2005-sdm meeting-flapping wing - with beer

8/14/2019 2005-SDM Meeting-Flapping wing - with beer

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Experimental Studies on Insect-Based Flapping Wingsfor Micro Hovering Air Vehicles

Beerinder Singh Manikandan Ramasamy

Inderjit Chopra J. Gordon Leishman

Alfred Gessow Rotorcraft Center, Department of Aerospace Engineering,

University of Maryland at College Park, MD 20742

Results were obtained for several high frequency tests conducted on biomimetic,

flapping-pitching wings. The wing mass was found to have a significant influence

on the maximum frequency of the mechanism because of a high inertial power

requirement. All the wings tested showed a decrease in thrust at high frequencies.In contrast, for a wing held at 90 pitch angle, flapping in a horizontal stroke planewith passive pitching caused by aerodynamic and inertial forces, the thrust was

found to be larger. To study the effect of passive pitching, the biomimetic flapping

mechanism was modified with a passive torsion spring on the flapping shaft. Results

of some tests conducted with different wings and different torsion spring stiffnesses

are shown. A soft torsion spring led to a greater range of pitch variation and

produced more thrust at slightly lower power than with the stiff torsion spring.

Some flow visualization images have also been obtained using the passive pitching

wings.

I. Nomenclature

c chordD drag, per unit spanFi inertial force, per unit spanFn force normal to wing chord, per unit spanFx force tangential to wing chord, per unit spanL lift, per unit spanm mass

Re Reynolds number,Vtipc

r spanwise coordinateT time period of one flap cyclet time

vn velocity normal to wing chordvx velocity tangential to wing chordy coordinate along the wing chord angle of attack wing pitch angle

Graduate Research Assistant, e-mail: [email protected] Associate.Alfred Gessow Professor and Director.Minta Martin Professor.

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American Institute of Aeronautics and Astronautics


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wing flapping angle kinematic viscosity

II. Introduction

Recent interest in miniature flying vehicles has been precipitated by the nearly simultaneousemergence of their technological feasibility, along with an array of critical new military needs,especially in urban environments (Ref. 1). This technological feasibility is a result of advancesin several micro-technologies, such as Microelectromechanical Systems (MEMS), miniature CCDcameras, tiny infrared sensors and chip sized hazardous substance detectors. For these small sensors,miniature aerial vehicles can provide a highly portable platform, with low detectability and lownoise, capable of real-time data acquisition. Towards this goal, the Defense Advanced ResearchProjects Agency (DARPA) initiated a program to develop and demonstrate a new family of verysmall or micro air vehicles (MAVs) having a maximum dimension of 15 cm and a gross weightof 100 grams.

Figure 1 shows the performance of some existing MAVs against the size and weight parametersset by DARPA. In terms of endurance, fixed-wing MAVs are currently most suited. However, theirmajor shortcoming is the lack of hover capability, which allows an MAV to perch and observe while

saving valuable battery power. All the hover capable MAVs, such as Micor and Mentor, have lowendurance and high weight. Mentor and Microbat are the two flapping wing MAVs shown in Fig. 1.Mentor uses a phenomenon called clap-fling, which is used by a few species of insects to hover.However, because of the clapping of its wings it has an adverse noise signature. The Microbat is a12 gram vehicle, but it has a very low endurance and is also incapable of hovering flight.

Figure 1. Existing MAVs.

In nature, flight has evolved into two different forms insect flight and bird flight. While boththese forms are based on flapping wings, there are important differences among them. Most birds

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flap their wings in a vertical plane with small changes in the pitch of the wings during a flappingcycle. As a result, most birds cannot hover because they need a forward velocity to generatesufficient lift. Caltechs Microbat is based on this type of bird-like flapping, and so it cannothover. However, the insect world abounds with examples of hovering flight. These insects flap theirwings in a nearly horizontal plane (Fig. 2), accompanied by large changes in wing pitch angle toproduce lift even in the absence of any forward velocity. Among insects there exist animals that arecapable of taking off backwards, flying sidewards, and landing upside down. Moreover, birds like

the hummingbird, which are capable of hovering, have wing motions very similar to hover-capableinsects. Thus, insect-based biomimetic flight may present a viable solution for hover-capable MAVs.

The flight of insects has intrigued scientists for some time because, at first glance, their flightappears infeasible according to conventional linear, quasi-steady aerodynamic theory. Ellington(Ref. 2) showed that a quasi-steady, linear analysis of insect flight under-predicts the lifting capa-bility of insects. A number of unsteady and nonlinear phenomena have been used to explain therelatively high lift generated by insects. Weis-Foghs clap-fling hypothesis is one such lift generatingmechanism, but it is limited to a few species of insects and so does not explain the flight of otherspecies. Recent experiments conducted on a dynamically scaled model (Robofly) have shown thatinsects must take advantage of unsteady aerodynamic phenomena to generate thrusts greater thanthose predicted by quasi-steady analyses (Ref. 3). Figure 2 shows the typical motion of an insect

wing. This motion mainly consists of four parts: a) downstroke, in which the wing translates witha fixed collective pitch angle, b) near the end of the downstroke the wing supinates so that theblade angle of attack is positive on the upstroke, c) upstroke and, d) pronation at the end of theupstroke so that the angle of attack is positive on the downstroke. During the downstroke andupstroke (i.e. the translational phases) high lift is produced because of a leading edge vortex on thewing (Ref. 4). Supination and pronation also produce significant lift from rotational circulation,which is also known as Kramer effect (Ref. 5). The third effect, wake capture, occurs as the wingpasses through its own wake, which was created during the previous stroke.

The Robofly experiments have shownNet Force

Stroke

Plane

Downstroke

Upstroke

Wing Path

SectionWing

Figure 2. Insect wing kinematics.

that the leading edge vortex is the key toexplaining the high thrust generated by

insects at low chord Reynolds numbers (Re 150). The presence of this attached vortexon the wing has sometimes been explainedby the presence of spanwise flow throughthe vortex core that transports vorticityfrom inboard to outboard regions of thewing (Refs. 4,6). However, Birch et al.(Ref. 7) have shown that although span-wise flow does exist on the Robofly wingsat an Re of 1,400, it is absent at a lower Re of 120. Ellington and Usherwood (Ref. 6) also showedthat in rotary wing experiments conducted at Re from 10,000 to 50,000, the lift coefficients at highRe dropped significantly as compared to lower Re, indicating a weaker leading edge vortex. Thus,the effect ofRe on the leading edge vortex is not clearly understood. This is significant because ofthe fact that flapping wing MAVs operate in the Reynolds number range 103 105.

Most of the analytical studies on the aerodynamics of flapping wings have examined either rigidwings or wings with a prescribed motion (Refs. 89). Some of these studies look at ornithopticor bird-like flapping, i.e., flapping without the pronation and supination phases of insect-like flap-ping. Some are restricted to small disturbances while others are computationally intensive CFDsimulations. DeLaurier (Ref. 10) developed an aerodynamic model for ornithoptic flapping, whichhas been applied to the aeroelastic analysis of a large-scale ornithopter (Ref. 11). Walker (Ref. 12)

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recently developed an analysis that can predict the translational and rotational components of theairloads on the Robofly wings. The development and validation of a comprehensive theory forunsteady force generation by insect wings is partly hindered by a lack of experimental data at thechord Reynolds numbers of interest (103 105).

An important feature of insect wings is that they can elastically deform during flight. Also,unlike birds or bats, insect muscles stop at the wing base so any active control of the wing shapeis not likely (Refs. 1314) Passive aeroelastic design is therefore very important for insect wings.

The Robofly measurements are based on very low frequencies of motion because the fluid usedhad a high viscosity. Thus wing bending and passive aeroelastic effects are likely to be very smallin the Robofly experiment. Tarascio and Chopra (Ref. 15) presented experimental results for aflapping wing prototype that operated in air at high flapping frequencies. Recently, the presentauthors measured the thrust generated by insect-like flapping wings mounted on this flapping wingprototype (Ref. 16). Thrust measurements for a number of flapping wing stroke parameters havebeen presented in Ref. 17, along with vacuum chamber tests and some flow visualization studies.The flow visualization studies showed a leading edge vortex on the wing even at a mean chord basedReynolds number of 15,000. The main drawback in the above studies was the limited frequency(10 Hz) that could be attained on the flapping wing mechanism. Also, the flapping motion wasnot measured so the aerodynamic and inertial power was not known. In the present paper, thrust

and power measurements for some high frequency tests conducted on the flapping wing mechanismare presented. Wing mass was found to have a great impact on the flapping frequency. The testingof a passive pitch flapping mechanism, that generated greater thrust than the biomimetic flappingmechanism, is also described.

III. Biomimetic Flapping Wing Test Setup

A. Flapping Wing Mechanism

The flapping wing test apparatus is a passive-pitch, bi-stable mechanism capable of emulatinginsect wing kinematics (Fig. 3). The desired flapping and pitching motion is produced by a HackerB20 26L brushless motor, which is controlled by a Phoenix PHX-10 sensorless speed controller

in combination with a GWS microprocessor precision pulse generator. The motor shaft is rigidlyattached to a rotating disk, which in turn is attached to a pin that drives a scotch yoke. The scotchyoke houses ball ends, which are attached to shafts that are free to flap with the motion of theyoke. As the shaft is actively flapped, pitch actuators, which are rigidly attached to the shaft, makecontact with Delrin R ball ends at the end of each half-stroke. This causes the shaft to pitch and,hence, generate the wing flip at the end of the half-stroke.

The rotation of the shaft or flip at the end of each half stroke is generated by the pitchassembly, which also serves to fix the pitch angle of the shaft during the translational phases of thewing motion. The pitch assembly consists of the main shaft, which is rigidly attached to a cam,and is, in turn, held in place by a Delrin R slider and a compression spring (Fig. 4). In combinationwith the pitch stop, the entire assembly is bi-stable, in that it allows the shaft to rest in only two

positions. As the pitch actuator makes contact with the ball stops at the end of each half-stroke,the cam is forced to rock over to the other stable position, with the compression spring holding itin place until the next rotation.

B. Force Transducer

Measurement of the flapping and pitching motions, and the small airloads generated by a wingmounted on the flapping mechanism, poses a significant challenge. To measure these airloads,a load-cell was designed and built using Entran ESU-025-500 piezoresistive strain gauges. The

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Figure 3. Flapping wing mechanism (Con-cept by M.J. Tarascio (Ref. 15).)

Figure 4. Components of the pitch assem-bly.

load-cell had a narrow beam cross-section on which two strain gauges were mounted to measurethe loads in two orthogonal directions (Fig. 5). Each strain gauge was connected in a half-bridgeconfiguration with a dummy gauge, which provided temperature compensation. The load-cell was

mounted at the end of the flapping shaft, with the wing being mounted at the end of the load-cell.

Figure 5. Load Cell.

Figure 6. Pitch motion sensor.

Because strain gauges were used on the load-cell, only the moment acting at the base of thewing was measured. To convert this moment into an equivalent force, the distance from the wingbase at which this force acts must be known. The resultant aerodynamic force on the flappingwings was assumed to act at the point defined by the second moment of wing area (Ref. 2). Thisdistance, r2, was used to determine the forces acting on the wing from the measured moments.These forces were then transformed into vertical and horizontal components using the measuredpitch angle. The mean aerodynamic thrust was calculated by taking the ensemble average of the

vertical force over a number of flapping cycles.

C. Motion Transducers

The load-cell measured the forces normal and tangential to the wing chord. To obtain the verticaland horizontal components of these forces, the pitch angle of the shaft was measured. This wasdone by using a Hall effect sensor in combination with a semi-circular disk mounted on the shaft(Fig. 6). The disk had a tapered flexible magnet in a semi-circular slot, with the Hall effect sensormounted on the pitch housing. The pitching motion of the shaft caused the magnet to move in

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Figure 7. Flap motion sensor.

relation to the Hall effect sensor, producing a change in its output. A flexible magnet was usedbecause it could be easily cut to a taper and molded into the semi-circular slot on the disk. InRef. 17, ten small magnets were arranged in a semi-circle on the disk, which caused the Hall sensoroutput to change from its maximum positive value to its maximum negative value every 18 degrees.This required careful manual application of the calibration curve to convert the raw signal into thepitch angle. However, in the present case, the calibration was simpler because of the monotonic

nature of the Hall sensor output.In addition to a pitch motion sensor, another Hall sensor was used to measure the flapping

motion of the mechanism. In this case, another tapered magnet was mounted on the cross-slide ofthe mechanism, with the Hall sensor fixed to the flap bearing assembly, as shown in Fig. 7. Becausethe taper on the magnet was not very smooth, the calibration was nonlinear for both the motionsensors. The flapping motion was used to determine the flapping velocity, which, when multipliedwith the horizontal force on the wing, yielded the total aerodynamic and inertial power. When theflapping motion was differentiated to determine the flapping velocity, it was passed through a lowpass filter to eliminate the noise introduced by numerical differentiation.

D. Flow Visualization

The flow visualization test stand consisted of a steel frame bolted to the ground, on which theflapping wing mechanism was mounted approximately 4 ft. above ground level (Fig. 8). Aluminumplates extended from ground level to approximately 3 ft. above the mechanism to provide an imageplane for the single wing. At the top of the aluminum plates, an aluminum honeycomb extended 2ft. horizontally. The seed for the flow visualization was produced by vaporizing a mineral oil intoa dense fog, which passed through a series of ducts before reaching a diffuser mounted on top ofthe honeycomb. The diffuser reduced the vertical velocity of the fog, while the honeycomb helpedto eliminate any swirl or turbulence in the flow.

Flow visualization images were acquired by strobing the flow with a laser sheet generated by adual Nd:YAG laser, as shown in Fig. 9. This laser was triggered once every flapping cycle by a Halleffect switch mounted on the flapping wing mechanism. A charge coupled device (CCD) camera

was used to capture the images.

IV. High Frequency Tests

Thrust measurements for two aluminum-mylar wings mounted on the biomimetic flapping mech-anism have been presented in Ref. 17. These tests were carried out to a maximum frequency of10.5 Hz. In this section results are presented for some high frequency tests carried out on WingIII, as shown in Fig. 10. The wing planform was based on a scaled-up fruit fly wing similar to

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Figure 8. Flow visualization test setup.

Camera

Wing

Laser Sheet

Laser

FlappingAxis

Figure 9. Flow visualization schematic.

the Robofly (Ref. 3) wing, with its pitching axis at the 20% chord location. The wing was madefrom a 0.02 inch thick aluminum plate and covered with a self-stick mylar sheet. For all the resultspresented here the flapping stroke angle was 80, i.e., the angle in the stroke plane varied from40 to +40. The wing was tested at a pitch angle of 45, i.e., the pitch angle was 45 duringthe downstroke and changed to 45(135) during the upstroke. In Ref. 17, this combination ofWing III with 45 pitch was found to produce the maximum thrust. All the load measurementswere carried out with the image plane in place. Figure 11 shows the dimensions of the wing andthe root cut-out.

Figure 10. Wing III.

14.3 cm

5.0 cm

4.2 cm

Figure 11. Schematic of planform showingroot cut-out.

Figure 12 shows the measured thrust and power for Wing III up to a frequency of11.6 Hz.The dashed lines show curve fits through the data points. The thrust showed an increase upto

a frequency of 10.6 Hz, and then decreased sharply. The frequency range for which these testswere carried out was very small because Wing III weighs 1.3 grams, which requires a lot of powerinput to the mechanism. It must be noted that the power shown in Fig. 12 is computed from themeasured stroke velocity and the measured forces at the base of the wing. Therefore, this powerincludes the aerodynamic and inertial power needed to move the wing at a particular frequency,but does not give any information about the power required by the mechanism as a whole. Withoutthe wing, the mechanism could be run at almost 20 Hz. This indicated that the mass of the wingwas preventing the mechanism from moving at high frequency. Also, only a limited amount of data

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could be acquired because, when the frequency was increased further, the pitch stop (shown inFig. 4) failed because of the high forces.

9 9.5 10 10.5 11 11.5 121

2

3

4

5

6

7

Frequency (Hz)

Thrust(grams)

(a) Thrust

9 9.5 10 10.5 11 11.5 120.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Frequency (Hz)

Power(Watts)

(b) Power

Figure 12. Thrust and power measured for Wing III at high frequency.

Because of the large effect of wing mass on flapping frequency, several lightweight wings werebuilt with composite frames instead of aluminum. Figure 13 shows one such wing with a carboncomposite frame covered with a Mylar sheet. Table 1 shows the properties of these wings. Allwings with a rectangular planform had the same mean chord as the wings with fruit fly planforms.Wings IV, V and VI were covered with a lightweight film called RC Microlite, which is similar toMonokote. Wings VII and VIII used the same frames as Wings V and VI, respectively, covered witha mylar sheet which is stronger and heavier than RC Microlite. All the composite wings were madeof rectangular planform because it was easier to cut these shapes out. The first flap frequenciesshown in Table 1 were determined from the impulse response of the wings, when mounted on the

load cell.

Carbon composite frame

Mylar

skin

Figure 13. Wing VII.

Figure 14 shows the measured thrust and power for Wings IV and V. The thrust and powermeasured for Wing III are also shown on these plots. It is evident from the range of frequenciesfor each wing that a lower wing mass helped in attaining high frequencies on the mechanism. Thelower wing mass also led to lower power as compared to Wing III. However, the thrust generatedby Wings IV and V was much lower than Wing III. Also, like Wing III, the thrust attained amaximum value and then decreased with increasing frequency.

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Wing Planform Pitching axis Frame Covering Mass (g) First flap

material material freq. (Hz)

II fruit-fly 0.5c Aluminum Mylar 1.3 35.1III fruit-fly 0.2c Aluminum Mylar 1.3 32.1

IV rectangular 0.1c Carbon composite RC Microlite 0.49 24.4

V rectangular 0.1c Carbon composite RC Microlite 0.65 34.9

VI rectangular 0.1c Fiberglass RC Microlite 0.39 13.0

VII rectangular 0.1c Carbon composite Mylar 0.86 34.2

VIII rectangular 0.1c Fiberglass Mylar 0.61 -

IX fruit-fly 0.2c Fiberglass mylar 0.58 15.03

X rectangular 0.1c Carbon composite mylar 0.68 -

Table 1. Wing properties.

6 8 10 12 14 161

0

1

2

3

4

5

6

7

Frequency (Hz)

Thrust(grams)

Wing IV

Wing V

Wing III

(a) Thrust

6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Frequency (Hz)

Power(Watts)

Wing III

Wing V

Wing IV

(b) Power

Figure 14. Thrust and power measured for lighter wings at high frequency.

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Figure 15 shows the thrust and power measured for Wings VI and VII. Again, thrust and powerfor Wing III are also plotted for reference. Wing VI was the lightest wing tested but it was alsohighly flexible. This is why the thrust generated by this wing was very low. Wing VII was madeto determine the effect of the skin material on thrust. Wings IV and V used RC Microlite, whichalthough lighter than the Mylar sheet, had many wrinkles on it in addition to being very pliable. Incomparison, the Mylar sheet provided a relatively stiff, smooth membrane. Using the Mylar insteadof RC Microlite increased the thrust for Wing VII by a small amount, although the frequency range

was reduced because of the higher mass of the Mylar sheet. A significant increase in the powerwas also noted. For both wings, the thrust increased and then decreased with increasing frequency.Also, the scatter in thrust measurements increased at high frequency for Wing IV and Wing VII.

6 8 10 12 14 161

0

1

2

3

4

5

6

7

Frequency (Hz)

T

hrust(grams)

Wing VI

Wing VII

Wing III

(a) Thrust

6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Frequency (Hz)

P

ower(Watts)

Wing III

Wing VII Wing VI

(b) Power

Figure 15. Thrust and power measured for lighter wings at high frequency

It is evident from the thrust measurements that all the wings showed a decrease in thrust at

high frequency. It is not clear yet whether this reduction in thrust was because of the elasticdeformations of the wing or whether it was caused by some aerodynamic phenomena related to theReynolds number increase. Flow visualization studies can be very useful in identifying the reasonfor this phenomenon, but these are yet to be conducted.

V. Pure Flap Tests (Passive Pitch)

To determine the thrust generated by the wings in a pure flapping motion, the ball ends wereremoved so that there was no flipping of the shaft at the ends of the stroke. However, there wassome pitch flexibility in the mechanism because of the spring loaded cam. For these tests, the wingwas held on the shaft at a pitch angle of 90. When the mechanism was turned on, the wing moved

in a horizontal stroke plane and pitched passively because of the inertial and aerodynamic forcesacting on the wing.Figure 16 shows the thrust and power measured for Wings II, VII and VIII at various flapping

frequencies. Because the wing was held at 90 to the flow, like a bluff body, the aerodynamic andinertial power was much higher compared to the biomimetic flapping case. However, the surprisingresult was the thrust produced by Wing VII, which was nearly 14 grams at a frequency of 19 Hz.Wing VIII could also generate nearly 5 grams of thrust, but Wing II produced very low thrust andalso required more power because of its higher mass. Figure 17 shows the minimum and maximumvalues of the pitch angle variation for the three wings. The lower set of dashed lines show curve fits

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through the minimum pitch angle values, while the upper set show curve fits through the maximumpitch angle values. For Wing VII, which produced the maximum thrust, the pitch angle changedfrom 10 to 20 about the 90 position, at the maximum frequency. Wings II and VIII generatedlower thrust with a smaller pitch angle variation.

6 8 10 12 14 16 18 20

0

5

10

15

Frequency (Hz)

Thrust(grams)

Wing VIII

Wing II

Wing VII

(a) Thrust

6 8 10 12 14 16 18 200

0.5

1

1.5

2

2.5

3

3.5

Frequency (Hz)

Power(Watts)

Wing VIII

Wing II

Wing VII

(b) Power

Figure 16. Thrust and power measured for pure flapping motion with passive pitching of the wing.

VI. Passive Pitch Mechanism

Based on the results presented in the previous section the flapping wing mechanism was modifiedto include a torsion spring at the base of the wing. This enabled passive pitching of the wing becauseof the inertial and aerodynamic forces caused by the flapping motion. Figure 18 shows the details ofthis mechanism. The flapping shaft passed through a set of bearings in the pitch bearing assembly.

This enabled the shaft to rotate to any angular position. This rotation was prevented by a torsionspring made from a carbon fiber flexure, which was held rigidly to the shaft. The rotation of theshaft caused the carbon fiber bar to flex, thus providing the torsional stiffness. By moving theshaft-flexure connector further inboard, the torsional stiffness could be increased.

6 8 10 12 14 16 18 2070

80

90

100

110

120

130

Frequency (Hz)

Min

andMaxpitchangle

Wing VIII

Wing II

Wing VII

Wing VII

Wing VIII

Wing II

min

max

Figure 17. Minimum and maximum valuesof pitch variation.

Figure 18. Passive pitch mechanism.

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Figure 19 shows the measured thrust and power for two positions of the shaft-flexure connector,one providing a stiff spring and the other a soft spring. Wing VII was used for both tests. Figure 20shows the minimum and maximum values of the pitch angle variation for both cases. It is evidentthat the soft torsion spring allowed a larger pitch variation and produced more thrust at a slightlylower power than the stiff spring case. However, even with the spring in the stiff position, the wingcould generate approximately 9 grams of thrust with a pitch variation of just 10. This may bebecause of the flexibility of the wing itself. To achieve high frequency, and hence high thrust, the

wing had to be made light weight. However, a light wing also became very flexible. This made itvery difficult to separate the effect of the pitching of the shaft from the torsion of the wing causedby its own flexibility.

4 8 12 16 200

2

4

6

8

10

12

14

16

18

Frequency (Hz)

Thrust(grams)

Stiff Spring

Soft Spring

(a) Thrust

4 8 12 16 200

0.5

1

1.5

2

2.5

3

3.5

4

Frequency (Hz)

P

ower(Watts)

Soft Spring

Stiff Spring

(b) Power

Figure 19. Thrust and power measured for passive pitch mechanism with stiff and soft torsion spring.

4 8 12 16 2040

50

60

70

80

90

100

110

120

130

Frequency (Hz)

MinandMaxpitchangle

Soft Spring

Stiff Spring

Soft Spring

min

max

Figure 20. Minimum and maximum values of pitch variation for stiff and soft spring.

Figure 21 shows the measured thrust and power for Wings III, VII and X for various flappingfrequencies. Figure 22 shows the corresponding values of minimum and maximum pitch angle.The difference between Wing VII and Wing X was that Wing X was machined rather than beingcut with a blade like Wing VII. Thus Wing X was lighter than Wing VII, and it could attain ahigher frequency on the flapping wing mechanism. However, at the same frequency, the pitch anglevariation for Wing X was smaller than Wing VII. This was reflected in the lower thrust generated

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by Wing X as compared to Wing VII. The smaller pitch variation for Wing X may be related to itslower mass and altered center of gravity location. The location of the center of gravity behind thewing elastic axis is important to generate a greater pitching motion because of the inertial forcesacting on the wing.

4 8 12 16 20 240

2

4

6

8

10

12

14

16

18

Frequency (Hz)

Thrust(grams)

Wing VII

Wing X

Wing III

(a) Thrust

4 8 12 16 20 240

0.5

1

1.5

2

2.5

3

3.5

4

Frequency (Hz)

Power(Watts)

Wing VII

Wing XWing III

(b) Power

Figure 21. Thrust and power measured for passive pitch mechanism with various wings.

4 8 12 16 20 2440

60

80

100

120

140

Mina

ndMaxpitchangle

Frequency (Hz)

Wing VII

Wing III

Wing X

Figure 22. Minimum and maximum values of pitch variation for various wings mounted on the passivepitch mechanism.

Figure 23 shows the time variation of the thrust for Wing X, at high frequency, during oneflapping cycle along with the stroke position and shaft pitch angle. The top figure also showsthe mean thrust, and the pitch angle is plotted on the bottom figure along with arrows showingthe direction of motion of the wing. The results are plotted against non-dimensional time in theflapping cycle. When the wing motion was such that the pitch angle was less than 90 with respectto the direction of motion, the thrust was positive. This was especially evident for non-dimensionaltimes between 0.7 and 0.9, where the thrust was nearly equal to its mean value. It is also evidentthat the pitch angle variation was not in phase with the flapping motion. This implies that withproper design and tuning of the torsion spring it may be possible to further increase the thrustgenerated by the wings.

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0 0.2 0.4 0.6 0.8 1200

0

200

Thrust(g)

0 0.2 0.4 0.6 0.8 150

0

50

Stroke

(deg.)

0 0.2 0.4 0.6 0.8 160

80

100

120

Nondimensional time (t/T)

P

itch

(deg.)

Figure 23. Time variation of loads and motion for Wing X at 22.3 Hz

VII. Analysis

Experiments have shown that the lift and drag coefficients on flapping wings are higher becauseof the leading edge vortex (Ref. 3) Previous quasi-steady analyses, such as Ref. 2, did not account

for this increased performance and hence failed to accurately predict the lift generating capacity ofinsect wings. However, quasi-steady analyses can explain the lift produced by an insect wing if theeffects of a leading edge vortex, on the lift and drag coefficients, are accounted for. This has ledto a revival of quasi-steady models in recent years.5 However, such models cannot account for theforce peaks resulting from the induced inflow and wing wake interactions because these effects areunsteady and three-dimensional in nature. A blade element model developed by Walker (Ref. 12)is used to predict the airloads on the flapping wings. In this analysis, the wing is assumed to berigid, i.e., the effects of elastic bending and torsion are ignored.

The reference frames used to model the motion of the flapping wing are shown in Fig. 24. Theinertial reference frame XiYiZi has its origin at the center of rotation. The flapping angle denotesthe rotation of the flapping reference frame x1y1z1 about the Zi axis as shown. The wing reference

frame xyz is obtained by rotating the flapping reference frame by the wing pitch angle , aboutthe x1 axis.

At a particular instant of time t, the forces parallel (dFx) and perpendicular (dFn) to the wingchord, at a radial station r, are given by,

dFn(r, t) = dL(r, t)cos + dD(r, t)sin (1)

dFx(r, t) = dL(r, t)sin dD(r, t)cos (2)

where, dL(r, t) and dD(r, t) are the circulatory lift and drag which depend on the angle of attack,

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X

Y

Z

i

i

i

x

y

z

1

1

1x

y

z

Figure 24. Reference Frames

Figure 25. Blade Element

, as given by,

= tan1vn(r, t)vx(r, t)

(3)

and where vx(r, t) and vn(r, t) are the velocities parallel and perpendicular to the wing chord,respectively (Fig. 25). Based on thin airfoil theory, these velocities are determined at the 3/4 chordlocation, which was found to give good agreement with experimental results for the Robofly wings(for lift resulting from translation and rotation). It must be noted that the velocities vx(r, t) andvn(r, t) were determined based on kinematics alone, i.e., the induced inflow was not included in theanalysis. Although this is a serious shortcoming of the analysis, this model was found to give goodcorrelation with experiment in Ref. 12. The forces dFn and dFx were transformed to the flapping

reference frame through the pitch angle to determine the vertical and horizontal circulatory forces.Non-circulatory forces generated by the acceleration of the wing in a direction perpendicular to thechord were calculated and added to the circulatory forces.

A. Thrust Comparison

The measured flapping and pitching motions have been used to determine the analytical thrustbased on the above analysis. The analysis required velocities and accelerations of the pitching andflapping motions, while the measured quantities were positions that had to be differentiated. Thisintroduced some numerical noise in the calculated velocities and accelerations. To reduce this noise,the differentiated signals were passed through a low pass filter, before being passed to the analysis.Figure 26 shows the comparison between measured and analytical thrust for Wing III undergoing

biomimetic flapping with active pitching. For each measurement point, the flapping velocities andaccelerations for one flapping cycle were passed to the analysis to get a corresponding point forthe analytical thrust. The analysis shows a lower thrust than the measured value. This underprediction of thrust was also noticed in Ref. 17 for the case of Wing III flapping with a stroke of80 and a pitch angle of45.

Figure 27 shows the comparison between measured and calculated thrust for Wings VII and Xwhen mounted on the passive pitch mechanism. Again, the velocities and accelerations used in theanalysis were obtained from the measured flap and pitch positions. In this case, the analysis did

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much worse than in the case of biomimetic flapping, severely underpredicting the thrust. It is notclear yet whether this underprediction was caused by the higher flexibility of the wing, which wasnot accounted for in the analysis.

9 9.5 10 10.5 11 11.5 120

1

2

3

4

5

6

7

Frequency (Hz)

Thrust(grams)

Wing III

Experiment

Analysis

Stroke : 80o

Pitch : +45o/45

o

Figure 26. Experimental and analyticalthrust for Wing III.

4 8 12 16 20 240

2

4

6

8

10

12

14

16

18

Frequency (Hz)

Thrust(grams)

Wing VIIExperiment

Wing XExperiment

Wing VII

Analysis

Wing X

Analysis

Figure 27. Experimental and analyticalthrust for Wings VII and X on the passive

pitch mechanism.

VIII. Flow Visualization

Flow visualization tests were conducted on the passive pitch mechanism using wings similarto Wing VII. During flow visualization, the flapping mechanism had to be run continuously forseveral minutes. This caused a lot of structural fatigue at the base of the wing, especially at highfrequencies, resulting in a lot of wing failures. This was the reason why tests could not be conductedon the same wings that were used for force measurements. However, the new wings were carefullymade to be as similar to Wing VII as possible. Figure 9 shows a schematic of the laser sheetand the camera location. During testing, two types of tests were conducted based on the strokelocation at which the laser was fired. In the first case, the laser always fired when the wing wasat midstroke. In the second case, the laser strobe frequency was adjusted to be very close to theflapping frequency but slightly smaller than it. This effectively slowed down the motion, with thelaser firing at a slightly different stroke position for successive flapping cycles.

Figure 28 shows the wing at one end of the stroke. This picture shows the large amount ofdeformation in the wing. The line on the wing created by the laser sheet, also shows some camber.Figure 29 shows the flow structure behind the wing at mid-stroke. At this point, the wing has apitch angle that is greater than 90 with respect to the flap motion, and thus it acts like a bluffbody with two vortices, one on top and one below. This is a very high drag condition, as expected.

Figure 30 shows a combination of two images at two different stroke positions. As the wing

moved from the right position to the left its pitch angle reduced from an angle higher than 90 toone lower than 90. The image on the right shows completely separated flow behind the wing as inFig. 29. However, when the wing pitch angle was below 90, there was only one prominent vortexon the wing. This seems to be very similar to the leading edge vortex observed on the biomimeticflapping wing in Ref. 17 (as shown in Fig. 31), except that the wing pitch angle was higher in thepresent case. This confirms the positive thrust generated by the wings when the wing pitch anglewas less than 90, as shown in Fig. 23.

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Wing flexing

Shaft

Cambered mylar

Figure 28. Strobed image showing wingflexing and camber.

Motion

Vortices

Figure 29. Flow visualization image for apassive pitching wing at mid-stroke.

Figure 30. Flow visualization images for two locations of the wing at 11.8 Hz.

Figure 31. Flow visualization image for biomimetic flapping of Wing III Ref. 17.

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Summary and Conclusions

The thrust generated by biomimetic, flapping-pitching wings has been measured at high fre-quencies. The mass of the wing was found to have a large impact on the maximum frequencyattainable with the mechanism. Because of this, a number of light composite wings were manu-factured and tested at high frequencies. However, all these wings showed a drop in thrust at highfrequencies. By measuring the stroke position of the wings, the total aerodynamic and inertial

power was computed at the base of the wing using the measured loads. The effect of wing mass onpower required was also evident from the power curves. However, some of the lighter wings wereso flexible that they did not produce any significant thrust.

Preliminary tests for a pure flapping motion with passive pitching of the shaft because of theinertial and aerodynamic forces acting on the wing, showed significant thrust generation by one ofthe wings tested. In this case the wing was held at a 90 angle and flapped in a horizontal plane.Because of the pitch flexibility of the shaft, the inertial and aerodynamic forces caused the shaft topitch in a passive manner.

To further explore the lift generation capability of a passive pitch flapping wing mechanism, thebiomimetic flapping-pitching mechanism was modified to include a torsion spring on the flappingshaft. The torsional stiffness of the spring could be easily adjusted from a stiff condition to a

soft one. When the spring was kept in the soft position the pitch variation was larger than thepitch variation for a stiff spring. Also, the larger pitch variation for the soft spring helped generategreater thrust at a slightly smaller power consumption than the stiff spring. The time variationof thrust combined with the flapping and pitching motion of the shaft showed that the pitchingmotion was not in phase with the flapping motion, leading to a reduction in total thrust since thewing had an adverse angle of attack during part of the flapping cycle. Thus, with proper designand tailoring of the spring stiffness, the thrust generation capability may be further optimized.

Some flow visualization images have been presented for wings mounted on the passive pitchingmechanism. These images demonstrate the high-drag condition of passive-pitch flapping. However,it was also noticed that, when the wing pitch angle was favorable for thrust generation, a leadingedge vortex exists on the wing similar to the leading edge vortex noticed on a biomimetic flappingwing at similar Reynolds numbers (Ref. 17).

Acknowledgments

This research work was supported by the Army Research Office through MAV MURI Program(Grant No. ARMY-W911NF0410176) with Dr. Gary Anderson as the Technical Monitor. Theauthors also wish to acknowledge the contribution of Mr. M. J. Tarascio (now with SikorskyAircraft), who built the flapping wing mechanism.

References

1 McMichael, J. M. and Francis, M. S., Micro Air Vehicles Toward a New Dimension in Flight,

Defence Advanced Research Projects Agency TTO Document, 1996.

2 Ellington, C. P., The Aerodynamics of Hovering Insect Flight, Philosophical Transactions ofthe Royal Society of London Series B, Vol. 305, No. 1122, February 1984, pp. 1181.

3 Dickinson, M. H., Lehmann, F., and Sane, S. P., Wing Rotation and the Aerodynamic Basisof Insect Flight, Science , Vol. 284, June 1999, pp. 19541960.

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4 Liu, H., Ellington, C. P., and Kawachi, K., A Computational Fluid Dynamic Study of Hawk-moth Hovering, Journal of Experimental Biology, Vol. 201, No. 4, 1998, pp. 461477.

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Wings,Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications

, edited byT. J. Mueller, Vol. 195 of AIAA Progress in Aeronautics and Astronautics, Chap. 12, AIAA,Reston, VA, 2001, pp. 231248.

7 Birch, J. M., Dickson, W. B., and Dickinson, M. H., Force Production and Flow Structure ofthe Leading Edge Vortex on Flapping Wings at High and Low Reynolds Numbers, Journal ofExperimental Biology, Vol. 207, 2004, pp. 10631072.

8 Lan, C. E., The Unsteady Quasi-Vortex-Lattice Method with Applications to Animal Propul-sion, Journal of Fluid Mechanics , Vol. 93, No. 4, 1979, pp. 747765.

9 Wang, Z. J., Vortex Shedding and Frequency Selection in Flapping Flight, Journal of FluidMechanics, Vol. 410, 2000, pp. 323341.

10 DeLaurier, J. D., An Aerodynamic Model for Flapping Wing Flight, Aeronautical Journal,Vol. 97, April 1993, pp. 125130.

11 Larijani, R. F. and DeLaurier, J. D., A Nonlinear Aeroelastic Model for the Study of Flap-ping Wing Flight, Fixed and Flapping Wing Aerodynamics for Micro Air Vehicle Applications ,edited by T. J. Mueller, Vol. 195 of AIAA Progress in Aeronautics and Astronautics , Chap. 18,AIAA, Reston, VA, 2001, pp. 399428.

12 Walker, J. A., Rotational Lift: Something Different or More of the Same? Journal of Experi-mental Biology, Vol. 205, 2002, pp. 37833792.

13

Wootton, R. J., The Mechanical Design of Insect Wings, Scientific American, Vol. 263, No-vember 1990, pp. 114120.

14 Wootton, R. J., Herbert, R. C., Young, P. G., and Evans, K. E., Approaches to the StructuralModeling of Insect Wings, Philosophical Transactions of the Royal Society of London SeriesB, Vol. 358, August 2003, pp. 15771587.

15 Tarascio, M. J. and Chopra, I., Design and Development of a Thrust Augmented Entomopter :An Advanced Flapping Wing Micro Hovering Air Vehicle, 59 th Annual Forum of the AmericanHelicopter Society, Phoenix, AZ, May 6-8, 2003.

16 Singh, B. and Chopra, I., Wing Design and Optimization for a Flapping Wing Micro AirVehicle, 60th Annual Forum of the American Helicopter Society, Baltimore, MD, June 7-10,2004.

17 Singh, B., Ramasamy, M., Chopra, I., and Leishman, J. G., Insect based flapping wings forMicro Hovering Air Vehicles: experimental investigations, American Helicopter Society Inter-national Specialists meeting on Unmanned rotorcraft, Chandler, AZ, January 18-20, 2005.

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2005-sdm meeting-flapping wing - with beer

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