Design and Nature - Comparing Design in Nature with Science and Engineering Eds. Brebbia, C.A., Sucharov, L.J. and Pascolo, P., WIT Press, Southampton, UK, 2002, pp. 67-76.In the past few years aeronautical engineers have recognized the possibility of building very small air vehicles, so-called Micro Air Vehicles (MAVs), in response to specific military and commercial needs. Remotely controlled or autonomous MAVs are difficult to detect because of their small size and low noise emission or, if detected, they may be mistaken for small birds or insects. Yet video cameras and other sensors have become so miniaturized in recent years that it is possible to mount them on MAVs for the purpose of transmitting information which may be difficult to obtain in other ways. In this paper the authors first explain various aspects of the physics of thrust generation due to wing flapping and then review the major computational and experimental results which they achieved during the past few years. They conclude with a description of their MAV which is currently under development

Jones, K.D.

Platzer, M.F.

Calhoun, Institutional Archive of the Naval Postgraduate School

Calhoun: The NPS Institutional ArchiveFaculty and Researcher Publications Faculty and Researcher Publications2002On the Design of Efficient Micro Air VehiclesJones, K.D.Jones, K.D. and Platzer, M.F., "On the Design of Efficient Micro Air Vehicles," Design andNature - Comparing Design in Nature with Science and Engineering Eds. Brebbia, C.A.,Sucharov, L.J. and Pascolo, P., WIT Press, Southampton, UK, 2002, pp. 67-76.http://hdl.handle.net/10945/37215On the design of efficient micro air vehiclesK. D. Jones & M. F. PlatzerDepartment of Aeronautics & Astronautics,Naval Postgraduate School, USA.AbstractIn the past few years aeronautical engineers have recognized the possibility ofbuilding very small air vehicles, so-called Micro Air Vehicles (MAVs), in responseto specific military and commercial needs. Remotely controlled or autonomousMAVs are difficult to detect because of their small size and low noise emissionor, if detected, they may be mistaken for small birds or insects. Yet video camerasand other sensors have become so miniaturized in recent years that it is possibleto mount them on MAVs for the purpose of transmitting information which maybe difficult to obtain in other ways. In this paper the authors first explain variousaspects of the physics of thrust generation due to wing flapping and then reviewthe major computational and experimental results which they achieved during thepast few years. They conclude with a description of their MAV which is currentlyunder development.1 IntroductionAlthough early flight pioneers, such as O. Lilienthal, were fascinated by the birds’ability to fly by flapping their wings, attempts to build flapping-wing flight vehicleswere soon abandoned in favor of fixed-wing or rotary-wing aircraft. On fixed-wingaircraft the thrust and lift generators are clearly separated, whereas on rotary-wingaircraft thrust and lift generation are accomplished by a single system, i.e., therotor (or rotors) only. It is noteworthy that fixed wing aircraft preceded rotary-wing aircraft by some forty years due to the difficulty of building flight vehicleswith integrated propulsion/lift systems.Birds and insects have mastered the use of integrated propulsion/lift systemsfor many millenia. It is therefore appropriate to ask whether Nature can provideinsights and guidance for the design of flight vehicles which may have new andpractical applications. In this paper, we present a brief overview of our currentunderstanding of the thrust and lift generation mechanisms used by birds andinsects. We then describe a micro air vehicle under development at the Naval Post-graduate School which uses the flapping-wing principle, and we conclude by sum-marizing the connections between the bird/insect flight sciences and the emergingfield of micro air vehicle technology.2 The Physics of Thrust Generation due to Wing Flapping2.1 Elementary TheoryKnoller [1] and Betz [2] in 1909 and 1912, respectively, were the first ones topropose an explanation of the birds’ ability to generate thrust by means of wingflapping. The basic principle is illustrated in Fig. 1, where the airfoil is in thedownstroke in the left image and in the upstroke in the right image. The sinusoidalz(t)=h sin(kt)LTNz(t)=h sin(kt)TN LDownstrokeUpstroke−z’(t)VeffV αeff−z’(t)VeffαeffV Figure 1: Thrust production during flapping flightflapping motion, 	 , results in an induced velocity,   , such thatthe effective velocity, ffflfiffifi , is at an angle of attack with respect to the chordline,flfiffifi . According to linear theory, the resultant force vector,  , is normal to thevelocity seen by the airfoil, and is therefore canted forward, yielding a net lift,!, and a net thrust, " . During the upstroke the induced velocity changes sign,resulting in a lift force that is downward, but the thrust is still in the direction offlight.2.2 Two-dimensional Flapping Foil Propeller TheoryThe Knoller-Betz elementary theory does not account for the effect of the vor-tices which are being shed from the trailing edge of an airfoil which executes thesinusoidal plunge motion. It is well known that any change in airfoil incidenceangle is accompanied by the shedding of a so-called starting vortex. Therefore,Figure 2: Wake vortices for a sinusoidally plunging airfoil ( #%$ , #&ff')(+* ).U/U 8Figure 3: Reverse Ka´rma´n vortex street, indicative of thrust ( ,$ , #-&.')(+* ).the sinusoidal plunge motion can be regarded as a series of step changes in inci-dence angle which causes the shedding of vortices. This concept is illustrated inFig. 2, where an unsteady panel-code solution is shown for an airfoil plungingsinusoidally with an amplitude of 20 percent of the airfoil chord, * , at a reduced fre-quency of 3 ( ,(0/21*ffi30465 ). The largest changes in positive or negative incidenceangle occur when the airfoil moves through the top or bottom positions, respec-tively. Therefore, during one cycle, the airfoil sheds counterclockwise vorticity asit passes through the top position (dark gray), followed by clockwise vorticity as itpasses through the bottom position (light gray). As a result, a vortex street is beinggenerated downstream of the airfoil. In Fig. 3, the results of an experimental inves-tigation at the Naval Postgraduate School [3] are shown, where the wake is behindthe flapping wing is visualized in a water tunnel by injecting colored dye into theflow. The conditions are the same as that of Fig. 2. It is seen that the counterclock-wise vortices are arranged in the upper row, the clockwise vortices in the lowerrow, thus inducing a velocity increase between the two rows (shown in Fig. 2).The sinusoidally plunging airfoil therefore acts like a conventional propeller whichcaptures a certain amount of fluid and gives it an increased time-averaged velocity.Laser-Doppler measurements, performed at the Naval Postgraduate School, indeedshowed a jet-like time-averaged velocity profile downstream of the trailing edge,confirming that the flapping airfoil can be regarded as a jet engine which propelsthe bird (or flapping-wing vehicle) forward by ejecting a certain amount of fluid inthe opposite direction.2.3 Three-dimensional Flapping Wing TheoryThis two-dimensional flow theory is still somewhat incomplete in explaining theactual flow features downstream of a finite-span flapping wing. While no detailedflow visualizations and velocity measurements are available as yet, modern com-putational techniques already make it possible to obtain a better understanding. InFig. 4, example calculations are shown for the flow downstream of a sinusoidallyplunging finite-span wing, computed using the CMARC code [4]. It is seen thatthe wing generates a series of vortex rings of alternating sign. A side view of themid-span flow would yield a vortex street similar to that shown in Fig. 2.2.4 Effect of Combined Pitch and Plunge MotionThe question naturally arises whether it is better to flap a wing in pure plunge orpitch motion or to use a combined pitch and plunge motion. Again, these questionscan be readily answered by performing modern panel code calculations. Sampleresults from a two-dimensional panel code, developed at the Naval PostgraduateSchool, are compared to Garrick’s linear theory [5] in Fig. 5, for a NACA 0012 air-foil pitching about its quarter chord with a pitch amplitude of 4 degrees, a plungeFigure 4: Perturbation velocity vectors illustrating the cyclic vortex rings.07 90 1808 2709 360:phase angle, ; φ0.00.20.40.60.81.0as indicated<  Ct×20  Cp×20  η   η= plungeCtplunge×20 Garrick> Panel?Figure 5: Predicted thrust & efficiency.amplitude of &.')(* , and a reduced frequency of 0.5 [6]. The predicted thrust andpower coefficients as well as their ratio (the propulsive efficiency, @ ) are shownas a function of the phase angle between pitch and plunge, A . The two horizontallines indicate the thrust and efficiency of a purely plunging airfoil. A combinedpitch/plunge oscillation is clearly more efficient than a pure plunge oscillation,provided the pitch oscillation leads the plunge oscillation with a phase angle ofabout 90 degrees. A pure plunge oscillation produces a higher thrust than a com-bined pitch/plunge oscillation, but at a lower efficiency. Furthermore, thrust can beincreased by either increasing the flapping amplitude or the frequency. However,it is always more efficient to increase the amplitude rather than the frequency, pro-vided the flow remains attached to the airfoil. In effect, it is more efficient to imparta small velocity surplus over a wide region than a high velocity surplus over a nar-row region. A pure pitch oscillation (not shown) will produce thrust only if theairfoil oscillates at rather high frequencies, and the efficiency will be quite low.2.5 Ground EffectPilots are well aware of the favorable ground interference effect at take-off or land-ing which increases the wing lift and reduces the so-called induced or vortex drag.A similar effect occurs for a flapping wing flying in close proximity to the ground.The effect can be simulated computationally by adding a second airfoil whichflaps in counterphase as shown in Fig. 6, where the symmetry-plane between thetwo wings represents the ground-plane. Panel code calculations predicted that thethrust would increase, and this was confirmed experimentally, as shown in Fig. 7[6]. In this case the airfoils plunge with an amplitude of &.'CBD* and a mean heightFigure 6: Wake of a wing flapping in ground effect.0E 5F 10freestream speed, U∞ (m/s)00.20.4thrust (N)G2 Hz (panel)4 Hz (panel)H6 Hz (panel)8 Hz (panel)(exp)(exp)(exp)(exp)Figure 7: Thrust for a wing flapping in ground effect.above the ground plane of &.')I+* .2.6 Dynamic Lift/Stall EffectHelicopter pilots know that the flow can become separated from the helicopterblade leading edge thereby causing dynamic stall. This effect occurs because theblade is oscillating. The basic physics is illustrated in Fig. 8 where a sequence(top-to-bottom left column, then top-to-bottom right column) of images during thedownstroke is shown from a Navier Stokes simulation of a NACA 0014 airfoil thatis sinusoidally plunged at a reduced frequency of 1, with an amplitude &.'CB0* , andFigure 8: Dynamic stall on a plunging airfoil.at a Reynolds number of J &+K . Note, the Reynolds number is a non-dimensionalparameter that is loosely defined as the ratio of inertial to viscous forces actingon a wing. Commercial jets fly at Reynolds numbers on the order of J &0L , whereasbirds fly at Reynolds numbers on the order J &+K , and insects fly at Reynolds num-bers on the order of J &DM . A strong so-called dynamic stall vortex forms near theleading edge which propagates over the upper surface and is then swept down-stream past the trailing edge. While the vortex is over the airfoil upper surface liftis generated which is significantly greater than the static lift which would be gener-ated at the corresponding static incidence angle. As soon as the vortex approachesthe trailing edge this lift is reduced quite suddenly and dramatically. While thepresence of dynamic stall is generally adverse on aircraft, there is evidence thatbirds and insects may benefit from this effect. Indeed, we have made measure-ments and computations which show that dynamic stall occurs on the micro airvehicle described in the next section.3 Flapping-Wing Micro-Air VehicleThe preceding computational and experimental studies led us to the micro air vehi-cle configuration shown in Fig. 9. The 15 cm square model uses two small wings atthe back, arranged in a biplane fashion, to provide the propulsion, and the remain-der of the vehicle is essentially a large wing, providing most of the lift and all ofthe internal volume. The two aft wings flap in counterphase, with an amplitude thatis constant in the spanwise direction. The biplane arrangement provides the per-formance benefits of flight in ground effect without having to be near the ground.Additionally, the system is aerodynamically and mechanically balanced such thatFigure 9: 15 cm flapping-wing MAV model.the body of the aircraft does not oscillate with the flapping, and therefore no workis expended on periodic accelerations of non-lifting mass.The wings are only driven in plunge, but they are elastically mounted such thatthey aeroelastically pitch, yielding tunable, but mechanically simple pitch/plungemotions. Similarly, the wing camber is elastic, and is aeroelastically coupled to themotion, yielding significant improvements in thrust.Early test models included only the aft flapping wings and a slender fuselage,and were driven using a 5 mm geared stepping motor. Flapping frequencies ashigh as 40 Hz were achieved, but elastic deformations of the structure led to per-formance losses at frequencies above about 25 Hz. Preliminary experimental thrustmeasurements indicated significant losses in thrust with increasing speed, a strongindication of adverse dynamic stall effects, as shown in Fig. 10 [7]. In recent statictests of improved models, thrusts as high as 14 grams have been achieved, and amodel was developed that could take off vertically and hover while under tether.It is hoped that improvements in the design as well as proper tuning of the elas-tic pitch and camber deformations will result in beneficial effects from dynamicstall, in the same way that most insects do. The model shown is driven by a smallDC brushed motor, like those used to vibrate pagers, powered by a single NiCad50mAh rechargeable battery and a DC-DC converter. It has a total weight of about12 grams. Current work is directed toward achieving sufficient lift and control forremotely controlled flight.0N 10 20 30 40frequency (Hz)020406080thrust (mN)static1 m/s2 m/s3 m/s4 m/sO5 m/sFigure 10: Thrust measurements for the rigid-wing MAV.4 Considerations on the Design of Micro-Air VehiclesThe design of micro air vehicles presents the aeronautical engineer with the chal-lenge of understanding and optimizing flight at very low Reynolds numbers. It istoo early to say whether the propulsion system which has no analog in nature,namely the conventional propeller, will remain the better choice at the micro airvehicle scale. Nature evolved various flapping wing systems for fully integratedthrust and lift generation. This indicates the desirability, and perhaps even neces-sity, to provide the micro air vehicle designer with the same wealth of aerodynamicdata aeronautical engineers use for the design of high Reynolds number vehicles,i.e., airplanes. Our studies indicate that computational data which are based on theassumption of purely inviscid attached flow are of only limited value for the designof micro air vehicles. This is clearly seen in Fig. 11, where high and low Reynoldsnumber results are compared to experimental results. Birds and insects appear tomake very effective use of the dynamic stall phenomenon briefly described above.Indeed, some birds and insects seem to exploit the interaction between dynamicstall vortices shed from two closely spaced wings. These are phenomena whichare as yet poorly understood, difficult to compute and unrealizable on an experi-mental model. Hence, there is still very much to be learned from Nature for thedesign of micro air vehicles.5 AcknowledgementsThe authors gratefully acknowledge the support of the Naval Research Laboratoryand of the Naval Postgraduate School.0P 0.5 1Q 1.5 2Rreduced frequency, S k00.20.40.6thrust coefficient, TC Tpanel codeUNS, V Re=106NS, V Re=104exp., Re<20kexp., 20k<Re<40kexp., Re>40kFigure 11: Reynolds number trends in performance.References[1] Knoller, R., Die Gesetze des Luftwiderstandes. Flug- und Motortechnik(Wien), 3, No. 21, pp. 1–7, 1909.[2] Betz, A., Ein Beitrag zur Erkla¨rung des Segelfluges. Zeitschrift fu¨r Flugtechnikund Motorluftschiffahrt, 3, pp. 269–272, Jan. 1912.[3] Jones, K.D., Dohring, C.M. & Platzer, M.F., Experimental and ComputationalInvestigation of the Knoller-Betz Effect. AIAA Journal, 36, No. 7, pp. 1240–1246, 1998.[4] Ashby, D.L., Dudley, M.R., Iguchi, S.K., Browne, L. & Katz, J., PotentialFlow Theory and Operation Guide for the Panel Code PMARC 12. NASA TM-102851, 1992.[5] Garrick, I.E., Propulsion of a Flapping and Oscillating Airfoil. NACA ReportNo. 567, 1936.[6] Jones, K.D., Lund, T.C. & Platzer, M.F., Experimental and ComputationalInvestigation of Flapping Wing Propulsion for Micro Air Vehicles (Chap-ter 16). Progress in Astronautics and Aeronautics, Vol. 195, Fixed and Flap-ping Wing Aerodynamics for Micro Air Vehicles, ed. T.J. Mueller, Ameri-can Institute of Aeronautics and Astronautics, Reston, Virginia, pp. 307–339,2001.[7] Jones, K.D., Duggan, S.J. & Platzer, M.F., Flapping-Wing Propulsion for aMicro Air Vehicle. AIAA Paper No. 2001-0126, 2001.

On the Design of Efficient Micro Air Vehicles

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