Analysis of factors affecting net lift increment attainable with trailing-edge split flaps on tailless airplanes


Material Information

Analysis of factors affecting net lift increment attainable with trailing-edge split flaps on tailless airplanes
Series Title:
National Advisory Committee for Aeronautics wartime report."--Cover
Physical Description:
23 p., 16 ℓ. : ill., charts ; 26 cm.
Pitkin, Marvin
Maggin, Bernard
United States -- National Advisory Committee for Aeronautics
Place of Publication:
Washington, D.C
Publication Date:


Subjects / Keywords:
Aeronautics -- Research   ( lcsh )
Airplanes, Tailless   ( lcsh )
Lift (Aerodynamics)   ( lcsh )
Trailing edge flaps -- Aerodynamics   ( lcsh )
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )


Includes bibliographical references (p. 22-23).
Statement of Responsibility:
by Marvin Pitkin and Bernard Maggin.
General Note:
At head of title: National Advisory Committee for Aeronautics.
General Note:
Caption title.
General Note:
"Originally issued September 1944 as Advance restricted report L4118."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003804825
oclc - 68838093
System ID:

This item is only available as the following downloads:

Full Text

AC A L- /b


September 19'. as
Advance Restricted Report L4II8

By Marvin Pitkin and Bernard Meggin

Langley Memorial Aeronautical Laboratory
Langley Field, Va.


LLE, FL 3 11-70
II SIJLLE, FL 326.1 -701 1 IJo,


NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.

L 64

ARR No. L4Il8

Digitized by the Internei Archive
in 2011 wilh lundlng Irom
Univeisilly o Florida, George A. Smalhers Libialles wilh support from LYRASIS and the Sloan Foundaiion

hllp: delays analysisollaclorOOLunit

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NACA ARR No. L4ll8






By M.arvin Pitkin an! Pc-riiard :lacgin

An analysis has been mnade of factors affecting the
net lift increment attainable v'ith traili.n,.-zdi-e split
fla-.s on tailless airplanes. The flaps investigated in
the anal-sic w'.ert desjlned to contribute zero pitching
moments about the '.vr'n aerodynamic center when deflected.
Calculations were made of the lift and pitching-moment
chcracttc-rist cs of "lac.s of this t-;, .* ov.-r a ran-e of
design conditios .n .:.hich s'.:ept il: angle, asr ect ratio,
taper ratio, flap ahcbord, ard r a:;- dkflecticn .::ere v:idely
v.aried. In addition, calcula.ton3 \~er :.,ade to determine
thl effect of' tha vr.riou- parc..etls up-or the loss in
lift incurred in tri.rLmin" the r ability moments of a
taill-s: airplane. A methcd is iven for roughly esti-
mabrinn- l' e mnaxim_!um lift ,.oefficienc of tailless airplanes.

TIe results of the analysis indicated that. aspect
ratio and sweepback anile C::ir- t i'6 principal parameters
influrnc.r.g -he not lift inr3r::;ent attainable v;ith the
flaps on tailless airplanes in tri;.Jred flight. An
increase. of these 1para:,.et.ers allo:"cdV the use of larger-
span fi?'s. values of' both rra:.ueters w;er' required
to obtair. sizable lift incre-ents and t-o i-inii.ize the loss
of lift caused by the lon:itudrinal ccncrol siurfaccs. In
order to utilize fully the high-lift advantageZ associated
with flaps on swcpt-.ack wings, t;i? use of tip slots or
washout .will probably be required to elir-.inate the unde-
sirable tip stalling and the accomrpanying stability losses
caused by large angles of sveepbac':.

The allov:able flap span and hence the net lift
increase of some wing confi.-Lurations could be further
increased b- the addition of a trivr flap located at the
wing tins and deflected upward.


Ex:_ersivc- rin.r taper was shownn to reduce the net
lift increment. obtainable irrm f'lp systems, whereas
inr'..'i-ase flap chord and Ceflection increased the net
lit: increment.


Tle, application of high-lift flaps to a tailless
airplane: requires a flao arrangement that produces only
small retching moments about the center of -,'avity of
the airPplane. Such an -jrrangre-,ent is necessary because
the elevators on tailless airplanes o-perate on short
moment a-r.s and thus ^roduce r. lacively small pitching
,m1 ents.

The pitching rmomeents produced by flaps imay be kept
snall by the use of a basic flap design that has a small
section i:itchin .inonen! or- by the use of partial-span
flnaps or. V.iJngs within sweepback. Another method of reducing
the oitchino moments of flap- is to cancel out the diving
mo-ments of one flap deflected doanv;ard (designated lift
flap) by means of a se.conid flap deflected upward (desig-
nated tri.m fllop) and ::-.osessirn a lonlr?r lever arm. An
e::a;;ple of this methodd of Oot in.nilng increased lift by
m.ans of such a multiple-flap system is shown by the con-
ventional airplane in .-,hich the trim flap (elevator)
possesses a moment arm from 10 to 1 times as long as
that of the wiria lift flaps.

7Tuch information is available on the section pitching
monmnt and lift produced by various flap designs, and
sone work has been done on methods of computing conimlete-
,wi;ng mor-:ents from section data although the data have not
been directly applied to tailless airplanes. In the
present report, the res,..lts of an analytical investigation
are *.iven for a v'ide range of wjing and flap paraamters.
The effect of these parameters upon the net lift increment
obtainable from flaps on tailless cir :ianes in trimmed
flir-ht has been treated. Conventional split flaps were
chosen for the investigation because of their simplicity
and because they produce relatively small section pitching
moments for a given lift increase.

Calculations v.ere made To dst.rimine the effect of
svWcepbacl-, aspect ratio, taper ratio, flap, chord, and
flap delrlection upon the lift increment obtainable at a

NACA ARR ITo. lll8

fixed angle of attack by meanri of flaps creating zero
pitching moments about the wing aercdynar.ic center. Addi-
tional calculations were made to determine the losses in
lift resulting from the elevator deflections required to
trim stability moments. A brief study was made of
available empirical data concerning the effect of sweep-
back and flaps upon the maximum lift probable in trimmed

The lift increments of different flap arrangements
were determined by the method of reference 1 with a
simple ebord correction factor being applied. The
pitching moments were computed from a consideration of
the incremental lift due to bhe action of the flaps at
each spanwise section and the center of pressure of this
incremental lift. This prozedur.e is somewhat similar in
basic principles to the method of reference 2. The
accuracy of the present method was determined by calcu-
lating by means of this methoo the lift and moment incre-
ments of flaps on 10 different finite wing-flap combina-
tions for which wind-tunnel data wJere available.


a angle of attack, degrees

CL lift coefficient (Lift
SqS /
Ci ax maximum lift coefficient

ct section lift coefficient (Section lift)

(CTma;t maximum lift coefficient in trimmed fliEht

ACL increment of lift coefficient

Cm pitching-moment coefficient (Pitchin smornmnt)

cm section pitching-moiront coefficient
Section pitching ,iorent

NACa ARR o. LLll8

AC..., increPenI of pttchin,-:o'.Omont coefficient
/ i n\
q dyniulc pressure I (oVf

p den-ity of air, slus per cubic feet

S wing area, squ..'e fet

V true ;irspeei, rest Ter second

b rlnl rpan, e:< ;drt 's CesilI.at3d otherwise by
s3tU sc-2i:pt, f ''-.t

c cn-ord'. et a:iy sec tion, exccirt as designated
otherwise ob vuOb.ript, feet

cs root chord, feet.

0 t*ean% v.)f* c1ord, f2set (S,'h)

c. o ce: .tr o przescure o- incr.c:nientai lift load
c i.l b r, fl. df.lecicrn, fraction of wing

c.i'sc' ? i.rono cent of pr':-ssure to reference
,, n:It, c st

t/c"oi.l tiiUciknesS,, frction wing chord

%a equi'.aulent rhanr,. in ang-le of attack for a
civ-n fiLp deflection, degrees

A aspectt ratio (b2K.'S)

K taper ratio; rat*o of tip ehord of Ning to
root onld o1 w'in;vi

A :ngle of sueepo-Acl: o7 qua:,rtr-chord line,
de,;re e-

F, I tlheoretical fact.:rs that are functions of
aspect ratio and taer ratio

h statilc-rar.gin factor (6Cm /cCL)


Xa distEnce to erodyn. .niic center of win, from
quarter chord of root section, feet

c/14 quarter-chord line

- control-surface defection, degrees

a slope of lift curve, per degree (6CL/6a)


f flap

L lift flap

T trim flap about center of gravity

a.c. about wing aerodynamic center

o infinite aspect ratio

theor pertaining to theor~itical wing plan forms
given in reference 1

max max imum

1 over flapred pert of wilng

2 over unflapped part of wing

p longitudinal (pitch) control

w unflapped finite 'ving

bw basic wing with zero sweepbaclk of quarter-
chord line


Calculation of Tncremental Lift Caused by Flaps

The increp.ental lift caused by flap deflection at a
constant angle of attack was obtained by integration of
the section incremental load distribution across the


wing span. These sponr lord di-'tributions were calculated
by the influence-lines methc described in reference 1.
Inasmuch as the dabs in reference 1 apply rigorously only
to the wing shapes shown in that report, a chord correc-
tion was applied to the span load distributions obtained
from such data. No correction was applied to the span
loading to account for the effect of sweepbaclc, however,
because available data on the subject were inconclusive.
The soan loading war corrected for chord by multiplying
the loading at each spanwise station of the wing shape
most similar to that under consideration by the ratio of
the chord of the wing under consideration to the chord
of the wing shape of reference 1.

The method of reference 1 gives the value of incre-
mental lift caused by flaps that create an effective
change in angle of attack of 1 radian over the flapped
parts of the wing. In order to convert such data to the
incremental lift caused by a different flap deflection,
the equivalent Increm:enc of angle of attack Aa for that
deflection had to be found. For the present analysis,
values of La were obtained from data for wings of
infril.te .;ran at a lift coefficient of 1.0, which corre-
sponds to an angle of attack of 10 for the average
unflanped wing section. This value was chosen because
the angle is far enough below thc stall to yield con-
sistent results and, at the same time, is in the high-
lift ran'c at ,jhich flaos are utilized. A typical incre-
rental span load distribution caused by flap deflection
is presented in figure l(a).

The vslurs of ua used in the analysis were obtained
from referer-:e 5 for splic flaps of various chords and
are plotted against flap dcfl-.ction in figure 2. The
lift increments of constant-chord flaps or arbitrary-
chord distributions v:ero calculated by use of a value
of Aa ba-ted on the mean flan chord.

Calculation of Pitching Mo.n nts Caused by Flaps

The incremental pitching imoients caused by the flaps
were calculated by multiplying the incremental lift loads
cause by flaps at each spanwise station by the corre-
sponding mion.ent arms that is, the distance between the
local center of pressure of the lift load and the moment
axis. Graphical integration of the span:wise distributions
of pitching moments thus obtained yielded the incremental
pitching moments created by flap deflections.

NJACA RR lTo. 11!Il8

Calculation of centers of ,rea:Fure of fi-ap loads
over flapped parts of wvlng.- T'h.- cente:- cf ?rcssureC of
the increrrental lift loads over the flaprped parts of the
wing c.p.f was calculated fro.n section data by the
si-Dle relation
c.p.f = -c.f 0.25) + 0.25 (1)

'4uuation (1) can be rigcrously applied only to a
finitL wing that is equippe? with full-span flaps for
which t'-.e local lift-curve slopes are equal to that of
the wing as a whole. This equation, however, was found
to define the center of pressure of the flap load over
any flapped part of the wing with satisfactory accuracy.

'a]ues of the lift-curve slope for wings of infinite
aspect ratio a vary with airfoil thickness and were
selected from the data of refcrsnce 2. Values of the
lIft-curve slcpe for finite wings a were calculated by
the formula

a = (2)
i +

also presented in reference 2. The factor r, which is
a correction factor involvJigi aspect ratio and taper ratio,
varies between 0.55 and 1.0u. A value of 0.99 was used in
the present repo-t.

A study of d.ta for the .;'CA 250-series airfoil
(reference 5) indicated that the center of pressure of
incremental flap loads on wings of inf.-nite aspect ratio
c.p.f vwas inde-jendent of flao deflection but varied
somewhat with angle of attack and considerably with air-
foil thickness and flap chord. All values of c.p.f
were chosen at an angle of attack of 100, the angle of
attack: et which the lift increments were calculated. The
effect of flap chord and airfoil thickness upon c.p.P
was determined from the force-test data of reference 3
and is shown in figure 5. The variation of c.p.f with


flap chord, as calculated by theory for
wins of infinite aspect ratio, is also given in figure 5
for co:,.parisor.

?v us'0 of equation (1), calculations we.e -made to th- centerZ of pressure of the incremental. flap
loads '-.-r the flappei parts of che finite '-ing c.p. .
Figur 1, prepeints the circulated variatcins of c.p.fl
with aspect ratio for snlit flaps of various chords on
:noOeratuly thlcic '(16 percent) airfoils. Agreemnent of
these calculated values with available acta for rectan-
gular :'igs with' fu]ll-spanr flps ::es fornd to be good.

Center oi pr.-,ssurc cf incre-iertal flap loads over
unflapn)c1 pDarts of tlhe winw .- The cencer-of-pressure
diitrTbi.ticn of th. inrcieme'nal flo loads over the
'uflappedc parts of the wiing c.p..f2 was obtained from
the prcFsure-distributio.n jata of rfierlnce 6 that are
shown in fig-ure 5. Tnh-:te daL' i.iziicatedi that the vale
of c.D.f mray be satisfactoril-. calculated by equation (1)
and that the span.:ise distribution cf c.p.f5 may be simu-
lated by a line faired between the C.400 station at the
flap and to the n.25c station ct a point 0.30- from the
flap *n'.; the induced loans dure to tre flap miay thereafter
be considered to sct along the 0.25,c line. By use of the
values thus obtained, the center-of-pressure distribution
of inc:e-r.ental loac's caused 'y flape may be readily
dcte.rined for any desired wing-flap configuration.
FiLure 1(b) illustrates typical certer-of-pressure dis-
tributricns for constant:-chor;l flap'. The pitching-moment
distributions obtained b: use of such data in conjunction
with the span loading are illustrated in figure 1(c).

accuracy of .iethocds

In order to deterin.le L-he over-all accuracy of the
method E.nd dcta presented hrcein, tha Incre.,ental flap
lift anrd pitching-moment coefficients w./ere calculated
for 10 finite win--flap combinations for which wind-
tunnel force-test aata were available. The close agree-
ment of' cal.ulated with measured values is shown in
f gure 6.


Lift Evaluation under Trmnined-Flight Conditions

A certain percentage of the lift crea-;d by the
lifting Lur-fsces of an airplar.e is lost in trimmed flight
owing to the action of the tri.rming- surfaces in balancing
pitching moments. Such a lors of lift is considered
herein to be divisible into two oerts. The first part is
the loss of lift that is encountered in trimming flap
moments; the second part is the loss encountered in
tri.nning the pitching moments created by the longitudinal
stability of the airplane. These lift losses have been
treat.:d separately in the- present analysis.

iJet lift in caused b:' flans.- If the basic-
wing --itching- moments at zero lift arS neglected, the
lift lost in trimming the flap moments is caused by the
trimming surfaces in balancing the flap moments about
the wing aerodynamic center. The net ,ain in lift caused
by flap deflection is, therefore, the lift increment
caused by flap reflection minus the lift lost in trimming
the flap moments about the .'ing aerodynamic center.
The net gain in lift caused by flaps in tri.ned flight is
therefore automatically obtained for the flaps that
create zero pitching moments about the wing aerodynamic
center. All flap combinations investigated in this
analysis were, for this reason, designed to create zero
incr--:iental pitching moments about the wing aerodynamic

T'or each design configuration investigated, the
incremental lift of the flaps was obtained for a series
of lift flaps of various spans extending outboard from
the carter line of the v'in. and for a series of trim
flaps rxtendingr inboard from the ving tip.

The location of the aercdynar.ic center for the wing
shape urner investigation was then determined from the
fc.llo-ir.g formula given in reference 2:

x.c. = Hb ten A (3)

where H is a function of aspect ratio and taper and
may be obtained from reference 2.

After the location of the w,"ing acrodynrmiic center
has been determined, the incremental pitching moi;,ents of

NACA APR No. 1l18

the lift and tri- flaps were calculated about the .:ing
acrcdyi-ric center. Each lift flap was then matched with
a trim flap so that the combined incremental pitching
moments of the two flaps were eqaal to zero. For some
arrangements, a lift fl-p existed that created no moments
about the aerodynamic center. Tnis type of flap is
referred to herein as a "s.l.f-tri .iinr flap." The net
lift tirremert used to ealu.iate a give flap system was
then obtained, by deducting the loss in lift due to the
trim flap from the lift inc;ei..ent created by the corre-
spunding lift flap.

Equation (3) does not tac'e account of the rearward
shift of aeerodynaric center caused by the hiift of loading
tow.;arl the winng tip as the -ving is swept bad:. The data
of reFeence 10 and unpubliahed force-test data from the
NACA 19-foot Fressure 'inrnl indicate that this shift may
be as large as 5 percent cf the mean aerodynamic chord.
The results of the analysis are therefore believed to be
sor-Lewhat conservative alnd sBhould probably indicate net
lift increments larcsr than those actually determined.

Li.ft ln.s caused bo lon.-itudinal .stability.- The
lift lost bh- the longitudinal control surfaces in trimming
stat.ility -orfcnts is msociated with a pitcniing inocent
abcut the iing saerodyn.amic center equal and opposite
Ln hCL, where h is the static-margi.n factor 6Cmc /6CL.
This loes is zero when the lon-tudinal stability is zero
(h: = 0) and niia therefore b6 attributed to the airplane
design ra.thicr than to the flap h-ar-acceristics.

Tinsjriuc as the longit':.iinal control surfaces of
taill's- airplaneE: are ncrmai.y .iount-d at the wing tips,
the dat-L front. the tr-im-flan -calcil&ttions were used to
obtain the lift lost hb su-,h conc-rols for various sta-
b -llc1 tT moments.


All calculations made in the present analysis were
hbaed o;.r val-ies of flan effectiveness andt the center of
press Ure of the fla_ load o'.,Xcined by averaging section
force-test data for the IACA 23012 and UACA 25021 airfoils.
The' calculations are therefore mort applicable to air-
planes equipped :-ith moderately thick 'ing sections
(about 1l percent) of the NACA 230 series.

riACA AB-R r'o. L 118

Clcul'aions were made first of the net lift
increases, at a constant angle of attack, caused by
0.30c flaps deflected 600 and installed on a wing with
aspect ratio of 7.3, sw'eepbac&" angle of 200, ar.d taper
ratio of 0.25. Each of these wiipn and flap parameters
was theji varied independently of the others. The design
pr.ra eters were varied as follows:

Sweepbac.l: anCle, degrees . 10, 20, 30
Aspect ratio . 6, 7.3, 10, 16
Taper ratio . 0.25, 0.50, 1.00
Flap chord, percent c .. 10, 20, 30, 40
Flap deflection, degrees .. .... 0 to 00

The lift loss c iFud by trim flaps of various spans was
also calculated over the range of design parameters in
order to permit estimation of the lift lost by deflection
of the longitudinal control surfa.e. The maximum lift
coefficient of a tailless airplane that incorporated the
dcsijn featuLres shown to be favorable for obtaining hi-h
lift was then estimated.


The results of the analysis are :resented in
fiEur'-s 7 to 14, which show th2 variation of the allowable
flap span and the net lift incr.:,icnts due to flaps with
each of the bEsic design parameters. A gain in the net
lift increment obtained by the varJjation of one design
para-neter cannot be added directly to the gain obtained
by the variation or another para..ieter because these gains
were -enerally obtained by an extension in flap span.
Two deFsin bhanaes, each of ';rhi1h permits an extension
of a -iven flap equal tc 0.,0b 'would not therefore
necessarilTy permit an extension of SO perceiit when acting
together. Such changes would result in a larger e.llow.ble
flap span, hut the actual quantitative. r:.acnitude of the
increaFc woiild have to he r~-salculated.

Effect of Flap Chord

Lift-flap chord.- Tha effect of increasing the chord
of the lift rlap is shown in figure 7. Arrows and points
are included as an aid in usinc the chart, and an exa.-ple
of the use of this figure folJlovs

NACA ARR to. iLI18

If the chord Pnd span of a self-trimming flap
that fieldss (ACL ) = 0.51 are to be found,
r ret
point a is f;rst located on the net-lift scale
and the arro-. is follo.ved to point b. Point b
Indicates that a liflt-fap chord of C.235c is
reiuniired. Following the arrows front point b to
pointt c and than to cooirnt indicates that the
required flap extends o er the inboard section a
lirtancc equal to 0.20b. In ra similar manner, the
li-iensional characteristics of a multiple-flap
system may be obtained. For examnple, following the
a-rcrsj from point a to points ., f, and g shows
that the same net incre.iental lift may be obtained
frnomr a cysten consisting of i CG.56b lift flap and
a C.20b trim flap, both cf 0.157.

ThL data presented in i:cure 7 show that an increase
in flat chord on a taillers airplane causes an almost
linear increase In th3 inet lift increment due to the
flaps. Although thiis lift increase is caused largely by
thc increase in Aa that accI'!,Lmn-nies an increase in flap
chord, this action is further reinforced by the forward
shft of the center of pressure ofr flap loads with
increstEd flap chord. This c:enter-of-pre ssurc change
all]cevs extension of the flp span for a givc.n flap
pitching nimmcnt and hence increases the net lift attainable
in tririnled flight.

The data of figure 7 show also that the addition of
trim flays to the outboard wingz sections permits an
extension of the allowable lift-flap span and results in
increased net lift increments for a given pitching moment.
The increase in lift with a given increase in flap chord
is more pronounced for the rmltiple-flap systems because
of the greater allowable span of the lift flaps. A
multinle-flap system occupies iiore span for a given lift
increment, however, than a self-tri'uming flap and conse-
quently leaves less snan for lateral and longitudinal
control surfaces.

Trtr-flap chord.- The effect of varying the chords
of the trim flaps required to trim a series of constant-
chord lift flaps is: shown in figure E.. These data show
that v.ryinr the trim-flap chord hacd no appreciable
effect upon t-he net lift produced by a multiple-flap
system but th:.t the principal effect was to decrease the
required trim-flap span as the trim-flap chord was increased.

NACA ARR iTo. Ll18

The variation of trim-flap cnord had no effect on
the net lift produced by a multiple-flap system, because
the rearw.v~r shift in center of pressure of the local
flap loais with decreasing fl-p chord was offset by the
decrease in moment arm that result,--J fron the required
Increase in trim-flp span. Varying the trim-flap chord
thus caused little or no variation in the effective
moment arm of tri:n flaps for a given pitching moment; the
lift lost by these f-aps therefore was, for practical
purposes, independent of fla:; chord. If the primary con-
sideration is the span available for control surfaces,
larLe-chord trim flaps would generally be desirable.

The data of figure 8 indicate that, for the wing
conditions specified, a lift flap of 0.215b is self-
trinming. Flo.p spans snsller than 0.21%b create stalling
moments and consequently require trim flaps that are
de flec ted downward.

Effect of Flap Deflection

The effect of flap deflection upon the net lift
increments produce by flaps is a function only of the
resulting increase in angle of attack Aa because the
center of pr sure of fl.a loadc was found to be almost
independent of flap deflection. The variation of net
lift increment with flop deflection is shown in figure 9.
These data indicate that the largest practicable flap
deflection should be used. For split flaps on thin to
mo-l.ratsly thick wings, howcvJr, there is little increase
in Lo. and hence in net lift for deflections greater
thin i60 0

Effect of Sweeback.

'The results of the calculations mrs-e for a range of
sweepback angles from 100 to 300 are shown in figure 10.
Arrange:r.ents of self-tri:mrin, flaps are not possible for
a wing of zero swel;pbacl, because the resultant centroid
of lap loads woull Jct behind -chl iving -erodyn:rmic center
and would not satisfy tihe requirerments of zero pitching
moment. Sweepback o0 the wing, however, so shifts the
wing aerodynamic center and thf- wing sections that the
lift-flap controids -f incrc.:,e-ntal load move forward


relative to the wing aerodynamic center and trim-fl.p
ceit.i.roid move rearpri. As .he cw-epback an'.:le is
iicresse:d, therefore, 0:1':: anrlu is reached at :'l.-ich the
c-n-ter of pressure of flap io'is at the vwin center line
act, at uLh same fore-ani-aft location as th6 wing
a drc''oJynam] c cn:mter. l.i3 s'.Vicpbsac!: &ngle is the minimum
an;,]e at which s.lf--triT',,.iing fl.aps nay be emr.loyd. For
th,-u r.art5culir win;- in the calcula.Sons shown in
fit.-L.ur. 10, this :ninirh'nm svwe.-e ck ainlo :was 11..50. Further
increase iin .'.-.c phi ck .r-nr1 ] 3 thL use- of largur-span
scl.f-tr'Lr-ln"- fla-.w: ani inl sizahle not lift coef-
flr'icnt .. fic foljcwi. i. alue ta'-cn from .iguro 10
illum trat.c t, ir r:: r.. c :c tf n t i:ft c.efriciLnt with
sw ,ee=r...:].ck rngl. :

ict lift in1cr.s, Allourbl span for an., (6CL s.l f- trl'-iuin, flap
1 t-I_ *), net o(pv erccit b)
1' 0 0

13 .LL- 16
2u .- 22
S., 55 values do not include cc;.siderstion of the effect
of sweoepacl oi tiv stA.l11n in nd hence on the nma:ximum
lift characteristics -.:f :;a airplane.

Thle results -reseuted in figure 10 indicate that
net litt increments lsrc"r-r tl.1n these attaibable from
self-trim.riin, flap.s mr:; be obLal.'ied by couplinL the lift
fl.ips with trim 'i l.s locate -1 t t he tips particularly
if the sweep bck a'riE1].: i;s s'.:.1.. Use of thesu multiple-
flnp s;:terms provides tlhe m r.ns of cbtainin:l lift incre-
mcnts flrorn tr: 'llin,-cd';. fl-,:.: for aw.t-;.b?:.c;: angles below
the. min.rr.mum anrl for etlf -tr'irin fla'-s. A multiple-
fl.ap ,r ho vc-r, pr, vid .-. i:allor lift increase
i;"r unit sptn..I utiliz'-1 ry t:. fla'.t than the sclf-t ril:-ing
fl p.

The lift incrc .s dus to inr.as3e 'in allowable flap
span -.i.ith sw-~ pbaz": an-l.c is n;c t all gain inas-
much a- an incro-ijo In .-.v:c. pbck r ..,1, -:.1so reduci.s the
lilt-curv.3 .lope -.:a j ;-hfit tlL :.ii, L 3t:.]1 to the wins
tis. .' L!'hor, tic: l .:..rcZ is r, f wjr, nc, 11 indicates

FACA ARR ;o.L';-11

that the loss in lift-curve slope varies approximately as
the cosine of the angle of sweepback, As a rough approxi-
mation, the maximum lift coefficient of a win.7 also was
assumed to vary as h.j cosine nf the on'.! of sweepback.
Fi-iure 11 pre-eents available w'i'nd-t.iniel forc3-test data
concerning the reduction of CL due to sweepback
angle, In addition tc reducing maximum lift, wing-tip
stilling may also pro-ruce undesirable long-itudinal and
lateral stabilit-.y chsracterisbics, Some feature that
would ell'intte or "'rduce the effects of the wlg--tip
stalling should t'-.hrofore be incorporated in the design
of the wirg. ,n\: -tip slots or washout has alref-ly
proved to be beneficial in this res3cct.' Ihe results of
reference 15 indicate that as much as 30 percent of the
lift loss due to sweepback mra be recovur- l '? v'&:hout
Part of the lift loss due to sweep back will probably be
recovered on most tailless airplanes, inasmuch as some
washcut is usually used.

Effect of Aspect Ratio

Results of the aspect-ratio cal.ulstions are pre-
sented in figure 12 and indicated that s..zable net lift
incr en.t: cannot be cbt.ain:-i, even for win--_ '..ith
sw-b'i-bik n s, hen the asy,,.ct ratio is small (less
tha! .). Inc-reasi:n the as,;-ct ratio above 5 resulted
in :~ ra.i'-, increase in the allowable flap span. At high
asnpct r't:ios (about 10), lift .ncri;r nts comparable
with t-J-s-e for cv:v i.tional ai.clanes i:.'Ge calculated
for airFlne-s. These tr:-i are illustrated in
th; cable.

Allowable span for
A ( sf) tri:rL->in fl apr
\_ /not (pc.cant c)

5.5 0 0
t..o .13 9
o 251, 29
10.0 45
1i.0 1.00 56
1..0 1.10 1____________

The r-sul].ts of f i 'r& iu '.-\o.i lso tta-t t.he -fficivncy
of the trim 'l.,p in pitching mIoi;..lnt.s without

I!ACA ARR ;1o. L4I18

undue loss in lift decreases with increased aspect ratio
ai- that use of this flap c;Fter. is not warranted at high
aspect ratios. For high ?:pect ratios, the single self-
tris ,!iIng flap occupies almost all or all the span that
can be allowed for flaps wvitho'.it redu.,cng ;he span neces-
sary for lateral contr-l and, as previously shown, the
self-trjrim ing flap yields higher lift inc." .ents than
the riultiple-flap system of equal span,

The aspect-ratio calculations explain the diffi-
culties encounteral in trying to obtain high lifts on
tailless fighter airplanes. In an investigation in the
LiAC. free-flight tu -nel (unpublis.>ed data) of a model of
a tailless fighter airplane with asnoct ratio of 5.1 and
with sweepback angles of 240 and 50, a maxinmur increase
in the not incremental rma:ximum lift coefficient of only
0.11 was obtained with the best of a large variety of
flap systems operating under conditions.
The r resent calculations show that a lift increment nine
times this value would b obtained for a siiiilar airplane
having twice the aspect ratio. Trailing-edle-flep lift
increr'enits saorcrachTg those of flapped conventional
ai.r Jlanes thus seem to be obtaina-le only on tailless
airplanes of fairly ,hi-h aspect ratio.

The results of the aspect-ratio calculations can be
'-xplalnai by consideration of the action of increased
as rpct ratio upon t.e I rodyna..iic center of a swept-back
wins. Ac previously shown by _qust'on (3), the fore-and-
aft location of the winj aerotynanic center is defined
by the relati;o x,.. = rb tan A. For a Eivcn wing
area, an incrersse in aspect ratio iinreases 'both H
ai-d b and canCDjcqU.-~: tly risul.'s in a rearward shift in
tie v.:in,3 ,erod.'n'.t.? ce-nter. T-is ar'tion r-esul].s in a
rCdluctirn of the *jivnLg ;, rr:ents ci~-._ted oy flaos and
hence allows e.;tensrin r of the Lift-fiap s.pans for a given
piicchiing ioniment. T'PliIs fat explains the r.pi increase
in net lift incr:.-.,nt with in!creL-sed. tspszct r tio. Thie
mo<-,nt arnms of ic.7. chA.-tbjoadc9 section: ru similaL'ly
reduced ,iLth incream7 in cazpeci ratic and L g'r:ater lift
loss is th-reby incurred fcr L giv-n required Lrirumming
r!o:0.-nt. Inspection of tiie formula X. = Hb tan A
inlicc.tes thjt the iirgest effect if aspect rai.j.o occurs
when the sweepback ar.15: is slrge. hiigh lift are most
readily attained, trlrcforz, f'r rc.lativ.,ly large values
of booh aspect ra.ti-' and swavcpRback angle.


Effect of Ta,.er Ratio

Results of taper-ratio calculations are presented in
figure 15, which shows that an increase in taper ratio
allows a sizable increase in the net lift increments of flaps only when the taper ratio is initially
small. 'or values of taper ratio hfgh)r than 0.5, the
rain in net lift increment with in-icreased taper ratio is
negligible. For the airplane investigated, increo-sing
the taper ratio from 0,25 to 0.50 increased from 0.42
to 0.66 the allowable net lift increnenl obtainable by
self-trirring flaps. A iurthEr increase in taper ratio
to 1.0 increased the net lift increment to only 0.70.
The results of figure 13 also show a successive decrease
in trim-flap efficiency as the tajier ratio is increased
from small values to 0.5. Above 0.5, however, a slight
gain in the trim-flap efficiency is afforded by increased
taper ratio. This value seems to indicate the point at
which the direct effect of increasing the tip chord
offsets the decreased moments of the outboard sections
caused by the shift of the aerodyiamLic center.

An increase in taper ratio results in a rearward
shift of the 'ing aerodynamic center. It would thus be
expected that, as the taper ratio is increased, the flap
moments would be reduced and, therefore, that self-
trimming flaps of larger span could be used. Increasing
the taoer ratio of a given wing, however, causes also a
reduction in the chords of the inboard sections and an
increase in the chords of the outboard sections. The
gain in lift-flap span allo,:wable, due to the aerodynamic-
center movement with increased taper ratio, is thus
increasingly opposed by the decreasing chord of the
inboard sections. In a similar iaanner, the decrease in
trim-flap efficiency caused by shortened moment arms with
increased taner ratio is offset b- the increase in chord
of the outboard sections.

In addition to the favorable effect of moderate
taper ratio (about 0.5) upon the lift produced by flaps
on tailless airplanes, further advantages are realized
by taper ratios of this order. The wing-tip stalling
characteristics are more satisfactory for moderately
tapered wings than for hignly tapered wings. Moderately
tapered designs therefore allow use of larger angles of
sweepbaci: before sizable losses in lift are incurred.
Reference 17, in addition, shows that moderately tapered
wing designs (taper ratio between 0.33 to 0.5) are
structurally most efficient.

18 NACA ARTR Ho. Ll1l8

Lift Loss in Cbtar:ing Longitudinal Trim

The cElculatiDnr made t3 Oeeternine tlhe effect of
the para.,eters on the lift and pitchir.,n-nor:lent character-
istirs o.' the trim flaps are .iipo saprliable to the study
of the lift loss incurred in balancing the stability
mo..ents nr the air'plnea. The effects of varying the
trin-fla-' cho"d are pres-ntle in figure ', which shows
that no rpkreicb-bl-3 chance in lift occurs with varying
the trim -flad rl.o1r for a given ritching moment. A study
of Lbe u?Zfect nf taer i-t o also indcica te6- that this
effect :n the lift loss due to tri:. would be negligible.
Tha3 eff -at of' tap ratio on the lift lo-c incurred in
trir;,jn:. a momernt o0' 0'.0 about the aerodynamic center
of vi wit'i h tweentac': angle of 200 and aspect ratio
of 7.5 is nhown in the foll.c-wi-ng table:


0.25 -0.25 I
FO -.21
1.00 -.d

The effects of ason-ct ratio and sweapbac'-: on the lift
lo-Ps remul.tlin fro.n the additional i.rirn required for
lo:-n itiJ.nal control s'-nimarizeA in figure 1L These
dse, c -l.ccte That isr-e *ralules of aspect ratio and
swe "'-'': pnr le are- required zn trinminze the lift loss
res.Jut-I'L fro.-. the additional trim requirements.

I':i rt.at3 of figure 1'4 may be applied to trim controls
usinr.- i *1'ereiqt chords or 'efleet ionc or to control
surl.t.-.. ,-A-her than the plain split flap, if the centroid
cf ~i' .' .'.':-tal flap load is located at anproxinetely the
sam: r. I.. "'se station as that of the solit flap. An
in>:'. .. .1i angle of sttaci: Aa = 9.1,o wvas used to make
the e(r .-.uat ions required for figure 14. In order to
convert the data of figure ~ 1 to other flap cords, flap
del'lectioni, or airfoil sections, the scales of the graphs
can be multiplied by the ratio of incremental angles of


Estimation of :TxPimum Lift Coefficient of Flepped

Tailless Airplanes in Trirmed Flight

During the course of the investigation, it was
recog-iied that the data obtained in the analytical and
empirical studies could be emploj-d to give an indication
of the maximum lift coefficient attainable with trailing-
edge split flaps on tailless airplanes.

TTLe mrxixum- lift coefficient of a tailless airplane
in trirmed fli-:ht with flaps deflected may be e:.:piessed
in suimary form as

(C = (CL + LCLf Losses
SImax)tr imax f

The lift losses of a tailless airplane may be con-
sidered to originate from three sources the loss due
to the longitudinal control surface, the loss in maximum
lift induced by sweepback, and the loss due to change of
wing stalling characteristics when the flaps and lcngi-
tui:nal! control surface are deflected. The first two
sources have already been discussed. The loss due to
tri:n Is riven in figure 14, and the loss induced by
sEwetack can be assumed to vary roughly as the cosine
of the anle of sweepback. The change in stalling char-
actetiistics of a wing, when the fla-js and longitudinal
control surface are deflected, may change the angle of
attac!- at which the maximum lift occurs and may change
also the characteristics of the nonlinear portion of the
lift curve. These effects may cause the increase in
maximum lift produced by flaps to vary from the value of
the lift increase produced by flars at a wing angle of
attack of 100. Because stall prediction is uncertain
and b:cLause of the complex nature of the problem, no
attempt has been riad: in the pre-sent investigation to
analyze accurately the factors affecting the flapped-wing
stall. A statistical study, however, was made concerning
the ratio of incremental miaxi.r.i:: lift coefficient pro-
duced by flaps (ACLf)x to the incremental lift coeffi-
cient produced by flaps at an angle of attack of 100
(ACLf)a=,0. These d;-ita were obtained from available

wind-tunnel force-test data and are presented in figure 15.


These data indicate that a ra'io of (ACLf)m x/(.CL)a=10

of 0.9 would be a good mean value. An indication of the,.um trim lift coefficient can now be obtained from
th.. relationship

(tax) = GTa + 0.9 A0L \ cos A AC (4)
tr axj t Lax f p

where ACI corresponds to the lift lost by a control
surface that -1elds a pitc-hilm-moment coefficient abcut
the aerod--n.amnc center equal to h Lmax and may be

obtained from figure l!). It should be noted that CGLp

is a function of (Cmax)tr and hence equation ( has
to be solved by the trial-as;l-error r;etrhod.

Eigh-Lift Design for Tailless Airplanos

The present analysis has indicated that by proper
design a tailless airplane may obtuan maximum lift coef-
ficients conno-rable with those of conventional aircraft.
A design that comin.nes tle f,- tuyrs chowin by the present
rerults to be favarabl3 for achieving high values of
nma:imum lift ccefficient is shovn in figure 16. '.ith
thi. dLesign, it is estimated that a maximum lift coeffi-
cient oi 2.0 in trinummed fliEht 'ith a 5-percent static
margin may be obta.ned.


The concli.sionp drawr'n for an an analysis of factors
affecti-ng the net lift increment obtainable from trPiling-
e-i;de solit flaps on tailless airplanes in trimmed flight

1. 'Te maximniim lift coefficient of tailless airplanes
may be of the crder of 2.0 or greater for reasonably large
values of aspect ratio (10) and sweepback anjie (200).
Low values of aspect ratio ( ) and sweepbacK angle (100)


will limit the incremental lift obtained with flaps to
small values End will also result in excessive lift
losses due to longitudisnl control.

2. The highest net lift increments will be obtained
from f]o-:; on wJ, dlesiCns that allow use of single
inboard self-tri;: in.T lift f].-3 Ywhich ocsup:.. all the
wins span not takeen~ up by other control surfces.

5. TPo ir.3 cs'esir that limit the span of the
inboard self'-+.-r n: ng lift f]s&p to a fraction of the
spa ot},-.. .se allowable, further increases in net lift
may be ti: -ind by use cf a .multiple-flap s--tem con-
sisting of an inbo-:."- lift flap deflected d.-vnwurd and
an outboard trim flap deflected upward.

4. Excessive taper will r,-duce the net lift obtainable
fro.n flaps on tailless air-'nr-nes. Tap,-r ratios of 0.5 or
greater are recori'.nidcd for tailless-airclane designs.

5. Incres.-.- flap cho:d and deflection will lead to
increased net lift increments due to flaps.

6. For wing-tip elevators, aspect ratio and sweep-
back are the controlling- factors in -.irn-.zing the lift
loss fcr obtasi~ing trim of a given pitc]hi:rg moment.
Taper ratio and elevator chord have little effect on the
trim 1os.2.

Lan..l- "rri al Aeronautical Laboratory
"-tio-. A dvisory Committee for Aeronautics
-" ,1.; ield, Va.,


1. Pearson, Henry A., and Jon.s, Hobert T.: Theoretical
Stability and Conr.rol'istics of 'Jings
'liiQ Various Amounts of Taur,. and Twist. NiCA
Rep. :.o. 635, 198.

2. Fearson, TTenry A., and. Anderso', F-ayor.d F.: Cal:u-
lation of the Ae:rodynamic nriaracteristics of
marered Wringq with PastI-til-Sptn Ilaeps. i:ACI Rep.
No. 665, 19?9.

$. '.7enzinger, CSrl J., aPd R-rrpi .:-.:,-s .: 'id-
inrl-9i Investigat-cn 1.. .C.k. C'012, 23021,
and 23050 Airfoils -..,ith Va.ilou~ Sizes of Solit
Flap. IAV.C4 Ecp. O. .C, l

':.'nzireer, Carl J.: 'ind-'Tunnl In-.-estii action of
Ordinary and Spli' Fla, -. n Airfoils of E'iff6rent
Profile. NACA 30p. Pl'. 5 T', 1').

5. "eick, Fred E., and Harris, T iL.s A. Ti-e Aerodynamic
Characteristics of a 'o,.-el "irz H.avinn a Split Flap
Deflected Downward and :cve'J to the Rear. NACA T:r
No. 422, 1932.

6. WNenz1nrnr, Carl J., and H'~.rris, Thmcas A.: Pressure
Distribution ovr: a Re-ean'guilr Airfoil with a
Partial-Spon Split Flap. !T.CA Rep. No. 571, 1956.

7. Weick, Fred Z., and Sander .o -rt: Aerodynaric
Tc-sts of a Low Ar.Sect Fatio TaperEd l!ing with
Various FlipF, for Usu on '2Tilless Airplanes. NACA
TN No. !63, 19 ).

8. Keely, Robert T.: '"lrd-runinel Tests of T:'w Tapered
Wings with Str3aight 'railinr- Ed.:e and with Constant-
Chord Center Sections of Dif'ferent Spans. 7iACA
ARR, a-rch 194 .

9. .nz linger, Carl J. : ind 'Tunncl Investtigetion f
Tcr ered .'ings with Orirary-r Ailerons and Partial-
Span Split Flaps. Ni A Fe hep. ;o. (11, 1937.

10. Anderson, Pay3-ord F. D et.r-ination of the Character-
istics of ar.ar3cld 'in-s. !i.CA Rep. No. 572, 1930.


11. ~'utterperl, William: The Calculation of Span Load
Distributions on Swept-Back Winrgs. NACA TJ IHo. 83L,
12. house Rufus 0., and .':allace, Arthur P.: .'ind-Tunnel
Investigation of Effect of Interference on Lateral-
Stability Characteristics of Four ITACA 23012 Wings,
an Elliptical and a Circular Fuselage, and Vertical
Fins. 7ACA Rep. :;o. 705, 1911l.

13. Rossell, H. E., and Prand, C. L.: Sviept Back";ins.
Part VIITI, hero-ts on "'ind Tunnel r..opriments in
AerolJynam.ics. 3!'ithsonian risc. Coll., vol. 62,
no. 1, 1916, pp. 55-7T.

14. 'Kni-ht, P.'ntgomery, and 'Ioyes, Ric'-ird 71.: Svan-Load
Distribution as a Factor in Stability in Roll.
iACA Rep. No. 593, 1951.

15. A.nderson, Rayrmir.d F.: T-t experimental and Calculated
Characteristics of 22 Ts :ared 'ings. FAC.' Rep.
No. 627, 1358.

16. f"illiams, D. H., and i~allidry, A. S.: Experiments on
Swept-Back &r.d Swept-Forward Aerofoils. R. & iM.
ITL. 1491, British A.R.C., 1C?7.

17. Anderson, RayrT'ond F.: A Jc. oarison of Several Tapered
X.YIIr. s Desigced to Avoid Tip Stalling. UIACA TN No. 715,

18. 'lallace, Rudolf: Investigation of Full-Scale Split
Trsiling--dgre " .aps with Various Chords and
"ir ce Locations. ,NACA Rep. To. 559, 1935.

19. Jacobs, Eastman :N., rin':erton, Robert :'., and Greenberg,
iHa;rr7 Tests of Related Forward-Camber Airfoils
in the Variable-Density 7ind Tunnel. NACA Rep.
No. 61c, 1957.





d ^

I/cremental /h/f due to
tr/rn //C C

(a) Typ/cal incremen/l s~a ,d -
dMtr/but/on caused by f7op delflec'on.

Aeyng'mic center

(t) Ty7w2/ 5panwv se center-of- a
pressure Ci5sribution of /inrementol /oad due

to f/os.
/0 A0,05.

ornet /-Increm~en ta plching ment due
Sto // f/aop
1 \rrew/nAe t hpflkhIng
7z rmonwent u4e to
Percent semip /an

(c) 7yf/ca .-ncremenoa/ no'xnent d/str/tbu/on due /o /ea os.

/7qure / Samnpe /f/t center-c'f-presre, and p/cin/r"-rxwment
d/sfr/ru/cvnsa cAle /o prvt/a/- san foaps on a jweial-
aL2t wI/ng.

Fig. 1

NACA ARR No. L4118 Fig. 2

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NACA ARR No. L4118


NACA ARR No. L4118


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Fig. 11



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Fig. 12





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NACA ARR No. L4I18 Fig. 16

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