characteristics of butterfly wing motions and their ... · the butterfly used for our study is a...

American Institute of Aeronautics and Astronautics

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Characteristics of Butterfly Wing Motions and Their application to Micro Flight Robot

Masaki Fuchiwaki1

Kyushu Institute of Technolog, Iizuka, Fukuoka, 8208502

Tadatsugu Imura2


and

Kazuhiro Tanaka3


Many researchers have attempted to develop MAV and micro-flight robot with various actuators and devices so far however their studies have not led to practical applications yet. One of the reasons is that flying mechanism of birds and insects has not been clarified sufficiently. In this study, we evaluate dynamic behaviors of a wing observed from the butterfly's viewpoint in its flight. The authors conduct a flight observation experiment of Cynthia cardui performing a free flight and fixed flight and an image analysis and calculate flapping angles, lead-lag angle and feathering angles of the butterfly performing flapping flight to clarify the relation between them. Furthermore, we aim at developing the micro flight robot like the butterfly using these results. The micro flapping robot flied stably for 12 minutes, which was the battery's duration.

Nomenclature c = wing chord length f = flapping frequency l = wing span length m = weight s = wing surface t = measuring time T = flapping cycle x = horizontal location y = vertical location β = flapping angle ζ = lead-lag angle θ = feathering angle θt = body angle

I. Introduction Small flap flying objects and Micro Air Vehicle (MAV) are developed actively at home and abroad in recent years

(1)(2). These technologies are developed with the aim of lifesavings in the area with the risk of secondary disasters, maintenance works for constructions such as bridges, information collection on planet searches, monitoring of security risks for the purpose of security means. A number of researchers have attempted to develop small flap flying objects and MAV with various actuators and devices (3)(4)(5). Tanaka et al (6) have developed a very small and

1 Associate Professor, Department of Mechanical Information Science and Technology, 680-4 Kawazu 2 Dr course student, Department of Mechanical Information Science and Technology, 680-4 Kawazu 3 Professor, Department of Mechanical Information Science and Technology, 680-4 Kawazu.

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-1019

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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light butterfly-type ornithopter (BTO) to investigate butterfly flight. Its weight is 0.4 g, wing span is 140 mm and flapping frequency is 10 Hz. They visualized flow field around the BTO and revealed that free body motion caused a stable attachment of leading edge vortex. Moreover, they attracted attention the deformation of flapping wing and have compared two types of the venation to clarify the function of the inner veins (7). They clarified the effect of the inner veins on flight performance. Zaeem et al (8) investigated designs of flapping mechanisms that allow high amplitude and high frequency of flapping. They reported the mechanism utilizes springs and passive flapping, a concept motivated from the study of wing motion of insects and hummingbirds and the mechanisms simulate transverse bending effect of insect wings to achieve high flapping amplitudes. Singh et al (9) addressed the aerodynamics of insect-based, biomimetic, flapping wings in hover. They measured the thrust generated the by a number of wings, mounted on flapping-pitching mechanism for a number of wing and stroke parameters. However these robots have not reached practical use at the present time. One of the reasons is that flying mechanism of birds and insects has not been clarified sufficiently.

It is well known that a butterfly combines flapping motion of its wing with gliding to fly and the figure of flying is very beautiful (10). Moreover, it does not perform linear flying motions such as a dragonfly (11)(12) however it flies like dancing by flapping with low frequency. Maxworthy (13) suggested certain minor modifications to the Weis-Fogh – Lighthill explanation of the so-called ‘clap and fling’ mechanism for the generation of large lift coefficients by insects in hovering flight. Dickinson et al. (14) reported three important motions called delayed stall, rotational circulation and wake capture. Sunada et al. (15) observed a butterfly in a taking-off motion by a flying observation experiment of Pieris melete and reported on characteristics of behaviors of a wing and forces that a butterfly generates. Senda et al. (16) analyzed motions and measured forces of Parantica sita by a flying observation experiment. In addition, they simulated its wing's motions by numerical calculation. Lee et al. (17) conducted the detailed numerical simulation to investigate aerodynamic characteristics of unsteady force generation by a two dimensional insect flapping motion under a forward flight condition.

The authors have conducted a flight observation experiment of Cynthia cardui and clarified behaviors of its wing in its flight. By spacial evaluation of the wing in a flapping flight, the authors have clarified that flapping angles of the butterfly have periodic triangular waveforms and the ratio of the time needed for flap-up and flap-down is approximately 1:1.25. Moreover, we have clarified that the wing deforms elastically not only in the wing chord direction but also in the wing span direction (18). Furthermore, by a visualization experiment with particles, we have evaluated two-dimensional vortical structures formed around a wing qualitatively and clarified that a couple of large-scale vortex is formed on the top face of the wing in the wing span direction (Fuchiwaki, 2006). However, these results are from spacial evaluations and different from wing behaviors observed from the butterfly's viewpoint.

In this study, we evaluate dynamic behaviors of a wing observed from the butterfly's viewpoint in its flight. The authors conduct a flight observation experiment of Cynthia cardui performing a free flight and fixed flight and an image analysis and calculate flapping angles, lead-lag angle and feathering angles of the butterfly performing flapping flight to clarify the relation between them. Furthermore, we aim at developing the micro flight robot like the butterfly using these results.

II. Experimental setup

1. Butterfly for our experiments The butterfly used for our study is a Cynthia cardui shown in Figure 1. It was captured in the campus of Kyushu

Institute of Technology. Its wing chord length c, wing span length l, wing area s and weight m were 25[mm], 30[mm], 245[mm2] and 160[mg] respectively. Figures 2(a), (b) and (c) show observation equipments for free flights, bound flights and towing flights, respectively. The free flight observation equipment shot a butterfly flying freely in an acrylic container(300×500 mm2) by a halogen lamp and a high-speed camera. For bound flight experiments, the legs of the butterfly were bound on a shaft set in the acrylic container to shoot flapping motions of the butterfly.

2. Coordinate conversion to viewpoint from the butterfly itself From the images obtained from a flight observation experiment, as shown in Figure 3(a), coordinates of the

leading edge ● and trailing edge ■ at l/4，l/2 and 3l/4 for the right wing span length l and those of the butterfly's center of gravity ● (CG: between chest and abdomen), head ■, and right wing tip ▲were extracted for each frame. As shown in Figure 3(b), these coordinate points around the Y-axis were converted to a coordinate of the butterfly's viewpoint by rotating them from the XYZ space coordinate system with a center of gravity as an origin by an attitude angle θt [rad.] (angle between a straight line from the center of gravity to the head and spacial horizontal

c

l

c

l

(a) Plane view (b) Side view

Fig. 1 Cynthia cardui used in our study

Butterfly

Halogen light

Acrylic box

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Halogen light

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(a) Free fkight (b) Fixed flight (c) Towing flight

Fig. 2 Experimental equipment for flight observations of the butterfly

l/4

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3l/4

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CGHeadRight wing tipLeading edgeTrailing edge

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Head

θt

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l/4

l/2

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θtθt

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(a) Measuring points on a butterfly wing (b) Coordinate conversion to viewpoint from butterfly

Fig. 3 Measuring points on a butterfly wing and coordinate conversion to viewpoint from butterfly line). The authors calculated flapping angle β [rad.] for up and down motions of the wing, lead-lag angle ζ [rad.] for back and forth motions and feathering angle θ [rad.] for twisting motions using the converted coordinate point and the wing span length l of the butterfly, as shown in Figures 4(a), (b) and (c).


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(a) Flapping angle (b) Lead-lag angle (c) Feathering angle

Fig. 4 Flapping angle, lead-lag angle and feathering angle of a butterfly

ζ [rad.]0 1 2

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.]

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.]ζ [rad.]

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.]

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.]

(a) Free fkight (b) Fixed flight (c) Towing flight Fig. 5 Traces of the wing tip of the butterfly performing a free flight and fixed flight

III. Results and discussions

1. Flapping angle, lead-lag angle and feathering angle of a butterfly wing Figures 5 (a) (b) and (c) show traces of the wing tip of the butterfly performing a free flight, fixed flight and

towing flights, respectively. The horizontal axis and a vertical axis indicate lead-lag angles ζ [rad.] and flapping angles β [rad.], respectively. Moreover, the blue and red lines in the figures indicate traces on the flap-up and flap-down motions of the wing, respectively and the black bold line indicates the average trace.

For a free flight, as shown in Figure 5(a), the butterfly drew a moderate curve in downstrokes and almost a straight line in upstrokes. In other words, the butterfly quickly changes only lead-lag angles in a flap-down motion and quickly change only flapping angles in a flap-up motion. From the past results, it is already clarified that the ratio of flap-up and flap-down is approximately 1:1.25 (Fuchiwaki, 2006) and the above result also proves it. On the other hand, for fixed and towing flights, as shown in Figure 5(b) and (c), variations of lead-lag angles are small in either case of flap-up or flap-down motions and the butterfly greatly change only flapping angles. In other words, these types of flights are similar to take off flight motions since the butterfly attempts to gain large lift forces only by changing flapping angles. Moreover, the authors have confirmed that wing behaviors in a fixed flight are similar to those in a taking-off motion. In other words, the butterfly was trying to obtain a great lift similar to that in a taking-off motion since its legs were fixed and greatly change only flapping angles, the authors presume.

The above results show a butterfly moves its wings not only in upward and downward directions spatially but also anteroposteriorly when it flaps. That is, it was clarified that lead-lag angles are one of the important parameters


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t =1.0 [s]

t =2.3 [s]t =0.0 [s]

t =4.0 [s]

t =0.4 [s]

t =7.3 [s]

t =1.0 [s]

t =2.3 [s]t =0.0 [s]

t =4.0 [s]

t =0.4 [s]

t =7.3 [s]

Fig. 6 Micro flapping robot in our study Fig. 7 Flight trajectories of the micro flapping robot

for free flights. On the other hand, for bound and towing flights, the butterfly changed flapping angles more greatly than lead-lag angles trying to escape from the towing since its legs and body were bound. In other words, the authors presume that flapping motions in bound flights are different from those in free flights and are similar to take off flight motions.

2. Micro flight robot Figure 6 shows a micro flapping robot (micro flight robot) that the created for this study. The micro flapping

robot has two wings and does not have a tailplane. Moreover, the wing chord length, span length and wing load were 240 [mm], 80 [mm] and 1.5 [N/m2], respectively. This robot has a motor and battery and the overall weight is approx. 1.9g. Rotary motions of the motor are converted into flapping motions of two wings by a crank mechanism and the flapping frequency is around 10Hz. Duration of the battery is around 15 minutes. Moreover, the flapping frequency drops to around 9Hz for voltage drop of the battery. The wing of the micro flapping robot draws triangular waves. Moreover, the ratio of the flap-up and -down motions is approx. 1:1.5. The authors reported that flapping angles of a butterfly wing drew triangular waves spacially and the time ratio was approx. 1:1.25 in the past (18). The micro flapping robot we developed in this study also performs flapping at the same level. However, the flap-up and -down motions were not mechanically controlled but passively controlled. We have confirmed that stable flying cannot be obtained in the case that the time ratio of the flap-up and -down motions is 1:1.

3. Flight performance of micro flight robot Figure 7 shows flight trajectories of the micro flapping robot we created for this study. The flying trajectories are

shot by a fixed digital video camera and the shooting rate is 30 [fps]. The moment when the flapping robot is separated from the hand is assumed t = 0.0 [sec] and flight trajectories till t = 7.3 [sec] are drawn.

The flying posture of the micro flapping robot becomes unstable and the height drops during the time from the moment when the robot separated from the hand to t = 0.4 [sec]. The flying posture is unstable till t = 1.0 [sec] however the robot raise the height. After t = 1.0 [sec], the flying posture turns nearly constant and the robot moves up drawing a large great turn trajectory in right and left.

The authors confirmed the micro flapping robot flied stably for 12 minutes, which was the battery's duration. The micro flapping robot moves upward for 7-8 minutes slewing and then moves downward slewing. This is because that the revolution speed of the motor drops by voltage drop of the battery and the flapping frequency given by the crank mechanism drops for it. Moreover, we confirmed that a slewing direction in a flight of the micro flapping robot turns counter-clockwise by reversing the rotary motion of the motor given to the crank mechanism.

4. Dynamic behaviors of micro flight robot Figure 8 shows flapping and lead-lag angles of the micro flapping robot's wing in a stable flight. The horizontal

and vertical axes indicate flapping and lead-lag angles from a viewpoint of the micro flapping robot, respectively.


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ζ [rad.]0 1 2

–2

–1

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1

2

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ad.]

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ζ [rad.]0 1 2

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ad.]

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Fig. 8 Traces of the wing tip of the micro flapping robot

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Micro flapping robot Butterfly

t / T0 1 2

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Micro flapping robot Butterfly

Fig. 9 Time variations of feathering angles of a butterfly's wing and the micro flapping robot’s wing

Flapping angles of the micro flapping robot's wing are smaller than those of a butterfly's wing. It is needed to use a larger crank mechanism to give the wing flapping angles at the same level as those of a butterfly. In order to achieve it, it is necessary to use a motor with high frequency of rotary motions. Moreover, deformations of the lead-lag angles of the micro flapping robot's wing are much smaller those of a butterfly. From these, it is clear that the micro flapping robot's wing does not need flapping and lead-lag angles that are at the same level as those of a butterfly's wing.

Figure 9 shows time variations of feathering angles of a butterfly's wing and the micro flapping robot’s wing in a stable flight. The horizontal and vertical axes indicate flapping cycle and feathering angles, respectively. Feathering angles are converted to those from the viewpoints of the butterfly and the micro flapping robot. The red and blue lines indicate feathering angles of the butterfly and the micro flapping robot, respectively. These results are from the middle points of the wings.

It is clear that feathering angles of the butterfly and the micro flapping robot tend to be the same in the scale and phase. In other words, twisting motions of the wings are at nearly the same level. We have confirmed that feathering angles of the wing of the micro flapping robot in an unstable flight do not correspond to those of the butterfly's wing at all. In other words, when the micro flapping robot's wing is too soft or too hard, it does not fly stably. It is seen that proper elastic deformations of the micro flapping robot's wing realize twisting motions of the wing and stable flights.

We have found that elastic deformations of a wing are one of the important parameters for a stable flight of the micro flapping robot. Therefore, we evaluated elastic deformations of the wing three-dimensionally. We marked 29 points on the wing surface of the micro flapping robot stably flying, as shown in Fig. 14, and shot the behaviors of the wing by a high-speed camera with the shooting speed of 1125 [fps]. We calculated displacements of the wing surface by image measurements to evaluate elastic deformations of the wing surface.


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IV. Concluding remarks The butterfly realizes its flapping motions by changing not only flapping angles but also lead-lag angles in free

and fixed flights. In particular, in a free flight, a butterfly performs flapping by greatly changing feathering angles in the wing span direction. The micro flapping robot has two wings and does not have the tail plane. Its wing chord length, span length and overall weight were 240 [mm], 80 [mm] and 1.9g, respectively. The micro flapping robot flied stably for 12 minutes, which was the battery's duration. The proper elastic deformations of the micro flapping robot's wing realize twisting motions of the wing and stable flights.

References 1Tanaka H., Matsumoto K., Shimoyama I., 2008, Design and Performance of Micromolded Plastic Butterfly Wings on Butterfly Ornithopter, IEEE / RSJ International Conference on Intelligent Robots and Systems, pp. 3095-3100 2Regan W., Breugel F., Lipson H., 2006, Towards Evolvable Hovering Flight on Physical Ornithopter, 10th International Conference on the Simulation and Synthesis 3Pornsin-sirirak T.N., Lee S. W., Nassef H., Grasmeyer J., Tai Y. C., Ho C. M., Keennon M., 2000, Mems Wing Technology for a Battery-Powered Ornithopter, 13th IEEE Annual International Conference on MEMS, pp. 709-804. 4Jones K. D., Platzer M.F. 2000, Flapping-Wing Propulsion for a Micro Air Vhicle, 38the Aerospace Sciences Meeting and Exhibit, AIAA-2000-0897. 5Jones K. D., Duggan S. J. and Platzer M. F. 2001, Flapping-Wing propulsion for a Micro Air Vhicle, 39the Aerospace Sciences Meeting and Exhibit, AIAA-2001-0126. 6Tanaka H., Hoshio K., Matsumoto K., Shimoyama I., 2005, Flight Dynamics of a Butterfly-type Ornithopter, 2005 IEEE / RSJ International Conference on Intelligent Robots and Systems, pp. 2706-2711. 7Tanaka H., Matsumoto K., Shimoyama I., 2008, Deformation and Aerodynamics Performance of a Flapping Artificial Butterfly Wing in Free Flight, Annual Meeting 200-8 Society for Experimental Biology. 8Zaeem A., Sunil K., Agrawal K., 2006, Design of Flapping Mechanisms Based on Transverse Bending Phenomena in Insects, IEEE International Conference on Robotics and Automation pp. 2323-2328 9Singh B., Chopra I., 2008, Insect-Based Hover-Capable Flapping Wings for Micro Air Vehicles: Experiments and Analysis, AIAA Journal, Vol. 46, No. 9, pp. 2115-2135. 10Inoue M., Azuma A., 2002, Flight Profile of a Butterfly，Sasakia charonda The first step on the Analysis of Locomotion of a Butterfly，10th International symposium on flow visualization, ISFV10-F0246. 11Sato M., Azuma A., 1997, The flight performance of a damselfly ceriagrion melanuram selys, Journal of Experimental Biology, Vol. 200, pp 1765-1779. 12Okamoto M., Yasuda K., Azuma A., 1996, Aerodynamic Characteristics of the Wings and Body of a Dragonfly, Journal of Experimental Biology, Vol. 199, pp.281-294. 13Maxworthy T., 1979, Experiments on the Weis-Fogh mechanism of lift generation by insects in hovering flight.Part. 1 Dynamics of the ‘fling’，J.Fluid Mech. 93-1，pp. 47-63 14Dickinson M. H., Lehmann F. O., Sane S. P., 1999, Wing Rotational and Aerodynamic Basis of Insect Flight Science, Vol. 284, pp. 1954-1960. 15Sunada S., Kawachi K., Watanabe I., Azuma A. 1993, Performance of a Butterfly in Take-off Flight, Journal of Experimental Biology, Vol. 183, pp. 249-277. 16Senda K., Sawamoto M., Shibahara T., Tanaka T., 2004, Study on Flapping-of-Wings Flight of Butterfly with Experimental measurement，Atmospheric Flight Mechanics Conference and Exhibit, AIAA 5004-5368. 17Lee J. S., Kim J. H., Kim C., 2008, Numerical Study on the Unsteady Force Generation Mechanism of Insect Flapping Motion, AIAA Jornal, Vol. 46, No. 7, pp. 1835-1848. 18Fuchiwaki M., Tanaka K., 2006, Vortex flow on a Butterfly Wing, 12th International Symposium on Flow Visualization, 12ISFV-156.

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