Aerodynamics Of Insect S Flight

School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University
Final Year Project 2010 Technical Paper
Aerodynamics of Insect’s Flight
Nunthadech Rodcheuy (s3252444)
Bachelor degree of aerospace engineering-BP069
Supervisor: Assoc.Prof. Hadi Winarto
ABSTRACT
In the past, aerodynamicist has proved that
bumblebees should not be able to fly due to
insufficient lift force. However, the
knowledge at that time was mainly based on
steady-stated aerodynamics unlike insect‟s
flight where the flow behaviour is unsteady-
stated and involving significant effects in
which some of them resulting in a huge lift
force incremental. The two dimension
flapping wing motion of insect‟s flight will be
analysis mainly on lift force generation and
wake structure with fundamental knowledge
from steady state numerical vortex panel
method. The insect‟s flapping kinematics
parameter will be investigated for the
influence of wake structure on lift generation.
1 INTRODUCTION
There is a need for MicroAerialVehicle
(MAV) for in-door mission whether civilian
or military. In civilian aspect, MAVs are
required for rescue mission such as
earthquake. Small camera or microphone
devices can be installed in to MAVs searching
and indicating the precise position of
survivors. This can help improve safety for
rescue team. In military aspect, MAVs are
extremely suitable for spy mission due to
their size is very small. UAVs are not capable
for those missions because their design base
on fixed wing aircraft which low agility as a
high maneuverability is required for avoiding
obstacle in in-door mission. Moreover, the
fixed wing design is not possible to perform
Vertical Takeoff Landing ability. In fact,
there are some fixed wing aircrafts such as
The Harrier Jump Jet that can perform VTOL
but this ability comes from adjusting direction
of engine thrust not that wing mechanism. In
this approach, engine weight, power
requirement and complexity wouldn‟t be
possible for MAV. Another design approach
to meet VTOL and also hovering as well as
good agility is rotary-wing, however, there
are wall-proximity problem, noisy which is
not good for military mission and as the size
of MAVs are very small, rotary-wing is
inefficient. As a result from those limitations,
these bring us to “flapping-wing” design.
Insect‟s flight is the most simple
wings kinematics among bird‟s and bat‟s
flight because the controlling wing muscles
are at root chord unlike bats and birds in
which the muscles contribute along wing. As
a consequence of this simplicity, the insect‟s
wing weight is approximately 1% of total
weight. In this project, only insect-like
flapping wing motion will be studied while
the other two types are not concerned due to
the kinematics complexity.
In 1930, aerodynamicist has done a
preliminary calculation. The result was shown
that bumble bee can generate lift force only
one-third of its body weight; hence, it
shouldn‟t be able to fly. However, the
conclusion at that time is mainly based on
steady-stated aerodynamics. This method is
referred to fixed-wing aircraft or rotational
propeller. The insect‟s flight is unsteady-
stated aerodynamics and involves number
unsteady effects which are the key of lift

augmentation. Despite the unsteady-stated
condition, a fundamental of steady-stated can
applied to analyze the insight on insect‟s
flight with proper model, and this is called
quasi-steady stated and will be described on
later section.
1.1 Wing kinematics and unsteady effects
In 1868, an advanced in camera
technology provide us to be able to capture
the wing‟s movement of insects. The
movement composes of three main parts.
First, sweeping is the movement of forward
and backward on horizontal plane. Second,
plunging is the movement of up and down.
Third, pitching is the movement of varying
angle of attack. In general, insects have wing
frequency range from 5-200 Hz and Reynolds
number range from 10-1000 [1]. Flapping
kinematics function was defined by simple
harmonic function [2], trapezoidal [3] or
sinusoidal [4]. Simple harmonic function has
been suggested to be the closest one to
efficient flyers [5]. During the initial of first
down stroke (see fig.1), Leading edge vortex
formation (delayed stall) is constructed and
this will result in lower pressure in this
leading edge region.
Figure 1 Down stroke
As wing flap down (see fig. 2), the
pronation phase that will rotate the wing this
will cause Kramer effect (rotational lift).
After the down stroke reversal, the up stroke
begins. During this upstroke, the insect‟s
wing will experienced the wake from
previous stroke resulting in increase lift force
and this is known as wake capture [6].
Figure 2 Up stroke
For low Reynolds number, viscosity is
considerably large enough and must be taken
into account. Consider a solid particle passing
with a certain velocity through a fluid, fluid at
the foremost position of the particle separate
with acceleration to let the particle passing
through and this is an expenditure of kinetics
energy. As the particle has passed, however,
the fluid start to accelerate and return to the
same position, kinetics energy has been
recovered, this is the case where there is no
friction force. On the other hand when
viscosity is presented, as the particle passing
through the fluid, all of kinetics energy would
not be recovered because some portions of
energy must be extracted to overcome the
friction force caused by viscosity [7].
Although unsteady aerodynamics
effects were discovered to enhance the lift
force of insect‟s flight, it was still insufficient
to compensate insect body‟s weight. This was
a mystery until 1996, Ellington et al.
discovered leading edge vortex by the
experiment of scale-up model of the
Hawkmoth Manduca Sexta [8]. For wing
during flapping motion at high angle of
attack, the flow is separate at the leading edge
producing LEV and before the flow reach
trailing edge, it reattaches to insects wing‟s
surface. The structure of LEV is similar to
vortex of low-aspect ratio delta‟s wing [9].
At instantaneous beginning of stroke,
kutta-conditions is not hold since the
stagnation point move away from trailing
edge. Another circulation must be generated
to force the stagnation point to be at trailing
edge such that kutta-conditions hold.
However, to re-establishment of kutta-
conditions an amount of time is needed;
therefore, during rapid pitching motion, we

could not observe for the conditions. The
additional circulation either support or reduce
total lift force depends on the direction of
circulation. It‟s also important to note that
Kramer effect is not analogous with Magnus
effect of what occurred in rotational cylinder
since the fundamental is difference [10].
Wake capture was first observed by
Dickinson in 1994 on 2D model. During the
stroke reversal either pronation or supination
begins, wing shed both LEV and trailing edge
vortex. In the region between these two
vortices, the induced velocity is generated by
the two vortices. As the wing begins half
stroke, the wing would experience additional
velocity that empowers the wing velocity;
therefore, lift force is increased [11]
However, Sun and Tang has performed CFD
analysis similar to Dickinson et al.[3] 3D
model of mechanic fruit fly and reported that
forces related with wing‟s acceleration rather
than wake-capture. In contrast, Dickinson et
al.‟s experiment showed that even stopping
wing at stroke reversal, there was a force and
this force must only come from wake-capture
rather than the acceleration since the wing
was at stationary status. Moreover, the
induced velocity field from wake-interaction
was observed by using Particle Image
Velocimetry (PIV). At this day, no one can
indicate the conflict between CFD simulation
[11] and PIV experiment observations [3]
1.2 Quasi-steady method in literature
review
An unsteady motion was discritization into an
array of time, where each time step the
problem is analyzed as steady stated. Quasi-
steady method is considerably accurate for
fast forward flight, as velocity increase,
unsteady effects were reduced [12]. The
recommendation on how fast the forward
speed is need to obtain accurate model has
suggested that “reduced frequency should not
exceed 0.5” [13].
(1)
Where k = reduced frequency
f = flapping frequency
c = mean aerodynamics cord
U= flight velocity
The 3D quasi-steady stated method
Ansari et al. with blade element approach is
claimed to be the most comprehensive and
successful modeling approach for insect
flapping flight to date [7]. The wakes were
shed from both leading edge (LEV) and
trailing edge modelled as continuous
distribution of vorticity. At each array of time
Then the flow were solved by potential
method with Neumann Boundary condition
(zero-through-flow on the airfoil surface) and
Kelvin condition stated that the total
circulation in a control volume enclosing the
system must remain constant was applied
incorporate at wake-inception points. The
sheded vortices (LEV and trailing edge wake)
disturb the Neumann boundary condition and
the Kutta-Joukowski condition. Furthermore,
the LEV separation must present the flow
stagnation there since there is no force across
the vortex sheet; hence, local velocity must be
zero. In order to restoring the Neumann
boundary condition, image vortices were
added inside airfoil. Then more vorticity was
then added on the airfoil surface to satisfy
Kutta-Joukowski condition. The forces and
moments were computed by the momentum
based method of vortex pairs used by von
Karman and Sears [14]. The concept is for
every shed vortex, the circulation is opposite
where equivalent in strength magnitude. The
momentum per unit span of the system can be
expressed by the sum of the momentum of the
vortex pairs that constitute the system from
which force and moment data can then be
extracted
Figure 3 Lift and thrust from Ansari‟s et
al.‟s method [7].
A quasi-steady method alone is unable
to predict the force generating on the wing
accurately. A possible way to validate the
method is enhancing it by a correction base

on empirical data. This method is known as
semi-empirical method. The advantage of this
method is giving the interaction of complex
phenomena in which quasi-steady has ignored
due to problem simplification. The simplified
equation from quasi-steady can be adjust
either by a factor or adding more variable in
which the theoretical results will reach the
consensus with experimental results. The
semi empirical method is highly rely on
experimental data and the corrections are lack
of theoretical support, interpolate the solution
is possible; however, extrapolating the result
beyond experimental range might not valid. A
semi empirical with blade-element theory
including Wagner‟s and added mass effects
[15]. However, this model is lack the present
of far wake influence on force generation.
Therefore, wake capture only some part of the
remaining force. Traub analyze the insect in
hover with the focus on stroke-averaged
rather than instantaneous force [16]. Unlike
other with blade-element theory, he used a
simple actuator disk to derive the lift force
expression. The method is simplified to the
state that the lift force is generated from two
components which are attached flow and
vortex flow.
2 METHODOLOGIES
A 2D insect‟s flight was studied with quasi-
steady stated method. The fluid flow was
assumed to be inviscid, incompressible, and
irrotational and it was called potential flow
problem. A thin flat-plate represents an
insect‟s wing section. Lumped vortex panel
method with Neumann Boundary condition
was chosen to analyze potential flow problem.
A combination pitching and plunging of a flat
plate simulate insect‟s flapping mechanics.
Pitching angular velocity and plunging speed
is assumed to be an average value which keep
constant during each half stroke. A centre of
pitching rotation is about 0.25%c [18].
Figure 4 Quasi-steady state time array
2.1 Vortex panel method
The first step is discritization a flat plate
into a number of panels and identified vortex
and collocation point at 0.25c and 0.75c
respectively, then, apply boundary condition.
Neumann boundary condition states zero-
normal flow to the airfoil surface. Therefore,
the governing equation will involve the
induced flow velocity by lumped vortex at
collocation points and the normal components
will subject to zero. Considered a vortex of
circulation γ at point (x0, y0), at any point T(x,
y), the velocity induced by the vortex will be
(2)
(3)
Where u is horizontal velocity, w is vertical
velocity, and γ is lumped vortex.
Considered each collocation point, the
condition of zero velocity normal to the
surface will be applied
(4)
Where wi = the normal velocity induced
by i vortices along flat plate
α = flat plate angle of attack
U∞ = Flight forward speed

Equation can be applied to 2nd, 3rd, 4th, …..,
nth collocation point and rewritten as follow
(5)
Where
(6)
(7)
There will be „n‟ equations since „n‟
collocation points with „n‟ unknowns. The
system of algebraic equation can be solved for
vortex strength and circulation
2.2 Quasi-steady stated
A total incoming velocity against a flat plate
composes of three components which are
uniform free stream wind, plunging velocity,
and pitching velocity. For the first two
components, a flat plate experienced identical
both magnitude and direction; however,
pitching angular velocity will induced a linear
distribution of normal velocity along panel as
show below.
Figure 5 Tangential pitching velocity
Due to the variation, the total incoming
velocity will be different for each collocation
point; thus, recall eq.(7), RHSi which express
the free stream velocity and flow angle of
attack will not hold a single value all over a
flat plate, instead, they will have an individual
for each collocation point.
(8)
(9)
Where Utotal,i is total incoming velocity at
collocation point i, U∞is uniform wind
velocity (flight‟s speed), Vh is plunging
velocity, Vp,i is tangential velocity induced
by pitching angular velocity at collocation
point i.
In the potential flow region, the angular
momentum is reserved; thus, circulation Γ
around a fluid curve enclosing the airfoil and
its wake is conserve. This statement is called
“Kelvin condition”.
(10)
Kelvin condition can be applied for quasi-
steady stated method to calculate for wake
circulation
(11)
Where Γw is wake vortex circulation, Γt is
summation of lumped vortex along a flat plate
at time t
The wake structure of flapping airfoil
will be modelled as discrete vortices
shredding from trailing edge as shown in
figure 4. The circulation strength is calculated
by Kelvin condition. Wakes vortex are force
free such that its position is displaced by its
local stream velocity which influences by
uniform stream, induced velocity of panel
lumped vortices, and induced velocity of
other wakes.
(12)
Where is induced velocity of lumped
panel vortices, is induced velocity of other
wake vortices
The position displaced can be calculated
(13)

Where is Wake discrete vortex
displacement.
In vortex panel method for quasi-steady
stated, not only lumped vortices on flat plate
that induced velocity at collocation point but
also wake vortices do induce. The objective
of constructing wake structure is to study
wake discrete vortices influence on lift force.
Recall eq.(5). This system of algebraic
equation is derived from panel vortices induce
only. When wake which modelled as discrete
vortices is present, it also contributes an effect
the system as follow. Consider at time = tth
,
there will be t-1 discrete vortices shredding
from trailing edge and form a structure
according their displacement profile moving
by local stream velocity. The system of
algebraic equation which represents Neumann
BC with wake influence is
(14)
Where VΓwt is normal velocity induced by
wake vortex. Since Γw is known and can be
calculated form Kelvin condition, these
known terms can be moved to RHS.
(15)
Then solving for lumped vortex circulation γj
with Gaussians elimination method. From
Kutta-Jowkowski lift theorem
(16)
From this theorem force, denote by F, always
perpendicular to free stream flow. Consider
free body diagram of a flapping flat plate at
time t
Figure 6 Lift force
Where θ1 is pitching angle, θ2 is flow angle of
incidence, and Utotal ,i is total local velocity at
collocation point i. From figure 6, Lift force
at collocation point i
(17)
(18)
Total Lift force over a flat plate
(19)
Assume that the effect of plunging and
pitching speed is very small and can be
neglected, and then the lift coefficient can be
computed as
(20)
The quasi-steady stated method mention
above has been implemented on MATLAB.
However it contains undiscovered bugs
resulted in obtaining only initial results. It
was found to be wake structure part since the
panel method has been verified with thin-
airfoil theory [20]. Only initial 5th
time
stepping algorithm is validated where the
expected resulted should be any time step
says 200 time stepping such that it complete a
number of flapping cycle.
3 RESULTS AND CONCLUSION
As discussion on section 1.2, an analysis on
flapping motion with quasi-steady method
shall be analyze with a limited range of flight
velocity and flapping frequency such that the
unsteady effects are suppressed. Reduced
frequency (k) and multiplication of reduced
frequency and stroke amplitude are two
parameters determining the suitable range of
the analysis. The criteria are listed as follows,
1. Reduced frequency should be less
than 0.5 (k < 0.5)
2. Multiplication of reduced
frequency and stroke amplitude

should be less than 0.1 (kh < 0.1)
[20]
Stroke amplitude is restricted by the
possibility of trailing edge separation
indicated by kh value; however, the flat plate
pitching angle has not yet been discussed on
its limitation. The pitching angle shall be
restricted by the maximum angle where the
vertical trailing edge displacement is equal to
the maximum stroke amplitude. Under the
limitations, 4 insect‟s steady forward flight
case were studies
Level of
refinement*
Case
(1)
Case
(2)
Case
(3)
Case
(4)
k 0.5 0.5 0.1 0.1
kh 0.1 0.05 0.1 0.05
Table 1 Flight case analysis
1 1.5 2 2.5 3 3.5 4
0.1332
0.1332
0.1333
0.1334
0.1334
0.1334
Time increment
Lift
Coefficient
Case 2
Wake influences
No influences
Figure 7 Case 1 Lift coefficient
1 1.5 2 2.5 3 3.5 4
0.2654
0.2656
0.2658
0.266
0.2662
0.2664
0.2666
0.2668
0.267
Time increment
Lift
Coefficient
Case 1
Wake influences
No influences
1 1.5 2 2.5 3 3.5 4
0.247
0.248
0.249
0.25
0.251
0.252
0.253
0.254
0.255
0.256
0.257
Time increment
Lift
Coefficient
Case 3
Wake influences
No influences
1 1.5 2 2.5 3 3.5 4
0.1312
0.1314
0.1316
0.1318
0.132
0.1322
0.1324
0.1326
Time increment
Lift
Coefficient
Case 4
Wake influences
No influences
The result shows that the vortex wakes being
shed from trailing edge tend to increase the
lift coefficient on the airfoil with very tiny
amount. However, it cannot be concluded that
the wake structure will enhance lift force.
This model provide only initial result where
the conclusion can be drawn after full result
of wake structure is constructed with a large
number of shed vortex wakes after several
flapping cycle in order to study the influences
of these vortices on lift force.
4 RECOMMENDATION
A quasi-steady stated method is applied to
study insect‟s flight. The simulated model of
flapping motion fails to present the essence of
insect‟s flight. A number of unsteady effects
is neglected to simplify the problem. The
simplification leads to limited range of flight
characteristics. The model has been limited to
two condition the flight velocity must be fast
enough to suppressed the unsteady effects
which indicate by maximum reduced
frequency and multiplication of reduced
frequency and stroke amplitude which
indicate the flow separation at trailing edge.
As a consequence of last constraint, the
plunging amplitude is limited to a very small

number such as 1c where the actual insect‟s
amplitude is around 3 to 4 chord. With this
large stroke amplitude it is necessary to
incorporate trailing edge separation and also
Leading edge vortex
Although unsteady effects are included
such as Leading edge vortex, and wake
capture, the flow is assumed to be inviscid,
irrotational, and incompressible which is
potential flow problem. Despite the fact that
incompressible flow is proper assumption for
insect‟s flight, viscous drag is very significant
for low Reynolds number, a case in point is
insect‟s flight. CFD analysis will provide
capability to analyze Navier-Strokes equation
and also good problem visualization.
5 ACKNOWLEDGEMENT
I owe my deepest gratitude to my thesis
supervisor, Assoc.Prof. Hadi Winarto, for his
warm welcome regards many thesis
consultation, continual suggestion and
guidance, and assistance on the encountered
problem. Without my supervisor, the thesis
would not have been possible.
I am grateful to my advisor at Kasetsart
University,Dr. Nanyaporn Intaratep, for her
support during the beginning of this thesis.
I would like to thank to my family and
friends for their support during the hard time
in this semester.
6 REFERENCE
[1] Azuma A (1992). The biokinetics of
flying and swimming. Berlin: Springer.
[2] Sun, M. and Lan, S.L. (2001).
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structures of two airfoils in flapping
motion. Acta Mechanica Sinica,
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[3] Dickinson, M. H., Lehman, F. O. and
Sane, S. P. (1999). Wing rotation and
the aerodynamic basis of insect flight.
Science 284, 1954-1960.
[4] Wang, Z.J., Birch, J.M. and
Dickinson, M.H. (2003). Unsteady
forces in low Reynolds number
hovering flight: two-dimensional
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460.
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aerodynamics of hovering insect
flight: IV. Aerodynamic mechanisms.
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[6] Dickinson, M.H. (1999). Catching the
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http://www.scientificamerican.com/art
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(2006). Aerodynamic modeling of
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[9] Martin LJ, Carpenter PW(1977).
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