An Overview of NACA 6-Digit Airfoil Series Characteristics with Reference to Airfoils for Large Wind

13 Pages·2009·0.3 MB·English

AIAA 2009-268
47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition
5 - 8 January 2009, Orlando, Florida
An overview of NACA 6-digit airfoil series characteristics
with reference to airfoils for large wind turbine blades.
W.A.Timmer1
DelftUniversityWindEnergyResearchInstitute,DUWIND,TheNetherlands
[Abstract]ThispaperinvestigatestheNACA63and646-digitseriesofairfoilstestedin
the NACA LTPT in view to verify the RFOIL calculated airfoil characteristics for high
Reynolds numbers. Some anomalies in the zero-lift angles of 15% and 18% thick airfoils
from these series are identified, both in the airfoil clean case and in case of wrap-around
roughness. It is found that RFOIL predicts the maximum lift coefficient at a Reynolds
numberof3 millionwell,butconsistentlyunderpredictstheC forReynoldsnumbersof
l,max
6 and 9 million. It is, however, based on other comparisons at high Reynolds numbers
unclearifthisisduetoaninabilityofthepredictioncodeortoadeviationinthetestresults.
The drag coefficient is under predicted with about 9% for a wide range of airfoils and
Reynolds numbers. Due to wrap-around roughness the maximum lift coefficient decreases
with18%to20%.
Nomenclature
(cid:1) = angleofattack(degr.)
C = liftcoefficient
l
C = designliftcoefficient
l,i
C = maximumliftcoefficient
l,max
C = dragcoefficient
d
c = airfoilchord
i = indicationofdesignlift
M = Machnumber
n = amplificationfactorinRFOIL
Re = Reynoldsnumber
I. Introduction
I
In the beginning of the revival of wind energy as an energy source in the seventies of the last century, NACA
airfoils were adopted for wind turbine blades as a result of the availability of two-dimensional aerodynamic
characteristics,evenforairfoilswithafairlylargerelativethickness.TheNACAfourandfive-digitserieswerelater
onabandonedfortheirsensitivitytoroughness,butairfoilsfromtheNACA63and64six-digitseriesarestillbeing
usedinwindturbinebladestoday.
Since the seventies special wind turbine dedicated airfoil designs have found their way to blade and turbine
manufacturers. ManyofthesedesignswereexperimentallyverifiedinwindtunnelsuptoReynoldsnumbersof3to
4million.
With the present trend towards very large turbines the Reynolds numbers have grown to about 10 million.
Testingatthese highReynoldsnumbersisveryexpensive since thisrequiresa large atmospheric tunnel, a pressure
tunneloracryogenictunnel.Forallthreetypesoffacilitiesafairlyexpensivemodelisneededaswell.Thisleadsto
the situation that little experimental data is available for existing wind turbine dedicated airfoils at Reynolds
numbers higher than 4 million. Blade designers now have to rely on the predictive value of airfoil analysis codes
suchasXFOILorNavier-Stokessolvers.
Since the NACAairfoils we are discussing here were tested atReynoldsnumbersup to 9 millionthese data canbe
used to verify the accuracy of the prediction codes and even a renewed interest for these airfoils may be noticed
amongwindturbineblademanufacturers.
1Assistantprofessor,TUDelft,FacultyofAerospaceEngineering,Kluyverweg1,2629HSDelft,TheNetherlands
1
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Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
The designand testingofthe NACA airfoilssome 70 years ago wasa tremendous effort and rendered valuable
informationto manyaerodynamicistsworld wide.However, whenusingitforverification, we have totakeacloser
look at the various test results. It appears that some anomalies in the data can be detected, which invites us to
criticallyinvestigatealltherelevantdata.
In this paper the accuracy of these NACA measurements will be discussed and comparisons will be made with
calculationsanddatafromotherfacilities.
II. MeasurementsintheLangleyLTPT
A.Models
The measurements of the well known NACA airfoils1 were performed in the Langley low-turbulence pressure
tunnel.Thisisapressuretunnelwithacontractionratioof20:1andatestsectionof3x7.5feet(0.914mx2.29m).
The two feet (0.61 m) chord models were made of laminated mahogany. The model surface was painted with
lacquer and sanded with no. 400 carborundum paper. The models completely spanned the three feet test section
width. The maximum test section velocity at atmospheric pressure was about 130 m/s. The measurements had a
maximumMachnumberof0.17.
The airfoils considered here are airfoils from the 63 and 64 series designed in the forties of the last century. The
shapeoftheseairfoilsisformedbythevariousthicknessdistributionsandfractionsofthea=1camberline.
B.Testsetup
The lift coefficient was determined using the difference of the pressure reaction upon the tunnel floor and
ceiling. To this end pressure orifices are located over a length of 13 feet (3.96 m) on both floor and ceiling. Since
this doesnotcover the entire pressure footprintof the model(whichtheoreticallyextendsto infinityboth upstream
and downstream of the model) a lift efficiency factor was calculated which gives the ratio of measured lift to the
actuallift,dependingonthebasicmean-lineloadingoftheairfoil.
The drag coefficient was determined by integrating the total pressure loss in the wake, measured with a rake.
Assumingthestaticpressureisconstantacrossthewakeandassumingthevariationofthetotalpressureinthewake
can be represented by a normal probability curve, the uncorrected drag was calculated using the static pressure
coefficientandthemaximumtotalpressurelossinthewake.
C.Windtunnelwallcorrections
To the lift and drag coefficients the basic corrections for blockage and lift interference have been applied, as given
byAllen&Vincenti2.
1.5 1.5
c c
l l
1.0 1.0
0.5 0.5
Re=3.0x106
0.0 0.0
NACA63-618
NACA63-418
-0.5 -0.5
NACA63-218
NACA63-018
-1.0 -1.0
0.000 0.008 0.016 0.024 -10 0 10 20
c (cid:1)(o)
d
Figure1. Theeffectofcamberonthecharacteristicsofan18%thickairfoilfromtheNACA636-digitseries
ataReynoldsnumberof3x106.Forclaritytheindicesintheairfoildesignationshavebeenomitted.
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III. Two-dimensionalaerodynamiccharacteristics
The characteristics for the various airfoils presented here are digitized curves taken from reference 3, since this
reportgivesthelargestandclearestgraphsofthemeasureddata.
A. Liftcurves
In figure 1 the characteristics are depicted of the 18% thick airfoil with the 63-series thickness distribution and
with different camber lines derived from the a=1 camber line distribution. Due to the increased camber the lift
curves shift to higher lift values at the same angle of attack and the low-drag buckets in the left hand graph shift
alonganenvelopwithamoreorlessconstantminimumdragcoefficient.
1.5 1.5
c c
l l
1.0 1.0
0.5 NACA643-x18 0.5
Re=6.0x106
0.0 0.0
64-018
64-218
-0.5 -0.5
64-418
64-618
-1.0 -1.0
0.000 0.008 0.016 0.024 -10 0 10 20
c (cid:1)(o)
d
Figure2a.Theeffectofcamberonthecharacteristicsofan18%thickairfoilfromtheNACA646-digitseries
ataReynoldsnumberof6x106.
1.6 1.6
c
c l
l
1.2 1.2
0.8 0.8
NACA64 -x18
0.4 3 0.4
Re=9.0x106
64-018
0.0 0.0 64-218
64-418
64-618
-0.4 -0.4
-0.8 -0.8
0.000 0.008 0.016 0.024 -10 0 10 20
c (cid:1)(o)
d
Figure2b.Theeffectofcamberonthecharacteristicsofan18%thickairfoilfromtheNACA646-digitseries
ataReynoldsnumberof9x106.
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Thegraphsinthe figures2aand2bshowbasicallythe sameaerodynamicbehaviorasin figure1, nowforthe18%
thick airfoil from the NACA 64 series. However the lift curves are not equally spaced. If we studythis in terms of
the zero-lift angle of attack (see figure 3) we see a distinct difference in values for the different design lift
coefficients. Also plotted in the graph are the calculated values using RFOIL4, a modified version of XFOIL and a
measured value fromreference 5.The RFOILcalculationswere performed witha non-linear amplification scheme,
which has an effect on the drag coefficient at the upper end of the low-drag region and consequently on the
predictedmaximumlift-dragratiooftheairfoil.
1
Designliftcoefficient,Cl,i
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
ees) -1 NARCeA=66x4130-x618
gr
e
d
gle( -2
n
a
o-lift
Zer -3 Inviscid
RFOIL
NACA
-4
Ref.5
-5
Figure3.Thezero-liftangleforan18%thickairfoilfromtheNACA64serieswithdifferentdesignlift
coefficients.Re=6x106.
Itmustbenotedthatwhathereiscalleddesignliftcoefficientdiffersfromthecommonlyuseddefinition,beingthe
lift coefficient at which the maximum lift-drag ratio occurs. Here the design lift coefficient is derived from the
fractionoftheunitcamberlineandroughlygivesthemiddleofthelow-dragbucket.
Since the thickness distribution of the airfoils is the same and the camber line is formed by taking fractions of the
sameunitcamberlinethezero-liftanglesessentiallyformastraightline.Thisistruefortheinviscidvalues,butalso
for the angles calculated with RFOIL. The boundary-layer thickness de-cambers the airfoil, giving zero-lift angles
closer to zero relative to the inviscid values. Since with increasing camber the upper surface adverse pressure
gradients increase, giving thicker boundary layers, the distance between the inviscid and viscid curves grows with
increasing C . Figure 3 shows that the measured zero-lift angle of NACA 64-618 is too small (about 0.4 degrees)
l,i
compared to the theoretical value. As this difference occurs at every Reynolds number tested, it is most likely
causedbytheorientationofthemodelinthetestsection.Figure4showsthemeasuredliftcurvecorrectedwith-0.4
degreesrelativetoRFOILcalculation.
1.6 1.6
cl cl
1.2 1.2
0.8 0.8
0.4 NRAeC=A66.403x-160168 0.4 NACA-0.4degr.
RFOIL
0.0 0.0
0.000 0.005 0.010 0.015 0.020 -20 -15 -10 -5 0 5 10 15 20
-0.4 cd -0.4 (cid:1)(o)
-0.8 -0.8
-1.2 -1.2
Figure4. ThemeasuredperformanceofairfoilNACA64 -618atRe=6x106relativetothecalculationsafter
3
modificationofthezero-liftanglewith-0.4degrees.
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B.Definitionofairfoilchord.
Another possible source for differences between theoretical zero-lift values and the measurements is the
definitionofthechord.IntheNACAtraditiontheshapeoftheairfoilistheresultofacamberlinecombinedwitha
thicknessdistribution.Infigure5theprocedureismadevisible,apartfromtheinsertionofanosecircletodefinethe
noseregionwithmorepoints.Withthisschemeitislikelythattheairfoilleadingedgeprojectsforwardofthey-
7.5
y(%)
5
Yt(thicknessordinate)
camberline
2.5
(cid:3)
0
-5 0 x 5 10 x(%) 15
xu=x-yt*sin(cid:3)
-2.5 xL=x+yt*cos(cid:3)
-5
-7.5
Figure5.TheNACA-proceduretoestablishtheairfoilco-ordinates
axis. The airfoil should be redefined, with the chord now connecting the leading edge and the trailing edge (the
longestdistance).
Reference 2 refers to the chord as being the original x-axis for the camber distribution. Would this definition be
maintainedinthewindtunnelthanthezero-liftanglewouldbedifferentrelativetotheredefinedairfoilshapeonthe
longest distance. On the other hand, if the unmodified originally calculated coordinates would be fed to a program
like XFOIL, the characteristicsare calculated relative to the originalchord. Since the originalchord for the camber
lineishardtofindintheactualwindtunnelmodel,itisassumedthatallmeasurementsareperformedrelativetothe
right(longest)chord.
1.6 1.6
c c
l l
1.2 1.2
0.8 0.8
NACA63 -615
2
0.4 0.4
Re=6.0x106
0.0 0.0
Roughnessoff
-0.4 -0.4
Roughnesson
-0.8 -0.8
0.000 0.008 0.016 0.024 -10 0 10 20
c (cid:1)(o)
d
Figure6.Theeffectofwrap-aroundroughnessonthecharacteristicsofairfoilNACA63 -615atRe=6x106.
2
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C.Zero-liftangleinrelationtoroughness.
Figure 6 depicts the characteristics of the NACA 63 -615 airfoil with and without NACA standard roughness.
2
According to this graph up to 8 degrees angle of attack the airfoil shows improved lift performance due to wrap-
around roughness. Unfortunatelythiscannotbe true. Figure 7 providesa closer lookatthe zero-liftanglesrelative
tothosefor15%thickairfoilsfromthe63-serieswithdifferentdesignliftcoefficients.
1
Designliftcoefficient,C
l,i
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
s)
ee -1 NACA63-x15
egr Re=6x106
d
(
gle -2
n
a
o-lift -3
er Roughness
Z
Clean
-4
RFOIL
-5
Figure7.Theeffectofwrap-aroundroughnessonthezero-liftanglesfor15%thickairfoilsinthe
NACA63-series
The figure shows the trend in zero-lift angles and clearly the ones for a design lift coefficient of 0.6 do not follow
thetrendlines.
In the roughness off case the zero-lift angle should lie around -4.27o while -3.44o was measured. In the rough
situation-4.78owasmeasured,whereasthetrendlineindicatesavalueof-3.75o.
1.6 1.6
c c
l l
1.2 1.2
0.8 0.8
NACA63 -615
2
0.4 0.4
Re=6.0x106
0.0 0.0
Roughnesson
-0.4 -0.4 Roughnessoff
RFOIL
-0.8 -0.8
0.000 0.008 0.016 0.024 -10 0 10 20
c (cid:1)(o)
d
Figure8.ThecleanandroughperformanceofairfoilNACA63-615aftermodificationofthezero-liftangles.
RFOILcalculationswithn=9
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Figure 8 depicts the situation after modification of the zero-lift angles. Also in the graph the RFOIL calculated
performance of the airfoil. The picture shows a good match of the theoretical and experimental lift curves and the
expectedlowercalculateddragcoefficient(about9%to10%)intheairfoilsmoothconfiguration.
1.5 1.5
c c
l l
1.0 1.0
0.5 0.5
RFOIL
NACA64 -018
3 positiveangles
Re=6.0x106
negativeangles
0.0 0.0
0.000 0.008 0.016 0.024 0 8 16 24
c (cid:1)(o)
d
Figure9.Thedifferencebetweentheliftanddragcoefficientsofasymmetricairfoilatpositiveandnegative
anglesofattack.
D.Maximumliftvalues
The maximum lift coefficient is important in view of the maximum static loads on the blade. The experimental
value of C depends on the tunnel test section turbulence, the model blockage in terms of the model chord -
l,max
tunnel height ratio in combination with the wind tunnel wall correction scheme and the accuracy and state of the
wind tunnel model. As an example figure 9 gives the measured performance of the airfoil NACA 64 -018 at a
3
Reynoldsnumberof6x106.Thefiguredemonstratesacleardifferenceintheexperimentalmaximumliftcoefficients
whereas one would expect the lift curves for the positive and negative angles of this symmetric airfoil to coincide.
The lift curve in the graph has been corrected for a 0.11 degrees zero lift angle offset. In general these differences
canbeattributedtodifferencesinthemodelupperandlowersurfacecontours(especiallyintheleadingedgeregion)
oranaberrationintheangleofattacksettingmechanism.
1.7
NACA64-i18
1.6
nt
e
ci
effi
o
c
lift1.5
m
u
m
axi negativeangles
M NACARe=6x10E6
1.4
RFOILRe=6x10E6
NACARe=9x10E6
RFOILRe=9x10E6
positiveangles
1.3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Designliftcoefficient
Figure10.Themeasuredandcalculatedmaximumliftcoefficientsfor18%thickairfoilsfromthe
NACA646-digitseries.RFOILcalculationswithn=9
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Inthiscase there isa 0.09difference invalue ofthe maximumliftcoefficients. Withoutanyadditionalinformation
one would not know what value to pick, the more since the calculated curve gives a value more or less in between
thetwovalues,albeitatadifferentangleofincidence.
Thenextpictureshowsusthatthemostlikelyvalueinthiscaseistheonefromthenegativeanglesofattack.Figure
10givesthemeasuredandRFOILcalculatedmaximumliftcoefficientsfortheNACA64-i18seriesattheReynolds
numbers of 6x106 and 9x106. The calculated values are consistently lower with a 3.5% difference at a Reynolds
numberof6x106.ForthehigherReynoldsnumberthedifferencebetweencalculatedandexperimentalmaximumlift
coefficientincreaseswithincreasingdesignliftcoefficienttoabout6.5%fortheNACA64-618.Adversely,figure4
showsanoverpredictionofthemaximumliftcoefficientatnegativeangles.
Inthe public domain no experimentaldata canbe found to compare withthe LTPT measurementsatthese high
Reynoldsnumbers. ForRe=3x106datafromthelow-speed windtunnelinStuttgart,Germanycanbe used6. Figure
11 shows the lift curves of three NACA airfoils from the 63 series measured in both wind tunnels. In the German
wind tunnel the lift was also derived fromthe wall pressures. The Stuttgart maximum lift coefficients appear to be
consistentlylower, for the non-symmetric airfoilsabout6.5%compared to the LTPT data.The RFOILcalculations
matchtheLTPTmaximumliftwellatRe=3x106.
1.5 1.5 1.5
cl cl cl
1.0
1.0 1.0
0.5 Stuttgart LTPT
NACA63-018 0.5 LTPT 0.5 Stuttgart
RFOIL RFOIL
0.0
-20.0 -10.0 0.0 10.0 20.0
(cid:1)(degr.) 0.0 0.0
-0.5 -10.0 0.0 10.0 20.0 -10.0 0.0 10.0 20.0
(cid:1)(degr.) (cid:1)(degr.)
Stuttgart
-0.5 -0.5
-1.0 LTPT
RFOIL NACA63-418 NACA63-421
-1.5 -1.0 -1.0
(a) (b) (c)
Figure11.AcomparisonofNACA-airfoilliftmeasurementsintheLTPTandthelow-speedtunnelofthe
IAGStuttgart6.Re=3x106.
ComparingtheRFOILcalculationswiththeLTPTmeasurements,itseemsthat,withrespecttothemaximumlift
coefficient,thepredictivevalueofthecalculationsforthistypeofairfoilsdecreaseswithincreasingReynolds
number.Asmentionedbefore,therearelittledataavailabletoserveasacheck.Measurementscomingclosestare
theonesperformedinthecryogenicwindtunneloftheDNW-KKKinCologne,Germany7onthe30%thickairfoil
DU97-W-300Mod.Figure12showsthemaximumliftcoefficientsofthisairfoilmeasureduptoaReynoldsnumber
of10x106atvariousMachnumbers.Alsointhegraphthecalculatedmaximumliftcoefficientsattwodistinct
valuesoftheamplificationfactorn,toshowthedifferenceforasituationwithincreasedturbulence(n=5),sincethe
coolingofthetunnelgasnecessarytoreachthehighReynoldsnumbersinducesahigherturbulenceintensity.The
modificationtothebaseairfoilconsistedofareductionofthetrailingedgethicknessfrom1.74%cto0.49%c,
whichresultedinasmallreductionoftheliftcoefficients.Thelow-turbulencetestsresultsofthebaseairfoilare
shownaswell.ThiscomparisonshowsanoverpredictionoftheC bytheRFOILcalculations(withtheMach
l,max
numbersetto0.2),whentheusualamplificationfactorn=9isused.However,whentheincreasedturbulenceinthe
testsectionisaccountedfor,thecalculatedmaximumvaluesmatchthetunneldataquitewell.Ofcourseonecould
questionthefactthattherightturbulenceintensityisrepresentedbyn=5,howeverthefigureshowsthatusing
RFOILnotnecessarilyleadstounderpredictionofthemaximumliftcoefficientatthehigherReynoldsnumbers.
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IfandtowhatextenttheRFOILcodefailstopredicttherightmaximumliftcoefficientremainsinconclusivefrom
theforegoing.
1.8
C
l,max
Baseairfoil,Delft
1.6
RFOIL,n=9
RFOIL,n=5
1.4
1.2
KKK,M=0.1
Du97-W-300Mod
KKK,M=0.2
1.0
0 2 4 6 8 10 12
Rex10-6
Figure12.ThevariationofthemaximumliftcoefficientswithReynoldsnumberasmeasuredandcalculated
forairfoilDU97-W-300Mod.
E.Airfoildrag
Thefigures4,8and9havealreadyshownthatthedragcoefficientpredictedbyXFOIL/RFOILisconsistently
lowercomparedtothemeasurements.Figure13showsthemeasuredandRFOILpredicteddragcharacteristicsof
airfoilNACA64-618forReynoldsnumbersof3x106and9x106.Thepredicteddragcoefficienthasbeenmultiplied
byafactorof1.09.
1.5 1.5
c c
l l
1.0 1.0
RFOIL
NACALTPT
0.5 0.5
NACA64 -618
3
Re=9.0x106
0.0 0.0
Re = 3x106
-0.5 -0.5
0.000 0.008 0.016 0.024 0.000 0.008 0.016 0.024
c C
d d
Figure13.TheRFOILpredicteddragcoefficient(multipliedbyafactorof1.09)comparedtotheLTPTwind
tunnelmeasurements.
Thefigureshowsthatthereisagoodmatchbetweenthepredicteddragdatawitha9%increaseandthewindtunnel
data.Infactthisfactorof1.09tomatchtheexperimentalvaluesisapplicabletothepredicteddragofmostairfoils
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and-asfigure13shows–inarelativelybroadReynoldsnumbersrangeaswell.TheLTPTdragdataarefoundto
beingoodagreementwithdatafromothersources.AtthelowerendofthelowdragregionRFOILseemstopredict
afastertransitionshifttowardsthelowersurfaceleadingedgeastheangleofattackisreduced.Itcanbeconcluded
that,usinga9%higherdragcoefficient,RFOILmaybeusedforpredictionofthedragandthemaximumlifttodrag
ratioofairfoilsinthecleanconfigurationatReynoldsnumbersupto9x106.
F.Roughnesseffects
Thecontaminationofrotorbladescansometimesbesignificant.Thedegreeofcontaminationmayvary,depending
ontheturbinelocationandthetimeoftheyear.Airfoilsarechosenfortheirlowsensitivitytoroughnesseffects,but
unfortunatelythedegradationinperformanceduetoacontaminatedleadingedgeisdifficulttopredict.Simply
specifyingafixedtransitionlocationneartheairfoilleadingedgewillnotdo,sincethisdoesnotincorporatethe
increaseinboundarylayerthicknessandmomentumlossduetotheroughnesselementscausingthetransition.The
effectontheairfoilperformanceofroughnesselementsistypicallysomethingthatcanbestudiedduringwind
tunneltests.Inmanyexperimentszigzagtapeisusedtotriptheboundarylayeranddependingonthelocationand
thethicknessofthetapethisgivesafairlygoodideaofthesensitivityoftheairfoiltoprematuretransition.
However,inrealitythingsmaybeevenworsethantheconfigurationwithzigzagtape.TheNACAtestswithwrap-
aroundroughnessmaybeconsideredasaworstcasescenario. Figure14givestheperformanceoftheairfoilsof
figure2awithNACAstandardroughnessconsistingofno.60gridroughnesswrappedaroundtheleadingedgefrom
thelowersurface8%chordstationtotheuppersurface8%station.
1.5 1.5
c c
L L
1.0 1.0
0.5 NACA64-x18 0.5
Re=6.0x106
gridroughness
0.0 0.0
64-018
-0.5 -0.5 64-218
64-418
64-618
-1.0 -1.0
0.00 0.01 0.02 0.03 -20 -10 0 10 20 30
c (cid:1)(o)
d
Figure14.TheeffectofNACAstandardroughnessfora18%thickNACA64seriesairfoilwithvarious
designliftcoefficients.
Comparedtothecleansituationnotonlythedraghasincreasedconsiderably,butduetotheroughnesstheairfoils
sufferfromasignificantlossinmaximumliftcoefficient.
Figure15depictsthevariationofmaximumliftwiththemaximumairfoilthicknessforthe64-4xxseriesbothinthe
cleansituationandinthecaseofNACAstandardroughness.Itappearsthatduetotheroughnessthelossin
maximumliftamountsto18-20%.
Theliftcurvesinfigure14donotshowaregularincreasewithincreasingcamber.Thezero-liftanglesdepictedin
figure16showadeviatingvalueforNACA64-418.Accordingtothemeasurementsthezero-liftangleis-3.01
degrees,whereasthetrendlineindicatesavalueof-2.47,adifferenceof0.54degrees.
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