7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 1/9

Effect of Aspect Ratio on Gurney-Flap Performance

Libin Daniel∗ and Lance W. Traub†

 Embry Riddle Aeronautical University, Prescott, Arizona 86301

DOI: 10.2514/1.C032140

A low-speed wind-tunnel investigation has been undertaken to establish the effect of wing aspect ratio on Gurney-

flapperformance. Characterization is accomplished usinga forcebalanceand flowvisualization. The Gurney-flap lift 

incrementdueto a shiftin thezero-liftangleof attackwasobservedto scalewiththatof thelift-curveslope fordifferent 

aspect ratios. As the aspect ratio reduced, a Gurney flap of greater height was required to maximize aerodynamic

efficiency. The dependence of aerodynamic parameters (zero-lift angle of attack, minimum drag coefficient, and

lift-curve slope) on the Gurney flap’s height-to-chord ratio was also examined.

Nomenclature

a0   = two-dimensional lift-curve slopeAR = aspect ratioc   = chordCD   = finite wing drag coefficient CD min   = finite wing minimum drag coefficient 

CL   = finite wing lift coefficient CL∕CD   = finite wing lift-to-drag ratioCL max   = finite wing maximum lift coefficient CLα 

  = finite wing lift-curve slope

C3∕2L   ∕CD   = endurance parameter 

CM    = finite wing pitching moment coefficient Cp   = center of pressureh   = Gurney-flap height h∕c   = ratio of Gurney-flap height to chordL∕Dmax   = finite wing maximum lift-to-drag ratioRec   = chord Reynolds number a.c.∕c   = aerodynamic center position relative to chordα    = angle of attack α stall   = stall angle of attack 

α ZL   = zero-lift angle of attack Δα ZL   = shift in zero-lift angle of attack 

Introduction

T HE driving force behind the ever-increasing use of smallunmanned aerial vehicles (UAVs) can be attributed to their 

utility and cost effectiveness.The creation of educationaldegrees that focus on UAVs supports the ever-increasing demand in this field [1].Today, UAV usageis diverse, ranging from military search and rescueand reconnaissance to urban highway traffic monitoring [2]. The sizeof a UAV is defined by its application. With a focus on localizedsurveillance, UAVs are generally diminishing in size. However, if thewings are scaled down, the effective Reynolds numbers become verylow. To attain a higher Reynolds number, the wings need a higher 

chord length. If the wing area is constrained, this implies a lower aspect ratio (AR).

Zimmerman [3] observed a reduction in the maximum lift coefficient with a decrease in aspect ratio. However, this trendreversed at aspect ratios below 1.5. The effects of a low aspect ratio(below 1.5) include an increase in the maximum lift coefficient,“due

to a delay of the onset of the laminar separation bubble, causedprobably by the end flow” [3]. Some of the consequences of wing-tipvortices are a nonlinear lift-curve slope and very high values for thestall angle [4]. The lift generated by low-AR wings can be modeledto be composed of two different sources: linear and nonlinear. Thelinear source represents the presence of bound circulation. The

nonlinear source embodies the presence of the wing-tip vortices,which cause strong crossflow on the upper surface of the wing,leading to a reduction in pressure and generation of additional lift at moderate and high angles of attack [4]. The lift-curve slope is nolonger a constant value for moderate to high angles of attack. Anincrease in nonlinearity of the lift-curve slope and an increase in thestall anglewere observed by Torres andMueller [4] witha decrease inaspect ratio. On a slender (delta) wing, such nonlinearity has beenassociated with the loss of leading-edge (LE) suction [5].

Mission performance is directly related to the maximum range andendurance or the payload capabilities of the UAV. An increase in thelift capability can provide an increased payload capability. One of thesimplest lift augmenting aerodynamic devices is a Gurney flap. AGurney flap is a small rectangular flap (0.5 to 1.5% of the chord)attached to the lower surfaceof a wing/airfoil. It is generally placedat 

or near the trailing edge of the wing/airfoil and perpendicular to thesurface. The Gurney flap functions by increasing the downwarddeflection of the trailing-edge flow. In essence, it violates the Kutta condition at the trailing edge by creating a finite pressure differencebetween the upper and lower surfaces. The final pressure recoverywould then occur off surface, which is analogous to a violation of theKutta condition [6]. The Gurney flap increases the effective chordand camber of the airfoil, thereby increasing the circulation. Liebeck [7] suggested a flow pattern in which a virtual cusped trailing edge isformed downstream of the Gurney flap from the shear layersmerging downstream of the flap. It has been documented that Gurneyflaps, of appropriate height, provide lift augmentation without mucheffect on drag production [8]. In some cases, a drag reduction hasbeen observed. It has been theorized that if the Gurney flap stayswithin the boundary layer, no increase in drag is observed [8]. Someof the main benefits of a Gurney flap include no serious structuralmodifications, no significant drag increase, and significant lift augmentation.

It would be of value to the community to ascertain the effect of aspect ratio on Gurney-flap performance as this is a topic that hasreceived little attention. This study is a step toward such anunderstanding. Moststudies on Gurneyflaps havebeen conducted onairfoil profiles [6–8]. This study focuses on low-aspect-ratio(AR ≤  3) wings, which is consistent with the aspect ratio of smallUAVs in operation.

Equipment and Procedure

Wind-tunnel tests were conducted in Embry-Riddle’s 2 by 2 ft blower wind tunnel. This facility has a measured turbulence intensityof 0.5% and a jet uniformity better than 99% in the jet core. Force-balance measurements were undertaken using a six-component NK 

Received 2 October 2012; revision received 28 January 2013; accepted for publication 1 February 2013; published online 13 June 2013. Copyright ©2013 by Lance W. Traub and Libin Daniel. Published by the AmericanInstituteof Aeronautics andAstronautics,Inc.,with permission. Copies of thispaper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222Rosewood Drive, Danvers, MA 01923; include the code 1542-3868/13 and$10.00 in correspondence with the CCC.

*Undergraduate Student, Aerospace and Mechanical EngineeringDepartment.†AssociateProfessor, Aerospaceand Mechanical Engineering Department.

Member AIAA.

1217

JOURNAL OF AIRCRAFT

Vol. 50, No. 4, July–August 2013

7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 2/9

biotechnical sting balance. A dedicated interface coded in VisualBasic 6 was written for this balance. Balance output voltages weredigitized using a National Instruments 16 bit A/D board. Voltages

were converted to loads using an internal calibration matrix. Eachpresenteddata point is theaverage of 5000 readings. Uncertainties for the lift, drag, and pitching moment coefficients were estimated as0.01, 0.005, and 0.01, respectively. The reference area used to obtainthe aerodynamic coefficients corresponded to the wing’s projectedarea.

The model’s angle of attackwas setand measured using a feedback loop in conjunction with a Midori angle sensor. Angle-of-attack repeatability was established as better than 0.1 deg. Wall correctionswere notapplied as thetestswere comparative in nature. Wind-tunneltesting was conducted at a freestream velocity of  35 m∕s, yielding a Reynolds number of 2.5 × 105 based on the reference chord lengthof 0.127 m. During testing, the models were pitched from −6 to 28 degin 2 deg increments.

The variable-aspect-ratio wind-tunnel model was rapid prototyped

from acrylonitrile butadiene styrene using Embry-Riddle’s rapid-prototyping facilities, as shown in Fig 1. The airfoil section was a S8036 with a thickness of 16%. Gurney flaps as shown in Fig. 2 wereconstructed using thin brass shim stock and were bent and cut toshape using a metal bender and shear. The angle was kept as close to90 deg as possible to maintain commonality with other studies. The

flaps were attached to the pressure side trailing edge using tape that spanned the length of the flap, as shown in Fig.  2. The length of theside that was attached to the trailing edgewas keptconstant for all thecases at 0.25 in. Each Gurney flap spanned the respective model.Wind-tunnel tests were carried out for ARs of 1, 2, and 3 and for Gurney flap heights of 1, 2, and 4% of the chord along with a cleanconfiguration case. The Rec was kept at  2.5 × 105 for each test caseby setting a test section velocity of  35 m∕s. This resulted in a total of 12 different test cases. A repeatability test was also carried out for an

AR of 3 and Gurney-flap height of 4%. The pitching moment reference location was the quarter chord.

Results and Discussion

Repeatability plots for AR   3 anda Gurney-flap heightof 4% areshown in Fig. 3. The repeatability is seen to be good. The baselineconfiguration refers to that with no Gurney flap (h∕c   0%).

For all cases, lift augmentation is observed with the incorporationof the Gurneyflap, as shown in Fig. 4. A negative shift in the zero-lift angle of attack suggests that the Gurney flap adds camber to theairfoil profile. However, unlike a normal trailing-edge flap, nosignificant impact is observed on the stall angle. The lift-curve slopefor the Gurney-flap configurations is observed to be higher than that 

of the baseline configuration. A Gurney flap violates the Kutta condition at the trailing edge and reduces the adverse pressuregradient on the suction surface [9]. This may reduce the upper-surface boundary-layer displacement thickness leading to a reduceddecambering effect, at moderate angles of attack [10]. Additionally,the thinning of the lower-surface boundary layerwith α maymake theGurney flap more effective with incidence [9]. The lift curves for AR   1 are notably nonlinear. This can be attributed to thevortex lift produced from the side-edge sheets [5]. It is also of note that theAR   1 wing didnot stall forany configuration. This ischaracteristicof low-AR wings [3,4].

The effect of the Gurney flap on drag depends on the height of theGurney flap [7], as shown inFig. 5. The dashedline represents thedrag-due-to-lift component assuming elliptical loading, in which theOswald efficiency factor is assumed to be 1, for h∕c   0%. It can be

seen that themajorityof thedrag is this drag-due-to-lift componentas

Fig. 1 CAD drawings (in inches) and model image showing spanwiseextents of the removable panels.

Fig. 2 Gurney flap on the wing model with AR 1.

CL

0.0

0.1

0.2

0.3

0.4

     C     D

RUN 1

RUN 2

AR = 3

h/c = 4%

-0.3

-0.2

-0.1

0.0

     C    m

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

-5 0 5 10 15 20

,deg

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

     C     L

α

Fig. 3 Data repeatability.

1218   DANIEL AND TRAUB

7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 3/9

opposed to airfoil pressure drag. The 1% Gurney-flap configurationshave a lower minimum drag than the baseline configurations(yieldinga drag curve lowerthan that for 100% leading-edgesuction)for AR   2 and3. This could be attributed to theheight of theGurneyflap being less than that of the boundary-layer thickness. Also, theGurney-flap configurations are at a lower angle of attackas comparedto the baseline configuration for the same lift coefficient. This mayresult in a sectional pressure drag benefit. However, a drag penalty isobserved for a 4% Gurney-flap configuration. This may be due to anincrease in the base drag because a 4% Gurneyflap probably does not stay within the boundary layer.

The 4% Gurney flap’s drag penalty is observed to diminish with a reduction in the aspect ratio, as shown in Fig.  5. With a reduction inaspect ratio, the spanwise pressure gradients are more pronounced.Consequently, the flowfield near the trailing edge for a small-aspect-ratio wing could be highly three dimensional. Three-dimensional(3-D) disturbances have been observed to lead to a decrease in thedrag values for Gurney-flap configurations as observed by Meyer 

et al. [11]. Gurney flaps on an airfoil have been associated with theperiodic shedding of a von Karman vortex street [12]. At low aspect ratios, this three dimensionality of the flow may serve to disrupt theperiodic shedding fromthe Gurney flap, leading to a decrease in basedrag.

Figure 6  summarizes longitudinal moment-based characteristics.The effect of the Gurney flaps on the pitching moment coefficient isshown in Fig.  6a . A cambering effect due to the Gurney flap canbe observed in all the cases. The nose-down pitching moment magnitude increases with an increase in the Gurney-flap height, a characteristic of an increase in camber. With greater aspect ratios, a reduction is observed in the change of the pitching moment curveslope (dCm∕dCL) with flap attachment. A more negative pitchingmoment curve slope is indicative of the rearward movement of theaerodynamic center.

For AR   1, nonlinearity in thepitchingmoment is observed.Thiscan be attributed to the vortex lift from the wing-tip sheets, whichvaries with sin2

α  [13]. The increase in loading due to a Gurney flap

would increase thegradient in the spanwise load distribution near thewingtips and, thus, the strength of the trailing vorticity. Figure  6bshows the correlation between the pitching moment and lift 

coefficient increments for a given  α 

, a dependence theoreticallyestablished in [14] for an airfoil. The increment is with respect toh∕c   0%. As seen, the correlation with the sectional thin airfoiltheory results of Liu and Montefort [14] (denoted as   “TA”  whereΔCL    −4ΔCm) improves as AR increases, a consequence of thediminishing impact of 3-D effects on the location of the wing’saerodynamic center, as will be clarified.

Figures 6c and 6d present the calculated location of the wing’scenter of pressure and aerodynamic center (a.c.). The addition of theflap is seen to movethe center of pressure aft for all ARs compared toh∕c   0%. For a given flap dimension, the center-of-pressurelocation is weakly affected by AR for moderate to high CL. The Cp

initially moves forward rapidly at low CL andthen levelsoff at higher loadings. The aerodynamic center, Fig. 6d, shows a moderate aft shift with the addition of the Gurney flap. The height of the flap does not 

appear to have a marked impact on the a.c. location. Note that, for AR   1, the a.c. moves progressively back with increasing CL. Thisis shownwith greater clarity when thea.c. is presentedas a function of the angle of attack. Also, for AR   1 and 2, h∕c   0% shows an a.c.location in front of thequarter chord (the momentreference), whereasfor h∕c > 0, thea.c. is located aftof thequarter chord.Accounting for the a.c. deviation from the quarter chord and its movement (i.e.,multiplying this deviation by   CL   accounting for the sign of theimposed moment) yielded a correction to themoment incrementdata,shown in the right-hand-side plot of Fig. 6b. As seen, the correlationwith the two-dimensional theory of Liu and Montefort [14] isimproved.

The lift-to-drag ratio and the endurance parameter are shown inFigs. 7 and 8. It canbe observed that the 1% Gurney flap provides thehighest lift to drag ratio and endurance parameter value for aspect ratios of 2 and 3. For  AR   1, a 2% Gurney flap provides a slightlyhigher value for the lift-to-drag ratio and endurance parameter thanthe 1% Gurney flap. This is due to the small CD min penalty observed

-5 0 5 10 15 20 25 30

, deg

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

   C   L

h/c=4%

h/c=2%

h/c=1%

h/c=0%

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

   C   L

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

   C   L

AR=1

AR=2

AR=3

α

Fig. 4 Effect of Gurney-flap height and aspect ratio on lift coefficient.

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

CL

0.0

0.1

0.2

0.3

0.4

0.5

0.6

   C   D

h/c=4%

h/c=2%

h/c=1%

h/c=0%

0.0

0.1

0.2

0.3

0.4

   C   D

0.0

0.1

0.2

0.3

   C   D

AR=1

AR=2

AR=3

100% LE Suction

Fig. 5 Effect of Gurney-flap height andaspect ratio on drag coefficient.

DANIEL AND TRAUB   1219

7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 4/9

for the2% Gurneyflap coupled with lift augmentation. A 4% Gurneyflap generally provides attenuated performance. This can beattributed to the drag penalty associated with this flap. The 1%Gurneyflapleads toan increase of13, 19, and 17% and anincreaseof 4, 12, and 9% in the maximum lift-to-drag ratio and the maximum endurance parameter for aspect ratios of 1, 2, and 3, respectively,compared to the baseline configuration. The minimum dragcoefficient benefit of some flap configurations yields Gurneygeometries with  CL∕CD  and  C

3∕2L   ∕CD  ratios greater than that with

100% suction (which are based on CD min for  h∕c   0%).

Thevariation of themaximum lift-to-drag ratio versusthe Gurney-flap height-to-chord ratio is shown in Fig.  9. The greatest increase isobserved for a 1% Gurney flap. The drag penalty associated with the4% Gurneyflap reduces itsmaximum lift-to-drag ratio. It is observedto be comparable to the baseline configuration. For an aspect ratio of 3, a 1% Gurney flap has a greater maximum lift-to-drag ratio than a 2% Gurney flap. However, as the aspect ratio is reduced, the 2%Gurney flap is observed to be comparable to the 1% Gurney flap.Within the realm of the data collected in this experiment, it can besuggested that, with a reduction in aspect ratio, the height of the

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4CL

-0.3

-0.2

-0.1

0.0

     C    m

h/c=4%

h/c=2%

h/c=1%

h/c=0%

-0.3

-0.2

-0.1

0.0

     C    m

-0.3

-0.2

-0.1

0.0

     C    m

AR=1

AR=2

AR=3

-0.12 -0.09 -0.06 -0.03 0.00

CMChange

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

     C     L

     C     h    a    n    g    e

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.70.8

0.9

     C     L

     C     h    a    n    g    e

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

     C     L

     C     h    a    n    g    e

AR=1

AR=2

AR=3

h/c=4%

h/c=2%

h/c=1%

TA Theory

-0.12 -0.09 -0.06 -0.03 0.00

CMChange

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

     C     L     C     h    a    n    g    e

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.70.8

0.9

     C     L     C     h    a    n    g    e

AR=1

AR=2

Data corrected fora.c. movement

a) b)

0.0 0.2 0.4 0.6 0.8 1.0CL

0.0

0.5

1.0

1.5

2.0

     C    p

     /    c

h/c=4%

h/c=2%

h/c=1%

h/c=0%

0.0

0.5

1.0

1.5

2.0

     C    p

     /    c

0.0

0.5

1.0

1.5

2.0

     C    p

     /    c

AR=1

AR=2

AR=3

0.0 0.2 0.4 0.6 0.8 1.0CL

0.00

0.25

0.50

0.75

1.00

    a .    c .     /    c

h/c=4%

h/c=2%

h/c=1%

h/c=0%

0.00

0.25

0.50

0.75

1.00

    a .    c .     /    c

0.00

0.25

0.50

0.75

1.00

    a .    c .     /    c

AR=1

AR=2

AR=3

0 4 8 12 16, deg

0.00

0.25

0.50

0.75

1.00

    a .    c .     /    c

h/c=4%

h/c=2%

h/c=1%

h/c=0%

0.00

0.25

0.50

0.75

1.00

    a .    c .     /    c

0.00

0.25

0.50

0.75

1.00

    a .    c .     /    c

AR=1

AR=2

AR=3

c)   d)

α

Fig. 6 Effectof Gurney-flap heightand aspectratioon longitudinalmoment-based characteristics: a) pitching moment, b) momentincrement, c) center-of-pressure location, and d) aerodynamic center location.

1220   DANIEL AND TRAUB

7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 5/9

Gurney flap that provides the greatest lift-to-drag ratio is observed toincrease.

Liu and Montefort [14] suggest a   “benefit ”  parameter, whichevaluates the performance of an aerodynamic effecter accounting for its impact on both the lift and drag. The relation is given by

g  −6

7

ΔCD

CD

 9

7

ΔCL

CL

(1)

where thedifferencesare with respect to h∕c   0%. A gvalue greater than zero indicates a net benefit. As seen in Fig. 10, flap heights of 1and 2% show a net benefit, which decreases with incidence. The 4%flap, despite its significant lift increment, is hampered by its dragpenalty such that g is greater than zero for low to moderate incidenceonly.

In this study, the stall angle is defined as the angle in which the lift coefficient has an identifiable maximum. For a Gurney-flap height of 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

CL

-2

0

2

4

6

   C

   L   /   C   D

h/c=4%

h/c=2%

h/c=1%

h/c=0%

0

2

4

6

8

10

   C   L   /   C   D

0

2

4

6

8

10

12

14

   C   L   /   C   D

AR=1

AR=2

AR=3

100% LE Suction

Fig.7 Effectof Gurney-flapheight andaspect ratioon lift-to-dragratio.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4CL

0

2

4

   C   L

   3   /   2 /   C   D

h/c=4%

h/c=2%

h/c=1%

h/c=0%

0

2

4

6

8

   C   L   3

   /   2 /   C   D

0

2

4

6

8

10

   C   L

   3   /   2 /   C   D

AR=1

AR=2

AR=3

100% LE Suction

Fig. 8 Effect of Gurney-flap height and aspect ratio on enduranceparameter.

0 1 2 3 4

h/c, %

4

6

8

10

12

14

   (   L   /   D

   )   M   A   X

AR=3

AR=2

AR=1

Fig. 9 Effect of Gurney-flap height on maximum lift-to-drag ratio.

0 5 10 15 20

, deg

-1

0

1

2

3

4

5

6

   B  e  n  e   f   i   t   M  a  r  g   i  n ,  g

h/c=4%

h/c=2%

h/c=1%-1

0

1

2

3

4

5

6

   B  e  n  e   f   i   t   M  a  r  g   i  n ,  g

-1

0

1

2

3

4

5

6

   B  e  n  e   f   i   t   M  a  r  g   i  n ,  g

AR=1

AR=2

AR=3

α

Fig. 10 Effect of Gurney-flap height and AR on the benefit margin.

DANIEL AND TRAUB   1221

7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 6/9

less than 2%, the stall angle is observed to remain unaffectedcompared to the baseline configuration as shown in Fig.   11, asinitially observed by Liebeck [7]. The 4% Gurney flap reduces thestall angle. A Gurneyflap leads to a higher leading-edge suction peak anda lower adverse pressure gradient [9].A4%Gurneyflapmayleadto such an increase that theadverse pressure gradient is notattenuated[9].

Thezero-lift angle of attack wascalculated by extrapolating thelift curve. Data points from −4 to 4 deg were used for the extrapolation.Because the lift curve was observed to be nonlinear for  AR    1, a second-degree polynomial fitwas used to obtainthe zero-lift angle of attack. For theremainingcases, a linear curve fit wasused. An almost linear decrease in the zero-lift angle of attack is observed withan increase in the Gurney-flap height, as shown in Fig.   12. Adependency upon   h∕cp    as well as upon h∕c has been documented[14–16]. This behavior is seen to be preserved for finite-AR wingsand Gurney flaps of moderate length. The aspect ratio does not seem to affect the change in zero-lift angle of attack significantly because

all three cases are observed to have a similar slope, as shown inFig. 12.

The minimum drag coefficient also reduces with an increase in theaspect ratio, as shown in Fig 13. This is corroborated by the data obtained by Zimmerman [3]. An explanation by Zimmermansuggests a penalty associated with tip drag. As the aspect ratiodecreases, the penalty due to tip drag contributes more toward thetotal drag. Becausethe tipdrag values do notchange with aspectratio,at a lower aspect ratio, the total drag coefficient obtained is higher. Areduction in minimum drag coefficient is obtained for the 1%Gurney-flap configuration, as shown in Fig.   13, supporting theinference that it lies withinthe boundary layer anddoes notcontributesignificant base drag. For Gurney-flap heights greater than 1%, the

slope of the line increases with an increase in aspect ratio. A similar increase in the minimum drag coefficient was observed by Traub for an annular wing equipped with a Gurney flap [15].

Two different theoretical approaches were used to estimate the lift-curve slope for the clean configurations. The Lamar code [17] andHelmbold’s equation [13] were used to obtain the percent differencein the computed and experimental lift-curve slopes. The lift curve for a small-AR wing can be calculated using a simplified equation duetoHelmbold [13]:

CLα  

  a0

1 

  a0

π AR

21∕2

  a0

π AR

  (2)

0 1 2 3 4

h/c, %

0

5

10

15

20

25

     S     T     A     L     L ,     d    e    g

AR=3

AR=2

-5 0 5 10 15 20 25 30, deg

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

     C     L

Stall Angle

     α

α

Fig. 11 Effect of Gurney-flap height on stall angle.

0.00 0.05 0.10 0.15 0.20

(h/c)0.5

-6

-4

-2

0

   Z   L   (   d  e  g   )

AR=3

AR=2

AR=1

      ∆     α

Fig. 12 Effect of Gurney-flap height on normalized zero-lift angle of attack.

0 1 2 3 4

h/c, %

0.00

0.01

0.02

0.03

0.04

   C   D  m   i  n

AR=3

AR=2

AR=1

Fig. 13 Effect of Gurney-flap height on minimum drag coefficient.

Table 1 Comparison of computed andexperimental lift-curve slopes

CLα  values, 1∕ deg   AR1 AR2 AR3

Experimental 0.0259 0.0426 0.0555Helmbold’s equation 0.0259 0.0454 0.0587Lamar code 0.0259 0.0442 0.0598

Table 2 Percent difference between computedand experimental lift-curve slopes.

Method AR1, % AR2, % AR3, %Helmbold’s equation 0 6.57 6.72Lamar code 0 3.75 7.74

1222   DANIEL AND TRAUB

7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 7/9

where   a0   is the theoretical lift-curve slope, often assumed to be0.11 deg−1 or  2π   rad−1. Helmbold’s equation was chosen because it is valid for all relevant ARs.

Tables   1   and   2   give the   CLα   values obtained and the percent 

differencewhen compared to the experimental results. The differencedid not exceed 8%.

The variation in the lift-curve slope with Gurney-flap height, ascompared to the baseline configuration, is shown in Fig. 14. With an

increase in Gurney-flap height, a moderate increase in the lift-curveslope is also observed. This increase in lift-curve slope can beconsidered to be a viscous effect due to the relative displacement thickness of the upper and lower surfaces and the thinning of thepressure side boundary layer with   α , as explained before [10]. Thethinning of the boundary layer on the pressure side also makesthe Gurney flap more effective, as the angle of attack increases [9].

The observed variationin the lift-curve slope is small, as presentedin Fig. 14. For a given shift in the zero-lift angle of attack, the change

in the lift coefficient can thus be computed as

ΔCL    CLα α ZLh∕c0

 − α ZLh∕c   (3)

This shows that, with an increase in the AR, the change in the lift coefficient, for a given Gurneyflap, increases because of a larger lift-curve slope. This may be observed in Fig. 4. With an increase in theaspect ratio, the lift augmentation of the Gurney flap, at a given angleof attack, increases. Consequently, the effect of a Gurney flap may beestimated using sectional datato ascertainα ZL in conjunction withthefinite wing’s lift-curve slope.

Forall the clean configuration cases, at the angle for the maximum lift-to-drag ratio,a deflection is observed in thelift curve,as shown inFig.   15. This deflection coincides with the angle or   CL   in which

CL∕CDmax is achieved. A study by Lee and Pereira [18] infers that,at the maximum lift-to-drag ratio, the axial tip vortex switches from being a wakelike to a jetlike vortex. It may thus be inferred in thisstudy that the vortex lift becomes more predominant after the tipvortex switches to a jetlike vortex structure.

To further understand the dependency of aspect ratio on theGurney-flap performance, flow visualization was performed using a mixture of titanium dioxide, linseed oil, and paraffin at angles of attack of 2 and 10 deg. An  AR    2  clean configuration and a 2%

Fig. 14 Effect of Gurney-flap height on lift-curve slope.

CL

0

2

4

6

     C     L     /     C     D

AR=1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4-5 0 5 10 15 20 25 30

, deg

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

     C     L

     C     L

     C     L

AR=1

, deg

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

AR=3

-5 0 5 10 15 20 25 30

, deg

-0.2

0.00.2

0.4

0.6

0.8

1.0

1.2

1.4

AR=2

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4CL

-4

-20

2

4

6

8

   C   L   /   C   D

AR=2

0.4 0.6 0.8 1.0 1.2-5 0 5 10 15 20 25 30 0.0 0.2 1.4CL

0

2

4

6

8

10

12

   C   L   /   C   D

AR=3

α

α

α

Fig. 15 Angle in which vortex switches from wakelike to jetlike.

DANIEL AND TRAUB   1223

7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 8/9

Gurney-flap configuration were used for the flow visualization. Withan increase in the angle of attack, a forward shift in the bubble isobserved, as shown in Figs.   16a   and   16b. Unusually, the bubbleseems to increase in size as well. Side-edge vortices are also observedto be larger with more pronounced sidewash, yielding to a stronger 

crossflow over the wing. The Gurney flap is observed to strengthenthe crossflow over the wing, as shown in Figs. 16a  and 16c. This canbe observed by the stronger tip-vortex-induced sidewash and a morepronounced attachment line for Gurney-flap configurations. Thisfurther implies that the increased loading due to a Gurney flapintensifies the side-edge vortices. Similar trends were observed for aspect ratios of 1 and 3, as well.

IV. Conclusions

A low-speed wind-tunnel investigation was undertaken to explorethe effect of aspect ratio on the aerodynamic characteristics of a Gurney flap. At a given angle of attack, the lift augmentation due tothe flap increased with aspect ratio. It was seen that the Gurney flaplift increment, referenced to the shift in the zero-lift angle of attack,

scales well with the lift-curve slope change due to aspect ratio. Theincrease in the lift-curve slope and the shift in the zero-lift angle of attack due to a Gurney flap were independent of the aspect ratio. Thedrag penalty due to a large Gurney flap was observed to reduce withaspect ratio.The shift in zero-lift angle of attack wasobservedto havea 

  h∕c

p   dependency. The height of the most aerodynamically

efficient Gurney flap was noted to increase as the aspect ratiodecreased.

Acknowledgments

The authors would like to thank the associate editor and reviewers,whose comments and suggestions improved the clarity and focus of this article.

References[1] Bossert, D. E., Royer, G. E., Rathbun, T., Schorsch, T., White, A.,

Patrey, J., and Pack, D.,   “Teaching Unmanned Aerial Vehicle (UAV)

Concepts at theUndergraduate Level: OneApproach,” AIAA Atmospheric

FlightMechanics and Exhibit , AIAA,Austin, TX,11–14 Aug. 2003; alsoAIAA Paper 2003-5619.

[2] Ro, K., Oh, J., and Dong, L., “Lessons Learned: Application of SmallUAV for Urban Highway Traffic Monitoring,”   45th AIAA Aerospace

Sciences Meeting and Exhibit , AIAA, Reno, NV, 8–11 Jan. 2007; also

AIAA Paper 2007-596.[3] Zimmerman, C. H.,“Characteristics of ClarkY Airfoils of Small Aspect 

Ratios,” NACA TR-431, 1933.[4] Torres, G. E., and Mueller, T. J., “Aerodynamic Characteristics of Low

Aspect Ratio Wings at Low Reynolds Numbers,” Fixed And Flapping

Wing Aerodynamics For Micro Air Vehicles Applications, edited byMueller, T. J., Progress in Aeronautics and Astronautics, Vol. 195,AIAA, Reston, VA, 2001, pp. 115–139, Chap. 7.

[5] Polhamus, E. C.,   “Predictions of Vortex-Lift Characteristics by a Leading-Edge-Suction Analogy,”  Journal of Aircraft , Vol. 8, No. 4,1971, pp. 193–199.doi:10.2514/3.44254

[6] Traub, L. W., and Agarwal, G.,   “Aerodynamic Characteristics of a Gurney Flap at Low Reynolds Numbers,” Journal of Aircraft , Vol. 45,No. 2, 2008, pp. 424–429.doi:10.2514/1.28016

[7] Liebeck,R. H., “Designof a SubsonicAirfoilsfor High Lift,” Journal of  Aircraft , Vol. 15, No. 9, 1979, pp. 547–561.doi:10.2514/3.58406

[8] Gigue’re, P., Dumas, G., and Lemay, J.,   “Gurney Flap Scaling for Optimum Lift-to-Drag Ratio,”  Journal of Aircraft , Vol. 35, No. 12,1997, pp. 1888–1890.

[9] Maughmer, M. D., and Bramesfeld, G.,   “Experimental Investigationof Gurney Flaps,”   Journal of Aircraft , Vol. 45, No. 6, 2008,pp. 2062–2067.doi:10.2514/1.37050

[10] Traub, L. W., andAgarwal,G., “Exploratory Investigation of GeometryEffects on Gurney Flap Performance,”  Journal of Aircraft , Vol. 44,No. 1, 2007, pp. 351–353.doi:10.2514/1.28385

[11] Meyer, R., Hage, W., and Bechert, D. W., “Drag Reduction on GurneyFlaps by Three-Dimensional Modifications,”   Journal of Aircraft ,

Vol. 43, No. 1, 2006, pp. 132–

140.doi:10.2514/1.14294[12] Jeffrey, D., Zhang, X., and Hurst, D. W.,  “Aerodynamics of Gurney

Flapson a Single-ElementHigh-Lift Wing,” Journal of Aircraft , Vol.37,

h/c=0% h/c=2%

α=2º

a) c)

α=10º

b) d)

Attached

Laminar Flow

Attached Turbulent

Flow

Attachment

Line

Tip Vortex

induced side-wash

Separation

Line

Laminar

Separation

Bubble

Wing tip

Fig. 16   TiO2  flow visualization pictures for AR 2 (flow is from top to bottom).

1224   DANIEL AND TRAUB

7/21/2019 Effect of Aspect Rato

http://slidepdf.com/reader/full/effect-of-aspect-rato 9/9

No. 2, 2000, pp. 295–301.doi:10.2514/2.2593

[13] Thwaites, B., Incompressible Aerodynamics, Dover, New York, 1960,p. 341.

[14] Liu, T., and Montefort, J., “Thin-Airfoil Theoretical Interpretation for Gurney Flap Lift Enhancement,”   Journal of Aircraft , Vol. 44, No. 2,2007, pp. 667–671.doi:10.2514/1.27680

[15] Traub, L. W.,  “Effect of Gurney Flap on Annular Wings,”  Journal of 

 Aircraft , Vol. 46, No. 3, 2009, pp. 1085–1088.

doi:10.2514/1.43096

[16] Cavanaugh, M. A., Robertson, P., and Mason, W. H.,“WindTunnel Test of Gurney Flaps and T-Strips on an NACA 23012 Wing,”  25th AIAA

 AppliedAerodynamics Conference, AIAA,Miami, FL,25–28 June 2007;also AIAA Paper 2007-4175.

[17] Lamar, J. E., “Extension of Leading-Edge Suction Analogy to Wingswith Separated Flow Around the Side Edges at Subsonic Speeds,”NASA TR-R-423, Oct. 1974.

[18] Lee, T.,and Pereira,J., “Nature of Wakelike and Jetlike Axial Tip VortexFlows,” Journal of Aircraft , Vol. 47, No. 6, 2010, pp. 1946–1954.doi:10.2514/1.C000225

DANIEL AND TRAUB   1225