Airfoil-contour modifications based on epsilon-curve method of calculating pressure distribution

MISSING IMAGE

Material Information

Title:
Airfoil-contour modifications based on epsilon-curve method of calculating pressure distribution
Alternate Title:
NACA wartime reports
Physical Description:
14, 9 p. : ; 28 cm.
Language:
English
Creator:
Theodorsen, Theodore
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Aerofoils   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: A method, based directly on the so-called epsilon-curve method published originally in 1931 in NACA Report No. 411, is presented for use in making modifications to the shape and pressure distribution of a given air-foil. In particular, it may be desirable to remove excessive irregularities or local peaks in the distribution. In this process it may be required that certain parameters of the airfoil be kept unchanged; for instance, the angle of zero lift, the ideal lift coefficient, or the moment coefficient. From an academic viewpoint, an altered distribution cannot be "prescribed" because compliance with the requirement of maintaining a Laplacian flow field is involved. A prescribed distribution can therefore not be obtained by iteration. The process, however adequate, is necessarily one of qualitative modifications. Several numerical examples illustrating the use of the method are given in the appendix.
Statement of Responsibility:
by Theodore Theodorsen.
General Note:
"Report no. L-135."
General Note:
"Originally issued July 1944 as Advance Restricted Report L4G05."
General Note:
"Report date July 1944."
General Note:
"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 previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003609112
oclc - 71126264
System ID:
AA00009430:00001

Full Text
' k L C- S,


ARR No. L4G05


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WAllRTIME RE PORT
ORIGINALLY ISSUED
July 19"1 as
Advance Restricted Report LAG05

AIRFOIL-CORTOUR MODIFICATIONS BASED ON -CURVE
NMTEOD OF CALCULATING PRESSURE DISTRIBUTION
By Theodore Theodorsen

Langley Memorial Aeronautical Laboratory
Langley Field, Va.








NACA..


WASHINGTON
NACA WARTIME REPORTS are reprints of papers originally issued tu 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.


DOCUMENTS DEPARTMENT


L 135







































Digitized by the Iniernel Archive
in 2011 Wilh funding Irom
University ol Florida. George A. Smalhers Libraries willi support from LYRASIS and Ihe Sloan Foundallon


hllp: www.archive.org details airtoilconloLurmoOOlang









TATTON'AL ADVISORY COMMITTEE F'OR .ER'LIAUTICS


T-.'.. -.' ~ _r. TT D FTPOP?

kl -FOIL-CONTOUR .ODTFICATIOIlS BASED ON e-C.1VE

"'ETHOD OF t.LCULATI I3 PRESSU'FE DISTRT 3TIO

By Theodore Fheodorsen


SLU"4.RY


rethor', based directly on the so-' alld (-cir"
mr:thYd nr'ublished originally in i--31 in .7. Z -oo:-rt
..,. 411, s nires :-nted for use in l.kin? rmotifi .t'.`r
tl the shso-e '.n1 -ressure distributing nc. a ,- i Cir-
_1il. In "o-I i lar, it may be dcsir.bl t, r ',ovc
-*cessive irne .uj -ritisx or local ...a':. in the dis-
t r t tion. In t.is process it rrai b:- re .,.i-ed ta.t
c :rtain oar-imcte rs rf the ai-f'.oil be k-,pt u.-i. i -ed;
for in stnce:. th: a.'r.l of Zcro lIft, i-he i.i' :1 lift
coeffic-'ent, or the n.o:- nt .-.ff.-'f ent. Fr an aca-
det-ric v'ev int, :rn altered distr- but_ -n cr.not .
"prescribed" bee-.;e c.:m:l ance .v' th h:- re i e'r.mnt of
marinta_.ning z La..Locian flow field is .nvol'.ed. A
nrese'r.'_t ..d distr "'utit can therf-ore _'t :- obtained
:. t,-r" t i ,. .'m rc'cess, how',e 1 2..'.- u L.e, is
ces."-'il7 one of q,.a-l itati ve mo-ili atio s. Several
nu.ir:' r i ev- mr.,le- ill .it rat Lrna the use of the method
re z1 ,--n in the ur'-.enl x.


T UTRODICTI ON


Tr, 151 the author lntwoduced the so-called c-curve
mrethod for ca]culatin; the pressure distribution on air-
foils of ar'.itrar-" shapt:. tSee reference 1.) The
r.-rit of ti me *: d depend? e .ss;.nti al :. n the fr- ct
tl.et the rs',.ltin; int.~gral rellatinn ca~n be csolv,. by a
Ur'idly' conv, r'g.n pro. ess. In the or-.se:it pao-r the
problem of -effceti-n. change in a given pres;z..- dis-
tribution is cons der-cd. The m-thod is bas 3ed d1rc.tly
on th imrort!rt.nt v-lozity formula IXIT) of r,-fer.nce 1
rewritten as formula f('') in ref-rence 2, a later
rep.rt. Deference to these papers is made repeatedly
.-erein v:ith subsequent omission of the details con-
cerning the use of the (-curve method.









I.ACA AFRP N0. LL305


,orri1der *a ,'vr n rf 1. rlc1m rhe E-curv= .4f
r-fe rtneie 1, r an0 r ar.. cbti'-nred; mnd from formula
'XTTI ,f r- rrc.rr 1 t.pe p'.c ure-, or T*.e equivalent
vr 1 .i:' 1. i-7 e1inc !, !' ve locity a' be wr-tten :ir
t-'r-s It thr cua:!n' tie; p, $' 1 a + Er., and v
as l.i fori'Rpe :.') .if refe-erce L"

., Ir. (a + p) s..n (a + ET)
- = .-'--- (1)



'"E rc. thl reeder r- rr'e rred to references 1 and 2 for
t!'e m ar.in- of thE various s:.mrbolo.

.iv. conr ice- a sl'ghtly alItered p:,esr ue diLtribu-
- on,. '.bis r..-'v ,re ".sure distributionn Is o 'rious';\
r- at to r, n w ir. 'oll c tourou. It :- pe:-tinent to
rrrrmar' ere- tLat fr-m- s pu'nly .,atbFat:' cal vlewpnint
'ie. n-v. di tricu:"nr: c, innrt be "pre scrited" unl s- the
'nwr airfoll con-r, '-r al-o is yrescrbed. I:- ". Dtrntial
" -,v .' tho t r .i -u] art' e 7 ere exi-t- a un i .e i la-
..r i.' bt .' .E Cl Lhe cor:nt:u.r and tLe p-e7 suwe diLtri-
l.ti n ir. th.e flov fic-ld. A presrsure d -itr rlhution
cannot therefore be -r.ne rribed (.LuthemTtic 1l] ;) for
the si j-le ee( s: ri. e 'r c ated contour must be
i-iv.n in ordc r to r-. : rcbe it. Thus the problem of
spcif 'yi.-n' ri.t ro.'u, l.< 7 a r ezsur'- r "stribiutlor is
redrced C, d &.urd n.. T ro.' an a-ead!.ic -t.indnoint the
so-c-alled inr.rr rr-.,rm! '- thE ref'e d.ocs not exit as such.

Ccrtalr. lt:c rati 91n? of C qua'_litative nature may be
rc rf- r' d 1i, sop.it- r- f t',e act thaLt a prc s-ure. ehIlnr e
r:nf & Fr,, t r s fscr.il' Jd. It i- t',Et rur-p-l e of this aperer
to indicated a s~t1.d by Vhch oialitatlve alteration
may be perfo.re. Tt 'Ill be nocrd that thp pre-ent
method, of cont-ur rod.li.cation will serve the intended
r.urpo -. of the inu eror n.etlt'-n'c.

IATUR.T /"LTERATCI"-

It Is uoef'ul to observe that several types of
independent alteration are possible. By riefrence to
the velccity formula (1), ftr instance, a chL-nge in ,1n
w'.11 appear mainly in the multiplyin- factor e'0 and
will tl.us effect an increase or a decrease in the. veloc-
'tieCz Lverwhere on thr contour. Thi change results









NACA AP. No. L14GO5


s irnnl- in a series of ei r-cIls of different thi -kness ns
the rmPjor effe-t. It is interesting% to observe thet
r.neither the angle of zero lift nor thL ide.ja a!.le of
attack has been changed in this oper -tion. The quanti-
ties E n'd ',11 oc urring in the velocity for.muls ar-'-
considered availsole for the original airfoil .:'citour by,'
the e-curv,- rrmthod of reference 1.

The effect of a change in the an,.le of attack a
is well known and need not be di.scasied hc-re. In fact,
the rain interest lies in ircrovin- the pressure dis-
tribftion at saird near the iptinrur, r ideal, angle of
attac-'. In the followin.g discuss n-., therefoo'- thec
proposed change a Ere pe rf rr.ed at the ideal .ancle Df
attack only. In ot.er words, the p-r'ssu'r' distriL ution
is examinEd at the ideal an,,l-? of attack, tc-ntative
chanries are proposed, and results are. co-.".1-ired at the
ideal a: 7'1e of attack. The reztr.cti on that the ai-le
of zero lift reirmain unchianLed ;ay or :say not be incrjed.
For airfoil 2Dntours of zero 'owmrent coeff i' ient, as used
in helicopter blades, the rest-ricti.n m'- Le ir'n-ocsed that
the rroment cocflii.'r.t r nr'in z:-ro. In the following
section the nature .of .- cn.-r;-ies is examined with
several t-pes of re stri Ur on 'i- d to fulfill s.ec ifed
req'.i re:ret s S Uch ch ; s :,e:-. be ;' r r.'ed in the
cre sur-. distribut'.n:. s Ib 4ect to an'"; one restriction or
to a com':i1nstion of sever-.-! si::ultaneous restrictions.


MZTH7 'T 7 F 7'.7A'T:GT THE -c-RVF


The c--3urve c'n readily be ootsained aEs c (r 0*; the
method of reference 1. in mrst cas-s it is desirable
to keep the ideal lIft coefficient constant in order to
obtain improver,.ent at the exa-t value of the lift. In-
asmuch as the e:0pression for the ideal lift coefficient
contains the factor


2 T )

this restri tion is eq iv.lent to maintaIning a fixed
difference between c.. and E the values 01 at
the nos3 and at the tail, r-s'.ctively. The absolute
values .,:ay or nray not be pct the same. If both CE
and T are kept constant in the process of charge,









14 MACA A4P ;-o. 14Q00


the ile-A l lift -.ooff-'.c'ent, the 1 deal anr l' of attack,
,r'd the an-ile of cero ift ,re r.-t in::d. This chan-e
) 1nlely -local ard ovtre.rily restricted' n nature; only
1i no-" ha"nes 'vill ')thIii t 0o t'riz strlr,:enu tppe of
r t raa r.nt. In ordar to mfe. E a C.r-cer change, the con-
Aiti)n of .flnstlAt angle of zero lift ray' be relaxed but
ti1e tr-qI' 1ir.ent uf a constant idn-al 1'ft cocffici nt
r t a i nd.

n ...mponrt *ai1 ca'.i- cf aiteraticn is th- csse in
which tha :,n, en" cc f efficientt is kEout r, start It is
s wn Cn re"erence 2 that the. rr...mcnt d1.pends en the tv:wn
oIve.?t aror iat s in th v m)--pa-'ve. y prescr'ibin.; n
alt -r:iati n L (cF c nta inin! higher harmonics than tne.
sEc-nJ the -res_-',.re di.ctrr autiin maiy e altered without
affe-.t4 nrp Lub moT'nt noreff.ic crnt. Yrc, aiso, further
re.stri-ctions (a3y or ma.,; nr t eo impos-:d. Tn encral,
th.5 ore restrictions mpo.3:d, tnc morc manipulations
I.? rt*q;.. r. to iad j t tn ( -.E arve.


TIMI TATTVF D "'.: R' CH4'2rL'S


T"oT, t. nt'- t ve n assL1r' chMruie is traiislated inb-
- ?ha:j'e in the F -c ire 'i11 n)-" be .ndist-d. The
t,)- and .'Q')-.-, rv3s re :r .- ime'd to ne available from
the rmeh.-fd rf re tre.-e 1.

A nres.-.urg vri.t~ 'n ;' long th]R contour may be
tent ati, 1 l e pies nI i r S.tice thi s e>:xP t hange is not
exacted en;. a", .aY.t relatio.nshins involving Aon need
nnt oc used. Tt is ser 3 ?n fron. t. velocity formula that
1 2
*.- or its pq'i val ?nt, tn -:r?9s'ire n- mrnasured from
Ithe staL-nation pressuF.ire, is given ver.! nearly as



A + 1 +


wh.ere. A is a function cf position cnly. With similar
acncuracj, therefore,


S-- d E)
c ).
P s C4









TACA AT, r'o, 1 ,5


-:1, finally,



2 1Ps


-"..ere t!.e inte.grli is to be taken o'er the rsr.ge in
"'-.ich the tentative ores i"ur ch.anie is ,I ve Because
tr.is pressure e change is imoroperl:. .Iho n n, the value ..f



Ac = / ,^
0 s

for t"-., h le' r .re in v.bi zh the chai,- is -i'.en v:ill
not, in general, c -o'ne zero nor '.:ill .he ar-.-c u.vl, r the
LE-curve


AC d'T


oeccrm., zero as reLjquire.-d oy the conditi.?ns on E given
ir. r-fcre -.-.-- 1. It Is of n.rarn-iunt L importance at the's
poinL to repeat that the ori finally prescribed or-. ssure
is nef.esssrilv unatt9ina-ble, as is shown cy the ff.t thnt
't-e t,"' fore oln,' inte-,rals are, in general, di ff'crer t
I ro zero. It vill -)e noticed, however, in the foliov, ini
c2tstussi.'n that the essential shoeo" .-ffn.? t may oe re-
t iner i. The -,rocess is si-iply to ma-ke the A -.,.irve
-..n rn: to tne :.-iven requirer,.ents by a suiti'ble acldusc-
".:I-.t involving the least possible ?haan-e iM the in.-.feral
. r'-: -i tne Ac-curva. This adjustment is .ada .-l
h'an'in the location of the maximrtn. and mTnimurr'Li points
cr tht curve or b5 externding the curve beyond the
.",ri.--insl rar.:-e. The area under the -c--surve can alsc.
oec m:ade zer,- bt chanlring the referen>-! or m,':-a: valu.-.
Tvw b'asij rdi t ions imnist there f-re o, impn-sed on the
(-curve: namely, that the two fore-g.Oing int': r'als be
zero. Several examoles are treated in the appendix.

Finally, a pressure change for constant moment o)ef-
ficient must be considered. It will be seen from ref-
orence 2 that the moment depends on the two lowest
harmonics in tne c(,,)-curve arid the value of E The








6 IACA ARR Iro. LG00o

.roce"s is as f llowv: Prt- Fcribe a tentative pressure
chan-e so, fi:.-. the corr-as-or.'dirn Ae, adjust to cnpnly
vith the twr. basic crnditior.s or:viously mentioned, and
Ietenr:i'ne che followin- four integrals


_ = TYo


S- K T

12 T y

A3


TT


aE sin c dp



ar cos C; d:r



Ae sin ?2p ti0



Ac cos 2c 141


By removing

A. s-n 0 + ? :3.3 C + .A. sia 2 + b cos n2Q
S- c 2
frr.r tlhe initial -fr:-. ti -., the resulting .E is rade
free if ths wo 1 :'est h2 r:r..nii-s.

In gcnr- l, n ,'oi. u. ch-an- ed sli,.htly by the
removal of the twr,, low:s:t narr'onics. By adding a third
harmonic c

A. sin 53 + 2 cos0 50

both the msagaitude and the slope of c at the trailing
edlge may be left unchanged. This end is attained by
choosi%2 the proper values of A and B3. Thus, in the
function

Ae = -A1 sin Qp 31 Ds (c A2 sin 2p


- B cos 2$ + A s'-n 5; + B cos 5qp









"ACA ARR 1',.,. t4G05


the constants


A and B3 are determined by making


AIe = 0

d- A6 = 0
dcp 1


for


P = Tr + P


where


second order


A = 1(A 2A2)


in there results for A
in there results for A3


and


+ (8B1 5B)P3 + 1(4A, 5A2)P...


B3 = B B2 (4B1 B 2 +...


Thus, the siy: constants are known and the desired change
in the AB-curve is given.


CONCLUD ING REMARKS

It has been pointed out that the so-called inverse
problem does not exist in a strict sense of the term,
because a possible pressure distribution cannot be pre-
scribed unless the new airfoil contour is actually given.
An, airfoil corresponding to a given pressure distribution,
therefore, cannot in general be arrived at by an itera-
tion process or by any other method. It is shown that
only certain qualitative modifications may be effected.
Such alterations fall logically into several independent
groups. Attention is given to localized variations, in
which not only the thickness factor but also the ideal
angle of attack and the angle of zero lift are kept con-
stant. Of interest, also, are the pressure changes


To the
B3









, I;PCA APE ?F L'J 5


r rf )-rfme.d 'ifr h t:i restri c.on Lt- t'e momt nt -oeff ient
:r-d tca af .lc of Ier lift re-r-in unchara ed. Thils cdse
: f ir. oot-nrc for- i rf ji iscd in hel i other L1sdes.


T.n: '-, I I jrlia 'eroe.,utio Lra-ora.tLliy
Sat ioonal Adv' sor:, Conom:c ttee f or o'ron?.Aics
Lanr i 3,', F r 1C, 'J.









-ACA A7R '. L-t39


ADPENDI' X


EX.APPLE


Fiv, casss are t related as ex.am.les ,f tn.? a.iricil-
cnntour-mco.difica'rin rethod of calculPtinig, presc'ire :lis-
tribu.ti n:

I. R.A.F. 1I cirfoil fsee tale I); lo al '- ltr.jes on
l- 3er s.rface; sI le of er. lift, ideal 9. a l.e
)f atta-k.', a-d ideal l'ft 3-Deffi.-1* r.t '."rjt .on-
stant

II. F. A. P. 15 inr' f l ; lo':cal :La ej s -i low er curface
moment t .oeff' ie-t nr.J a.n le r.f zero 1'ft pt.
Sons t int

TITT. Airfc.il c:,nt, Ar ene-r te .t fror' = .1 s'. t a ),
= 3'. fs-ee table IT): ideal lift ?-,effi i ent
keot conrts t-: a i zl e of zer' li ft and ideal .ang-le
of -ttuac: 2.- ':.e

IV. Airfol *-ntour s? rnm 3 n ca_-e !IT: angel1 of zero
lif t :.t 2. tYnt

V. Airf.oil 2on to.ir sa're as in case 7TT : restrictions
sa-e a.s in 'aS.;e -. & sn example of too severe
r t r i t 1i ens

Case T is based "r. tLCe '.A.T 15 airfDil for wLhich
figure 1 -hov.s the si-'-oe an:d tn. e-re sure d istribut i.-,n.
The o rDosze of ti-e Inter. e.i ul ter-.ti, -n is to r:-.rove the
vavy line n the uott.r.m s'irfsac. The first step as
indic -ted Is to draw b tent -tive rressurer distrib Lti oin.
In tie crve at the to:. of fi-._re 2 the ;orrcesoLdin
tentative cha,;: in pressur- is ',lott':d alg inst the
&rnle Tn I' ne;'t steo is to draw the adjusted curve
for which the area



Ps

Thus a closed Ac-cir'.'e is assured for case T; this 3urve
is called the adjusted curve and is shown in the center
of figure 2. It is also .iccess.ary to make the area
under the Ac-curve








10 iCA', ARR 11o. T.LG05






.Thi. r c: on? rea il'y ithcut .i terine L -, or AC ,
a: ..'."n b:,7 cle line for case I, for which


I/t.E d, =- 0


he e co:reound n Aig t".-urv-'e is sho-vr. at the nottrn of
fi -ure' 2. "'T e ;nm ffied lOr] ci2 r.1 h}-.ape '-.i'd :)re sure
d .-tri ur.iuti n if r I s r rre s.ow. "n : i ure 1. :lote
tV-,t the r- : r.re dlist: .-..,t'Uie s t".- 11' oot Ulr.d differs
from the ter.L nt i ',' -r s r-1e dis..tr ,,-L'.ti-'ri s3ni that no
ch' r.~e h-e :icur-..,. i,1 te ',1le of zero lift or -r. the
ideal ,'-..le f st1ac':,.

C3'-e TT is eI.o_ o.scd on tib ".A.F. 15 irfoil,
v'i th LI'.- re -i rrm .rit L.i''.: sed thatt th-.e i,,'imment ccef cieat
sa:'d tn: r.;' .I of -rc i ft r-':.Q n .co-rs -r t. Tn; tcnta-
tive :r..-sure di tribt'irn i the s..re .:: that used in
? I. The --ur-v;- a1u ted for zero arr's and the
-s
Ar-cuvur d..tit e cor c a"9 ar ; therefore identical
wi' tY the'e :e.e 7. Tr. th s :Ys,? it is :1ecesar~ i to
omplv v'ith the re- nire:'.ert ret the first and second
hsrmoni-z tie ierr '.-' ani' thnt Eomt third rsrmon ic be
ad,'edl to ret-in the vsl of e. As shown in the dis-
cussion, t f.ri t ir.

A- = -9.1 o n C, 31 ..:" sin 2. B2 cos 2p

+ A5 sin 53' + B3 cos 7e


is to b, aided, whve-re


A = / A3 sin cp
tio








AC"i AR" TT 'o, T ..005


1I -- -
2r
A2 = f'


2nT

9rr
B. 1-
5 =


Ac cos c dcp




Ac sin 2,p dmr



AC cos 2 C dcP


- 21) +f23 532 b +


8 (L 22
2+...


By adding A,e to Ac of case I, the AC-aurve called
case IT -n' the corre -orodi.nig AY-curve in figure 2 are
ottatiemx. The r-eulting modified 9srf 1l contour nnd
pressure distribution are shown in fi..ure 5. This case
i-. best suited fa.r maint ,inin._ z-ero monicnt coeffieirt
.n sirfoil sections us:.d in autogyrros and helicopters.

The following th-re c.-ss, cases TI to V, are based on
the sirfoil section 'rnerat.tsd from E = 0.1 in 1 ( n L5'
' = 0.1. Thi original and th.z tentative ;Pressure
distributionn. are shown in figure L (a). In I'i''r-- L b),
n/.p is shown nlotted ra irnst the angle f,. The
t-:nt:-"tive nressure i u rve ia adjusted for zero 9r.-t as
rf .: re. The correso.-incin: tLEc-urve i. mrrarled "Csse
I" "n figure 5 ":nd the 2orresoondin: AW -c'-irve Is
.- rved "Ca.- ITI" in figure b. Thus fl three choices
heve e .?cn tr..r t:-d:

(1') The exact .har.e 31 curve ITT is retained by
changing the zero line, or rfr-r.ce 1ire, for ac,
which chaner on-ch c end b.t r'o- L 13 the dif-
ference and ther'cre ihe ideal ilIt c'.f"i lent. The
resulting airfoil co.tour aond or'izsure di stit utinn for
case TTI are shown in figure 7.


and


A3 = (A1


L3B = B -
*1








:fACA ARR No. I&G45


() In cas, V th' arePt u.',-ur th,- Ac-curve cor-

re:spo'-jlinrg Lo the tentrtii.ve ,-cu"'''e h-a be an mnad zero

h- eyt nl n, tr,' ranr o zIf.-tLed b'rond the nose. Tn
ti"s e e, only the anlJe o.. "er 1 3ift I3 ',ept constant.
,'e result s cmrpai d ,.thi the o'ir:inal is shown .in
figure L.

(.) Tii ca9se V the restriction is purooqely made
ton severe iy soe..ifyrlni tnat no chE,ne shall occur
either !..n the ideal Iift, the an.le of zerD lift, or
the ankle of ideal lift.

C,-se V ir. fi ;ure. be !or,,e.s distorted in attempting
t .. ful. fill t.!,e z r:-a rea re'r r-1..r nt 'and th' 3 f nal results
sl.nv.n in fi,,ire are ,- rres .nd,' ;i-l,,' unsat II factory.
Thie corncl .n frf-,. tale exI -x.,ple I t-hai .lthou.h cer-
t L'n requirenrier, ts ire .:I i raIle -Jr re luree it i3 r.ot
w-Lv,.'s a pr s e.ule to ibt i' ; *'.d vcolut tn wi thin Lhe
mi t ta.ti ons of s i,.' r a4 ir:rr.ents. -n sucn a case an-
other basic t oe more suitsaie to the UTrpose must be
s ,! e ct -d.






T'.. F i:E. i CHS


1. h r Thr'od..ro.- : Th ,'r o~,; nT V'ing '--; ti ons of
/rti L-url, Si' itc. 1:/CA 1E : 11, 1r.

., Theadc.rs3n, T. anrd .ar.ic -, T. Gen r&Il Fotential
T'_-e.r7 of k.bi tr,.rr -T.,i. C.. ti ns. "t .0. Rep.
,**. 15-, 1 5.








P"TACA AR? 1T. 11105

TAL E T


Q)Fri'ATr^ 2-) .A.:-. LS R"r^L S.TTD


r)IrITr ';-jrT *: T.s I A" TT

Fstatonr.s nd ord 'eter in.' -:-r;nt
"of v, ing chord-]


'..er rurf -e


St .ti n!


Lov,?r '-urf a .:


Orin ir.al


0

2. O

U...0-
'. ul
C "7

2 *
5,. L
5..
9L.


L 1.7

S-"5

3 9


I -r -
I I
-- I I -r

C. 1.11) -.73 [ -. 6 -..5
C..t i .> -. o I --0 -- 2
I .7.. -].1 -1'.* .'9
. 22 -5 -] 5 I -1.] -1. "
S.7K L.7 -1 .25 -1.2 -1.32
r- r. I F 2' 1 ;r I1


.55

a.

/ .0)
*. ,0


~!
p 'A. Lj

Ca
I')

I (
a")
1'
I .'


-.75
-.2:
-- .
-.'t?
- 7.



-.0
0


-1.^1

-1.25 .
- .17
- LO




i r
- .. i
i c.
-I'-


-.l
-. l

-.65
- C..)
-.L0
-. L .

-.63


:i
,U


i'AT EAL -'7 'r-c.l
: 9 I TTLL 0" .: ; J.lUTJ CC


r.
1.25:
c.,
5.0
7.5
10
15
^~0
A?
r.t
(.0

1-0
9'9
qr
100


















--F j.-'_qr


.1 I *
f ,- r t r J -r -rj I
r-. p. .i -',* -( ** .u r f r--i M i.-*.
>. i r '- .- ,IJ .' .- Pr" ,r f '" j ,J*-- I ,
rI I I I I I I I I I I I

-' .C- r' N r ,[- '.., -[ L .0 .
Sr." ,) "- '"1 T.. r.-- --, ,- .: Jr. .
( ". . .
r --4 ..- r--- r *' I J 'J -' I I I C
(N ___________________________
1 I | I- l I i il J I I l l rl i1 J l




I -'. L'-- ...)C ,'. .- r, .. )..



I *-u-':r-* -2 .***'*z* -z*i
iJ . I I
I I I I I I I I I I



,'d L"- ,-- 'L '-' -----



I
[-I



I

SI c- 4 ,..- t r -' _i r-QC t'"t -- u "
*,' 1 C J a + (i "- u C : OC .- I

I . .
I '.
I "J_ "- ,-- *. ~ r"- 1 -' i'"" -' "-':1 ---U ^"Jl .- `
c' I *:j *j ^ r c -" ~ *
I .
1- I- --^ 1- -^ -


I -
j! --- I I






' I


,2 e-
aii Il) C r-
LI_|____


i 1 ,.
r,
CI

I
I 'C


-r -- J 1 .C -^
, ,.* ". r r -" -. .r"




* r '-z, ... J r J "--r 0 CN.--i r'
r h '.' l', C r'o C. r-", r '
* ."J _-- L. ," D"-v- 3 C'-. CO .- -"i- 'J r- 0


Prrl L'.C) '" O -o-J RJ N L- NJ JN

'" ril L N.' L'*C '. .i '.r-I .





SI L.' % 0 U
Sr-i r .L-~, ,j r 0 0 0 0 C --'7
f- l 'J rC --. *'P' N"-O C C- 0
r-4


T;.''A AR .ro. rl ,3005


C "'
C)

fr0

C'





-4 C.



SE-



C,.







NACA ARR No. L4G05


Original


/Modified


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


-- Original
- [enijfu/e
o /lod'fed


f/ qure / Shape and


Percent/ chord
pressure distribuhon, case 1. (2A //s5 airfol/)


pA?


',0


Fig. 1







NACA ARR No. L4G05 Fig. 2






I 0 -



o I o
1



"^ -ft- ii .
c U.








S II
08













t,/
-I -r-F !















IL







v N
o o
-- -I -


I g0




-- 5
____ ___ '__ ___ __ __ __ __
0- 0 r 0-







NACA ARR No. L4G05


Original








Modified


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


0 20 40 60 80
Percent/ chord
Figure 3 .- Shape and pressure distribution,
(R.A F /5- airfoil.)


case II.


Fig. 3







NACA ARR No. L4G05


- Original
- Tentative


P/q


Percent chord
(a) Oriqinol and tentative pressure distributions.


- Tenlaoive
- -Adjused


for I = 0
*c


3.0 3.5 4.0 4.5 5.0 5.5 6.0


(b) Tentative and adjusted pressure changes.

NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS
Figure 4. Pressure distributions and pressure changes, case III.


40/P4


Fig. 4











NACA ARR No. L4G05


U


-z

~
~iO
.~ U-
z
I--


o ~
C-, ~
a

N
~~1


U
I-


o
I.-


'U







a.


Fig. 5










NACA ARR No. L4G05 Fig. 6


CD
C,
U.


S a

-S 0
El~


8












I'

q^







NACA ARR No. L4G05 Fig. 7





Original








Modified







NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS




-- Original
-- -- lodifed


PAY


0 20 40 60 80 /00
Percent chord
Fg7ure 7. Shape and pressure distrlbullon, case III .







NACA APRR No. L4G05


Original








Alodlfied









NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


-- Original
- -Modified


p/9


0 20 40 60 80 /00
Percent/ chord
Figure 8 Shape and pressure dis/trbubon, case IV


Fig. 8







NACA ARR No. L4G05 Fig. 9





Original








AModified








NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


-- Ongnal
---- Alodified


p/


0 20 40 60 80 /00
Percent chord
Figure 9.- Shope and pressure d/sri/bulion, case Y .










UNIVERSITY OF FLORIDA

3 1262 08103 315 0


UNIVERSrTY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA



































q '