An Experimental Study on Effect of Wing Geometry of Hummingbird-like
Flapping Wing in the Hover
Yanghai Nan1*, MatČj Karásek2, Mohamed Lalami1, Hussein Altartouri1
1
Active Structure Laboratory, Université Libre de Bruxelles, Belgium
2
Faculty of Aerospace Engineering, Delft University of Technology, Netherlands
ABSTRACT
Wing, as one of important components of a
flapping wing Micro Air Vehicle (MAV), is directly
related to aerodynamic performance such as lift force
and torque around body. Therefore, design of
efficient flapping wing has become an interesting
research topic recently. In this paper, the
aerodynamic performance of flexible micromembrane flapping wing under the condition of
hovering was investigated to ascertain the best
combination of wing geometric parameters. For this
purpose, a flapping wing mechanism and an
experiment setup were built to measure the
aerodynamic forces and power usage of the flapping
motion. Then four different families of wings were
fabricated. The lift and power usage was measured at
different flapping frequencies with different shapes of
wings. In order to investigate the effects of wing
geometry, only one parameter of wing was varied at a
time. The results indicate that the aspect ratio and
wing surface have a critical impact on the force
production and wing efficiency. The best
performance was obtained with a trapezoidal wing
with a straight leading edge; both its shape and aspect
ratio (‫ ܴܣ‬ൎ ͻǤ͵) are similar to a typical hummingbird
wing.
1 INTRODUCTION
1
MAV is a class of unmanned aerial vehicle
(UAV) with restricted size and remote or autonomous
characteristic, which can be utilized for civilian and
military application such as terrain reconnaissance,
video surveillance or search and rescue missions after
earthquakes, etc. The bio-inspired MAVs, like
hummingbird and insect robots, are dramatically
developing during recent years. Many researchers are
exploring and researching them, for instance
Berkeley micro mechanical flying insect [1], Harvard
robotics insect based on Diptera [2], Beetle-like
flapping wing MAV [3] and Hummingbird-like robot
[4, 5]. All these MAVs can perform hovering flight;
the necessary lift force is produced by a pair of small
‫ כ‬Email: Yanghai.Nan@ulb.ac.be
flapping wings. Besides, another important advantage
of flapping wing MAV is that they have high
maneuverability and capability to sustain hover flight
in constrained space. This is because flapping wing
with small scales may offer some unique
aerodynamic advantages compared with traditional
fixed and rotary wing modes of propulsion [6, 7].
Flapping wing MAV consists of different
components such as a flapping mechanism, a pair of
flexible wings, a micro control system, a motor and a
battery. The flexible wing is one of the most
important subsystem of flapping wing MAV since it
directly relates to the aerodynamic forces and torques
around the body. In nature, we can find surprisingly
many different wing materials, wing shapes, sizes,
configurations, and components, even kinematics of
the wings. Therefore, wing design becomes a
significant challenge because it influences the
unsteady aerodynamics. In other words, how to
design the wing and how to keep the wing geometry
during flapping motion are considerably important.
Flapping wing is required to be light, strong and
fatigue resistant, to be able to properly flap during
flight. Thus, the wing material and wing geometry
plays an important role.
Numerous studies were done on the mechanism
and aerodynamics of flapping wings, employing both
unsteady flow simulation methods as well as
experiments. These works were developed based on
the natural species such as dragonfly [8, 9], manduca
sexta [10, 11] and other flying insect like beetle [3].
They analyzed the flapping wing kinematics. The
effect of wing geometries was studied as well [12].
The optimization of flapping wing based on
simulation model was reported by two categories
wings: symmetric wings and asymmetric wings. The
result shows that best performance for the wing shape
has nearly straight leading edges with more surfaces
outboard [12]. However, we note that these works
focus on rigid wing rather than flexible wing. This is
because that the aeroelastic interaction between the
wing and surrounding fluid can be neglected and the
overall complexity of the problem is reduced for the
rigid wing [13]. Moreover, it is difficult to accurately
calculate the aerodynamic loads generated by a
flapping wing since the 3D transient computational
fluid dynamics (CFD) solution with low Reynolds
numbers is necessary [14]. Although some results
from numerical studies can capture experimental
behaviors, any conclusion cannot be extrapolated by
these numerical studies [15, 16].
Many researchers have begun to pay attention to
the flexible wings due to its important role in the
aerodynamics of flapping flight, but there exist few
studies to research optimization of flexible wing,
especially for the hover situation. Therefore,
experimental study of the flexible membrane flapping
wing under condition of hovering is necessary.
The designed membrane flapping wing has
bending and torsional flexibility. It can be deformed
by varying wing speed, time-dependent pressure, and
local acceleration of the wing surface. These dynamic
quantities decide the instantaneous wing deformation.
That is, lift force is determined by the dynamic
coupling between the wings and surrounding air.
Changing wing deformation will influence the
aerodynamic and subsequently the wing performance.
Therefore, the study of flexible membrane wing
geometry is considerably meaningful.
In this paper, the objective is to optimize the
wing geometry such that the wing produces maximal
lift per power delivered to it. The effects of wing
geometry, for example, wing length, aspect ratio,
wing surface, wing chord, are investigated by
comparing mean lift force over one wingbeat while
only one parameter is changed at a time. Each mean
lift force is achieved by three measurements. Four
different families of wings are fabricated. The
aerodynamic performance of these wings for
hovering situation without wind was experimentally
studied by mean lift force and electric power. The
generated mean lift is measured at different geometry
wings, different flapping frequencies and powers.
The frame and links, which are made of material
Digital ABS, are built by an Objet 3D printer. The
links are connected by aluminum and steel rivet.
Wing bars are made of carbon material. The flapping
frequency is controlled by the input voltage of the
DC drive. The maximum flapping frequency is
approximately 26 Hz; the maximum amplitude of
flapping angle is about up to 180° at the tips,
including the leading edge bar deformation.
Fig.1: The flapping wing mechanism.
2.2 Wing parameters
Here the aerodynamic performance of a flapping
wing is studied to optimize wing geometry. In this
paper, mean lift force is used to estimate the wing
performance. Therefore, according to quasi-steady
aerodynamics, the mean lift force is function of
flapping frequency (݂), air density (ߩ), wing surface
ഥ஼௉ ).
(ܵ) and mean wing speed of center pressure (ܷ
The geometric parameters considered in our
investigation were wing aspect ratio ሺ‫ܴܣ‬ሻ , wing
length ሺܴሻ , wing surface, wing tapper ratio (see
Figure 2). Wing length is the distance from wing root
to its tip (i.e., length of single wing). Wing surface
refers to the planform area of each wing. ‫ ܴܣ‬is
computed from wing length and wing area as‫ ܴܣ‬ൌ
ʹܴଶ Τܵ. Taper ratio refers to the ratio between wing
tip chord ሺ‫ ்ܥ‬ሻ and wing root chordሺ‫ܥ‬ோ ሻ. Last, wing
planform shape refers to the actual shape of the wing
(i.e. rectangular and right-angled trapezoidal).
2 FLAPPING MECHANISM, WING
PARAMETERS AND WING DESIGN
2.1 Flapping mechanism
In this section, flapping mechanism, aerodynamic
parameters, wing geometry parameters and flexible
wing design will be studied. The flapping wing
mechanism was firstly designed based on a slider
crank and four-bar linkage which was presented in
[5]. Slider crank is used to generate a low amplitude
harmonic motion, while four-bar linkage is used to
amplify the motion to the desired amplitude. The
flapping wing MAV prototype, shown in Figure 1, is
composed of three components: the driving motor
(Faulhaber 0824), flapping mechanism and wings.
Fig.2: Flexible membrane wing structure.
The mean lift force of a pair of flapping wings
can be written as:
ଵ
ଶ
തതത௅ ሺʹܵሻܷ
ഥ஼௉
(1)
‫ܨ‬ഥ௅ ൌ ߩ‫ܥ‬
ଶ
With the assumption of flat and rigid wing, the
center of pressure is placed at the mid-length of
wingܴ஼௉ ൌ ܴΤʹ. Therefore, the mean wing velocity
of center pressure can be expressed as
ഥ஼௉ ൌ ʹȰ݂ܴ஼௉ ൌ Ȱ݂ܴ
ܷ
(2)
Based on the definition of the wing ‫ ܴܣ‬, the
cycle average lift force of a pair of wing can be
rewritten as
ଵ
തതത௅ ‫ܴܣ‬ሺܵȰ݂ሻଶ
‫ܨ‬ഥ௅ ൌ ߩ‫ܥ‬
(3)
ଶ
തതത௅ is the mean lift coefficient.
where‫ܥ‬
The formula (3) indicates that the mean lift force
depends on wing lift coefficient,‫ܴܣ‬, wing surface,
wing flapping amplitude angle Ȱ and flapping
frequency. In this work, we just consider the flapping
frequency, wing surface, ‫ ܴܣ‬and power to estimate
the wing performance. The flapping amplitude is
determined by the flapping mechanism. The average
lift coefficient cannot be constant because real wing
deforms more with condition of higher aerodynamic
loads and higher frequencies, etc.
wing root edge. The sleeves can rotate freely around
the two bars: leading edge bar and wing root bar. The
leading edge bar is connected to the output link of
flapping mechanism, while the root bar is inserted
into the frame which is aligned with the shoulder.
The carbon-fiber-reinforced polymer (CFRP) bands
are used as stiffeners to keep wing geometry when
flapping. Since the angle between the sleeves is
greater than the angle between the two bars, the wing
becomes cambered and twisted after the assembly. In
order to improve the durability of the two sleeves, the
Icarex material is glued on the wing root top corner
and wing root sleeve marked by red color shown in
Figure 3. Therefore, the strength of wing is increased
significantly, making it more suitable for large
amplitude flapping and high flapping frequency.
2.3Wing design
As we know, natural birds have many degrees of
freedom to change wing motion and wing geometry
as they maneuver or transition from one flight mode
to another, which is, for now, impossible in the
mechanical flappers. The only simple way is to
change wing kinematics via four-bar or other
mechanisms which is driven by rotary DC motor.
Therefore, changing the structure of wing may affect
the aeroelastic performance of the wing. This is
because the generation, growth rate and shedding of
the unsteaday leading edge vortex are completely
changed over the whole wing [13]. Thus, the
optimum wing structure is possible to find by testing
different wing designs.
Here the aeroelastic wings are designed to
understand how wing flexibility affects the
aerodynamic load. In this study, the wing motion is
constrained between the wing leading edge and wing
root edge. In other words, the desirable configuration
wing is obtained by passive elastic property.
Therefore, the desired lift force can be achieved by
changing elastic performance of wing such as wing
geometry and stiffener.
In this paper, the designed wing is inspired by the
Nano-hummingbird [4] and natural hummingbird.
The components of the wing include a carbon fiber
frame, a carbon fiber stiffeners, and membrane
(polyester membrane and Icarex membrane), shown
in Figure 2. The wing is made of a 15-ߤ݉ -thick
polyester membrane. Polyester membrane was
observed to have desired properties such as light
weight, flexibility, strength, fatigue resistance. It has
two sleeves, one is connected to the leading edge and
another is close to the robot body which is called
Fig.3: Assembled flexible membrane wing structure.
Four families of wings were designed and tested
which are presented in Table 1(see Appendix). The
wing is developed from rectangular wing to
trapezoidal wing through increasing the surface of
wing root. The wings of family 1 are rectangular
wings which are inspired by the Nano-hummingbird
[4]. The family 2 and 3 wings are right-angled
trapezoidal shapes to mimic natural hummingbird
wings. Firstly, the first three families’ planforms are
considered. Each of these wings planforms is
investigated depending on the geometry parameters
noted earlier. Only one parameter is varied at a time
to identify the trends of wing performance. The effect
of ‫ ܴܣ‬was investigated by varying wing length with
constant wing surface. Therefore, the result can be
comparable. These wings have lengths of 70-100
݉݉ and ‫ ܴܣ‬of 5.6-11.4. These parameters lie in the
scope of natural hummingbird shown in Table 2(see
Appendix). After that, the last family wing was
designed based on the best performance wing. The
effect of wing area was studied in last family wings
with constant‫ܴܣ‬.
3
EXPERIMENTAL SETUP
In order to investigate the wing’s aeroelastic
characteristics, an experimental setup was
constructed, illustrated in Figure 4. The experimental
setup was used to measure the motor voltage, motor
current, flapping frequency and mean lift force.
Measuring the effort of a flapping wing robot is a
challenging task because the measured force is
relatively small to order of 0.01N. A force balance is
designed by our team since there are no suitable
commercial sensors. The working principle of force
balance was already presented in [5]. The force
balance signals are processed by a dSpace 1103
digital signal processor with the voltage and current
reading of the DC motor. The flapping frequency can
be measured by the motor speed ݊ with relation
݂ ൌ ‫ܩ‬௥ ݊ ( ‫ܩ‬௥ is gear ratio). Lift force is measured
three times for each pair of wings separately, and the
average lift force is used in this study. The other
parameters (voltage, current, frequency and power)
are averaged in the same way.
Fig. 4: Diagram of experimental setup (input voltage, current,
system lift, and flapping frequency are all recorded).
4
RESULTS AND DISCUSSION
Here, we present the results of our experimental
investigation of the mean lift force of hovering
flexible flapping wings. Some important factors will
influence overall system performance such as motor
choice, wing kinematics, wing geometry and gear
ratio. In this study, the wing kinematics, the driving
motor and the gear ratio are kept constant in all the
experiment, so that the tested results are comparable.
The wing surface (1750݉݉ଶ ) is kept constant as
well for the first three families. The rectangular wing
with 70 ݉݉ wing length and 25 ݉݉ wing chord
serves as reference wing.
4.1 Varying aspect ratio
4.1.1 Rectangular wing
The rectangular wing is firstly studied in this
subsection. The wing length is increased from 70 to
100݉݉, and two wing chords (wing root chord and
wing tip chord) become narrow from 25 to 17.5݉݉.
Therefore, the ‫ ܴܣ‬is varied from 5.6 to 11.4. Figure 5
displays the effect of the wing‫ܴܣ‬. Figure 5(a) shows
that mean lift generally increases within ‫ ܴܣ‬of 5.6 to
9.3 for the same frequency, then decreases from 9.3
to 11.4. That is, the wing efficiency increases with
increasing AR, until a value of ‫ ܴܣ‬ൌ ͻǤ͵ is reached.
This behavior can be explained that as wing length ܴ
increases, the mean chord ܿҧ decreases, therefore, the
wing becomes narrow. It might be that the
‫ܥ‬௅ coefficient reaches maximum at ‫ ܴܣ‬of 9.3.
Therefore, the mean lift force increases by increasing
‫( ܴܣ‬5.6-9.3). In addition, by a quasi-steady
perspective, the formula 3 shows linear relationship
between mean lift force and ‫ ܴܣ‬. This has been
captured the experiment results. However, ‫ ܴܣ‬from
9.3 to 11.4, it is observed that the lift force
significantly reduces. It might be that the angle of
attack rises up with narrow wing after certain‫ܴܣ‬.
Therefore, the lift coefficient becomes smaller. The
same behavior is displayed in Figure 5(b) from power
perspective.
4.1.2 Trapezoidal wing with constant wing root chord
This family of wings mimics the hummingbird
wings. The wing length was being increased from 70
to 100݉݉, while decreasing the wing tip chord. The
wing root chord was kept constant (25݉݉) so that
the wing shape transformed from a rectangular wing
to a right-angled trapezoidal wing. The experiment
results are shown in Figure 6. The Figure 6(a)
presents that more lift force can be generated with
higher ‫ ܴܣ‬at the same frequency. However, from the
power viewpoint, it is observed that the lift force
increases with certain ‫( ܴܣ‬from 5.6 to 9.3) then
slightly decreases from 9.3 to 11.4 for constant power
shown in Figure 6(b). It indicates that there is not
much benefit by increasing ‫ ܴܣ‬beyond 9.3. In other
words, the wing of ‫ ܴܣ‬9.3 is a critical value in this
family.
Comparing between rectangular wing and
trapezoidal wing of family 2, it is indicated that the
‫ ܴܣ‬9.3 is a critical value in both families. This is
close from the ‫ ܴܣ‬of giant hummingbird (‫ ܴܣ‬ൎ ͻǤͳ).
Furthermore, it is observed that the aerodynamic
performance of trapezoidal wing of family 2 is better
than the rectangular wing by increasing‫ܴܣ‬. Despite
the performance of trapezoidal wing of family 2
decreases from power perspective after ‫ ܴܣ‬9.3, it’s
still better than the rectangular wing.
4.2 Constant aspect ratio
4.2.1 Trapezoidal wing with constant wing length
In this subsection, the performance of rightangled trapezoidal wing was investigated as well.
However, the wing length is kept constant (70 mm) in
this family, therefore, ‫ ܴܣ‬is constant. Wing root
chord is increased, while the wing tip chord is
decreased so that the taper ratio is smaller. In quasisteady model, the mean lift force is proportional to
the‫ܴܣ‬. Hence, the mean lift force should be constant
at the same ‫ ܴܣ‬and the same flapping frequency.
However, the experimental results show that the lift
force goes up by increasing ‫ܥ‬ோ Τ‫ ்ܥ‬then gradually
decreases as shown in Figure 7(a). We assume that
the mean angle of attack increases by increasing wing
root chord, which affects the lift coefficient.
Therefore, the lift force firstly rises up and then goes
down by increasing wing root surface. At the same
time, however, the lift force remains nearly constant
for a constant power, as is shown in Figure 7(b).
Therefore, increasing wing root surface does not
affect the wing efficiency.
4.2.2 Wing area
In this subsection, in order to investigate the
effect of wing area on wing performance, ‫ ܴܣ‬was
kept constant by preserving the overall wing shape.
Based on the previous results, the best wing of ‫ܴܣ‬
9.3 is selected. The wing surface is varied from 1059
to 2160݉݉ଶ . In quasi-steady models, the mean lift
force over flapping cycle is approximated
quadratically with wing surface. It is observed that
the lift slightly varies quadratically in the interval of
wing surface from 1059 to 1750݉݉ଶ . After that, the
lift tendency alters from 1750 to 2160݉݉ଶ , as is
shown in Figure 8(a). A possible explanation is that
by increasing the wing surface, the area close to wing
root chord grows significantly, and the angle of
attack may increase, affecting the mean lift
coefficient. Therefore, the parabolic relation changes
after wing surface 1750݉݉ଶ . Figure 8(b) displays
that the lift force increases at certain wing surfaces
then gradually decreases from 1750 to 2160 ݉݉ଶ for
a constant power. It means that there is no benefit of
increasing wing surface beyond 1750 ݉݉ଶ .
Therefore, we can conclude that the wing with
surface of 1750݉݉ଶ and ‫ ܴܣ‬9.3 is the best wing in
our study.
Since the goal of the project is to mimic the
natural hummingbird, their characteristics are
summarized in Table 2. Comparing with the natural
hummingbird performance, it is demonstrated that the
designed wing in this study has a reasonable
performance as shown in Figure 9. Eventually, wing
of 90݉݉, 9.3 ‫ ܴܣ‬and 1750 ݉݉ଶ wing surface is
chosen to serve our robot. Consequently, a 17.2 g
robot take-off test was achieved as demonstrated in
Figure10.
16
18
10Hz
14Hz
16Hz
18Hz
20Hz
22Hz
24Hz
14
12
14
12
Lift [g]
Lift [g]
10
8
10
6
8
4
6
2
4
0
5
6
0.3W
0.5W
1W
1.5W
2W
2.5W
3w
16
7
8
9
10
11
2
5
12
6
7
8
AR
9
10
11
12
AR
(a)
(b)
Fig.5: Relationship between the lift force and‫ܴܣ‬. Lift vs. AR at different flapping frequencies (a). Lift vs. AR at different electrical power (b).
All the measurements taken from family 1 (rectangular wing with constant wing surface).
18
16
14
16
14
12
10
Lift [g]
Lift [g]
12
18
10Hz
14Hz
16Hz
18Hz
20Hz
22Hz
24Hz
8
10
8
6
6
4
4
2
2
0
5
6
7
8
9
AR
10
11
12
0.3W
0.5W
1W
1.5W
2W
2.5W
3w
0
5
6
7
8
9
10
11
12
AR
(a)
(b)
Fig.6: Relationship between the lift force and‫ܴܣ‬. Lift vs. AR at different flapping frequencies (a). Lift vs. AR at different electrical power (b).
All the measurements taken from family 2 (right-angled trapezoidal wing with constant wing surface).
13
13
13Hz
17Hz
21Hz
24Hz
27Hz
12
11
11
10
9
9
8
8
Lift [g]
Lift [g]
10
0.3W
0.6W
1W
1.5W
2W
12
7
7
6
6
5
5
4
4
3
3
2
1
1.5
2
2.5
C /C
R
3
3.5
2
1
4
1.5
2
2.5
C /C
T
R
3
3.5
4
T
(a)
(b)
Fig.7: Relationship between the lift force and ratio ‫ܥ‬ோ Τ‫ ்ܥ‬. Lift vs. Ratio‫ܥ‬ோ Τ‫ ்ܥ‬at different flapping frequencies (a). Lift vs. Ratio‫ܥ‬ோ Τ‫ ்ܥ‬at
different electrical power (b). All the measurements taken from wing of family 3.
20
18
10Hz
14Hz
16Hz
18Hz
20Hz
22Hz
24Hz
18
16
14
14
12
Lift [g]
Lift [g]
12
16
10
10
0.25W
0.5W
1W
1.5W
2W
2.5W
3w
8
8
6
6
4
4
2
2
0
1000
1200
1400
1600
1800
2000
2200
2
wing surface [mm ]
0
1000
1200
1400
1600
1800
2000
2200
2
Wing surface[mm ]
(a)
(b)
Fig.8: Relationship between the lift force and wing surface. Lift vs. wing surface at different flapping frequencies (a). Lift vs. wing surface at
different electrical power (b). All the measurements taken for the same ‫ ܴܣ‬of family 4.
(a)
(b)
Fig.9: Comparison wing characteristics with natural hummingbird wing. ‫ ܴܣ‬vs. wing length (a) and single wing surface vs. wing length (b).
Wing of ASL is marked by black square.
5
CONCLUSION
The effect of flexible wing geometry on the
aerodynamics performance in hovering was studied
for four different families of wings. The experimental
results indicate that the mean lift force increases by
increasing‫ܴܣ‬, wing length, and wing surface within
certain range. The value of ‫ ܴܣ‬9.3 was found out to
be optimal for our system and is also close to
hummingbird wings. The best wing in this study is
right-angled trapezoidal wing of 90݉݉ length, 9.3
‫ ܴܣ‬and 1750 ݉݉ଶ wing surface. The planform has
straight leading edge and the chord length decreases
towards the wingtip. The constraints of size, and
wing loading, power, even weight were considered
when designing wing. Therefore, the final wing
design delivers maximal lift for a given amount of
power. Finally, the wing performance was
demonstrated by a take-off a 17.2 g flapping wing
robot. The study presented here focused mostly on
hummingbird-like MAV in the hover. Nevertheless,
the current study provides a useful dataset for the
future study of flapping wing MAV.
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Fig. 10: A hummingbird-like robot take-off [17].
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APPENDIX
Tab.1: The designed wings.
Wing
name
Length
(࢓࢓)
Root Chord
࡯ࡾ (࢓࢓)
Tip Chord
࡯ࢀ (࢓࢓)
࡭ࡾ
Wing surface
ࡿሺ࢓࢓૛ ሻ
Normal wing
Family 1
MLF 46
MLF 47
MLF 48
MLF 49
MLF 50
MLF 51
MLF 52
MLF 53
MLF 54
MLF 55
MLF 56
MLF 57
MLF 58
MLF 59
MLF 60
MLF 61
MLF 62
MLF 63
MLF 64
MLF 65
MLF 66
MLF 67
MLF 68
MLF 69
Family 2
Family 3
Family 4
70
75
80
85
90
95
100
75
80
85
90
95
100
70
70
70
70
70
75
80
85
90
95
100
25
23.3
22
20.6
19.4
18.4
17.5
25
25
25
25
25
25
30
32.5
35
40
19.4
20.2
22.2
23.6
25
26.4
27.8
25
23.3
22
20.6
19.4
18.4
17.5
21.7
18.8
16.2
14
11.8
10
20
17.5
15
10
10.8
11.6
12.4
13.1
13.8
14.7
15.4
‫ چ‬Wing name: wing material + serial number of design.
5.6
6.4
7.3
8.3
9.3
10.3
11.4
6.4
7.3
8.3
9.3
10.3
11.4
5.6
5.6
5.6
5.6
9.3
9.3
9.3
9.3
9.3
9.3
9.3
1750
1059
1215
1383
1561
1750
1950
2161
Tab. 2: Summary of wing parameters of natural hummingbird.
Mass (g)
ࡸ (mm)
ࢌ (HZ)
S(࢓࢓૛ )
࢖࢝ ሺࡺΤ࢓૛ ሻ
Blue-throated
[18]
8.4
85
23.3
1762.95
23.5
8.2
Magnificent
[18]
7.4
79
24
1485.95
24.7
8.4
Hummingbird Species
AR
Black-chinned
[18]
3
47
51.2
622.25
23.5
7.1
Rufous
[18]
3.3
42
51.7
476.75
33.6
7.4
[19]
3.2
46.1
-
599.2
36.7
7.1
[20]
4.24
45
53.25
494
42.11
8.2
4.24
48
49.1
584
35.61
7.89
Anna (male)
Broad-tailed
4.1
51
47.3
668.5
30.08
7.78
4.54
52
42.57
662.5
33.6
8.16
[21]
4.52
54.5
45.9
713.95
-
-
[22]
5.6
50
-
588.2
-
8.5
9.2
[20]
Ruby- throated(male)
[23]
Ruby- throated(female)
Amaziliafimbriata
[23]
5
50
-
543.5
-
4.7
59
-
838.8
-
8.3
4.22
55
41.32
780.5
26.52
7.75
3.46
54
36.38
736.5
23.05
7.92
3.66
55
38.71
748
24.01
8.09
5.16
57
39.25
799.5
31.67
8.13
3.6
52
39.53
680.5
25.96
7.95
3.61
56
37.17
817.5
21.66
7.76
3.93
55
38.1
860.5
22.4
7.03
7.76
4.1
57
37.94
837.5
24.02
3.58
41
-
460
38.4
7.34
3.67
41
-
485
37.3
6.96
4.01
40
-
445
44.1
7.17
4.16
43
-
455
44.9
8.13
4.36
49
-
635
33.6
7.55
4.36
48
-
640
33.3
7.18
8
4.18
49
-
600
34.2
[24]
3.1
44.5
52
-
-
-
[25]
5.1
58.5
35
850
29.4
8.05
22.7
-
15.3
-
-
-
Giant hummingbird(male)
[26]
(female)
(meal)
(female)
[27]
20.4
-
-
-
-
-
22.6
143
13.9
4508.35
24
9.1
19.6
139.7
13
4307.8
21.5
8.3
‫چ‬The empty data cells are due to data being unavailable. ࢖࢝ is wing load.
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