Document
ARR N o . L4003 • . NATIONAL ADVISORY COMMITTEE FOR AERONA UT I CS ORIGINALLY ISSUED April 1944 as Advance Restricted Report L4D0 3 W IND-TUNNEL INVESTIGATION OF CONTROL-SURF A CE CHARACTERISTICS XVI - PRESSURE DISTRIBUTION OVER AN NACA 000 9 AIRFOIL WITH O. 30 -AIRFOIL-CHORD BEVELED - TRAILING-EDGE FlAPS By H. Page Hoggard, Jr., and Marjor i e E. Bulloch Langley Memorial Aero na utica l Laboratory Langley Fie ld, Va.
WASHING TON 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 - 20 5 NA'T'IONAL ADiJISO:1.Y COT.!MITTEZ FOR AERONAUTICS • 'VrrT"l - TD:nCL DTVr.S~IGATI()IT OF C0N'rROL- SURFACE CHArlAC '=.'FRISTICS O . 30 - AIRrOlL - CH~ l UJ 13EVELED - 'rRfI ILIIW - EDGE FLAPS ay B. Page HOGgard , Jr ., and Marjorie 3 . Bulloch SmTI\IARY Pressure - distribution tests have been made in the
lJACA 4- by IS - foot vertical t1.nnel of d plain flap with
intercllangeabl'3 beveled trailin6 edges on an NACA 0009 airfoil . ~he flap cl1.ord was 30 percent of the airfoil chord and t_ill ~evel chords were 15 and 20 percent of the flap chord . The 15 - percent bevel was tested wi th :;he bevel corner .faired wi th both large and small radii .
'rhe Durpose of these tests 'I;/as to sU'lply pressurc-
. distribution data that may be used for structural and
. " aerodynamic desion of horizonta ..... and vertical tail sur - faces .
~he results are pres'3nted as diagrams of resultant pressure coefficients and of increments of resultant pressure coefficient for the airfoil with the flap h~ving be veled traili:1g edge s . The dia.gra:ns are pre sen ted for the control surface "Ii th the gap a tt;he flap nose sealed and unsealed .
A comparison of the beveled - fla:!) pressure data vdth plain - flap data indicated th:..t the addition of a bevel reduced the pressures over the entire airfoil, including the peak at the airfoil nose , and caused a reversal of pressure over the beveled part of tl1.e flap . The normal - force coafficient for the beveled - trailing - edge flap was les" L an the co()f':'~icient for the plain-airfoil - contour flap . ~ho open gap produced a tendency toward o"l.Terbalance by dccr0asin the nogati ve prc.;ssuros over o the upper 3urfJ.cG of u flap 'wh e n deflected dO'.'lnward .
The results gan~rally wer e in f&ir dgreembnt with force - test d.s..ta pr 3 viously published .
2 NACA ARR No. Li+D03 IN Tl-{ODFC TION The National Advisory CommIttee for Aeronautics has insti tuted an extensive investigation of the aerodynal'?1ic characteristics of various control surfaces. The force - test data from th:i.s in Testlcation have been summarized in reference 1 . The two-dimensional pressure-distribution cata obtained as part of the inv e stigation have been analyzed and the varl etion with flap chord of the various aerodynamic charactGr1.stics of a flap has been presented in rc fe rence 2 .
':!Wo - dj_mensional force tests have been previot~sly run on a similar mode l of an I'JACA 0009 airfoil with several beveled trailIn g ed.~es; thfl results of these tests are presented in reference 3 (8130 ~un~arized in reference 1) .
From the results of these force tests of tr&iling-edge shapes having voir-ious incluced trailing-sdge 3.1131e8 and other airfoil tests , a method based on the included angle at the tra ilinJ edge has beun fOlJ1d I'or predicting the values of hinge ~ momellt p'1'a:m8te:rs to te expeet~-:ld from a bevdl . This correlation cun be found in figure 150 of ...
r e ference 1 .
The two - dimensional - flow tests presented herein were made to in ve s tiga te the pre s su~'e ae ting on a control 811r - face with a beveled trailIng edge . Such data should be valu able for strl1ctl.l.ral design of the control surfaces, for e, planatton of ~he balan cin b action of th~ "hev31, and [c·r ~t lCy of bO""J.ndarJ- la yer con cH tions .rr':) l.l",-es ti - e;aLLon v:as Ih8.c'e at all a?l<3les of attack .lne. fla}J c:oL'.E:' c - tiOllS c(Jnsiderea necessary for the struc tUl'al design of atlcrons , ele va lors, and rudders .
T S y:\I 30LS cf flap clJ.ord rC 'll'v'8.rrl. of flap hinge a:v:is, percent airfoil chord c chord of basic airfoil w5th flap n8utral q dynamic pressure of free air stream p pressure coefficient -- .~-- .
NACA ARB po . LL1·D03 p resulta~t pressur0 coe~ficient < H .
• increment of r esu l t& nt p r essure coefficient Ll PR static pressure a t a point on airfoil P statt c pl'essure in fl'ee air stream Po angle of attack for infinite aspect ratio a o f l ap deflectio n
of
M Mach number , ratio of l ocal velocity to speed of sound c airfoil section nOJ'mal - force coeffIcient (n/1.c) n c airfoil section pitchlng - momGnt coefficient m about quarter - chord point of airfoil (m/qc ) c flap s~ction normal - force coefficient (nf/~cf) nf ..., \
( flap section h~nge-moment coefficient hf/~cfL)
Ch f normal force of airfoil se c tion pel' unit span n • m pitching moment of a rfoi l section about quarter- chord point. er unit span normal force of flap s"3ction per unit span nf hinge moment of flap section per lmit ~pan hf OC \ (
cnafree = oa: ) c~ =0
~.lf n
i
= ( GC ')
oa
o Of
J
- -- - - - -_._- - },TAC/\ jI , r-m Jo .
:U~Do3
Cn-f." =Cc n ~
.10 OOf / a Chf
= ( ~O c: 0 0 6f
a o .1 _
(C C h
C}lf o
= 66f )a
P
=
a
(0 : }0
f p
Pc:, =
e \
GOf )a The subscripts outside th'3 parentbese.'3 indico. te the f8.c tors he 10. cons tan t durin,-: the :m e asurement of the • pa ram ete r .
Subscrip ts: U point on upper s~face L point on lower surface l-{ resultant APPARAT:JS ANn J'.~OD:':<';LS
The t es ts were made in the NAC4 4- by [ - foot v ert ical
tunnel. The test section of th is tunnel has been con -
verted from the o ri gina l open , cj rcular , 5 - foot - diame ter
jet (reference J~) to a clos ed rectangular 4- by 6 - foot
test section , a3 shown i n figure 1. The modal complete l y spanned the test section ; therefore , two - dimensional flow was approxima t'3d.
lTACA ARR rT o. 1) ~D03 ~he model used for the pressure-distribution tests • of th~ . s investi3Eition v:as designed to be an exact co')y of the model used for the force tests in reference 3 but uith only the 0 . 15cf and O.20cf beveled-trailing-edge shapes . '.C he 0 . 15er bevel was tested wi th the bevel corner faired wi th both large and sm.all rar111. The 2-foot - chord model was made of IF~llinated mahogany to the modified NACA 0009 profile (table I). The airfoil was equipped with a 0.30c plain flap, as shown in figure 2(~ .
A gap of 0 . 005c was provided at the flap nose. The flap was constructed with interchangeable blocks that formed a beveled trailing edge and a thickened profile, as shown in figure 3 of reference 3 .
A single chordwise row of pres sure orifices was built into the urper and lower surfaces of the airfoil and flap at the midspan locatio:l. The orifice loca- c tions are presented in figure 2(b) in percent of airfoil chord from the lea d ·'1g edge. The copper tubes from the pressure orifices ware brought OTIt of the mode l at one end through the torque tube and the tunnel wall to a mul ti_ple - tube, open-faced manome tel" . neadings were recorded by a ca nera .
• TESTS All of the tests, except those ~ith large flap de - flection and high pos~tive angle of at tack (flap deflec- 0 0 0 tion, 30 and 45 ; a:lgle of attA.ck~ 14.3 and 19.3°) were run at an average dynamic pres:lure of 15 pounds '('IeI' square foot . 'l'he ltirge flap deflections at high posi ti ve angles of attack required more power than was available to maintain a dynamic pressure of 15 pounds per square foot; therefore , th~se tests were run at all average dynamic press'ure of 12 pounds per square fc:)t The airspeed in Q the t6st s('ction cRt dynamic pressures of 15 and 12 Dounds
per square foot is auout 76 and 69 miles per hour, respec -
tively , at standard sea - level conditions. The corre- sponding values of 0 ffective le:~olds number are 2,760 , 000 and 2,208,000 . (Effectiv e :heynolds num-
ber = Test Reynolds number x Turbulence factor; the turbu-
lence factor of the iJi,CA 4- by 6-foot vertical tunnel is
1.93 . ) The tests were made at angles of attack ranging from 0 0 - 20 to 20 at in tei.'vals of 50 Eii1d at angle s gi ving maxi - mum posl ti ve and neg" tl ve li ft . It may be noted that all angles of attack are offset from the exact values of 0 0 0 00 , So , 10 , l ~o , and 20 by - 0 . 7 owing to an error in setting the zero angle of att<::.ck . This error was found to be conslstent throughout the tests and the data vvere corrected accordingly . Tne model was tested with 0 0 0 t~e 0 . 30 c nlain f l ap deflected 0 , ' 1° , 2 , 50, 10 , 0 0 0 0 0 15 , 20 s 25 , 30 , and 45 c 'ilie tests were run i th the flap gap both open (0 . 005 c gap ) and sealed with 0 0
plasticine . During the tests with 30 and 45 flap
deflection , pressure orifice 15 ~or the lo wer surface (fi g . 2 ( b)) was sealed bec aus e its osition at both l arge fl ap deflectio~s was inside the gap .
Check t ests were made for each flap deflectio n as an in d ication of the accuracy of the test results .
When the 0 . 005c cap JaS used , the check tests '.'Vere made after both angle of attack and f l ap def lection had been reset . The sealed - ~~p check tests had only the ang le of attack reset , bec~use the plasticine seal would have to be refaired if t he flap ceflection were chanbed .
The speed of the tunnel was maintained at the test value of q for approx i mate ly 2 mlnutes before readings • were recor ded in order t o &llow the alcohol in the manometer tubes to reach th e correct height .
,.
hESW-,TS Presentation of Data The results of the pressure - distrib ution tests a r e gi ven in t he form of diagrams of resul tant pressures wi th fla p neutral and re sul tant - pressure increments caused by varyi n g the flap d efl ec tion . The resultant pressures and i ncrements of resultan t pressure are presen ted for the various beve l and gap combinations and for various ang l es of attacK in fiLures 3 to 1 0 . The resultant normal pressure at any point a l ong the c hord of the airfoil wa s det e rmin ed by t&king the algebraic difference of the pressures norm al to the upper and lower surfaces of the airfo il at that point . All di~grams of resultant pres - sur es or resultant - pressure increments of the airfoi l and f l ap combinations are plotted as pressure coeffi -
ci e nt P or as .iP . The resul t8.nt p:eessure coeffi -
R
n
ci en t i s1defined as NACA ARB No . L4D03 7 where PH - Po
P = -
u
q p pressure coefficient p static pressu~e at a point on airfoil Po static pressure in free air stream q dynanic pressu: ' e of free air stream and the s"..lbscripts U upper surfac~ L lower surface R r esultant ..
The resultant-pressure diagram for any condition may be obtained by addill13 the distribution at E:.. given angle of attacx and the distribution at a given flap deflection .
A comparison of resultant-pressure dlstributions over the bevel juncture with large and small -"'adii is presented in figure 11 at several angles of attack and flap deflec - tions .
Pre3sure distri~utions for the upper and lower sur - faces of the flap having a 0 . 15cr bevel wjth sealed gap are pre~entej in figure 12 fo?" v ~ riol} .. s angles of attack and flap deflections . he r)sultant pressures over the NACA 0009 airfoil with 0.30c plain flap and sealed gap (reference 5) are compared wi~h ~he resultant pressures over the modi~ied airfoil with O~15cf - bevel flap in f:i.gure 13. }<'igure 14 presents upper- and lower-surface pressures over the plain flap and the 0.15cf - bevel flap for the same conditions for which resultant pressures are given in figure 13.
The rates of change of pressure coefficient with angle of attack mld with flap deflection are presented for TACA ARR No . I4D03 the various bevel and gap comb~nQtions in figures 15 to 18 for convenience in calcu l ating distributions at
small values of a and of . '.1'he flap section norma l-
o force coefflciellt as a function of f:tap deflection is presented for all combinations of' bevel and gap in
figures 19 and 20 at sevaral angles of attack . Com-
plete chordwise pressure distributions for various combinations of ao and Of that might occur on the horizontal tail of a oive homber in highly accelerated maneuvers at various 8peecls are presented in figure 2 1 for the 0 . 15cf - bcvel flap with sealed gap .
The section aerod~,~nanic coefficients of the airfoi l and flap are presented as functions of angle of attack for all bevel ano gap comojnations in figures 22 to 2L~ .
The coefficients were obtained in each CB3e by mechanica l integration of the original pressur~ diagrams .
The paramete r vQl~es for beveled flaps are pre- sented in table II along wi th -"alue s for the plain - airfo i l- contour flap for cen venien~ compari son . The plain - flap parameter val~e~ were obtained from refer - ences 1 and 6 .
• Precision The angles of attaclc are believed accurate within t o . l 0 . :'li::l.p deflections are belieVed aC(;llrate wi thin ± 0 . 2° . Plotted values of pr0ssure coeffjcient Pare corre ct within ±2 percent except for peaks at the leading edge and flap hinge axis or for stalled con - ditions .
Coefficient values calc~lated from check test points
ha ve been plo t ted in figiu'e s 19 an"l 22 and are de signa ted
by flagged symbo l s . ..!any of the points com8 wi thin the accuracy of the plot; others vary a negligible amount .
The a c curacy of the corrected zero angle of attack i~ indi cat ed by the deviation from zero of lift and moment
c oefficients at zero angle of &ttdCt . Prom figures 19
and 22 , it appears tha t the maximu.'11 error in setting the angle of attack at zero lift is 0 . 2 • rrhis discrepancy may be caused by flow misa l inement in the tunnel or by an asymmetTical nodel .
Two-dimensional f l ow having been approximated , the resu l ts may b8 considered as sectIon characteristics .
NACA ARR No . L4D03 Experimental tunnp,l correction s were applied only to the airfoil s e ction normal - force co efficie nt cn . Although no corr e ctions were made for th e otber coeff icients, the tunnel values are be li e ve d to be ~igher than the free -air values and he nce are on the c onser v 8.tive side for struc- tural purposes . 'l'he magnitude of tbe airfo il r esultant pressure coeffici e nts as renr esen t ed in the resultant- prossure diagrams (figs . 3 to 10) is h~own to be too large by about 7 n e rc en t be c ause th e s e cur v es were o lott ed dire ctly from ma~ometer r e cor ds wi t ho ut the application o f the exper imental tunnel corr e cti on , which ~ llows for th e incr ea s e in lift produced by t unne l- wa l l int erference .
DISCUSS I O~~ Resu l tant - Pressure Distribution The r esu lt ant - press1..1.re diagrams should prove useful in determining loadin6 conditions for the structural des i gn of ailerons and horizonta l ~~d vertical co ntrol surfaces. Tests have lndicated that the increments of pressure and the incr3ments of section aerodynamic coefficients cau sed by flap def l ection are approximately independent of the airfoi l sec ti on for airfoils of approxinately the same maximum thi c kness and thickness
dis tri but ion (references 7 and 8) . It is therefore
believed th at , for structural design, the incremental data presented here in may be applied to other basic sections of apnroximately the SRne thickness and thick - ness distribution . rhe increments of the section aero - dynami c c oeff ic ients may be taken from .:'ioures 22 to 24 by us ing t ~1e fla - neutral curve as a reference l ine .
F rom a study of t he inc remental - resultant -nr essure 0 0
curves for the stfllled conditions (a = 1 9 .3 and - 20 . 7 )
o for bo t h beve l cho r ds andrsap conditions (figs . h, 6, 8 , and 10), i. t anpears that th e be ve 1 c ontinue s to reduce t0 e flap hinge momen t in t~e stalled c nditio~ from th e hinge moment for a plain flap under the same conditions.
The tests of be v eled ele va tors on th0 fusel&ge of a typical pur.sui t &irplane also i ndi c ated that the bevel was effe ct ive i n the stalled attituje and reduced the floating angle of the elevators by about 10 (r eference 9) from the ~l1g1e at whIch air.i.~oi l - cont our elevators would f loat . The resultant - pressure curv es (fi gs . 3 to 10), espe ci a lly for the 0 . 005 c gap , show a tendE'Hl cy to ward a de cr Gase of resul tant p r esst:re o ver the main airfoil just ahead of t he f l ap .
-~-~ -- The results indicate that the size of the radiu.s at the bevel juncture is ~elatively unimportant in its effect on the loa ds OV3r a bevelad-trailing - edge flap (fi C . 11) .
Pressure Distribution over Upper and Lower Surfaces of Beveled Flap The diatrlbutions presented at various angles of attack and flap deflections in fi gu re 12 indicate that only on the urface of the flap which is deflected against the relative wind does the bevel affect the pressure distribution to any great extent. The only exceptions occur at low angles of attack and small flap deflections, for which the upper- and lower-surface distributions show near::'y equal effect of bevel . The pressure distribution on the side away from the rela - tive wind , when at lar6e an;les of attack or flap deflec - tion, resembles t ~la t 0:::' &. flap and tab in a stalled condition e
It will be notic~d in figure 13 that the r esultant -
pressure peak at the flap hinee axis is higher for the beveled flap with the 0 . C05e gap than for the beve l ed flap with tho sealed gap . Inasmuch as the resultant pressure is the algebraic di~ference o f the upper- and lower - surface pres 8 ures at any point , the positive peak on the lower surface tnal{es the resul tant-pressure peak higher . ( SAe fig . 14 . ) The pressure ~istribution produced over the upper and lower surfaces of a flap by a beveled trailing edge i3 com pa red with the pressures over a plain flap in
figure 14 . The effect on the pressure distribution of
the bevel on the surface deflected Etgainst the relative Nind is more pronounced v.-hen the ; ~ap is open . The main effect of the open gap on the flap pressure distributio n anpears to be the decrease in ma~nitude of the negative pressures over t~e upper surface 01' the flap, which r e suI ts in a tendency toward lo wer or even overbalanced hinGe moments .
Curves of P and Po a For conv6ni ence in calculating the pressure distri - butions over b oth surfaces for small values of a o - ---~ -- 1 1 and of, the curve s of P and Po were calculated and a
are presented in figures 15 to 18 . From the experi-
men tal data, it '.vas four..d impos si ble to predi c t vii th any degree of accuracy the variation of pressure with angle of attack over the nose of the airfoIl because the stagnation point moves considerably and the pressures change ra-oidly and are not linear with angle of attack .
s::'he v ariation of pressure with angle of attack over the rest of the airfoil appeared from these tests to re~ain
a linear variat io n only from 0 to 50; therefore, the
Pa -curves should not be used for calculating pressures beyond a value of ao of 50 .
The variation of J ressure with flap deflection for any point on the airfoi 1 con tour app3 ared fl'om the se
tests to be linear to 50 . ~he Po - curves therefore
spould not he used fon fla~ deflections gre~ter than 50 .
The final Dressure distribution required is found by Multiplying the valul3s of P and Po by tr .e values a of a and of for which the 1istribution is desired o and adding algebraically to the basic djstributiOD (P at a = Of = 0 ) £i ven in the Im 'l er part of fig- o ures 15 to 18 .
Flap Section Tormal - Force Coefficient For all comblnations of bevel and gaD tested, the val ue s of cnf were sn,allAr tharl for the pl ain flap v!i th sealed gap at the sane ansles of attack . 'l'he values
of c n and c for beveled and plain flap m~y oe
nfo fa conveniently conpared in table II . The variat~on of cnf as a function of angle of attack is clearly
shown in figures 19 and 20 . The eflect of a is small
at Of = 280 with t he gap open and at Of = 20 with
the gar. sealed.
Pressure Distribution on _:orizont3.1 Tail For Highly AccelE:rated ianeuvers The flight condition during which high structural loads and the formation of a crnapression shock on the horizontal tail are ~ost likely to occur is a highly
12 NhCA ARR No . L4D03
accelerated T'1""neuvor in which the horizontal tail is operating at a high an~le of attack at 1J.igh speed . The pressure data presented he r ein are not applicable to e ail design for hie-t.-speed flight unless they a re ccr - r8ct e d for the varib.ti on of !-,1'eSSU1' e wtth .M8. ch number, whieh is gi v en anproximately by th e rel:.::.. tion l!/~ rvr .
' rheoretica l vpriati .o ns of pr'ossur . wi th ~1::.t.ch number are compared with experimental p~essure-distribution dat a at various Iv'ia ch numbers in referenc 8 10 . The pressure d i stributiom p r es'3nted in fig1. .re 2J . at p,nele s of atta c k of - 0 . 7° , 5 . 7 , and 10 . 7° and with f l ap defle ctions of 0° , - 50, - 10 , and - 15° are test data th~t cov er the hi gh l y accelel'ated maneuvers estimated f rom unp u bl ::i .shed dive - bomber te st data .
Ael'odynanic 3ecti . on Charac t eristic3 Normal - fo r ce coeff:'8ient . - The force -t est li ft data of r efe~ence 3 are bivon in t e r ms of section lift c oeff ic Ien t wh er eas the pressure-distribution data are gi ven in te rms a f normal - force CO'3.J.. ~fi c ien t . InasI'lUch as t he lift CO J ffi cien t and norr.1al - f or ce coe ffi c ien t ha V'3 ne a1' l y the sanie v ~ l ue , ch i s value l s 1"0 ferr0d to as II li ft!l in the fol lo wing discus810n .
n ) OC Thp. s lo :')0 0 f the li ft c urve -- from table II ( ':Ja o Of for tha airfoi l with 0 . 15cf bevelsd trailing edge and sealed gap is 0 . 088 as compared with 0 091 from the force - t est data in 1'efer>e nc e 3 . T hese results are in fair a 3reeffient if account is t aken of the f~ct that different mojels and methods of calculation were used for t he force and pressure tests .
The l i ft - cu rv e slo:nGS from ehe fo·~ce and p r essure t e sts for t"1 e O. 20cr beysl 'Iv: th s ea] ed gnp have tIl e same value, 0 . 092 . For t he open sap the lift - curve slopes from t he forc e anj pressure tests ~re , recpectively ,
0 . 088 and O .oS? (t at l e 11 and. ref eren ce 1) . The lift -
curve slopes obtained f"'om the pr')spur0 - cUstrjbu ti on tests app6ar to C h8Ck v ery we2-1 wi-'-;h t ho force - test resu~ts .
Openin3 the g&P appeared to chenga the angle of attack a t whi ch the stall occurred by about 1°. This b.ngle of attack, a~p r ox i mately ±12° with flap neutral , wa s not af fe c ted by be ve 1 chord .
NACA .APR TIT o. L4D03 13
/oa ~
The vnl ne s of' lif't effecti venes 3 (0 5 ~)cn gi ven in
tabl'3 II were taken at zero lift and show the expected decrease in effectiveness as a :l'esult of the beveled trailing edge . The small radi u s on the bevel jl..mcture lncreased c about 0 . 003 for open and sealed gap Nhen na compared with the lift-curve slope for the large - radius bevel . Reducing the radius at the bevel juncture decreased the eF.fectiveness from - 0 56 to -0 . 52 . .
r:2he param8ter c ( table II) is a measur'3 of n a free
c ontrol - free stability only at ao = of = 0° . The
values in table II indicate the eX-93cted tend-:mcy of the beveled flap to float upward at a sms.1Jer angle than the plain flap .
A method for e3timatinc; the pre.3sure rHstr:i_bution (and nor~al force) 0 er a be vel from e.. vailc-ble tab pres ure-distribution data is ;;ive n i:1 the appendix.
The results of this 1.1etbod are i. llustl'ate and a com- parison is wade ill fieure 25 , at several angles of attack and flap deflections , between actual and estimated pres - S!.l.re distribut':'ons tOl' a 0 . 20"'f bevel with sealed gap and an included angle at the tr'ailing edge of 25° • . Flap hing e - r.lOment coefficient .- The values of ch fa (table II) were taken over the line 'J..r part of the hinge - moment curve , which './as over a small :"'a"1ge (±5°) for the 0 . 005c - gap tests a nd a larber range (±lOO) for the sealed - gap tests (fi gD . 2c and 24) . Th'3 values of Chfo
(table II) were taken from of = 00 to o~ = 50 because
the curve appeared linear over tYis range . For a com- plete picture of the effect of variolls bevel and gap com- binations , all the ~inge - moment curves (fi g s . 22 to 24) must be taken into consideration and too much reliance should not be placed on the slope values measured over a small part of each curve , exce_t for stick - free stability calculations .
The values of c h and c h as found for the fa fo 0 . 15cf and 0 . 20cf bevels with sealed gap are in fair agreement wi th the values of reference 3. Values of both hinge - moment parameters for the 0 . 20c bevel with 0 . 005c gap ~TACA A.RR No . Ltl-D03 were road f.i."om the curves in figure 49 of reference 1 and were found to be ~n fairly close agreement . T~e values of Chfa and Ch1'6 for ';:loth bevel chords were found to fall ne'll" the eorreJation curve of figu"C'e 150 in referen ce 1 v, 'i th less scatter than the average scntter of the correlation points .
From the val_ues of hi'1ge - m'Jment T _ arameter s in tnble II it ar-pears chat decreasing the rad~us at the bevel juncture tends to decrease the negative values of ChfB for both gap con Jitions . Decreasing the radius had no effect on the value of c~fa when the gap was open b ut d o creased the positlve value when the gap was s e a le d .
Pitching - moment coefficieDt .- The s l opes of the cur v es of pi tching - r.1onent coefficien~ as a function of lift coefficle:1t 8.t 8. cO[ls~ant c.ngle of.' att'ck and at a constant fl.s.p deflection are gi vpn in table II. The aer od ~~a~ic cen~er of additional lift c ausod by varying the angle of attack beLer311y was loc ated at approxi - mately t'}e 0 . 22c sta~:ton for the sealed - gap tests and the U. 2 1 c station for the O. OOjc-gap tes·~s . T1:e ';Jevel chord had little effect on the location of this aerodynamic center .
The aerod 'mar; ic center at 'IV iich the lift ~roduced by flap deflection may ')e considered to act is located at aoproximately the O.hlc station for either gap condition .
A ll aerodynami c - cen tel" 1 oca tions for the e:;ap - sealed condi - tion are in falr agreement with the values presented in re ference 3 .
C Oi~CLU3Io} ' S Pre3s1~re - d::_strlbution tests have be8n made in the rACA 4 - ;:':T 6-..:'"'oc,t vertiG3.l tunnel ot b. plain flap wi th f int e rchan e;eabl ' bevoled tr'2.iling e dges on an NACA 0009 airfoil . The flap chord was 30 percen t of the airfoi l chord und the bevel c hords WEJre 15 and. 20 percent of the flap chord . The results of these tests indicated the following conclusions ; NACA ARR No. L4D03 lQ At a given angle of attack and flap deflection, the addition of a bevel reduced the resultant pressures over the entire airfoi1 except for the pressure at the flap h~nge axls , includlng the peak at the airfoil nose, and caused a reversal of pressure over the beveled part 0:' the flap .
2 . The normal-force coefficient for the beveled- trailing - edge flap ~as less than the coefficient for the plain - airfoil - coni:;our flap with the airfoil at the same an g le of attack and the flap deflected through the same angle .
3 . The open gap at the flap nose 8a ve the flap a tendency toward overbalance because of a decrease in the negati VG pressures over the upper surface of a dov/llward deflected b<;}veled flap and because of a slight increase in the negative peak on the lo ~er -surf ace bevel juncture .
4. The size of the radil.s 'J.sed to fair the bevel
juncture appeared to have no appreciable effect on the pressure distribution deve loped .
5 . The results obtained froo the pres.:::;ure- distribution tests generally were in fair agreement with for c e - test results of a com parabl e arrangement.
Langley Memorial Aeronautical Laborato~y, National Advisory Co~~ittee for Aeronautics, Langle y Fie Id , Va .
i
I
16 NACA ARB. No . L4D03
j'!::TEOD FO[~ C.4LCl.TLAr::'ING PRESSURE DISTRIB'J~IO"T OVER A BEVE L FJQrll TAB PR:<:SSURE - DIST " "UBDTION DATA.
Vilhe n an elevator , aileron , or rudder is designed, t he gen ral practIce is to use the total load over the surface . No tion p ictures of bu l ged fabric on ailerons in high - speed dives in d':'cate that the pressu res along t he chord should be used to de ter mine how securely the coverin g must be fastened to the struct~ra l members . In th e cas e of a beveled surface for which a pressure pea~ occurs a t t~e be ve 1 j mcture , 8. study of the chordwi se distribution might pr0vent a cov ering failure . A method for predicting the chordwise pressure djstr l bution over a be vel ed surfa c e with out hav in g to test it is advan- tag eo us , particularly as such a method supplements a method already estab lis hed for predicting the hinge - moment characteristics .
A ne t~od for predicting the chordwise load distribu - tion on the flap is described herein. No attempt is made to predict fl ap s ection hinge -mome n t coeffic~ents; t he hInge - momen t c or relation baseel on the in cluded angle at the trail ing edge (for sealed - gap condition) may be found in figure 150 of reference 1.
The bevel contour was deve l oped ( fig . 3 of r efer -
ence 3) by def l ecting a 0.20cf t ab ±100 and deflecting the flap sli gh tly each w ay to keep the tab trailing edge centered on the air fo il ch ord li ne . Inasmuch as the bevel profile was de v810pe d by using dei'lected - t ab contours , it w as decided t o use t ab press ur e diagrams to es ti mate the preosure distribu ti on of a beve led flap .
Only the U I)per - surtace distrib ut ion for a t ab deflected do n warcl and the lo wer -surf b.ce distribution for a tab deflected upward are considered . It is necessary to
correct these pressures by means of Pa to a llow for the
small flap deflections necessa r y to keep th e tab trailing edge c en t e r ed on the airfoil chord line . The r e sulting diagrams (fi g . 25) were inte g rate c. and found to gi ve values of c that w"ere in go od agreement with the nf bevel test data for flap deflections of 10 and 20 at 0 0 values of ao of - 0.7 and 4.3 ( figs . 25(c), 25(d) , 25(g) , and 25 (h)) . 1he value o f c baseel on tab nf -----~ data was in general sOMewhat larger than the bevel test value.
At the 3maller flap de fIe c tions, the value s of C n l' from tab data were generally much larger than from bevel test data but , from a comparison of the values with those for a plain flan in figure 20 , the estimated values were found to be closer to the bevel test values than to the plain - n . ap values.
In order to use the present correlation method, it is necessary to l-J.ave pressure - distribution diac;rams for a flap and tab of the desired chords. The tab chord should approx:imately eqilal the distance from bevel juncture to trailinz edge .
The included angle of the bevel must be reproduced by the correc t tab and flap def10ctions. These deflec- tions must be fOlmd in order tha~ th~ tab - deflection d agram may be chosen and corrected The following equation gives the n~ount that the flap must be deflected to keep the tab traIling edge centered on the airfoil chord line: ¢bevel - ¢airfoil . - 1 Ct sir 2
= S In -------
where incl uded anDle at tra iltng edge of be ve 1 (for ¢bevel which prediction is being made) Inclurled angle at trailing edge of airfoil ¢airfoil from te~ts of w~ich f lap rund tab pressure diagrams are to be used chord of tab , ",?ercent airfoil chord chord of flap , nercent airfoil chord cf nth 6.0 ¢be vel , and ¢airfoil known the angle f ' through which the tub 1s deflected ±Ot to reproduce the included allGle of the bevel may be found by the fol- lowing equation :
.0be vel - .0 irf011
a = /jEf + ( 1 )
_
-----~ 18 MACA ARR I o . L4D03
It may be noticed in figure 25 that the tab data used
':,ere for 6t = il Oo whereas equation (1) gi ve s
6t = ±8 . 400 . By using the diagrMls for 6t = ± 100 , the
in81uded angle was found to be 27.6 instead of the
correct value of 25 ; but, in8.smuch as the correlation
for th e hinge - momen t pi:lrame tel'S based on included angle shows a chan ge of 0 . 001 in the value of the hinge - moment nar8.meters for a chan68 of 2° in the included angle , there could "8e only a slight change in the size or shape of the pressure diaeram .
NACA ARR N o. L4D03 19 fLEFERENCES 1 . Sears , Richard 1. : Wind - Tunnel Data on the Aerody - nami c Characteristics of Airplane Control Surfaces .
VACA ACR No . 3 L08 , 1 94 3.
2 . Ames , Milton I3 ., Jr ., and Sears , Richard r. : Deter -
mination of Contro l- Surface Char&cteristics from NACA Plain - Flap and Tab Data . NACA Rep . No . 72 1, 1 941 .
3 . Jones , Robert T ., and Ames , Milton B ., Jr .: Winct - Tunnel Investigation of Control - Surface Character - istics . V - The Gse of a Beveled Trailing Edge to Reduce the Binge JJoment of a Control Surface .
RACA ARR , ~rch 1942 .
4 . Wenzinger , Carl J . , and HarriS , Thomas A .: The Vertical Wind Tunnel of the I Jational Advisory Committee for Aeronautics . K-.CA Rep. No . 387, 1931 .
5 . Ames , 5lton B ., Jr ., and Sears , Richard I . : Pressure - Distribution Irnestioation of an N. A.C . A. 0009 Air - foil ~ith a 30 - Percent - Chord Plain Flap and Three Tabs . NACA TN No . 759 , 1940 .
6. Sears , Richard r. : ind - Tunnel Investioation of
Control - Surface Characteristics . I - Effect of Gap on the Aerodynamic Characteristics of an NACA 0009 Airfoil wit_ a 30 - Percent - Chord Plain Fl ap . NACA AR~ , June 1941 .
7. Al len , H. Julian : Ca l culation of the Chordwlse Load
Distribution over Airfoil 0ect_ons with Plain, Split, or Serially Hin~ed Trailing - Edge Flaps .
NACA Rep . No . 634 , 193b .
8 . Allen , H. Julian : A Simplified Method ~or the Calcu -
lation of Airfoil Pressure ristribution .
NACA TN No . 7 0 8 , 1939 .
9. Gil_lis , Clarence L .: Characteristics of Beveled - 'l'rai ling - Ede;e Sle va tors on a Typical Pursui t Fuselage at Attitudes Simulating Normal Flight and Spin Conditions . NACA ARR , De c. 1942 .
20 NACA ARR No . L4D03 10 . Stack, Tohn, Lindsey, W. F., and Littell , Robert E . : The Compressibility B urble and the Effect of Compressibility on Pres sures and Forces Acting on an Airfoil . NACA Rep . No 646, 193 8 .
o 2 1 lJACA ARR No . Li.+D 03 TA3LB I OSDDTA 'J:'BS C'~ P(YCI'?IC::D ~\:Ac.:A 0009 AIRF()IL
L~tati _ on3 and oroi:1ates in percer..t of airfoil chordl
---- - --- - -- j !
1-------------------+-----------
I
NAGA 0009 airfoi l section
I
1 -- ---
I
Straight portion I- i
I
,- i • [\) f\)
~ ~:> o ~ ~ 0
$'- ~
I '
I
-
"
· - _ _ f
-
__ 9 0 ?
'-
··
-
OS , 22
\
GO 006 00 008 0 -- . .01 .
.0
n1'
-a-') ---
c 0 O.G 0. 0 .
-'-'
___________
I\-o
l(o ~ 1 I
_I.
~1
-)
A ···--r-··
· 030 027
- f' Lao o~o 029
---
. OL7 . .
cn
-_ o. 0.03 0 .
-o . 0 . 0.59
2;-b
\
--.------,--------- I
1 1 I I
-- --
I I
-~
11 '-
ao . 5 1 §~ )
59 4b --1------+------
)-1(
lS lR~1
FLftPS , .
.1 m 11
-
-
0 .1 -.1 o - . 1
-.1 -.1
- 0 . - 0 - -
oc
- c -- ----- .
----
/-
l 6
1 i
\ I 1\ 1- 1
t
f
010 ~2~ 03/ 02~ 03<;- O~~ 0~
---
BEvTLZD
)
. . .. ' .
. 01 0 .
n
-
0 O
c- 0 . O
oc," - '
A!"!D r --.-- 1 1------4- \
(
,' I
1 1 I
-[
--t-I I cn 60 56 ~Z -
?6 47 -+ 4Z
)-
· : f
-o
F:!:;AP
-
-. O -. ~
u -.
00 - -
- 0 . - o.
(o
i---------
I
1\-
II
+----~-
PLAIN -=Ol-I
~
r ---t--- t
Cllr 066 066 087 a8') 102 320
ee 102 154 OF . ____ . .
.
)
TABLE 0 . 0 . 0 . 0 .
on f r
: _
-- : ( C __
~ I J
1!
f --i-- l tro
)0
082 087 OQ 085 098 092 TERISTICS . C96 . . .
:: 0 . 0 . C88 0 . Oo
(~?n
~lXO~)+_
',
I 1 1
f J
_
-(: 1; ) 0 1 CHA2f~C 0030:
f\ 0065 00G6 001< 00 0002! 00071
o.
-)
.
. .
or -. 0 . 0.0006 0 .
Ch -
o-a
___
- 0 . -
,-
( O
l, I 1 l
r
"0 3 0 1
_+
~-
01201 0118 005h 0016 0068 0C)~5 00 SUtTI\iARY
-)
- .0005
o-p
-
-. -. -. -
O
- 0 . - 0 . - 0 . - 0 .
OCh!
(-
\-
i
cl -l 5 C 5 ec.
-
D0 00 005c 005c Gap
seale!" ~ea v . Sealed. 0 . Sealed
__
I O« I 10 .
I f-
i
r -
J .J.. l l f l
in c.f' Cf ll u s ) all ~ 5 c C:; of eve 20 -- .l .1 .f' sna Type - 1 Pla beve b beve ( O 0 . 0 radi ---
__
I
1-----+--
NACA ARR No. L4D03 Fig. 1 I PIlch axIS a/
:1 : --t- -
..30e
-t-
Rectangular
lest seclion
r
Model mOtlnled in IVACA 4-blj 6-'001 peaical funnel Model / II. unne wa lS SlJppori
~
~
I
~~r I ~~ -'-:<J < !()~
Pr',§ ~
~~ ~-Q I ~ '?
--- -- - --- --- - - -- --- -- t" ~ I
~
1\ 4.. of orifices
/ .
.1."
~ r- ~i6 1(3
:24"
: 48"
l
NATIONAL AOVISORY C IIMMITTEE FOR AERONAUTlC5
Figure I .- Ins/allalion or beveled - lrOl!in9- edge pressure-
dislnbulion model In NACA 4-o!! 6-(001 verlical funnel
Fig. 2 NACA ARR No. L4D03 f-+I : ------- 100.00 ------- ~ ~ ---- 5S.00 - -----_+_i R=333 .30. 00 '. £108 R = 8.~ Chord line 4.50~ Slra/9ht conlour from here Gap sealed /0 heyeled trailing edqe or .00.5 copen Airloll wtlh ./5c, heyel R =12SI
\ ! r .I!XJ i _ ?- l[./90
(!
- 6.00r~ t!095' - -- ~ tI
A
. R 2B3 R=J33 ~.~~
c . 20c/" beyel .l5c beyel wilh F small radius (a) Two - (001- chord NACA OOO!) airfOIl model wilh a 0.30 c plaIn flap hayinq 015c/" and 020cI oeyeled /rallin9 edqes . Dimensior?s are in percent 01" alrl"oil chord.
NA TlOIIAl ADV I SOIIY C UMMITTEE fOIl AERONAUTICS /"lap hintje axis (0 ) Chordwise loca/ions of preS.sure orifices on airlOil and on Ihe Ilaps haYin9 Oloe/and 020c/ Deyels .
• Figure 2. -Dimens/ons and chordwise pressure-orilice loca/ionoS lor NACA 000.9 heyeled-lrailli?9-ed98 presslIre-dislribu!ion model DImensions and orifice loca/ions are Ii? percenl or airlbil chord.
Fig. 3a NACA ARR No. L4D03 Fig. 3b ~ACA ARR No. L4D03 C it r 111,,' ! EI' ' . Li, ill .1" li'fj I':~ lj' ;h l.t fl" 1 +''1:- IA . I,":, c,"'UrtH~ ii' :.~ ;1, !;, I;;~.:" i;r i';, Hi, !,y iffi F ig . 4a NACA ARR No. L4D03 .. . t: .
. ....
• l liffij. ,. I.•.
,'i I :;;' _ 1.- ' ,". ,it;. ,. , .,' t.- • ~f· : >n' '"hiJ ., .
.0 ; I I i I ,-" ,'+-'-B ..
'r I Ii: .~ •. ·ltJ: • I: ~ ~ II .. i-"- !t ~ -H- _ ~V ~;,.- ---i..t---,. H- -f-+-; .• -'- L ~f-.
g..;Q;' , ...j -+-+=H-i- +-I H4 " 1--P+ ,, -+ K~ ,1 l L .~. ~~ - ~ ',- ' i': i :l~ J NACA ARR No. L 4D03 Fig. 4b :1· ,r, I 'l. ~ ~ 8-: ... + ....
.f I~
rL I"
. ~ ..L L: , I c->.
1"- ~r e:¥' IW . .-: r0- n li' ~ +,-- I--' ..
, . ,i' .[1' '41; ic ' 1/ ,t::i! fi j, § .c= I~ ~ :,t' L i't J ILL "'-, - !': J..-'-'", ~ ~ i~ , .~ , .. ' p.~ r"l iii, .'r I'''.
r :L I .... ~ r: 'j c:..!
F I '"
Ii F-.i't I ~ ~ ~ \ l:!: ~ Ii :,' V iI.
. I'"' fl t?: 1!4Ji~ ,W f~ f"-.
"-
: :a
.,", , ilL, l iiLI U fll' J ~ . hi . ~ n· I ' I,~ I . Ii'~; V I!> Ii' c i I:::: l ~J.
....:: '.
t!, I'~ , p . ;.' '';'' ~ I i b'111: I --1- /rp>- rr ~ , ~~ M'ti lfl:
i-+: r V 1--1-
•
I ,.;,y r !, -!- Ii 7M-- : ', ,~ r (/ .
I;' ~ ' r..lj ' rr . ~ ,
P\ :i~ l rI' , li-
11 tlif 'c' r~ ~ ....
~r , I ~ 1 If' ,J fvl if II H F": ! '- ~ ' eJ..-: c' I:' b'" ,I 1 (' '21£::
'" ~ t L
I ~; .I h ':'iii Itf ~ i, hi I,~I C" 171 ,.:: r" t); [;, I V .. ' I" U' , ;;, .
~I-- I' f-:' I': 1- I/f ~Y.1 r' i ~ r
I
AI'..
I'~ ~
'"
. --r '1' L t: L ~ b.
1.1' I':"E'· "r' ~ ( !:; '.Ir:~ ~
rrf cpr
:;~ P I·" .
!r r-.
L :l i - r t;r ,;,; !~ifl" , ~li! .
h .,~lli': L!c ..
l Ii': I nn F r" 'lli:.
I IJIi: :'!: !"', f ~i~" ; ~1'4t t·· ;j: .J' t1t". "'~ I." Fj~ I .... i\ t..; F'llili Ii!
:, h~ I!;J:; i "t.
It'.
II L'i ( ,:;1'.: I± Il.. :" b
...
iii,.
I,'l I','., L : I" I " j,;..
:J: II 1\ I l'f rb/S , . F'rI '.).v ;t bk F .\ \ " "," .
I',: ~~.
J; I'·; :J..
.'.
11 ....
tJi.'I-' 1 .-[ ',.,
tr5 1'\1 1"' ~Ir. I "' 7'l IQ l
:;t, 1 '<: -.i-- 11 I 'W I lill' I". IiIJi.
'" r .\ , f;;I rl 'tl "'" Ii I I iffi ft' A;' " hi' '1'1 .1£ ',\ IL 1 I"
"
r.;.
IL j
"" n
P. I: Ii ' f f~ !Ii ./ ]'.:.
K ..'l ", ,~ .- "", ' ~ ," :-t 1 IH ;'-1--' 'j," ,.
rl'" .1.
f r- ± ~ ..: 1 '- .\ \ " -~ 1"- -."
r'·"
-7cL r"'"-
r,;.
f. '1
I :f, 'i" f 1/ ~~ ~ L ~ ~.~ p.;; I-' "'1- ' I ~ i ; I 1\ '.
.....
''I- 'i- ..... b .1 " I :'.
'I HE ...
-.I.
."'~ r~ I ? ~ 'f I ~ .'..
Iv J.
~ ..L 1- -
--r- +
I,
rJ1 r+-' I ! I
.... _.
[;:..-~ Vi -
i-
I ~ i !
I i L L I..
1-' .+- I-~ IT I I ' u"rL ro' U. t 1-· :...
'-" ;-- r~ i-f- 1-1- r "1- , ~.
1- r I- 'v> , '; ""'" ~'''r~ f-._- r- ! ~ I J: :- r+ ~ t2;:::: r
r-M - 6
1! , 7~ ;; 1- I- ,(J,J (1
'J H 1l ~ ...... - ~..;....
i l- ;;./ , H..:.- . I t- 'h
1-+
i t ,1
l
J 1 :-- .
I- -
r- . 'j '- I'"
1·-+
H· -+ ~j 1- '-'1
t
+
In ~/)c f':), !JIll' 'M '1 ..
I- .-
~ r-
" ,-
J
± J
Fig. 4c NACA ARR No . L4D03 ~~r+~~ ~+1~~~~~4I r~I"<~~_~~ 4 _~~L ~ '+r ~ -+t'-4_,,1~i;~~'4r_, ~ ~4~~~~+~ 4 + - ~ + --t~~++-L ~ -+~1 ~,.-++~+-+-+-I-t--++-I~~I;4-+H I --H'+-+--l_+--+-H~+--l--+--l1 - -' + I i~H"'+-+-+-+-+-H-I---;-++ i:i+-t-+--++l"-++++-'+-+--f-"l""-t'-",,*.j-+,+,+++-++c+4.,..j..,-h4--"+-+-++4, 4- : W '~++++~'"""t~+-l-4-H"""" : 1 '" ! ", !
~, ~ l ~ , I ·-I~ ....
~Hfi. Hi j:oi l i.P · I- p.. ~ ~f--- , H.
I " I I'" l>:i:i± , r.qJ J if Iii, If ",4 ,',j If:i! ' i.;.;1k; ~} ;i:' let I '±o' m; I' l dt .
, ,'
itl l';';,?; Ilfi "',
,"'
I ,,; 11': tr' ,~, 'l!" 'f" ,¥ #" Ilk p , ':: ,,'ft' "'1I!It'.t.
IP I,,,, i ..
3 ,!f l tlj 1 :d !
I~ $e h blE~'" ¥-+±H 4rH--+"~"4--h.~ .. r"'14--l.1 I
'"
E!!~";j V ,... , r : 4-!'I-+. · ".. I"' -tr~ ~,*" I-'I "-:!-" ~ ,j:-I' I :· 1 I j tr- ~, ' ' ,Ih FIE' J I- , : .. t IT; ,J t-i'- 1:£: , ."
':: r~ i."
r It" fll', I~'J ' ' ~, ~" ,~, 1.; 1 , c..; ~I \ II!~ ~~ 'fl 'I l'i '"~ I .... '" I,,· 'tl / 1\ I.:.'
. A rF" , 1;( f;':- I!?'
II "~ '\ "" -: !-I- 1- " ~
f ' p,,-
K'
II
,Ii; H V . '- 14 Ii" i . 1 "4 E ~+4~~~ I~J +-+~++ ~ ~~~ ~+-+ --l~ ~~~jI ~~ 4--l~ ~ 4r++ ~~ ~J~"J r+4--l~ ~ 77~lf ~ ~~ :; 1-1-1- H+t-I-+I / ;t-}ja1:~r ,c. *-;trf,1t-: 1 H;t:tVJ;:i _~I -:- f-'-, I Fig. 5a NACA ARR No. L4D03 l .
l il i· It .. ,j ' •. j!
' i!'~ : ;'l:"~ I ~
, .1 ~ ,:; ,; ~j!
~i:l11 :' :;,"; !, c < r4" r-s- tli "- ft:'.
", f;;: "', -- \ I ,' 1j NACA ARR No. L4D03 Fig. 5b • NACA ARR No. L4D03 Fig. 6a Fig. 6b NACA ARR No . L4D03 NACA ARR No. L4D03 Fi!:l. 6c _ _ -1 NACA ARR No . L4D03 F' ig . 7a I I J I I :-;,.~-, I ~ 1'-+- I ~ f-, L.;.T '--'- f- """r" P-I ' !'- 1 ;-, I ~~' - ~ ; f- H-- r--I-".
~~
rt , , G;l :-1 '- ~~- H r=- ::::1 r:;;g ,; ~l::- I- I" HI+' I'-- Iii .". } t . \ .
I ..
J,. ..
I ~ If; I -~ f, F.· I "!: ~ ~J
•
Fig. 7b NACA ARR No. L4D03 • • Fig . 8 a III>.
i' ' I ~ I~ l _i~+ i 1\ ' i '!:'·I;" I" .
II h- k r ;l~ , [ \\ 1'\ t;r p.,.1-+ + +.+,. ,.,,1 H I , .---1 " ""-l+r-rh'1- ++ i\--t,...j+j~p. h- +-++- + + + +M-'+- I -1t I l J .\ 1-'-'1-:: 1 "'1'.,.10-· r. ;c: ." \ \ t- ,r, !-k:"'~ ·+-j..~H~~ K Iif , ..
Fig. 8b NACA ARR No. L4D03 iff . ilt ..
.r ; .. , .- : w;. .- ' . . ' J z l .f ,.., .' : •. · 1 'f T. IT .
..
"
'" ---+ . ~ ~ . " I : ,:,; ' '' '-,- ~' I::' ....L 'I" •• it , . I· ' 1 1l!
! ' ,.
,, : Ip : 1';:: +' ;.j.-!~'+'-1. """. ~
"fi" +- p~+- :l ~ ",." ~2 i;s i~~ , ! :j: ~ " Fi g. 8e NACA ARR No. L4D03 • • NACA ARR No. L4D03 F i g. 9a ..
NACA ARR ~o. L4D03 Fig. "9b • NACA ARR No. L4D03 Fig. lOa NACA ARR No. L4D03 Fig. lOb • Fig. lOc t'ACA ARR No. L4D03 N~llOijAl ~dVISORr • COMMITlEE FOR AERONAUTICS I + NACA ARR No. L4D03 Fig. 11 • . .
l
Fig. 12a NACA ARR No. L4D03
~- ..:: I--" T-:::::'jr.--~-r-i-H~, ~~T~ -1, ,'rT:::j: ~ fFF 1- :-f t ~~ -"-w 1 -~t L,",~
,.~, jf£-Z1 r- ~ ~ 7* ' , i - '0 c4- T t-T rt f~ -+4,++I'+,~~~
I' J ~ ... ,.,- - . f,-o, . ~ -" -±+t--f.-."H-cbb'l-++ 'r i-"" .,... .,T'. +- }f. "'=tr ~ '~-+lFf ..
l Fig. 12b NACA ARR N0 . L4D03 ., *,I'~I,;'H' ,".;1.'" I I 1'1 I'~ " I ,~ I-- T, I' " .," I-- !~- I I~ ;;.+,~ , I'," /-. , -.
,~ I-- . -,- !-, h4- 'i ..
"T 'L '--: !'C V If l;tl 1 n
. ,- j.+
I-- ! H'" '" i"7 I, l!L I-- '-r""~ I,,' .+.., q I.;' I'- I~'
" t-
I-- ~,..
t-h "';' f'~~ ~p;: 11"1.<; '",.
""'"
\-JL t" ~ H-
h., t r- i:-
1'", :~ .- r',; r l::- Hl. IJr
Il F
:0; !', t
... ;..;. I-,- II
;+'F H·- r i"' ,
I
,J, p-,...,
:~,r
!~r IiI ;,-:; I;': "h IT [",p'E, b- , ..
.".~ 1--.
!:...I·'L 1"":-1';: I' , ·1 I, ~I;Z :T ._, , j,,-l, I'~ t-'; , 1.; ::,..
H-·-r:;., :" -".; !L .... j;-.
ifHr r,;.1, I" ;""
8· I
+
."" l:if-liEf l.., !~
(0/-
~~
.f ~ -Ii' j;;, r:= I"~ h' :' 10 Ii ...:: '7 1#;. r ~ ,i" k~ ,(.. hili,) .J! .L , .. , 't .1'" 'iI'~ , . ~ , I}
,-
I?F h·'" ,f! '# "I", j.' [ rr- hi 'To hI;: ~: ~ ;/
l+
,...;.. '
:-; ~"j h+- 'f ,I 1"'+ p: -;- ", '- ,i" T T f,,,i ,~ 7'"
v'
.L f :- ;Af ;.
~ '1l 'X ~"7.;.
-,- l:., ~ ~'''''' Irj..
... , lE " f, 1', ~ "'''h ...0;.
;)' -.,; ~R t .. ~~ ,r,; J.
I, l',1-,- j-':;:;: ~-:?>
-;- ... '-
f-'· . Ii ;:..; 1-: I, I'! .1' ,,..
.L ..
~ "p- r-
H h' 'T ~1JiI
f !- ,.L,
[.--:)'-- i,,-p ,-
I-- + rr+-
;"'h "-- rr/ "
bi- ~ i:'l:!
-
,,I ...- IL ," iI;-j-.- ~f7'" I-'~r- 'i, ,~ r j;.."'" f":;'-: I': 1': I'\.
r- i
pp v v,/
'-'- ~ io-' ,.
~- I?' ~ i: .1' h J I .... i . ,:...;, p ~c ~.;c H", r
F-F
P+b ;?
Ff
" , :/ h ,....
·1 Hili b'-Q t- hN l:+F f.T ~+- ,- j'/1 j)(
..t rn !
L ".".., v jJV '" I-- ~ K- Pf:
H-
t+- v UK
I i' ""le-
I I'ATfll r~:~lwl :T ,-8 f::: ~ UII"
,,- t;t 1-+ ICQ -
H- I'
t+ I~ '~
..,.
1 , h' .1 1-: ~- 1tJ ~, ' ,,>, ;; Of) i jr, 'J;\ ;) [ b i .I . Ii I i-..,.
-t:. ;;;", !-+- :~ b:n ,
H- H-
; ,j I r.)
i 't In' on.
'- .......
~~ f i !' L -I-,-' r': j:-i ;, I' h- ",.
~ '( tr/( 'J/' IS' k::' rnl WI' ~LYI"~L j ,- jf- , i I'
".L + i I+t--
f I' 1 ~, ' , f-+-
t,t .. Il-
:t
f l'
1..;·- i 'I~ ~ - I, ,J It i 1 I J Fig. 12c NACA ARR No. L4D03 Fig. 12d NACA ARR No. L4D03 Fig. 12e NACA ARR No. L4D03 ___ J
----- .----------~=
FiE.. 13 NACA ARR No . L4D03 ._ -- --- - -' - - -------, NACA ARR N~. L4D03 Fig. 14 • • NACA ARR N("'. TAD03 Fig. 15 ..
• F '-- L 16 NACA ARR No. L4D03 • Fi g . 17 NACA ARR No o L4D03 bif4h' kF ;; 1"!i4=+4=Ii+Ti 1 +.-1['+ I '" .,fo,--I-I-+-+' f,,1,+ I- -+--I-ccr"f-,t" t h [;-1- j- -::~ l ~~h 010 !-- k- rb f,-1--t:-i'+7!--,tr--f'-il';+h~H I-j,~ I ~I- '-I-+",+,;.jl--I--b-I'-~~ h~ :J L 4i I ·,r-P ~JH-+-+4-"'i1-'-+ -h--+-'-l;.4-8-·+-i-+H'-4-+il4'-++'~1 I2H"JI;'+:·+-+.,*-~-I- r= rh-+-+-'I--+,!;!
1 #1' ::i -, "I P;IVHI-r~ IJ 1~.i= l-- t '-* P~b- t= FtI-J1 T:r Tttl-~~~. T ~r$$$=R; =+ ;- 6,;f =tl + qi;;- tj:tt ttL t- 1~tt ~ ~tt.+J-:t4-M+iI ~ I;:+i I'-'rt' ~ b- rH- 1,j 'I ~ I-'-r " ~ ': T H'd-: b M;
~ PH I,>, i,' I r~~t +- J w- I-- I -L, + '11 " ;,1\ '-1- " I;c ..:t ~
ri-c""I-"E-+ '"" i=fi;C+1 lti I'i .+1-+- r'-'l' "1 , '" c.,r .... ff- r+ f'i h~_ ~ _1 1lV, [,t E- I F f~ 1--+ : ~ L+-'H+ :l~,~ P+-"i++,-'P-t=t p' +-1--1+ -I- "-+4-H~'F+4.--I' --1- 4 ·..,j~'-l-.rti-+-I~-+.,+-I •• + 1 -·,&+·±-+,,!hd~8 ~j!: ~ .:11,[6 .' I t"
~ Ii- ~ci'( H" I \ , "" I " IJ n ~ I_e l -ji-+ l~ I-Isl--S. iT rl :,: ID r ~
I -t l~ II ' I" l;;i t ~r ' " k 'l, r+ 1 ,-4;, ~ 1 ..,d;<"'h'I' I .. ft' I- - l b-If,.,-I-'+"~1-1L.4h·-'i4 1 'i-li-+d--df- h+ bJ,r1-- ~ r<T ~ EH~ L ", -l, -i·d,=p+-++ " 4i pi 1--+-'\,-=' I:F I :. ~ ;;: 7 :;,j":l +g 1P i I4*lL ~ ' ~m ' '4' +l+#t.,.,+,:H-+-!++++-l"':,;f.i+:++--.,,++-+4-II-H + H~- ~- .~,~
, , ;j ~t ti,I:;' , t I'Tf-= +-!-'" ~- f,-,- I~ 1-.- p!. ~- ,t t
..
NACA ARR No. L4D03 Fi g. 18 !E- • F'ig. 19 NACA ARR No. L4D03 • NACA ARR No. L4D03 Fig. 20 • •
-_ ... _ - _._ --
NACA ARrt No. L4D03 Fi g 213.
NACA ARR No. L4D03 F i 5 . 21 b NACA ARR No. L4D03 Fig. 22a /6 20 -20 4 (4nq/e of 4Jlad,cX deq o ' -r- -f&,tSeaied-q:;P -I--- ---"i - r - - - ngd(e 2.2. -SeMon cl1al'acferisiics of llie NA~A 0009 aM/oIl wllh ~ 030c ffap havln1 a odcl' bef'el.ferel r~usJo0846f; mc/LJdf{Jd anq/e -aI/he In:ll/mc; edqe, OJ4~ NACA ARR No. L4D03 Fig. 22b -12 -4 @ 4 8 12 /6 -20 - /6 , Angle 011 aJlack,C4,deg (b/ '7ap,a005c .
Figure 22 -Concluded Fi g. 23a NACA ARR No. L4D03 ______ ______ __ ________________ ~_J Fig. 23b NArA ft~R ~o L4D03 j NACA ARR No. L4D03 Fig. 24a ..
Fig. 24b NACA ARR No. L4D03 -- ~----------------j NACA ARR No. L4D03 Fig. 25a.b .
•
. I
..
_ _ .-J F ig. 25c . d NACA ARR No. L4D03 !
r i " .. ,. .< "i.
, I ,; .1 I- ~ ! .
. r .~ r I .L I--
r
It t • I" ·, , I. ", ..
F" 1 g . 25e. f NACA ARR N o. L4D03
/00
NACA ARR No. L4D03 Fi fo . ' 25g.h • .8 -- ,.
~ -+ eo-
+ ~ -
Percen! cnb7d -
r·-
--+- ~ h9ul:e:?5. -=Cdnc/uoeo.
I