1. No category

SECURITY
—.-
INFORMATION
—~
COPY T! 7
L .“.i
RM A52E01
.
——. . .-.
.- .
.—— ..-.
-.
-
.—--
-“
RESEARCHMEMORANDUM
EFFECTS OF THREE TYPES OF BLUNT TRAILING EDGES ON THE
AERODYNAMIC
CHARACTERISTICS OF A PLANE TAPERED WING
OF ASPECT RATIO 3.1,WITH A 3-PERCENT-THICK
BICONVEX SECTION
By DuaneW. Dugan
Laboratory
Ames Aeronautical
Moffett
Field,Calif.
NATIONAL ADVISORY COMMITTEE
FOR AERONAUTICS
2/’ 9 %0’4?
WASHINGTON
Jdy 22, 1952
‘
TECHLIBRARYKAFB,NM
Il!lllllllullllllillllllll
“-’-—
il14i7nz
G
lC
F
NACARM A52E01
NATIONAL
A.
DVISORY
COMMITTEE
FOR AERONAUTICS
.
RESEARCH
MEMORANDUM
EFFECTS
OF THREETYPESOF BLUNTTRAILING
EDGESON TEEAERODYNAMIC!
--
CHARACTERISTTC!S
OF A PLM?ETAPERED
WINGOF ASPECTRMTO 3.1}
WIm A 3-PERCENT-TEICK
BICONWEX
SECTTON
By DuaneW. Dugan
SUMMARY
.
.
Effectsof wingtrailing-edge
bluntness
upontheaerodynamic
characteristics
of a wing-body
conibination
havebeenexperimentally
investigated
at Machnumbers
ranging
from0.6.
to 0.925andfroIu
1.2
to 1.7forReynolds
numbers
of 1.5and3.8million.Modifications
were
madeto therearhalfof a basicplanetapered
wingof aspectratio3.1
hatinga s-percent-thick,
circular-arc,
biconvex
section.Threet~es
of trailing-edge
shapeswereused;nsmel.y(1)constant
thickness
aft
of midchord,
withzeroboattail
angle;(2~ constant
thickness
frommidchordto seven-eights
chordfollowed
by constant
slopeto one-half
maximumairfoil
thickness
at trailing
edge,withboattail
angleequalto
trailing-edge
angleof bastewing;and (3)one-half
msximumthickness
at trailing
edgefairedby meansof a tangentto thebiconvex
surface,
withboat@ilamgleof 2°.
.
Resultsof theinvestigation
showthatemployment
of blunttrailing
edgesreduced
or eliminated
unstable
p-itching-moment
chmacteristics
exhibited
by thebasicwing-body
conibination
at lowliftcoefficients
and
subsonic
speeds.In particular,
at thesupercritical
Machnumbers
O-g1
and0.925,
“neutral
or slightly
positive
staticlongitudinal
“stability
of
thewing-body
configuration
wasattained
by usingtrailing-edge
bluntness.
Increases
in lift-curve
slopemeasured
throughzeroliftwerealso
obtained,
although
at thecostof increased
minimumdraganddecreased
;1
maximum
lift~ag ratios.
...
Comparison
of theaerodynamic
characteristics
of thethree
modified
wing-body
cotiinations
indicates
thatforthegivenbasic~
thetrailing-edge
thichesswhichgivesthemostimprovement
in pitchingmomentcharacteristics
withtheleastdecrease
in maximum
lift-drag
ratio
.--
—
.
—
2
-,
._.A
,-+.-.
—
,
.-
~-%
.
NACARM A52E01
in thesubsonic
speedrangeis lessthanone-half
maximumairfoiltihicknessjandthatutilization
of a Wge boattail
angleis undesirable.
X ,.
.
INTRODUCTION
Previous
experimental
investigation
of theaerodynamic
characteristicsof a wing-boiQ
_eonibination,employing
a planetapered
wingof aspect
ratio3.1witha s-percent-thick,
circular-arc,
biconvex
section(reference1) has sho’wn
undesirable
pitching-moment
characteristics
nearzero
liftin thesubsonic
Machnuniber
range,particularly
forthesupercritical
Machnimibers
0.9and0.925. (Thecritical
Machnumberforthis
wingis approximately
O.83.) Thephenomena
werebelieved
to be dueto
significant
changesin chordwise
loadings
causedby theinfluence
of the
terminal
shockwave. Resultsof investigations
of airfoils
at highsubsonicspeeds(references
2 and 3) demonstrated
theachievement
of more
satisfactory
pitching
momentsthroughchangesto theairfoilthickness
distribution
whichmovedthepointof maximumthickness
rearwar
d, thereby
confining
the adverseinfluence
of theterminal
shockwaveto a smaller
portionof theairfoil.In addition,
ithasbeenpointedoutin reference4 thatadvantages,
including
greaterlift-curve
slope,lowerprofile
drag,anddesirable
structural
features
, arepossible
at s~ersonicMach
nuu.ibers
withblunttrailing-edge
airfoils.Consideration
of such
evidence
ledto thepresentinvestigation
of theeffectsof trailingedgebluntness
on theaerodynamic
properties
of the s-percent-thick
biconvex-profile
wingof reference
1.
In thisinvestigation,
no attempt
wasmadeto compareaerodynamic
characteristics
of thevariouswingsoh thebasisof equivalent
strut- “.
turalcharacteristics.
!l%erefore,
theterm“optimum
thickn~ss”
as used
in thepresentreportis basedsolelyon theaerodynamic
Characteristics
of a givens-percent-thick
wingmodified
to obtainvarioustrailing-edge
shapesandthicknesses
withoutregardto the structural
strengths
Which
differed
fromonemodification
to theother. Furthermore,
becauseof the
small.thickness
ratioof thewingandtherangeof Machnumbersof this.
investigation,
andbecausethemodifications
to thebasicwingdidnot
reducemsxinmmthiclmess
nor include
changesin theprofileforwardof
themidchord,
no reduction
in minimumdragat supersonic
speedswas
anticipated
fortheblunttrailing-edge
wings.
—
‘–-.
.—
-.-—...
‘_...
NOTATION
.“!
.—
NACARM fi2EOl
‘3
.
10CS3wingchord,feet
lengthof body$including
portionremovedto accommodate
sting,inches
.
lift-dragratio
maximumlift-dragratio
M
free-stream
Machnudber
P.
staticpressure,
poundsper squarefoot
.free-stream
%
pressure
at baseof blunttrailing+dge
wings,po~ds per
squarefoot
-wingbase-pressure
coefficient
9.
free-stresm
dynamic
pressure,
poundsper squsrefoot
R
Reynolds
nuniber
basedon themeanaerodynamic
chord,C
r
radiusof body,inches
r.
msximnnbodyradius,inches
s
totalwingarea,including
areaformedby extending
leadimg
andtrailing
edgesto planeof symmMmy,squarefeet
x
longitudinal
distance
fromnoseof body,inches
Y
dist=ceperpendicular
to planeof symetry,feet
a
angleof attackof bodyaxis,degrees
dragcoefficientdrag
()T
liftcoefficientlift
()F
pitching
-moment
coefficient
referred
to quarter
pointof
/.
pitching
moment
meanaerodynamic
chord
qsE
, )
(
CD
.
.
4
NACARM A52E01
.1..
dCL
-z
.-
slope of
lift
.—.
—
curve measured
at zerolift, per degree
.
curve measured
at zerolift
slopeof pitching-moment
,..
APPARATUS
WindTunnelandEquipment
Theexperimental
investigation
was conducted
in thelines
6- bY
6-footsupe&onicwindtunnel;In thiswindtunneltheMachnunibe~
can
be variedcontinuously
andthestagnation
pressure
canbe regulated
to
maintain
a giventestReynolds
n~ber. Theair is driedto preventthe
formation
of condensation
shocks.Furtherinformation
is presented
in
reference
5.
‘-
Themodelwas stingmountedin thetunnel,thediameter
of the
stingbeingabout82 percentof thediemeter
of thebodybase. A
balancemountedon thestingsupport
andenclosed
withinthebodyof
themodelwasusedto measuretheaerodynamic
forcesandmomentson
themodel. Thebalancewas thek-inch,
four-component,
strain-gage
balancedescribed
in reference
6.
.
Models
A plananda frontvtewof themodelsandcertain
modeldimensions
aregivenin figure1. Thebiconvex
profileand thethreetrailing-edge
modifications
areillustrated
in figure2. Thebasicwingof circularuc biconvex
section(wing1) was constructed
of solidsteel,andwas
modified
by addingbismuth-tin
alloyaftof themidchord
pointsto obtain
~S
2, 3, =d 4* Wing2 has constant
thickness
frommidchord
to
trailing
edge;wing3 has constant
thickness
frommidchord
to the
8T.5-percent
chordpoint,followed
by constant
slopeto one-half
the
maximumthickness
at thetrailing
edge,witha boattail
angleof 6.88°
(sameas included
trailing-edge
angleof wing1);winghhas a traiMngedgethickness
equalto thatof wing3,but eqploysa constant
slope
fromtrailing
edgeto a pointof tangency
on thebiconvex
surface
with
a boattail
angleof 2.02°. Thebodysparwas alsoof steelandwas
covered
withaluminum
b formthebodycontours.Thesurfaces
of the
bodyandwingswerepolished
smooth.Otherimportant
geometric
characteristics
of themodels~e tabulated
as follows:
“. ‘“
.
,
..”
-.).
.:
0
NACARM A52E01
.
.
..
wings
Aspectpatio. . . . . . . . . . . . . . . . . . . . . ...6..3.1
Taperratio .. o.....
. . . . . . . . . . . . . . . .. ,0.39
thickcircular-arc
biconvex
Airfoilsection(streamwise)
. . 3-percent
Includedangle
atnose,degrees . . . . . . . . . . . . . . . . 6.88
Boattail
angle,degrees
wing2. . . . . . . . . . . . . . . . . . .
* . .* . .0
wings. . . . **.
.. ..9.. *.
.
. 6.88
wingk. . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.02
●
●
●
●
●
●
●
●
●
●
●
●
Wtalarea s~ squarefeet. . . . . . . . . . . . . . .
Meanaerodynamic
chord~, feet . . . . . . . . . . . .
Dihedral,
degrees . . . . . . . . . . . . . . . . . . .
Caliber.
. . .. ............ .... ....
TuiSt,degrees. . . . . . . . . . . . . . . .S .
Sueepback
of 25-percent+hord
station,
degrees. . .
Incidence,
degrees.. . . . . . . . . . . . . . . . . .
Distance,
wing-chord-plane
to bodyaxis,feet . . . . .
●
●
●
●
●
●
●
●
. . . .2.425
. . .. 0.94-4
. . . . . .0
. . . . None
. . . . .0
. . . . ~.4
. . . .“..0
. . . . . .0
●
Body
Fineness
ratio(basedUponlength1, fig.1) . . . .
Cross-section
ahage . . . . . . . . . . . . . . . .
Msximumcross-sectional
area,squarefeet . . . . .
Ratioof msximumcross-sectional
areato wingarea.
.
.
.
.
.
.
.
.
.
.
.
.
. . . ~05
. circw
. . 0.1235
. . 0.0509
TESTSAND PROCEDURE
Theaerodynamic
characteristics
of themodelswithwings2, 3,andk
of a@Le of attack)wereinvestigated
fora rangeof Mach
(as a function
numbersfrom0Y6to 0.925andfrom1.2to 1.7,andReynolds
ntmibers
of 1.5~d 3.8UiOL
Data
forthemodelwithwing1 wereobtained
fromreference
1 for comparison.
In a few instances,
as no~d in the
figures,
datafora Reynolds
nuniber
of 1.5millionwerenotobtained
for
wing1; thesubstitution
of dataobtained
at a Reynolds
numberof 2.4milliondidnot invalidate
comparison
withthemodified
wings,inasmuch
as
no appreciable
difference
couldbe obsemedbetweenthedataobtained
for
wing1 at R-1.5millionandthoseobtained
at R=2.4miUion in theMach
numberr-e concerned.
In addition
to forcemeasurements,
wingbase-pressure
measurements
weremadeby meansof a staticorificeinstalled
in thetrailing
edgeof
eachof themodified
wingsat approximately
the50-percent-semispan
position
of theright-hand
wingpanel.
.
.—
J—
-HE===&
6
NACA
RM A52E01
.— -.
.—
Reduction
of Data
ThetestdatahaveMen reducedto stand=ml
NAcAcoefficient
form.
of theseresultsandthecorrec
Factors
whichcouldeffecttheaccuracy
arediscus
sedin thefollowing
paragraphs.
tionsapplied
-=
Tunnel-wall
interference.
- Corrections
to thesubsonic
resultsfor
effectsof thetunnelwallsresulting
— fromlifton themodelweremade
according
to themethodsof reference
7. Thenumerical
valuesof these
coi?rections
(whichwereaddedto theuncorrected
data)were:
.
&fJ= O.m CL
.—
.
ACDu 0.0100
CL2
No corrections
were=
to thepitching-moment
coefficients.
Theeffectsof constriction
of theflowat mibsonic
speedsby the
tunnelwallsweretakenirito
account
by themethodof reference
8. This
correction
was calculated
forconditions
at zeroangleof attackandwas
applledthroughout
theangle-of-attack
rang4. At a Machnmher of 0.925$
thiscorrection
amounted
to a 3-percent
increase
in theMachnumberover
thatdetermined
froma calibration
of thewindtunnelwithouta modelin
place.
.
For thetestsat supersonic
speedszthereflection
fromthe-el
wallsof theMachwaveoriginating
at thenoseof thebodydidnot cross
themodel. No corrections
wererequired,
therefore,
fortunnel-wall
effects.
Streanvariations
.-Testsat subsonic
speedsin the6- by 6-foot
supersonic
windtunnelof thepresentsymmetrical.
modelstn boththe
normalandtheinverted
ppsitions
haveindicated
no streamcurvature
or
inclination
in thepitchplaneof themodel.,Nomeasurements
havebeen
made,however,
of thestreamcurvature
in theyawplane. At sfisonic
speeds,
thelongitudinal
variation
of staticpressure
in theregionof
themodelis notknownaccurately
at present,
buta preliminary
survey
has indicated
thatit is lessthan2 percentof thedynamic
pressure.
No correction
forthiseffectwasmade.
A surveyof theairstreamat supersonic
speeds(reference
5)has
shownstreamcurvature
andstreaminclination
onlyin theyawplaneof
themodel. Theeffectsof thiscurvature
and inclination
on the
measured
characteristics
of thepresentmodelsarenotlumwn,but ae
judgedto be smallaccording
to theresults
‘of“reference
9. Thesurvey
alsoindicated
thatthereis a static-pressure
variation
in thetest
section
of sufficient
magnitude
to affectthe dragresults.A correction
~w
.
—.
.
1
1
‘---
HACAFM A52E01
7
was addedto themeasured
dragcoef
f’icient,
therefore,
to accountfor
thelongitudinal
b~cy
causedby thisstatic-pressure
variation.
~is correction
~ied fromas much,
as -0.00U7
at a wh n-r
of ~.3
to +0.0006at al&ch numberof 1.’7.
Suppo
rt interference
.-At subsonic
speeds,theeffectsof suFPofi
interference
on theaero@namiccharacteristics
of themodelssrenot
lmown. For thepresenttailless
models,it is believed
thatsucheffects
consisted
primarily
of a changein thepressure
at thebaseof themodel
fuselage.In an effortt6 correctat leastpartislly
for thisswport
titerfe~ence,
thebasepressure
of themodelfuselage
was =asured and
thedragdatawereadjusted
to correspond
to abase pressure
eqti to
thestaticpressure
of thefreestream.Thesecorrecti- wereof tie
orderof 2 percentof themeasured
dragat zerolift.
At supersonic
speedsztheeffectsof s@Port fi~rference
of a
body-sting
configuration
s~-to
thatof thepresentmodelsare k!hown
by reference
10 to be ccmfinedtoa changeinbasepressure.Thepreviouslymentioned
adjustment
of thedragforbasepressure,
therefore,
was appliedat supersonic
speeds.Thecorrections
in thesecasesr~ed,
in general,
from6 percentof themeasured
dragat zeroliftat M = 1.2
Thecorrected
drag,consequently,
is forebody
to 15 percentat M= 1.7.
drag.
RESULTS
ANDDISCUSSION
.
.
Figure3 showstypical.
basic-data
plotsof aerodynamic
ch=acteristicsobtained
in thisinvestigation
forwing4. Becauseof the slight
as-try in thedragpolarsnearzeroliftfor thelowerMachnumbers>
thevaluesof dragat positive
liftwereusedin mibsequent
figures.
Subsequntfiguresdo not,in general,
showtestpointsin orderthat
comparisons
maybe mademoreclearlyin respectto thevsmiouspropertiesof thefourwings. A comparison
of theaerodynamic
characteristics
of thefourwingsispresented
in figuresk, 5$ 6, =d 7. In figure8,
thewingbase-pressure
coefficients
of themodified
wingsarecomp=ed
at severalsubsonic
and supersonic
Machnumbers.Figure9 showsthe
valationof lift-curve
slopemeasured
throughzeroliftwithMach
nuniber
foreachwing. Theeffectof Machn&er uponliftat seversl
anglesof attackis givenin figure10;the sameis donefordragin
figureU, andforpitching
momentin figm?e12.
LiftCharacteristics
.
Ap reciable
increases
in lift-curve
slopemeasured
at zerolift
(fig.97 h therangesof Mach;~ers
investigated
wereobtained
by
, --.<*
8
NACARM A52E01
substituting
blunttrailing
edgesfortheclosedtrailing
edgeof the
basicwing(wing1),’
psx?ticularly
at thesupercritical
Mpchnumbers
0.9
and0.925,.
Thisis attributed
to reduction
of separation
at allspeeds
testedandto theadditional
reduction
of theadverse
effects
of the
terminal
shockat thesupercritical
speedsthrough
therearwar
d shiftQf
theshock.Of thethreetypesof blunttrailing
edgestested,
that
represented
by ting4, whichhasa finaltra-iling-edge
thickness
of onehalfmaximum
airfoil
thickness
fairedby meansof a tangent
to the
biconvex
surface,
demonstrated
themost”
satisfactory
lifting
properties
in regardto lift-curve
slopeandvariation
of liftwithMachnumber.
Thissuggests
thedesirability
of usingthe~mallest
possible
boattail
anglein attaining
thefinal.
trailing-edge
thickness
whichtheresults
indicate
shouldbe lessthemmaximumsection
thickness.
Figures
9 and10 showa markedscaleeffecton theliftcharacteristicsofwing1 at anglesof attacklessthar”u”
in thesubsonic,
supercritical
spee’d
range,an effectnotobserved
forthemodified
wings.The
decrease
of lift-curve
slopemeasured
through
zeroliftforwing1 at the
highersubsonic
speedsandlowerReynolds
numberindicates
thata cotii~tionof boundary-layer
qndterminal-shock
effects
causeslos~of lift.
Increasing
theReynolds
nuuiberto 3.8 million,
or shifting
theposition
of theterminal
shockrearwardbychanging
thethickness
distribution
.@
thatof wing2, 3, or 4, reduces
theeffects
of separation
andof recompression,
resulting
inmoreliftat smallanglesof attack.Thatthe
sameeffectis notobserved
at somewhat
largerangles(asat a = 4°)is
attributed
to thechangein thenatureof theflowat theseangles
(fig.10(a)
). As first&scribedinreference
3, an expansion
at supersonicspeedsaroundthesharpleading
edgeredirects
theairto the
surface
of thewing,at whichpointan oblique
shockturnstheflowso
thatit follows
thecontour
of thesurface,
withtheresultthatseparationis eliminated
overa considerable
distance
aft-oftheleading
edge..
Pitching-Moment
Characteristics
.
Improvement
of thepitching-moment
characteristics
of thebasic
wingby employing
blunttrailing
edgesof thetypesrepresented
by
wings2 and4 is apparent
in figure5, particularly
at thetwohighest
subsonic
Machnunibers
andlowerReynolds”num~er.
Wing3 produces
pitching-monent
properties
generally
lesssatisfactory
in respect
to
staticlongitudinal
stability
thanthoseof thebasicwingat 1.7million
Reynolds
niimber
andlowersubsonic
Machnumbers;
at thehigherReynolds
nuniber,
thesecharacteristics
areslightly
s@eriorto thoseof wing1
at subsonic
speeds,
hutremainlessdesirable
thanthoseof theother
twomodified
wings.At supersonic
Machnumbers,
theinfluence
of
trailing-edge
thickness
in-dete~ining
pitching-&oment
characteristics
is slight.
_,=—
--’
“=--
2C
P
NACARM A52E01
9
Themiti@tionof Machnuniber
effectsuponpitching-moment
through
theuse of blunttrailing
edges-is
shownin figure.12
wherethevariation
of pitching
momentwithMachnumberat severalanglesof attackis prein this
sentedforeachof thefourwings. Wings2 and4 appearsuperior
thickness
of wing3
respectwhereaswing3 doesnot. (Thetrailing-edge
is thesameas thatof wing4, but theboattail
angleof theformeris
morethanthreetimesthatof thelatter.)Thedataindicate
thatthe
useof fullbluntness
is scarcely
moreadvantageous
thanthatof half
bluntness
as typified
by ting4 in reducing
theMachnumbereffects
justdiscussed.
Theaberrant
variations
of pitching
momentwithliftof wings1
and 3 in thesubsonic
speedrangeat thelowerReyTlolds
nuber} in
contrast
to thenmreconsistent
trendsat thehigherdynamicscale,as
shownby figure5, merita briefdiscussion.
,Inthecaseof thebasicwing(wing1),therapidincrease
in positivepitching
momentat smallliftcoefficients
at the supercritical
Machnumbers0.9and0.925andthelowerReynolds
numberbanbe ex@ained
as follows:Assumethatat zeroliftlaminarflowexistsoverbothupper
andlowersurfaces
of thewing,but thattransition
to turbulent
boundarylayerflowoccursaheadof theterminal
shockon theuppersurfaceat
smallanglesof attackdueto thepressure
peakin thevicinity
of the
sharpleadingedge. Thepressure
distribution
overtheuppersurface,
then,wouldresemble
thatobtained
experimentally
at supercritical
speedson a circular-arc
airfoil
withturbulent
boundary
layer,whereas
thepressure
distribution
overthelowersurface
wouldbesimilarb
thatobtained
withMminar flowin theboundsry
layer. Suchpressure
distributions
srepresented
in reference
11 fora biconvex
airfoilat 0°
and showthattheterminal
shockwaveproduces
a greater
incidence,
pressure
risein a shorterchordwise
distance
in thepresence
of a turbulentboundary
layerthanin thepresence
of a laminar
boundary
layer.
!Ihis,
then,wouldaccountfor thedevelopment
of negative
liftoverthe
resrof wing1 at supercritical
speedsandthelowerReynolds
mmber~
andexplainboththeincreased
positive
pitching
moment(fig.5(a)),and
thedecrease
in lift-curve
slope(fig.9(a)). Exsm@esof suchpressure
distributions
overan airfoilidentical
to thatof wing1 canbe seen
foranglesof attackof 2° and4° in reference
3.
At thehigherReynolds
nuniber
of 3.8 million,
it canbe deduced
fromthedataforwing1 thatturbulent
boundary-layer
flowoccursover
theloweras wellas theuppersurface
at smallanglesof attack,with
theresultthatthen~gative”lift
described
aboveis largelyreducedor
eliminated.
.
.
Thepitching-moment
characteristics
of wing 3 at lift coefficients
nearzerofor supercritical
speedsat thelowerReynolds
numberare
contrsry
to thoseof wing1 (fig.~),andthusrequirea different
‘
10
.
emanation. A clueto theparadoxis givenby thediscontinuity
in the
profileof wing3. In thiswing,theupperandlowersur?aces
aftof
themidchord
pointcontinue
par&fiel
tc-thechordplaneas farrearward
as the87.5-percent-chord
Positionj
at which-~intthey cl.iange
direction
“by an angleof 3.4.4°. Sucha profileis conducive
to separation
behind
thediscontinuity
at lowReynolds
numbers.Thatseparated
flowdoes
prevailoverbothsurfaces
at therearof wing 3, not onlyat zerolift
but alsoat smallanglesof attack,in thesubcritical
speedrangeis
indicated
by themorepositive
pitching
momentsof thiswingcompared
to
thoseof wings1,~~d 4. However,
as supercritical
speedsareattained,
thesupersonic
eqansionaroundthediscontinuity
on theuppersurfaceis
probably
of sufficient
degreeto reattach
theflowthereandproduce
greatlyreduced
pressures
at even small”
anglesof attack,as studyof
thedataandschlieren
observations
of reference
3 indicates.Thelower
velocities
on thelowersurface
of thewingat smallanglesof attack
preclude
thepossibility
of as complete
reattachment,
withtheresult
thatmorepositive
liftis developed
overtherearof thewingat supercritical
speedsthanat lowersubsonic
speeds.Sucha phenomenon
would
e-lainboththerapidincrease
of liftandof divingmomentwiththe
adventof supercritical.
speedsat thelowerReynolds
mmiber
shownby the
datapresented
in figures10(a)and1.2(a),
respectively.
At thehigherReynolds
nuniber,
theflowovertheupper“marsurface‘
of wing3 wouldnotbe e~cted to differsignificantly
fromthatat the
lowerRe~lds numberJon theotherhand,theextentof theseparation
on thelowersurface
aftof thediscontinuity”
wuld be e~ectedto be
largelyreduced.‘l’he
tendency
in thiseventwouldbetowardlesslift
anda decrease
in divingmoment.Comparison
of theliftandthepitching
momentsof wing3 at thetwoReynolds
nunibers
(figs.10 and12,respectively) showsthisto be thecase.
.%
T
\-
.“.
..
-.
:
.
.
In viewof thescaleeffectsnotedforwings1 and 3 in thesupercritical
rangeof speeds,thelimitations
to thedirectapplication
of
thesewings,sayto missiledesignwherethe dimensions
arecomparable
to thoseof themodelshereinvestigated,
areobvious.Thetestconditionsat the-twosupercrikical
M&:hnumbers0.9”and0.925,andat the
lowerReynolds
nuniber
of 1.5millionareequivalent
to flightof the
testmodelsat thesesamevaluesof theparameters
at approximately
&0,000feetabovesealevel. Wings2 and& wouldnotofferthesame
drasticproblemof controlat smallliftcoefficients
in thesubsonic
supercritical
speedrange.
DragCharacteristics
.
As couldbeeqected,theminimumdragof eachof theblunttrailing- e~e wingswas considerably
greaterthanthatof thebasicwing,bothat
subsonic
andsupersonic
speeds.Forwing2 thedragincrements
were
.
-.
NACARM A52E01
‘“~
11
threeto fourtimesas largeas forwingk at zeroliftandat small
anglesof attack(fig.11);in general,
thedragof wing3 resembled
thatof wing4 exceptat supersonic
speedsandthehigherReynolds
?nxiber
wherethedragof wing3 exceeded
that”of
wtng2 in thehigher
Machnumberrange(fig.U(b)).
The influence
of thetrailing+dge
shapesof themodified
wingsin
—
creating
additional
dragthroughthedevelopment
of lowerbasepressures
is shownin a qualitative
way in figure8. Thedecrease
of basepressure ‘“
coefficient
withincreasing
supersonic
Machnumbershownin figure8 is I
reflected
in thediminishing
difference
betweenthedragcoefficients
of
themodified
wingsandthoseof thebasicwingas theMachnumber
increases
beyond1:2 (fig.11). Thephenomenon
of decreasing
basepressurecoefficients
withincreasing
angleof attacknearzero,shownfor
wing2 in figure8 forsubsonic
speeds,servesto explaintheunusual
shapeof thedrag-pol~curvesof thatwingnearzerolift(fig.6).
Figure6 showsthattheincrease
of dragwithliftis lowerforthe
modified
wingsthanforthebasicwing,as couldbe deducedfromnoting the greaterlift-curve
slopesof thef&aer. At liftcoefficients
of
the orderof 0.5,thedragcoefficients
of theblunt-trailing-edge
wings
axe generally
lowerthanthatof thebasicwing.
.MaximumLift-Drag
Ratio
Figure7 showstherelative
magnitude
of themsxtiumlift-drag
ratiosof thefourwingsfor subsonic
and supersonic
Machnumbers.It
is uncertain
justhowmuchof thedifference
obsewedbetweenthevalues
of theratiosat the twoReynolds
numbersis dueto scaleeffectandhow
muchis dueto thelackof complete
definitiveness
in thefairingof the
individual
lift+ag curvesnearthemaximumvalues.Theadvantage
of,
usinglessthanfullbluntness
is obviousin respectto theachievement
of thelargestpossible
lift-drag
ratios. Thedataindicate
.someslight
s~eriorityof wing4 overwing3 in comparing
theirrespective
liftdragvalues.
At thehighestMachnumberof thepresentinvestigation
(M = 1.7),
thereis an indication
thatat leastforwings3 and4 thevaluesof
maximumL/Dareincreasing
withfurtherincrease
in Machnumber;from
reference
1, wing1 showedno suchtendency
up to a Machnumberof 1.9
anda Reynolds
numberof 2.4million.Thisincrease
in (L/D)- is
no doubtassociated
withthedecrease
in basedragwithincreasing
supersonic
Machnuniber
shownin figure8. It is possible
thatat Mach
numbers
higherthan1.7theorderof thevaluesof (L/D)m forthe
Ji?
-~
NACARM A~2EOl
monblunt
andforthemodified
wingsmightbe reversed.Furtherinvestigationat higherMachnunibers
thanherepresented
is required
before
definite
conclusions
canbe reached.
A.
—
.—
.
CONCLUDING
REMARKS
Fromthedataobtained
in thisinvestigation
of thee$fects
of
blunttrailing
edgesupontheaerodynamic
characteristics
of a plane
tapered
winghavinga 3-percent-thick,
circular=c~biconvex
section,
ithasbeenfoundthatunstable
pitching-moment
characteristics
exhibited
by theabovewingat smallliftcoefficients
in thesubsonic
rangeof speedsconsidered
canbe reduced
or eliminated.
mis was
accomplished
”(atthecostof increased
dragtidlowermaximum
lift-drag
ratios)
by theemployment
of trailing
edgeshavingthicknesses
equalto
themaximumandone-hslf
themsximumthickness
of thewing. Increases
in lift-curve
slopemeasured
through
zeroliftals~resulted
forall
Machnumbersinvestigated
(0.6-to
0.925,and1.2to 1.7)whentheoriginalwingwasmodified
by %luntness
at thetrailing
edge.
.-,
.—.—
-.
Comparison
of theeffects
of fullbluntness
on theonehand,and
ofhalfbluntness
on theother,uponpitching
moment,
lift-curve
slope,
andupondrsgindicates
thattheopt@mmthi~ess fortheblunttrailing
edge,disregarding
structural
considerations,
is something
lessthanonehalfthemsximwn
thickness
forthetypeof winghe= considered.
Testsof
a rectangular
wingof aspectratio4 witha 4.-percent-thick
cfrctiar-arc
biconvex
section
modified
in thesamemanner-as
wing4 of thispresent
investigation
(reference
12)showthatemployment
of a trailing-edge
“
thickness
0.3thatof themaximum
airfoil
thickness
gaveno increase
in
minimumdragoverthatof thebasicwing. Thisphenomenon,
in conjunction
witha-greater
lift-curve
slope,produced
a somaihat
highervalueof msximumlift-drag
ratioin thesribsonic
speedrange.!Ihe
improvement
in
pitching-moment
characteristics
wascomparable
to thatobtained
with
trailing-edge
thicknesses
0.6and1.0timesthemaximum
air?oil
thickness.
Needforfurtherinvestigation
of theeffects__of
trailing-edge
thickness
uponaerodynamic
characteristics
is indicated.
Thefairing
of thetrailing-edge
thickness
to thecircular-arc
profile
by mans of a straight
linetangent
to thecurvedsurface
appears
to be superior
to theinclusion
of a discontinuity
in slopein
theprofile.
“,
.-
Dataobtained
in thisinvestigation
indicate
thatthemsximumliftdragratiosfortheblunt-trailing-edge
wingsareincreasing
invalue
withincreasing
Machnrmiber
in theneighborhood
ofM = 1.7. Testing
at
speedshigherthanthisappears
desirable
to investigate
thistrend.
AmesAeronautical
Laboratory
National
Advisory
Committee
forAeronautics
Moffett
Field,Calif.
%..u...~
-—
-+....-...,JU
.
.
NACARM A52E01
.
.-
~
13
R3mERmcEs
1. Reese,DavidE., Jr.,andPhelps,E. Ray: Lift$Drag,andPitching
Momentof Low-Aspect-Ratio
Wingsat subsonic
andSupersonic
SpeedsPlaneTapered
Wing,ofAspectRatio3.1With3-Percent-Thick,
Biconvex
Section.NACARM A50K28,1951.
2. Eggers,A. J.,Jr.: Aerodynamic
Characteristics
at Su%criticsl
and
Supercritical
MachNumbersof TwoAirfoilSections
HavingSharp
of Msxinrum
Thickness.
Leading
EdgesandExtre~ RearwardPositions
NACARM A7C1O,1947.
Lindsey,
W. F.,Daley,BernardN.,andEumphreys,
MiltonD.: The
FlowandForceCharacteristics
of Supersonic
Airfoils
at High
Subsonic
Speeds.NACA!CNMU, 1947.
3.
4. Chapman,
DeanR.: Reduction
of profileDragat Supersonic
Velocities
.
.
by theUseof AirfoilSections
Havinga BluntwailingEdge.
NAcARMA9m, 1949.
5.
Frick,Clmrles
W., andOlson,RobertN.: FlowStudiesin the
Asymmetric
Adjustable
Nozzleof thehnes6- by 6-footSqersonic
WindTunnel.NACARMA9E24,1949.
6.
Olson,RobertN.,andMead,MerrillH.: Aerodynamic
Studyofa
Wing-Fuselage
Conibination
~lo@ng a WingSweptI@ck630.Effectiveness
of an Elevenas a Longitudins3.
Controlandthe
Effectsof Csmiber
andTwiston theMaximumLift-Drag
Ratioat
Supersonic
Speeds.I’tACARMA50A31a,
1950.
.
7. Glauert,
H.: TheElements
of Aerofoil
andAirscrew
Theory.The
University
Press,Cambridge,
England,
1926,ch.XIV.
8.
Herriot,
JohnG.: Blockage
Corrections
forl%ree-Dimensional-Flow
Closed-Throat
WtndTunnels,
withConsideration
of theEffectof
Compressibility.
NACARM A7B28)
NACARep.995$1950. (Formerly
HenryC.: Aerodynamic
Studyof a Wing-Fuselage
Combination
9. Lessing,
~lo~ng a WingSweptBack630 - Effectof Sideslip
on Aerodynamic
Characteristics
at a MachNuniber
of 1.4WiththeWingTwistedand
Cambered.NACARMA50F09,1950.
10. Perkins,
EdwardW.: ~rimental Investigation
of theEffectsof
SupportInterference
on theDragof Bodiesof Revolution
at a
MachNumberof 1.5. NACA~ 22$)2,
1951.
—
,“
14
NACARM A52E01
-~
o! theInteraction.of_
_ .,___ 3
11. Liepnann,
HansWolfgang:Investigations
.=.+
Boundary
LayerandShockWavesin Transonic
Flow. AF Tech..
—
Rep.5668,1948.
.
22. Cleary,
JosephW.,andS*vens,GeorgeL.: TheEffectsat.Transonic
Speedsof Thickening
theI&ailing
Edgeof a WingWitha h-PercentThickCircular-Arc
l!drfoil.
NACARMA51Jll,
1951.
“.
. —-
-.
..
.
.—
..
..-
...
---
.-
..
...—-—
1.
– .:+
.=+.
-.
.
.
.
*
Equation
of
fuselage
dimensions
radii:
shown
in
Inches.
II
I
-,( F-— .
——
+
r,:2.38
-T-
I
-
2-—r
{\
—-—
‘-----,—
------
-
x
w
/9.
47’
5.68 +
-+595 1-
I
w
k—-15.21-
~1=59.50
1
Figure
1.-
Plan
and
front
views
of
the
models.
o
/
2
3
Percent
Figure
.
.
I
60
40
0
2,-
Profiles
‘
of
basic
chord,
and
80
/00
100 x
~
b/unt
trailing-edge
wings.
,
.
●
1,2
/.0
.8
,
.6
.4
.2
0
:2
;4
76
.R
.“
O
4
8
12
/6
Angle
20
of
(0)
Figure
3.- The variation of the oerodpamic
numbers
for M=O.6
ottock, Q
CL w
u
characteristics
Reynolds numb~,
wifh /iff
/.5 million,
coefficient at various Mach
Wing 4”
.-
/2
g
1.0
.8
.6
6’
-G
a
3
~
~
.4
./?
2.
go
+
-.2
-.4
Y6
Y8
o
Y04 T08 +2
,/6
Plfchlng-moment
(b)
Figure
;20 for M=O.6.
coefffclenf,
Cm
CL VS cm
3-Continued.
1
4,,
m
I
1
1’
J
,
.)
,
.
.
,
*
.-
0
.04 .08 .12 .16 .20 .24 .28 .32 for M EQ6.
Drag coefficient, CO
(c)
figure
.
c’
VS CD
3-Continued.
.-.
I
I
I
Lift
(d)
Figure
,
#
.
s
cot?ffi’’ient, CL
‘/D
3-
KS
CL
w
x
.
~
Concluded
I$J
P
‘
.
I
-8
.
-4
0
4
8
20 for M=0.6.
A&e o;60tMck, u, a%grees.
“
w
(a) Rewelds number. ).5 million.
Figure 4.- Variation of fiff coefficient with angleOf a~tuc~ wingsI, 2, 3,and4.
I
R
.’
“1
i
-8
-4
0
4
8
/2
for M= 0.6.
Angle of attock, a, degrees
f6
20
(b) Reynolds numbe< 38 roil/ion,
Figure 4- Concluded
~
“
.
I
“1
:,,
—
1.
/.
.*
.4
I
J#l
I I i I
i
.2
0
‘.2
-.
II
-.
~1
-.
(For bicomw profi/e at
111
M=L2, 1.4, 1.~
Pitching-momentcoefficient. Cm
(a) Reynolds number, [5- rnjllion.
figure 5. - Comparison of pitching-moment characteristics of sharp -and blunt t’raifing-’edge wings,
1
.-
lz
1.0
.8
-*
o
4
.4?
Z4
76
-R
:;4
o
;04
.08
712
716
-20
T24
-28
-32
for Al=. 6
Wdng-moment
coefficient, cm
(b) Reynolds m.mhw, 3,8 million.
Figure
=%=’
5- cancluded.
.,
I
,.
1.0
.8
.6
.4
.2
0
-.2
Winf
-.4
‘.6
-.80
.04
.08
.12
.16
.20
!+
1 ‘1 0.9
--
.24
Etmt
.2u
.
..z?
kW’ M’U.
-
(For
biconvar profile at
b
Drag coet%ienf, CD
(o) Reynolds nmber, 1.5 mifion
Figure 6.- Voriotionof drag coefficimt with iift cmffiaent for wtngs ~ 2, ~ and 4.
0?
Iv
cm
liiiiii
.U
ii
iiiiiiiiiii
iii
iiil
.6
A
,7-
I
1A
M
M MT
/
-
,
1~
,
,
1
1
1
I
I I
VI
I
i
.2
n
“m
<
!
w.*
I
I
1111
.-
0
.04
.08
.12
.16
.2C
u
.24
‘-
‘.28
#----Drug coerrfcw?r,
‘.52
I
I
I
HII
~/~9~
—=—__—J—
wif193
win94
~-------
For y=O.6
———
~–-–-—
-
GD
(b) Reymfds numlwr, 3.8 miflim.
F@ure 6.- Concluded.
,,
2
I
t
,,!
,
.
,1
.1
1:
ii’ .::’.
1
.
,
!
#
—
wing 2
~
Wiflg4
~
7
R=I.5 x/Oe
7
—
0
‘O
.2
Figure
.4
.6
7. – Variation
.8
of
[O
L2
Mach number
maximum
wings
~” 2,
lift-drag
3,
and
/.4
L6
/.8
with
Mach
M
2.0
w
ratio
4.
number,
2.2
M= 0.6
M=O. 8
hf=o, 7
/4
/2
/0
8
6
4
2
00
-.2
-,4
-.6
M=(9.9
-8
0
72
-.4
Y6
-.8
0
-.2
-.4
-.6
Af=/.2, 1.4, /.7
-.8
F5=3
/4
/2
/0
8
6
4
2
00
-,2
-.4
-.6
o
-.8
Pressure
@
Figure
-.2
-.4
-,6
coefficient,
Reynolds
(% - ~)/q
numbe~
%.- Comparison of wing base pressure coefficients
o
-.8
-.2
-.4
-.6
~
/.5 ‘million.
for three
types of trolling-edge”
‘;8
~
M
“bluntness. $
I
1
I
M=O. 7
0
-.2
-.4
-.6
~*oa925
-.8
*
,
i!
win92
~/4
z /2
;
~––––
win93
~-------
wln9-4
~–-–-–
10
.S8
G
06
24
2
0
0
‘,4
‘.4
-.6
-.8
0
%s5wfe
(b)
-,2
-,4
-.6
coefflclent,
Reynolds
Figure
number,
8.-
0
-.8
(~-~)
3.8
Concluded.
~q
million.
?2
-.4
-.6
-.8
NACARM A52E01
30
.
,.
4 --;4
.6
.8 LO /.2 /.4 16
Mffch
number
/.8 2.0
(b) Reynoldsnumbe~3.8 mj//jon.
F7gure 9.
Variation of /ift -curve s/ope with Much
numbe~ wlhgs 1, 2,3,and4.
.
.
I
,1
,
,
1
.5
.4
/,
.
.3
1
1
\
\\\
I
#
2“
\
Q..
-
.1
0
/
+
4
.6
.8
f.O
1.2
L4
1.6
Mach number
(o) Reynolds number, 1.5 miilion.
Figure IO- Vortbtionof iift
1.8 ,20
.4
i.o
L6
1.8
(b) Reynoids numbe~ 3.8 miiiion.
—
.
.8
i.2
1.4
2.0
Mach number
coefficient at sew?roiongies of attack with Ma& number, wingsi, 2,3, and 4.
.03
.02
—
I
—
.0/
1.
.
@
@o
—
.
—
—
%.
\\
●✎✼
.
+??’
—
}
“1
//
—
—
.0/
o
—
~
–––”–
w@3
~
-------
w~n94
~–-–-–
I
Q“r?”
.8
LO
12
(7;4.
1.4
[6
[8
2.0
.4
.6
.8
Mach number
LO
Mach
(0.) Reynolds
Figure 11. -
number.
1.5
1, 2,
+
1.2
L4
16
18
number
million.
Variation of drag coefficient ut seveml angles of attack
wings
i,,,
W9 I ~.
win9~
with
#a&
3, and 4.
1.
1
7
,,1,
,,.
number,
2.0
.03
.
.02
/
----
--
/
---
__
+
~
~
. -
.0/
u=o”
0
c!
I
t
‘
#-/
N
)
\-.
_
.02
./’
-.--~
\
\
::
.
\
0
v
Wing I
~
wh9P
~––––
%
2
—
wing3
~
wlllg4
~–-–-–
-------
.01
a=z”
0
.6
.8
1.0
f.2
.L4
Mach number
A.
L6
[8
2
.4
.6
.8
1.0
Mach
(b) Reynolds number, 3.8
Figure
1~ -
-w
1.2
1.4
/.6
1.8
2.0
number
million,
Concluded.
w
LAJ
w
.03
&
.04?
.0/
4°
o
-.01
be$ -.OE
-,03
.
2“
-.
-.
1°
-.
---
.4
.5
,6
.7
,8
.9
Mach number
(Q) ReY@dS number, [5 milfion.
Figure i2 - Voriation
of pitching-moment
LO
.4
.5
.6
Ma&
~)
Repolds
.7
.8
.9
i.O
numbw
nutnbe~
3.8 million.
cotw%lcien}with Moth number, wi~gs ~ 2, 3,
ond 4.
~