WIND TUNNEL AERODYNAMIC TESTS OF SIX AIRFOILSFOR USE ON SMALL WIND TURBINES

Michael S. Selig∗and Bryan D. McGranahan†

Department of Aerospace EngineeringUniversity of Illinois at Urbana–Champaign

Urbana, Illinois 61801

ABSTRACT

This paper presents detailed wind tunnel tests datataken on six airfoils having application to small windturbines. In particular, lift, drag and moment mea-surements were taken at Reynolds numbers of 100,000,200,000, 350,000 and 500,000 for both clean and roughconditions. In some cases, data was also taken at aReynolds number of 150,000. The airfoils included theE387, FX 63-137, S822, S834, SD2030, and SH3055.Prior to carrying out the tests, wind tunnel flow qual-ity measurements were taken to document the lowReynolds number test environment, and also oil flowvisualization data and performance data were takenon the E387 for comparison with measurements takenat NASA Langley in the Low Turbulence PressureTunnel. The new results compare favorably with thebenchmark NASA data. Highlights of the performancecharacteristics of the six airfoils are then discussed.

INTRODUCTION

This paper documents the aerodynamic character-istics of six airfoils, which were also examined in acompanion study dealing with their aeroacoustic prop-erties.1 These projects together were motivated by twointersecting factors. First, the U.S. Department of En-ergy, National Renewable Energy Laboratory (NREL),has initiated research into the aeroacoustics of windturbines, which is an important design considerationwhen a potentially valuable wind resource and a popu-lation center coincide. Such an event—the confluenceof wind technology and people—is increasingly proba-ble as wind turbines become more efficient and betterable to exploit lower wind speed sites, which are oftenfound near U.S. load centers. Improving our under-standing of the aeroacoustics will help designers ex-ploit advances in noise mitagation design strategies. It

∗Associate Professor, 306 Talbot Laboratory, 104 S. WrightSt. email: m-selig@uiuc.edu. Senior Member AIAA.

†Graduate Research Assistant, 306 Talbot Lab, 104 S. WrightSt. email: mcgranah@uiuc.edu. Student Member AIAA.

Copyright c© 2004 by Michael S. Selig and Bryan D. McGrana-han. Published by the American Institute of Aeronautics and As-tronautics, Inc. or the American Society of Mechanical Engineers,with permission.

is anticipated that having a reliable and self-consistentairfoil performance dataset may be helpful in validat-ing aeroacoustics prediction codes in support of suchdesign activities. Second, small stand-alone wind tur-bines operating in close proximity to residential areasposed a noise concern. Given that the aerodynamicefficiency increases with the tip speed and hence windturbine noise, advances in the development of smallwind turbines can be envisioned using a suite of com-putational tools capable of predicting both the aeroa-coustic characteristics and aerodynamic performance.Thus, an aerodynamic dataset of representative windturbines airfoils should help pave the way toward thedevelopment of the necessary design methodologiesneeded by the small wind turbine industry seeking toimprove efficiency as well as acceptability.Prior to testing the airfoils for their performance

data, an extensive study of the wind tunnel flow qual-ity was carried out. This precursor study includedmeasurements of the freestream turbulence as well asvariations in dynamic pressure and freestream flow an-gle across the center region of the test section. Theresults of these flow quality tests are presented. Thispaper also includes validation data on the E387 air-foil as compared with results from NASA Langley.Following this, the test results on the six airfoils arediscussed.

WIND TUNNEL FACILITYAND MODELS

All experiments were conducted in the University ofIllinois at Urbana–Champaign (UIUC) subsonic windtunnel (Fig. 1), which has a nominal test section thatis 2.81-ft high and 4-ft wide. The test set-up de-picted in Fig. 2 was used for this study.2,3 As seenin Fig. 2, two 6-ft long Plexiglass splitter plates areinserted 2.8 ft apart into the test section to isolate theairfoil models from both the support hardware and thetunnel side wall boundary layers. The 1-ft chord airfoilmodels were inserted horizontally between the splitterplates with nominal gaps of 0.040–0.080 in. betweenthe end of the airfoil model and the splitter plates.Performance data were taken at Reynolds numbers of

pmiglioreAIAA 2004-1188

pmiglioreWIND TUNNEL AERODYNAMIC TESTS OF SIX AIRFOILSFOR USE ON SMALL WIND TURBINES

pmiglioreMichael S. Selig* and Bryan D. McGranahan**Department of Aerospace EngineeringUniversity of Illinois at Urbana--ChampaignUrbana, Illinois 61801

pmigliore**

pmigliore**

pmigliore*

Fig. 1 UIUC low-speed subsonic wind tunnel.

Fig. 2 Experimental setup (Plexiglass splitterplates and traverse enclosure box not shown forclarity).

100,000, 200,000, 350,000 and 500,000. In some cases,data was also taken at a Reynolds number of 150,000.The lift was measured using a strain gauge load cell,and the drag was determined using the momentumdeficit method.2 To account for spanwise drag varia-tions at low Reynolds numbers,4 the drag was obtainedfrom an average of eight equidistant wake surveys overthe center of the model so that a 10.5-in. wide spanwas covered. The overall uncertainty in both the liftand drag measurements was estimated at 1.5%.2,3 Alllift and drag measurements were corrected for windtunnel interference and validated with data from theNASA Langley Low Turbulence Pressure Tunnel.2,4–6

The wind tunnel tests included a broad variety ofairfoils that are summarized in Table 1. It should bementioned that later suffixes are added to the airfoilnames (e.g. ‘(E)’) and used in the captions to indicatethe wind-tunnel model versions of those particular air-foils. For instance, the E387 (E) case is the 5th modelof the E387 airfoil in the UIUC collection.

Table 1 Airfoils Tested

Airfoil Relevance/Usage

E387 Benchmark Eppler airfoil testedin NASA Langley LTPT

FX 63-137 Aeromag Lakota, SouthwestWindpower H-40, H-80 andcandidate for next-generationsmall wind turbine

S822 AOC/Windlite, Havatex 2000 andcandidate for next-generation smallwind turbine, patented by DOE NREL

S834 New low-noise, low-Re airfoiland candidate for next-generationsmall wind turbine, patent pendingby DOE NREL

SD2030 Southwest Windpower Air 403 andAir X turbines

SH3055 Bergey Windpower Excel turbine

The airfoil models were shaped in a computernumerically controlled milling machine out of Ren-Shape high-density foam, structurally reinforced,fiberglassed, then sanded and painted. A coordinate-measuring machine was used to digitize the models.3

The differences between the nominal and measured co-ordinates were calculated, allowing the computation ofan average accuracy for each model (mean of the dif-ferences). For the airfoils used in the current study,the differences between the nominal and measured co-ordinates are indicated in Fig. 3 underneath the airfoilnames.

TUNNEL FLOW QUALITYAND VALIDATION

As has been well documented, low Reynolds numberairfoil flows are highly sensitive to the tunnel flow qual-ity. Consequently, tunnel flow quality measurementswere taken and documented as described below.

TURBULENCE INTENSITY MEASUREMENTSThe turbulence intensity was measured using hot-

wire anemometry. In particular, the hot-wire systemwas a TSI Incorporated IFA 100 anemometer in con-junction with a TSI Model 1210-T1.5 hot-wire probe.The probe makes use of a 1.5-micron platinum-coated

E387 (E)(0.0091 in.)

FX 63−137 (C)(0.0031 in.)

S822 (B)(0.0074 in.)

S834(0.0056 in.)

SD2030 (B)(0.0060 in.)

SH3055(0.0037 in.)

Fig. 3 Airfoils tested and their corresponding av-erage error in inches for the 12-in. chord modelspresented in this study.

tungsten wire. The probe was mounted in the tun-nel end-flow orientation with the wire perpendicularto the tunnel floor in order to measure the axial turbu-lence intensity. A PC equipped with a data acquisitioncard was used to log the signal from the anemometer.A HP 35665A Dynamic Signal Analyzer, which per-formed a FFT (Fast Fourier Transform) analysis, wasemployed to allow the turbulence spectrum to be mon-itored over a broad range of frequencies. More detailsof the method are given in Ref. 7.The turbulence intensity was calculated from data

using a total of 50,000 samples with a sample frequencyof 10,000 Hz. Figure 4 shows the resulting turbulencelevels for both the tunnel empty case and with thefull measurement apparatus installed. In general theselevels are considered to be sufficiently low for takinglow Reynolds number airfoil measurements.

DYNAMIC PRESSURE SURVEYS

The variation in the dynamic pressure in the testsection of the UIUC low-speed subsonic wind tun-nel was obtained by comparing the dynamic pressureat a pitot-static probe mounted near the entrance ofthe splitter plates with that measured by a down-stream probe. The upstream probe was located atthe centerline of the tunnel in the spanwise direction

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(X = 0 in.), 0.97 ft below the centerline of the tun-nel in the vertical direction (Y = −11.66 in.), and1.323 ft upstream of the quarter-chord location of theairfoil model when mounted in the test section. Thedownstream probe was traversed in the X-Y plane per-pendicular to the freestream and coincident with thequarter chord. Measurements were made both withthe test section empty and with the test apparatusinstalled.The measurement plane extended from 5.5 in. above

the tunnel centerline to 14.5 in. below in the verticaldirection Y , and from 10.5 in. to the left of the tun-nel centerline to 10.5 in. to the right in the horizontaldirection X. A grid spacing of 1 in. was used for themeasurements, resulting in a total of 462 measurementpoints for each case tested.Figure 5 shows contours of ∆Q for various Reynolds

numbers plotted against its X and Y location for thecase with the test rig installed. Several observationscan be made. There is a slight increase in the flowspeed in going downstream. It is likely that the ve-locity measured at the location of the model is higherthan the upstream velocity because of the growth ofthe boundary layer along the splitter plates, ceilingand floor as well as the blockage that occurs betweenthe splitter plates and the tunnel sidewalls. This per-centage increase in the flow speed grows larger as theReynolds number is reduced, which is consistent withthe thicker wall boundary layers at the lower Reynoldsnumbers. This rise in the velocity is accounted forin the airfoil-performance data-reduction procedure.Second, it is observed that over the region where themodel is located, the net change in flow speed is rela-tively small. For instance, Fig. 5 shows that at Re/l =200,000/ft the increase in the flow speed ranges from

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approximately 1.4% to 1.8%, which is a relative differ-ence of ±0.2% in the working range of the test section.As stated in Ref. 8, it is desirable to have the variationin dynamic pressure in the working range of the testsection be less than 0.5% from the mean, i.e. ±0.5%.The results show that the flow is well within the “ruleof thumb.” A third observation, is the existence of aslight asymmetry in the flow, noticeable mainly in the+X:−Y quadrant (bottom right corner in Fig. 5). Theasymmetry is present with the tunnel empty and withthe test rig in place, hence it is unrelated to the test rig.Moreover, the lines of constant Q are parallel to thetunnel floor at X = 0 (centerline), so the effect is neg-ligible with respect to the performance-measurementquantities in the center region of the test section.

FLOW ANGULARITY SURVEYSJust as it is important to have uniform flow velocity

in the wind-tunnel test section, it is equally importantto have the flow parallel to the axial direction.8 Forthe most part, pitot-static probes are insensitive toflow angles in the range ±12 deg, so a large flow angleis required to introduce an error in the dynamic pres-sure measurements. Similarly, large flow angles arerequired to introduce errors into total head measure-ments. Apart from pressure measurements, a smallchange in pitch angle, however, contributes to a changein the effective angle of attack of the airfoil model andthereby such an error can skew the lift and drag mea-surements when they are plotted versus the angle ofattack.The flow angularity in the test section of the UIUC

low-speed subsonic wind tunnel was measured using anAeroprobe Corporation Model S7TC317 7-hole probeshown in Fig. 6. The probe has a total-head port lo-

Fig. 6 Illustration of the 7-hole probe used forflow angle measurements.

cated at the center, and six chamfered ports equallyspaced circumferentially around the center. The probewas mounted in the wind tunnel on a special two-beamsting attached to the computer-controlled LinTech tra-verse. The flow measurements were all taken with thetest rig installed in the wind-tunnel test section, with-out the model. A more detailed description of the useof the 7-hole probe is found in Ref. 9.The 7-hole probe was traversed in a plane perpen-

dicular to the freestream flow over the range fromX = ±6.5 in. to Y = ±10 in. The traverse wasnot extended to the edges of the test section due toequipment limitations. Traversing this central corewas acceptable because one would expect to find thelargest flow angle variation in the center of the test sec-tion rather than along the walls were at a minimumthe flow is parallel to the wall (yaw or pitch is therebyzero). A grid spacing of 1 in. was used, resulting ina grid of 252 sample locations for each case tested.The 7-hole probe tip was located approximately 1.5chord lengths behind the quarter chord of the airfoilmodel. To set the tunnel speed, one pitot-static probewas located at X = 0 in., Y = −11.66 in. For redun-dancy an additional probe was located at X = 5 in.,Y = −11.66 in. Both pitot-static probes were mountedat the same streamwise location, 1.323 ft upstream ofthe location of the quarter chord of the airfoil model.The results shown in Fig. 7 indicate that the total

flow angle (pitch and yaw combined) were smallest atRe = 500,000, becoming more pronounced at lowerReynolds numbers. The pitch angle measurement (notshown) was generally between 0 and 0.2 deg (±0.1 deg)across the working region of the test section where theairfoil model is located. According to Ref. 8, a flowangle variation of ±0.2 deg is acceptable, but ±0.1 degor better is the preferred. The current measurementsmeet this latter desired level of flow quality.

AIRFOIL DATA VALIDATION

In this section, data taken on the E387 is com-pared with results from NASA Langley in the Low-Turbulence Pressure Tunnel (NASA LTPT).5,6 Fourtypes of data are compared: surface oil flow visualiza-tion, lift data, moment data and drag polars. In this

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order, these data are presented and discussed below.

SURFACE OIL FLOWVISUALIZATIONThe surface oil flow visualization technique made

use of a fluorescent pigment (Kent-Moore 28431-1) sus-pended in a light, household-grade mineral oil thatwas sprayed onto the surface of the model using aPaasche Model VL double-action airbrush. The modelwas then subjected to 20–45 min of continuous wind-tunnel run time at a fixed Reynolds number and angleof attack. During this period, the oil moved in thedirection of the local flow velocity at a rate dependenton the balance of forces dictated by the boundary-layer skin friction coefficient Cf and surface tensionof the oil. As a result, regions of the flow could beidentified and compared with the NASA Langley Low-Turbulence Pressure Tunnel (LTPT) data.5,6

Figure 8 shows a photograph of the surface oil flowpattern made visible under fluorescent light. Figure 9conceptually illustrates the connection between thesalient surface oil flow features and the skin frictiondistribution. Note that the skin friction distribution,though conceptual, is consistent with the results ofmany computational studies.10–15 The authors be-lieve that the unique shape of the Cf distribution,in particular the strong negative Cf spike, has yet tobe experimentally verified (as no experimental datacould be found); however, the oil flow patterns ob-served seem to confirm the validity of the negative Cfspike concept.Several important flow features can be identified and

related to the underlying skin friction and surface ten-sion forces. In Fig. 8, laminar flow is seen to existfrom the leading edge to approximately 0.40c. The

Fig. 8 Representative upper-surface oil flow visu-alization on the E387 (E), Re = 300,000, α = 5 deg.

oil streaks are characteristically smooth in this regionuntil laminar separation occurs, which is identified inFig. 9 as the point where Cf = 0. (Note again thatthe flow shown in Fig. 9 is conceptual, and it is notintended to match Fig. 8 in detail.) Downstream ofthe point of laminar separation, the original airbrushed“orange-peel” texture that existed prior to running thetunnel still exists, indicating that the flow is stagnantin this region. This stagnant flow is consistent with theknown behavior of flow in the interior leading-edge re-gion of a laminar separation bubble. As sketched, theCf magnitude in this region is quite small due to thelow flow speed and negative in sign due to reverse flowat the surface.In the presence of a laminar separation bubble, tran-

sition takes place in the free shear layer above thesurface of the airfoil. Downstream of this point, reat-tachment occurs in a process that is known to beunsteady as vortices are periodically generated andimpinge on the airfoil surface.15,16 These unsteadyvortices colliding with the surface lead to a relativelyhigh shear stress that tends to scour away the oil atthe mean reattachment point, pushing oil upstreamor downstream of the reattachment point. As seen inFig. 9, the reattachment line is less distinct becausethe bulk of the oil has been pushed away revealing theunderlying black airfoil surface. In Fig. 8, the tunnelrun time was long enough that the reattachment lineat 0.58c is even harder to see than in Fig. 9. In theoriginal high-resolution color photographs that werearchived, this feature is clear and easily quantifiable.Downstream of reattachment the boundary layer is

turbulent. The high skin friction in this area relativeto the laminar boundary layer upstream tends to clearaway more oil, again making the black surface down-stream more visible than in the upstream region.The remaining visible feature of the flow is a line

where the oil tends to pool, termed here the “oil accu-mulation line.” This intrinsic feature of the oil flow has

Fig. 9 Conceptual illustration of the relation-ship between the surface oil flow features and skinfriction distribution in the region of a laminar sep-aration bubble plotted against the airfoil arc lengthcoordinate s/c.

no direct connection to laminar flow, reverse flow inthe bubble, or the ensuing turbulent flow downstream.However, it does indicate a relatively important fea-ture of the flow with regard to the nature of the skinfriction in the vicinity of reattachment. The negativeCf spike shown in predictions and sketched conceptu-ally in Fig. 9 is most likely responsible for generatingthe oil accumulation line. Assuming that this is thecase, the fluctuating high skin friction that is gener-ated over the unsteady reattachment zone will tend topush the oil upstream ahead of the mean reattachmentpoint. At some location on the airfoil, however, the oilmoving upstream will experience a balance of forcesbetween the rapidly weakening skin friction force andthat of the surface tension and oil adhesion that is re-tarding its motion. At the location where these twoforces balance, the oil accumulates into a line that be-comes the most distinguishable feature of the oil flow.Consequently, it is speculated that this flow featureis sometimes mislabeled as “reattachment” as will bediscussed below.Figures 10 and 11 show the previously described flow

features compared with data obtained at the NASALangley LTPT. In the low drag range between −2 degand 7 deg angle of attack, the agreement in the laminarseparation line between the NASA LTPT and UIUCdata sets is mostly within 0.01c to 0.02c, which isvery near the uncertainty of the method. As previ-ously discussed, the next feature to appear is the oilaccumulation line. The UIUC oil accumulation lineagrees fairly well with the “reattachment” line identi-

fied in the NASA experiment. It is believed, however,that based on the previous reasoning this label givenin the original reference6 is a misnomer. Had theUIUC tests been performed for a longer duration, thereattachment zone would be scoured clean with no dis-tinguishing feature, leaving only the oil accumulationline to be labeled as the “reattachment line,” knowingthat one must exist. Hence, it is speculated here andin prior UIUC work3 that such a scenario took placein the NASA study, i.e. the oil-accumulation line wasmisinterpreted as the reattachment line.Guided by this working assumption, the two re-

sults again are in good agreement. It must be stated,however, that the oil accumulation line might changeslightly from one facility to the next since it is dic-tated by a force balance that depends on the skinfriction forces of the boundary layer relative to theadhesion forces of the particular oil used. The predic-tions, however, show that the negative Cf region hasa sharp upstream edge, which is most likely where theoil accumulates regardless of the surface tension char-acteristics. Differences in the oil accumulation line dueto differences in the type of oil used are therefore be-lieved to be small. The good comparisons betweenUIUC and Langley data tend to support this assump-tion.Moving further downstream, the UIUC reattach-

ment data is plotted, but unfortunately no directcomparison can be made because of the ambiguitywith respect to the reattachment data reported in theNASA study. However, close inspection of the datasuggests that at a Reynolds number of 300,000 andbetween 5 deg and 7 deg angle of attack, the LTPTline merges with the UIUC reattachment line. Per-haps in this case, the measurements at Langley wereindeed the reattachment points.The conclusion to be drawn from this comparison

of the oil flow visualization results is that the twofacilities produce airfoil flows that are in close agree-ment. Moreover, if the arguments regarding the oilaccumulation line are correct, then the agreement canbe considered excellent and within the uncertainty ofthe measurements.

LIFT DATA

Lift and moment data comparisons between theUIUC and LTPT data are shown in Fig. 12. Discrep-ancies can be seen for a Reynolds number of 100,000as well as in the stalled regime. For Re = 100,000 dif-ferences are most likely attributable to measurementaccuracy. In stall for α > 12 deg, taking the Langleydata as the benchmark, the UIUC data differs mostlikely as result of three-dimensional end effects. Nev-ertheless, the results show good agreement over the

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Fig. 10 Comparison of major E387 (E) upper-surface flow features between UIUC and LTPT forRe = 200,000.

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normal unstalled operating range, and this agreementimproves with higher Reynolds number.

DRAG DATA

Figure 13 shows a comparison between UIUC andNASA LTPT drag data for the Reynolds numbersof 100,000, 200,000, 300,000 and 460,000. To beginthis discussion, data at a Reynolds number of 200,000and 300,000 are considered. For these cases, the oilflow results were in close agreement as well as thelift data which taken together suggest that the dragdata should likewise be in good agreement. Indeed, forRe = 200,000, the agreement is quite acceptable. How-ever, Re = 300,000 the agreement is not as good. Asfor the other cases, for a Re = 460,000, the agreementimproves, while for Re = 100,000, there is less agree-ment. When these cases are studied in more detail, itis seen that the edges of the drag polar are in quiteclose agreement for each case, with the Re = 100,000perhaps being the exception.There can be many reasons for the observed dis-

crepancies, not the least of which is the fact thatat low Reynolds numbers the drag data when deter-mined from downstream wake measurements variesalong the span—the further downstream, the morevariation. The current measurements were taken 1.25chord lengths downstream of the trailing edge, whilethose in the NASA study were taken 1.5 chord lengthsdownstream. Because of this variation in spanwisedrag, ideally many wake profile measurements shouldbe taken along the span and the resulting drag co-efficients summed and averaged. This approach ofperforming multiple wake surveys was taken in the cur-rent study (as mentioned previously eight wake surveyswere taken), but in the NASA study wake rake datawas taken at only one station for the purpose of acquir-ing the full polar data that was reported. However,some limited spanwise data was taken in the NASAstudy, and the degree of spanwise variation observedis quite similar to that found in the current study.7

Consequently, the discrepancies in part must be re-lated to the variation in drag. In the NASA study,had data been taken at many stations, it is likely thatbetter agreement would be observed.For the Reynolds number of 100,000, which was not

critical to the current investigation, the discrepanciesare larger. This result cannot be attributed solely tospanwise drag variation. Figure 13 shows that at aCl = 0.7 and Re = 100,000, the eight Cd data pointsobtained from the eight wake measurements fall nearlyone on top of the other. Therefore, the spanwise vari-ation in drag is small on a percentage basis, and asimilar variation in Cd for this particular case was seenin the NASA data. Consequently, for Re = 100,000

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

α (deg)

Cl

E387 Re = 100,000

UIUC Lift

UIUC Moment

LTPT Lift

LTPT Moment

Cm

0.1

0.0

−0.1

−0.2

−0.3

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

α (deg)

Cl

E387 Re = 200,000

UIUC Lift

UIUC Moment

LTPT Lift

LTPT Moment

Cm

0.1

0.0

−0.1

−0.2

−0.3

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

α (deg)

Cl

E387 Re = 300,000

UIUC Lift

UIUC Moment

LTPT Lift

LTPT Moment

Cm

0.1

0.0

−0.1

−0.2

−0.3

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

α (deg)

Cl

E387 Re = 460,000

UIUC Lift

UIUC Moment

LTPT Lift

LTPT Moment

Cm

0.1

0.0

−0.1

−0.2

−0.3

Fig. 12 Comparison between UIUC and LTPT E387 lift and moment coefficient data for Re = 100,000,200,000, 300,000, and 460,000.

the cause for the bulk of the difference in the dragmeasurements must be something other than spanwisedrag variation.When sources of error were being considered to ex-

plain the discrepancies, several factors were ruled outin light of the excellent agreement in surface oil flowvisualization and also lift and moment data. Of thosethat remained, no sources of uncertainty in the cur-rent data lingered after investigation. Thus, the stateof the agreement for the Reynolds number of 100,000remains unexplained. It is recognized that the sourceof this discrepancy might likely relate to some of thediscrepancies for the higher Reynolds number cases aswell. Nevertheless, the agreement overall is good, es-pecially in light of past historical comparisons of lowReynolds number airfoil data, which vary widely.2,17

Regarding the accuracy of the current data overall,this section has made several important points thatshould instill confidence in the data presented in thispaper. First, it was shown that surface oil flow dataobtained on the E387 airfoil exhibited excellent agree-ment with NASA LTPT data for Re = 200,000 and300,000. Second, current lift data was shown to havegood agreement with LTPT data for all Reynolds num-bers up to stall, after which point three-dimensionalend effects and unsteady aerodynamics produced slightdiscrepancies. Third, the pitching moment data wasshown to agree well with LTPT data over a broadrange of angles of attack. Lastly, in support of thethree previous conclusions, the drag data showed goodagreement, with some discrepancies yet to be fully ex-plained.

RESULTS AND DISCUSSION

In the remainder of this paper, the performancecharacteristics of each of the airfoils are discussed indetail. Rather than organizing this discussion by com-menting on broad categories of various effects, insteadthe airfoils are discussed in the order presented inFig. 3 (alphabetically).It should also be stated from the outset that each

airfoil presented here was designed with unique anddifferent constraints and desired performance charac-teristics in mind. Consequently, the airfoils collectivelyrepresent a broad range of performance characteristicsand geometric properties. Hence, to compare directlythe performance of one airfoil to the next and declareone airfoil better than another would be misleading.Therefore, again, the focus will be on highlighting in-teresting and important performance characteristicswhile leaving design decisions and the establishmentof various figures of merit to the wind turbine bladedesigner whose task goes beyond the scope of topicsdiscussed here.

Fig. 14 Boundary layer trip geometry used to sim-ulate the effects of leading edge debris and errosion(dimensions are in inches).

Finally, to simulate the effects of roughness causedby leading-edge debris and errosion, the airfoils weretested with three-dimensional zigzag boundary-layertrips afixed to the upper and lower surfaces near theleading edge. In particular, the upper-surface andlower-surface trips were located at 2% and 5% chord,respectively. These data are discussed along with the“clean” airfoil data, that is, data taking on the air-foils without boundary layer trips. Figure 14 shows adrawing of the boundary-layer trip used in this study.It is denoted as “zigzag trip type F” because it is the6th different zigzag trip geometry tested at UIUC.

E387

The E387 airfoil was designed in the early 1960sby Richard Eppler for model sailplanes where it wasquickly successful and is still used. Beyond this, ithas taken on the additional role of becoming a bench-mark section used to compare low Reynolds numberairfoil measurements from one wind tunnel facilitywith another. In fact, the E387 airfoil is likely themost widely tested low Reynolds number section hav-ing been tested at Delft in the Netherlands, Stuttgart,Princeton, NASA Langley and UIUC prior to and in-cluding the current tests. Having already discussed thecomparison between the UIUC data and that of NASALangley, the focus in this chapter is on elucidating thelow Reynolds number performance characteristics.Figures 15 and 16 show the drag polars and the

lift and drag characteristics at Reynolds numbersof 100,000, 150,000, 200,000, 300,000, 460,000, and500,000. [The Re = 460,000 case was added for com-parison with Langley.] For the lowest Reynolds num-ber of 100,000, the most prominent manifestation of alaminar separation bubble is observed in the drag po-lar. Between the limits of the low drag range, there isan increase in drag associated principally with a lam-inar separation bubble. In the vicinity of corners ofthe low drag range, the laminar separation bubble isshort or nonexistent in which case the drag is not ashigh. However, as the angle of attack is increased fromthe lower corner, the adverse pressure gradient on theupper surface becomes stronger and as a result thebubble drag grows until the drag is a maximum neara lift coefficient of 0.7 (α ≈ 3 deg). Beyond this point,

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

Cd

Cl

LTPT

UIUC

E387 Re = 100,000

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

Cd

Cl

LTPT

UIUC

E387 Re = 200,000

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

Cd

Cl

LTPT

UIUC

E387 Re = 300,000

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

Cd

Cl

LTPT

UIUC

E387 Re = 460,000

Fig. 13 Comparison between UIUC and LTPT E387 drag coefficient data for Re = 100,000, 200,000,300,000, and 460,000.

the size of the bubble begins to decrease (see Fig. 21of Ref. 12), which results in lower drag until the uppercorner of the polar is reached where transition takesplace on the surface without a drag producing bub-ble being present. As the Reynolds number increases,the advantages of higher Reynolds number as well asa reduction in the length of the bubble (due to earliertransition, see Fig. 8) leads to correspondingly lowerdrag.

As mentioned, for this airfoil and all of the others, azigzag boundary layer trip was added on the top andbottom surfaces near the leading edge to simulate theeffects of roughness caused by debris and errosion thatoccurs on wind turbine blades over time. In general the

main effect of the trip is to promote transition shortlydownstream of the trip. If a bubble is present in theclean case, the trip has the effect of shortening thelaminar separation bubble. When there is no bubble,transition is forced to occur sooner than it otherwisewould.

In terms of performance, the beneficial effect ofshortening the bubble and hence lowering the drag isto a some degree offset by the increased length of tur-bulent flow. The net effect can be either beneficialwhen the bubble is otherwise large or a hinderencewhen the bubble is small or not present at all. As aresult, the performance with boundary layer trips usedat low Reynolds numbers is often complex.

For the E387, the effects of the trip are clearly seenin the drag polars shown in Figs. 15 and 16. ForRe = 100,000, the drag is overall reduced due to theshortened laminar separation bubble. In the middleof the polar, the kink where the drag begins to reducewith increasing angle of attack occurs at a lower lift co-efficient (Cl ≈ 0.55) due to transition being promotedby the boundary layer trip in addition to the pressuregradient effect that is beneficial in both the clean andtripped cases.The effects of the trip are also apparent in the lift

curves.7 For the clean case at Re = 100,000, the liftcurve is offset slightly below the curves for the higherReynolds numbers. This offset is caused by a decam-bering effect that results from the added displacementthickness produced by the large bubble. When thebubble is reduced in size by using a trip, this dis-placement thickness effect is smaller, and the lift curvefor Re = 100,000 nearly coincides with the higherReynolds number cases that have smaller bubbles.For Re = 200,000 with the boundary layer trip, only

at a lift coefficient of ≈ 0.47 is the drag lower than theclean case. Thus, for this condition, the tradeoff be-tween having lower bubble drag and higher turbulentskin friction drag leads to lower net drag, while forall other points the added turbulent skin friction dragoutweighs the reduction in the bubble drag, resultingin higher drag with the trip. This tradeoff leading tohigher drag is particularly true for the higher Reynoldsnumber cases.Finally, from the lift curves presented in Ref. 7, it

is interesting to note that there is a negligible drop inthe maximum lift coefficient due to roughness effectsfor this airfoil. This results from transition occurringvery near the leading edge prior to reaching the airfoilmaximum lift coefficient. Thus, at maximum lift theflow on the upper surface for the most part behavesthe same whether or not there is a trip, and hence thestall performance has little dependence on the pres-ence of the trip. This general understanding of theconnection between the airfoil maximum lift and tran-sition, which is discussed in Ref. 18, can be used toprovide insight into the case when at stall there existsa leading edge separation bubble, which is what hap-pens at low Reynolds numbers. In such a case, theboundary layer trip can be completely or partially im-mersed in the recirculating zone of the bubble. Whenthis occurs, the airfoil stall can be quite insensitive toa discrete roughness element such as the type testedin this study.

FX 63-137

This airfoil was designed by F.X. Wortmann for theLiver Puffin human-powered aircraft. It has since been

used for many low Reynolds number applications onaccount of its high-lift, soft-stall characteristics in ad-dition to the overall good performance. In particular,in the small wind turbine arena, it has been used byAeromag (Lakota wind turbine) and Southwest Wind-power (H-40 and H-80 wind turbines) and the nowdefunct Worldpower Technologies.The original coordinates for this section as well as

several other early Wortmann sections19 are not ana-lytically smooth presumably due to a small numericalerror in the design method. As described in Ref. 20,the original coordinates were smoothed for use in com-putations, and those coordinates have been used in thisstudy.As deduced from the high camber, this airfoil should

be expected to produce considerably more lift thanthe E387. Indeed, as shown in Fig. 17, the FX 63-137produces a Cl,max of approximately 1.7. However, forRe = 100,000, the airfoil suffers the consequences of alarge laminar separation bubble. In fact at the lowerangles of attack, it is likely that the bubble does notclose on the airfoil, but instead extends into the wake.Two observations support this assumption. First, thelift curve at Re = 100,000 for low angles of attackfalls considerably below the curves for higher Reynoldsnumbers. Second, for the same low Reynolds numbercondition, the drag is quite high. At an angle of attackof approximately 4 deg, the situation improves as thebubble begins to attach to the airfoil. The lift increasesand the drag is correspondingly reduced.This airfoil along with the S822 and S834 was tested

at an intermediate Reynolds number of 150,000 toobtain more resolution in the low Reynolds numberrange where the drag changes dramatically. As seenin Fig. 17, a large drag reduction is observed for theRe = 150,000 case. Concurrent with this, the largeoffset in the lift curve is absent. Both of these obser-vations indicate a reduction in the size of the laminarseparation bubble vs. the Re = 100,000 case. Aswould be expected the performance continues to im-prove with higher Reynolds number.When boundary layer trips are applied, the perfor-

mance follows trends similar to those described for theE387. First, for Re = 100,000, the effects of the bubbleare mitigated as seen by the slight rise in the lift curveand by the reduction in drag. For the higher Reynoldsnumbers, the polars tend to collapse onto an envelope,which indicates that the flow on the upper surface issimilar indicating early transition and the absence ofa laminar separation bubble. For points that fall oneither side of this envelope, a bubble still exists.In the polars, there is an interesting trend reversal

where the drag first decreases and then increases asthe Reynolds number is increased for a fixed angle of

attack. One instance of this is seen for an angle ofattack of 4 deg corresponding to a lift coefficient ofapproximately 0.7. This same type of behavior wasseen for the E387 at an angle of attack of 1 deg (Cl ≈0.47). As previously described, there is first a dragreduction due to a shortening of the bubble and thena drag rise due to the added turbulent flow as theReynolds number is increased. This same behavior canbe indentified in the performance of all of the trippedairfoil polars.Other items to note include the following. Unlike

the E387 airfoil, the maximum lift performance ofthe FX 63-137 suffers from the addition of simulatedroughness. Overall the drop in Cl,max is 0.2. An-other difference is that while the E387 had a highlyunsteady stall leading to a sharp break, the FX 63-137exhibited a soft stall with little unsteadiness. Finally,the pitching moment curves7 unlike the E387 do notshow nearly constant Cm,c/4 over the low drag range.Instead, the nose down moment is gradually reducedwith increasing angle of attack. This behavior is mostlikely produced by two phenomenon. First, a decam-bering effect results from the displacement thicknessthat grows with increasing angle of attack and thehigher drag that results. Second, and probably moredominant, is the added aft load that results from thepressure distribution produced by the laminar separa-tion bubble. For this airfoil the bubble starts far aftand migrates toward the leading edge with angle of at-tack; whereas, for the E387 the upper surface bubblemoves over a shorter distance.

S822 AND S834

As described in Ref. 20, the S822 and S834 wereboth developed by NREL for use on small wind tur-bines and are now available under license. The S822airfoil has been used on the AOC/Windlite and Hava-tex21 small wind turbines. Briefly, the S822 and S834were designed for the outer blade span of rotors hav-ing diameters in the range 3–10 meter and 1–3 meter,respectively. The newer S834 was designed for low-noise, which was not a consideration in the design ofthe S822 section.The performance of these airfoils is shown in

Figs. 19, 20, 21, and 22. Many of the general char-acteristics previously described are exhibited by thesetwo airfoils. Differences in the details are of course dic-tated by the associated design goals that collectivelylead to the resulting performance discussed below.For both airfoils, an often characteristic high-drag

knee in the drag polar due to the presence of a lam-inar separation at the lower Reynolds numbers is ob-served. The associated nonlinearities (offsets) in thelift curves are also seen, except for these airfoils, as

compared with the Wortmann section, the offsets oc-cur for Re = 100,000 and 150,000 as well as 200,000 toa slight extent. This behavior is also reflected in thedrag polars where the high-drag knee is more exagger-ated than that for the FX 63-137.Adding the zigzag boundary layer trips to both air-

foils yields lower drag at the lower Reynolds numbersas would be expected from the past cases examined.Also, as would be expected, the nonlinearities seen inthe lift curves are mitigated somewhat by the bound-ary layer trips. However, the boundary layer trip onthe upper surface is not large enough to completelyeliminate the bubble for Re = 100,000 where over a2 deg range in the middle of the polar the lift increasesnonlinearly (∆Cl ≈ 0.5) for both airfoils.

The S834, being designed for smaller rotors, wasdesigned for lower Reynolds numbers. This trend isapparent in the drag polars where it is observed thatthe S834 has better performance than the S822 at lowReynolds numbers. The differences are mostly slightas one might expect from the similarities in the geome-tries and pressure distributions.7

For both airfoils, unsteadiness at stall prevented tak-ing high angle of attack data for Re = 500,000. Thedegree of the unsteadiness during the tests was ob-served to be somewhat less than that for the E387.

SD2030This Selig/Donovan airfoil presented in Ref. 17 was

originally designed for model sailplanes. It has sincebeen used on the Southwest Windpower Air 403 andAir X small wind turbines. Figures 23 and 24 showthe performance characteristics.As compared with the other airfoils discussed, this

airfoil has quite low drag at the expense of a nar-rower drag polar. A high-drag knee is present forRe = 100,000; however, the peak drag at the kink ismuch lower than that seen for the other airfoils tested.This low drag is achieved by having a long transitionramp, or “bubble ramp,”17 that leads to a thin laminarseparation bubble. The causes for other general effectsseen in the figures have been previously explained.Of the six airfoils tested, this airfoil displayed the

most unsteadiness in stall, and this limited the angleof attack range for the Re = 500,000 case.

SH3055The Selig/Hanley airfoil (see Figs. 25 and 26), de-

rived from prior SH/Bergey designs, is intended fora 7-meter diameter variable-speed wind turbine to bemanufactured by Bergey WindPower, Co. For the low-est Reynolds number case (Re = 100,000), there is aconsiderable drop in lift as compared with the higherReynolds number cases. This drop and associated highdrag is likely caused by a laminar separation bubble

that does not reattach to the airfoil over the major-ity of the lift range. Moreover, at the lowest angles ofattack tested, it is speculated that the lower surfaceof the airfoil is stalled as well, which further decam-bers the section. For the higher Reynolds numbers,the performance improves as was seen with past ex-amples. Boundary layer trips applied to the airfoillead to improved performance for Re = 100,000, butat higher Reynolds numbers the performance is mostlyhandicapped as has been observed with the other sec-tions. Finally, for this airfoil, the stall behavior wasquite gentle.

SUMMARY

An extensive database of performance characteris-tics on several low Reynolds number airfoils applicableto small wind turbines has been documented and dis-cussed. Prior to the collection of these data, an exten-sive wind tunnel flow quality study was performed tovalidate the test environment. Moreover, the data ac-quisition and reduction procedures were validated bycomparing UIUC data on the E387 airfoil with thattaken at NASA Langley. These data compliment acompanion study that focused on the aeroacoustics ofthese airfoils. Collectively the performance data pre-sented in this paper and the related aeroacoustic datashould aid designers in balancing the tradeoffs betweenrotor noise and performance.

ACKNOWLEDGEMENTS

The authors wish to thank Dr. Paul Migliore, tech-nical monitor, of the National Renewable Energy Lab-oratory for his helpful input and guidance during thecourse of this research. Also, Yvan Tinel, Tinel Tech-nologies, is thanked for his skillful and meticulouswork in making the six wind tunnel models presentedin the study. Appreciation is extended to Dr. AndyP. Broeren and Biao Lu (UIUC) for their assistance inhelping take the tunnel flow quality data. Finally, adebt of gratitude is owed to Benjamin A. Broughton(UIUC) for his dedication in helping to ensure thequality of the data acquisition and reduction method-ology used to obtain the performance data which formsthe central core of this work.

REFERENCES1Oerlemans, S., “Wind Tunnel Aeroacoustic Tests of Six

Airfoils for Use on Small Wind Turbines,” NREL SR-500-34470,2003.

2Selig, M. S., Guglielmo, J. J., Broeren, A. P., and Giguère,P., Summary of Low-Speed Airfoil Data, Vol. 1, SoarTech Pub-lications, Virginia Beach, Virginia, 1995.

3Lyon, C. A., Broeren, A. P., Giguère, P., Gopalarathnam,A., and Selig, M. S., Summary of Low-Speed Airfoil Data, Vol. 3,SoarTech Publications, Virginia Beach, Virginia, 1998.

4Guglielmo, J. J. and Selig, M. S., “Spanwise Variations inProfile Drag for Airfoils at Low Reynolds Numbers,” Journal ofAircraft, Vol. 33, No. 4, July–August 1996, pp. 699–707.

5Evangelista, R., McGhee, R. J., and Walker, B. S., “Corre-lation of Theory to Wind-Tunnel Data at Reynolds Numbersbelow 500,000,” Low Reynolds Number Aerodynamics, editedby T. J. Mueller, Vol. 54 of Lecture Notes in Engineering,Springer-Verlag, New York, June 1989, pp. 131–145.

6McGhee, R. J., Walker, B. S., and Millard, B. F., “Experi-mental Results for the Eppler 387 Airfoil at Low Reynolds Num-bers in the Langley Low-Turbulence Pressure Tunnel,” NASATM-4062, October 1988.

7McGranahan, B. D. and Selig, M. S., “Wind Tunnel Aero-dynamic Tests of Six Airfoils for Use on Small Wind Turbines,”NREL report in preparation, 2004.

8W. H. Rae, Jr. and Pope, A.,Low-Speed Wind Tunnel Testing, John Wiley and Sons,New York, 1984.

9Bragg, M. B. and Lu, B., “Experimental Investigation ofAirfoil Drag Measurement with Simulated Leading-Edge Ice Us-ing the Wake Survey Method,” AIAA Paper 2000-3919, August2000.

10Briley, R. W. and McDonald, H., “Numerical Predictionof Incompressible Separation Bubbles,” Vol. 69, No. 4, 1975,pp. 631–656.

11Kwon, O. K. and Pletcher, R. H., “Prediction of Incom-pressible Separated Boundary Layers Including Viscous-InviscidInteraction,” Transactions of the ASME, Vol. 101, December1979, pp. 466–472.

12Davis, R. L. and Carter, J. E., “Analysis of Airfoil Transi-tional Separation Bubbles,” NASA CR-3791, July 1984.

13Walker, G. J., Subroto, P. H., and Platzer, M. F., “Transi-tion Modeling Effects on Viscous/Inviscid Interaction Analysisof Low Reynolds Number Airfoil Flows Involving Laminar Sep-aration Bubbles,” ASME Paper 88-GT-32, 1988.

14Huebsch, W. W. and Rothmayer, A. P., “The Effects ofSmall-Scale Surface Roughness on Laminar Airfoil-Scale Trail-ing Edge Separation Bubbles,” AIAA Paper 98-0103, January1998.

15Alam, M. and Sandham, N. D., “Direct Numerical Simu-lation of ‘Short’ Laminar Separation Bubbles with TurbulentReattachment,” Journal of Fluid Mechanics, Vol. 403, 2000,pp. 223–250.

16Lin, J. C. M. and Pauley, L. L., “Low-Reynolds-NumberSeparation on an Airfoil,” AIAA Journal, Vol. 34, No. 8, 1996,pp. 1570–1577.

17Selig, M. S., Donovan, J. F., and Fraser, D. B., Airfoils atLow Speeds, Soartech 8, SoarTech Publications, Virginia Beach,Virginia, 1989.

18Somers, D. M., “Subsonic Natural-Laminar-Flow Airfoils,”Natural Laminar Flow and Laminar Flow Control, edited byR. W. Barnwell and M. Y. Hussaini, Springer-Verlag, New York,1992, pp. 143–176.

19Althaus, D. and Wortmann, F. X.,Stuttgarter Profilkatalog I, Friedr. Vieweg & Sohn, Braun-schweig/Weisbaden, 1981.

20Somers, D. M. and Maughmer, M. D., “Theoretical Aero-dynamic Analyses of Six Airfoils for Use on Small Wind Tur-bines,” NREL SR-500-33295, October 2003.

21Vick, B. D. and Clark, R. N., “Testing of a 2-KilowattWind-Electric System for Water Pumping,” WINDPOWER,Palm Springs, CA, May 2000.

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

Cd

Cl

Re = 100,000

Re = 200,000

Re = 300,000

Re = 350,000

Re = 460,000

Re = 500,000

E387 (E)

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

2.0

α (deg)

Cl

Fig. 15 Drag polar for the E387 (E).

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

Cd

Cl

Re = 100,000

Re = 200,000

Re = 350,000

Re = 500,000

E387 (E)u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c = 0.11%)

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

2.0

α (deg)

Cl

Fig. 16 Drag polar for the E387 (E) with trip type F.

0.00 0.01 0.02 0.03 0.04 0.05 0.0

0.5

1.0

1.5

2.0

Cd

Cl

Re = 100,000

Re = 150,000

Re = 200,000

Re = 350,000

Re = 500,000

FX 63−137 (C)

−10 0 10 20 0.0

0.5

1.0

1.5

2.0

2.5

α (deg)

Cl

Fig. 17 Drag polar for the FX 63-137 (C).

0.00 0.01 0.02 0.03 0.04 0.05 0.0

0.5

1.0

1.5

2.0

Cd

Cl

Re = 100,000

Re = 150,000

Re = 200,000

Re = 350,000

Re = 500,000

FX 63−137 (C)u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c = 0.11%)

−10 0 10 20 0.0

0.5

1.0

1.5

2.0

2.5

α (deg)

Cl

Fig. 18 Drag polar for the FX 63-137 (C) with trip type F.

0.00 0.01 0.02 0.03 0.04 0.05−1.0

−0.5

0.0

0.5

1.0

1.5

Cd

Cl

Re = 100,000

Re = 150,000

Re = 200,000

Re = 350,000

Re = 500,000

S822 (B)

−10 0 10 20−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

α (deg)

Cl

Fig. 19 Drag polar for the S822 (B).

0.00 0.01 0.02 0.03 0.04 0.05−1.0

−0.5

0.0

0.5

1.0

1.5

Cd

Cl

Re = 100,000

Re = 150,000

Re = 200,000

Re = 350,000

Re = 500,000

S822 (B)u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c = 0.11%)

−10 0 10 20−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

α (deg)

Cl

Fig. 20 Drag polar for the S822 (B) with trip type F.

0.00 0.01 0.02 0.03 0.04 0.05−1.0

−0.5

0.0

0.5

1.0

1.5

Cd

Cl

Re = 100,000

Re = 150,000

Re = 200,000

Re = 350,000

Re = 500,000

S834

−10 0 10 20−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

α (deg)

Cl

Fig. 21 Drag polar for the S834.

0.00 0.01 0.02 0.03 0.04 0.05−1.0

−0.5

0.0

0.5

1.0

1.5

Cd

Cl

Re = 100,000

Re = 150,000

Re = 200,000

Re = 350,000

Re = 500,000

S834u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c = 0.11%)

−10 0 10 20−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

α (deg)

Cl

Fig. 22 Drag polar for the S834 with trip type F.

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

Cd

Cl

Re = 100,000

Re = 200,000

Re = 350,000

Re = 500,000

SD2030 (B)

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

2.0

α (deg)

Cl

Fig. 23 Drag polar for the SD2030 (B).

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

Cd

Cl

Re = 100,000

Re = 200,000

Re = 350,000

Re = 500,000

SD2030 (B)u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c = 0.11%)

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

2.0

α (deg)

Cl

Fig. 24 Drag polar for the SD2030 (B) with trip type F.

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

2.0

Cl

Re = 100,000

Re = 200,000

Re = 350,000

Re = 500,000

SH3055

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

2.0

2.5

Cl

Fig. 25 Drag polar for the SH3055.

0.00 0.01 0.02 0.03 0.04 0.05−0.5

0.0

0.5

1.0

1.5

2.0

Cl

Re = 100,000

Re = 200,000

Re = 350,000

Re = 500,000

SH3055u.s.t.: x/c = 2%, l.s.t.: x/c = 5%Zigzag Type F (h/c = 0.11%)

−10 0 10 20−0.5

0.0

0.5

1.0

1.5

2.0

2.5

Cl

Fig. 26 Drag polar for the SH3055 with trip type F.