Ornithopter 2

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A Micro-Sized Ornithopter Wing Design

Emily Craparo and Ben Ingram

Massachusetts Institute of Technology, Cambridge, MA

This paper describes the design, construction, and performance of a micro-sized or-nithopter wing. A novel sectioned design that performs well and can be built quickly andinexpensively is presented. Wind-tunnel test results that demonstrate the p otential ofthe design are also presented. The design can be built in 3 person hours and achieveda propulsive efficiency of about 83%. An inertial effect known as propeller moment wasobserved, and its effect on micro-sized ornithopter wing design is described.

Introduction

ORNITHOPTERS, vehicles that flap their wingsto generate thrust, represent a promising alter-

native to conventional propeller-driven vehicles. Thepropulsive efficiency of flapping flight has been shownto meet and possibly even exceed that of more tradi-tional propulsion systems.13 Based on observationsof birds, researchers assert that ornithopters are ca-pable of superior maneuverability compared to fixed-wing vehicles, can take off and land without a runway,and can be made to hover more easily than conven-tional aircraft. Because small ornithopters can bedesigned to look like birds, they could also be morestealthy than conventional vehicles. These qualitiesmake ornithopter propulsion particularly well-suitedto the micro air vehicles (MAVs) being funded byDARPA for reconnaissance, surveillance, urban oper-ations support, targeting, and biological and chemicalagent detection.4 Unfortunately, the mechanical andaerodynamic complexities inherent in ornithopter de-

sign have limited the success of most man-made or-nithopters. Recent research, however, has solved someof the aerodynamic difficulties,3, 5 and new applica-tions, like MAVs, warrant another look at ornithopterpropulsion.

Previous Work

Humans have long been fascinated by flapping flight.More than 100 years ago, in 1874, Penaud built asuccessful rubber-powered ornithopter.6 Over thefollowing 100 years, ornithopter designers mimickedPenauds wing designs in which a sheet of thin materialwas attached to a leading edge spar to form a mem-

brane wing. However, these designs were inefficientbecause of their very thin cambered cross-sections andbecause their designers did not understand the aero-dynamics of flapping flight.

More recently, some designers have begun to incor-porate efficient airfoil cross-sections and aerodynamicmodeling into their designs. In 1985, for example,

Undergraduate Student. Department of Aeronautics and

Astronautics. AIAA Student Member.

Copyright c 2002 by Emily Craparo and Ben Ingram. Pub-lished by the American Institute of Aeronautics and Astronautics,Inc. with permission.

AeroVironment, Inc. built a flying pterosaur replicawith a 5.5 meter wingspan based on wing motions de-rived by Kroo.7 In 1991, DeLaurier built a flying,engine-powered ornithopter with a 2.5 meter wingspanusing an asymmetric airfoil designed by Selig.8

The wings designed for these ornithopters, however,are an order of magnitude larger than those that wouldbe required to propel a micro-air vehicle. The struc-

tural layout of the wings and the construction tech-niques used to build them are not suitable for micro-sized wings. Furthermore, these designs cannot beadapted easily to take advantage of recent minimum-induced loss flapping research.1, 3 These minimuminduced loss results are based on the Betz criterionfor minimum induced loss propellers9 and extensionsto the Betz criterion for the forward flight of heli-copters.10 They show that an ornithopter can achievepropulsive efficiencies of about 85%, and they give thecirculation distribution required to achieve this effi-ciency.

Objective

The goal of this project was to design and buildan efficient micro-sized ornithopter wing and to exper-imentally characterize its performance. The projectfocussed on developing a structural layout and con-struction techniques that can be used to build ef-ficient micro-sized wings. Wind tunnel tests wereconducted to measure the wings quasi-steady per-formance, namely its thrust and propulsive efficiency.The wing was scaled to accurately capture the mate-rial selection and structural layout choices involved insmall flexible wing design.

Technical Approach

Overview

This project consisted of three phases: wing design,construction, and evaluation. First, an aerodynami-cally efficient wing that could be constructed at a smallscale was designed. During the construction phase, aniterative process of fabrication and verification tookplace in order to ensure that the wing behaved accord-ing to design predictions. Verification was achievedthrough measurement of the torsional stiffness of the

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Copyright 2003 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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wing and the thrust it produced in static tests. Duringthe evaluation phase, the wing was spun on a propellerbalance to simulate flapping as shown in Figure 1.Spinning was used instead of flapping because the fo-cus of the project was on the structural design problemof creating a micro-sized wing, not the unsteady aero-dynamics and structural dynamics of flapping flight.This also eliminated the need to create a flappingmechanism.

Spinning Simulates

Flapping

Strut

Wind Tunnel

Motor

Insulated

Propeller Balance

Ornithopter Wing

Fig. 1 Ornithopter wing fitted to propeller balance

Wing DesignRequirements

In order to be competitive with traditional propul-sion systems, the wing must be efficient and easy tomanufacture. To be efficient, the wing should havean airfoil cross-section and should not stall duringflapping. Since the optimal ratio of airspeed to tipspeed (advance ratio) for flapping flight is less than1,3 the wing tip must feather almost 45 degrees toavoid stall. The wing must be very torsionally com-pliant to achieve such a significant deformation. Tobe practical, the wing should also be inexpensive and

the design should take into account the challenges ofsmall-scale manufacturing.

Structural Layout

In order to twist appropriately during flight, thewing was designed to have a combination of high bend-ing stiffness and low torsional stiffness. To achieve thiscombination, the wing was divided into sections sup-ported by two spars. Each wing is divided into 6 rigidfoam sections that can rotate relative to one anotheras shown in Figure 2. The inner spar is a solid cir-cular rod that supports bending loads, and the outer

spar is a 76m-thick C-section that provides torsionalcompliance. The two spars are only connected to oneanother between the two wings. Only one point oneach section is attached to the outer spar. The foamaround the spar is cut away so that it does not pre-vent the spar from twisting. Thin fiberglass is used toreinforce the foam near the cutout for the spar.

Sectioning the wing has many advantages. One of

the most important of these is that the wing usesaeroelastic feedback instead of sensors and actuators toachieve an efficient lift distribution. The sensors andactuators that would be necessary to achieve an effi-cient shape would add significant weight and would beextremely difficult to integrate at this scale. Instead,aerodynamic forces balanced by the outer spars tor-sional stiffness cause the sectioned wing to twist intoan efficient shape. A wing of this configuration is alsoeasy to construct at a small scale, since it consists ofa relatively small number parts whose interfaces arestraightforward. Furthermore, the sectioned wing hasno skin to wrinkle and degrade the aerodynamic per-

formance when the wing twists. Finally, the sectionsdo not contribute to the torsional stiffness of the wing,because they do not deform when the wing twists; theouter spar provides the only torsional stiffness. Sec-tioning the wing should not significantly degrade itsaerodynamic efficiency, because most of the flow overthe wing is chord-wise and does not collide with thesurfaces between sections.

Spar Design

The inner spars function is to support bending loadswhile allowing the outer spar to rotate freely over it.

To allow free rotation of the outer spar, a circularcross-section was chosen for the inner spar. A 1/16inch diameter solid steel rod was chosen, although ahollow rod could have been used instead to reduce theweight while still supporting the bending loads.

The outer spars function is to provide the correcttorsional stiffness for efficient propulsion. The outerspar must be very torsionally compliant to preventsections of the wing from stalling. Open spar cross-sections are much more torsionally compliant thanclosed cross-sections, so a C-shaped cross-section waschosen. Then, the aeroelastic models of the wing (seeIngram11) were used along with MATLABs non-linearoptimization routines to find the torsional stiffnessthat would yield the highest propulsive efficiency. Thegeometry of the C-section was chosen to achieve thisoptimal torsional stiffness while fitting loosely aroundthe inner spar.

The final dimensions of the wing are summarized inTable 1.

Airfoil Selection

Once the overall structural layout of the wing wasdetermined, the airfoil was selected. The most ap-

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Fig. 2 The sectioned wing concept

Dimension Value

Tip to tip span 20.3 cmNumber of sections per side 6Section chord 3.9 cmSection width 1.3 cmSection airfoil NACA0012/

E168 blend

Outer spar diameter 1.6 mmInner spar C-section thickness 76.2 mInner spar C-section height 2.1 mmInner spar C-section width 1.7 mm

Table 1 Final wing dimensions

propriate airfoil for a micro-sized ornithopter is onethat is suitable for low Reynolds number flight and isrelatively insensitive to errors in angle of attack. Inorder to improve efficiency, a high lift to drag ratio isfavored. Finally, the selected airfoil should be thick

enough to accommodate torsionally compliant struc-tural members. A blend between the NACA 0012 andthe E168 airfoil was well suited to this application.

Construction and Verification

Two novel construction techniques were developedto build the MAV ornithopter wing. The first tech-nique was to use a CNC sanding bit fashioned fromdrill rod, a short rubber tube, and a Dremel sandingbit as shown in Figure 3 to produce a smooth airfoilsurface. Standard tools, on the other hand, tore outchunks from the foam. A second technique was devel-

oped to trim the outer spars C-section. The C-sectionwas placed over a parallel with the same width as thethe vertical leg of the C-section. The C-section andparallel were then placed between pattern blocks andclamped in a vise as shown in Figure 4. The steel usedto construct the outer spar was so thin that it couldthen be cut with a few passes of a razor blade. While

the pattern blocks used for this MAV ornithopter winghad flat tops to cut a spar with uniform torsional stiff-ness, other patterns could easily be milled in the topof the blocks to cut a spar with a particular torsionalstiffness distribution. Because of these constructiontechniques and the wings simple design, only threeperson-hours were required to build the final wing.

After the spar was completed, its torsional stiffnesswas verified experimentally. The spar was used as thespring element in a torsional pendulum with knownmoment of inertia. Measurements of the natural fre-quency of this pendulum confirmed that the spar had

the correct torsional stiffness.Performance Characterization

This project used a thermally insulated propellerbalance to characterize the quasi-steady performance,namely the thrust and propulsive efficiency, of thewings. Spinning the wings simulated flapping, anddifferent rotation rates simulated different flapping fre-quencies. While at first spinning and flapping do notappear analogous, they are very similar motions. Bothspinning and flapping are rotations of the wing about acentral axis. Of course, there are differences between

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vice

pressure

vice

pressure

outer spar

pattern blocks

parallel

Side View Front View

cut line

Fig. 4 Spar trimming technique

Fig. 3 CNC sanding bit

spinning and flapping. Spinning removes the struc-tural dynamics and unsteady aerodynamics from theproblem. However, since the goal of this project wasto solve the structural design sub-problem of creatinga micro-sized wing, it was beneficial to remove thesecomplicating effects from the experiment.

The first performance metric, thrust, was measured

directly by the propeller balance. The other metric,propulsive efficiency, was calculated:

=Thrust Power

Motor Power Output=

Tv

(1)

where is the propulsive efficiency, T is the thrustproduced, v is the freestream velocity, is the torquegenerated by the motor, and is the angular velocityof the motor. Thus, T, v, , and were measuredto quantify the efficiency of the wing.

The instruments used to quantify the performanceof the wing are depicted schematically in Figure 5. The

wings were mounted on the propeller balance shown inthe center of the figure to measured thrust and torque.A strobe light shown at the left of the figure measuredthe angular velocity of the wings. The velocity wasmeasured by a system of pitot-static ports correctedfor temperature and humidity. The data was recordedby a computer for later post-processing.

The variables that affect the wings performance andcould be varied in this experiment were the freestreamvelocity and the motor angular velocity. The originalstrategy was to test a range of angular velocities andfreestream velocities about the optimal flight condi-tions to capture the wings efficiency and thrust peaksand the manner in which the wings performance de-graded under non-optimal conditions. However, atwist angle instability described in the high-speed test-ing section prevented testing at the optimal flightfreestream velocity of 21 m/s and angular velocity of275 rad/s. Instead, the wing was tested at 7 freestream

velocities between 0 m/s and 10.7 m/s and 13 angularvelocities between 0 rad/s and 262 rad/s.

Based on a complete quantitative error analysis forthe experiment,11 the most significant sources of errorwere the thrust and torque measurements taken by thepropeller balance. Before the balance was insulated,errors caused by ambient temperature fluctuations onthe same order as the expected measurements wereobserved. By insulating the balance and by taking fre-quent zero readings, more precise measurements couldbe be taken.

Errors in these thrust and torque measurementshad a particularly large impact on the calculatedefficiency under certain conditions, namely at highfreestream velocities, low angular velocities, and lowmotor torques. This was because a small thrust mea-surement error, dT, and a small torque measurementerror, d, cause a calculated efficiency error, d, of

d =v

w2(dT Td) (2)

Results and Analysis

This section describes the experimentally measuredperformance of the MAV ornithopter wing. First, the

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Strobe

Light

Signal

Generator

Propeller

Balance

Hygrometer

Thermometer

Computer

running

LabVIEW

PCI

Bus

Pressure

Static

Wings Thrust, Torque

Humidity

Static pressure

Data Aquisition

System

Temp.

Frequency

Ports

Sensor

PitotStatic

Baratron

Dynamic pressure

Fig. 5 Schematic of instrumentation used to quantify ornithopter wing performance

static performance results and an unexpected inertialeffect discovered during static testing are discussed.Next, typical low-speed test results are presented.Finally, the difficulties encountered when testing athigher speeds are described.

Static Performance

Figure 6 shows the thrust the wing produced dur-ing static testing at various angular velocities. Since

the freestream velocity is zero during static testing,the efficiency is not defined. The wing produced apeak thrust of 0.22 Newtons at an angular velocityof 180 rad/s. This is more than twice the steady levelflight design thrust of 0.1 Newtons, so an ornithopterusing this wing could easily accelerate for take-off froma stationary position.

However the thrust was expected to level off as theangular velocity was increased. As shown in the figure,the thrust dropped off for angular velocities greaterthan 180 rad/s. This was because the twist was notcaused solely by the aerodynamic thrust force; there

was also an inertial effect called propeller that twistedthe wing. This effect was unexpected, but when itwas modeled, the experimental results agreed well withtheory.

Propeller Moment

Propeller moment is an inertial effect that twists thewing. Fundamentally, it is caused by rotating the wingaround a non-principal axis, but it is most easily un-derstood by considering the centrifugal force actingon the wing as shown in Figure 7. Consider the mostoutboard wing section, for example. Where the spar

connects to this section, the centrifugal force acts ra-dially outward and does not cause a torque about thespar. At the trailing edge of the section, the centrifu-gal force also acts radially outward, but here it has atangential component. As shown in the side view, thistangential component causes a torque about the sparthat tends to twist the wing. The propeller moment,pm, is given by

pm = (Imaj

Imin)2 sin cos (3)

where Imin is the moment of inertia of the airfoil aboutits chord, Imaj is the moment of inertia of the airfoilabout the line perpendicular to its chord through thespar, and is the twist angle of the section.

When propeller moment was included in the wingmodels, it agreed well with the experimental results.Figure 8 shows this agreement for the 4.9 m/s case.The predicted thrust was much larger than the ac-tual thrust when propeller moment was not modeled,but the predictions agreed well with the experimental

results when propeller moment was accounted for.

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0 50 100 150 200 250 3000

0.05

0.1

0.15

0.2

0.25

Angular Velocity (rad/s)

Thrust(N)

Fig. 6 Static test results

Front View Side View

wing sections

spar

F

F

"centrifugal force"

component of

that causes twisting

Fig. 7 Centrifugal force view of propeller moment

0 50 100 150 200 2500

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5


Thrust(N)

Experimental ResultsPredictions w/o Propeller MomentPredictions w/ Propeller Moment

Fig. 8 Comparison of experiment with model including propeller moment

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0 50 100 150 200 2500

0.05

0.1

0.15

0.2

0.25


Thrust(N)

Wind tunnel data for freestream velocity = 4.4704 m/s

0 50 100 150 200 2500

0.002

0.004

0.006

0.008

0.01

0.012

0.014


Torque(Nm)

0 50 100 150 200 2500.1

0.2

0.3

0.4

0.5


Efficiency

Fig. 9 Low-speed (4.5m/s) test results

Low-Speed Performance

Figure 9 shows the data for a typical low-speed test.This data was collected at a freestream velocity of4.5 m/s. Because of propeller moment, the thrust dropsoff if the angular velocity is increased above 160 rad/s.The thrust reaches a peak value of 0.17 Newtons atan angular velocity of 160 rad/s. This is 1.7 times thesteady level flight design thrust, so an ornithopter us-ing this wing would have excess power to maneuver

or climb when flying at this speed. As predicted,the propulsive efficiency peaks over a range of angularvelocities. In this test, the propulsive efficiency wasbetween 45% and 50% for angular velocities between50 rad/s and 150 rad/s. The efficiency is far lower thanthe desired 80% because the wing is operating wellbelow its design speed of 21 m/s.

At higher freestream velocities, measurement errorsbecame more significant. The results at 8.9 m/s pre-sented in Figure 10 are one example. While the torqueresults vary smoothly with angular velocity, the thrust

results are noisy. The thrust measurement noise inturn causes significant errors in the calculated effi-ciency. As described in the error analysis, the error inthe calculated efficiency becomes quite pronounced athigh velocities, low angular velocities, and low torques,exactly the conditions under which the calculated effi-ciency of 2 appears in Figure 10. Measurement noisewas also more pronounced at higher freestream veloc-ities because more air flowed over the temperature-sensitive balance elements.

High-Speed Testing

As the freestream velocity was increased, the wingproduced less thrust but at higher efficiencies, as pre-dicted. At 8.9 m/s, for example, efficiencies between65% and 83% were measured. However, increasing thefreestream velocity accentuated the sensor noise, thusreducing the precision of the results.

An unexpected twist angle instability was also en-countered. At points of instability, the wing suddenlybecame completely twisted and began spinning very

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0 10 20 30 40 50 60 70 80 90 1000

0.02

0.04

0.06

0.08

0.1

0.12


Thrust(N)

Wind tunnel data for freestream velocity = 8.9408 m/s

0 10 20 30 40 50 60 70 80 90 1000

0.002

0.004

0.006

0.008

0.01

0.012


Torque(Nm)

0 10 20 30 40 50 60 70 80 90 1000.5

1

1.5

2

2.5


Efficiency

Fig. 10 Low-speed (8.9m/s) test results

quickly. It also generated large amounts of drag andwas subjected to extreme loading. This instabilityprevented the performance of the wing from beingcharacterized at its design point.

The instability can be understood by consideringthe motor and wing torque curves shown in Figure 11.For a given voltage, the intersections of the motor andwing torque curves are equilibria at which the motorprovides exactly the torque required to spin the wing.At low and very high angular velocities, the equilib-ria are stable; a small increase in the angular velocitycauses an imbalance in which the wing requires moretorque than the motor can provide. This imbalancecauses the wing to return to the equilibrium. Becausethe wings torque curve dips as propeller moment be-comes significant, there are also unstable equilibria.At an unstable equilibrium, a small increase in angu-lar velocity causes excess motor torque that furtheraccelerates the wing.

Only angular velocities for which stable equilibriaexist could be tested. Unfortunately, many of the

points in the original test matrix, including the ex-pected optimal flight conditions, could not be tested.This instability will not affect the performance of trueornithopters because they do not continuously spin atone angular velocity. Spinning could be used to test fu-ture ornithopter wings as long as the angular velocityof the motor is controlled instead of the motor voltage(as in a servo-motor).

Summary

In summary, the objective of this project was tobuild an efficient, inexpensive, and easily-constructedmicro-sized ornithopter wing and characterized its per-formance. The resulting design was a sectioned wingthat is stiff in bending but has an easily engineeredtorsional stiffness distribution. This design is robust,inexpensive, and takes into account the challenges ofmanufacturing small-scale wings. This project alsodeveloped construction techniques to facilitate rapid,inexpensive wing production. The resulting wingsperformance was partially characterized experimen-

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stable

equilibriumstable

equilibrium

equilibrium

unstable

Angular

Velocity

Voltage

wing torque curve

motor torque curves

Torque

untestable

angular velocities

Fig. 11 Motor and wing torque curves effect on twist angle instability

tally. Although the performance characterization wasincomplete, it showed that sectioning the wing wasnot detrimental to its performance, and thus, thatsectioned wings show promise for MAV ornithopters.

Testing also revealed that propeller moment is a sig-nificant effect for MAV ornithopters.

Future Work

Many improvements and refinements may be madeto both the design and experimental components ofthis project. In the design phase, wing performancemay be more accurately predicted by including thediscrete sectioning of the wing and three-dimensionalaerodynamic effects in the wing models. Addition-ally, higher efficiencies may be achieved if a spar withan optimal stiffness distribution is used instead of one

with uniform stiffness. The stiffness distribution canbe calculated from the optimal circulation distributionfound by Hall and Hall.3 To improve the experimen-tal portion of the project, the high-speed twist angleinstability should be eliminated. This could be ac-complished by using a speed-controlled motor, andit would allow the wings performance to be charac-terized across a more complete test matrix. Finally,to more accurately replicate the operating conditionsof an ornithopter wing, a flapping mechanism shouldbe constructed. This would allow the effects of wingdynamics to be examined, and it would address thechallenges inherent in the design and construction of

a small, light, flapping mechanism.

References1Hall, K. C. and Hall, S. R., Minimum Induced Power Re-

quirements for Flapping Flight, Journal of Fluid Mechanics,Vol. 323, 1996, pp. 285215.

2Betteridge, D. S. and Widnall, S. E., A Study of the Me-chanics of Flapping Wings, Aero, Vol. 25, 1974, pp. 129142.

3Hall, K. C., Pigott, S. A., and Hall, R. C., Power Re-quirements for Large-Amplitude Flapping Flight, Journal ofAircraft, Vol. 35, No. 3, May-June 1998, pp. 359360.

4Defense Advanced Research Projects Agency, FiscalYear 2001 Budget Estimates, Tech. rep., U. S. De-

partment of Defense, http://www.darpa.mil/body/pdf/DARPAFY2001BudgetEstimates.pdf, February 2000.

5Ahmadi, A. R. and Widnall, S., Unsteady Lifting-LineTheory as a Singular-Perturbation Problem, Journal of FluidMechanics, Vol. 162, 1986, pp. 261282.

6

DeLaurier, J. D., An Ornithopter Wing Design, Cana-dian Aeronautics and Space Journal, Vol. 40, No. 1, March1994, pp. 1018.

7Brooks, A. N., MacCready, P. B., Lissaman, P. B. S., andMorgan, W. R., Development of a wing-flapping flying replicaof the largest Pterosaur, Paper 85-1446, AIAA, 1985.

8DeLaurier, J. D., The Development of an Efficient Or-nithopter Wing, The Aeronautical Journal of The Royal Aero-nautical Society, May 1993, pp. 153161.

9Betz, A., Schraubenpropeller mit geringstem Energiever-lust, Gottinger Nachrichten, 1919, pp. 193.

10Hall, S. R., Yang, K. Y., and Hall, K. C., Helicopter rotorlift distributions for minimum induced power loss, Journal ofAircraft, Vol. 31, 1994, pp. 837845.

11Ingram, B., A Micro-Sized Ornithopter Wing Design, Mas-

sachusetts Institue of Technology, June 2001, 16.62x Final Pa-per.

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