on

the bottom surface of the hind wing owing to its downward

translational motion. Especially at r/R ¼ 0.75, the strength of

the LEV for the three models can be distinguished by the

magnitude of the pressure. A clear difference is noted in

the size of the LEV between the rigid and twisting wings.

twisting

spiral LEV

t/T=0.25pressure

1.00 y

x

z

y

x

z

y

x

z

y

x

z

y

x

zy

x

z

0.780.560.330.11

–0.11–0.33–0.56–0.78–1.00

flexible

rigid

Figure 7. Iso-surfaces of Q-criterion (left) and the pressure (right) distribution on rigid, twisting and flexible wings at t/T ¼ 0.25. The iso-surfaces of Q-criterionindicate the size of LEV, and the pressure contour shows high and low pressure zones on surface and vicinity of wing.

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The LEV detached and its core moved up and away from the

top surface in the rigid wing. On the other hand, it attached

easily onto the top surface in the case of the flexible wing

owing to its concave shape.

In a more detailed quantitative comparison, the pressure

coefficient at two sections was plotted, as shown in figure 8.

The strength of the LEV can be seen through the large negative

pressure coefficient on the top surface of the hind wing. In the

section with r/R ¼ 0.3, the pressure coefficient dropped sharply

to a negative value near the leading edge and then recovered

quickly, remaining constant towards the trailing edge. Mean-

while, it recovered gradually towards the trailing edge in the

section with r/R ¼ 0.75. Again, this phenomenon was caused

by the spiral LEV: concentrated on a small area near the wing

root and spreading over the wing area near the wing tip.

The difference in the positive pressure coefficient on the

bottom surface among these wing models also denotes the

effects of the camber factor and twist. The difference in the posi-

tive pressure in the three models was minor near the wing root

when the local flapping velocity was small. The difference

became significant near the wing tip; with the twist angle, the

chord line was well aligned with the relative velocity and a

low amount of positive pressure occurred on the bottom surface

in the twisting wing, whereas the positive camber strengthened

the positive pressure from the middle position of the chord line

towards the trailing edge in the flexible wing.

Similarly, figure 9 shows the iso-surfaces of Q-criterion

and pressure distribution on the three wing models with

t/T equal to 0.8, when the wing passed through the middle

position of the upstroke. An unstable vortex region appears

below the bottom surface of the wing. This was considered

to result from the rapid wing rotational motion during

the transition period from the downstroke to the upstroke.

A new strong spiral LEV is generated on the bottom surface

in the three wing models when the wing rapidly moves in the

upward direction. The negative pressure area on the section

with r/R ¼ 0.75 visually showed the strength of the spiral

LEV. At r/R ¼ 0.8, the effective AOA was 128 for the twisting

0

–1

–0.5

0

–1

–0.5

0.5

0

blue line: flexible wing

X-position (chordwise) X-position (chordwise)

solid line: bottom surfacedash line: top surfacered line with circles: rigid wing

green line with triangles: twisting wing

pres

sure

coe

ffic

ient

pres

sure

coe

ffic

ient

0.5 1.0 0 0.5 1.0

zx

y

zx

y

Figure 8. Pressure coefficient of the three wing models at (a) r/R ¼ 0.3 and (b) r/R ¼ 0.75 at the middle position of the downstroke (t/T ¼ 0.25); the subfiguresshow the cross section of the three models and location on the hind wing. Blue, red and green lines indicate flexible, rigid and twisting wings, while solid anddashed lines show pressure coefficient values on bottom and top surfaces, respectively. (Online version in colour.)

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wing and 408 for the rigid wing. Hence, the strength of the

spiral LEV on the wing surface in the twisting wing was

much smaller than that in the rigid wing. The instant nega-

tive camber strengthens the spiral LEV in the flexible wing

model. As a result, the rigid wing creates instant negative ver-

tical force that is larger than that of the other wings, as shown

in figure 6. The negative camber made the flexible wing pro-

duce the largest thrust. In terms of energy consumption, the

rigid wing required a considerable amount of power,

whereas the other wings needed less during this period.

The differences in the force among the three models were

apparent at the above two time steps, but they were not during

the other time intervals. Therefore, we selected one specific

time step (t/T¼ 0.35) to determine the factors that caused this.

When the hind wing passed through the middle position and

towards the end position of the downstroke, the spiral LEV

near the wing tip fully detached from the top surface and

was shed into the wake in the downstream. At t/T¼ 0.35, an

unstable vortex was observed near the wing tip, showing a

complicated structure of the vortices with the combination of

the spiral LEV and the tip vortex, as shown in figure 10. The

ring of the tip vortex broke down in the downstream in the

case of the twisting wing owing to its low strength. Correspond-

ing to the pressure distribution, the area shown in blue, which

exists only near the wing root, indicates that strong negative

pressure dominates. In other words, the spiral LEV is still

attached to the wing surface near the wing root. On the other

hand, the area in blue is diluted to green in the detaching

vortex area near the wing tip. At this moment (t/T¼ 0.35), the

forces and required power are small and the effect of the twist

and the camber is trivial. In general, the effect of the twist and

camber is not significant in the period when the spiral LEV is

detached from the wing surface.

3.3. Elytron – hind wing interaction considering theflexibility of the hind wing

The elytron–hind wing interaction was also studied when the

flexible hind wing was considered. In addition, numerical

simulation of the elytron only was conducted for comparison

purposes. Figure 11 shows the aerodynamic forces acting on

the elytron and hind wing with and without interaction. The

difference in the force was significant on the elytron, whereas

it was minor on the hind wing. This is the typical aerodynamics

of the beetle owing to the major difference in the size, materials,

and kinematics between the elytron and the hind wing. The

instantaneous vertical force on the elytron was increased,

especially at the middle position of the stroke, when both

wing positions moved closer to each other. In addition, the

horizontal force on the elytron also increased owing to

the interaction. The large size and high flapping velocity

of the hind wing significantly affected the aerodynamics of

the elytron, whereas there was no effect in the reverse case.

The downward velocity of the hind wing increased with

time from the beginning position to the middle position of

the downstroke. Hence, the free stream over top surface of the

elytron was ‘accelerated’ to move down along the trajectory of

the hind wing, while the hind wing flapped down at a high vel-

ocity. Therefore, the LEV on the top surface of the elytron was

enlarged, a difference in pressure between top and bottom sur-

face of the elytron became significant. Figure 12 shows the

difference in the size of the iso-surface of the Q-criterion of

the elytron when there was no interaction (figure 12a) and

interaction (figure 12c). Correspondingly, figure 12 also demon-

strates the pressure difference between top and bottom

surfaces in the case of no interaction (figure 12b) and interaction

(figure 12d). As a result, the instantaneous vertical force on ely-

tron of the case with interaction increased up to almost three

times as compared with that of the case without interaction.

Afterwards, the relative positions of the elytron and the hind

wing were far apart, and the wing interaction effect then

became weaker. Based on our experimental observation, the

wing sizes and flapping angles of the hind wing were two and

five times these of the elytron. Hence, the magnitude of the

forces on the elytron was much smaller than that on the hind

wing. Therefore, we explored the forces on the elytron with

respect to its weight. The gravity force of the elytron is

0.55 mN, which is quite high owing to its larger density than

that of the hind wing. The elytron could not support its own

weight by the aerodynamic force generated when the interaction

x

y

z

x

y

z

x

y

z

x

y

z

x

y

pressurespiral LEV

t/T=0.8–1.00 –0.78 –0.56 –0.33 0.33 0.56 0.78 1.00–0.11 0.11

z

x

y

z

Figure 9. Iso-surfaces of Q-criterion (left) and pressure (right) distribution on the rigid, twisting and flexible wings at t/T ¼ 0.80.

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is not considered (0.42 mN). However, the wing interaction

enhanced the mean vertical force on the elytron to 0.62 mN,

which yielded a 50 per cent improvement. Therefore, its weight

was fully supported by itself. The elytron–hind wing interaction

also increased the drag on the elytron from 0.025 to 0.23 mN.

4. DiscussionAfter exploring the basic mechanism of a flapping wing,

researchers became more interested in the optimization of

the flying mechanism of insect models. They currently focus

on wing flexibility, including wing twisting along the span-

wise direction and camber variation along the chord-wise

direction. The flapping power economy is used in evaluating

the performance of the flapping model. The locust flight

model was investigated by comparing a full-fidelity wing, a

twisting-only wing and a camber-only wing [14]. The highest

power economy was achieved in the full-fidelity model. The

low efficiency of the momentum transfer in the simplified

models was attributable partly to the flow separation at the

leading edge. Basically, the high lift of insect flight are typi-

cally associated with massive flow separation and a large

LEV during flapping [3,38]. However, the high lift is not

always required for all flight conditions; hence, the size of

the LEV should be controlled to obtain higher efficiency.

How the leading edge becomes well aligned with the incom-

ing flow during flight is dependent on wing flexibility. In an

experimental study of a dragonfly, the mechanism involved

in the foundation of the LEV was observed through a smoke

wire visualization method [38]. The role of the AOA for the

generation of the LEV was emphasized.

In a steady flow, the stall phenomenon usually occurs

when the effective AOA is larger than 158. Meanwhile, in

an unsteady flow, the flow is separated at the leading edge

of the wing and then reattaches to the wing surface behind

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

x

y

z

t/T=0.35

pressure1.000.780.560.330.11

–0.11–0.33–0.56–0.78–1.00

Figure 10. Iso-surfaces of Q-criterion (left) and the pressure (right) distribution on the rigid, twisting and flexible wings at t/T ¼ 0.35.

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the leading edge along the wing chord direction over 158 of

the effective AOA. This phenomenon is called the delayed

stall. For the rigid wing, the effective AOA was constant

along the spanwise direction, and it was changed in the

range from 458 to 608 during the downstroke. Hence, the

separation of the flow became massive near the wing tip of

the hind wing, where the local angular flapping velocity

was high. For the twisting wing, the effective AOA was

modulated towards the wing tip in the range from 308 to

408 and the smaller LEV is then generated. Thus, lower

power consumption by the smaller LEV is expected for the

twisting wing than for the rigid wing.

In our simulation result, the spiral LEV was considered to

be the main source of the high unsteady force at the middle

position of the stroke in the three wing models. The tendency

of the force distribution in these models was similar except for

the difference in the magnitude of the instantaneous forces at

the middle position of the strokes. Near the wing tip, the

strength of the spiral LEV was significantly different between

the rigid and twisting wings. The rigid wing generated a

stronger spiral LEV than the twisting wing, which yielded

higher aerodynamic force on it. In terms of momentum trans-

fer, massive flow separation occurred and a large amount of

energy was consumed as vortex activities in the wake. There-

fore, a high level of power was needed for lift generation at this

moment in the rigid wing. During forward flight, the beetle

only needs the mean vertical force to support its weight with

a large amount of thrust to fly forward rapidly. This indicates

that the average vertical force during one stroke of flapping is

much more important than the instantaneous force. The posi-

tive camber in a flexible wing not only generates high lift, but

also enhances the thrust as compared with the rigid wing, as

shown in figure 6. The aerodynamic force of the rigid wing

represents inefficient kinematics for the forward flight because

the high positive vertical force during the downstroke is

almost cancelled out by the high negative force during the

upstroke. Meanwhile, the mean vertical force was the lowest

among the three models. Furthermore, it takes highest power

t/T

forc

e (m

N)

forc

e (m

N)

0 0.25 0.50 0.75 1.0

–100

–50

0

50

100

150

200

FH with elytronFV with elytron

FH with hind wingFV with hind wingFH without hind wingFV without hind wing

FH without elytronFV without elytron

t/T0 0.25 0.50 0.75 1.0

–2

–1

0

1

2

3

4

5(b)(a)

–150

Figure 11. Aerodynamic forces on the (a) hind wing and (b) elytron with and without interaction. (Online version in colour.)

top surface bottom surface top surface bottom surface

only elytron

y(a) (c)

(b) (d)

x

z

yx

z

elytron-hind wing

only elytron

–0.10–0.08–0.06–0.03–0.01 0.01 0.03 0.06 0.08 0.10 –0.10–0.08–0.06–0.03–0.01 0.01 0.03 0.06 0.08 0.10

elytron-hind wing

Figure 12. Difference in iso-surfaces of Q-criterion on only (a) elytron and (c) elytron with hind wing. Corresponding, pressure distribution on top and bottomsurfaces in (b,d ).

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from the muscle of the beetle for high instantaneous force

during both strokes. A natural flyer will apply other efficient

wing kinematics instead of a rigid wing. By varying the

AOA along the spanwise direction and the camber along the

chord-wise direction, the leading edge of the hind wing can

align suitably to the incoming flow direction near the wing

tip; therefore, the flow can reattach to the wing surface well.

This is useful during the upstroke when the negative vertical

force needs to be minimized. The average vertical force of

the flexible wing was improved by 13 per cent compared

with that of a rigid wing, and it was close to the gravity

force of the beetle, which is in the range of 45–50 mN.

In addition, the flexible wing can reduce the required power

by 25 per cent with respect to the rigid wing. This highlights

the critical role of the effective AOA as well as the camber in

optimizing the flapping mechanism, as previously reported

[38]. It was demonstrated from our simulations that the aero-

dynamic power efficiency of beetles appears to derive from

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their ability of reduce the flow separation and the associated

loss of energy while maintaining the flight function.

Hitherto, fewer reports on the elytra and their role in

aerodynamic performance can be found in the literature.

Their main objective is apparently a protective function of

the hind wings in resting state. The coupling force owing to

the interlocking mechanism for opening and closing elytra

may be as high as 160 times the gravity force of its own

bodyweight [39]. The high force allows the beetle to safely

penetrate soil, wood and hard material and to protect a

thin and highly flexible hind wing that shows extraordinary

aerodynamic performance. Other previous studies focus on

geometry and mechanical properties of the elytra: hardness

and modulus of fresh cybister elytra are 0.31 and 6.13 GPa,

respectively, and the difference of ultimate stresses in trans-

verse and longitudinal directions has been reported [40].

The elastic properties of the wings are determined by resilin

(a rubber-like protein) distribution inside the vein system

[41]. The mechanisms of folding and unfolding of the hind

wing are strongly interactive movements of elytra, namely

as autapomorphic character states of Coleoptera [42]. These

results provide deep insights into the design mechanism

and structure for future flight vehicles by mimicking bio-

structure. Meanwhile, there are few comprehensive reports

for the role of the elytron in aerodynamic performance,

which is the critical factor for flight vehicles. One of the

main contributions of our work is findings about the role of

the elytron in aerodynamic performance while considering

the interaction of the hind wing.

Owing to the large difference in the size and the flapping

angle between the elytron and the hind wing, the interaction

effect was clearly observed only on the elytron. The wing

interaction not only significantly increases the vertical force

on the elytron, but also maintains the aerodynamic perform-

ance of the hind wing. Flapping in phase with the hind wing,

the elytron creates enough vertical force to support its weight.

Furthermore, during the motion in phase, the elytron can

avoid blocking the flow stream or having other negative

aerodynamic effects on the hind wing during free-forward

flight. Consequently, when the effects of wing flexibility

and interaction are combined, the vertical force from both

wings (48.4 mN) becomes larger than the gravity force of

the beetle (47.5 mN).

5. ConclusionThe role of the flexibility of the hind wing and elytra–hind

wings interaction of a beetle during free-forward flight was

studied through a numerical simulation. Preliminary exper-

imental measurements determined a large twist angle along

the spanwise direction and great variation of the camber

during flapping. These factors reduce massive flow separ-

ations on the leading edge, yielding a small amount of

instantaneous negative vertical force during the upstroke in

a flexible wing model. Therefore, a significant improvement

in the mean values of the lift and thrust was achieved; more-

over, less power was required in the flexible wing model. As

a result, the advantage of the flexibility of the wing was

clearly revealed owing to the enhancement of the power

economy. The elytron–hind wing interaction provided an

improvement in the aerodynamic forces mainly acting on

the elytron, and the total lift for wing flexibility and inter-

action is then enough to support the weight of the beetle

during free-forward flight.

This research was supported by the Basic Science Research Pro-gramme through the National Research Foundation of Korea (NRF)financially supported by the Ministry of Education, Science and Tech-nology (2010–0015174), and the New and Renewable Energy R&Dprogramme of the Korea Institute of Energy Technology Evaluationand Planning (KETEP) grant financially supported by the Korea gov-ernment Ministry of Knowledge Economy (No. 20113020070010).PLSI supercomputing resources of Korea Institute of Science andTechnology Information supported our numerical simulations.

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