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NATIONALADVISORYCOMMI~EE
FOR AERONAUTICS
[
TECHNICALNOTE 2486
THEORETICAL CHARACTERISTICS OF TWO-DIMENSIONAL
SUPERSONIC CONTROL SURFACES
By Robert R. Morrissette
and Lester F. Oborny
Langley Aeronautical Laboratory
Langley Fieldj Va.
“t
.--f
Washington
October 1951
.,
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NATIONALADVISORYCOMMITTEEFOR AERONAWICS
TECHNICALNCYIT2h86
THEORETICALCHARW91ERISTICS
OF TWO-DIMENSIONAL
SUPERSONICCONTROLSURFACES1
By RobertR. Morrissetteand LesterF. Oborny
,.U
!!RIWNEW “‘~.,.,.,.
REdRD.
.
‘:
The ‘kzsemsnnsecond-order-approxhationtheory”for the pressure
distributionover a two-dimensional
airfoilh s~ersonic flow was used”
to determinesome of the aerodynamiccharacteristics
of unceaibered
symmetricalparabolicand double-wedgeairfoilswith leading-edgeand
trailing-edgeflaps. The tivestigation was origkl~
titendedfor
applicationto aileronstudiesbut, since the analysisis based on twodimensionalflow, the resultsare applicableto all t~es of control
surfaces. The use of the term “aileron’’may
consequentlybe replacedk
the presentpaper by the term “controlsurface.“ The chemcteristlcs
presentedand discussedare: allemn effectivenessfactor,rate of
changeof hinge-momentcoefficientwith ailerondeflection,rate of
change.ofthe pitching-moment
coefficientabout the mldchordwith aileron
deflection,and the locationof the centerof pressureof the airfoilailezwnconibhation. h supersonicflow leading-edgeaileronswere found
to be nnzchmore effectivethen tmiling-edge ailerons. Neitherailercm,
however,is as effectivein supemonic flow es the trailing-edgeaileron
in Sul)sonic
flow. The calculationsshow that, for a given thictiess
ratio,trailing-edge
ailerons are more effectiveon wedge airfoilsthan
on parabolicairfoilsjwhereasleading-edgeaileronsare more effective
on parabolicairfoilsthan on wedge airfoils. The magnitudeof the
valuesof the rate of chengeof the hinge-momentcoefficientwith aileron
deflectionand the rate of changeof pitching-moment
coefficientabout
the midchordwith ailerondeflectionis greaterfor leading-edgeailerons
than for trailing-edgeailerons.
lXTRODUCTION
x
*
In investigations
of the aerodynamiccharacteristics
of ailerons,
the influenceof certainfactorsis not found in the predictionsbased
on a linearizedsolution. Higher-ordersolutionsare thereforenecessez’yand consequentlythe emalysismust be made for a two-dimensional
wing. The resultsere applicablenot only to aileronsbut to all types
of controlsurfaces.
Severalmethodsare k use at this time for [email protected] the P=ssue
distributionoyer thti airfoilsin a supersonicair stream. The
prevailingmethodsare: the graphicalmethod of references1 and 2, the
%zpersedes the recentlydeclassifiedNACAWMG12,
“Theoretical
Characteristics
of Two-Dimensional
SupersonicControlSurfaces”by
RobertR. Morrissetteand LesterF. Oborny,1948.
.
!2
.
~cA TN
2M16
Ackeretthin-airfoiltheory,the Busemannsecond-orderapproximation
used in reference3, and the power seriesof references2 aud 4. None
of thesemethodsare exactas they do noti-onsiderthe effectof the
bounda~ layeron the airfoil.
In this paper the 13usemann
second-ordera~yroxifition”is
used as
the best compromise%ecaueethis approximation
givesexpressionswhich
are simpleenoughto he used in desiguw~rk aud which are probablyas
accuatieas couldbe expectedof any method that neglectsthe boundarylayer thickness. The Busemannapproximation
uses only the first--two
terns of the power seriesfound in references2 and 4. Figures2, 12,
and 13 of reference2 show that the f’irsttwo terms of the power series
give resultsthat-arecloseapproximations
to the resultsobtained%y
we of the oblique-shock
equationsad the isentropic-eqansion
and compressionequations. The methodused herein is a closerapproximation
than the Ackerettheoryas the TJusemamn
approximation”
tshs into account
the effectsofllachnumber,airfoilthickness,and airfoilshape.
.—.
—
The second-orderap~roximation.is
limitedto sma~ anglesand thin
airfoils. Reference2 statesthat the theoryused is notmcmsldered
accuratefor Mach nwibersless than approximate= 1.3. This lower-limlt
has been used arbitrarilyM this analysis. Also, the theoryis not
good for I&ch rnmibers
below that at which the shockwave detaches.
Reference2 givesvaluesfor the minimumMach numberfor the existenceof
an attachedshockas a functionof the flow-de”flection
angle.
,.
The factorsvaried in this analysisare airfoilthicknessratio,
Mach number,airfoilshape,ratio of aileronchord to wing chord,and
locationof aileron. The characteristics
investigatedincludedaileron
effectiveness
factor,rate of changeof hinge-ant~uefficient with
ailerondeflection,rate of changeof pitching-umentcoefficientwith
ailerondeflection,and locationof centerof pressureof the alrfoilalleroncombination.The equationsused hereinand”a s~le derivation
are found i?ithe sectionentitled“ANALYSIS.
“
SYMBOLS
c
chord of airfoil (takenas = 1.0 herein)
c~
chordof aileron,fractionof airfoilchord
Cl and C2
constantsused in first and secondterms of Busemsmn
approximation
for pressurecoefficientin supersonic
flow
Cha
aileronsectionhinge-momentcoefficient(ha/qocZJ
m
...
—
m’
—
8-. –
3
NACA TN 2M6
●
cl
✎✎✍✌
%.5
airfoilsectionlift coefficient
airfoilsectionpitching-nnnent
coefficientabout
midchord (%5/w2)
centerof ~ressuremeasuredfrom leadingedge, fraction
of chord
aileronsectionhingemoment
airfoilsectionpitchingmoment aloutmidchord
free-streamMach nunher
free-stresmdynamicpressure ( $oTc?)
meximumthicknessof airfoilsection
free-streamvelocity
distancebehind leadingedge, fractionof chord
ordinatefrom chord line to any point on surfaceof
airfoil,fractionof chord
.
..
Ap/q
pressurecoefficient
dcza/d5a
dcZ/da
aileroneffectiveness
factor
airfoilangle of attack
a
deflectionof aileronrelativeto chord line (considered
positivewhen it gives ailerona positiveangle
of attack)
6a a
geometricparsmeterused in determiningcenter-of-pressure
location
e
localanglebetweenQ petit on surfaceof airfoil~d
free-streamdirection
I
free-streamdensity
ratio of specificheats (1.4)
)+ ..–.
NACATN
2A-86
Subscripts:
a
aileron
h
aileronhinge-lineposition exceptwhen used in c
%)
L
lower surfaceof airfoil
u
upper surfaceof airfoil
●
(
—
ANALYSIS
The analysiswed in this paper is based on the BusemannsecondAy
order approximation
for the pressurecoefflclenti~
in supersonic
flow* This coefficientis expressedin references-in the following
form:
Ap
—=
!I
Cle + [email protected]
..
where
“=l&-
—..—
yMo4 + M.2-Q2
( .
)
C2 =
%2(
1)2
—
The procedureused in deriv~ the equaliiou”f~r
the”-parameters
consideredIs illustratedby the followingderivationof the aileron
efTectlveness
factorof a parabolicairfoilwith a trailing-edge
aileron.
The otherparametersare obtainedby a similaranalysis.
.%
U
NACA TN 2h86
5
.—
--
.
AileronEffectivenessFactor
-?
Parabolicairfoilwith trailing-edgeaileron.- The equationfor the
u~yer surfaceof a parabolicairfoilwith the leadingedge at the [email protected]
and the trailingedge at x = 1.0 is
=
‘u
()
2LX-X2
c
The slope at any point on the upper surfaceof the airfoilis
()
u
E
=231
.—
- 2x)
u
The [email protected] 19 betweenany point on the surfaceof the airfoil
end the free-stresmdirection,therefore,is
‘%=-a+
()
f%!
G
u
= -~ + 2ql
c
.-
- 2x)
-T
and
‘L =a-
()
Q
dx
L
.a+2~(l
-2x)
It followsthen that
()
Ap
T
= Cleu +
c2eu2
---—
u
=C~ -a+ 231 - 2xjl + C2~a + 231 - 2x)12
[
NACA TN
and
‘“”
2M16
.
.—
(%L[
sc1Cz+231-
“1+C++2:’1-+12
.
The pressurecoefficientrfor
the airfoilthen Is
or
AP
—=c~(2CL)
~
+ C2 8CL#
[’-
-4
The lift-coefficient
of the airfoilis
P1. o
.
p.o
=2a
/[
cl+
4C23L
-2X)1
-.
dx
1.0
= 2CL c~x + 4C2;(X
[
- X2 ]
o
The rate of changeof liflrcoefficient
with emgle of attack thereforeis
.
NACA TN 2M6
7
The lift coefficientof the aileron Cza due to some aileron
deflection ba can le found in a similarmanner.
Becauseof the linearnature of the equationsfor pressurecoefficient,the pressurecoefficientat a point on the airfoilcan’befound
by addingthe pressurecoefficientfor the wing at angle of attack a
with unreflectedaileronsto the pressurecoefficientfor the wing at
zero anglq of attackwith the aileronat angle of attack 5a. The
contributionof the ailerondefinesthe controlforce on the wing and for
that reasonmay be treatedas a separateaileronpressurecoefficient.
The pressurecoefficientfor the aileron AL
()o)
therefore,is the
[’la
sane as that found for the airfoilexceptthat the ailerondeflection ba
is used in place of the angle of attack a. Thus,
Then, the lift coefficientfor the ailerondue to some deflectionis
rl”O
pl.o
.
28a
][
[email protected]
- 2X) Cuc
1
Xh
1.0
=28aC~X+4C&X
[
OJ ,
-X2
Xh
9
:..
.-.
8
NJ4CA
TN 2486
and, therefore,the rate of changeof lift coefficientof aileronwith
ail&rondeflectionis
-
=
2(’- ‘h)(+- ‘Q:xh)
The aileroneffectiveness
factorfor a parabolicairfoilwith trailingedge aileronthus is
—
.
dcl da =
2c~
/
(
=1
“hl
)(
-
C2
4- ~xh
cl c
)
Parabolicairfoilwith leading-edgeaileron.-The aileroneffectivefacturfor a pa?.%bolic
airfoilwith a leading-edgeaileronis
.
Wedge airfoilwith [email protected] aileron.-The aileroneffectivefactorfor a wedge airfoilwith a trailing-edge
aileronwhen
O.’jo is
—.
dcla dba
/
[email protected]
uld when
=1
(
.xhl-&—
)(
C2 t
c1 c
)
—
‘h ~0050,
.
‘cza?~a
dcllda
=l-xhl+z—-
()
.
C2 t
cl c
!
9
NACA TN 2M6
Wedge airfoilwith leading-edgeaileron.- The aileroneffectiveness
factorfor a wedge airfoilwith a leading-edgeaileronwhen xh .>o.~
-t
iB
dcza ma
/
‘=%+~f:(’-xh)
“l/&
and when ~h SO.50,
‘cza/d5a
,_=xhl+2~;
dcZ/da
()
C2 t
Rate of Chsmgeof AileronH%nge-MomentCoefficientwith Aileron
Deflection
&
Parabolicairfoilwith trai~~-edge aUenn.- The equationfor the
rate of changeof aileronhinge-momentcoefficientwith ailerondeflection of a parabolicairfoilhavinga trailing-edgeaileronis given .5a
Parabolicairfoilwith leadm-edge aileron.-The rate of changeof
aileronhinge-momentcoefficientwith ailerondeflectionof a parabolic
airfoilwith a leading-edgeaileronis
..
Wedge airfoilwith trail--edge aileron.- The rate of changeof
aileronhinge-momentcoefficientwith aile?xmdeflectionof a wedge airfoil with a trailing-edgeai
leron
when xh 20.50.
is
.
NACA TN
10
2h86
and when xh <0.%,
=
ach
g=
,
(1- 2%2)
41 + ~2;
(’ -‘J
Wedge airfoilwith leading-edgeaileron.- The rate of changeof
aileronhinge-momentcoefficknt with ailerondeflectionof a wedge airfoil having a leading-edgeaileronwhen ~
bha
—=%
at5a
~00~
(
. C2:
1 - k’xh+
is
)
2xh2
2
xh
and when %= <0.50,
Rate of Changeof Pitching-Moment
Coefficient-shout
Midchordwith
AileronDeflection
Parabolicairfoilwith trailing-edgeaileron.- The rate of ch~e
of pitching-mmentcoefficient–aboutnnidchord
with ailerondeflection
of-a parabolicairfoilhavinga trailing-edge
aileron is given a8
k.
3x~+ 1
)
Parabolicairfoilwith leading-ed~eaileron.-The rate of change
of pitching-mxnent
coefficientaboutmidchordwith ailerondeflection
of a parabolicairfoilwith a leading-edgeaileronIs
.
<
NACA TN
2&86
U
Wedge airfoilwith trailing-edgeailenm. - The rate of changeof
~itching-moment
coefficientabout midchordwith ailerondeflectionfor
a trailing-edge
aileronwhen Xh >0.50 is
.
and when xh <0.50,
.
Wedge airfoilwith leading-edgeaileron.- The rate of changeof
pitching-moment
coefficienta%out midchoniwith ailerondeflectionfor
a leading-edgeaileron
.
.
and when xh 5
0.50,
Rate of Changeof Pitching-Moment
CoefficientaboutMidchord
with Angle of Attack
%ralolic airfoil.-The rate of cha.uge
of pitching-moment
coefficient aboutmidchordwith angle of attack for a parabo31cairfoilis
—
.
a
% “51tt -,2—.
&
3C
—
—
12
NACATN
2M6
Wedge airfoil.- The equationfor the rate of changeof pitching?mxuent
coefficientabout.midchordwith angle of attackfor a wedge airfoil is given as
*
..
—
.—
.
“5
%
.
These equationswere obtainedfrom equationefound in reference3 end
are givenhere for the sdse of completeness..
—
Centerof Pressure
Parabolicairfoilwith trailing-edge
ailezxm.- The center-ofpressureequationfor a parabolicairfoilhavinga trailing-edge
aileron
is as follows:
1
CP =
4c2t
4e2t+8a
—1 + 3xh2 - kxh3
]
-Zq;
T1-=h2-3clc
(
[._...__._._...
5
2+ $1
-Xh 2- + >h
(
)(
)
1
.
.
Parabolicairfoilwith lead~-edge aileron.-The followingcenterof-pressureequatlanfor a parabolicairfoilwith a leading-edgeaileron
is expressedas:
L
—
=
Wedge airfoilwith trailing-edge
aileron---The centerof pressure
‘oep
aileronwhen xh =
for a wedge airfoilwith a trailing-edge
ia
r.
.
:-
WCA TN
2h86
and when Xh ~ 0.50,
.—
Wedge airfoilwith leading-edgeaileron.- The centerof pressurefor
a wedge airfoilwith a leading-edgeaileronWhOn xh >OC50 is
CP
and WhOn xh~ 0*50,
6
C2 t
l’-C—; +xh2+l+2~;
1
()
c
P=
2 + ~h~
C2 t
1+2— C2 t
C1 c
()
1
.—
NACA TN
14
2486
“
IaRu3ms
r.
Drawingsof the yarabollcand wedge airfoilsectionsused in the
calculationsmay be seen in figure1. These two shapeswere chosen
becausethey are frequmtly consideredfor use in the wings of supersonicaircraft.
In figures2 to 40 is shown the variation of the aerodynamic characteristics of aileronswith airfoilshape,locationof aileron,airfoil
thicknessratio,free-stremllachnuniber,
ratio of aileronchord to wing
chord,and the ratio of ailerondeflectionto the angle of attsck.
Table I is an indexof the figures.
ti fi~
2 (fig. 9 of reference5 excejt Busemanncurve)a comparison is shown of the resultsobtainedby the msthod of calculationWed
hereinaud the resultsobtainedby both the Ackerettheoryand the
in this paper gives results
method of reference1. The method‘presented
that approachthose of the method of reference1 much closerthan the
Ackerettheory. This closer result Is due to the fact that thickness “
ratio,Mach number,and airfoilshape are taken into considerationin
the second-orderapproximation,
whereasthese factorsare neglectedin
the Ackerettheo~.
Figure 2 also shows that the ailercmeffectivenessfor trailingedge aileronsin subsonicflow is much higherthen the aileroneffectivenessof [email protected] supersonicflow. The reaaonfor
this result is that the flow ahead of the aileronis affectedby the
ailenn in subsonicflow,whereasthe flow in this region is not
affectedby the aileronin supersonicflow.
-.
.
Unlike the Ackerettheo~, the analysisused hereingives the
followingresultsfor an airfoil-aileron
combinationin supersonic
flow:
(l) Leadfng-edgeaileronsare more effectivethan traillng-edge
ailerons. (Seefigs. 3 to 7.)
(2) The magnitudeof the valuesof ‘ha/bba ‘d
~.
51a6a is
—
greaterfor leadhg-edge aileronsthsn for tr&Lling-edge
ailerons.
(Seefigs. 13 to 1’7end 22 to 26. )
‘
(3) The centerof pressureof an airfoil-aileron
combination
havingmaximumthichess at the midchordand zero ailerondeflection
is ahead of the tidchord(figs.31 to 34)*
.. . .
.
Mach number.-An Increasein the free-streamlkch number gives the
followingresults:
(1) Above a Mach numberof approximately1.75 fdependlngon thickness ratio),the aileroneffectiveness
for leading-edgeaileronsis
XACA TN
2k86
increased=d the aileroneffectiveness
for trailing-edgeaileronsis
decreased. (Seefigs. 8to u.)
(2}
The magnitude of the valuesof
&h
aba and & ~.5[a6a ‘“
/
decreasedfor both leading-edgeand trailing-~dgeailerons(figs.18
to21and27to
30).
(3) b Keneti, above a Mach nuniberof approximately1.7 the
centerof pressureof an airfoil-aileron
combinationmoves forwardas
shown in figures31 to 34.
Thiclsness
ratio.-The main differencebetweenthe first-orderand
second-orderapproximationsis the thickness-ratio
effect. The secondorder approximationshows that an increasein airfoilthicknessntio:
(1) ticreasesthe effectivenessof leading-edgeaileronsand
decreasesthe effectivenessof trailing-edgeailerons. When the thickness ratio is zezm,the effectivenessis the saue for both leading-edge
and trailing-edge
ailerons. (Seefig. 12.)
.
(2) lhcreasesthe magnitudeof the values of ‘ha/aba ‘d
~b for leading-edgeaileronsand decreasesthe magnitudefor
%.5/
a
trail&g-edgeaileronsas shown in figures18 to 21 and 27 to 30.
.
tion forward (fig.40).
(3) ~~es the cent= of pressureof the airfoil-aileron
combinaAirfoilshape.-For a given thicknessratio of the airfoilscon- “
sideredherein,the surfaceslo~enear both the leadingand trailing
edges of the Tarabolicairfoilis greaterthan the slo~e at corresponding
poSitionson the wedge airfoil. In these regio~, therefore,the -p~bolic airfoilacts like an airfoilwith a largerthicknessratio. It
then followsthat:
(1) For a given value of t/c, trailing-edgeaileronsare more
whereasleadingeffectiveon [email protected] airfoilsthan on parabolicairfoikj
edge aileronsere ?mre effectiveon paraboMc airfoilsthan on wedge
airfoils. (Seefigs. 3 to 7.)
(2) The centerof pressureis fartherfommrd for the parabolic
airfoilthan for the wedge airfoil (figs.31 to 39).
.
-1
Ratio of aileronchord to winR chord.- An increasein the chord of
the aileronincreasesthe surfacearea of the aileron. As a resultof
this increasein aileronsurface:
(1) The aileron effectiveness is increased (figs. 2 to 7).
16
NACA TN
2k86
(2) The magnitudeof the value of b
&a increasesuntil the
%/ ●5
aileronchordreachesa value of half the wi~ chordjthen it decreases
as the ailem chord Is increasedfurther. (Seefigs.22 to 26. )
Since the pressuredistribution over the wedge airfoilis independent of the chordwise location aa long as the surface slqe is a
co~t~t,
the vake of achaj%-a is independent of the ratio of the
aileron chord to the wing choti. After the value of
ca/c
exceeds 0.5,-
however,the surfaceslopechangesand the pressurecoefficientis no
longerindependentof the chordwiselocation. Thus, for furtherincreases ‘- in ca/c beyondthis value,the value of bch /& a then decreasesfor
a
ailerons and increases negatively for tmiling-edge ailerons
leading-edge
(figs.14, 16, and 17).
The theoryshowsthe ~ressuredistributionover a parabolicairfoil
to be a functionof the chordwiselocation. As a result,when the
ratio ca~c is increased,the value of ?)ch bba decreasesfor leadingal
edge aileronsand increasesnegativelyfor trailing-edge
ailerons. (See
figs*13, 15, ad 17”)
Ratio of ailerondeflectionto angle of attack.-Ihcreasingthe
ratio of the ailerondeflectionto the angle of attackresults in a
relativelyhigherpressureon the aileron-surfaces
than on the rest of
the airfoil. The centerof pressureis thus shiftedforwardwhen
leading-edge
aileronsare us~d and backwardwhen trailing-edge
ailerons
are used. @ee figs. 31to 34.)
..
.~.
.
CONCLUSIONS
The %usemann second-orde~approximation
theory”for the pressure
distributionover a two-dimensional
airfoilin supersonicflow was used
to determinesome of the aerodynamiccharacteristics
of’uncambered
symmetricalparabolicand double-wedge
airfoilswith leading-edgeend
trailing-edge
ailerons. Within the limitatio~ of the thea?yused, the
followingconclusicmsmay be drawnabout the effectiveness
of.ailerons
in the Mach numberrange (1.3 to 4.0) investigated:
1. Neitherleading-edge
nor trailing-edgea
ilerons mea
effective
in supersonicflow as the trailing-edge
aileronin subsonicflowo
For a givenairfoilshayeat high Mach%umbers, leading-edge
aileronsare much more effectivethan trailing-edge
ailerons. However,
the relativeeffectiveness
of leading-edgeand trailing-edge
aileronsis
a functionof thicknessratio and the differencebetweenthe two becomes
smallerwith smallerthicknessratios.
2.
~,
.
NACA TN
17
2486
.>:’
3. For a given thicknessratio the aileroneffectivenessis greater
for leading-edgeaileronson parabolicairfoilsthan for leading-edge
aile?mnson s-trlcal wedge-shapeairfoilsjhowever,trailing-edge
aileronsare more effectiveon symmetricalwedge-shapeairfoilsthan on
parabolicairfoils.
-.
4. An incmmse in airfoilthicknesstends to decreasethe atleron
effectiveness
when trailing-edgeaileronsare used, whereas it increases
the aileroneffectiveness
when leading-edgeaileronsare used.
5. The magnitudeof the values of the rate of changeof the hinge-
—
moment coefficientwith ailerondeflectionand the rate of change of
pitching-moment
coefficientabout the midchordwith ailerondeflection
is greaterfor leading-edgeaileronsthan for trailing-edgeailerons.
.
LangleyAeronauticalLaboratory
NationalAdvisoryCammitteefor Aeronautics
[email protected] Field,Va., April 13, 1948
RlmEKENcEs
6
.
1. Ivey, H. Reese,Stickle,GeorgeW., and Schuettler,AIberta: Charts
for Determiningthe Characteristics
of Sha~-Nose AirfoilsinTwoDimensionalFlow at SupersonicSpeeds. NACATN 1143, 1947.
2. Laitone,EdmundV.
:
=t
cmd ApproximateSolutionsof Two-Dimensional
O%liqueShock Flow. Jour. Aero. SCi., vol. 14, no. 1, Jan. 1947,
PP. 25-410
3. Bonney,E. Arthur: AerodynamicCharacteristicsof RectangularWings
at SupersonicSpeeds. Jour. Aero. Sci., vol. 14, no. 2, Feb. 1947,
pp. UO-U6.
4. Busemann,A.: &rodynamic Lift at
Supersonic Speeds. Rep. No.
BritishA.R.C.,Feb. 3, 1937. (FromLuftfahrtforschung,
Bd. M?, Nr. 6,-Ott.3,’1935, Pp: 23-0-220.)
2844,
5. Ivey, H. Reese: Notes on the TheoreticalCharacteristicsof Two.
DimensionalSupersonicAirfoils NACA TN 1179, 1947.
●
~,
,,~.:-. .. . ........
.. .
-=
.—
!,-.-
●
NACA TN
2U86
TABZE I – lXOEX OF FIGURIS
~
1
2
tiation
~
airfoil aileron
TJW of
Plot
‘me
of eJrroil
sectionswed
........-
‘2a~6a.
—
egakt ca/o VeQe
‘%1~
-..-.-—
Trailing
edge
‘Z.#a
—
‘cl/b “
4
‘Za~a
egainet
caJo VeQe
doda
Z/
5
‘la~a
—
egatitcaio parabolicLaada
edge
do da
II
7
‘Z~~a
do#a
t/c cap baja
------a- ----
4.0
----
---
0 to
0.05 ~.~ ---
TraiLlng 1.5,3.0,.05,Oti
.10 1.0 --‘a/c ‘-ho’io
*e
4“0
3
6
-_
%
~almt oaic
Wedge
Traillng 1.5,3.0,.05,ok
edge
4.0
.lo 1.0 ‘-1.5,3.0,.05,Otu --4.0
.lo 1.0
Leadlrlg
“ 1.5,3.0, .05,Oto --edge
%a a%
‘are.bcmc ‘rrail.lng
and
/
agaiDEt
ca/o
endwedge Leadingedgaq
&c da
4.0
4.0
.10 1.0
.10
to0
lo
--.
ll
dcla d8a
/
againet
~
—
9
‘laP 8a
-W
dc11b
~
We&e
la
‘laP 8a
egahet
dc1/da
~
‘arabollc
11
acl~a
—
‘ilk ‘tit %
dc G
11
1.3to
4.0
09“05> .2 ...10
Tralllng
edge
1.3b
4.0
0,“05> .2 .-.
.lo
Leading
1.3to
4.0
0,.05, ,2 -=.10
1.3to
4.0
0>“05) .2
.io
‘arabom Trailing
e-
8
Wedge
edga
LZlading
edge
-..
‘l#a
‘“
w
“akt “c
13
%
—
egaixlet
Cafe
&a
“out
‘Zega
‘:;’3”0;‘;F
“2
‘--
1.5,2.0,.05,oh
‘mbolic ~rtiling
edge
4.0
.-1o1.0 ‘--
.-.
2k86
NACA TN
19
TABLE I – INDEZ OF FIGURES-Continued
Pint
~c
~,
%
~
egalnet Cajc
15
b%
—
16
%
—
egainet Gala
a%
egalnet ca/c
Type of
airfofl
LOoationof
e.ilercm
Wedge
Trailing
edge
1.5,2.0> 0.05, 0 to
.I.o 1.0
‘--
ParabolicLeading
edge
1.5,2.0, .05, Oto
.lo 1.0
4.0
---
,
;.~,2.o, .05, oh
.
1.0
.10
---
Wedge
&a
*,
‘h
17
—
18
b
‘a
—
egalllet~
19
‘%
—
Z.
a6a
egalnet oa/c
a5a
a~a
%
q
age.inet
~
~ht
~
[email protected]
edge
t/o
%
4.0
and
Parabol.ioTrell.lng
endwe~e leadingedges
4.0
.lo
ca/o
::
.
6~a
---
Tre.illng
edge
1.3to
4.0
“053 .2
.10
---
TrailAw
edge
1.3b
4.0
.05, .2
.lo
---
ParaboUa
Leaahg edge
1.3 to
.05, .2
.lo
---
4.0
Wedge
L9ad.hg
1.3to
4.0
.lo
“05>
.2
---
.05, Oto
.I.o 1.0
---
1.5,2.0, .05, Ot o
---
Parabo13c
Wedge
.
%
21
—
22
—
23
—
a6a
againet ~
a%.5 agalsLetCalc
a~a
%.5
PexalIolfo TrailiIw
edge
%.5
—
Wedge
[email protected]
againet Ca/c
Parabolic
Leading
1.5,2.0,
Wedge
IeaCmlg
edge
a~a
25
%.5
—
agalnetca/o
26
%.5
agalnet ca/c
&a
a8a
1.5,2.0,
k.o
a&ahlet ca/c
&a
24
edge
edge
eUge
Parabollo Tmiung and
.lo
4.0
1.0
.05, Ota
---
1.5,2.0,
.05, Oim
.lo 1.0
---
4.0
k.o
edges‘
=a wedgeleading
2.0
.lo 1.0
.lo ;0
.h
=3=”
--.—
NACA TN
2J
2h86
TABLE I..-INDEX OF FIGURES-Concluded
{
Plot
Ugure
27
Typeof
alrfo11
%.,
—
aoa
[email protected]~
Locationof
aUeron
%
1.3to
t/c
a/o
0.05, (3.2
.lo
8+
..-
Parabolic
Trailing
edge
Wedge
Trailing
edge
1.3to
.05,
.10
.2
---
4.0
4.0
28
%.,
—
29
%.3
—
againet~
ParaboMo
Leding
edge
1.3to
4.0
.lo
.05,
.2
---
30
%.5
—
Egainat
-~
Wedge
Leaahg
edge
1.3ia
4.0
.05,
.10
.2
---
Pambollo
Traillng
edge
1.3to
.I.o
.2
om~
Wedge
Trailing
edge
1.3to
.I.o
.2
oa~
i3gainat~
,
&a
~
&a
&a
31
‘P
32
Cp EgaIllEt
~
33
(+ agalnet
~
34
~
[email protected] ~
Wedge
35
Cp egahet calc
Parabol.io
36
Cp against cap
Wedge
37
Cp O&Etit oa/o
Parabollo
egalnet o
Wedge
38
39
CP
eg.aillEt
~
Cp [email protected]
J
ca/c
Parab9Mo LeedlI12
edge
Iad~
eke
4.0
4.0
1.3to
k.o
.I.O .2
o~to
1.3to
4.0
.lo
.2
0~~
.05, Oto
~,.
Trailing
4.0
.10 1.0
Trailing
e‘>
4.0
“05? Oto
.10 1.0
l,o
Leading
edge
4.0
.05, oh
1,()
Lsadlng
4.0.
edge
Parabolic TraIllngand
and w’@3~ ~
*e
4“0
.lo
1.0
.05, 0 to
.10
1.0
lo
“
.10
;m:
1.0
.
40
($ againet t/c
ti
Perabo130 .TrailJng
leadinged.gw
;.:,3.0,
.
oJb
,2
1.0
.
.
NACA TN
2M6
21
.
“
n
(a) Parabolle airfoil.
*.
.
‘0
(b) Wedge airfoil.
Figure 1.- Airfoil seotlons used In caloulatlons.
,--
NACA TN 2486
22
1.0
09.
.8
Sutmonio
(Xe= o)
*7
.6
●5
.
●4
,.
●3
.2
.1.
T
o
0
,2
.k
.6
.s
1.0
Aileron oho~wing ohoti, odo
.
rlgure2.- Aileraneffeetiveneeeau a ?unotlonof the
ratio of a:lwonchord to wing ahord for ● n unoamberedwedge airfoilhavingWImum ttitokneen
at midohordand trailing-edge
aileron. = 0.05.
5
(~urvea
tithexoeptlon
or~unemani
curveapefrom
figure9, referenoe5.)
NACA TN
2U6
23
1.0
.
.
,
.9
●g
●7
.6
,4
.3
.2
.1
0
.6
●L!
1.0
AilerondIord/wingohord, o~o
.
(a) ~ = 0.05.
Figure
3.-Aileron
etfestiveness
ae a ~unotlkn
of the
.
ratio-of aileronohorclto ulng ahord for an uncamberedparabolloairfoilhavin maximumthiokness
et midahomiand trailing-edgealferon.
.-. .._ . .,
1.0
-.
●9
F
.-
.
●2
.1
0
0
.
●2
.4
.(
“d
1.0
—.
-..
-.._ .—
_..
.—.
—
_
Aileron ohord/wingohord, odo
(b) ; = 0.10.
Figure 3.-Oonoluded.
-,
.
4
NACA TN
.
25
2h86
1.0.
I
Y
.9
●g
●7
.6
.5
1.5
.0
.0
.4
93
.2
y
●1‘
o
-o
.2
.4
.6
●g
1.0
AileronohorcVwingohord, OJO
.
.
(a) J
a = 0.05.
lUgure
4.-Aileron effeatlveneseas a funotionof
the ratio of aileronohord to wing ohord for an
unoamberecl
wedge alrfollhavingmaximumthlokness
‘at mldohordand trailing-edgeaileron.
-.
—
.
,,
,
I
.8
●
1.0
Aileronohord/wingohord, Oa/O
(b)
;
=
0.10.
.
Figure4.- Oonoluded.
.
NACA m
.
27
2h86
.-
“m
.
.
.6
.-
T
w
●
5t———7—7
.4
4.0
3.0
!11
.3
●2’ .“
.1
,
.g
Aileron ahord/ulngohord,o~o
(a) { = 0.05.
50-Alleron effeotiveneaa an
a funotlonof
the ratio of aileron ohord to wlna ohord for an
unoamberedparabollaairfoilhavlfig
maximum
thloknessat midohordand leading-edgeaileron.
Figure
1.0
.
1.C
Ho
—
.$
[email protected]
I
.7
I
.6
I
●5
.4
k?
.
.3
.2
4-
●1
=K?=”
o
●
.
●
.
1.0
Aileronohord/wLngohord,OJO
(b) $ = 0.10.
0
Flgur65.- Oonolutled.
.
““
.--
29
NACA TN 2486
.
.g -
●7
I
I
,
.6
M.
4.0
.5
.4
.
●3
.2
.1
omv
.Z
1.
.+
●
,
Q
.
.e
.
1.. 0
Aileron ohord/wingchord, o~
.
.
(a)
$=
0.05.
6.-Aileron effeotlveaee8
a8 a funotlonof
the ratio of aileron ohord to wing ohord ror an
unoamberedwedge alrfollhaving maximumthloknese at
ml&ohordand leading-edgeaileron.
Figure
—
.
1.0
.
●
9“
.8
.7
.6
●5
,4
.
.3
,2
.1
Aileron
ohord/wingohord,e~o
(b) +=0.10.
>
Figure 6.- Oonolu&ed.
.
—
NACATN
31
2k86
L.o
—Parabollo
alrfotl
—.
Wedge airfoil
.9
/
.8
●7
.Leadlng-edgeaileron
I
1} ‘
.6
/
I
I
95
/
I
*
.4
u
Tralltng-e&geaileron
/ //
●3
/
.2
/
/
/’
‘
.1
-
0
/
.2
.
●
.8
1;0
Aileron ohordiwlngohoti,o~a
Figure 7.-Aileronerfeotiveneaeas a funotlonof
the ratio of aileronohord to wing chord for unoambtired
airfoilshe?lng.msulmumtblqkneee●t
mldohord. M. =4.0;;: 0.10.
32
WA
TN
2M6
●22
.eor
Aakeret
“’
.M
T
●
t/c
o
1
.16
.14
.12
●
/
Y
10
\
,0s
.06
.04
#
T
,02
0
1.0
—
1.5
2.0
2.5
~.o
3.5
4.0
Free-stream
Maoh number,MO
Flgurag.- Aileroneffeotlveneaa
as a funotlonof the freeetreamMaoh numberfor an unoamberea
parabolioairfoil
havingmaximumthickness at midohordand tralllng-edge
aileron. ~: 0,2.
.
NACATN
2M16
33
-. .—
.22
I
I
I
/
.20 “
.18
/
-
.16
-
.14
-
●
12
.10
.
.
,0111
.06
..
.
.02
0.
1.0
1.5
23
2.5
3.0
3.5
4.0
I%ee-stream
Mach number,M.
.
Figure9.- Aileroneffeotiveneas
as a funotionof the free-rntream
Maoh numberrop an unoamberedwedgealrfOllhavingmaximum
thlokness
at mldohord and trailing-edgeaileron. := 0,2.
NACA
TN 2M16
.
.36
.
tfo
.
●9
.32
●“Y
.211
.- .—
-
.26
.
.
.24
.22
.2a
,la
1(
o
Aokeret
1.5
2.0
2.5
3.0
3*5
4,
Free-stream
Maoh number,M.
Figure10.-Aileroneffeotlveneas
as a funotionof the free-stream
prabolio airfoilhaving maximum
Maoh numberfor an unoambered
thiokneasat mldoho~dand leading-edge
aileron. ~ = O*2”
.
NACA
35
.36
.
.*
—
.32
.30
.2/3
.26
*
.
,24
.22
.20
hokeret
o
T
I
,:a
1.5
(
.
.
“2.5
2.0
“’3.0
3*5
4.0
Free-stretim
M6iohnumber,Ho
,...
ng a funotlonof the free-atreem
[email protected] 11.-Alleroneffeotlveneee
~ maximum
Ueh. nwber.f9pafl.
W~~?rp.d. ,wd&?e
airfoil.m?$~
thldsnetis”at
rntdohord
and-lea’~ln~-ed%e”’allerona
..
J.rj
T +..;:
TJ.‘.
..it, . .’ ,.. l ~ = Oeza
,-----
.-
,... ,~. ., ~.’
,-
.--!
... ;-, .: ~.
.
WA
36
.2
.l!J
.16-
●
14“
\
.12
\
,10
.Og
\
.06
.04
.02
T
00
.02
.04
.06
Thlckneesratio,
●M
.10
t/o
(a) Trailing-edge●ileron.
Figure 12.- ALleron effeotlveneaean a funotion
of
thiokne~aratioforan unoamberedpa*olio #rfoll having maximum thlokneoaat midohord. += 0.2.
TN 2h86
●38
I
●
36
Ii.
I
●
34
/
.32
●3O
.2U
.
.26 .
.24
,22~
.20
●
w
.06
I
●
Thieknesa ratio, t/e
(b) badlng-edge aileron.
.
.
Figure 12.- (lonoluded.
(0
NACAl!N
2486
-l.&
I
.
-1.6
,,
-1,4-
-1.2
-1.0
,
_lL
-od
.
.
-*6
4.0
-.4
I
—
-*2
‘o
.2
,4
●
o
Aileronohord/wing
ohord,e~o
(a) : = 0.05,
Figure13.-Rateof ohangeof aileron hinge-moment
ae a
ooeffioient
withaileron tlefleotion
funotlonof theratioof aileronohordto wing
ohordfor an unoembered
parabolio
airfoilhaving
maximum thlokness at midehord
and trailing-edge
●ileron.
.
NJWATN2M6
39
.
%)-
2.0
.
.
/
0
.4
.2
.6
.l!l
Aileron ohord/ning
ohord,o~o
.
(b)
~ =
0.10.
Figure13..Oonoluded.
.
1
---
40
NACA TN 2#6
-2.0
.
#
.
Ho
-leg
1.
/
-1.6
,
—
-1.4
-1.2
2.0
-1.0-
—
—
-cg
.
.
-*6
.
-* 4
-02
I
I
00
I
.
●
I
I
.6
.8
1,o
Aileron ohortl/wing
ohord, OJO
(a) &
0.05.
Figure 14.- Rate of ohango of aileronhinge-moment
ooeffioitint
with ailerondefleotlonas a
funotlonof the ratio of aileron ohora to wing
ohord for an unoamberedwedge alrrollhaving
maximum thlokneesat midohordand trailing-edge
aileron.
NIWATN
2486
41
-2.0 .
.
-log
-1.6
1.5
/
-1.4
-1.2-
-1.0
/
.
-*a T
.
-*6
-04
\
-.2
T
O(j
.
.
.
I
●
Aileron ohord/wingohomi, o~o
(b) .{ = 0.10.
.
Figure
14.-Uonoluded.
1.0
42
.
.—
.
2.4
2,0
1.6
1.2
.8
.
.4
=5=”
0.n
b.
.4
.
,b
1.0
Aileron ohord/wing ohord, Oa/o
(a)
{=0.050
15.- Rate of ohange of aileron hinge-moment
ooeffloient
with aileron
deflection
as a
funotion
of the ratio of aileron
ohord to wing chord
for an unoambered parabolic
airfoil
having maximum
thiokness
at midchord and leading-edge
aileron.
Figure
.
,
mm m 2k86
43
*
2.4!
2.4 -
2,0
d
106
1.2
.
.
.s
.4
=s=
o~
●
Aileron
chord/wl.ng
(b)
.
●
●
Figure
chord,
1 : 0.lO.
0
15.- Concluded.
9
1.0
mm m 2J186
44
.
3.2
.
2.8
2.4
2.0
.
.
.-
—
I
O.!
.2
●
.6
l,,
t!/
1
o
Aileron chord/wingchord,o~o
.
16.- ~te of change d aileronhinge-moment
ooeffioientwith ailerondefleotlonas a
funotlonof the ratio of aileronchord to wing
ohord for an unoambered wedge airfoil having
maximum thlokness at midohotiand leading-edge
aileron.
Figure
.
NACATN
45
2M6
*
2.8
2,4
2.0
1,6
1.2
.
.
.tl
.4
“o
.4
.2
.6
Aileron ohord/wing ohord,
(b) ~ = 0.10,
Figure 16..
.
Ooneluded.
.g
OJO
1.0
NWA TN 2W6
46
1.2
1.0
.s
.6
.4
—
-
—
Parabolloairfoil
Wedge ●irfoil
.2
. —
0
.
Tralll~edgo aileron
-.2
—
\
—.
\
-04
—
-*6
.—
=s$=
-*‘o
—
.2
.4
.6
.8
1.0”
Aileron ohord/uingohord, oa~o
B’lgure
Z7.. Rate of ohange of aileron hinge-eoment
aoeffloientwith aileron&efleotionaa a
funotlon of the ratio of aileron ohord to wing
ohord for unoamberedairfoils having maxiDWE
thlokne8sat mldohord. Ho= 4.0; ;
= 0.10.
.
NACA TN
“ 47
2486
-log
\
-1.6‘
.
-1.4”
“
!
-1.2‘
-1.0-
-mg
.
.
\
-06
I
I
-.4
I
●
-o
2
0
i.o
—.
1*5
2.0
3.0
3*5
4.0
E%ee-8trehm Maoh number, M.
.
~igure 18.- Rate of ohange of aileron hinge-moment eoefflolent
with aileron deflection as a function of free-stream
Maoh number for an unoambered parabolio klrfoll having
maximum thloknetaeat mldohord and trailing-edge aileron.
a 0.2.
+
-.——
.
-2.0 -
.
-1.s
-1.6-
\
-1.4
-1.2
-1.0
-*8
-06
-o
-.2 ‘
?. o
1.5
2.0
2.5
3.0
3*5
Free-streamMaoh number, If.
Tlgure 19.-Rateof ohange of aileron hinge-momentooeffiolent
with aileron defleotlon as a functionof free-stream
Maoh numberror an unoamberedwedge airfoil havin2 EUIMUQ
thiokness
at midohord and trailing-edgeh~lerofie ~ = 0.2.
.
49
4.0“
3.6
3.2
2.t4
2,b
-,
2.0
.
1.6.
.
1.2
.g
.4
n
i.o
1.5
2.0
2.5
3.0
3*5
4.0
Free-streamMaoh number, M.
.
Figure 20.- Rate or ohange or aileron hinge-momentooerfiolent
with aileron defleotlonas a function of free-stream
Haoh number for an unombered [email protected] ●irfoil baring
ma&IIUUQthlokneseat tidohord and leading-edgeaileron.
~ a O*2.
50
.
3.6
—
.
3.2
2.g
2.4
2.0
1.6
.
.
1.2
.g
.—
.4
I
?
5
2
)
2.5
II
3.0
i
3*5
4 o ““ ‘-
Free-stream
Maoh number,M.
Figure21.- Rateof ohangeof aileronhinge-moment
ooeffioient
with ailerondeflectionas a functionof free-stream
wedgeairfoilhavingqaxlmum
Maoh numberfor an unoambered
thlokness
at midohordand leading-edge
aileron.
$Z 0.20
.
.
NXA TN 2W6
-.4[
06
-% .
-.40
-*
32
-.24
-.16
-.08
.
0
.
.da
.16
.2k
.32
Aileron ohordlwfng,
ohord, a#3
(A) g=o.05.
Figure 22.- Rate of ohange or pltoting-momentooeftiolent
about mldohordwith aileron defleotlonas a
funotlonof the ratio of ai$eron ohord to wlqg ohord
for an unoamberedparabolloalrft)ll
htivingmaxlmun
thioknessat midohordand trailing-edge●ileron.
52
NACA TN 2~6
.
-.48
.
-.40
I
-* 32
-.24
-.16
-.00
.
0
\
<
●
OIJ
.16
.24
.320
.2
.4
.6
1.0
Aileron ohord/wingohord, o~o
(b) ~= 0.10.
Figure22.- Oonolufied.
.
NACA TN 2U6
53
‘
-*U
“
,.
..
.
,,
I
.
0
-.40
-.32
.
f
-.24
/
-.16
-.og
.
/’
#
.
o
.Og’
.16
.24
.2
.6
.&
1*O
Aileron ohord/wing
ohord,o~o
(a)
~ = 0.050
Figure 23.- Rate of ohangeOr pitching-moment
ooefrioient
[email protected] withailerondefleotlon
as a
runotlonor theratioor aileronohordto wingohord
ror an unoambered
wedgeairfoilhavingmaximum
thiokness
at mldohoti
and trailing-edge
aileron.
WA
54
~
2h86
-.48
.
-.40
-.32
-.24
-.16
-cog
o
.Og
,16
.24,
.2
.$
.&
.$
1.0
Aileron ohorU/wingohofi, OJO
(b) ~= 0.10.
6’lgure23.- Uonoluded.
.
1.0
99
.8
●7
.6
.5
.
,4
.2
.1
0
0
.2
.
Aileron‘ohord/uing
ohord,e~a
(a) : = 0.05.
24.Rate of ohange of pltohlng-moment
coeffloient
about mldohordwith ailerondefleotlonas a
fumtlon of the ratio of aileronohord to wing ohord
for an unoamberedparabolloairfoilhaving maximum
thloknessat mldohordand [email protected]
Figure
.
.
.9
.8
●7
.6
?5
.k
.
.
●3
,,
/
●2
.1
0
I
I
● IZ
.
.b
●
●o
Aileronohordiwlngohofl,o~o
(b) ~= 0,10.
.
Figure24.- :Oneluded
.
57’
100
.9
.8
●7
.6 -
●5 “
.
/
—
1
MO
.4
.
/
.3
.2
‘.1
0
.
.
0
.2
.
.6
.6
1.0
Aileron ohordlwingohord, o~o
(a) :=0.05.
Figure25.- Rate of ohange of pltohlng-momentooeffioient
about mldohordwith aileron defleotlonas a
fUnotlOnof the ratio of aileron ohord to wing ohord
for an unoamberedwedge airfoilhaving maximum thioknees
at mldohordand leading-edgeaileron.
.
1.0.
a
<
s
●9
if
.—
.8
.7
.6
●5
.
.4
.
●3
.2
/
.1‘
.2
,4
.6
‘“
.8
Aileron ohord/uingohord,o~o
-
1.0
.
(b) ~= O.1OO
[email protected]
25.-
Oonoluded.
.
59
NACATT?2M6
.6
●5
●4
I
●
3
//’’’.adli
g-edge
.11.,0.
\
.2
\
\
.1
0
-.1
Trailing-edge
\’
aileron,
-.2
—
Parabolioairfoil
——Wedge
airfoil
-.3
-oq
.
.
y
.2
4
●
.tf
o
Aileron ohordlwingohord, ado
Figure 26.- Rate of ohange of pltohing-momentcoefflolent
about mldohord with aileron defleotlonas a
func!tlonof the ratio or aileron ohofi to wing ohord
maximum’thtokneseat
for unoamb,ered
airfoils having
midohoti, M. : 200; { = 0,10.
NACA TN 2~6
60
●
.
-.40
.
-.36
.
-.32
-.28-
-.24.
.
.
t/o
$4
0
t-l
o
i
1-.0
1*’5
2.0
Wee-stream
2W5
3.0
3.5
4.0
Maoh number,M.
Slgure 27.- Rate of ohangeof pitohing-nonentooeffiolentabout
mldohordwith ailerondefleotlonan a funotionof freeetream Maoh number for an unoamberedparabolloairfoilhaving
maximum thloknessat midohord and trailing-edge aileron.
+
: 0.2.
61
d
.
1.0
.
,
1*5
2.0
2.5
3.0
3.5
Free-streamMaoh number,M.
Figure 2&l.-?late of ahange of pitohing-momentaoeffioient
about mldohordulth ailerondefleotlonas a
Maoh number for an unoambered
funotlonof free-stream
wedge airfoilhaving maximum t.hlokneea
at midohord
and trailing-edgeaileron. !?S= 0.2.
4.0
62
NWA TN
.-
2k86
Y
““’rr
.
●9
,eg
97
.6
.s-l-.
.
H-
---F=k3
.1
Q
1.0
1.5
i o
T
2s5
3.0
3*5
Free-streamMaoh number,No
U’igure
29.- Rate of ohangeof pitohing-momentooeffioient
about ml~ohordwith ailerondefleotlonas a function
of free-etreamMaoh number for an unoamberedparabolic
maxlm~ thioknefre
‘atmldohordand leadingai~roil having
&a= Oz.
edge aileron.
“
4 ,0
.
.
.
63
NACA TN 2W6
1,0
.9
#
TTT
.8
.7
.6
Free-streamHaah number, Ho
Figure 30.- Rate or ohange
0? pltohlng-momentooeffleientabout
midohord with aileron deflectionas a funotlon of freeetream Xaoh number for an unoamberedwedge airfoil having
maxim~ thidsnetas
at midohordand l,eading-edge
aileron.
!& 0.2,
,-
64
1.0
T
6a/a
●9’
.
.Go
“
.
-—
—
p-o
.8
●7
10
.6
3
2
●5
/-6
,
0
.4
.
T
93
●2
T
,1
7
2
3
1.5
2.0
2.5
3
)
3.5
Free-stream Maoh number,M.
FL-
31.- Looation
of oenter of pressure ae a runction of
Parabolio airtree-etreamMaoh numberfor an unoambered
foil having maximqm thiokness at mldohord and traillngedge aileron. +:0.2;
{=0,10.
.
65
NACA TN 2U6
m
10
F
2
1
0
I
,+,5
.
—
,0
.
.
I
I
,,
,0
.
Free-stream
.
,5
.
Maoh number,M.
32.- Looatlon of oenter of preeaureae a funoti.onof
free-streamMaoh number for an unoamberedwe e alrfoll
having maxlmqm thlokneseat midohox and tral
Y Ing-edge
aileron. +~0.2;
~= 0.10.
Figure
“
,0
.
66
NJK!A
TN 2k86
●
.—
.6“
J
●5
6a/a
o
.b
2
.3
.2 —
-
—A
Au
●
—
~
—
100
.1 “
00
t
T
o
1.0
1*5
2.0
Free-stream
E.y
3.0
Maoh number,
3*5
4.0
MO
Figure 33.- Looation Or oenter Or pressure as a funotlon Or
free-streamMaoh number for an unoamberedparabolioairfoil having maximum thioknessat midohord and leadingedge aileron.
+$=0.2;
;.
t - 0.10.
.
NACA TN 2U6
67
w
.6
.5
.4
.
●3
.2
.1
0
1.0
195
2.0
Free-stream
Figure 34.-
295
3.0
3*5
Maoh number, MO
Looation of center of pressure as a funotion
of
free-stream
Maoh number for an uncambered wedge airfoil
having maximum thickness
at mldohord and leading-edge
3
=
0.10.
+=
0.2;
=
aileron.
.
.
4.0
NMATN2A86
68
●
k
54
4
,52
,50
.4$
.46
—
.44
.42
.40
.38
.36
7
.340
.4
.2
.6
1.0
Aileron ohordlwlngohord, o~o
Figure 35.- Looatlonof oenter of pressureae a
funotionof the ratio of aileron ohord to wln&
ohord for an unoamberedparabolloairfoilhaving
maximum thlokneesat mldohordand trailing-edge
aileron. M. =
4.0;
:
=
1,0.
●
.
NACA TN 2h86
69
.54
.52
.50
.4a
&l
.40
●
38
.36
●
340
.2
.4
.6
.8
.—
1.0
Aileron ehordivlngohord, o~o
of oenterof preoaure an a funotion
Figure 36.- Looatlon
of the ratio of aileron ohord to wing chofl for an
unoamberedwedge airfoil having maximum thlokne:sat
&dohord and trailing-edgeaileron. Ho s 4.0; $ = 1.0.
.
.
●
●
1
—
✎
✌
‘e
/
*
4
7 -1--
,
.
.2
●
.
D
chord,o~o
Aileron ohord/wing
I’lgure37.- Lcwtlon of oenterof pressurean a runotlon
or the ratio of aileron ohord to wing ohord for an
unoamberedparabolioairfoil having maximum thlolcqess
‘a
at midchordand leading-edgeaileron. M. = 4.0; ~
s 1.0.
NACA TN
2M6
●
●
✎
r
u
.
L
u
●28
.260 ‘
I,
.2
.4
I1
.6
.8
1
Aileron ohordlwingohord, ode
Figure 3&J.-Looatlon of oenter of preeaure ● e R runotlon
of the ratio of aileron ohord to wing ohord for an
unoamberedwedge airfoil having maximum thlokn~a at
mldchord and Ieadlng-edgeaileron. Ico=
4,0;+= 1,0,
——
NACAm 2k86
72
.46 P
\
/
●
\
/
/
.44
/
\\
/
/
/
.42
\
/
\
Ja
.40- I
\
1/
I
P
lling-edgeaileron
\
—
/
/
.YLl---
\
7
I
i~a~i~-edge aileron
\
.32
,/
/
\_/
/
/
.30
.2LI
\
I
.26;
/
—
——
[
I
I
.2
,4
—
Parabollohlrfoll
Wedge alrroll
-
I
.6
.a
1
1.0
Aileron
ohotiiwlng
ohord,
ado
Figure 39.- Looatlonof oenter of preaaureaO a function
of the ratio of aileron ohofi to wing chord for unoamberedalrfolla having maximum thickneeeat midohord.
M. =4,0;
:=1.0;
:=
O.1O*
10
NACATT?2M6
73
.
.
.6:
.
.9
Ho
.4(
.4+
.
.
,0
●Y
.
L-
L
I
.C
.02
Thlokness ratio,
●
1
Og
.10
t/o
(a) Trailing-edge aileron.
@,Looatlon of aenter of preaaure aa a funotlon
of the thlokness ratio for an unoarabered?xrabollo
alrfoll havln% maximum tblokness at midoh&3.
Figure
.
Ca
—=
G
0.2; :
= 1.0.
74
NACA ~
2W6
.
.62.
.
“
.58 -
●
54
,50
.46
.42
,
.y!!
.
●*
●
\
\
30
=E!T=
.26
0
.02’
.04
.06
.o&l
..
.
Thiokness ratio, t/o
(b) Leading-edge aileron.
Figure 40.- Conoluded.
.
NAcA-I.ang16y
-lo-24-51-
1000