Tucker, Warren A

English

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NATIONALADVISORYCOMMITTEE
FORAERONAUTICS
TECHNICALNOTE
No. 1601
r ‘:’
,.
‘CHARACTERISTICSFTHINTEUANGULARWINGSWITHCONSTANT-CHORI
FULL-SPANCONTROLSURFACESAT SUPERSONICSPEEDS
ByWarrenAl Tucker
LangleyAeronauticalLaboratory
LangleyField,Va.
=q’JiE’iip=
Washington
July1948
—— -—— ___
https://ntrs.nasa.gov/search.jsp?R=19930082249 2020-06-17T20:44:57+00:00Z
NATIONALADVISORYCOMMITTEEFORAERONAUTICS
TECHNICALmTE Ho.1601 -
CHiARACTE&ICSW THINTRIANGULARWING-SWITHCONSTANT-CHORD
FULL-SPANCONTROLSURFACESAT SUPERSONICSPEEZM
By Wmen A. Tucker
A theoreticalnalysiswasmadeof thecharacteristicsof constit-
chordfull-spancontrolsurfaceson thintriangularwingsat supersonic
speeds3Y useofmethodsbasedon thelinearizedequationforsupersonic
flow. Expressionswerefoundforthelifteffectiveness,pitching-moment
coefficient,bin@-momentcoefficientduetocontroldeflection,and
hinge-momentcoefficientduetoangle“ofattack.Theseexpressionswere
. givenasfunctionsof theratioofflapchordtowingchordandtheratio
of thetangentcf thewing-semiapexengleto thetangentof theMachangle.
l Highvalueswerefoundforthelifteffectiveness,definedas the
ratioof theliftcoefficientproducedby a unitflapdeflectiontothe
liftcoefficientproducedby a unitangleofattackofthewing. For
certaincombinationsofflapsi20,wing-apexangle,andMachnumber,the
liftproducedby a unitflapdeflectionwasactusllygreaterthanthe
liftresultingfroma unitangleof attackof theentirewing. These
hi@ valuesoflift,sffectivenessweretheresultof thelowlift-curve
slo~eof thewhg ratherthanofanyremarkable’lift-proticingcapability
on thepartoftheflap.
Whentheratiooflifteffectivenesstohinge-momentcoefficientdue
to controldefl.ectionwascomparedwiththecorrespondingratiofora
two-dimensionalwing-fla~cotiinationhavingthesaneratioofflaparea
towingarea,thepresentarrangementwasslightlyinferiortothetwo-
dimensionalcasewhentheMachlineswerebehindtheleafingedge.As
theMachlinesmovedaheadof theleadLngedge,theefficiencyofthe
present?mreagementreachedandexcee~dthatofthetwo-dimensional
conibination.
INTRODUC%EON
A varietyofcontrol-stiace arrangementshas bsen suggestedforuse
. on triangularwingsat supersonicspeeds.Someof themoreobviousare
thetriangular-tipflap(reference1),theconstant-~rcent-chordflap,
andtheconstit-chordflap. Of thesevariouscontrol-surfacetypes,
. perhapsthesim~lestisthefamiliarconstant-chordfull-spmtrailing-
edgeflap.‘
2 NACATN No.1601
.
Thecharacteristicsof thistypeofcontrolsurfaceare.anal.yzedin ,
thepresentpaper%y use ofmethods%asedonthelinearizedequatimfor
supersonicflow. Simplexpressionsareobtainedforthelifteffactive-
ness,pitching-momentcoefficient,hinge-mamentcoefficientdueto con-
troldeflection,andhinge-momentcc%ficientdue to angle ofattack.
—
Theresults,hatingbeenfoundlymethods‘basedon thelinearized
equation,arevalidonlyforsmallcontrol-surfacedeflectionsandangles
ofattack.
SIMBOIS
II
c
c1
Cf
Ef
CL
%1
CP
maximumwingspan
wingrootchord
winglocslchord
wingman aerodynamicchord(,[’2C,2;=$
flapchord
flaproot-mean-squarechord (j=)
,.
liftcoefficient
()
Lift
T
pitching-momentcoefficientaboutwingaerodynamiccenter
(
Pitchingmoment
qsz ) ()Hhinge-momntcoefficient—qbGf2
liftingpressurecoefficient()
P
5
E($-:>)completellipticintegralof secondkindwithmodulus
d’==
H flaphingemoment
.
—
.
.5
3
.
M free-streamMachnumber —
P~
s
Sf
v
X)Y
Xcp
a
liftingpressureonflap
()
p+free-streamdynamicpressure~
()wingarea ~
,flaparea
free-stresrnvelocity
Cartesiancoordinates
streamdirection
3
distancebehindwinga~ex
fromflapdeflection
an@e ofattack
\.c/
parallelandnormal,respectively,tofree-
% lifteffectiveness~+ j
l-ii=
8 sngle offlap
e. ting-semiapex
dsflectim
angle
v Machangle ()
*-1 1
E
P free-streamdsnsity
fl disturbance-velocitypo ential
ofcenterofpressureofliftresulting
6X U.sturlacevelocityinx-direction
.Subscripts: .-..—
.!.,
a
5
CL
m
.>
partialderivativeof coefficientwithrespecto a
( )
a% .~ -VI~—...-.:
exemple:c~==
,., .... ~.....a ., !- . . . . . . =
partialderivativeof coefficientwithrespecto”5 (except
whenusedin ~)
.
partialderivativeof coefficientw threspecto ~
two-dimensionalc se
AIJanglesareinradiems,unlessotherwisespecified,
:, :.,,. T.,.- --- .,-
.’
—. ,,, ..-A3rm-im”” ...”’
.
-,
*
—
LiftEffectiveness
,.. , :..’ ..... . .,.-”.-..- ...........-~,-~-..,I...T .. -*
.
Thecontrol-surfacec mfigurationunderinvestigationisshownin
figure10 In calculatingtheliftcausedby a fiap”deflection5, the k
angleofattacka .maybeassumedtobe zero.Thedeflectedflapmay
thenconvenientlyberegardedasa tr#pezoi@lwingat@g snQe ofattack
equal to 5. Tworegionsof floware~stin@lshedindeterminl.n
—
lift. (Seefig.2.) firegionS~, thepressureis constantarl%Ud-
to thepressureona wing ofinfinitespsn.In eachof theregionsS~
theeffectof thefinitetipmustbe considere~. ,.#!., --:.
ThepreesureinregionsS11 maybe cdculatedbya powerfulmethod
developedbyEward (reference2). Figure3 showsthenotationusedin
reference2. Theequationsoftheleadingedgeandthetiparedefined
inreference2 in termsofan olillqm u,v-coordinatesystemwhoserxes
aretheMachlinesoriginatingat thetiy. For.~epres~t.case,the
valuesof kl and k2 (fig.3) become
kl=l
k2= l+ptezle1 -ptenE’ J
,., . . .. . . .
(1)
Thevelocitypotentialata po$nt (x,y),ononesurface.is givenby
equati.cm(20)ofreference2 fora’tig havinga wedge-shapedsection.
As pointedout inreference2,onlythesecondterm(whichis independent
oftheairfoilsection]contributestotheliftduetoangleofattack.
The}otentialata point (x)y)on onesideof thesurfaceforthe
presentcaseis thusgivenby
—
—
—
—
.
NACATN No.l&ll 5
.
. r,{Jw (kl+k2)(x + E@[(k2- + - (k2+qw]$ =—3-q3 k22
where kl and k2 havethevaluesnotedinequation(1).
In orderto oltainan expressionforthepressure,thedisturbuce-
velocitycomponent~ onwhichthepressureis dependentis obtainedby
tifferentiatingequation(2)withrespect
yields
l+!g
Forconveniencewrite
m=~teae
where o~nlgl and
o x. Thedifferentiation
+tan-1
(3)
where -l~v<m. men m=l, theMachlineliesalongthewingtiy;
when m . 0, &e tipisrectangul~(forMachnumbersgreaterthsmunity).
ThevalueV = m definesthewingtip;thevalueV . -1 definesthe
tipMachlinelyingon thefla~. Theequationfor ~ thenbecomes
(4)
NACATNNO.” 1601
.
By defininga pressurecoefficientas
. . . -., . . .
. ,.
,..!P=~”
whereP istheliftingpressurem theflap,
or
.
.—
l
Valuesof C_#3/5areshown5nfigure4 forseveralvalues of m.
.
When m“=0, equaticm(~)correctlygives,thepressmedistributionver
thetipofa rectangularwingasfound-byather.investiga$oi.f3. v
Withthepressureknownat allpoints,”determinationofthelift
.
coefficientperunitflapdeflectionisnowpossille.Thederivationis
carriedout forthecaseshowninfigure2,wherethe~ch linesdonot
—
intersecteachother.As ispointedoutsulmequehtly,theresultobtained
isalsovalidwhentheMachlinesintersect,solongas theMachlinefrom
onetipdoesnotcrosstheoppositetiy. Thelifton one til? is
or
>
.
EACA~ HO. l&)~
.
. ‘Iheintegrals my w evaluatedwiththeaidofequation(3JJ-),(161),
sn& (169)ofreference3 andtheresultis
%1 c~2(3m+l)
—=—
qj P2!
Theyressurecoefficientin theregion
value 45/p, andthem?ea S1 oanbe shown
s~ = I)cf - $(1+
so that
~ hasthetwo-dimensional
tobe
%4
[
—=-p 1-$1+a)qs
H theliftcoefficientisbasedon thetotalwingarea ?)0/2,thenthe
liftcoefficientperunitflapdeflectionia
,k ;2(!3+ 23
bc
Substitutingtheexpressionsfor 11/qb * ~1/q~ res~tsb
% ‘&- R%$l (6a) ‘
Cf
Thecase ~ . 1 representsa completetriangularwing,and
when m = 1 equation(6a)correctlygivesthelift-curveslopeasfound
by otherinvestigators(references4 emd5). However,when m isdif.
ferentfrom1,equation(6a)doesnotgivethevaluesfoundinreferences4
snd~. An exsminatlcmof therangeofapplicabilityis thusinorder.
.
Equation(2)isnotedtobe validonlyfor O <m <1 (Machlines
aheadof theleadingedge),sothatequation(6a)shouldnotbe expected
. b holdfor m>l. A furtherestrictionisnecesmryform<l.
8Equation(6a)was
doesnotmeetthe
derivedfor”thecasewherethe
Machlinefromtheothertip.
NACATN
Machlinefrom
Thecasewhere
NO.1601
oneti.y
theMach
linesintersecthasleenexsmined,andequation(6a)hasl)eenfoundto
applyalsoto thiscasesolongas theMachlinefromonetipdoesnot
crosstheoppositetip. Thissituationissimilartothatarisingin
thecaseoftheliftofa rectmgularwing. (seereference6, for
example.) Yorthe_presentconfiguratim,thelimitingconditioncorre-
Cf
qyn’ldsto ~ ~ +m. Thersngeofapplicabilityfor m <1 is shown
infigure5. Thesamerangeis.alsoapplicabletothere8ultsfor
pitchingmomentandhingemomentdueto controldeflectiontolefo~d
subsequently.Therestrictionwill%e foundunnecessaryIn thecaseof
hingemomentduetoangleofattack.
Forthecaseswhen m >1 (Machlinesbehindtheleadingedge),
usemaybemadeofemanalysisinzwference5 whichshowsthatthellft
coefficientandcenterofpressurearethesameas if theflapwere
suljectotheuniformliftdistributionfan infinitespanairfoil.
(Notethesimilarityof,thiscaseto thatofa triangularwingwiththe
Machlineslehindtheleatttngedge.) Forthiscaseequation(6a)apylles
if m issetequaltounity.
-Thequanttiyinbracketsthenbecomesthe
flaparearatioSf/S.
Nowthattherangeinwhichther6sults”aieapplicableiebowh,
thecompletequationsmsy%ewritten
%5:=- (6b)
.
.
L.
-1
cf/c <
where—= m~lmd.
.-
Cf
2C-—
(6c)
where re al..
Thenondimensionalquentity~ iscustomarilyusedtoexpressthe .
lifteffectivenessofa controlsurface,whichmayle regardedas the
ratiooftheliftcoefficientproducedby a unitflapdeflectionto the
liftcoefficientproducedby a unitangleofattackofthewholewing. l
NACATNNo.1601
In’reference4 an expressionhasbeenobtainedforthellft-curveslope
ofa triangulartingfor m $1. Rewrittigtheex~ressionofreference
inthenotationof“the
withmodulus11- ma.
presentpapergives
“=%757-)
9
4
Thelifteffectivenessi
or
where m> 1.
foranyvalue
(7a)
thecomplete ellipticintegralofthesecondkind
Forthecase m~l, thevalueof ~ hasbeen
foundinreference7 andissimply
~=;
Cfjc
where— ~m~l sndCf
2 .—
c . .
(73)
(8a)
(8-I))
Cf
Valuesof ~ aregiveninfigure6. At —— = 1, ~ = 1
c
of m becausethecontrolsurfacenowcomprisestheentire
wing. Theveryhighvaluesof ~ sreduemoreto theiOwlift-curve
slopeof thewingratherthantoanyparticularefficacyon thepartof
theflap.Forcertainccsnlinaticmsofc /c and m, ~ isgreater
thsnunity;thisfactIndicatesthata unitflapdeflectionwillproduoe
moreliftthana unitangleofattackofthewholewing.
A standardofcomparisonforcontrol-surfacerrangementsi the
two-dimensionalwing-flapcombination.Forthiscase,thelifteffec-
tivenessismerely ...
%.= (:).=(:).
.
WhentheMachlinesarebehindtheleadingedge (m? 1),
(9)
..,.
% ~ ‘-sothatforequalflaparearatios— = . A moreccmpleteco~arison
%.
withthetwo-dimension~tcaseismadeinthesecthnentitled‘rDiscussion
andConcludingRemarks.
PitchingMoment
An impor~’t_par~terinstabilityandcontrolcalculationsi the
pitchingmomentabout.thewingaerodynamiccenteresultingfroma given
liftontheflap. If thepitching-momentcoefficientisbasedon the
total.wingarea
andifthewing
wingayex,then
be expressedin
— ()~andthewingmeanaerodynamicchord sothat3
~ . Pitoh@gmoment.~Pitch@g moment
m qs~ 2 qsc
.
.
-...
l
#
—
—
aerodynamiccenterisnotedto%e at ~ behindthe .-
thepitchingmomentresultingfromlif~on theflapoan
coefficientformas ,
.
NACATN No.1601
l
.
%=
where
‘w/c is the
behindthewingayex
l
11
distance(expressedas a fractionof therootchord)
of thecenterofpressureof theliftresultingfrom
flapdeflection.Thisdistanceisfoundtobe
()
2
=Cp 12m-(3+ $hn]~+(l+3m)~
—=
c
12m- (3+ 3m~
Cf/c
where—$msl smdCP —
2 c’-—
Xcp
c
>1 so thatwhere m .
()z.4m-(l+7m)~+(l+3m)~
k =-
&.-(2 +2m)~
cf/c <where—= m$l .md
c-f
2C-—
c-f ()Cf21 -2T+
%=-
T
2.?
(lOa)
(10%)
(ha)
(lm)
where m z 1. VsJ.uesof
-~L are givenin figure7.
12
HingeMomentDue
Thehinge-m-ntcoefflci6nt
NACATN No.1601
l .
toControlDeflection .
caused”bya unitflapdeflection~
canle foundinthesanemanneras ~ ifmcmentsaretakenaboutthe ‘
hingelineratherthantheaerodynamiccenter.If thehinge-moment
coefficientisbasedonthemaximumflapspan b andthesquereofthe
root-mean-sqpareflapchordGf sothat “
.
(12)
~3
-2Cfl
=92-:+
then
cf/c <where—= m$l andCf
2C-—
(lsa)
(13b)
where m ~ 1. Valueeof -c~P/2 aregiveninfigure8. me vtiues
r+
of -C~p/2 for ~ . 1 (shownly circles)arethevel.uesof -c@/2
Cf
takenfrmnthenextsection,sinoeat ~ = 1 C% mustnecessarily
equal C~e Thevalueof ~ forthetwo-dimensionalc seIssimpu
(14)
NACATN NO.1601 13
so that thevaluesof
-~~1~ W fiw 8 arealsothevaluesof
I% %.”
HingeMomentDuetoAngleofAttack
k expressionfortheflaphingemomentresultingfroma chsngein
angleofattackofthewing ~ maybe o%tainedevenmoresimply_
theexpressionsderivedpreviously,sinceinthiscasetheonlyknowledge
requiredis thatof thelift-curveslopeofa triang’darwing,whichhas
beenfounilby otherinvestigators(references4, 5, and7).
Theschemeemployed.is showninfigure9. If theareaofthewhole
Wingis denotedby S andthewingareaminustheflapareaby S - Sf,
thentheflaphingemomentH canbemittinas
or
If as%eforetheflaphinge-momentcoefficientisbasedon 3%2 so that
then
Sulmtitmtingtheexpressionsfor C% givenby equations(7a) and(7b)
l gives
.
NACATN NCI. 1601 *
.
%=-;
where m $ 1 and
m“( .——2Efi-m2 )( )c-f3 -—c3-2$
()Cf3C-—Ck=d; - 2—3: (153)
where m ~ 1. Motethattheexpressionfor C% for ~>1~ —
identicaltothato%tainedfor @b for m ~ 1 (eqmtion(13b). This
identityshouldbs truelecause whentheMachlingsare%ehindthelea~ng .
edgeeithertheliftona triangulxmwingortheliftonthetrapezoid
wingconsideredtoreyresentheflayarethesameas ifthepressureon
—
—
the
for
wingwereconstantandhadthetwo-dimensicmslva ue., ,
valuesof -C@/2 arepresentedinfigure10. Thevalueof ~
thetwo-dimensionalwing-flapcotiinationis
Q%’-; (16)
i
so that figure10 isalsoa plot.of ~ C%.
DIWUSSION~ eoNciJuD~G~
Severalquantitiesmayle usedtoevaluatetheefficiencyofa
control-sutiacesystem.Onecommonlyusedquantityistheratio~/C@,
whichisem.indicationof theliftresultingfromtheapplicationfa
givencontrolforce.Byuseof thisratio,thepresentcontrol-stiace
arrangementcsn%e compared.witha two-dimensionalwing-flaycomhinaticm
onthebasisofequalratiosofflapareatototalwingarea. The
compsxisongives
.
.
. .
()%p~‘%9/% ()Sf Sf—.—Ssm . (k=)= m 1.
—.
.
... .
. . .’ .
.)
,-.
., ..,!,
,,
1 ..
.1
[13-4-m)3-$(1-J=),,,
,,
,“
. . .
.’ ‘.
.;
.._.,
.,
..
,,.
,;
,.,
.,-
. . i.’,
,’
and
,,
r , .;:-1:’-~‘s<~~l!-=
r,.,,Sf “.’,,;1+ ‘“-F- “,:,’ :,,-
:.:” :. ,, ,.
.$, ,’ . .
,.
,-:
,’
...
.,
,. ,,
,.
,,
.. .
. .
,!
‘ii-).’(J” q:, ,,::%3/c~ ;:: 3“’- :,.,- ,:= -r. ,“q~c
~~” ‘-(1-G)’:’”, ,“%5
,T=
.
.
.
.,
,.
...:
.,
,., .,
,.
.,
(lp)
where m ~ 1. Valuesfrom eqpaticms(17)we “ahoti n RI.gureU. For theusual&nge of the
ratioof Klapareataw@ area(lessthan0.5,for examp~), the valueof ~/~ for the
.,
presentarrangementisneverleesthem0.9ofthevaluefor the twodlmensI&al cdination. As
,.
theMach linesmoveaheadof the leadhg eQa, the effIciencyof thepreEeat“bagmmnt increasea “P
u
sndSOOIl
rangeof
NACATN No.1601
.
l
.
exceedsthatofthetwo-dimensionalcombinationfora wide
flaperearatios.A largepartof ~is increasermsultsfrom
thedroppingoffof thelift-curveslopeof thetriangularwing.
Inreference1 theefficiencyofa triangular-tipflapona trian-
gularwingwiththeMachlinesbehindtheleqdingedgewasshowntobe
equaltothatofa two-dimensionalwing-fla~combinatimhavingthessnw
flaparearatio.Solongas theMachlinessrebehindtheleadingedge,
then,thetriangular-tipcontrolsurfaceayyearstobe suyeriorto the
constant-chordflaponthe%asisof ~/~ (althoughforflaparea
ratioslessthanabout0.5thedifferenceinefficienciesi notcon-
siderable).Theresultsofananalysisofthetriangular-tipflapwith
theMachlinesaheadoftheleadingedgean
a comparisonof theconstant-chordflapwith
casecannotyetbemade.
Forcertaincombinationsof ~/c and
iSea~r th~ ~ity. (Seefig.6.) ~se
notyet-available,sothat
thisperhapsmoreinteresting
m, thelift’effectiveness~
veryhih valuesaremorethe
resultof thelowli.ft-ctiesl~~eof thewingfirl~wvaluesof m
ratherthanofanyremarkable lift-producingcapabilityon thepartof
theflap.
l
Althoughtheparsmeterm arisesnaturallyin theanalysisof tri-
angularwings,expressionofcontrol-suzTacecharacteristicsas direct
functionsoftheMachnumberM is oftenconvenient,especiallyfor
desiwpurposes.Figure12 showsthevariationof control-stiacehar.
acteristicswithMachnuniberforoneparticularconfigurationwith e = 45°
%?and ~ = 0.2. Othersuchplotscanben@e fromtheequationspresented
inthispaperorfromthefigures.
LangleyMemorialAeronauticalLaboratow
NationalAdvisoryCommitteeforAeronautics
LangleyField,Vs.,March~, 1948
REETRENCH
17
1.Tucker,WarrenA.: CharacteristicsofThinTriangularWingswith
~ismgular-TipControlSurfacesatSupersonicmeeds withkkch
IdnesbehindtheLeatigEdge. NACA~~0. 1600, lg48.
2.Eward,JohnC.: DistributionfWaveDragsndLiftin theVicinity
ofWingTiPs
3. Peirce,B. O.:
1910.
4. Stewart,H. J.:
QuarterlyAp@. Math.,vol.IV,no.3, Oct.1946,PP.246-254.
atsupersonicSpeeds.NACXTNNO.1382,1947.
A ShortTableofIntegrels.Secondcd., Ginnmd CO*)
TheIiftofa DeltaWingatSupersonicSpeeds.
~.Brown,CltitonE.: TheoreticalLiftsmdDragofThinTriangularWings
atSupersonicSpeeds.KACATNNO.u83, lg46.
6. sIIOW,R. M:,sndBonney,E.A.: AerodynamicCharacteristicsofWings
atSupersonicSpeeds.BumbleleeRep.No.55,me JO~S Eopk~s
univ.,APp~.p~sicSMb.,March1947.
7. Puckett,AllenE.: SupersonicWaveDragofThinAirfoils.Jour.
Aero.Sci., vol.13,no.9, %Pt. 1946,pp*475-484.
.
—L----- +------l
Figure1.- Control-surface
. . .
I
v
Iv
cotiguration.
/ /
/
t“ –
hj
Figure2.- Theflapregardedasa trapezoidalwing.
# . .
..
NACATN NCJ.1601 19
.-
Iv
/
e /#“Yfl//
/’
u
-If
Figure3.: Notationforthecase consideredinreferenceZ.
. .
NACATN NO.1601
.
1v
7 —
/
6
5 /
4
3 \
2“ \
=&=/
‘-L6 “12 -.8 -*k o .4 .8 i
v
Figure4.- Pressuredf.stf}lwtjonm Me
61pfegion 0/ a trqpezod hong.
#
.
2
.
~ tan&m f3Y17/u“ l
. .
4“—AAppkwbk
3? .8 Lo
.
. ,
/2
/.0
.8
.6
.4
.2
% ,2 .4 :6 .8 /0
Figure6.-Liftef’eckjvenes~ oi con.5&7nt-
si#/47ces 0/?
.5
\
.4 \
.3
.2 \
.2
N\’% --”-
1
./
.
,4 Ai/Yuk
I n
f)- . .
-,0 ..2 .4 .6 .8 L@
Rgure Z - Pitchlq - rnanent cAvmcter-
WKS d Constutit- m W-spun
control .swA7ces on WviguA2r wjogs.
. .,
II
I%p chord ratio, ~/c
Ffqvre 8.- ChimackerzsbcsOFIwye moment-
o’ue to LWtd d%lechon. i23nsh7nt-
ChOd Ail-spun Conhzi sur&ces
on trfongulur wings
, ,
lNACATN No.1601 23
.
CenLet-
/ \
*
c
Figure9.- Notationusedinderivationof hingemomentdueto angle
of attack.
.
.
.. .- 1
.
‘O .2. .4 .6 .8 LO
Figtire /0.- Ozzrocter/st/cs of hinge
moment due to cv7qle d dtachv
[w)stw- dof-c? Al- .p7n conhrol
Slf-h’ces 0/? tfw?gukw /#1/7g3.
“,.
‘ 1. 1“1 I
5
I
4 m
.2
/ -
3 ,
.25
.3
2 : m
/
~~ .2 ‘ .4 .6 .8 /0
hgffre //.- ReA7iWe eA9c/encyof constun.t-
chord fulkyw Cw7t..d surfuce.5 m
trkzn~ular wmg~ as compured WILY?
two- dimensknwl wmg-flup @vb/no’t/w
hwwg sumz Flop Oreo fwtm.
.
‘5
2
a
!gl
.
Pmo
P
.
.
. .
.5
.2
.
5
4
I
.6
t?
.4
.2
.
\
_aJ
+
,-
U
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Characteristics of thin triangular wings with constant-chord full-span control surfaces at supersonic speeds

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