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Aircraft Engineering and Aerospace TechnologyISSN: 0002-2667

Online from: 1929Subject Area: Mechanical & Materials EngineeringContent: Latest Issue | Latest Issue RSS | Previous IssuesOptions: To add Favourites and Table of Contents Alerts please take a Emerald profile

Downloads: The fulltext of this document has been downloaded 616 times since 2009

DOI (Permanent URL): 10.1108/00022660910926908

Article citation: Jih-Lung Lin, Chin-Yi Wei, Chi-Yu Lin, (2009) "Aerodynamic performance of thin wings at low Reynolds numbers", Aircraft Engineering andAerospace Technology, Vol. 81 Iss: 1, pp.51 - 58

Aerodynamic performance of thin wings at low Reynolds numbers

The Authors

Jih-Lung Lin, Department of Aeronautics and Astronautics, Air Force Academy,Gangshan, Taiwan

Chin-Yi Wei, Department of Aeronautics and Astronautics, Air Force Academy, Gangshan,Taiwan

Chi-Yu Lin, Airforce Institute of Technology, Gangshan, Taiwan

Acknowledgements

The authors would like to thank the National Science Council of the Republic of China, Taiwan, forfinancially supporting this research under Contract No. NSC 92–2212–E–013–003.

Abstract

Purpose – The purpose of this paper is to explore the aerodynamic performance of wings withdifferent shapes at low Reynolds numbers.

Design/methodology/approach – The airfoils of these wings are made from aluminum plates,and the maximum chord length and wingspan are 15 cm. Wings A-D are plates with 6 percentGottingen camber but different wing platforms. The forward-half sections of wings E and F aredragonfly-like, whereas the rear-half sections of wings E and F are flat and positively cambered,respectively. The aspect ratios of these wings are close to one, and the ratios of plate thicknessto the maximum chord length are 1.3 percent. Experimental results indicate that the wings withGottingen camber have a superior lift and lift-to-drag ratio, whereas the wings with dragonfly-likeairfoils perform well in terms of drag and pitch moment.

Findings – The aerodynamic measurements of the wings demonstrate that the wing with theGottingen camber airfoil, a swept-back leading edge and a straight trailing edge is suitable for theuse in micro aerial vehicle (MAV). An MAV is fabricated with this wing and the aerodynamicperformance of the MAV is examined and compared with the bare wing data.

Originality/value – This paper develops several criteria to the design of MAV-sized wings. Forexample, the thickness ratio of airfoil must be small, usually less than 2 percent. Besides, the airfoil must be cambered adequately.Furthermore, a wing platform with a swept-back leading edge and a straight trailing edge would contribute to the successful flights ofMAVs.

Article Type: Research paperKeyword(s): Aircraft; Aerodynamics; Flow.Journal: Aircraft Engineering and Aerospace Technology: An International JournalVolume: 81Number: 1Year: 2009pp: 51-58Copyright © Emerald Group Publishing LimitedISSN: 0002-2667

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AR=aspect ratio = b 2/s

b=wing span

c=maximum chord length

C D=drag coefficient = 2D/ρU 2 S

C L=lift coefficient = 2L/ρU 2 S

C M=pitching moment coefficient = 2M/ρU 2 Sc

D=drag force

e=Oswald efficiency factor

K=induced drag factor = 1/πeAR

L=lift force

M=pitching moment

Re=Reynolds number = Uc/ν

S=wing area

t=thickness of airfoil

U=freestream velocity

Greek symbols

α=angle of attack

ν=kinematic viscosity

ρ=density of air

Introduction

The micro aerial vehicle (MAV) is a palm-sized aircraft whose maximum dimension (the largest linear distance between any two pointslocated on the vehicle) does not exceed 6 in. or 15 cm, and is remotely controlled or flies autonomously. An MAV can be easily carriedby one person and can be used within restricted space or short range. Applications of MAVs include battlefield reconnaissance, visualsurveillance, communication relay, covert inspection of military installations, hostage rescue, border patrol and air-sampling for civilpurposes, among many others.

One aerodynamic problem of an MAV is the effect of a low Reynolds number on its flight. Typical Reynolds numbers of 104∼106, aremuch lower than those of traditional airplanes. Therefore, the aerodynamic performance of MAVs differs significantly from that oftraditional airplanes (Jenkins et al., 1998; Lissaman, 1983; McMichael and Francis, 1997). For example, the boundary layer on anMAV wing surface is usually laminar and the local flowfield is easily separated, resulting in poor aerodynamic performance, such as alow lift-to-drag ratio. Furthermore, the chord length of an MAV is almost the same as the span and the aspect ratio of the wing istypically near one to provide a largest wing area under the limitation of wingspan. The restricted size of the MAV raises anotheraerodynamic problem: the low-aspect-ratio can reduce the slope of the lift curve of the wing. However, the low-aspect-ratio mayincrease the stalling angle of the wing.

According to earlier investigations on low-aspect-ratio wings at high angles of attack (Hsiao et al., 1989; Mueller and Batill, 1982;Tang, 2001; Torres and Mueller, 2004), the tip vortices were observed to affect the large part of the upper wing surface. The lowpressure caused by the vortex increases both the lift and the drag forces of the wing. The energy of the boundary-layer flow can beenhanced to resist the adverse pressure gradient on the upper wing surface and the flow can be prevented from separating until avery high angle of attack is reached. The stalling angle of attack for a typical MAV may be higher than 30°.

An MAV is lightweight and small, so in flight, it is easily disturbed by environmental airstreams. Hence, more aerodynamic tests of theMAV-sized wings at low Reynolds numbers must be performed to develop a wing with excellent aerodynamic performance andachieve stable and successful flights. Various researchers have proposed various designs of MAVs (Song et al., 2001; Watkins,2003), some of which have been shown to be operational and capable of carrying payloads. Aerodynamic data concerning variouswings at low Reynolds numbers are still limited. This work examines the aerodynamic performance of various MAV wings withreference to previous results obtained at low Reynolds numbers (Lin, 2004; Tang, 2001). Based on the present experimental results, awing with the best aerodynamic performance is adopted to fabricate an MAV, and the aerodynamic characteristics of the MAV arediscussed and compared with the bare wing data.

Experimental setup

A low-speed open-circuit wind tunnel with a cross-section of 44 × 120 cm and a length of 90 cm was employed in the presentexperiment. The blockage ratio of the wing in the test section of the wind tunnel was below 1.5 percent when the angle of attack ofthe wing was 20°. Therefore, the blockage effect of the model was assumed to be negligible in this experiment. The wind tunnel canbe operated at flow speeds from 2.0 to 21.0 m/s. The turbulent intensity of the flow in the test section, measured using a singlehot-wire anemometer, is below 0.5 percent at the operating flow speeds. Under certain conditions, the energy of the acoustic wavecan influence the measured aerodynamic performance of wings at low-operating Reynolds numbers (Grundy et al., 2001). In thepresent experiment, the sound pressure level of the wind tunnel does not exceed 60-78 dB at the operating speeds and does notaffect the flow characteristics over the wings.

A Pitot tube was utilized to measure the freestream velocity in the test section. A three-component external force balance, as shownin Figure 1, was used to detect the aerodynamic performance of the models, such as the lift, the drag and the pitching moment of thewings. The load limits of the present force balance are 1.0 kgf along the normal axis (lift) and 0.2 kgf on the horizontal axis (drag) andthe limiting pitching moment is 0.03 kgf cm.


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The analog voltage signals of the force balance and the pressure transducer are transformed by an analog-to-digital converter andanalyzed by a personal computer. The resolution of the analog-to-digital converter is 12 bit and the sampling rate applied to measurethe forces and moments of the wings is 10,000 Hz. The distribution of the repeated measurements of the force balance is close tonormal. The data presented in the following figures are the average of five repeated measurements. Although the measurementuncertainty of lift and drag increases with the angle of attack, yet it is reasonably small. For example, the 95 percent confidenceinterval of the lift and drag coefficients ranges from 0.01 to 0.03, depending on the angle of attack. The measurement uncertainty ofthe pitching moment is also reasonable. For instance, the maximum standard deviation of wing E for measuring the pitching momentwas 5.7 percent at a Reynolds number of 7.5 × 104 and an angle of attack of 20°.

Based on the results of Mueller (1999) and Jenkins et al. (1998), the airfoil with a thickness ratio (t/c) of less than 6 percent is mostsuitable to the flight of an MAV at low Reynolds numbers. Tang (2001) proposed that adequate camber is important and indicated thata dragonfly-like zigzag airfoil section offered excellent aerodynamic performance at high angles of attack. An earlier work by thepresent author Lin (2004) on NACA 00XX series and Gottingen 329 airfoils with various thickness ratios indicated that the slope of thelift coefficient decreases as the aspect ratio falls, but the stall angle of attack increases with the decrease of aspect ratio. Moreover,an airfoil with a lower thickness ratio performs better in terms of the slope of the lift coefficient, the minimum drag, the induced dragand the lift-to-drag ratio during flight at low Reynolds numbers.

According to the above results, this study designs six wings with various shapes, as shown in Figure 2 (wings A ∼ F). These wings areall fabricated from aluminum plates with a thickness of 2.0 mm. The maximum chord length and wingspan of those wings are 15 cm.The aspect ratios of those wings are close to one, and the ratios of the plate thickness to the maximum chord length are all 1.3percent. Wings A-D are plates with 6 percent Gottingen camber and the camber is maximum at 0.2 c (Figure 2(a) and 2(b)). Themajor difference among wings A to D is the shape of the wing platform. Wing A has a straight leading edge and a round trailing edge;wing B has a swept-back leading edge and a straight trailing edge; wing C has a wavy leading edge and a round trailing edge, andwing D has a swept-back leading edge and a round trailing edge. The forward-half sections of airfoils of wings E and F are zigzag-shaped to imitate the airfoil of the dragonfly, and the rear-half sections of wings E and F are flat and 4 percent positively cambered,respectively, (Figure 2(c)-2(e)).

Results and discussions

Following the previous study on NACA 00XX series and Gottingen series airfoils (Lin, 2004; Tang, 2001), the airfoil with 6 percentGottingen camber is adopted to fabricate low-aspect-ratio wings. The aerodynamic characteristics of those wings with various wingplatforms are further studied experimentally herein to design a better wing platform of MAV size at low Reynolds numbers. Theaerodynamic characteristics of two dragonfly-like zigzag airfoils (wings E and F) with rectangular platforms are also examined andcompare with those of 6 percent-Gottingen-cambered wings.

Lift of the wings

Figure 3(a) and 3(b) show the variation of the lift coefficient with the angle of attack for the six wing models at Reynolds numbers 5 × 104 and 7.5 × 104, respectively. Although the slope of the lift coefficient for wing C is better than that of other wings at Reynoldsnumber 5 × 104, the slope of the lift coefficients for wings A-D are quite similar at Reynolds number 7.5 × 104. However, the liftcoefficient of the dragonfly-like zigzag airfoils, wings E and F, is considerably worse than those of wings A ∼ D. Therefore, the liftperformance of the Gottingen wing with a 6 percent positive camber is clearly better than that of zigzag airfoils. The worst liftcoefficient is exhibited by wing E with a zigzag airfoil at the forward-half section and a flat airfoil at the rear-half section. Wings A ∼ Dand wing F are slightly positively cambered, so an appropriate positive camber promotes the lift performance of a low-aspect-ratiowing at low Reynolds numbers (Tang, 2001).

An interesting result is that no stall is observed, even at an angle of attack of 20°. This result confirms the existence of wingtipvortices, which augment lift and prevent the wings from stalling at high angles of attack (Torres and Mueller, 2004). For wings E and F,the generation of vortices not only puts off stalling, but also increases the nonlinear lift of the wing. Figure 3(b) shows the slightlynonlinear increase in the slope of lift coefficient at Re=7.5 × 104 as α>8°.

Drag of the wings

Figure 4(a) and 4(b) show the variation of the drag coefficient versus the angle of attack for six wing models at Reynolds numbers 5 × 104 and 7.5 × 104, respectively. The results indicate that the differences among the drag coefficients for the six wing models at lowangles of attack (−6 ∼ 4°) are quite insignificant. The drag coefficient of wing C grows rapidly with the angle of attack, suggesting thatthe wavy leading edge does not favor drag at high angles of attack. Although wing E exhibits the worst lift behavior, it exhibits thelowest drag coefficient of any wing in the present experiment. Besides, the drag coefficient of wing F is also lower than that of theGottingen-airfoil wings. The promotion of the turbulent boundary layer by the zigzag configuration of wings E and F is attributed to bethe main cause of the reduction in drag. This result confirms the observation of Tang (2001) that the drag of a wing may besignificantly reduced by a zigzag airfoil at high angles of attack. Wing E with a straight airfoil in the rear-half section is found to bemore effective in reducing drag than wing F with a cambered airfoil in the rear-half section. Briefly, the wings with Gottingen airfoilhave higher drag coefficients than those with zigzag airfoil sections.

Lift-to-drag ratio of the wings

The lift-to-drag ratio is an index of the lift of wings and affects the efficiency of the generation of lift. It directly affects the range ofpowered flight and the rate of descending during gliding. Figure 5(a) and 5(b) show the variation of lift-to-drag ratio with the angle ofattack for the six wing models at Reynolds numbers 5 × 104 and 7.5 × 104, respectively. The angle of attack for the maximumlift-to-drag ratio of each wing ranges from 0 ∼ 8°. Figure 5(a) and 5(b) show that wing D has superior performance on lift-to-drag ratioin comparison with the other wings. The poor drag coefficient makes the lift-to-drag ratio of wing C poorer than that of wing D.Furthermore, wing C has the lowest lift-to-drag ratio among all wings when α>8°. The relatively poor lift performance of wing E makesits lift-to-drag ratio the lowest of the six wing models at angles of attack from −6 to 6°. But the lower drag coefficients of wing E athigh angles of attack increase the lift-to-drag ratios of wing E at angles of attack from 8 to 20°. Wing F, whose rear-half section ispositively cambered, has a better lift-to-drag ratio than wing E, for angles of attack ranging from −6 to 6°. Therefore, the wing with anappropriate positive camber still prevails against the wing with straight airfoil section on the lift-to-drag ratio performance, especiallyfor the common flight angles of attack.

The C L /C D curves of the six testing wings are similar when α>8°. The wingtip vortices become stronger, preventing the wings fromstalling, so the vortex lift dominates the lift force as the angle of attack increases. Since the suction force generated by the vortices istypically normal to the wing, the lift and drag forces are the cosine and sine components of this suction force, respectively.


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Accordingly, the lift-to-drag ratio tends to be a function of: Equation 1 Figure 5(a) and 5(b) also show the relation of 1/tan α versus α.The results indicate that the experimental lift-to-drag ratio generally follows a 1/tan α curve for α>8°. Notably, the magnitude of thenegative gradient of the experimental curves is smaller than that of the 1/tan α curve, especially for Re=5 × 104, revealing that thevortex lift is less dominant for Re=5 × 104.

Pitching moment of the wings

Figure 6(a) and 6(b) show the pitching moment versus the angle of attack for the six wing models at Reynolds numbers 5 × 104 and7.5 × 104, respectively. The pitching moment is strongly related to the flight stability and the control feasibility of the aircraft, especiallyfor an MAV that may be easily influenced by flow disturbance. Accordingly, a moderate stable pitching moment of the wing is animportant consideration of a designer in fabricating a successful MAV. The pitching moment must be slightly negative and close tozero, and the variation of the pitching moment with the angle of attack should be as small as possible, to stabilize the flight of a taillessMAV. The results in Figure 6(a) and 6(b) indicate that the pitching moment of wing E satisfies the above requirement quite close. Theworst case is wing C in spite of its high-lift performance. The pitching moments of the other wings are acceptable when compared tothat of wing C. Notably, although the pitching moment of wing D is satisfactory at Reynolds number 5 × 104, it behaves worse thanwing C at Reynolds number 7.5 × 104. With respect to the required pitching moment, the wings with the zigzag airfoil outperform thosewith Gottingen airfoils.

Choice of the wing of MAV

The above wind tunnel measurements indicate that no specific wing can prevail against others in all aerodynamic aspects. Hence, acompromise must be made to select the wing for practical MAV fabrication, and the factors to be considered must include lift-to-dragratio, pitch moment and the size limit of MAVs. Finally, wing B is adopted, because the aerodynamic characteristics of wing B have anabove-average performance as compared to the six models studied. For example, wing B has the second highest lift-to-drag ratio at−2°≦α≦6°, which is a common flight scope (Figure 5(a) and 5(b)), and the variation of pitch moment is smaller than that of the otherwings (Figure 6(a) and 6(b)). In practical fabrication, the negative slope of the trailing edge of wing B is modified to near zero, tofurther reduce the pitching moment and increase the longitudinal stability of the MAV. In addition, the airfoil thickness ratio of wing B isreduced to 0.67 percent to save weight, and due to the fact that the lift-to-drag ratio increases as the thickness ratio falls forlow-aspect-ratio wings at low Reynolds numbers (Lin, 2004; Mueller, 1999).

Aerodynamic characteristics of the MAV

The aerodynamic performance of the MAV (Figure 7) is measured and compared with the corresponding data of bare wing (wing B),to elucidate the effect of the fuselage, the propeller and the vertical stabilizer that are added to the MAV. Figure 8 shows the liftcoefficients of the MAV versus the angle of attack at Reynolds numbers 7.5 × 104, 1.0 × 105 and 1.25 × 105. Figure 8 shows that therelative zero-lift angles of attack of the MAV are −7.67, −5.33 and −2.65° at Re=7.5 × 104, 1 × 105 and 1.25 × 105, respectively, so thezero-lift angle of attack of the MAV decreases as the Reynolds number increases. The slopes of the lift coefficient curve for the MAVare almost the same at various Reynolds numbers. Accordingly, the lift coefficient of the MAV increases as the Reynolds numberdecreases at a given angle of attack. The same result has been obtained by Lin (2004), in a study that presented the measurementsof a Gottingen 3 percent airfoil with AR = 1.

The lift coefficient of the MAV is lower than that of the bare wing at the same Reynolds number. The interference of the flow causedby accessories such as the fuselage, the propeller and the vertical stabilizers may reasonably be considered to reduce theaerodynamic performance of the MAV. The vertical stabilizers at the wingtip of the MAV also block the generation of tip vortices andreduce the effect of nonlinear lift. Moreover, the modification of the negative slope of the trailing edge to near zero somewhatdecreases the lift of the MAV. Notably, the slope of the lift coefficient curve of the bare wing is almost the same as that of the MAV,indicating that the accessories of the MAV substantially influence the zero-lift angle of attack but not the slope of lift.

Figure 9 shows the drag coefficient of the MAV versus the angle of attack at Reynolds numbers 7.5 × 104, 1.0 × 105 and 1.25 × 105.The drag coefficients drop as the Reynolds number increases, revealing that the flow field becomes more turbulent as the Reynoldsnumber increases. The turbulent boundary layer on the upper wing surface of the MAV reduces the form drag of the MAV. For thecambered airfoil, the drag polar relation C D=C D,min +K(C L−C L,min drag)2 yields the relationships among drag coefficient, minimumdrag coefficient and induced drag factor K, as follows: Equation 2 The above relation shows that K is dependent on Re, which is aspecific character for the wing with AR = 1. For wing with AR>1, K is only a function of aspect ratio, platform shape, and leading-edgeconfiguration, and can be expressed as: Equation 3 Based on the above relation, C D,min decreases as the Reynolds numberincreases, which finding agrees with the results of bare wing measurements of Lin (2004). The drag coefficient of the MAV exceedsthat of the bare wing at the same Reynolds number. This result is reasonable because the interference drag of the accessoriesincreases the total drag of the MAV. Figure 9 shows that the interference drag is significant at low angles of attack.

Figure 10 shows the lift-to-drag ratio of the MAV versus the angle of attack at Reynolds numbers 7.5 × 104, 1.0 × 105 and 1.25 × 105.The lift-to-drag ratios drop as the Reynolds number increases for angles of attack from −6 to 0°. However, the lift-to-drag ratiosincrease with the Reynolds number at angles of attack from 0 to 20°. The lift-to-drag ratio of the MAV is significantly lower than that ofthe bare wing. Hence, the data for the bare wing cannot be applied directly to predict the aerodynamic performance of an MAV. Theeffect of accessories on the aerodynamic performance of the MAV is significant. Notably, the C L /C D curves of the MAV do not followthe curve of 1/tan α for Re=1.0 × 105, α>8°, indicating that the generation of the tip vortices is blocked by the vertical stabilizers of theMAV. However, the C L /C D curves of MAV are relatively more similar to the curve of 1/tan α at Re=1.25 × 105, revealing that thevertical stabilizers of the MAV do not considerably inhibit the generation of the tip vortices, and the vortex lift dominates the flow fieldat high angle of attack when Re=1.25 × 105.

Figure 11 shows the coefficient of the pitching moment of the MAV versus the angle of attack at Reynolds numbers 7.5 × 104, 1.0 × 105 and 1.25 × 105. The absolute value of C M decreases as the Reynolds number increases for a specific angle of attack. The prowthus tends to decline as the Reynolds number decreases, favoring longitudinal instability. Furthermore, C M of the MAV is lower thanthat of the bare wing at the same Reynolds number, indicating that the modification of the trailing edge slope to about zero reducesthe pitching moment effectively, especially at high angles of attack.

Concluding remarks

This study focuses on the aerodynamic performance of six wings with low-aspect ratios at low Reynolds numbers. Based on theresults of wind tunnel tests, wing B was selected to be the wing used to fabricate the MAV. The trailing edge of the wing of the MAV is


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slightly modified to improve pitching-moment performance. And the airfoil thickness of the MAV wing is further reduced to decreasethe weight and increase the lift-to-drag ratio. The aerodynamic characteristics of the MAV are measured and the results comparedwith corresponding measurements of wing B. The main conclusions are summarized as follow:

The wing with Gottingen camber, a wavy leading edge and a round trailing edge had the best lift coefficient; the dragonfly-likewings performed poorly.The dragonfly-like wings performed excellently in terms of drag coefficient – especially that with a straight rear-half section.The wing with Gottingen camber, the wavy leading edge and the round trailing edge performed most poorly.No wing always exhibited a better lift-to-drag ratio than the others at angles of attack from −6 to 20°. However, the wing withGottingen camber, a swept-back leading edge and a round trailing generally outperforms the others. The dragonfly-like wingsperformed poorly on lift-to-drag ratio at angles of attack from −6 to 6°, but improved rapidly for angles of attack from 8 to 20°.The dragonfly-like wing with straight rear-half airfoil shape had better pitching moment characteristics than the others and thewing with a Gottingen airfoil, a wavy leading edge and a round trailing edge performed worst.The wing with a Gottingen airfoil, a swept-back leading edge and a straight trailing edge is selected in the MAV design. Itprovides above-average performance, as revealed by a comparison among the six models studied. The aerodynamicmeasurements of the MAV indicate that the coefficients of lift and drag and the pitching moment of the MAV differed from thoseof a bare wing, but followed similar trends. The data of bare wing cannot be applied directly in practical situations, as theaccessories significantly affect aerodynamic performance.Fabrication processes and successful flight tests of MAVs will be demonstrated in another paper to validate the present study.

Equation 1

Equation 2

Equation 3

Figure 1Schematic diagram of the open-circuit wind tunnel, three-component force balance and testing wing model


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Figure 2(a) Platforms of wings A ∼ D; (b) airfoils of wings A ∼ D with 6 percent Gottingen camber; (c) rectangular wing platform ofwings E and F; (d) zigzag airfoil of wing E with straight rear-half section; (e) zigzag airfoil of wing F with cambered rear-half section


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Figure 3(a) Lift coefficients of the wings at Re=5.0 × 104; (b) lift coefficients of the wings at Re=7.5 × 104


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Figure 4(a) Drag coefficients of the wings at Re=5.0 × 104; (b) drag coefficients of the wings at Re=7.5 × 104


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Figure 5(a) Lift-to-drag ratios of the wings at Re=5.0 × 104; (b) lift-to-drag ratios of the wings at Re=7.5 × 104


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Figure 6(a) Pitching moment coefficients of the wings at Re=5.0 × 104; (b) pitching moment coefficients of the wings at Re=7.5 × 104


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Figure 7Schematic diagram of the MAV

Figure 8Lift coefficients of the MAV


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Figure 9Drag coefficients of the MAV

Figure 10Lift-to-drag ratios of the MAV


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Figure 11Pitching moment coefficients of the MAV

References

Grundy, T.M., Keefe, G.P., Lowson, M.V. (2001), Effect of Acoustic Disturbances on Low Reynolds Aerofoil Flow, Fixed andFlapping Wing Aerodynamics for Micro Air Vehicle Applications, AIAA, Inc., Reston, VA, pp.91-113.

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Hsiao, F.B., Liu, C.F., Tang, Z. (1989), "Aerodynamic performance and flow structure studies of a low Reynolds number airfoil", AIAAJournal, Vol. 27 No.2, pp.129-37.


Jenkins, D.A., Shyy, W., Sloan, J., Klevebring, F., Nilsson, M. (1998), "Airfoil performance at low Reynolds number for micro airvehicle applications", paper presented at 13th British International RPV/UAV Conference, .


Lin, C.Y. (2004), "Investigation of aerodynamic performance on low-aspect-ratio wings at low Reynolds numbers", Institute ofAeronautics and Astronautics, National Chang-Kung University, Taiwan, MS thesis, .


Lissaman, P.B.S. (1983), "Low-Reynolds-number airfoils", Annual Review of Fluid Mechanics, Vol. 15 pp.223-39.


McMichael, J.M., Francis, M.S. (1997), "Micro air vehicles – toward a new dimension in flight", DARPA, Department of Defense,Washington, DC, report to TTO, .


Mueller, T.J. (1999), "Aerodynamic measurements at low Reynolds numbers for fixed wing micro-air vehicles", paper presented at theRTO AVT/VKI Special Course on Development and Operation of UAVs for Military and Civil Applications, VKI, Brussels, .


Mueller, T.J., Batill, S.M. (1982), "Experimental studies of separation on a two-dimensional airfoil at low Reynolds numbers", AIAAJournal, Vol. 20 No.4, pp.457-63.


Song, Q.Y., Guo, C.S., Zhou, T.H., Tang, D.W. (2001), "Design and fabrication of micro aerial vehicles", paper presented at AA-223-AA-230, CIROC/CSCA/AASRC Joint Conference, Taiwan, .


Tang, D.W. (2001), "Studies on the low Reynolds number airfoils", Institute of Weapon System Engineering, Chung Cheng Institute ofTechnology, National Defense University, Taiwan, MS thesis, .


Torres, G.E., Mueller, T.J. (2004), "Low-aspect-ratio wing aerodynamics at low Reynolds numbers", AIAA Journal, Vol. 42 No.5,pp.865-73.



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..

Watkins, S. (2003), "Development of a micro air vehicle", Aeronautical Journal, Vol. 107 No.1068, pp.117-23.


About the authors

Jih-Lung Lin

is an Assistant Professor in the Department of Aeronautics and Astronautics, Air force Academy, Taiwan, Republic of China. Jih-LungLin is the corresponding author and can be contacted at: [email protected]

Chin-Yi Wei

is an Associate Professor in the Department of Aeronautics and Astronautics, Air force Academy, Taiwan, Republic of China.

Chi-Yu Lin

is a Lecturer in the Department of Aircraft Engineering, Air force Institute of Technology, Taiwan, Republic of China.

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