design and aerodynamic analysis of a flapping-wing micro aerial vehicle
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Design and Aerodynamic Analysis of a Flapping-wing Micro Aerial VehicleTRANSCRIPT
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Aerospace Science and Technology
Design and aerodynamic analysis of a flapping-wing micro aerial vehicle
Bor-Jang Tsai ∗,1, Yu-Chun Fu
Department of Mechanical Engineering, Chung Hua University, No. 707, Sec. 2, Wu Fu Rd., Hsinchu, Taiwan 300, ROC
a r t i c l e i n f o a b s t r a c t
Article history:
Accepted 9 July 2009
Keywords:
MAV
This paper presents the design and aerodynamic performance of a planar membrane wing as shape airfoil
for the micro aerial vehicle. This simulation calculates the average lift force, L as the criteria weight of
the flapping wing (weight must be lower than 8.78 g), to make one ultra-light, small size flapping wing
MAV. In here two phases are discussed. First, the 3D aerodynamic calculation and flow field simulation
of a planar membrane wing as shape airfoil for a MAV were studied. Analyzing the flapping wing under
different frequencies and angles of attack, investigates the pressure distribution, the airfoil-tip vortex and
the up-wash situation of the air flow. Second is to average lift force, L 8.78 g for designing weight limit
of the MAV. The specifications of flapping wing MAV are 8 g gross weight, the 15 cm wingspan, and
5 cm chord length. In this vehicle, we employed the concept of four-bar linkage to design a flapping
mechanism which simulates the flapping motion of a bird. The angles of upstroke and downstroke can
be varied in the design. The total flapping angle is 73. The flapping frequency of wing is 25.58 Hz.
The power source comes from motor with a Li–H battery. A simple flight test was carried out and the
result of the flight is going well. The actual flight distance is approximately 8 m, and the primary goal is
achieved. By the way, we found the rigidity of tail wing is crucial and should be enhanced to prevent the
flapping-wing MAV will be unable to revise if the MAV in a crooked condition and it will cause a crash.
© 2009 Elsevier Masson SAS. All rights reserved.
1. Introduction
The micro aerial vehicle, in English is abbreviated as a MAV,
according to the Defense Advanced Research Projects Agency
(DARPA) of USA, the size of various aspects of micro aerial vehi-
cle (MAV) is limited to 15 cm, the flying speed is 10–20 m/s, the
Reynolds number must be below 106. Regarding a flapping wing
for a MAV, the most important issue at present is the aerody-
namic performance. The Reynolds number of a MAV is about 10 5,
this range of Reynolds number will cause laminar separation phe-
nomenon occurred on the surfaces of the body. Moreover, since
the definition of a MAV includes size limit, and the challenge of
this work is to design an ultra-light and small size of a flapping
wing MAV comparing all literatures [1,7,9,10,13], therefore by us-
ing very low aspect ratio of MAV to obtain enough lifting force,
L. However, small aspect ratio will increase the three-dimensional
effects on flow field. The MAV is small and the speed is low, the
flight stability of a MAV is affected easily by the external wind
shear or other disturbances.
alyzed a planar membrane wing under the low Reynolds number.
Each pattern of the flap movement initiates a complex and un-
* Corresponding author. Tel.: +886 3 5186478; fax: +886 3 5186521.
E-mail address: [email protected] (B.-J. Tsai). 1 Professor.
steady flow field. Calculation of aerodynamic performance becomes
crucial. To predict lifting force, L needs to solve the whole un-
steady flapping flow field of a wing. Approaches of solving this are
divided into two steps; first, we do the flow field simulation and
analysis, second, we design and manufacture it.
Regarding the literature survey, in 2000, Neff and Hummel [9]
studied the two- and three-dimensional flow fields by plunging
and pitching movement for NACA 0012 airfoil, they solved the Eu-
ler equation to simulate the flap and twist movement for the rect-
angular wing. In 2003, Tuncer and Kaya [13] made the movement
of the upstroke and downstroke flap by using the two-dimensional
NACA 0014 and they analyzed the reason which is thrust force, T
produced and observe the overflow situation of its turbulent flow.
In 2001, the Caltech, Pornsin-sirirak made a MAV [10], they used
the titanium alloy wing of the xylene thin film, complete the al-
together weight is 10.5 g, also fly for 5–18 sec successfully. In
2005, Delaware University in USA, Agrawal imitates an insect flight
and they studied the multi-dimensional flapping movement and
the twisting movement to simulate the hummingbird flap and but
not becomes a MAV [1]. In 2006, Lin, Hwu and Young reported
the trust and lift of an ornithopter’s membrane wings with sim-
ple flapping motion on the journal [7], they revealed the lift force,
L of a flexible flapping wing will increase with the increase of
the flapping frequency under the corresponding flying speed. For
the same flapping frequency, the flying speed can be increased by
decreasing of the angle of attack with the trade of loosing some
lifting force. The flapping motion generates the trust to acquire
1270-9638/$ – see front matter © 2009 Elsevier Masson SAS. All rights reserved.
384 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
Nomenclature
P pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pa, psi
L lift force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N
T thrust force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N
C L lift coefficient
C D drag coefficient
K reduced frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hz
AOA angle of attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
U flying speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s
t time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s
ν dynamic viscosity
the flying speed. The flying speed and angle of attack combine
to generate the lift force, L for flying. This paper is the most im-
portant reference to us. In recent, the design of precision balance
and aerodynamic characteristic for micro aerial vehicle to measure
lift, drag, rolling-moment, and pitching-moment of a MAV was re-
ported by Suhariyono et al. [12], but measurement is for the fixed
wing MAV only, not for flapping wing, the measurement of flap-
ping wing is critical. Only Singh et al. [11] studied an experimental
apparatus that incorporates flapping wings and measures the small
amount of thrust generated by these wing motions is described.
This methodology is used to measure the thrust generated by two
wings at different wing pitch settings. Also, the effect of change
in pitch phase during a flapping cycle is examined experimentally.
Regarding the simulation, Larijani [6] proposed a nonlinear aeroe-
lastic model for the study of flapping wing flight in the 2001, this
paper conducted the Huang’s [5] numerical analysis for the flap-
ping wing MAV later.
From Refs. [9] and [7] we know the three-dimensional move-
ment of many birds flapping is used the standard NACA shape
airfoil as wings, but actual flapping wing of MAV to be restricted
in the volume and the weight. It’s unlikely to use the NACA series
of wing section. On the contrary, the most of the flapping wing
for MAV, a planar membrane wing are used primarily. In order to
imitating the insect flutter and the flight pattern, therefore, this
investigation does take the planar membrane wing as a study tar-
get vehicle, discussing its aerodynamic characteristic and to predict
average lift force, L as the criteria weight to manufacture a future
MAV. The actual MAV was made by the wingspan is 15 cm, the
mean chord is 5 cm, the weight is 8 g, the wing area is 75 cm2,
the flapping frequency is 25.58 Hz of a flapping wing MAV.
2. Numerical analysis
2.1. Numerical method
In the numerical simulation solves the speed and the pressure
on this pattern flow field. It is an integral control volume method.
In the control volume definition, each physical quantities is sig-
nificant because the separation variable is the integral of control
volume for the governing equation, therefore we must first take
the separation of the governing equation to control volume of the
flow field computation.
+ div(ρur φ − Γ φ gradφ) = S φ (1)
ψ: On behalf of any independent physical quantity (ui , e, k . . .)
Γ φ : Diffusion coefficient
S φ: Source coefficient
After the numerical computation of the convergence condition
which in the volume change rate is smaller than after each time
the iteration that we give.
C kφ =
2.2.1. Estimation of the MAV weight
The MAV weight (W Total) may include a MAV main body weight
(W Fuselage ), a wing weight (W Rudder), the load weight (battery and
switch or joint) (W Payload) and the power unit (motor) ( W Power ).
2.2.2. Aerodynamic parameter estimates
Wing tip speed (6)
3.1. Numerical simulation
3.1.1. Geometry contour and grid establishment
In order to conform to DARPA’s definition of the MAV, there-
fore this research takes 15 cm as the wingspan length and only
constructs the single wing (half wingspan) of grid. The main con-
sideration of chord length is for hoped the induced drag is small
but the wing induced drag following the lifting force, L occurs, the
lifting force, L is bigger and the induced drag is also bigger. But
the wing induced drag is directly related to the aspect ratio and
if the aspect ratio is bigger, relatively, the induced drag will be
smaller. Therefore, this research designate the aspect ratio is 3, the
chord length c is 5 cm, the thickness of planar membrane wing
B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392 385
Fig. 1. The grid disposition of the rigid wing section for a three-dimensional planar membrane wing.
non-constructive grid, the non-constructive grid is easier than the
constructive grid to process the complex geometry, has the con-
venience to use the three-dimensional dynamic moving grid skills
[4] as well. The connecting positions of wing entity and the flow
passage will have the boundary layer effect, therefore the grid be-
came dense but the entire flow passage used the dispose for the
C grid, the total grid point is 854,090, shown in Fig. 1. The com-
putational domain; the length is 32.5c , the extended is 12.5c , the
height is 25c .
The predetermined MAV flying speed is 10 m/s, therefore in-
coming air speed is 10 m/s. The outflow is an atmospheric pres-
sure. Because of flow field assuming sliding, therefore the hypothe-
sis of flow passage flank is the sliding boundary, then, the position
of boundary will not have the boundary layer effect. The flapping
angle is 30 .
The convection terns of momentum equations use different ap-
proaching principles by spatial separation variables, two principles
were employed in this study, the pressure term uses staggered
type of PRESTO (Pressure Staggering Option) principle. In addition
to the speed-pressure field coupling uses the SIMPLE principle. For
the time accuracy, the time step is carried on iterations by the two
step implicit expression law (2nd order Implicit Algorithm) [3]. The
important parameter settings are as follow:
1. Reduced frequency K setting: the K value is 0.1 and 0.2 and
0.3, from Eq. (5), may know the actual flight of birds conver-
sion to the flapping frequency.
K = 0.1, is equal to flap of 6.369 times in each second.
K = 0.2, is equal to flap of 12.739 times in each second.
K = 0.3, is equal to flap of 19.108 times in each second.
2. Angle of attack setting: designates the angles of attack is 0 ,
5 and 10 .
3.2. Program validation by a case of three-dimensional rigid wing
Based on 2004, Ref. [5], in view of aerodynamic analysis for
a three-dimensional flapping wing, simulates the behavior of the
NACA 2412 rigid wing flap. Case uses the same wing section and
the flow field conditions. That is the NACA 2412 rectangular wing
and AR is 8, and the single wing of grid was constructed, namely
half wingspan is 4c (c is the chord length 3.4 cm), the Φ is 15 ,
the angle of attack is 0 , the U is 8.6 m/s, the flap frequency is
8 Hz, 16 Hz and 24 Hz respectively, carries on the computation of
dynamic flap of unsteady flow field. The grid distribution is shown
in Fig. 2, and the total grid number is 641,624. Fig. 3 is a com-
parison of lifting coefficient in condition of unsteady state, result
of lift coefficient between this research and Ref. [5] is quite close,
Fig. 2. The grid system of the rigid wing section for the three-dimensional NACA
2412 under the upstroke and downstroke.
this proves that the setting of boundary conditions and numerical
model is accuracy and correct.
3.3. A three-dimensional case of planar membrane wing in different
K −AOA= 0 , K = 0.1, 0.2, and 0.3
3.3.1. Lifting force and thrust force
When the angle of attack is 0 and the K value is 0.1, 0.2
and 0.3 respectively, investigates the increasing of K to influence
on the aerodynamic forces. Fig. 4 shows the comparison of lift co-
efficient, C L and different drag coefficient, C D based on different
K values, in the lift coefficient, C L portion, the movement of flap
wing starting the downstroke and arriving the center point posi-
tion from the highest peak, the lift coefficient, C L elevates to the
maximum value, the movement of flap wing flapping again from
the center point downstroke to the perigee position, and the lift
coefficient, C L falls to the starting value. Therefore, in downstroke
for the lifting force, L is positive. Starting to upstroke, the flap
flapping from the perigee to the center point position, the lift coef-
ficient, C L falls to the minimum value, the movement of flap wing
flapping again from the center point to the peak position, the lift
coefficient, C L rises to the starting value, thus the lifting force, L is
negative value in upstroke.
The increase of K causes the profile of top and bottom oscil-
lation amplitude for the lift coefficient, C L to become the pro-
portional increasing, while in downstroke, the positive lift coeffi-
cient, C L becomes the proportion to increase. While K = 0.1, the
maximum of lift coefficient, C L is 0.1. While K = 0.2, the maximum
of lift coefficient, C L is 0.2. While K = 0.3, the maximum of lift co-
efficient, C L is 0.3. While in upstroke, the negative lift coefficient,
C L becomes the proportional increasing. While K = 0.1, the small-
est lift coefficient, C L is −0.1. While K = 0.2, the smallest lift co-
efficient, C L is −0.2. While K = 0.3, the smallest lift coefficient, C L is −0.3. Increase of the positive and the negative counterbalances
386 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
(a) This research (b) Ref. [5]
Fig. 3. The comparison of lift coefficient, C L under different frequencies for the NACA 2412.
Fig. 4. The comparison of the lift and drag coefficient, C L , C D under different K (AOA = 0).
to the average lifting force, L (equal to zero), therefore flapping like
this way is unable to generate the lifting force, L.
Moreover, in the drag coefficient, C D portion, while the K in-
creases, the drag coefficient, C D has the big variation only when
the flap starts flapping. While K = 0.1, the biggest drag coeffi-
cient, C D is −0.0125. While K = 0.2, the biggest drag coefficient,
C D is −0.014. While K = 0.3, the biggest drag coefficient, C D is −0.015. The drag coefficient, C D reduces relatively when the
K value increases, after the first flap cycle, no matter how K value
is, both in downstroke and in upstroke will not have big change,
the mean drag coefficient, C D is −0.018. As a result, while the an-
gle of attack is 0 , the increase of K value does not have a quite
big contribution to the average thrust coefficient.
3.3.2. Wing tip vortex
In order to ensure the accuracy, the second period of flap cy-
cle in numerical calculation was selected to observe, it separately
picks six points of time period in the cycle to observe. Fig. 5 shows
the t /T = 0/6− t /T = 5/6 are in order. Figs. 6 and 7 show the ve-
locity vector diagrams for K = 0.1 and K = 0.3 respectively, at the
position of 1/4 chord length observes the wing tip vortex. While
the t /T = 0 starting downstroke, then curls up the counterclock-
wise rotation of the wing tip vortex, the strong turbulent flow
causes the low pressure region for the upper wing surface, there-
Fig. 5. The schematic drawing of the flapping points of time period.
fore it may bring the upward lifting force, L for the plate wing.
While the t /T = 3/6 in the perigee position of downstroke, instan-
taneously, the turbulent flow can be absorbed because of the big
reacting force. While the t /T = 4/6 starting upstroke, then curls
up the clockwise rotation of the wing tip vortex, the strong turbu-
lent flow causes of the low pressure region for lower wing surface,
therefore the negative lifting force, L is not favor for the MAV
flight.
While K = 0.1, no matter how the downstroke or upstroke
B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392 387
(a) t /T = 0/6 (b) t /T = 2/6
(c) t /T = 3/6 (d) t /T = 5/6
Fig. 6. The velocity vector diagram of a flapping cycle (K = 0.1, AOA = 0).
tip vortex can be seen obviously and the average vortex velocity
is 8.02 m/s for the wing tip. As a result of the K increase can
cause the maximum vortex velocity increasing quickly for the wing
tip, wing tip vortex became obvious, it affects the pressure be-
tween upper and lower surfaces of airfoil, and influences on lifting
force, L and thrust force, T as well. Regardless of the increasing
of K , the upstroke and downstroke have the same clockwise and
counterclockwise strength of the vortex, therefore the positive and
the negative of lifting force, L is mutually offset. This causes the
average lifting force equal to zero. This result verifies that C L and
C D of different K at AOA = 0 as our expectation.
3.4. A three-dimensional case of planar membrane wing in different
angle of attack – K = 0.3, AOA = 0 , 5 and 10
3.4.1. Lifting force and thrust force
K = 0.3, AOA = 0 , 5 and 10 , investigates the increasing of K
to influence on the lift coefficient, C L and the drag coefficient, C D .
Fig. 8 is the comparison of the lift coefficient, C L and the drag
coefficient, C D under the different angle of attack, so the increas-
ing angle of attack conducive to favor the lifting force, L and the
thrust force, T generation, while in downstroke the positive lift co-
efficient, C L becomes the proportion to increase. While AOA = 0 ,
the maximum lift coefficient, C L is 0.3. While AOA = 5 , the max-
imum lift coefficient, C L is 0.5. While AOA = 10 , the maximum
lift coefficient, C L is 0.7. While in upstroke, the negative lift coef-
ficient, C L becomes the proportional reducing actually. While the
AOA = 0 , the smallest lift coefficient, C L is −0.3. While AOA = 5 ,
the smallest lift coefficient, C L is −0.15. While AOA = 10 , the
smallest lift coefficient, C L is 0. According to this, while AOA = 10 ,
the lifting force, L is no longer negative. Thus, the angle of attack
moderate increasing will help the average lift coefficient C L in-
crease.
In addition to the drag coefficient, C D in the downstroke and
upstroke, the profile change of oscillation amplitude is obvious.
When flapping wing starting downstroke and arriving the center
point position from the highest peak, the drag coefficient, C D falls
to the lowest. Again wing flapping from the center point down-
stroke to the perigee position, the drag coefficient, C D elevates to
the starting value, this may know while in downstroke the thrust
force, T is positive. Then wing flapping starts to upstroke from the
perigee to the center point position, the drag coefficient, C D rises
to the highest. The movement of wing flaps to upstroke again from
the center point to the peak position, the drag coefficient, C D falls
to starting value, this means while in upstroke the thrust force, T
is also positive.
Although in downstroke the minimum drag coefficient, C D as-
sumes that the linear proportion to reduce, but it reduces rela-
tively along with the angle of attack increase. While AOA = 0 ,
the minimum drag coefficient, C D is −0.018. While AOA = 5 ,
the minimum drag coefficient, C D is −0.06. While AOA = 10 ,
the minimum drag coefficient, C D is −0.135. But in upstroke
the biggest drag coefficient, C D actually assumes that the linear
proportional increasing. While AOA = 0 , the biggest drag coeffi-
cient, C D is −0.015. While AOA = 5 , the biggest drag coefficient,
C D is −0.005. While AOA = 10 , the biggest drag coefficient, C D is −0.02. It increases along with the angle of attack increase, al-
though in upstroke the biggest drag coefficient, C D does not as-
sume that the linear proportion to reduce, but for all cases, the
angle of attack increases will help the entire cyclical of the aver-
age thrust force T .
388 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
(a) t /T = 0/6 (b) t /T = 2/6
(c) t /T = 3/6 (d) t /T = 5/6
Fig. 7. The velocity vector diagram of a flapping cycle (K = 0.3, AOA = 0).
Fig. 8. The comparison of the lift and drag coefficient, C L , C D under different AOA ( K = 0.3).
3.4.2. Wing tip vortex
Figs. 7 and 9 are the speed of vector diagrams for AOA = 0 and AOA = 10 , when K = 0.3 and at the position of 1/4 chord
length observes the wing tip vortex. While AOA = 0 , regardless of
in downstroke or upstroke, they all have the wing tip vortex. Also,
the average vortex velocity is 8.02 m/s for the wing tip. While
AOA = 10 , the average vortex velocity increases to 12.4 m/s for
the wing tip. In addition, the scope of turbulent flow increases
gradually. While the angle of attack increases, the average vor-
tex velocity was already bigger than the free-stream speed for the
wing tip. While the angle of attack increases, the upper and lower
surfaces of wing have the pressure difference, producing the wing
tip vortex of the wing to form the lower pressure area, it creates
a function of suction force to the flow field and causes the flow
field to form an acceleration feature in the turbulent flow region.
However, in upstroke, because it has the influence of the angle of
attack, causes of the frontal area of lower surface of wing to in-
crease and resulting in the pressure of the lower surface of wing
relative to enhance and it with upstroke the lower surface of wing
produces the lower pressure region mutually to balance, therefore,
there are no the wing tip vortex, the negative lifting force, L rela-
tive to be smaller is good for the flight of the flapping wing of a
MAV.
Along with the angle of attack increasing, in downstroke the
speed of average wing tip vortex is accelerated gradually. The in-
tensity is strengthened gradually and the scope of turbulent flow
is expanded gradually, relatively, upper and lower surfaces of wing
B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392 389
(a) t /T = 0/6 (b) t /T = 2/6
(c) t /T = 3/6 (d) t /T = 5/6
Fig. 9. The velocity vector diagram of a flap cycle ( K = 0.3, AOA = 10).
Table 1
The average lifting force and thrust force of the different angle of attack (K = 0.3).
C L C D L (g) T (g)
AOA= 0 0 −0.018 0 0.4214
AOA= 5 0.1875 −0.0325 4.39 0.7609
AOA= 10 0.3625 −0.0775 8.4874 1.8146
naturally bigger as well. But in upstroke, as the pressure difference
balances the upper and the lower surfaces of the wing tip vortex,
the negative lifting force, L relative to be smaller. This can verify
the C L and C D under different angle of attack.
3.5. Aerodynamic performance
The K = 0.3 is under the different angle of attack of the anal-
ysis result to the average lift and drag coefficient, C D , substitution
for Eqs. (3) and (4) may result in the average lifting force and
thrust force, T of flap in the single wing, the thrust force, T value
(Table 1), calculates that the value might help for designs in the
future whole of the weight reference for the flapping wing MAV.
4. The design and actual manufacture
The design parameters of flapping wing for a MAV: the
wingspan is 15 cm, the aspect ratio is 3, the mean chord is 5 cm
390 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
Table 2
Components Weight (grams)
Airfoil 1.5
Joint 0.7
Motor 2
Total 8
and the wing thickness is 0.03 cm. The overall design configuration
is shown in Fig. 10.
4.1. Overall design
The prediction of numerical calculation tells us, the gross
weight has to be lower than 8.78 g to be able to fly. Therefore
aspects of weight to take off is estimated, weights of various com-
ponents are listed in Table 2. From Table 2 we can see that the
total weight estimate to take off is 8 g, lower than 8.78 g. Eliminat-
ing crosswind shear and projection angle problems, this flapping
wing micro aerial vehicle should be able to fly ideally.
4.1.2. Overall designs of fuselage, actuation and electrical power system
By Refs. [2,8], in general, the length of fuselage is approximately
0.7–1.1 times of the main plane wingspan, the area of the hori-
zontal tail is approximately 7–12% of the main wing area, and its
position is approximately 1.5–2.5 times length of chord away from
center of gravity of the airplane. Thus, the fuselage length is 12 cm
and the horizontal tail is installed away from the nose 9.5 cm, the
wing area of horizontal tail is 5.625 cm2.
In order to avoid the overweight of battery and the motor af-
fects the lifting force, L, therefore the choice of the weight of
battery is 1.5 g and the output voltage is 3.7 V of the lithium bat-
tery, shown in Fig. 11(a). Weight of motor chooses 2 g, as the input
voltage of high efficiency motor is 3.7 V that the output rotational
speed can reach 28,000 rpm.
4.1.3. The reduction gear of transmission
Four-bar linkage was used as the actuating transmission unit.
The flap angle of 30 cannot just make it because of the ratio
of gears and spacing problem of transmission unit. Therefore, the
optimum design of the flap transmission system employed the pro-
gram “flap design”, numerical result decides the angles of upstroke
and downstroke are 35 and 38 respectively. The transmission
system unit is shown in Fig. 11(b). The MAV vehicle wants to be
able to fly, the K = 3 at least. However, rotation speed of motor is
(a) Lithium battery (b) Transmission mechanism
(c) The MAV entity (d) The MAV components
B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392 391
(a) (b)
(c) (d)
Fig. 12. The MAV flying test.
466.667 Hz while the input voltage is 3.7 V. This frequency is too
high and torque is too small resulting in the flap wing cannot flap
efficiently, it is necessary to reduce the gear ratio to 18.24:1, and
the final flapping frequency of wing is 25.58 Hz.
4.1.4. Estimation of aerodynamic parameters
By using the above conditions of the MAV, Eq. (6) calculates the
J is 2.047, in which the speed of wing tip is 4.886 m/s. We know
the wind speed is bigger than the wing tip speed, in other words,
the flap frequency excessively small. The flight characteristics of
flapping wing displace the unsteady state to the quasi-steady state
that is a contradictory phenomenon. If the speed of wing tip can
be promoted, it will cause the J equal to about 1, so that the flight
of unsteady flapping wing become realistic, then using Eq. (7) to
calculate the Re is 16,733, small than 106 just right to describe
the flight region of MAV. In the situation of the flap angle, the
wingspan and the aspect ratio fixed, the flap frequency then be-
comes the main variable of the Reynolds number.
4.2. Manufacture and test flight
The manufacture of wing contains an airfoil outrigger or bone
rib between the wing root and the wingspan skeleton, in order to
maintain stiffness and shape for the thin film of airfoil does not
distort excessively and to keep the change of lifting force, L won’t
happen dramatically in upstroke or downstroke. The thin film wing
has made by the ethylene material. The main body of fuselage uses
carbon fiber stick. The MAV is shown in Fig. 11(c), (d).
While a simple flight testing, throws the MAV by hand, the
best far range of flight may reach 8 m and discover the vibra-
tion of transmission system small, in addition to the horizontal
tail is quite beneficial for the flight stability of MAV. While the
horizontal tail adjustment supremely curls upwards to 10 , the
flight condition is the best. In addition, throws by hand if not
has suitable skill, it often causes the angle of attack oversized or
slightly has created loses speed then crash. Test flight as shown in
Fig. 12.
5. Conclusions
(1) The numerical analysis is a tool to help the design of micro
aerial vehicle.
(2) While AOA = 0 , the K is increased and does not have the
contribution to the average lifting force (all are zero), but the
mean drag coefficient, C D all is −0.018. While K = 0.3 and
AOA = 5 , the average lift coefficient, C L climbs to 0.1875, the
392 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
the mean drag coefficient, C D reduces again to −0.0775. Thus,
it may be known that a moderate increase of the angle of at-
tack is quite advantageous to the production of average lifting
force and average thrust force T .
(3) While AOA = 0 , the K is increased. It causes the average
speed of wing tip vortex speed relative to increase relatively,
but the upstroke and downstroke of the clockwise and coun-
terclockwise strength of the vortex is equal. Therefore, the
average lifting force is zero. While K = 0.3 and the angle of
attack increases, the counterclockwise rotation average wing
tip vortex speed is bigger than the free-stream speed of the
downstroke that lifting force, L relative to promotion. Because
the lower airfoil frontal area to increase in upstroke will cause
the pressure enhance and it with lower pressure region bal-
ances each other of the lower airfoil. Therefore, the wing tip
vortex production is not discovered. It’s relative to smaller of
the negative value for the lifting force, L.
(4) As a result of the MAV, it must fly with minimum angle of
attack is 5 . Therefore it uses the horizontal tail to produce
a downward force. By pulling up the nose will produce the
angle of attack and it discovered adjustment supremely curls
upwards 10 , the flight condition is best.
(5) The result of using motor that make the output rotational
speed excessively quickly, therefore it needs the gear group to
reduce the driven rotational speed to obtain more torsion and
enhances the transmission system supplies to the flap wing to
output the lifting force, L and the thrust force, T . Otherwise, it
is will be insufficient for the torsion and unable effectiveness
to flap the wing.
(6) After the actual test flight to prove that horizontal flight reach
above 8 m, and it discovered the smaller transmission system
vibration and addition to the horizontal tail are quite benefi-
cial for stability of the flapping wing MAV flight.
Acknowledgements
The authors acknowledge the support of the MRL of the ITRI,
ROC 2007 and the funding of the National Science Council in Tai-
wan under the contracts of NSC 94-2212-E-216-004.
References
[1] S.K. Banala, S.K. Agrawal, Design and optimization of a mechanism for out-of-
plane insect wing-like motion with twist, Journal of Mechanical Design (2005)
841–844.
epowerfly/diypage.htm.
[3] Fluent 6.1, User’s Guide, 2003.
[4] Gambit 2.0, User’s Guide, 2003.
[5] Shi-Ming Huang, Numerical simulation of flow over a flapping wing, PhD Dis-
sertation, National Cheng Kung University, 2004.
[6] R.F. Larijani, J.D. DeLaurier, A nonlinear aeroelastic model for the study of flap-
ping wing flight, in: T.J. Mueller (Ed.), Fixed and Flapping Wing Aerodynamics
for Micro Air Vehicle Applications, in: AIAA Progress in Aeronautics and Astro-
nautics, vol. 195, AIAA, 2001, pp. 399–428 (Chapter 18).
[7] C.S. Lin, C. Hwu, W.B. Young, The thrust and lift of an ornithopter’s membrane
wings with simple flapping motion, Aerospace Science and Technology 10 (2)
(March 2006) 111–119.
CG.mav/.
[9] M.F. Neff, D. Hummel, Euler solutions for a finite-span flapping wing, in: Con-
ference on Fixed, Flapping and Rotary Wing Vehicles at Very Low Reynolds
Numbers, 2000, pp. 5–7.
[10] T. Nick Pornsin-sirirak, Y.C. Tai, H. Nassef, C.M. Ho, Titanium-alloy MEMS wing
technology for a micro aerial vehicle application, Sensors and Actuators A:
Physical 89 (2001) 95–103.
[11] B. Singh, M. Ramasamy, I. Chopra, J.G. Leighman, Insect-based flapping wings
for micro hovering air vehicles: Experimental investigations, in: Proceedings of
the 60th Annual Forum of the American Helicopter Society, June 2004.
[12] A. Suhariyono, J.H. Kim, N.S. Goo, H.C. Park, K.J. Yoon, Design of precision
balance and aerodynamic characteristic measurement system for micro aerial
vehicles, Aerospace Science and Technology 10 (2) (March 2006) 92–99.
[13] I.H. Tuncer, M. Kaya, Thrust generation caused by flapping airfoils in a biplane
configuration, Journal of Aircraft 40 (2003) 509–515.
Aerospace Science and Technology
Design and aerodynamic analysis of a flapping-wing micro aerial vehicle
Bor-Jang Tsai ∗,1, Yu-Chun Fu
Department of Mechanical Engineering, Chung Hua University, No. 707, Sec. 2, Wu Fu Rd., Hsinchu, Taiwan 300, ROC
a r t i c l e i n f o a b s t r a c t
Article history:
Accepted 9 July 2009
Keywords:
MAV
This paper presents the design and aerodynamic performance of a planar membrane wing as shape airfoil
for the micro aerial vehicle. This simulation calculates the average lift force, L as the criteria weight of
the flapping wing (weight must be lower than 8.78 g), to make one ultra-light, small size flapping wing
MAV. In here two phases are discussed. First, the 3D aerodynamic calculation and flow field simulation
of a planar membrane wing as shape airfoil for a MAV were studied. Analyzing the flapping wing under
different frequencies and angles of attack, investigates the pressure distribution, the airfoil-tip vortex and
the up-wash situation of the air flow. Second is to average lift force, L 8.78 g for designing weight limit
of the MAV. The specifications of flapping wing MAV are 8 g gross weight, the 15 cm wingspan, and
5 cm chord length. In this vehicle, we employed the concept of four-bar linkage to design a flapping
mechanism which simulates the flapping motion of a bird. The angles of upstroke and downstroke can
be varied in the design. The total flapping angle is 73. The flapping frequency of wing is 25.58 Hz.
The power source comes from motor with a Li–H battery. A simple flight test was carried out and the
result of the flight is going well. The actual flight distance is approximately 8 m, and the primary goal is
achieved. By the way, we found the rigidity of tail wing is crucial and should be enhanced to prevent the
flapping-wing MAV will be unable to revise if the MAV in a crooked condition and it will cause a crash.
© 2009 Elsevier Masson SAS. All rights reserved.
1. Introduction
The micro aerial vehicle, in English is abbreviated as a MAV,
according to the Defense Advanced Research Projects Agency
(DARPA) of USA, the size of various aspects of micro aerial vehi-
cle (MAV) is limited to 15 cm, the flying speed is 10–20 m/s, the
Reynolds number must be below 106. Regarding a flapping wing
for a MAV, the most important issue at present is the aerody-
namic performance. The Reynolds number of a MAV is about 10 5,
this range of Reynolds number will cause laminar separation phe-
nomenon occurred on the surfaces of the body. Moreover, since
the definition of a MAV includes size limit, and the challenge of
this work is to design an ultra-light and small size of a flapping
wing MAV comparing all literatures [1,7,9,10,13], therefore by us-
ing very low aspect ratio of MAV to obtain enough lifting force,
L. However, small aspect ratio will increase the three-dimensional
effects on flow field. The MAV is small and the speed is low, the
flight stability of a MAV is affected easily by the external wind
shear or other disturbances.
alyzed a planar membrane wing under the low Reynolds number.
Each pattern of the flap movement initiates a complex and un-
* Corresponding author. Tel.: +886 3 5186478; fax: +886 3 5186521.
E-mail address: [email protected] (B.-J. Tsai). 1 Professor.
steady flow field. Calculation of aerodynamic performance becomes
crucial. To predict lifting force, L needs to solve the whole un-
steady flapping flow field of a wing. Approaches of solving this are
divided into two steps; first, we do the flow field simulation and
analysis, second, we design and manufacture it.
Regarding the literature survey, in 2000, Neff and Hummel [9]
studied the two- and three-dimensional flow fields by plunging
and pitching movement for NACA 0012 airfoil, they solved the Eu-
ler equation to simulate the flap and twist movement for the rect-
angular wing. In 2003, Tuncer and Kaya [13] made the movement
of the upstroke and downstroke flap by using the two-dimensional
NACA 0014 and they analyzed the reason which is thrust force, T
produced and observe the overflow situation of its turbulent flow.
In 2001, the Caltech, Pornsin-sirirak made a MAV [10], they used
the titanium alloy wing of the xylene thin film, complete the al-
together weight is 10.5 g, also fly for 5–18 sec successfully. In
2005, Delaware University in USA, Agrawal imitates an insect flight
and they studied the multi-dimensional flapping movement and
the twisting movement to simulate the hummingbird flap and but
not becomes a MAV [1]. In 2006, Lin, Hwu and Young reported
the trust and lift of an ornithopter’s membrane wings with sim-
ple flapping motion on the journal [7], they revealed the lift force,
L of a flexible flapping wing will increase with the increase of
the flapping frequency under the corresponding flying speed. For
the same flapping frequency, the flying speed can be increased by
decreasing of the angle of attack with the trade of loosing some
lifting force. The flapping motion generates the trust to acquire
1270-9638/$ – see front matter © 2009 Elsevier Masson SAS. All rights reserved.
384 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
Nomenclature
P pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pa, psi
L lift force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N
T thrust force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N
C L lift coefficient
C D drag coefficient
K reduced frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hz
AOA angle of attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
U flying speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s
t time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s
ν dynamic viscosity
the flying speed. The flying speed and angle of attack combine
to generate the lift force, L for flying. This paper is the most im-
portant reference to us. In recent, the design of precision balance
and aerodynamic characteristic for micro aerial vehicle to measure
lift, drag, rolling-moment, and pitching-moment of a MAV was re-
ported by Suhariyono et al. [12], but measurement is for the fixed
wing MAV only, not for flapping wing, the measurement of flap-
ping wing is critical. Only Singh et al. [11] studied an experimental
apparatus that incorporates flapping wings and measures the small
amount of thrust generated by these wing motions is described.
This methodology is used to measure the thrust generated by two
wings at different wing pitch settings. Also, the effect of change
in pitch phase during a flapping cycle is examined experimentally.
Regarding the simulation, Larijani [6] proposed a nonlinear aeroe-
lastic model for the study of flapping wing flight in the 2001, this
paper conducted the Huang’s [5] numerical analysis for the flap-
ping wing MAV later.
From Refs. [9] and [7] we know the three-dimensional move-
ment of many birds flapping is used the standard NACA shape
airfoil as wings, but actual flapping wing of MAV to be restricted
in the volume and the weight. It’s unlikely to use the NACA series
of wing section. On the contrary, the most of the flapping wing
for MAV, a planar membrane wing are used primarily. In order to
imitating the insect flutter and the flight pattern, therefore, this
investigation does take the planar membrane wing as a study tar-
get vehicle, discussing its aerodynamic characteristic and to predict
average lift force, L as the criteria weight to manufacture a future
MAV. The actual MAV was made by the wingspan is 15 cm, the
mean chord is 5 cm, the weight is 8 g, the wing area is 75 cm2,
the flapping frequency is 25.58 Hz of a flapping wing MAV.
2. Numerical analysis
2.1. Numerical method
In the numerical simulation solves the speed and the pressure
on this pattern flow field. It is an integral control volume method.
In the control volume definition, each physical quantities is sig-
nificant because the separation variable is the integral of control
volume for the governing equation, therefore we must first take
the separation of the governing equation to control volume of the
flow field computation.
+ div(ρur φ − Γ φ gradφ) = S φ (1)
ψ: On behalf of any independent physical quantity (ui , e, k . . .)
Γ φ : Diffusion coefficient
S φ: Source coefficient
After the numerical computation of the convergence condition
which in the volume change rate is smaller than after each time
the iteration that we give.
C kφ =
2.2.1. Estimation of the MAV weight
The MAV weight (W Total) may include a MAV main body weight
(W Fuselage ), a wing weight (W Rudder), the load weight (battery and
switch or joint) (W Payload) and the power unit (motor) ( W Power ).
2.2.2. Aerodynamic parameter estimates
Wing tip speed (6)
3.1. Numerical simulation
3.1.1. Geometry contour and grid establishment
In order to conform to DARPA’s definition of the MAV, there-
fore this research takes 15 cm as the wingspan length and only
constructs the single wing (half wingspan) of grid. The main con-
sideration of chord length is for hoped the induced drag is small
but the wing induced drag following the lifting force, L occurs, the
lifting force, L is bigger and the induced drag is also bigger. But
the wing induced drag is directly related to the aspect ratio and
if the aspect ratio is bigger, relatively, the induced drag will be
smaller. Therefore, this research designate the aspect ratio is 3, the
chord length c is 5 cm, the thickness of planar membrane wing
B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392 385
Fig. 1. The grid disposition of the rigid wing section for a three-dimensional planar membrane wing.
non-constructive grid, the non-constructive grid is easier than the
constructive grid to process the complex geometry, has the con-
venience to use the three-dimensional dynamic moving grid skills
[4] as well. The connecting positions of wing entity and the flow
passage will have the boundary layer effect, therefore the grid be-
came dense but the entire flow passage used the dispose for the
C grid, the total grid point is 854,090, shown in Fig. 1. The com-
putational domain; the length is 32.5c , the extended is 12.5c , the
height is 25c .
The predetermined MAV flying speed is 10 m/s, therefore in-
coming air speed is 10 m/s. The outflow is an atmospheric pres-
sure. Because of flow field assuming sliding, therefore the hypothe-
sis of flow passage flank is the sliding boundary, then, the position
of boundary will not have the boundary layer effect. The flapping
angle is 30 .
The convection terns of momentum equations use different ap-
proaching principles by spatial separation variables, two principles
were employed in this study, the pressure term uses staggered
type of PRESTO (Pressure Staggering Option) principle. In addition
to the speed-pressure field coupling uses the SIMPLE principle. For
the time accuracy, the time step is carried on iterations by the two
step implicit expression law (2nd order Implicit Algorithm) [3]. The
important parameter settings are as follow:
1. Reduced frequency K setting: the K value is 0.1 and 0.2 and
0.3, from Eq. (5), may know the actual flight of birds conver-
sion to the flapping frequency.
K = 0.1, is equal to flap of 6.369 times in each second.
K = 0.2, is equal to flap of 12.739 times in each second.
K = 0.3, is equal to flap of 19.108 times in each second.
2. Angle of attack setting: designates the angles of attack is 0 ,
5 and 10 .
3.2. Program validation by a case of three-dimensional rigid wing
Based on 2004, Ref. [5], in view of aerodynamic analysis for
a three-dimensional flapping wing, simulates the behavior of the
NACA 2412 rigid wing flap. Case uses the same wing section and
the flow field conditions. That is the NACA 2412 rectangular wing
and AR is 8, and the single wing of grid was constructed, namely
half wingspan is 4c (c is the chord length 3.4 cm), the Φ is 15 ,
the angle of attack is 0 , the U is 8.6 m/s, the flap frequency is
8 Hz, 16 Hz and 24 Hz respectively, carries on the computation of
dynamic flap of unsteady flow field. The grid distribution is shown
in Fig. 2, and the total grid number is 641,624. Fig. 3 is a com-
parison of lifting coefficient in condition of unsteady state, result
of lift coefficient between this research and Ref. [5] is quite close,
Fig. 2. The grid system of the rigid wing section for the three-dimensional NACA
2412 under the upstroke and downstroke.
this proves that the setting of boundary conditions and numerical
model is accuracy and correct.
3.3. A three-dimensional case of planar membrane wing in different
K −AOA= 0 , K = 0.1, 0.2, and 0.3
3.3.1. Lifting force and thrust force
When the angle of attack is 0 and the K value is 0.1, 0.2
and 0.3 respectively, investigates the increasing of K to influence
on the aerodynamic forces. Fig. 4 shows the comparison of lift co-
efficient, C L and different drag coefficient, C D based on different
K values, in the lift coefficient, C L portion, the movement of flap
wing starting the downstroke and arriving the center point posi-
tion from the highest peak, the lift coefficient, C L elevates to the
maximum value, the movement of flap wing flapping again from
the center point downstroke to the perigee position, and the lift
coefficient, C L falls to the starting value. Therefore, in downstroke
for the lifting force, L is positive. Starting to upstroke, the flap
flapping from the perigee to the center point position, the lift coef-
ficient, C L falls to the minimum value, the movement of flap wing
flapping again from the center point to the peak position, the lift
coefficient, C L rises to the starting value, thus the lifting force, L is
negative value in upstroke.
The increase of K causes the profile of top and bottom oscil-
lation amplitude for the lift coefficient, C L to become the pro-
portional increasing, while in downstroke, the positive lift coeffi-
cient, C L becomes the proportion to increase. While K = 0.1, the
maximum of lift coefficient, C L is 0.1. While K = 0.2, the maximum
of lift coefficient, C L is 0.2. While K = 0.3, the maximum of lift co-
efficient, C L is 0.3. While in upstroke, the negative lift coefficient,
C L becomes the proportional increasing. While K = 0.1, the small-
est lift coefficient, C L is −0.1. While K = 0.2, the smallest lift co-
efficient, C L is −0.2. While K = 0.3, the smallest lift coefficient, C L is −0.3. Increase of the positive and the negative counterbalances
386 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
(a) This research (b) Ref. [5]
Fig. 3. The comparison of lift coefficient, C L under different frequencies for the NACA 2412.
Fig. 4. The comparison of the lift and drag coefficient, C L , C D under different K (AOA = 0).
to the average lifting force, L (equal to zero), therefore flapping like
this way is unable to generate the lifting force, L.
Moreover, in the drag coefficient, C D portion, while the K in-
creases, the drag coefficient, C D has the big variation only when
the flap starts flapping. While K = 0.1, the biggest drag coeffi-
cient, C D is −0.0125. While K = 0.2, the biggest drag coefficient,
C D is −0.014. While K = 0.3, the biggest drag coefficient, C D is −0.015. The drag coefficient, C D reduces relatively when the
K value increases, after the first flap cycle, no matter how K value
is, both in downstroke and in upstroke will not have big change,
the mean drag coefficient, C D is −0.018. As a result, while the an-
gle of attack is 0 , the increase of K value does not have a quite
big contribution to the average thrust coefficient.
3.3.2. Wing tip vortex
In order to ensure the accuracy, the second period of flap cy-
cle in numerical calculation was selected to observe, it separately
picks six points of time period in the cycle to observe. Fig. 5 shows
the t /T = 0/6− t /T = 5/6 are in order. Figs. 6 and 7 show the ve-
locity vector diagrams for K = 0.1 and K = 0.3 respectively, at the
position of 1/4 chord length observes the wing tip vortex. While
the t /T = 0 starting downstroke, then curls up the counterclock-
wise rotation of the wing tip vortex, the strong turbulent flow
causes the low pressure region for the upper wing surface, there-
Fig. 5. The schematic drawing of the flapping points of time period.
fore it may bring the upward lifting force, L for the plate wing.
While the t /T = 3/6 in the perigee position of downstroke, instan-
taneously, the turbulent flow can be absorbed because of the big
reacting force. While the t /T = 4/6 starting upstroke, then curls
up the clockwise rotation of the wing tip vortex, the strong turbu-
lent flow causes of the low pressure region for lower wing surface,
therefore the negative lifting force, L is not favor for the MAV
flight.
While K = 0.1, no matter how the downstroke or upstroke
B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392 387
(a) t /T = 0/6 (b) t /T = 2/6
(c) t /T = 3/6 (d) t /T = 5/6
Fig. 6. The velocity vector diagram of a flapping cycle (K = 0.1, AOA = 0).
tip vortex can be seen obviously and the average vortex velocity
is 8.02 m/s for the wing tip. As a result of the K increase can
cause the maximum vortex velocity increasing quickly for the wing
tip, wing tip vortex became obvious, it affects the pressure be-
tween upper and lower surfaces of airfoil, and influences on lifting
force, L and thrust force, T as well. Regardless of the increasing
of K , the upstroke and downstroke have the same clockwise and
counterclockwise strength of the vortex, therefore the positive and
the negative of lifting force, L is mutually offset. This causes the
average lifting force equal to zero. This result verifies that C L and
C D of different K at AOA = 0 as our expectation.
3.4. A three-dimensional case of planar membrane wing in different
angle of attack – K = 0.3, AOA = 0 , 5 and 10
3.4.1. Lifting force and thrust force
K = 0.3, AOA = 0 , 5 and 10 , investigates the increasing of K
to influence on the lift coefficient, C L and the drag coefficient, C D .
Fig. 8 is the comparison of the lift coefficient, C L and the drag
coefficient, C D under the different angle of attack, so the increas-
ing angle of attack conducive to favor the lifting force, L and the
thrust force, T generation, while in downstroke the positive lift co-
efficient, C L becomes the proportion to increase. While AOA = 0 ,
the maximum lift coefficient, C L is 0.3. While AOA = 5 , the max-
imum lift coefficient, C L is 0.5. While AOA = 10 , the maximum
lift coefficient, C L is 0.7. While in upstroke, the negative lift coef-
ficient, C L becomes the proportional reducing actually. While the
AOA = 0 , the smallest lift coefficient, C L is −0.3. While AOA = 5 ,
the smallest lift coefficient, C L is −0.15. While AOA = 10 , the
smallest lift coefficient, C L is 0. According to this, while AOA = 10 ,
the lifting force, L is no longer negative. Thus, the angle of attack
moderate increasing will help the average lift coefficient C L in-
crease.
In addition to the drag coefficient, C D in the downstroke and
upstroke, the profile change of oscillation amplitude is obvious.
When flapping wing starting downstroke and arriving the center
point position from the highest peak, the drag coefficient, C D falls
to the lowest. Again wing flapping from the center point down-
stroke to the perigee position, the drag coefficient, C D elevates to
the starting value, this may know while in downstroke the thrust
force, T is positive. Then wing flapping starts to upstroke from the
perigee to the center point position, the drag coefficient, C D rises
to the highest. The movement of wing flaps to upstroke again from
the center point to the peak position, the drag coefficient, C D falls
to starting value, this means while in upstroke the thrust force, T
is also positive.
Although in downstroke the minimum drag coefficient, C D as-
sumes that the linear proportion to reduce, but it reduces rela-
tively along with the angle of attack increase. While AOA = 0 ,
the minimum drag coefficient, C D is −0.018. While AOA = 5 ,
the minimum drag coefficient, C D is −0.06. While AOA = 10 ,
the minimum drag coefficient, C D is −0.135. But in upstroke
the biggest drag coefficient, C D actually assumes that the linear
proportional increasing. While AOA = 0 , the biggest drag coeffi-
cient, C D is −0.015. While AOA = 5 , the biggest drag coefficient,
C D is −0.005. While AOA = 10 , the biggest drag coefficient, C D is −0.02. It increases along with the angle of attack increase, al-
though in upstroke the biggest drag coefficient, C D does not as-
sume that the linear proportion to reduce, but for all cases, the
angle of attack increases will help the entire cyclical of the aver-
age thrust force T .
388 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
(a) t /T = 0/6 (b) t /T = 2/6
(c) t /T = 3/6 (d) t /T = 5/6
Fig. 7. The velocity vector diagram of a flapping cycle (K = 0.3, AOA = 0).
Fig. 8. The comparison of the lift and drag coefficient, C L , C D under different AOA ( K = 0.3).
3.4.2. Wing tip vortex
Figs. 7 and 9 are the speed of vector diagrams for AOA = 0 and AOA = 10 , when K = 0.3 and at the position of 1/4 chord
length observes the wing tip vortex. While AOA = 0 , regardless of
in downstroke or upstroke, they all have the wing tip vortex. Also,
the average vortex velocity is 8.02 m/s for the wing tip. While
AOA = 10 , the average vortex velocity increases to 12.4 m/s for
the wing tip. In addition, the scope of turbulent flow increases
gradually. While the angle of attack increases, the average vor-
tex velocity was already bigger than the free-stream speed for the
wing tip. While the angle of attack increases, the upper and lower
surfaces of wing have the pressure difference, producing the wing
tip vortex of the wing to form the lower pressure area, it creates
a function of suction force to the flow field and causes the flow
field to form an acceleration feature in the turbulent flow region.
However, in upstroke, because it has the influence of the angle of
attack, causes of the frontal area of lower surface of wing to in-
crease and resulting in the pressure of the lower surface of wing
relative to enhance and it with upstroke the lower surface of wing
produces the lower pressure region mutually to balance, therefore,
there are no the wing tip vortex, the negative lifting force, L rela-
tive to be smaller is good for the flight of the flapping wing of a
MAV.
Along with the angle of attack increasing, in downstroke the
speed of average wing tip vortex is accelerated gradually. The in-
tensity is strengthened gradually and the scope of turbulent flow
is expanded gradually, relatively, upper and lower surfaces of wing
B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392 389
(a) t /T = 0/6 (b) t /T = 2/6
(c) t /T = 3/6 (d) t /T = 5/6
Fig. 9. The velocity vector diagram of a flap cycle ( K = 0.3, AOA = 10).
Table 1
The average lifting force and thrust force of the different angle of attack (K = 0.3).
C L C D L (g) T (g)
AOA= 0 0 −0.018 0 0.4214
AOA= 5 0.1875 −0.0325 4.39 0.7609
AOA= 10 0.3625 −0.0775 8.4874 1.8146
naturally bigger as well. But in upstroke, as the pressure difference
balances the upper and the lower surfaces of the wing tip vortex,
the negative lifting force, L relative to be smaller. This can verify
the C L and C D under different angle of attack.
3.5. Aerodynamic performance
The K = 0.3 is under the different angle of attack of the anal-
ysis result to the average lift and drag coefficient, C D , substitution
for Eqs. (3) and (4) may result in the average lifting force and
thrust force, T of flap in the single wing, the thrust force, T value
(Table 1), calculates that the value might help for designs in the
future whole of the weight reference for the flapping wing MAV.
4. The design and actual manufacture
The design parameters of flapping wing for a MAV: the
wingspan is 15 cm, the aspect ratio is 3, the mean chord is 5 cm
390 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
Table 2
Components Weight (grams)
Airfoil 1.5
Joint 0.7
Motor 2
Total 8
and the wing thickness is 0.03 cm. The overall design configuration
is shown in Fig. 10.
4.1. Overall design
The prediction of numerical calculation tells us, the gross
weight has to be lower than 8.78 g to be able to fly. Therefore
aspects of weight to take off is estimated, weights of various com-
ponents are listed in Table 2. From Table 2 we can see that the
total weight estimate to take off is 8 g, lower than 8.78 g. Eliminat-
ing crosswind shear and projection angle problems, this flapping
wing micro aerial vehicle should be able to fly ideally.
4.1.2. Overall designs of fuselage, actuation and electrical power system
By Refs. [2,8], in general, the length of fuselage is approximately
0.7–1.1 times of the main plane wingspan, the area of the hori-
zontal tail is approximately 7–12% of the main wing area, and its
position is approximately 1.5–2.5 times length of chord away from
center of gravity of the airplane. Thus, the fuselage length is 12 cm
and the horizontal tail is installed away from the nose 9.5 cm, the
wing area of horizontal tail is 5.625 cm2.
In order to avoid the overweight of battery and the motor af-
fects the lifting force, L, therefore the choice of the weight of
battery is 1.5 g and the output voltage is 3.7 V of the lithium bat-
tery, shown in Fig. 11(a). Weight of motor chooses 2 g, as the input
voltage of high efficiency motor is 3.7 V that the output rotational
speed can reach 28,000 rpm.
4.1.3. The reduction gear of transmission
Four-bar linkage was used as the actuating transmission unit.
The flap angle of 30 cannot just make it because of the ratio
of gears and spacing problem of transmission unit. Therefore, the
optimum design of the flap transmission system employed the pro-
gram “flap design”, numerical result decides the angles of upstroke
and downstroke are 35 and 38 respectively. The transmission
system unit is shown in Fig. 11(b). The MAV vehicle wants to be
able to fly, the K = 3 at least. However, rotation speed of motor is
(a) Lithium battery (b) Transmission mechanism
(c) The MAV entity (d) The MAV components
B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392 391
(a) (b)
(c) (d)
Fig. 12. The MAV flying test.
466.667 Hz while the input voltage is 3.7 V. This frequency is too
high and torque is too small resulting in the flap wing cannot flap
efficiently, it is necessary to reduce the gear ratio to 18.24:1, and
the final flapping frequency of wing is 25.58 Hz.
4.1.4. Estimation of aerodynamic parameters
By using the above conditions of the MAV, Eq. (6) calculates the
J is 2.047, in which the speed of wing tip is 4.886 m/s. We know
the wind speed is bigger than the wing tip speed, in other words,
the flap frequency excessively small. The flight characteristics of
flapping wing displace the unsteady state to the quasi-steady state
that is a contradictory phenomenon. If the speed of wing tip can
be promoted, it will cause the J equal to about 1, so that the flight
of unsteady flapping wing become realistic, then using Eq. (7) to
calculate the Re is 16,733, small than 106 just right to describe
the flight region of MAV. In the situation of the flap angle, the
wingspan and the aspect ratio fixed, the flap frequency then be-
comes the main variable of the Reynolds number.
4.2. Manufacture and test flight
The manufacture of wing contains an airfoil outrigger or bone
rib between the wing root and the wingspan skeleton, in order to
maintain stiffness and shape for the thin film of airfoil does not
distort excessively and to keep the change of lifting force, L won’t
happen dramatically in upstroke or downstroke. The thin film wing
has made by the ethylene material. The main body of fuselage uses
carbon fiber stick. The MAV is shown in Fig. 11(c), (d).
While a simple flight testing, throws the MAV by hand, the
best far range of flight may reach 8 m and discover the vibra-
tion of transmission system small, in addition to the horizontal
tail is quite beneficial for the flight stability of MAV. While the
horizontal tail adjustment supremely curls upwards to 10 , the
flight condition is the best. In addition, throws by hand if not
has suitable skill, it often causes the angle of attack oversized or
slightly has created loses speed then crash. Test flight as shown in
Fig. 12.
5. Conclusions
(1) The numerical analysis is a tool to help the design of micro
aerial vehicle.
(2) While AOA = 0 , the K is increased and does not have the
contribution to the average lifting force (all are zero), but the
mean drag coefficient, C D all is −0.018. While K = 0.3 and
AOA = 5 , the average lift coefficient, C L climbs to 0.1875, the
392 B.-J. Tsai, Y.-C. Fu / Aerospace Science and Technology 13 (2009) 383–392
the mean drag coefficient, C D reduces again to −0.0775. Thus,
it may be known that a moderate increase of the angle of at-
tack is quite advantageous to the production of average lifting
force and average thrust force T .
(3) While AOA = 0 , the K is increased. It causes the average
speed of wing tip vortex speed relative to increase relatively,
but the upstroke and downstroke of the clockwise and coun-
terclockwise strength of the vortex is equal. Therefore, the
average lifting force is zero. While K = 0.3 and the angle of
attack increases, the counterclockwise rotation average wing
tip vortex speed is bigger than the free-stream speed of the
downstroke that lifting force, L relative to promotion. Because
the lower airfoil frontal area to increase in upstroke will cause
the pressure enhance and it with lower pressure region bal-
ances each other of the lower airfoil. Therefore, the wing tip
vortex production is not discovered. It’s relative to smaller of
the negative value for the lifting force, L.
(4) As a result of the MAV, it must fly with minimum angle of
attack is 5 . Therefore it uses the horizontal tail to produce
a downward force. By pulling up the nose will produce the
angle of attack and it discovered adjustment supremely curls
upwards 10 , the flight condition is best.
(5) The result of using motor that make the output rotational
speed excessively quickly, therefore it needs the gear group to
reduce the driven rotational speed to obtain more torsion and
enhances the transmission system supplies to the flap wing to
output the lifting force, L and the thrust force, T . Otherwise, it
is will be insufficient for the torsion and unable effectiveness
to flap the wing.
(6) After the actual test flight to prove that horizontal flight reach
above 8 m, and it discovered the smaller transmission system
vibration and addition to the horizontal tail are quite benefi-
cial for stability of the flapping wing MAV flight.
Acknowledgements
The authors acknowledge the support of the MRL of the ITRI,
ROC 2007 and the funding of the National Science Council in Tai-
wan under the contracts of NSC 94-2212-E-216-004.
References
[1] S.K. Banala, S.K. Agrawal, Design and optimization of a mechanism for out-of-
plane insect wing-like motion with twist, Journal of Mechanical Design (2005)
841–844.
epowerfly/diypage.htm.
[3] Fluent 6.1, User’s Guide, 2003.
[4] Gambit 2.0, User’s Guide, 2003.
[5] Shi-Ming Huang, Numerical simulation of flow over a flapping wing, PhD Dis-
sertation, National Cheng Kung University, 2004.
[6] R.F. Larijani, J.D. DeLaurier, A nonlinear aeroelastic model for the study of flap-
ping wing flight, in: T.J. Mueller (Ed.), Fixed and Flapping Wing Aerodynamics
for Micro Air Vehicle Applications, in: AIAA Progress in Aeronautics and Astro-
nautics, vol. 195, AIAA, 2001, pp. 399–428 (Chapter 18).
[7] C.S. Lin, C. Hwu, W.B. Young, The thrust and lift of an ornithopter’s membrane
wings with simple flapping motion, Aerospace Science and Technology 10 (2)
(March 2006) 111–119.
CG.mav/.
[9] M.F. Neff, D. Hummel, Euler solutions for a finite-span flapping wing, in: Con-
ference on Fixed, Flapping and Rotary Wing Vehicles at Very Low Reynolds
Numbers, 2000, pp. 5–7.
[10] T. Nick Pornsin-sirirak, Y.C. Tai, H. Nassef, C.M. Ho, Titanium-alloy MEMS wing
technology for a micro aerial vehicle application, Sensors and Actuators A:
Physical 89 (2001) 95–103.
[11] B. Singh, M. Ramasamy, I. Chopra, J.G. Leighman, Insect-based flapping wings
for micro hovering air vehicles: Experimental investigations, in: Proceedings of
the 60th Annual Forum of the American Helicopter Society, June 2004.
[12] A. Suhariyono, J.H. Kim, N.S. Goo, H.C. Park, K.J. Yoon, Design of precision
balance and aerodynamic characteristic measurement system for micro aerial
vehicles, Aerospace Science and Technology 10 (2) (March 2006) 92–99.
[13] I.H. Tuncer, M. Kaya, Thrust generation caused by flapping airfoils in a biplane
configuration, Journal of Aircraft 40 (2003) 509–515.