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2 . A des.i-gnaaaon systen was then devised, ktlerein the first digit inaicates the raxinum canber j.:r t of chorC. t'he second d.igit indicates the locaiion of naxj:nmr ca,nber in lenalls of the chord length, and t}le last two dj,gits inAnca.ie the maximur.l thickness of the airfoil as a tr=rcentage cf tlre chord length. For exanrple, NACA 241-2 indj-cates a 12? thlck airfoil with 2? rnaximur camber l0cated at 40t of chorc. l,tote thal the naxj:nun tirickness of this airfoj-l, as j-n al-l of the 4 and 5 digit airfoils ( turbulent ) i is at 30? of chord, as deterndned by the gerieral t_hickness distrib-_ ution formula givea belcnn:. with this systsn in place, an orderly fanily of airfoils was ccnstructec alrd tested, with various thicknesses, canber levers, and chord.wlse position of raxjmr"nn canrber. other va:iables that eiere tested, not incl-uded in t"!re designation systqn, included conditj,ons of "stardard roughness',. si:nulaled split flaps deflected 60 degrees, and Reynolds nurbers of 3, 6. and 9 nrillion. The first step was to desigp a ca-reful-ly spcified rhickness distribution. The |':AcA researchers noaed frcm earlier tests that ihe best airfoil-s, such as the Gernran Go ttingen *398 and tie l.] .s. clark y, had the cnximum tbj-ckness at 30g of chord. Accordrngly, the thickness distributlon for the 4 digit serj,es was sefected to corespond closely lo that for those wing sections, and is given by the fo.l1c'\ring equatj"on:

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B- liACA,?-dicir Airfoils. Fo]-lc'\ring the 4-di9i! airfoil r.rork, }.{AsA conducted a test program i.:r the early 1930's to see j-f zero pitching rTn:rents coul,d be acbj-eved on canbered ar:foils by using lead:-ng edge droop al-one, rather Lhan using a convent:i"onal camber schedule. ( Read Addendum *1 below. "Understind.:irg ei-rfoils,', for a d.iscussion of the relationshi"p betueen C1, d. and en in canbered a.d tutca,,nbered airfoils). zero p-itching nsnents on ca.nbered airfoils had been achieved earJier by refleci.ng the airfoil trailing edge, as on the M-6 and 2R11,2 ai:foi1s, bui this r€thod has :he d-isadvantage of reducing the na:
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:oJ pue 'uorl3npsJ 6erp luecr;ru6rs e st sr.ltJ 'ZTote \DVII uer{] ssaT tSZ sr frol-IrE ZTZ-,9 \p\dlf ar{f ro] uorl3nEE-r 6e:p uorlcas aq1 , aTdle:€ :oJ . afqeuosEeJun 1ou st 6utlr, truaTnqJnl JETTturs P o? pe:dua $gZ f o -Gp:o aq1 uo s5ur,ra arlf, Jo] uorlonpe: 6e:p ' snt{L 'afqe:}s alrnb sr puE ,.ATsnorna.:d pe^arT€q tr€€q psq Ueql :a1ee:6 sr , saueld:re uorlcnpo:d uo ue^a r sTTo]rrp esaq+ (Ilr^r I'roU JpuTurel Jo flr€1re aq? fprlt g aara.raJer ut s1:oda: \i51tr1,1 '?cef uI ',,fur.cd uorfrsup.rf,, ar{+ tp noTf luafnq:n1 01 ,,sdrrf,. ioTf aq1 a-:oJaq , SurA aqf Jo Fed lsa1Jrrll aq1 puolaq {1eq6r1s p{rp 01 XJEq e:e;rns do4 aq1 uo ,{1rsee -raqlpf p€Aarq3p €q upc l,4of J rpuruJpT , sTToJ-rTp ser-l:rs-g asarl+ g:}TM . sJTf.neuo.rap sluepn?s .snorr€s TTE rof lsnu p sr qJTr{q ,T aoua.lraJal .,,suoll ]o s I lrJoquacq uo^ pue floqqv ur pessnosrp sT r{.ro 1 srrll 'saurT rJs€tu -ceg 6u144 fo ^f,o€qJ,, (tT6T'tr-' JTToqPred aq1 acelda: o? , suortnqrrleirp ssaulcrrlt .dtTcofa^ fustsuoo arl] q:lTA ) 6uo1e o6 ol. sauTT uEa! lr.Jglsuoc Jo sarJ€s p [Esrnap osfE \DvN 'safp ?Er11 ^lTcoTaA ur trcuarcr3:g:a a,ro:dun 01 'uoTlaes ,,tr.Iaaoca: amssa:d,, iro .Ipoq.TafJe J'eUor{s ITTEJT -fTf,c eql ur .,sdsnJ,. asn osTp sadeqs asantr1 ',,fa{onq :gunueT,, arI} sp utnrD{ sr a6ue: 6e:p-rrro1 srrdl 'lueTnqrnl o1 sdlr+ xoTf aql efo]aq oJ€z un:; sea:6ap E snuru :o snld Xlalanrrxo:dde ;:o a6ue: {cEl1p Jo a16ue ue qbnort;l surr: rpurutpT 6uo1 rrreluruu o1 .d1r -frqp aI'Fl lTqTWcd sedeqs asaqg, 'X1anr1:edsa: , sadpqs sar.ras-gg EJe ,-99 '-Vg ,-tg aql .IoJ p:oqc Jo tgt p{re ,tot ,tg.Lt ,tgt 01 p.roqr Jo t0€ uDfl ?Jp pe^su ssau1rlI1 ummxEru Jo uorlrsod at51 Euraeq puE , rTppJ aSpe 6urpe:1 prrp suorlcas asou =lfTEurs .d1anr1e1a: trq pazrretce:Eqc , sedH{s .,.d1rco1an 4up1suoc,, Tprc€ds pesrnap sJa =)puaTs -q3-r?As€.r \n)VN ' e.rOJaJAql 'SfrtJrrT /noJ-rpu rExf+p.r UT[+IT1'1 ' ({lTcora^ fus}suoc ) asrApJoq3 se ffar'l se tr11ecr3:an , pa?erafaJJpun aq lsnu,.loTJ arll , rpurulpT urEuF-r qI, 'r!!oTf .rEuTurpT se Serp t{cnu sp acr,,.'1 r(laS.anrrxordde seq qcTqA ,reou laTnqrnl pup '6oTf reuTuel o:E scnrpqJ€ru pTnr} lo pTaTJ ar.n ur suorl'.tpuoc oolg: :o[au o f aq,L .

sTTOf

--rrE 'aoTJ JpururEf fo ' seT.r€s-g aq1 ur 6ur11nsa: ,s,0t6I pue s,0E5T a4pT aqt lo lJortl floTI rpurureT arlf seA ltrandolarrap ulvN lup3rlru6rs lxau aq,:EJJoJilv sar. Fs-9 vCvN 5 'AoTeq possn3sTp 'sanbTu{Jef reoT} -reurujpl 6ursn Iq ,sr ?prt+ ,sTroJ:Te acuan:ogred -:aq6rq +e6 crl .{erq ra11€q e sr a.reql leql sr aql 6uruopueqe .ro; ErElcuoo ,{1ag:es arp aprseq uosEa: rat1}ouv sTToJr.re 1T6fp-g 'pe16au Tsururrf3 uo srap-rcq 'asn :ran{f lsure6p s6uru:en 6uor1s ansst 01 lsEeT ae :o ' aJT. oueda-r :Taql U,OJJ slToJ:Tp TTE?s-dJeqs afrururfa of vwt{ Jo a-rnTref aIdL 'To-rfuo3 TE-ralpT fnor{lrjrr tr1a1a1drnc sr 1Je-ro:T€ aql aTTlliru€ai 'acel:Is do1 lro]rre eq+ uo ftoTl: peqcsflE qsrTqslsa-a-r o? (apnfrtTp Jo ssoT luanbesuoc q+T/'i ) {lressacau sr {oe1tp lo aT6up Jo uorlJnpe-r aTqpraprs -uoc E ' F€:n3co ssq TTsls drpqs p ra1;:g 'saueld:re atrr.Srra-u.rirr1 uo dlletcedsa 'sa,rr1 Iuprx peles alpq pTnoc pue 'sTroJre 11e1sdrals Jo arnleu snorprsur al+l pefpr-lsnTTT a^eq pTnor! qJrr.ln 'slsal eqdle 6wsea:cap TTP"s-1sod qcns pepnTJur :1.roq 1sal fro].rrp \D\dI{ ar{+ Jo auou 'FEf uI 'TTsts aW} un:;,{raloce: pellllalle ur sP ' panlcco sEq TTsfs I{fra srnf,so ?sr+ d@r srsa-ra1s.Aq aq1 d:eqs ar41 ralJe lcs+lE ;o a16ue E@ apnrcur lou prp sTToJ:rre asetd+ uo E+sp ?sal \ovN a$I ?eq+ a?PunFolun sT fI '11€f,oJre fe{rtrp uo pesn aq crf 4ou ,seTlT ,{:olefoqeT uet{+ alou 6urtgou sP pep.refu.r €q pf noqs sTroJ:rE 1T5T-p-E \P\dt{ 3ql -sor:nJ , 'suorleJTTdde uorlprae le:.arra6 ro3: alqe'ldanceun ,{p4a1d:m sr (sTTE+s ^I6urp-ro€ld dreqs 1 pred act:d arp lnq 'euofe doorp a6pe 6urpeal dq peaalqce €q pTnoo slustcr1;a -oc 1JTT q6rq dlqeuosea: sE TTar.r sP slueurau 6urg31rd orez 1eql perro:d slua:rrred ) xlrntrr3uocsSp arp ^dq -ra rro].raE 1T6Tp-9 \D\iI{ elll 'f,ST ' lP aurT trE€ l aqf tlr (}iu'rJ{ pesnec, TTE +s dr€qs aTgstdaJJEun up -e6elupAppsrp :ofE! p seq TroJ.rrp aq+ ' r.a^a/qoH .1,4oTeq f,X unpuapgg ur ncsrp uoueunuaqd lJTl,alqqnq uotle:edes,, erll 01 enp p sEq ' sTroJ:re 1T6fp,-t alqeredrnc uet1+ ra?ea:6:o o1 lenba firarorJ;mo lJrf uruxrxeu sfr .IoJ s-luno33P auoTP ua^a TTo]irre aq;, 'anrlce[qo uSrsap aq1 Eurfaau 'u{).^'toT ^r€Aqu-Dc srlll pue r pex€qusc doorp e6pe 6u1pea1 un:y 6ur,peo1 p-TeAJol: anFrf).e alIf Wlr,t'l p€ur. ,rc1 dllercadsa sr Tro]:re ar{f 'snt1t 'Ctg'I trel4l raqler t?'T .d1uo sr 7I3EZ \6rvl.l -rol: ,,-reqrE3,, aAr?ceJJa atll 'snrpe-f a6pe 6u1pe'a1 arFt fno 6ur,{e1 :o3 poqla[ ,,snrpe-r pup edoTs,, arlf puP sTqf o? anp puP 'pasn osTe sPr'1 saf.suTp-ro ( doo-Tp ) -Idqujec puP sssu

I

4 industry, especially considering the fact that these aj-rp.Lanes are in a Reynokls nunrber range that is especial.ly favorable for lanrinar flow aj-rfoirs. Furthernpre, the constant velocity rnean lines devetoped by I'lAcA for these airfoil-s includes one (a=0.5 nean lj-ne) that produces lc'qler pitching ntrrrents tlrough forward loading, with no drag penalty. a well-proven technique that was used in the prior (turbuleni) airfoils. Ttris mean line is designed to hold constant pressure ( therefore constant verocity) back to only 50t of chord, which is the practical lilrlt for larninar flo.r anyway, and then it tapers the J-oading linearly to zero at the trailing edge. For anyone acquainted with the t{AcA airfoil design methods, and wirring to derive their onrn airfoirs, ttris seerns to offer the "best of both r"orlds", that is, low Gn as wel,r as ro^r drag corpared to the publisbed "base line" 6-series airfoi.l-s, v,'l-rich have relatively high On due to nid-loading. In fact, Cessna did just that, by deriving and using the unpublished I'lAcA 64Mr5(a=0.5) for the root.. ;nd the ,rnputri=n.a naca 64A412(a=0.5) for the tip, of the Model 2L0 ,,Centurion', wing. spite of the potentiat l:erforrnance jmprovernent that could be nade by using lanirnr flo* wings. they have never gained wide acceptance in the cA fierd. I'rost snarl light planes continue to use the 4-digit and s-digit turbutent airfoils, and the great nrajority of light twins, and even ccrmuter transports, use tl,e obsotete and dangerous 5-digit airfoils, a horrible mis-nntch considering the consequences of sharp-stall airfoils in an engine-out situation, The I.lAcA 6-ieries airfoils are often avoided, since they have gained a reputation of being "kilrer airfoils. with sharP stall characteristics and 1ow naximum lift coefficients, as r.,eII as re]atively high pitching nErnent co€fficients. Read on. and you wi.rl see that this unfortunate situation has nothing at alr to do with the fact that these airfoirs are lanrinar flovrtype airfoils. IiACA sinply scre$ed up.

3.

CA AIRFOIL DE1/EI.oPMNIT

A. ordinate ccrnltrination

t',tethod. AlL of the NACA airfoirs, sunnrarized on figure 1, rierE-GEFgnd-5lEe-EIisEIE-EEtroa of ccrnbining a thickness distribution with a camber schedule to form a cambered airfoil. An obvious rnistake in t}Ie |IACA airfoil develogrent ,nprk was the method used for ccxnbining the thickness distribution ordinates with the camber ordj-nates. There are trno wiys to do this, the right way and the wrong way. von l'lises discusses both methcds in reference z, uut unf6rtunalely he does not indicate a clear preference for one or the other, The first (correctJ metrod is sinpry to add the ordinates together at each wing station. The second ( incorrect ) nEthod, hthich for scnre unknorr'n reason appealed to NACA, is akin to rolling a. circle of ever-changing radius aLong a curved nrean- line, top and bottcm, and then the area swept by the rorling circle beccnres the airfoil shape. This method. sho/rn on figr:re rrr-r belovr, is quite curplicated mathernaticarly, rrtlich ironi-calry nny be the reason that |lAcA picked it. unfortunatety, it leads to a distortion at the reading edge, h,hich is tben $rcthed by the so-carled "srope and radius" method for fornting tbe reading edge - rhis taulty prccess is used on all l|AcA airfoils. unfortunaLely, this has the bad effect of super-erevating the leading edge above the originar chord rine. Figure rrr-r sho^'s an exanpre- with ttre NACA ;4ls-airfoir the leading edge is lifted .486c above the original chord line, creating a new rnean line aborre the originar rean line. Tbis de-carnbers the airfoir, as a funition of the airfoil thickness, as shovrn by figure 5. As a result, the thinner t.lACA ail:foil-s have rDre camber, and thus m3re lift, than the thicker ones. this nlay explain McA,s fascination with thinner airfoirs, especially for wing tips- anittrer nlistake. see Mdendum Nurnber 2 belo^,. l^lorse yet, the incorrect rnetir"a ccnbining ordinates "r frattens the initial slope of the rnean line, and this detracts frun ine row-speed perfornance of the airfoil. But NACA never investigated this effect. Figure 2 shcnrs the beneficiar effect of using the correct rnethod of ordinate ccrnbination on a typicar }{AcA airfoir, the ubiquitous }.IACA 64-212. when tbe correct method is used to form the airfoil, redesignated 64-zrzc I the stall is softened appreciabry and the naxirnr.rn lift coeffi-cient with and without flaps is raised ' srightl-yf ccnpared to the originar airfoil. Accordingly, the "dirdt addirion" rnethod of ordinate ccnrbinaLion is used airfoils.

5 B.

Lines. Eigure 3 sha^is the wide variety of rnean rines that have been used in llAcA'/MsA airfoils. from extre{nsLy forvrard-l.oaded ones (230pr) to aft-loaded ones (cAw-r'-2). l'lost of the popular llAcA 4-digit airfoils use npderatery forward-Loaded nean ]ines (x4xx-see figure 1) with naximum carnber at 40t of cho;d, since it was kaown prior to 1930 that ion{ard loading produces lcw pitching nsrent coefficients, and this had been established in general telms as a deiirable airfoiL charasteristic. In splte of this, only 5 of t}le 52 6-series airfoil-s listed on figure I have forward loaded nEan lines (a=0.5,0.6), while a1r the rest have tl:e exaccly rr_id_loaded (a=I) nean }ine. !'lhy the contrad.iction? Srnply because these aj-rfoils are n'erely test airfoi-rs, not designed for actua-l- ai-rplane use. onry enough fon,Tard-]oaded airfoils (five) rrrere incl-uded in ttre test program to confirm the effeses of that variable. F\.:rther, the reLative inForbanc€ of the alrfoil pitchi,ng nE rent coefficient (en) co(rF ryred to the drag coeffj.cient (cd) has never been studied nor guantified by NACA or NASA- Horv can one intelligentty desigrn airfo.j-ls wj-thout knc,v,ring this relationshipu For exanple figure 6 shorrs tiree airfoils with various crrnbinations of drag co"ific' ient and rnrrent coefficient. Holi inportant is it to have lorr on, relative to @? rs it al-1-irportant, or just a nicetyz Do he need zelo qn? ans\"€r these guestions, ,,.E investigated the drag that is caused by airfoil On, -Tb. and- derived a formula ( figure 8) for calcuLating this ',tr:m arag,,, or drag associated with trirniring out the airfoi] pitching nErEnt, ior a typi.calty ;onfigured light p1ane. hltren tri:n drag is added to the airfoj-l seqEj-on drag, arrivl at a icorrected,, drag cefficient, Cd', which can nc'$r be used directl-y for 'nleccnparing candidate airfoils for a given application. the problen arises due to the fact that the center of pressure of cambered-eriefly, airfoil-s npves aft frcrn the c/4 position as the angle of attaci decreases- see figure 7- This causes an. aircraft nosedown pitching nc.rint at higher speeds that must be rea*ed b1r negative Iift in tie horizontal tail. Remqnber that Lhe aj-rcraft cG rnust stay at or near the c,/4 position for satisfacLory r-or-speed pitch stai:irity. But the negatj-ve li,ft in the taiL causes induced drag. e-lso, tne wing must nole gener_ ate an add-rtionaf incrsrent of lj-ft equal to the taii doern-Ioad, sin6e the sunrnatj,on of vertical forces on the airplane must be zero. Ttlis additional increnrent of wing l-ift also creates an incre{rent of induced drag. Add these tr,,D additional drag inciernents (wing and tail) togetber, and r,,e have trim drag. l.totlce frcrn figure g tlat the trim drag coefficient for the very high-on }{AsA GAw iirtoil= is approiirnateJ,y 20 drag c€unts at cruise for an application having a design rift coefficient of 0,2. when this is added to the section &ag coefficient of 53 drag c€unts, re obtain a corrected drag coefficient of 73 drag counts. This renders the t.{AsA GA!,1 airfoiLs unsatisfactory, or at least verlr disappointj-ng, for this type of application. As a result of analyses Like this, rde have concluded tfrat forward loading is necessity for general aviation airfoi-ls. Hoirever, it is not necessary to go to the a ridicu.Lous extrenE of the ill-advised 5-digit airfoil test progran {;airt6its f,rrri.,g the nExrmum camber unusuaIy far for^rard" ). In short. it is- noi necessary to have zelo qlt, nor is it necessary to reduce on to the point !^'l)ere other vital perfonrnnce characteristics of the airfoil. are curprcndsed. rhe IrAcA S-digj-t airfoil,s' achj-eved Gn, by! the price pa.id ( sharp stau) is unacceptabl-e. th&efore the S-digit air1"t9 foiLs should not be used, therefore, have selectd the IiACA (a=0.5) nean line to be the basis for the '.,eof only universal family_ four canrber profiles for alI of the "GA,, airfoils, turb_ urent as 'nell as laminar frovr type. The a=.5 nean line, h'hen substituted ln the NACA 64-2I2C airfoil. produces 64-212(a=.5)C. Figure 2 shorr"s that this results in a wider larLilar bu!\9t srightr,y higher naximum lift clefficient with flaps, and nnst impor' tantry' a 20t reducLion of pitcNng nrnent coefficient, with no oiher penalty. The next step is to contror the i-nitiar slope of the r'l3an line, an irportant parirEter for good slorspeed perfornEnce, Ttris was ccrpl,etely nr-issed in the ltAcA work..aLthough scne later IIASA airfoils have lead"ing edge droop, h'hich corrects ttlis oversi-ght. I{e have found t}rat the initial slope should ne a nLin:mum of 12 degrees for any airfoil, thus our GA-2 nean line inccrlnrates .3* drop, and the GA_3 rnean line has .2t leading edge droop- see Appendix ir. ne effeceiv;ess of the drmp l"'lean

6 can be seen in the perfornance of airfoiL C.A j7- .2, which has a much softer stall-, even wider laminar bucket, Io/r On, and yet higher Clmax with flaps, with no drag penalty. as shcl'Ir on figure 2. For this reason, all cA airfoi.l-s can be described as

ar

pitching nsnent, soft-stal-l- airfoils". In fact, rTt3re]-y by selecting a GA airan aircraft designer can be assu-red tlEt the pitching nsnent coefficient has been held as lc",r as practical, short of degrading other perforrnance features of the airfoil, thus for the rna jority of cases a trim drag analysis is not required. Horever, in ext.:rslE cases, such as a very high perfornance application with the design l-ift coefficj,ent less than .15, a fornal ':ri.lrr drag anatysrs may be advj.sable. Fort. ard loading has one possible disadvantage, descrj-bed on figure 10. Since forHard loadj.ng increases the velocity ratio slightly in the forward half of the airfoil canpared to nrid-foading, the critical Mach nunber fo! these airfoi-l-s is degraded slightly. Ho\^rever, this occurs in the 580 MPH range, far above our needs, hence this "

lc'e/

foi.I,

is of no concern to us. C. Thickness Distributions. For our ce arrfoils. only ninor changes have been made to ffibutions. The cA thicknes; distributions are listed in Appendix I belcr,/. For the turbul-ent airfoils (cA 30), the GA 30A015 shape is identicaf to NACA 0015. Hot^rever, this strape has a slightLy convex, or "boat-tailed" afterbcdy, rrtrich is rather unusual. Therefore, we have generated an alternate tu-rbulent shape, GA 30-01,5. with a strai.ght afterbcdy, that reduces the prof.ile drag frcrn 75 drag counts Lo 72 drag counts, with no structural disadvantage. One concern here, hov,lever' is the change in the tlaj,ling edge angle, h'hich affects aiLeron effecti-venesssee figure 9. Since the trailing edge angl-e is reduced in cA 30-015, the controleffectiveness nny be slightl-y }ess tlnn wj-th GA 30A015. Hs,Eve.r, the trailing edge angLe rsrlains generous. Further, there are better '.Eys to get effecLive ai-J-erons, such as naking "fat" or even "crowned" ailerons, which can then be used with the cA 30-)oor airfoils. For the GA 35 and GA 37 larninar shapes. no changes were nEde to the }IACA 63 alld 64 series shapes. which are conservatj.ve, utilita.rj.an l-arni,nar sections, having wide lamrnar buckets. Thj-s alloers airplanes with these thickness distrlbutions to operate over a wj-de range of flight conditaons, while still renaini-ng "in the bucket". This feature results in a profile drag penalty of perhaps on],y one or tr,ro dfag counts carpared to sqne other so-calJ-ed "superior, lore-drag " lam:-nar thickness distributj,ons that have been develo@ since, ard the drag penalty is a snrall- price to pay for the wider bucket on the c"l-assic t'lACA shapes . For the GA 40-015 shape, r,E use the NACA 65-015 tiickness distribution as is, Tae profil,e drag coefficient of this shape is also slightly higher than recent NASA ,'slar3" shapes, but tbe drag bucket is crrrrespondingly wider, for olErational flexibj_llty. For the cA 40A015 shap€, we have carefully avoided the }IACA 65A015 shape, which has a poorl-y designed, straight afterbody (high drag ) and should not be used, W1th the point of nraxirm:m thickness ncved aft to the 403 chord position, the design of the pressure recovery section krc.rEs critical, and a straight afterbody is no longer suitabLe, due to the unaccaptable drag penalty. Accordingly, l,ve settl-ed on a reduced cusp shape by ncdifying the I'IACA 65-015 to fj-]] in approxlnately one-half of the cusp. This gives the deslred strucEural and control effectiveness advantages of a true nocusp shape, with a drag penalty of .Iess than 2 drag counts. ttotice that the basic thickness distribution for the c"1 thi-ckness distributions j-s I5S thick, and then the 12t and 18* thicknesses a-re scaled proportionately up or dorn frorn the 15t thick shape. this is a departure frcrn the NACA schen-- for their landnar thj-ckness distributions, wherein unique syrnretrical shapes have been calculated and published for eacb thickness, and these shapes are not guj-te exact nruJ-tiples of each other. The difference is very srnal,J-, ho^'ever, and does not affect a-irfoil perforTnance, therefore ue have ignored it to si.nplify the process of generating fanil,res of airfoils. llotice tiat the ninjmun sestj-on thickness offered j-n "cA Airfoils" is 12?, for $e do not reconrend the use of wing sections thinner than this for any application, even for racing airplanes. In fact, the optjmrn airfoiL thickness rega.rding lift to

7

ratio is probably closer to 13? or l4B thick, for any airfoil systern. Sirply put, you lose nr3re than you gaj-n by using wing sections t-hinner than l2t thick. For tail sections. synnEtri-ca.l- shapes such as NACA 0009 or I.IACA 63A009 are ccrmonly used. Ordinates for these shapes are l-isted in standard I.IACA tabLes ( reference I)' or they may be scaled dcrrn frcrn the corresponding C,A thickness dj.stribution. D. ordinate Tables. Notice frcrn figure I tlEt the NACA "ordinate tables" are rnerely a-fGrino of-test sanples tJ:lat r,prt included in IIACA' s wind tunnel tests , and are thus incfipl"ete. In contrast, the GA airfoil ordinate tables. Appendix III| are a ccnplete matnx of 96 airfoj.ls, in four series, tiro styles (with and without cusps), four camber LeveLs, and tlree thicknesses, offering the designer a ccmplete "cook book" of airfoils fron \,tdch to choose, MSA's official position i-s that a ccnprehensive catalog or " cookbook" of airfoil-s is not necessary, and suggests that a unigue airfoil- should be custorn-designed for each and every nan airplane, one that "exacely fits the specificati-on for the ne\.r airplane", otherwise ttle lErforlnance of the nevr airplane will be ccnprqltised. This is, of ccurse I nonsense. there j.s no single, unique solution to a particular airfoi-] design problern, since there are so rlany value judgenents. intangibles, and perfonnance tlade-offs invofved. For exanPLe, hc,r "soft" is "soft". for a soft-stall airfoil? Therefore, there will always be a need for a good catalog of airfoils, if for no other reason than to serve as a standard to ccrnpare custcnFdesigned airfoils against. FlrCher, airplane designers are by-and-J.arge not airfoil designers, and ia^culd rather select frcrn a good catalog of standardized designs rather th,an take a chance on a custcm airfoil. NACATS thj-nking. evident frcrn reading reference L, was that "custcrn" I{ACA airfoj-ls could be s)mthesized using l{ACA's data and nethods. In other hDrds, IIACA assund tlnt a designer coul-d select a particular thickness distribution and a camber profile frcrn tlle text and then ccrnbine thern by the I'IACA rethod, to obtaj,n the desired custcrn airfoil, just ' as cessna did for the !'todeL 210 wing desigm. This is probabry t-trc reason that I.IACA was content to publish test data a1one, rather tllan to publish actual- catalogs of airplane arrfoi.l-s. Hot,rever, to thus s)mthesize custam NACA airfoi-1s is a dauntj-ng task, beyond the capabiJ-ity (or pa.tience ) of the average designer'. Further r due to the nfstakes and onissions in the NACA work, the airfoils vDuld still be less than ideal. For example, Cessna,s airfoils for the lbdel 210, r,,trile a step in the rj-ght direction, do not contain leading edge droop, and the ordinates are ccrnbined incorrectly. which is both rronic and unfortunate. liorse yet. on rrlf,st other airplanes, Lhe test airfoils r,rere used directly. warts ard al}, because of t{ACA's nrista.}<en assumtion that designers r^rould slmthesize "good" airfoil-s frcm the test data. The GA ordinate tables are arranged with the ,,cusp', tlpe airfoil-s at the top of each page, ajld the corresFonding "no cusp" airfoi]-s at the bottcn of the page. The ordj-nate schedules generally follora the NACA forrnat, hov,ever an additionai statj-on llas been added at .25tc, to herp define the leading edge. unlike the !,IACA airfoils. GA airfoil.s do not have a tlrue reading edge radius, and the readj-ng edge is j-nstead a curve defined by a series of discrete points. co],uru''s #2 and Jl3 of the ordinate tables are the thickness distribution (symnEtrical shape ) and tbe nean rine, respectivery, frcrn which the tirree airfoj,rs 1n each table are fornred. corunm #2 and +3 are listed for reference only. they are aLso usable for forrn-ing airfoils with th.icknesses other than the three li;ted in ttre table. The Procedure for this is to scal,e col-umn *2 frcrn I5t to the desired thickness, then add col-unn *3 to obtain the desired aj-rfoil, E. Aerodvnandc Characteristics of winq Sections. The aerodynaninc characterj-stics of each l-2t thick arld L5t thi.ck "no cusp" type cA wing section, as detern[ned by the "EPpler" prcgran, are given in Appendr-x rV. for Relmolds nunbers of 2 Irtillion and 6 ndLlion, corresponding approx-i:rateJ-y to stal1 conditions and cruise conditions respectively for tlpical light airplanes. The characteristics of the 188 thick wing sections are not shcrrn, but they are approxjrately the sarne as the 15t thick segtions, witn 2lr drag counts addltiona] profile drag. See fign:re 15. sjnr-ilar]y, the characteristics of the "cusp" t)pe sesLions are not sho^rn, horever: they are approxirnately the sare as the "no-cusp" shapes, wi,th 2 drag counts less drag. Sree figure 14. drag

o-ng

8 Tbe characteristics at Reynolds nurnbers other than 2 miU-ion and 6 rRil-Ii-on rIEy be estuated by interpolation and extrapolation. and by reference to figu-re 17. The data in Appendix IV j-s for the snDoth condition onJ.y. Pigure 18 shovrs the effect of surface roughness on the perforrnance of a tlpical GA airfoil, 37A31-5. The prjjnary perf orrnance degradation is ]-oss of lajrlnar f J-o,r', causing a substantial increase in profile drag, and there is also scan-- Loss of nraxirm:rn 1j-ft coefficient as wel-l-. Ttre data r-s for roughness conditj-on !=4, b'trich is approxirnately equj-valent to the NACA " stEndald rouglmess" condition used in their tests. According to reference I' this is eguivalent to a wing ",,e11 contanrinated with bugs". Ho+rever, the concensus is that the ''standard rouglmess" lrrposed in the I{ACA tests is unusually severe, and is not likely to be encounlered in actual alrcraft service. F\rrther, due to the superj-or leading edge shape of the cA airfoils, the perfonnance degradation of GA airfoils due to surface rouglness is proba-b1y not as severe as with llACA airfoLls. TLre perforrnance data in .\ppendix IV is for wings without f1aps, A]though rnuch experinentat raork has been done in wind tunnels with high-lift devices (see reference If chapter 8), there is no readj-l-y available ccmputer program ttlat can accuratel"y predict airfoii- section perfornence with flaps, due to the ccrnplicated flc,ld patterns in the flap systsn. AccordingJ.y, very littl-e data is presented herein for GA wings with flaps, except for figure 2, which illustrates the principLe that cA a.irfoi]-s have significantLy better fl-ap effectiveness, that j-s, increase of nraximum lift coefficient with a given flap system, due to the cumulative effect of the cA jjrproverpnts, than thei! IIACA counterpart. airfoils. However:, raE offer the folloering as a "ruLe of thunb" for estiratj-ng the naxj:num sestion l.ift coefficient achievabl,e with flaps, for cA airfoj-ls. For large, ,,e11 desi-gned f1aps, the greatest expectable factor of jrprovenEnt in section Clnax for sinple flaps is 1.5. for slotted flaps 2.0, and for Fc&vler flaps is 2,5, thus, for a cA airfoil with a no-fIap C]JrEx of 1.6, the Clrex with sirrple flaps coul-d be as higb as 2.4, slotted flaps as high as 3.2, and Fo/rler fl,aps as high as 4.0. ltese are section (2 dilrensional ) coefficients, and appropriate reduction must be made for ttrree-dinensional effests. AIso, they a.re the estirnated nnxirnum values for the best fl.rp systens, whereas existing production flap systers probably fal1 seII shorL of these nunbers.

4.

GA AIRFDIL SE ECTICbI AlqD AppLICATTONS.

Figure lI presents the matrix of the GA airfoils in this book, arri offers scflE guidelines for selection of [Erticular airfoils for given applications. A. Effect of Series. Figure 13 shc'vts the general performance differences betrr€en the tulbulent GA 30 series and the laninar cA 35, 37, and 40 series. The GA 30 airfoils are tie rrc)st @nservative, and are atrPropriate for l-or-po\^rered, cub type airplanes. GA 35 ai-rfoil-s are I'entry level" Larmnar flor airfoils, and are suitable for airplanes .Like the thorp T-18, at least when nndestly Fc ^rered as in the original desi.grn. GA 37 airfoils are general, purtrDse lanLinar florr' airfoils, to be used on a wide lange of ajrplanes. cA 40 airfoils are for onl"y ttle nDst soplListicated, high perfoFMnce designs, such as the Glassair or White Lightning, where rninjmr.un drag at high speed is a strong reguirenent. they reguire the rcst accuracy in nEnufacture to reafize their lc^d drag potential. ALso, the lanr-inar buckets on the cA 40 airfoils are the narroa€st of a-11 the C,A series, so the wing mrst be designed carefu11y to insure tlEt tie airplane is olnrating witlr-in the laninar bucket Lrnder alf

light cuditions. B. Effect of Cusps. Figrr:re 14 sho{rg the effest. of afterbcdy susps ofl airfoil perfornance. Although both "cusp" ard "no-cusp" airfoiLs are presented herein, for tbe great majority of applications tlle "no-cusp" airfoils are preferred. Ttre main reason is to irrprove aileron effectiveness, as liel-I as to si:rplify fa.brication. the t)pical drag i-ncrease (.0002) is usually insignificant. For appU,cations such as sailpl-anes and mtor-saj.1ers, r.here nLinirm-un drag is ijrportant, and especially with thicker airfoils, the "cusp" type a:-rfoils can be used. Ho\aever, with the "cusp" t)?e airfoils, specj.al "fat" aileron designs ttBt trave increased trailing edge angfes f

should be used,

to obtain acceptable aileron effectiveness.

I C. Effect of Canber. Fiqure .I5 shoe/s the effect of different camber levels on GA airfoiL perforlnance - Of c-ourse. the main reason for using camber in the first pl-ace is to increase Clnax, but the resulting increase in On reduces top speed. thus, it is a trade-off, and only as nuch carnber should be used as necessary to nEet the design reguire(ents. See Addendun #l for a discussion of the effects of increased On due to camber. In any event, l-arge, effestive flaps are the key to hi-gh aircraft lElforrnance, for they Fernlit the use of 1c{.Er cambered sections and reduced wing alea r ard tlds results in higher top speed. Accordingly I a good airplane design shouLd star! with the fl-aps, and then tJIe rest of the airplane shoutd be designed around the flaps. tn general, the tcffer camber levels are used with higher powered airplanes ard/or with large, effective flaps, while the higher carnber IeveLs are used with rrcdestly pcrwered alrpLanes, o! witi snaller or no f.Laps. Consideration nulst also be given to the design (cruise) Iift coefficient of the airplane to make sure tftirt the bottcm edge of the lami.nar bucket is bel,ckl the Cldesign. ' For exanple, referring to figure 15, lf the design l_ift cEefficient is .25, the cA 37A415 coufd be used, but not the 37A61-5. this concern is especially irrPortant with thinner ( lztthick) ai-rfoiJ-s. D. Effect of Ttrickness. wing B thickness is prinrarily a structural consj-deration, sare perforrnanc. lifferences due to thickness - As stated @ above, the tiinner ai-rfoils have narrc,hEr laniinar buckets, thus shou.Ld be used cautiously' nrreherncre, the starl tends t be ress soft with the thinner airfoils. in spite of thickness is so srall, the nrin n-rn arrfoil ttrickness to be used for npst laflLinar flcrvr apprications is l5t. see Adderdun *2 for a discussion of the effects 6f using airfoiLs that are too thin, especial].y at tie wing tips.

E. Effect of Reynolds Nunber. the design Relmolds nunber can affest the choice of notice t-Llat the lam-nar bucket narrc'vrs For exars)le, frcrn figure 17 considerably at fligher Reynolds nunbers, since l-arninar flol is tErder to ach-ieve as Re)nolds nunber increases. Iherefore, for tdgher Reynolds nr.rnlcer applications, thicker airfoils and/or lover canbered airfoils nay be nec.essary to insure that tie airplane is operating within the bucket at top sFed. @nversely, at 1*/ Rqmolds ntmr bers, cljnax drops off considerably, thus additional camber, andlor addi tj-onal thickness, and,/or nore wing area ftry be ne€ded ccfipared to a tligher Re)mol-ds nunber apPlication, for the safiE take-off/Iandi-ng sIE€d. For exarpl-e, the BD-5 has a stal1 Reynolds nunber of Less than 1 miuion, and uses a DJACA 64-212 airfoil for the r@t sestion- a terribLe choice for such a lor Relmol-ds nwnber, resultj-ng il nany needl-ess fataL accidents. ltle ajJfoil should have been thj-cker, or ftcre llighly cambered. or better yet- both. See Mdendwn #4 beL*r for a re-profiling schenE for BD-S wings. For very Lc'u/ Reynolds nr.mber applications, less than I/2 tnillion, such as in sailplanes. a phencnenon kncnn as " larrinar separation br:bbles " follcrqEd by turbuLent re-attachfiEnt near the erxi of the laminar run, may occur, on the top anVor the bottdn surface, j-f the curvature of the wing surface is too great at that Foint, this results j.n increased drag. Any nEthod to reduce the curvatule of the wing surface at that point will help, hcr^reve! the usual fji j-s to use " turbulator talEs " span-wise slightly foruard of the separation point to "trip" the flo* to normal attached turbul-ent flov'r, avoidr,ng the separation. Ttris subject is beyond the scope of this book, ard is nornally not a problern for @ airfoils, ltdch are forrerard Ioaded and thus iEve littfe camber in the afterbody, and tiis reduces the curvature on the a-irfoil surfaces in the afterbody ccnpared to other sailplane aj-rfoils, For this reason, "no-cusp" shaFes are better than "cusp" tlpe shapes regarding laninar separation bubbles. Afso. tlre laninar separation bubbl-e probl€m is nagrnified as the point of rna:cirm-rn airfoil thickness is noved farther aft, that is, beyond .40C, in r^hich case radical cusps are regui:ed for satisfactory pressure recovery, and this leads to separatj.on. "@" airfoils, especially the no-cusP shapes, do not have this problem, for there a-re no GA airfoil-s with linax beyond .40c.

airfoil-.

10 1n sunna;-y, there ajre tvJo ways to address the lamj.nar separation bubble problant at lor^, Relmolds nunbers. Tl're first }]ay is to try to prevent t}Ie separation frqn occuring in ttre first place. with the basic airfoil shape. This requ.ires thin, lctw cambered. a:-rfoi]-s, wr-th ltnax forward of -40c, utith no cusps. Hoi",ever, this is not Practical for sailplanes, for exanple, so the alternate solution is to 90 ahead and use the needed thiak, high-canberd shapes with long laln-inar mns and shorts (cusp t)pe ) pressure rec-overy secLions, and tben force the transition to turbufent flctut witi turbulator tapes located top and bottcrn near the end of the Lanrinar nrn, to keep the flc'vi attached. Ttre drag of tJIe turbufator tapes is less than the drag that vnuld otherw.ise occur frcm the laminar separation bubbles ' so everl,one is happy ror exceedingly Io.J Relmolds numbels, such as with very slow, indoor, small rubber bancl po"ered nndel-s . the f lc'vr is I00t l-anr-inar. Ib irprove l=rforflEnce. a trip wire is often placed spanwise in fron! of the leading edge, to make sure that the flctor over the enti-re rring is turbulent.

F. Applications. GA airfoils are currently being used on a wide range of applications Fron-a%I6Fl-rrestar" ultralite to a high-perf orrnance Nick Jones "Vl;1ite Lightning" ( bot.I. one-off, c'\,vner rrDdifj-ed). Producuion kitplanes using GA airfoils incl-ude the Skystar "K.itfox" and the Ultravia "Pelican". All experi:renters who have substituted cA ailfoils for the original aj-rfoils on their hq€builts have reported performance jrprovernents. wlthout o(ception. See fi$Ees 19 and 20 for tlpical appJ-ications. 5. AIRCRAFT PERFORI.,IANCE PREDIqIION Figures 2I afi. 22 can be used in predicting aircraft perfornunce. cc.nputer predicted perfonnance data is tr.io-dfiEnsional data,Iike wind tunnel data, that is. rt is idealized data for a wing of infillite aspest ratio. fte data rnay be clrrected for three-dlrensional. effests, that is, correstd for wing aspect ratio, using nethods descrlbed in standard aeronautj-cal teJrts. For exarple, in detenn-ining a suitabl-e angle of incidence for a particular alrfoil on a gj.ven airpJ.ane. tJ.is usually neans adding approxi:nately I to I degree angle of attack to obtain the design lj-ft coefficient ( average ) over the entire wing, dependj-ng on the aspest ratio. A higher astEcts ratio ne€ds Iess correcLion. For exanple- detenrLine a suitable angle of incidence, for a wing with an aspest ratio of 5 on an airplane with a wing loading of 15 fb/ft-, and a cruising speed of I50 MPH, usj-ng the cA GA 37A315 ai-rfoil,. Frc.n figure 22 deternine the thrcdiJrensional design lift coefficient as Cldes= .25. Frcrn figure Iv-13, deteqrline the angle of attack necessarl. to obtain this lift coeffi-cient as zero degrees- Nov/, since an aspecE ratio of 5 is a fairly Lorr nwrber, add I degree for threedinensj-onal effects, and set the wing on the fuselage at ar algle of incidence of +L degree to the fuselage reference U-ne. Ttris nethcd should be accurate enough for rost ca5e5.

As a double-check, note that the fourch digit in the "GA" airfoi.l designation (as in the NACA designation systsn for the 5-series airfoils) indicates ttle approxjrnate design lift coefficient of the airfoiL section, in tentis. tllat is, either .2, -3, .4, or .6. Ttrus. i-n our exanple v/ith tie cA 37A315 airfoi], the approxirrnte design lift c-oefficient of this airfoil is .3, so this apl=ars to fi.t \del1 enough wit.l- the desigrn lift cceffici-ent needed for tjtat pa-rticul-ar airplane, that is, 0.25. If these numbers do not have an approxjrate rnatch, the canber selection is probably not suitEble for tJ.e application, or the estlnated cruising speed of the airplane rnay be opt]Jru,stj-c.

6.

CEMPT'TER PROGFAM ACCURACY.

the ccnputer program used to generate the Predj-cted performance data of APpend1x 1y is tni: eppfer program "profil", published in Fortran in reference 5' and adapted tor perional 6c.teut. use (itS-DOS ) by referenc€ 6. Ttris is a sfuple program' and does not iterate on itre tunOary tayer, thus it gives accu.rate results for only rrclldesigned airfoiLs such as ,,GA" ai-rfoils, that have slrpoth, contj,nuous nean U5es, roi porly desigrned ai-rfoiLs witi discontinuj.ties in the n6an line, such as t]le !,IACA Z3-OIZ aj.rfoif ; it gives inaccurate results, especially for Clrlax ' because

11 it cannot fol.Lod the ccnplicated effests of premature setE-ration bubbles at higher angles of attick ccrnrpn in those aj-rfoiJ,s. But htro wants to use poorly-designed

airfoils

any/€y?

A cqrParison of cdrputer resu]ts and wind tunnel data for a t!?ical airfoi]-, NACA 64-215, j.s shcr,fi on figure 2j. Note Chat the accurasy of the cdrputer data is guite good, all tfrings considered, and is a credit to Dr. Eppler. The program appea-rs to be especiarl-y accurate i-n predicting laninar/turbulent phencmena, separation bubbles, etc. Ho^rever, the program aplEars to overstate drag by at ]east 109, ard to overstate, lift by about 53, The r€rst disagreenrent appears to be in ttle pitching nrnent coefficient, btrich tbe program overstates by at least 30t. For thi-s reason, as absolute data, t}le ccnputer results shouLd be used cautiousLy. Ho\rEver, for ccnparative purposes, such as shqn'n on figure 2, the program is exc€.]Ient. The program appears to be cal"ibrated for best accuracy for airfoil thi-cknesses of about L5t. ltre program shqrs a considerab.l-e loss of Cljnax for thinner (12t tnick ) airfoifs, ard a gain of cJ.lrEx for tldcker (18t thick ) airfoils, as shc,vrn by figu.re 16. Ttris does not agree with wind tunnel data, v,hich tlpically shows negU,gi-ble differenc€s of cl,rnax as a function of airfoil thickness. Dr. Eppler cffrents on this iI his book. reference (9), and suggests that, due to the lijn-itaLions of wind tunnel testing, especr-a]-l-y the change in the ratio of aijfoif cross-section area to the tunnel tlEoat size witi different ailfoil thicknesses, Ferhaps his qxrputer dat! is fipre accurate than wird tr.mnel data. In any event, lrE suggest that \r,hen ccf{Ering the perfornence of different airfoils with the cc(puter prcgram, one shoul-d use the sanE airfoil- tldckness for both airfoils being c.crpared, the Eppler prcgram has a routine for sirurlating the !=rforrnance of an aj-rfoi1 witi sjrpl-e flaps. Ho,$ever, tlre predicbed performanc€ is wildly opti-rdstic crcnpared to wind tunnel data, because the program of necessi-ty, wfien the flap chord and defl,eqtion are inputted, drav,,s a ccnpletely new, idealized airfoil tlrat is unrealistically snEothed so that the nenesis of the prcglan ( prenature flc'gr separation ) will not occur. Furtherlrl3re, tlle program caffiot begix to sjmulate the cffplicated flo\^' patterns of npre elaborate flap systens such as sl-otted and F* er flaps. Ttrus, rile did not spend nu:ch tirrE with the flap routine in this prcgram. In spite of this shortcurfng, ho$€ver, the flap routine is valuable for predicting relative differences of flap trerfornunce betrcen sj:nilar airfoils, as shGln on figure Z, Another use for the flap routine is to predist On vs clnax for a given flap systern. In other rnords, if a sirple flap systen yields a Clnax of 3.0 b}/ the prograrn, then the repDntd On will be reasonably acsurate for a flap systern with tbat CLlnax, even though it nay take a clonsiderably nDre elaborate flap confi,guration to achieve thatclnax in prachice. The Eppler program al-so does not incl,ude any correction for ctfi[)ressibility effects. treaLing the airflorr as bei-ng inccnpressible. Ilo€ver. this effect is so nlinor as to be insignificant, for the flight regi.res of typical-,light general aviation air planes. For exanple, the tdlng ]oading of a Piper cub, 1*/ft', yields an aEerage pressure dj.fference of only 7 */ft-/L44 = .05 psi betr"Een the top and bottcrn surfaces, Ccc$Ered to the atjrDspherj.c pressure of 14.7 psia, this arEunts to a pressure difference of only 0.3t, For higher perfonrEnce airplanes, such as a Bonanza with a wing loading of 20 */ft', ttre difference is sLill Iess than 1?. thus, the assrnption

tbat the flovi is ilccnrSrressi-b1e is not bad. ltre Eppler program for perfornance a''alysis calcufates ve.l-ocity ratios across the aj.rfoil at each algle of attack, top and bottqr surfaces, then arints these ve1ocity ratios (Foint velocity divided by free stream verocity ) in tairurar and graphic form. AJ-ternativery. it will calcurate and print out pressure ratios across the airfoir- then, the program catculates boundary layer data for each angle of attack at specified Reynolds numbers, including coefficienls of 1ift, drag, and pitching nrcnr ent' the turburent area. ani the separated a-rea. Ttrese values are also printed out in tabul-ar form, arld in a "boundary rayer swnary ptot". A salrple analysis print-out is shorr'n on figures 24-I thru 24-4.

12 Several- yea.rs ago Dr. Eppler brought out an "ifiproved" version of hj,s program. Ho\^/ever, the ner^, program seems to understate section drag, and also reports lalninar bucket width as j-ncreasing with an increase in Reynolds number, htrich is not the case. F\.Ether, the resuLts appear to be overly sensitive to data point (ordinate) accuracy, thus I still favor the old program. Eoth prcgrarns include routines for desigrn of airfoils by the nrcdern, one-step calculated, and then " inverse" rethod, whereby idealized velocity dj-agrams are first airfoil top and bottcm surface ordinates are ca.l-sul,ated frcm the velocity data. That is OK, but the Fossibil-ity exists of "creating a nonster", such as the very recent NASA NLF(I)-OII5F alrfoi], discussed in Addendun No. 5 bel-or^r. lbis is less likely to lEppen witb the "classic" nEthod used by },lAcA and "cA Airfoils". In any event, neither the airplane, the wind tunnel, nor the ccrnputer kncrds or cares htlich n€tiod was used to design the airfoil, and the final perfonrEnce figures a-re the only thing that caunts. Thus both nEthods are valid. Any airfoil, even if hand-sketched, can be broken dov'rn into a symrEtrical thickness distribution and a camber profile (nean Iine). and much can be learned about the airfoil- by inspeccing and analizj-ng these tllo ccmponents sepajately. 7

.

GA CIJFFS FAR WING

RE\.{CRK

As noted earj,ier , all of the NACA airfoils have Iffr nose prof i1es. due to the faulty NACA design nethods -The result j"s poor slcvr-speed Perfonnance, i-n rEny cases. me niCe 4-digit ( turbufent ) and NA6A 6-series ( laminar) airfoils can be irproved by adding a leading edge cuff to the airfoil, which drops the center of the leading edge ipproxirmtaly tt to 1? of chord length. The rpthod for deg these "drooped leiOing- eages,,, shq,n-r on figwe 25 for the !{ACA 64-212 airfoil, is to design a neur nean line iorward of 10SC to obtain at feast 12 degrees of initial nrean line slope, necessary for a soft stalI. Then, usj.ng the existing toP surface and the revised nean Iine, r,,e calculate the ordinates for the bottcm surface. Ttre perfornrance analysis for this cuffed alrfoil shclts a draratic jnprovenpnt in ttre stall ccrnpared tso the original 64-212, as r.vell- as a slightly wider lan.inar bucket- see figure 26. A-Iso shorvn is the perforrnance of an uPIEr sulface nbdification proFosed by Hicks et aL at NASA An€s. Ttlis cutes the sharp staff ' but it also reverts the airfoil to a turbuLent sectsion, causing hj-gh drag ' The perfornunce of the GA 37-212 is also sholvn, for ccnpari son. This cuff nndification should be used only as a "guick fix" on existing wings, not for ne$, constructsion- use a GA airfoil instead. A.Iso ' it does not \'tork on the NACA s-digit airfoils, like the ?3012' which already llave too much leadj-ng edge droop, and a different stall nrechanism, than the 4-digi-t and 6-series airfoils. See Addendum #3 belov;. 8. }4ISEIJANMUS AIASC AIRFOIIS !,iitb the cun-ing of the slEce age, NACA'S naflE was changed to NASA, and the agency's responsibiiities were e4xnded !o include national space Projects as r"eII as the old-line aeronautj.ca.l, Prolests. Ttre total budget is currently about 14 bi]lion do.llars yearly, of whi-ch about 1.2 billion is refated tg "aeronautics" projects, a fairly nstant arpunt yearLy. Ho$Ever, over the past Several decades, '.Jork related to @nera1 Avj,ation projects has dwindled to nearly zero, due to "budget restlaints", in NASA,S hDrds. Ttre only general aviation airfo.il r.ork, for exanple, has been the sporadic release of several randcrn airfoils. These have usual-ly been the brain-children of particul-ar NASA individuals, rather than any c,oncerted effort, and have been disappointmmts. A. N;\SA GAI,t-j- . In l-974, the NASA GA!.J-I and GAVFz "Whitc6nb" airfoils ( later designated 15(I)-041-3) vere released. Ttrese airfoil-s are characterized by a large EtlFb'qffi Ieadrng edge radius. and a slab-shaped profite having the maximum thickness at .40c. this pioduies a long Iaminar run, at the expense of lanr.inar bucket width. The leadrng of about .75tC, npre than it ne€ds to give the airfoil its soft stalf edge has a droop chiracceristic. Ttre 1c'vr profile drag i-s enhanced by the pronounced cusp in the afier-

13 body, and the blunt trailing edge, The brorst feature by far, hcturever, is the aftloaded camber profj-Ie- an outrageous nListake for an airfoil that was touted to be a general avj-ation panacea. This gives the airfoil a pitching rTDrnent coeffic.rent three tijnes as high as it ne€ds !o be for the alrpunt of canber in the airfoil-, and this produces very high Lrjr drag, rendering the airfoil unsuitabLe for genera.l aviation use, In effect, the airfoil has t'nlo notches of flap perrnanently buil-t into rt. Unbelievably, NASA chose this airfoj-l for their "ATLIT" project, described belo'v. Figure 27 sholas the bizarre press release concerning the NASA "ATLIT" (Mvanced TechnoLogy Light 1\,rin ) project in 1974, r"trlch turned out to be a disaster, perfornance-wise. The project was dccrned to failure frcrn the beginningdue to the seLection of the hj,gh-Gn NASA GAvl-I airfoil for the wing. the predicted perfornEnce figures \^rere no doubt calculated without regard to the high On of the airfoil. a rna jor blunder. The spoj.lers for rol.l- controL \rere also unsatisfactory, experiencing control reversal at ]ow and mediurn deflections. Nothing new was Learned by using a Longer sPan. tapered wing- these effects had been kno\^'n for decades. This merely contaminated the data, making it impossible to ccnpare to the base-l-ine ( factory ) airplane. I'IASA \das so ernbarrassed by the poor perfornnnce of this airplane that the pro]ect engineer never even bothered to hrite a final report on the projecc, but he got proncted any,ray. He no, has a top position at NASA Langley. In retrospect, I.iA.sA forgot that their function is to c.onduct basic aeronautical R&D, not to "shcwr the industry that they are \,rrong, and this is the proper way to build a GA 1i9ht twin". Ttris is an example of hhat can happen if R&D is not rnarket driven, bub is directed by irresponsible bureaucrats. Ttre airplane was bougbt back by piper for salvage of engines. instrulTEnts, etc, and \aras then sold to a technicar school for students to drill- hores in it. with the proviso t-tlat it never fly again. Figure 28 shc'v/s the lA\Si\ !'A'ILIT' airplane during wind tunnel tests at NASA l-angJ-ey. this j.s g! npney. The cAli.l airfoil was also used on the Beech Skipper and the Piper Tcmahawk, wj,th dj,sappointing resul,ts on both airplanes, parcicularly at high speed. A ccnnnn revrork for this airfoil is to fill in the bottcrn side cusp, as shcun on figure 6. This reduces the aft loading scmewhat. reducing Gn and trim drag, but the airfoil refiEins a rrr-ish-nash. B. MSA NLF(1)-02I5F Airfoil. This airfoil, due to Scnrers, and descriH in Reference oilg'inaTlt as a sailplane airfoil. thus it has too much carnber in it T was a$nfor typical porrered airplane applications. Accordingly, the trailing edge must. be reflexed approxjrraCely l0 degrees as shc'vn on figure 29, for powered airplanes, Even with the reflex, high aileron hinge rrnents (stiff ailerons ) renEin, so a ccnrncn rer^prk is to make the ailerons and f laps f lat-bottqned, as shc^,,'n on f i.gure 29 , to salvage Che airfoil. Of course, the better solution to the problen j.s sjrply to design an airfoil witl- less camber in it in the first place. Anothe! strange feature of this airfoil is the canber "diP' .60C, as shc'vzn on fj-gure 3. This is an attefipt to move the trans.itj-on point aft, "a extendj-ng the larninar run to reduce profi.Ie drag, which it does. Hcrvrever, the fallacy here is that the negative carnber at .60C causes negative lift, and this causes nore ( induced ) drag than is saved by the extended larninar run, reducing overall- airfoil efficiency. Al-1 in all, MCA,/NA9C has never reached a concensus as to the best shape for carnber profiles for general avj,ation airfoils, See the "GA" camber profiles in A5pendix II for a conparison, C. I{ASA NLF(1)-04I4F Airfoil. this airfoil, figure 30, due to viken, was envisioned as a very lo* drag lamjnar flovr airfoil for high-pornrered, high perforrEnce general aviation airplanes. the Foint of rnaxinum thickness on the airfoj-l is at .45C, and the nraximum camber, c.entrally loaded, is approxirnately 2.53c. This makes the airfoil ccnpa.rable to the }IACA 65-414 airfoil , Unlike the }IACA airfoil, hodever, the t\T,F airfoil has enough J.eading edge droop, approxjrrately .353C, to give the airfoil decent slc'vr speed perforfiEnce. Realizing that the price pa..id for locating the nraxi:rn:m thickness so far aft is a very nafrc'e, l-arninar b:cket, NASA fliSht tested the airfoil on a Cessna 2I0 with

14 narro^' chord (I2tC) "cruise fl,aps", reflexed upr,rards approxunately 7 degrees at cruise, and adjustable. Thj-s was an effort to shift the faminar bucket verEically as needed, to keep tbe airplane "in the bucket" under varj,ous flight conditlons, tirat is' at valious typical v€ights and speeds encounterd in aircraft service. lttis Proved to be difficult and jrpractical. and the net wlng drag turned out to be nlf,re than anticipated. The scheme was t]"ug considered to be unsatisfactory for the intended application. This is an example of a "single design point" airfoil. ltotice frdn figure 30 that the -7 degree cruise flap setting, necessary to reduce the rnaximum carnber frcnr 2\\C to IEC for Cruise. cleates a region of negative carnber at .85C. This causes a dlag penalty, simil-ar to what hE have seen prevj'ously fron ref)-exrng the tlailing edge of the NLF(1)-02L5 airfoil ( ccrnblned with the canber dj-P at .60C). reducing the efficiency of the airfoil. As before, the better choice would be to desj,gn the airfoil witlr less canrber (NLF(1)-02I4), to keep tJ-e airfoil clean at cruise- in short, a conventioal design approach. Ho^Iever, the airfoil ltoufd still be a single point design. Accordj.ngfy, our concLusion is tllat the point of maximum airfoiL thickness should be no further aft chan .40ct for typical general aviation app-

Iications . This airfoil has been nEdified. however, by Team Nsrxesis ' and j,s being used sucapplication' a cessfully on the Nernesis Formula I racer. this is a very special the airfoil is unour concLusion that point" and thj-s suPporEs airplane, "single satisfactory for mcst general, aviat.ion aPplications. It is interesting to note that I'JASA's Cessna 210 flight test progran for this airfoil, repofted in liAsA Tl,1 85788, was simi.Iar to the Poorly designed "ATLIT" flight test progran descrj-bed above. On the Cessna 2I0, the span Iras increased frdn 39 ftto 42ft, nraking it :mpossible to ccnpare the perfonnance of the nelJ airfoil to tire "base line" airfoil. ltre inescapable conclusion is that NASA was here again trying to shov,/ that they can design airplanes better than the priroe rnanufaceurer, ratber than bej-ng satrsfied with doing Iegitirnate research r\,ork. At }east, in both cases, llAsA proved hc)\d not to build a general avj-atiun airplane, and this j.s lvorth sonething-

I guess. 9. REIATED SIjBJECTS A. Blunt Ttailing Edqes. Al-I GA airfoils r,ave LEen desigmed with sharp traibng edges, for uniformrty. Hor,rever, sharp-edged airfoils, on wings and control surfaces, '.Drk bet'te! if they are cut off as sguare as possible at approx1rnately 998 of chord. Ttre reason for this is that the trailing edges have finite trailing edge angles, and this causes the flow to selErate before reaching the t.raiJ-ing edge anyway. So you might as weLl cut it off. Ttre airfoil will stilL acts as if it ',ere I00t 1ong, B. Flyinc Winq Airplanes. Due to the lack of a tail, flying wj-ng airplanes must use zero-o'o airfoils, thus GA airfoils are not suitabl-e. nlrttrer, due to pitch stability concerns. flaps cannot be used on flying wings. Ttrus, due to these tr.rc design constraints, the perforrr€nce of any flying wing airplane wiU be nrediocre ccmpared to

an egually sophrsticated canventional airplane. C. Canard Airplanes. This configuration has sinilar design constraints. Fl,aps cannot be used on the nEin wing. llrther, the forward surface rl[l.rst al\.Jays be rll3re heavi].y loaded than the main wing, so tlEt the carlard wilL alvays stall first. Since the rnain wing can never be allo*ed to stall. it never reaches its nexjmum lift coefficient, and j-s thus relatively inefficient. Ttrerefore, due to these tlro design constraints (no flaps. no-sta1l nrain wing), t}Ie canard configuration can never be as efficient as an equally sophisticated conventionaL ccnfiguration. Flrther, since full--stall landings are not possible, landing sPeeds are relatively higher than for canrlxrable conventional airplanes. D, Three-surface lirplanes. control surfaces placed in the taiL have longer rsrent arrns than those p)-aced in t]"e nose, tius .re npre effective. 5o htly bother with con-

t.ro] surfaces in the nose?

E. leadinq Edqe Devices, such as slots and slats. th1n airfoils, and other airfoj-ls

15 that are subject to leadlng edge separation, can benefit frsn these devices. GA aj-redge separation foils, hc,wevlr. ajre soft-stall- airfo1ls, htlich n*ans that lead-ing jfiprovement. Ttlere are offer much is not a problern, hence slots and slatsS cannot nDVe out fldn t]1e that novable slats case of tv,o exceplions, honEver. First, in the the insrmply frcm wil-l result lift ;rrea rrDre I leading edge and increase the wing (nose positive up) a sl-ats contribute edge Secondly. leading crease of iing "r.u. large pitchj"ng nEnent due to negative l-arge the offset pitching -traiung nterrent that can help of tiese edge devices, of leading advantages edge flaps. In spite tDtential with C,e airioils, the prir.nry effort at lift aug[rEntation should be \,rith effective trailing edge f1aps. F. Case Study, Rutan Canards, Figure 3I sho\ns that Rutan used fhe GAwt-l airfoil scaled \^rith its high Gn, E 6TA{-rhick"==-?6;-6-ari-Eze. Ttre cAw-l airfoil, however, to contributing travel, Pitch stabi-lity Probhas a considerable center of pressule Ioaded ( 1q"er a forward Rutan chose terns. Accord.ingly, for the successor l-ong-Eze, j:nprove pitch The Long-Eze Ho^'ever stabil-ity. Gn, Io,.rer c.P. tjcavel ) airfoil to ' wing, the lightly loaded nain 1ar9e, with such a vrby? airfoil is a turbufent airfoifwing. I donrt have an flonr stall laminar soft Gn, be a fs"r natural choice Seenls tso ans!',er to t].is puzzle.

16

Postscript As stated in the Introductsion above, tJre original NACA airfoils \,{ere never intended for astual airplane use, and, according.Ly, "GA Airfoils" has been eritten to address this need. tn retrospect, one must ask why NASA, in the forty-odd years since the NACA airfoil uork was done, has rnade no effort sJmilar to "cA Aarfoifs"? Hovr fiuch valuable tjne and effort. has been lost, and hc,vr nnny precious lives have been needlessly wasted, because llA.SA failed to address this problernz They certainly must have recognized the need, so why dj-dn't they acc? vitry did they fail to put an end to the lrlaLh that the I,IACA airfoifs were astual airplane airfoils, and why didn't they it that l,IAcA's mistakes and crnissions needed correctlon? It is trard to think of arr ans$er to these questions without beccnring cynical ' one possible explanation is ttlat NASA doesn't knctu hc'v/ !o do the job. TtEt is hard to believe, ho,i/ever, in vielr of the astroncndcal budget tllat l.IAsA is bl-essed wi-th each year to pay for talent and facilities. Another possible er
17 LIST OF REFERE}JCES

l. Abbott, I.H.,

and Von Doenhoff, A.E., "Theory Dover Publications. NYc, 1959. Available fron Oshkosh WI 54903-3086. Publication +2I-37f77.

of wing sections, the

EAA

b@kstore,

2. von I'lises, "Theory of F1ight'J Dover Publications, |{YC, 1959.

3.

Epp1er, R., "science and Technology of l.ovJ Speed and l4otorless Fli.ght" ' conference hrbLication +2085, Ms,A Langley R.c., 1979. Prouty, R.w., "Helicopter Aerodynamics". Eppler, R., and Scnprs, D., ''A ccrnputer Program for the Design and Analysis of l.ow speed Airfoil-s", !&qsA N80-29254, NASA Iangley R.C., 1980. Sawyer, R.D., 'A Program for Deg and Analyzing Airfoils, Airfoil II". Airware. P.o. Box 295, Canton Cf 06019, 1985. Saners. D., "Design arld ExperijTEntal Results for a Flapped Natural Lanrinar Flo,r Airfoil for General Aviation Applications, |IASA 1P #1865, NASA langley R.C. , June 1981. Holmes, et al- , "t'latllral Lann-inar Flold ExperjjrEnts on i'4odern AirPlane Surf aces", l.lASA 'IP #2256, NA,SA Iingfey R.C. , June 1984. Eppler, R.. "Alrfoi] Design and Data', u. of stuttgart, springer-verlag NASA

4. 5. 6.

7. 8. 9.

NYC, 1990.

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KII'FOX

SPEEDSTER

itA

Wirh a look relrriniscenl ofrhe.rcing fil:ine\ oftlre.l(l s. the Killbx Spcedslers{ruls itstlrff. Fl\'orah[: acrodynl].nlc churacleri\ficr ard an fi{l hf Rot!t c) l: rigin3 l:j\. it lol perfunnance. Chssic looks ud leadin! edge.ngrreeing xllo*\ il top sleed oi 5lintes ir\ rornxl rtlll \peed. oilerinf ntarimunr eiljcjcncy and sllcl-\'. The Specdstcr refre\cnls aarl spo pe bnnrncc ;rnd lnluL :r, .r prirc r'rrr r.rrr lflorrl. Worid renown lerobaljc pilorJinr F.! klin dcnto rtralcd thc Spe.dster xl O\hKosh 9l ard srve ll rale reriews, crlljng il".'\ lrcrl jiltjr llj$hne. I $dnl onel '

3OJ-i,tz-

?e,acen]

300-D Airport Rd., Marcouche, Quebcc, C'anada.!7K 3C1 Dear Mr. Ribicq

I

arn intleed using thc ir-

GA 30ll-315 airf,oil on lhe Peliean < ll" > and wo arc vcry happy l:ith

Jcan-Iicnf Lepage, P.ling^ Presidont

soN€{\Rl FLETCHER BURNS REPORTS From lhe Soneror Newslefer

ON HIS SONERAI II WITH RIBLETT AIRFOIT ( '\e /.r' a7 uAci (l -ztz) 1

The wings ore thjcker thon normai ofter o beni

\ring on my woy lo Oshkosh (which ls onother story). i corne up wlth o 15% ihicker oirioil lrom

ll.

don't ihink it slowed me down ol qll. l've sondboQced them down to I G's Horry Riblett ond I love

I

JAt/ tqss'

stolic wiihoul a wrinkle. Thick€r ls strongerl This is o generol oviotion oirfoll not o pylon roce oirfoll. ii

lcnd! muclr softer now. climbs belter wlih lwo cbocrd cnd lhe roll rcle reolly improved (oihough i.i didn'i need ta).

hh

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A

n

31 fr3t5

Technicot counselor News 7

f t&uR€ l1

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A New Wing for the Protech PT-z AirPlane ln Januarv oi 1993 Ken Fogers called me and iold me that he was disaopo nted with the perlo'mance ol his Subaru Leoacv oowered Protech PT'2 (see Conlacll isslre t11 ior en;ine rnstallalion oetails) ln thrs same issue of Contacll wa"s an a.trcle lhal I had written describing on of my airtorls GA 30U-613.5. This airfoil is designed io be a replacement lor hio'r-li+t 'Cub" type applications and Ken wondered if it miqhinot be a good choice for the PT-2. I assured him that it ;ould be. but suggested that since his arrplane was comDlere and {lying. there may be something that we could do to "patch ..:p" the oid wtag Acco'dingly Ken sent the details bf the old wing io me, and I made a perlormance analvsis usino the NASA "Eppler' code

{+

l'!5rlf Sibaetf 415 Ribtett Lane W,-lrninglon

t€

198t8

paz) 994 0479

however, Ken iell ihat in lhe long run it would be betler for him lo invest his etions in a new wing so in October oi 1993

he tore the old wings apart, salvaged whai he colld and began bujlding a new set oi wings using the GA 30U-613.5 airfoil.

The new \ryings include a set of Hoerne. wing lips that I sketched for Ken; lhey result in the wingspan being reduced by 16 inches. Since the new airloil has a di{'lerent lift curve that of the old wing it was necessary to decrease lhe angle of incidence ot the new wing, and also the existing horizontal slabilizer, by 4 degrees-

(pR6f trt, com-nercialized for PC use as'Aidoil code, but il qives e\cel'e4t

it" Tni. ir a simole

resulls, especialiy concerning laminar,turbuleni transition, llow separation, elc. The analvsis showed that the existrng airfoil has a separition problem on the botlom suriace near the nose at high speed and also a similar problem on the top sudace at 70 percent o{ the chord at allspeeds. This agreed with Ken s flight lest experience with the airplane, which showed

a low cruise speed, high landing speed'

and

poor rale of climb. Accordingly, lsuggested we attack the top surface problem first by installing

an array oi vorlex generators (VT) along lhe entire span al .70 C, in an atiempi to'Yill in" the separation problem in the "low spot' there, which he did. These VGs are simple, small pieces 01 bent sheei metal, glued to the wing sur{ace at a slight angle to the slipstream, and

Ken Rogers' n€w rring undel ggnstruction in January ot 1994.

can oflen cure separation probiems.

Ken flew the airplane in August 1994 and reported these results:

Sefore

85MPH Cruise speed 90 Top speed 6tr65 Stall speed-no flaps St3ll speed-w/rlaps and power 50'55 Rat€ ol

5m

climb(FPM)

After 100MPH 11o 45 35

"betterl"

In addition, Ken reports that the siall is vary genlle and

predictable, and that the handling characterislics are bettet at all spesds. An unexpected benelil is that the engine oil

temperalure now run 15 degrees cooler, due no doubt to the reduced drag of the new wing! Comparison ot the original PT-2 and new 6A 3oU-613.5 tldoils, Note lhe localion of the vortex generalo.s apptied io ths original wing to promote lurbulenl llow. Evidently the problem was quite severe, howeve., since Ken reponed that the vGs helped only a little bit, especially in prodr.rcrng sl ghtly bener aileron control, a slight imorovement in rate rn cl mb. and better handling at cruise speed. Overall,

Ken is alrue experimenter and is lo be congratuiated lor his perseverance and "can do" atlitude. He says, ''lt it ain't-righl, ix it". t would be glad to furnish details oi the new airloil or you can simply reler to ! issue #'1 1. For details of the new wing consiruction I suggest you Ken Rogers at 1450 Konnowac Road, Moxee WA 98936, or call him at {3€A 248-1a13. HB

{t1

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35 Aircrrft

Prediction (see a_tso figure 2l) Aircraft pcrformancc can bc cstimated from wind tunncl (compurer) data using formulas from standard tcxlbooks, which wc will summarizc below. Thcrs arc thrce dimensionlcss cocfficicnls of pcrformancc dctcrmincd for cach anglc of sltack as Performance

follows:

Ct = wing lift

coefficient

Ca = winS drag cocfficicnt C6 = wing momenl cocflicient From thcse. quantitative valucs as follows:

of lifi,

drag, and pitching momcnt can bc calculated

L = lifr = Clal Sw V2, pounds D = drag = ta* Sw v2, pounds M = pirching iooment = C.f 2 S* V2 C, foot wberc:

p=

mass dcnsity

of

Sw = wing arca, square

standard air =

pounds

-002378 @ sca lcvel .m1928 @ 7000 fr. .m1756 @ 10000 ft.

fcEt

V = airspeed, fectlsccond C = wing MAC (avcragc chord),

fcer

Thc tcrm p n Vz appears in all thrcc basic formulas, and "dyaamic pressurc", q, pounds/ft2.

is

somctimcs known

as

Notc that thc pitching momcnt (in wind tunncl tcsts) could be mcasurcd about any refcrencc point, but for conveniencc and standardization the quaner-chord point (C/4) is used. A ncgativc pitching moment is nosc dowl. Ccnter of Prcssurc = CI.=Cl4-[Csr/Cr(C)].

Thc flow coDdition (Rcynolds number = Rn) for cach wind tunncl tcst is mcasured and cootrollcd. Although Rn can bc dctermincd cxactly, for practical purposcs it can be approximated as follows: Rn = 90ffi (MPH) (wing chord, ft) Thus, an airplanc with a 4 ft. wing chord flying at 100 MPH has a Rcynolds number of approrimately 3.6 x 106 (3.6 million), somctimcs writtcn as 3.6E6. As wing chord and spccd decrcase, so does Rn, and performance drops slightly. Pcrformancc drops

rapidly bclow

R-n=5E5.

Test rcsults are usually givcn for wings with iDfiDitc aspect ratios. No significalt crror is introduccd down to an aspect ratio of abour 7, bclow which thc data should bc adjustcd in accordance with proccdurcs found in standard lcxt books.

is takcn rrith a pcrfectly smoorh surface (r=0). Incrcasing dcgrccs of surface roughness degrade the pcrformancc significantly. A surfacc faclor of r=4 approximalcs a wing surface wcll contaminaled with bugs, Laminar flow wings suffer nost. Most data

Usc

a "wing cfficiency" factor =.85 for

non-uniform span loading.

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COilPUTER

38 A

^JALYSIS

Eppler program)

A I RFIII L- i i. ERSIDnI 1- ?(l

proqram for design and analysis

air+oi1s

program are

o+ this

Fortions

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COFYFIGHT 1985, 19Bb

by A1

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11

4IRFtrIL,all5 UNA

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8.4-)O 1{:r. C)1:r NX ELATIVE TO THE 52 1 . {:)(:r{)()O .445 . Bi9

5. r li:);/,

TH I CI,INESS

-

(:)tl7. FLAF'

. (:'(:) DEGREES DEFLEI

1.(:){r . ()(:] !. ()(l :i. {:x_} 4.(:}(l (:r{:r -1.(r[r 1o . (J{:r 18. il(:, 14 . ()il Y VELOCITY DISTRIBUTIONS FOR THE AEOVE ANGLES OF CHORD LINE , r_)(:){)a_){:} 5E -. Ar5 858 ..8r-)g A57 .856 ?4 I nurler I Drta - 2-?6-19!A 1? .

hA t1 43tS

6.(iC ATTACF

y': Loca" \'/e uac-,r\ Vo. Fgg1

StftEA.\ y'eLa.tfu

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af,l5 ANGLE OF ATTACIT1 FELATM T0 THE trHORD LINE SUT4HARY AIRFOIL1 : 2.79 DEGREES * ALFHAO INDICATES BLIBELE ANALOG LONGER THAN . {)f,{] R = 6l:)O(l{)C){:} MU =.1 R = ?OCICIC)OO HU =: _1_Cro DEGREES =1S TURET S SEP CD UF PEF , 5{j45 . crr]34 - C,C)O{:| LEIIER .5865 . OO(IO . CrO?g TOTAL CL = .142 CD - . ol:t64 cM = -. ('529 ALF.HA = , {II1 DEGREES l STURB SEP CD UF'PER .517E1 S . (ittf,7 -O{)(){r (:lcx:r{:} LOWER .541C) . , (tct?7 TOTAL cL = .25? CD = . (i064 (1559 CH = -. ALPHA = 1, O(r DEGREES l STURE S SEP CD UFFER ,5f,49 . (){:)(l{:l , (:rcr4 t-OltEF .424(.t . C)C)(-r(r . C){)25 TOTAL CL = .362 CD = , ()a-t65 Ctl = -,{l=B? (rr_r ALF,HA = ?, DEGREES l STURE 5 SEF CD UF'PER .549f, . OOC){} . o(r4= ._)r)OC' LOU]ER .3Ct77 . . oo2f, TOTAL CL = .477 CD = . 0.-166 CM = -.('619 ALF'HA = f,. C)Cr DEGREES 1S TURB S SEP rJa_r46 CD UF'PER ,565C' , Cr(,()C) . ()ClC)Cr LOWEF ,3734 . . c,c) 1g TOTAL CL = ,5AA_,CD = . oa-t64 {:)69() CH = ALFHA = 4,Cr{' DEGREES r STURE S sEP CD UF.FER .=794 . CrOC)tr . of-r49 (r(r16 .3777 . . LOWER {)O{iO ToTAL CL = .692 CD = . c)o63 Cl4 = --(t681 O(r DEGREES ALFHA = 6. CD l STURE S SEP UFFER .6Ct7t - {tc).-){r . C)(r57 LOhIEF .24:E - CIOC)() .c)o12 TOTAL CL = .912 CD = Cl4 = --8t744 ALF.HA

(:)

? 5. TURB S SEP 557f, , . 5944 . OOC)tt C){rr_x_r

CL =

.142 CD

= cH = -.t)529

CD

. C){:r51 . (:)f_125 , Q(r56

2 S TUREI S(jtlaj(-) SEF CD . . (-){rf,f, - 573f, .5845 . OCI{-)C) . Qtr!4 . c\:t37 cN = _,(:,559 ? S TURE S(J{rctr-) sEF CD . SASS , , C)4r=5 .3723 . Cr()OC) . c)o22 CL = ,f,6?_.._1589 CD = . ctct17 cM = 2 S TURB S SEP CD .=97t . OOOC) - oof,B r-)Ol1 . 557r-) , C){rCrO , CL = .472_.1:)619 CD = . c)c)s8 CM = ? 5 TURB 5 sEP CD .6t.t67 , OC)OO . oQ40 . . OCIC)O , QC) l9 CL=4?A .5El2 CD = . oc)59 = CM o55O = -. 2 S TURE 5r-lOOCr SEP CD . E49t . oo45 .3772 , OOC,() -, oo 1B CL = .692 CD = . C)C)64 Cl4 = -. C)681 CD 2 S TURF S.r sEP 196 .9476 . (rO.-)O . cxlB4 3756 . . C)CtlS cL = ,89? CD = . t (t97 CM = -. O696 _

Ftduae

a4'3

41 ANGLE OF ATTACIi: RELATIVE TO THE CHORD LINE SUMI,IARY AIRFOIL af,l5 = ?. :9 DEGREES * ALFHA{I INDICATES BUEELE ANALOG LONGE R THAN . (:,f,O R = 6l:)(:)(:)0(-r( ) MU=3 R = 2(r{:)O(:,rf(j HU

ALPHA =

S TURE S

1

LONEF

TOTAL

CL

ALFHA = 1(J. I c UPPER LOTJEF

TOTAL

ALPHA = UF,F'ER

LOUIEF

TOTAL

CL

I

1.

CL

ALFHA = 14, 1 UF.PER 1. LOUJEF

TOTAL

CL

ALFHA = 16. I UF,PER

LONER

TtrTAL

trL

ALFHA = 18. C){] DE G 1 s TUFB UPFER 1. Cr23{r (lalt)o LOWER

TOTAL

CL

CD

a-)

1

_

DH

------

!,i

SEF

9812 . Cr4L9 . (rE . Qcr 10 .296L , (rcr)(r .(:r115 cL = 1,._)86 CD = CM = -. C)699 SEF CD S TURE S(:)822 . (11 f,6 1, O167 . . C)CrC)7 . 2081 - (]{:,{_x:r cL = 1.?52 CD = . c) 14f, CM = -.Cr631 S SEF CD 2 S TIJRB 1294 . C)16f, 1. (,1E}6 . (:r(rC)C) .1196 . . {Xr{:}S CL = 1.4(lO CD = ,.-1169 CM = -. OEB6 2 S TUREI S SEF CD I.t)797 .1gB(r .t:r!97 . (r69C) . {)Orjrl , O()(-)4 cL = 1.52? CD = .Q?(:rl CM = -. C)5Of, ? 5 TURE S SEF CD 1, C)?10 .2545 . O2f,9 . (Ja-)oa-) , ()()r-'a-) . otlll? cL = 1.619 CD = . C)241 CM = -. (:)4?6 ? 5 TURE S SEF CD 1.C):S5 . Ct297 ()o(:)f-) .. f,f,l2 o{x)o . (lcr{]? CL = 1.6€l? trD = .(t299 -, Of,7(l 0 DetrCH- =Z-?s-lr9{' 6A 3-i A3t{ ,

UPF.ER

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Page 44

IRST FLIGHT OF SENECA WITH MODIFIED WING SCHEDULED - National Aeronaulic: and l$ad-EAtnin-istrarion will supervis€ the {irst flight ol a Piper Seneca next month modified with a -Snew wing design that promises major performance improvemeflt3. The wing assembly for the aircraft - designated as the NASA GAW-!.- is being built and installed on the aircraft 8t Piper's Lakeland, Fla., facility. The low-speed airfoil features full-gan power flaps and spoilen for lateral control. Wind tunnel tests with models have indicated that the netv airfoil will provide inqqelq! of 90 oer cgnt in range,80 ocr-,cent in the single+ngine-rate+f+limb, 30 oer-ce?t in maximum lift, in cruise speed. Although the rving is being built by Piper g9_gg. c_elt-tgup and a;E install€d on a Seneca, NASA spokesmen emphasired that the program is designed to provide a more efficient wing for a wide range of generil aviation aircralt, not iust the Seneca. A full flight resr program will be conducted at NASA's Langley, Va., research facility after initial flights are completed in Florida. " AT u, fAcLtec-

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APPnDIX

I -

49

Bas.rc Thickness Forms.

T - 84stL a*rc
synretrical- shapes A ' "cusp' TrPe 7 Atc<+v€ss D tsrRrgurrorts (

. l5t thick)

GA 30 Aotl (nrRca oors)'

GA 3s-Ots INACA

,

Ll-ot5)

QA 31- 615 (,vncn 6+ -arr)

GA

4o-ots

.

{lncn al-ors)

o

lo

?.o

go

ao

ta

Lo

llote- For thicknesses other tllan l5t, these sba[Es up or dcnnr to the desired thickness.

.ro

go

qo

nc

nEy be sca]ed d-irectly

f I6LJAE -L-I

50 FoRmS

a - BAsrc THrcKt.]gsl

B.

PREFe-RR 1-,7

'fuo

Cus P

TF

(

symrEtrical shapes,

tc
thick

)

s. otsTRtgullarJs

Y = 6A 30-o

158

TRANsttT ror'), R =6xtoL

rs

GA 35AOl5 (ueca ut aors)

6A 37nots (NAcn 61 Ao rs)

CrA

4oAots

ttote- For thicknesses otier tjlan l'5t' these shapes up or do.rn to the desired thickness '

may be scaled

directfy

Frh T'L

-

APPNDIX rA

ctrso Tv.pe Thickness

Feb 94 sta 0.00

0

Ord 0. o00

1.090

0. 25

0,50 o.75 L 2

1.856 2-367 3 .264 4,443 5.250 5.853 6.681 7,172 7.427 7 .502 7.436

.25 .50

5.00

7 .50 10.00 15.00 20.00

25. 00 30. o0

35.00 40,00 45.00 50.oo 55,00 60.00

6.976 6.518 6.

75.00 80,00 85.O0

90.00 95.00 100.00 rB

Feb

-

ie1

5.704 5.166 4.580 3.950 3.279 2 .566 1.810 1.008 o.158

65.OO 70. oo

APPENDTX

015

Distributions

63-015

ord

0. o00

o.a75 I .204

L452

I .874

2.610 3.648 4 .427 5.055 6 - 011 6 .693

7.L55

7.42I

7.500 7 .346 7.O99

.665 6.108 5.453 6

4

.72I

3.934 3.119 2.310 1.541 0.852 o.300 o.000

(GA 30A,

35-' 37-'

54-01-5

65-015

r.442

r.702

ord 0.000 0.865 1,208 1.456

.528 3.504 4 .240 4 .442 5.785 6.480 6 .945 7 .379 7.442 7.473 2

7

.224

6.810 6 .266 5.620 4.895 4.1,13 3 -296

2.472 L.677 0.950 0.346 0. ooo

94

0.00

.324 .245 3.959

2 3

s04 .223

5-

6

6.764 7 -396

7.49A

7 - 427 7 .168

6.720 6 . 1.18

5.403 4.600 3.744 2.858 L .977 1.144 o-42A 0.000

ltlickness Distributions (GA 30-, 35A, 37A, 644015 4 04015 30-o15 63AO15

o -25

0.50 u. ta 1 .25

2.50 5.00 7.50 10.00 L5.oo 20.00 25.OO

30.00 35.OO

40.00 45.00 50. o0

55.00 60.00 65.00 70. o0 75. OO

80.00 85.00 90.00 95.00

ord

0.000 1.090 r .527 1,856 2 .367 3 .264 4 .443 5.250 5.853 6.581 7.172 7.427 7 ,502 7.440 7 .265 7.000 6.655 6 .240 5,755 5.190 4.540 3.817 3.053 2.290 L

.527

o.753

ord 0.000 0.a75 L .203

ord

o. o00

1.44S

0.855 1.l-93 1,436

.3A2

2.508 J.477 4 .202

1.844 2 .579 3.518 4

4.997 5.942 5.619

7.O91,

.344 .496 7.435 7 .2L5 6.858 7 7

6

.387

5.820 5.L73 4,468

3.73I

.99L 2.252 I .5L2 2

o

-772

r.815

I.L24

t_.356

I -702 2 -324 3 -245

3.959 .555 5.504 6 -223 6.764 4

7 -270

7.L52 7 .396

.463 7 .487 7,313 6.974 5 .5L7 5.956 5.311 7

4.

600

.847 3,084 2 .321 1.558 3

o.795 n - o??

40A)

ord 0.000 0.830

4 -799

5.732 6 .423 6.926

51

ord 0.000 o.830 L .724 1.356

I,Io Cusp

sta

40-)

7-

494

.427 7 .168 6 -720 6.118 5.403 4 .600 3.744 2.885 2.065 1.290 0.600 n. nnn 7

Ft6 T-3

APPENDIX

II -

Feb

l4ean

Lines

(

camber

canber

94

sta

GA-2

0.000 0.060 0.116 0.169

0. oo o .25

0.50 o.75

r.25

o -263

0.450 o.715 o .892 1.023 L .244 I .420

2-50 5.00 7.50 L0.00 15.00 20.00 25.00 30.00 35.00

r .557 1.663

r.737

t-.780

40. o0

r.792

45.00 50.00 55.00

1.764

I .672

50. o0

L

65.00 70.00 75.00 80,00 85.00 90.00 95.00

.537

L.374 1,,189

0.991 o.793 0.595 0.396 0.198

lo0,00

o. o00

9- cAt oEA

?2. F.Le

Camber GA-

3

o.000 0.063

camber

0. o82 0.1 52

0.L12

0.000

o.770 o.275 0.500 0.852 1. tL8 1.335 1.683

.2L3 0.323 o.570 o.970 o

.307 ,597 2.Q46 1

L

?.473 2.776 3.010

1- 958

2-r73 .340 2.457 2 .524 2

3.!75 J.Zb9

.543 .499 .368 2-L7a

3 .296 3.234 3.065 2.818

2 2 2

I

-947

2

1.685 t . 404

.5t9

2.180 L .8L7 1.454 1.090 o-727 o.363 o.000

1. L23 0.843

.562 0,281 o

o. ooo

GA-6 0. o00 o o

.207

,29L 0.441 o.777 r .323 L.7A2 2-17A

.444 3.372 2

3 -7A6 4. t- 04

4 .329 4,458 4.494 4.410 4.L?9 3.843 3.435 2.973 2-474 1.982 L .487 0.991 0.496

o. ooo

t

UE^tt r-J

r.e-z tlliA (^.|at!.1,r4 t"E D16'

- a1.'5'

Camber GA-4

o. t-20

bA .|CA,J L,,\r65 arvD TJACA t^€A^f Lt'|/et -

A.nla*.

52

profiles)

trocr-@

'2t*L

/ec..'.7 fyk .__.1.. t ,1.1 :L C ,(lc 7-S't'q. e.c.c ?.to :1. e .es c L .ao oh e.(tc-

Co'Jaa'1ttt1-

-"

As:*A

\\r

x/L ro

.L

2.tah-

Fta

I

APPmDIX

_--

53

rII - Airfoil- ordinates.

\

i

E

iE

o8 8.f o

lu lE

II +l L)

6

t E

!

f !+

I

4 8,

cl r \l

2

2

J

a

oo ' dd

lJ .-r o (to .ri k ]Jlr ..r o

^'HY'

..1

;l

sl'

a[c zl l

I

2

.l

.-l !

llct

?.

9t{

o

o

El p jlel #u EI

E

ri \'

tu Oo

OG

ai

f- li' rfd

zz \o

t'> + OF Ec oi F

Hl s

4

-9 I

o

9 a

\

lr E ln

!h

\' !'

at

a$

.

T .P

z

s

PilFE

rt88

;3t t

I

E:r I

I

r

a!t t

Ili

EI

EI

glt

f

dHiS: -. x

F o>

E

5;;E;

.iFtReda F=rq3x

5i

g I

I

If

-

sEe

ot

rl

, i

i

c:4

e333:

e

t a ,

l -Elr ,9 E d F 5 6 0--

3^

I .;. ; EEEE; :: 5 c€. a.l

U

I 3 1

2 zii,o;E=

a

gigi II t

I

gifrE=

g

'z

I

I

tlrrl

I

iE

!t

iz

Fl

CO

I

.lJ

6

!o

1*u

so

:

E

+) .-t c

1)

EI .,

\!; OJ

c) d,

5ig=i 5S5t8

6

?g : r. :' f t-

h

o /1,

_o =

dl

6* !.r

'.c,

a o

cl

t J:t

6J

II

^Fit)

c<

(,1

+l t

o

Bl ol

.t

+J

lg

)

,_a

0)

\

I I

I

o

tFSFB

9 o< E .9o -u: -.i I

!-! s >r <'a s'; t! | aZE' A i I= E Er

ii

0,

]J

|!

!llo fc !Jtr g

!U)-t

g!! !r-O of,..i )Ll

+J

!,)

s8.I irrd

. .ll'' .i tlJl o p

O Idjtc l! !. .-i tJI

!J l.l tr I L,

U c)

d ulc c

o ol..r

fl'.g lo c

i:I E Eii:€ ;ii ; EE€ E: !!t i i s:;€

gle E 8 4cl'n rJl

Ia-

t*[He nlo r,

tli ;€Es,i l3$

-. Cl-r.,

a StEEB F{'5'o!Il.

Irl-c .-l c n .r I rJ ql

11

ele E dsl.r B

E[e 3

eta

fr-I

q 6 -c o

...1

o

.lJ

.-l |!

LN

!

o

o

-1 ro

o

l.l

q IJ Itr

U

o .l-,)

c a a rd 0)

! 0)

ol 16

1 o

o o

a rd

u.

E

\t v v

I

F

c E U)

E -c

t)

*

+,

l{t

o

o

rtt

lr)

+J

c

3 a

]J t1

o

a !n 0,

U

-c ! OJ

u' a6

ct

oI

4

-.1

a.t

u')

o

.t)

o

1

o

)

tl 6

o

$

I (

o 0)

_c

.u OJ

r-.t

l[

U

(

o ]J

I

ll

t

8 I

I

0)

.lJ

\i\ r\

2

Fnf,-7

55 Feb

94

sta

30-015

ord

0.00 o .25 0.50 o.75

0.000 1.090

r.856

0.169 0.263 0.450 o.715 o.892 1.023 L-244 L .420 1.557 1.663

.367 3.268 4 .443 5 .250 5.853 6.681

.50 5.00 7 -50

10.00 L5, o0

7.I72

20 - oo

25.00 30.00 35.00 40. oo 45.00 50. o0 55.00 60.o0

7-

7 7 7

427

.502 .440 .265

7. O00

65. O0 70. o0

6.655 6 .240 5.755 5.190 4.540

100. o0

3.053 2 .290 L -527 o.?63 0.000

75.00 80.00 85.00 90.00 95.00

Feb

94

sta

0.00

3.81-7

0

015

Ord o.000 t-. o90

o-50 o -75 L 2

.25 .50

5.

OO

7.50 10.oo 15.O0

20.00 25.00 30. o0

35.00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 75.OO

80.00 85. O0 90. o0

95.00 100.00

GA- 2

0.000 0.060

2 2

Camber

L,856 2 .367 3 .268 4.443 5.250 5.853 6,681 7.172 7.427 7 .502

7.436 7 .254 6.976 6.618 6.191

R ?na

s.166 4.580 3,950 3,279 2-566 1.810 1.008 o. L58

0.1,16

r.737

.780 L.?92 L.764 L.672 1.537 L.374 1.189 0.991 o.793 0,595 0.396 0. r98 0.000

1

camber GA- 2

0.000 0.060 0.116 0,169 0.263 0.450 0.715 0.892 1.023 L -244 1.420 1 .557 1,663 r -737 1.?80 1.792

I.764

L.672 ! .537 L.374 1.1,89

0.991 o.793 0.595 0.396 0,198 o. o00

30-2L2

upper o.000 o -9J2 1.338 1.654 2-L57 3. 064 4.269 5.O92 5.705 6.589

?.rsa .499 .665 .689 .592 .392 7.088 6.664 6.L47 5.526 4.82L 4.045 3.235 2.427 1.618 0.808 0.000

7 7 7 7 ?

lower

0.000

-0.812

-1,.106

-1.316 -l-.631 -2.164 -2.A39 -3.308 -3.659 -4.101 -4 . 318

-4,385 -4.339

-4.2r5

-4.O32 -3.808 -3.560 -3.320 -3.067 -2.774 -2.443 -2,063

-1 .649 -l -237 -O.426 -O - 412

0.000

3042r2

upper 0.000 0.932 1.338 r-.654 ?.L57 3 .064 4.269 5.O92 5.705 6. s89 7.158 7 .499 7.565 7.6A6 7.583 7.373 7 .O5A 6.625 6. 100 5. so7 4.853 4. 151 3.415 2.64A 1.844 1,004 0.126

lower

0.o00 -0.81-2

-1,106 -1.316 -1,631.

-2.L64 -2 .839

-3.308 -3.659 -4.101 -4.318 -4.385 -4.339 -4 -2r2 -4 -O23 -3.7A9 -3.530 -3.281

-3 . 026

-2.759 -2-475 -2.L69 -1.830 -1,458

-L.O52 -o . 608

-0.126

30-21-8

30-215

upper o.000 1.150 1.543 2,O25 2.630 3 .718 5. 158 6.L42 6.a76 7.925 8.592 8.984 9.165 9.L77 9.045 a.792 8.419 7.9L2 7.292 6.564 5.729 4.808 3,846 2.885 1.923 o.961 0.000 3

lower 0.000 -L.030 -1.411 -1.687 -2.1o4 -2.818 -3.724 -4.358 -4.830 -5.437 -5.752 -5 . 870

-5.839 -5.703 -5.485 -5.208 -4.891 -4.564

-4.2I4

-3.816 -3.351 -2.426 -2.260 -1 695 .

-1.131 -0.565 0.000

0A2 t-5

upper 0.000 1 .150 1.643 2.O25 2,630 3.71S 5.158 6 -t42 6.876 7.925 8.592 8.984 9,1.65 9.]-73 9. O34 I . 768 8.382 7.A63 7 ,24r 6. 540 5.769 4.94r 4.072 3.16L 2.206 1.206 o.158

upper 0.000 1.368 1.948 2.396 3.103 4.372 6.O47 7,r92 LO47 9.26L 10.026 t 0.469 10.665 10.665 10.498 10.192 9.750 9.160 8.443 7 .602 6.637 5.57r 4 -457 3.343 2.?2e 1.114 0.000 3

lower 0.000 -1.030 -1.411 -1.687 -2,1.04

-2.

Sl.8 -1 -7 2a -4. 358

-4.830 -5.437 -5.752 -5.870 -5.839 -5.699 -5.47 -5 . 184 4

-4.854 -4.519 -4.16? -3.792 -3.391 -2,959 -2.446 -L.97L -1 .414 -0.81,0 -O.158

lower

0. o00 -L. ?44

-L,7L6 -2.058 -2.577 -3.472 - 4 .617

-5.408 -6. O01

-6,77i

-7 . L86 -7 ,355 -7 .339

-7.r9L

-6,938 -6.608

-6 .222

-5.816 -5.369 -4.854 -4,259 -3.589

-2.A7r

-2.153 -1.436 -0.718 0.000

0A218

upper 0. o00 1.368 1.948 2.396 3.103 4.372 6.O47 7.L92 a.o47 9.26L 10.026 10 .469 10.665 10.660 10.485 10.163 9.706 9.101 8.382 7.573 6.685 5.731 4.72a 3,674 2.568 1.408 0.190

lower 0,000 -r .244

-!.7L6 -2.0s8 -2 .577

-3.472

-4 - 617

-5.408 -6. 001 -6.773 -7.La6 -7. 355 -7.339

-7 .LA6

-6.925

-6 .57

9

-6.178 -5.757 -5.308

-4 . A25 -4 .307

-3.749

-3.r42 -2.444 -I .77 6 -1. OL2 -0.190

Fta f,-3

56 Feb

96

sta

30-015 Ord

0.00 o.25 0.50 0.75 L

0.000 1.090

25.00 30.00 35.00 40.00

O0

50,00 55.00 60.00 65.00 70.00 O0

85.

O0 O0

loo . o0

96

Sta 0.00 o .25 0.50 o.75

2.50 5. 7

OO

.50

10 . o0

15.00 20.00 25.00 30.o0

35.O0 40 . o0

45.O0 50. oo 55. OO

50.00 65.00 70.00 75.

OO

85.

OO

80.00 90.00 95.00 100.00

540

3.817 3.053 2 .290

90.00

Feb

0. oo0

5.190 4-

80.00 95.

-26a

.443 s.250 5.853 6,681 7.L72 7.42? 7 -502 7 .440 7 .265 7.000 6.555 6 .240

7.50

75.

o. ooo

3

4

OO

10. o0 15. O0 20. o0

45.

r-527 o.763

1.856 2 .367

2.50 5.

0.063 0.120 0.170 o.275 0.500 0.852 1.118 1.335 1.683 1.958 2.L73 2.340 2-457 2 .524 2-543 2 .499 2.364 2.L74 L .947 1.685 1.404 L.L23 0.843 0.562 0.281

| .527

.25

0

Camber GA-3 0. o00

015

ord o.000 1. O90 L .527

1.856 2 .367 3.268 4.443 5.250 5.853 6.581 7.172 7.427 7 .502 ?.436 7 .254 6.976 6.618 6.191 5.704 5.165 4.580 3.950 3.279 2 .566 1.810 1.008 0. t 58

canber GA-3

o.000 0. 063

0.120 0.170 o.275 0.500 o.852 1. t l-8

1.335 1.583 1.958

2.r73

?.340 2.457 2 .524 2-543 2.499 2.368

2.r74

L .947 t-.685 1.404 1.123 0.843 0.562 o.281 o.000

30-312

upper 0.000 0.935 I.342 1.655 2 -169 3.114 4 .406 5.318 6.Or7 7 .O2A 7 .696 8.115 a.J42 8,409 8.336 8.143 7.823 7.360 6 .782 6 . O99 5,3r7 4.458 3.565 2.675 r.7a4 0.891 0.000 3

lower

0.000

-0.809 -1.102 -1.3l-5

-1. .619

-2.!L4

-2,702 -3.082 -3,347 -3 .662 -3.7AO

-3.769 -3.662 -3.495 -3.288 -3.O57 -2 .425

-2.624 -2.426 -2.205 -r ,947 -1.650 -1.319 -0.989 -0.660 -O.329 0.000

0A31,2

upper 0. o00 0.935 r.342 1.655 2,t69 3.114 4.406 5.318 6.017 7.O28 7,696 8,115 4.142 8.406 8,J27 a.L24 7.793 7.32:I 6 .7 4r 6. O80 5.349 4.564 3 .7 46 2.A96 2.010 1.087 0.126

lor.ver

0.000

-0.809 -1.102

-1 .315

-1.619

-2.rL4 -2.702 -3. Oa2 -3.347 -3.662 -3.780 -3.769

-3 .662 -3 .492

-3.279 -3.038 -2.795 -2.585 -2. 385 -2 . 186

-L.9'79 -L.756 -1.500 -1.210 -o.886 -O.525 -0.126

30-315

upper lotrer o.000 0. oo0 1.153 -L . O27

r.647 -r .407 2.026 2,642 3.768 5.295 6.368 7.1.88 8.364 9,130 9.600 9.842 9 .897 9.789 9 ,543 9.154 8.608 7 .933 7.L37 6.225 5,22r 4,L76 3.133 2.089 t.044 0,000

-1.686 -2.O92 -2

-7 6e

-3.591

-4.r32

-4. s18 -4.994 -5 .2L4

-5.254

-5.!62

-4.983 -4.74L -4 .457

-4.156 -3.872 -3.577 -3.243 -2.855 -2.4L3 -1.930

-r-447

-O.965

-0.482 0.000

30A315

upper 0.000 1.153 L,647 2.026 2.642 3.764 5.295 6.364 7.l-88 8.364 9.130 9.600 9.842 9.893 9.778 9.519 9.LL7 8.559 7 .AA2 7.113 6.265 5. 354 4 .402 3.409 2.372 L.249 0.158

lower

0.000 -L.O27

-I.407

-1.686 -2 -O92 -? -768 -3.591 -4.L32 -4.51-8

-4.998 -5 -2L4

-5.?54 -5.162 -4.979 -4.730 -4.433 -4.119 -3.823 -3.525 -3.2t9 -2.895 -2.546 -2. 156 -L.7 23

-I .248 -O .7 27

-O.158

30-318

upper 0. oo0 L,37L 1.952 2.397 3.115 4.422 6.184 7 .4I8 8.359 9.700 L0.564 11.085 11 .342 11. 385 rr.242 10.943 10.485 9.856 9.084 8.175 7 .L31 5.984 4,747 3.591 2.394 L.r97 0.000 3

Iower 0.000

-L.245

-L -712

-2. O57 -2.565 -3.422 -4.480 -5. 18 2 -5.689 -6.334 -6 . 648

-5,739

-6 .662

-6,47L -6.194 -5 . 857 -5 .487

-5.l-20

-4 -7 28

4 .247 -3.?63 -3.176

-

-2.54I

-1.905 -1.270 -0.635 0.000

0A318

upper 0 . o00 1. 371 r.952 2-397 3.115 4.422 6.144 7 .4]-4 8.359 9.700 10.564 11.085 LL.342 11.380 IL.229 10.914 10.441 9 -797 9.O23 8.146 7 .]-8I 6 -L44 s.058 3.922 2,734 1.491 0. 190

lower

0.000 -L ,245

-L.7L2

-2 . O57 -2 ,565

-3.422 -4.480 -5. 182 -5.689 -6.334 -6.648 -6.739 -6 .662 -6.466 -6,181 -5.828 -5 -443 -5. 06 t-4.667 -4 -252 -3.811 -3.336 -2.812 -2.236 -1 .610 -O.929

-0.190

FrE trr -4

Feb

94

Sta 0.00 0.25 0,50

30-o15

ord

o. o00 1.090 L .5?7

o.?5

1.856 .367 3.268

2 2

.50

s.00

4.443 5.250 5.853

7 -50

10. o0

15.00

6.681 7.172

20. o0

25.00

.502 7.440 7 .265 7.000 6.655

30. 00 35.O0

7

40.00 45.OO 50. o0

55. OO 60. oo 65. O0

6 -240

5.755 5.190 4.540 3.817 3.053 2 .290

70.o0

75. O0 80.00 85. OO 90. oo 95. O0 l-o0.00

Feb

94

sta

o. o0

.25 0.50 o.75 L .25 2.50 o

5.

O0

7.50 10. o0

15.00 20.00 25.00 30.o0 35.00 40.o0 45.

O0

50,00

55. OO 60. o0

65.00 70.00

75.

OO

80.00 85.00 90. o0 95.O0 100. oo

.527 o.763 L

o.000 0

015

ord o,000 1.090 r .527 1.856 2.367 3.

268

4-44J 5.250 5.853 6.681

7.172 7.427 7 .502 7.4J6 7 .254 6 -976

6.618 6.191 5.704 5.166 4.580 3.950 3.279 2 .556 1.810 1.008 o.158

carnber GA- 4

0.000 o.082

o.r52 o.2l-3 0.323 0.570 o.970 1.307 L.597 2.086 2.473 2.776 .010 3.175 3 -269 3

.296 3.234 3.065 3

2.8r-8 2 .5L9 2.180 1.817 1.454

r.090 o.727 0.363

0. o00

canber GA-4 0. oo0

0.082 0.152 o.2L3 0.323 0.570 0.970 I .307 L .597 2.046 2-473 2.776 3.01-0 3

-r75

.269 3 .296 3.234 3.065 2.818 2 .5L9 2.180 3

1.81-7

1.454 1.O90

o.727 0.363 0.000

30-412

upper 0.000 o.954 L.374 1.698 2.2I7 3 , r- 84 4.524 5-507 6 -279 7 .43L 8.211 8.718 9.Or2 9 .L27 9.081 8.896 I . 558 8. O57 7,422 6.67L 5. 8t- 2 4 -A7 L 3.896 2.922 1.949 o .971 0.000

lower

0. o00

.790 -1.070 -O

-r.272

-1 .57r -2.O44 -2 .544

-2.A93

-3 .085

-3.259

-3 . 265 -3.l_65 -2 -992

-2.777 -2 -543 -2.304 -2.090 -L.927

-I.786

-1.633 -L.452

-L .237

-0.988

-O.7 42

-O.495 -O .247

0.000

30A412

upper 0.000 o.954 L-374 1,698 2.2t7 3.1.84 4.524 5.507 6.279 7 .43L 8.211 8.718 9.0t 2 9 .LZ4 9.O72 a -477 8.528 8.018 7 .3AL 6.652 5.844 4.977 4.077 3.143 2-I75 1. L69 0 . 126

lower 0.000

-0.790 -1. O70

-r

.27

2

-1.571 -2.044 -2.544 -2 .891 -3. O85 -3 .259 -3 .265 -3.166 -2 ,992 -2 .77

4

-2.534 -2.245 -2 . 060

-1,888

-L .7 45

-1.514 -1,484 -1.343 -1.169 -0.963 -O.72! -0.443

-O.126

30-415

upper o.000 r.172 1.679 2.O69 2.690 3 .8 3B 5.413 6.557 7 .450 8.767 9.645 10.203 l-o. 512 10. 615 10.534 10.296 9. BB9 9.305 s.573 7-709 6.720 5.534 4.507 3.380 2.254 ).-L26 o.000 3

lower

0. o00

-1.008 -L .375 -l-.643 -2.O44 -2 .698 -3.473 -3.943 -4.256 -4.595 -4.699 -4 . 651 -4 .492 -4 .265

-3.996 -3.704

-3 .42t

-3.175 -2.937 -2.671 -2.360 -2.000 -L. 599 -1,200 -0.800 -0.400 0.000

044 15

upper o.000 L.L7? 1.679 2.069 2.690 3.838 5.413 6.557 7 .450 4.767 9.645 10.203 10.512 10.611 l0,523 LO .27 2 9.852 9.256 8.522 7.645 6.760 5.767 4.733 3 .656 2.537 1.37I0.158

Lower

0.000 -1. O08 -1.375 -1.64 3

-2. 044 -2.698 -3.473 -3.943 -4.256 -4.595 -4.699 -4.651

-4 .492

-4,261 -3.985 -3.680 -3.3S4 -3 - 126 -2 - 886

-2.647 -2.400 -2.133 -1.825 -I.4? 6 -t- . O83 -O.645

-0.158

3

0-418

upper 0.000 1.390 1.984 2.440 3 . 163 4.492 6,302 7 .607 8.62r 10.103 r.1.079 11.688 12.Ot2 12.103 LL.9A7 11.696 rL.220 10.553 9.724 B-747 7 .62a 6.397 5.118 3.B38 2,559 t.279 0.o00

57

lower

0.

000

-t.226

-1.680 -2.014 -2.5L7 -3 .352 -4.362 -4,993 -5.427 -5.931 -6.1-33

-6.136 -5.992 -5 -753 -5.449 -5.104

-4 .? 52 -4 - 423

-4.088 -3.709 -3.268 -2

-7 63

-2.210 -1.658 -1.105 -0.553 0.000

30A418

upper 0, o00 1.390 1.984 2.440 3 .163 4 -492 6.302 7 .607 8. 621 10.103 1I.079 11.688 L2 -OL? 12.098 IL.974 Lr.667 11.176 10.494 9.663 8.718 7.676 6.557 5.389 4 . t 69 2.899 1.573 o.190

Iower

0. o00

-I.226

-1.68O -2 . 0I4

-2.5I7 -3.352

-4.362 -4.993 -5.427 -5.931 -6.133 -6.136 -5 .99 2 -5.748 -5.436 -5. 07s -4 .708 -4.364 -4,O27 -3.680 -3_316

-2.923 -2.481 -1.989 -1.445 -0.847 -o.190

Fl41 [l-

S

58 Feb 94

sta

30-0ls

Ord 0.000 1.090 7 .527

o.00 0.50 0 ,75

1.

2 2

856

.367

.264 4.443 5.250 5.853 6,681

.50

3

5,00 7 .50 10.00 15.00 20.00 25.00 30.00

7

-L72

65. OO 70. 00

7.427 7 .502 7,440 7 .265 7.000 6,655 6 .240 5.755 5.190 4.540

100. oo

3.053 2 .290 r .527 o.763 o.000

35.O0

40.00 45.

O0

55.

O0

50.00 60.00 75.00 80.00 85.00 90.00 95.00

Feb

94

sta

o.00 0.25 0.50 o.75 2

.50

5.

O0

10.00 15.00 20. o0

25.00 30.00 35.O0

40.o0 45.00 50.00 55.

O0

60 . o0

65.00 70.o0 75.OO 80. o0

85.00 90.00 95.00 100 . o0

0

015

ord

o.000 1.O90

|-527

l-.856 2 .367 3.268 4.443 5.250 5.853 6.681

7.!72

.502 7.436 7 .254 6.976 6.618 6.191 5.704 5.166 4.580 3.950 7

3 2

.279

.566 1.8L0 1.008 o. 158

camber GA-6 o. ooo

0.112 o.207 o

. 291-

0.441 o.777 1.323

r.7az

?.L74 2.844 3 -372

3.746 4.104 4 .329 4.458 4.494 4,410 4.L79 3,843 3,435 2.973 2.474 r,.982 L.447 0.991 0.496 o. oo0

camber GA-6 0. oo0

0.112 .207 -29L 0.441 o.777 1.323 L.742 2.L78 2.444 3 -372 3.786 4.104 4 .329 4.458 4.494 4.410 4.L79 3.843 o o

2.973 2 .474 1.982 L .447 0.991,

.496 o.o00 o

30-6r2 upper fow€r 0.000 0.000 o - 984 -O.760 L.429 -1 .015 L.776 -1.194 2.335 -1.453 3.391 -I.837 4.877 -2.23t 5.982 -2 .4!8 6,860 -2 . 504 8.189 -2.50]9.110 -2 -366 9-72A -2.156 10.106 -1.898 10,281 -L -623 to.270 -1.354 10.094 -1.106 9 -7 34 -O.914 9-L7L -O.813 8.447 -O.76r 7 -587 -O .7 t7 6. 605 -O.659 5.532 -O -576 4 .424 -O.460 3.31-9 -O. 345 2.2r3 -0.2 31 1.106 -0 . 114 0.000 0.000 3

0A612

upper 0.000 o.984 r.429 r.776 2.335 3. 391 4.a77 5.9A2 6.860 8.1-89 9.110 9 -724 10.105

lower

0.000 -O.760

-1.015 -1.194 -1.453 -L.A37 -2.231 -2 -4L8 -2.504 -2.501 -2.366 -2.L56 -1.898

1o.278 -r.620

10.261 10.075 9 .704 9.132 8. 406 7.568 6.637 5.638 4.605 3. s40 2.439 1.302 o .].26

-1.345 -1.087

-O.884 -O-774 -O -720

-0.698

-O.691 -O-682

-0.541 -0.566

-O - 457

-0 . 310

-0.

12 6

30-61s

upper 0.000 I.202 ),.? 34 2.L47 2.808 4.045 5.766 7 .O32 8.031 9.525 10.544 11.213 11.606 LL.769 tr-72f 1 1.494 11.065 10 - 419 9. 598 8.625 7.513 6.295 5.035 3.777 2.518 1.259 0.000

lower

0.000 -O.978

-1.320 -1.565

-L ,926

-2.49L

-3 . r20 -3 .468 -3 .675 -3.437 -3,800 -3.641 -3.398 -3.111 -2 -ao7

-2.506 -2.245

-2.O6L

-I -9I2 -L755 -r.567

-l-.339 -1,071

-0 . 803

-0.536

-O .267

0.000

30A515

upper 0.000 L.202 1_.734 2.L47 2.808 4.045 5.766 7 -O32 8.031 9.525 10.544 LI.2L3 11.606 1.1 . 765 rI.712 11.470 11.028 1"o.370 9.547 8.601 7.553 6.424 5.261 4.053 2.801 1.504 0.158

3

loerer 0.000 -O,978

-1.320 -1.565 -L.925

-2.49I

-3.120 -3.468 -3.675 -3.837 -3 .800

-3.641 -3.398 -3

30-518

upper 0.000 L.420 2.O39 2.518 3. 281 4.699 6.655 8. 082 9.202 10.861 11,978 L2.694 13.106 13 .257 13,176 L2.894 12.396 lL.667 IO.749 9.663 8.421 7. O58 5.646 4-235 2.423 r -4L2 0.000

. LO7

-2.796 -2.482 -2.205 -2.oL2 -1.861

-\.73L -!.607 -!.472

-]-.297 -1.079 -0.819 -0.512 -O.158

-1 . 196

-L.625 -1.936 -2 -3 -4 -4

,399 .145 .

009

.518

-4.A46 -5.L73 -5 -234

-5.t26

-4.898

-4 . s99

-4.260

-3 - 906 -3 .57 6

-3.309 -3.063 -2.793 -2.4'75 -2 -LO2 -1.682 -1,-261

-0.

841

-O.420 0.000

04618

upper 0.000 1.420 2.039 2.518 3 .281 4 -699 6.655 8. O82 9 -202 10.86L 11.978 12 .698 13.106 L3.252 13.163 12 .865 1't

lower 0.000

'lq1

11.608 10.688 9.634 8.469 7 -2tA 5.9L7 4.566 3.163 1.706 o.190 Ftq

lower 0.000 -1.196

-t -625 -1.936 -2 -399 -3.145 -4 . 009

-4.518 -4.845 -5.173 -5.234 -5.126 -4.898 -4.594 -4.24'l -J -a77

-1

R11

-3. ?50

-3 .002 -2 -764 -2 .523

-2.262 -1.953 -r-.592 -1 .181 -O.7L4 -0.190

fft -{,

59 Feb

94

Sta

0. o0

o .25 0.50 o.75 1.25 2.50 5.00 7 .50 10.00

63-015

ord 0.000 o.875 1.204

I-462

Camber GA-2 0. o00

0.060 0.11-5

5.055 6.011 6.693

0.169 o .263 0.450 o.7L5 o.892 1.023 r .244 1.420

30. oo

7.421

1.663

40. o0

? -3A6 7 -O99

1.780

15.

OO

20.00 25.00 35.00 45.00

50 . o0

55. O0 60. o0

55.00 70.00 75.00 80.00 85.00

1.878 2.610 3.648 4-

427

7.500

1,.764

3.934 3.119

1.189

4.72I 2.31-0

100. oo

Feb 94

63A015

95.00

sta

0.00 0.25 0.50 o.75 2.50 5.O0 7 ,50

10.00

ord 0.000 o.475 1.203 1.448 1.844 2.579 3.61-8

4.342 4

.997

15. O0 20. oo

.942 6.619

25.00 30.o0 35.00 40.o0 4s.00 50.00 55.00

7 -O9L

60. oo 65. O0

70.00

75.OO

80.00 85.

OO

90.00 95.00 100.00

t -?92

6.665 5.l-os 5.453

1.541 0.852 o-300 o.000

90. o0

r-737

5

7.384 7.496 7.435 7

.21 5

6.858 6 .387 5.820 5

.I71

4.468 3.731 2.991 )

)qa

I -5!2

o.772 0.032

1_.672

r-537

r.374 0.991,

o.793 0.595 0.396 0.198 o. oo0 caltrber GA-2

o.oo0 0.060 0.116 0.169 o -263

0.450 o -7L5 0.892 1.023 r .244 L.420 1.663

t.737

1.780 L

-792

r.764

L .672 r .537

r-374 1.189 0.991 o -793

o-595 o.396 o.198 0-

000

35-212 l-ower 0.000

upper 0.000 0,760 r.o79 1.339 r.765 2.538 3.633 4.434 5.067 6.053 6.774 7.zAL 7 ,600 ? .737 7 .6A9 7.47L 7 .0S6 6.558 5. 899 5. 151 4, 336 3.486 2.64r 1.828 1..078 0.438 o.000 3

-0.640

-O.447

-1.001 -1.239 -1.638 -2.?O3

-2.650

-3.O21 -3.565 -3.934 -4.L6? -4 .27

4

-4.263 -4.L29 -3 -887 -3.568 -3 .2L4 -2.425 -2.403 -1.958 -1.504 -1.055 -0.638 -o.246 -0. 04 2 0.000

5A21.2

upper o.000 o.760 1.078 L -327 1.738 2.5L3 3.609 4.398 5.021 5.998 6.71_5 7 .230 7 .570 7.734 7.72A 7.564 ? .250 6.742 6.193 5.512 4.763 3 .976 3.186 2-397 1.606 o.816 0. 026

lower

0.000

-o.640 -0.846 -0.989

-L.2r2

-1.613 -2. r79

-2.6t4 -2.975 -3.510 -3.875 -4

. 1l- 6

-4.244 -4.260 -4.168 -3.980 -3.722 -3.438 -3.119 -2.764 -2.3A5 -1.994 -1 .600

-r.207

-O.814 -O.420

-0.025

35-215 .Iower 0.000

upper 0.000 o.935 1.320 1.631 2 - I4)3 - 060 4.363 5.319 6.078 7.255 8.113 a -7L2 9.084 9 -237 9 . 166 8.891 I .429 7 -7AO 6.990 6.095 5.123 4.110 3.103 2 -t36 L.248 o.498 0.000

-0.815 -1. O88

-7 .293

-1.615

-2 .I50

-2.933 -3.53s -4.O32 -4 .7 67

-5.273 -5.598 -5 -754 -5 .7 63

-5.606 -5.307 -4.90L -4.436 -3,916 -3 -347 -2

-7 45

-2.t24

-1.517

-O.946

-0.456 -0. t-o2 0.000

3542r5

upper 0.000

lower

0.000

0.935 -0.815 1.319 -1.087 I.6L7 -t.279 2 -to7 -1.581 3.029 -2.L29 4.333 -2.903 5-274 -3.490 6.020 -3.974 7 .1_86 -4 , 698 8.039 -5.199 8.648 -5 . 534 9.O47 -5.72L 9.233 -5.759 9.215 -5,655 9.OO7 -5.423 a -622 -5.094 8. O59 -4 .7!5 7 .357 -4.283 6.547 -3.799 5. 657 -3 -279 4.722 -2 .7 40 3.?84 -2,198 2.847 -L.657 1.908 -1.116 o-970 -o.574 o.032 -0. o32

35-218

upper 0,000 t-.110 l-.561 l_.923 2.5I7 3.542 5.093 6.204 7.089 8 .457 9.452 10.143 10.568 LO -737 10.643 10.311 9 -762 9. OO2 8.081 7.OJg 5.910 4.734 3 - 565 2.444 1.418 0.558 0.000 3

lower 0.000

-o. 990 -t.329 -1.585 -1.991 -2.6A2 -3.663 -4.420 -5. O43 -5.969 -6 -6t2

-7 -O29 -7.242 -7 -263 -7.083 -6 -7 27

-6.234 -5. 558 -5.007

-4.29r

-3 ,532 -2 .7 52

-r.979 -t.254

.626 -0.162 0.000

-O

542L8

upper 0.000 1 - 1r- 0 1.560 1.907 2 - 476 3 .545 5 -O57 6.150 7 .Otg 4.374 9.363 10 . 066 10.524 LO.732 10.702 10 .450 9.994 9.336 8.521 7.582 6-551 5-468 4.382 3.297 2.2IO I.I24 o - 038

trt6

lower 0.000 -0.990

-1.328 -1.569

-1- 950 -2 -645 -3.627 -4 -366

-4.973 -5.886 -6 -523 -6 .952 -7.198 -7 .25A -7 .I42

-6.866 -6.466 -5.992 -5.447 -4.534 -4.173

-3 . 486

-2.796 -2.IO7 -1, ,418

-O.728 -0 - o38 IIf --7

60 Feb

96

Sta

0. o0

o.25 o.50 o.?5 1.25 ? .50 5.00 7 .50 l-0.00 15.00 20.00 25.00 30. oo 35.O0 40. o0

45.00 50.00

55. O0 60. o0 65. O0 70. o0

75.00 80.00 85.00

63-01-5

ord o.000 o.475

.204 L.462 l-.878 2.610 3.648 L

4

.427

5.055 6. O11 6.693 7 7

.L55

.42r

7.500 7 .346 7.O99

6.665 5.108 5.453

4.72I

3.934 3.119

2

.3LO

o.000 o.063 o.120 0.170 o .275 0.500 0,852 l- .

118

1,335 1.683 1.958 2-L73

2.340 2.457 2 .524 2 .543

t

aao 2. 368

2-r78

L.947 1.685 1.404

r-r23

100 . o0

0,300 0.000

0.843 0.562 0,281 o.000

Feb 96

63A015

camber

90. 00 95. OO

sta

o. oo

0.25 o.50

o -75

1.25

.50 5.00 7 .50 10.00 15.00 20.00 25.00 2

30. o0 35.OO

40.00 45.00 50, o0 55. OO 60. o0

65.00 70.o0 75. O0 80. oo 85. O0

90.00 95.00 100.00

1. s4t 0,852

camber GA-3

ord

0. o00

0.875 r .203 1,448 1..844

2.579 3.618 4.382 4 -997

5.942 6.619 7.O9r 7 .344 7 .496 7.435 7 .2L5 6.858 6 .347 5.820 5.173 4.468 3.73L 2.991 2 .252 L.512 o.772 0,032

GA-

3

o.000 o.063 0.120 o.170 4,275 0.500 o .452 1.118 1.335 1-.683

1,958

2.r73 2.340 2 2 2

.457

.524 ,543 2 .499

2.f64

2-17A

t.947

1.685 1.404 1.123 0.843 o .562 0.281 0.000

35-

upper 0. o00 o.763 1.083 1.340 L.777 2.588 3.770 4.660 5-379 6.492 7 .3L2 7 .A97 a.277 8.457 8.433 a.222 ?.a3L 7 .254 6.540 5.724 4.832 3.899 ?.97L 2.076 )-.244 0,521 0.000 3

3

t2

16_,)

logrer 0.000 -O .637

-0.843 -1.000

-r.227

-1.588 -2.066 -2.424 -2.709 -3.126 -3.396 -3.551 -3 .597 -3 . 543

-3.385 -3.136 -2.A33 -2.518

-2.r44

-!..830 -L.462 -1 ,091 -O.725

-0.390 -0.120

0.041 0.

000

5A312

upper o.000 o -763 1.082 L-328 I.750 2.563 f -746 4.624 5.333 6.437 7 .253 7.846 a -247 8.454 8.472 8 . 315 7.985 7.478 6.834 6. O85 5.259 4.389 3 .515 2.545 L.772 0.899 o.026

lower

0.000 -O ,637 -O .842

-0.988

-1,.200

-l-.563 -2,O42 -2. 348 -2.663 -3.071 -3.337 -3.500 -3.567

-3 . 540 -3 .424 -3 .229

-2.947 -2 ,7 42

-2 - 478

-2.r9r

-1.889 -1 . 581 -L -270 -0.959 -0.548 -O -337

-0.026

upper 0. o00 0.938 L,324 1.632 2.153 3. 110 4.500 5.545 6.390 7.694 8.651 9.324 9,76r 9 ,957 9.910 9,642 9,1"64 a.476 7 .63L 6.668 5.519 4.523 3,433 2.3A4 1.41.4 0.581 0.000 3

1

E 1 'r A

4.114 3.095 2.O74 1.053 0.032

upper o.000 1 . 113 1.565 r.924 2-529 3.632 5.230 6.430

lower

0.000 -O.812

-1.084

-r .292

-1.603 -2.110 -2.796 -3.309 -3.720 -4 -328 -4.735 -4.9A2 -5.081 -5.043 -4.462 -4.556 -4.L66 -3

-7 40

-3.275

-2 .77

4

-2.249

-1 .715

-t.187

-O,698

-0.

290 -O . 019

0. 000

5A315

upper 0.000 0.938 L.J23 1.618 2.LL9 3 .079 4.470 5.500 6.332 7 .625 4.577 9.264 9.724 9.953 9.959 9.?54 9.357 8.755 7.99A 7 .I20 6. t 53

35-318

C

lower

0. 000 -O.812

-1,083

-r.27a

-1.569 -2.079 -2,766 -3.264 -3 .662 -4.259 -4.661 -4.918 -5,044 -5.039 -4 . 911

-4.672 -4.359 -4.019 -3 .642 -3.226 -2 -743 -1

1.t.7

-r.858

-1 .409

-0.950

-0 .491

-0. o32

7

-1.584 -L.979 -2.632 -3.526 -4.L94

.40r -4.73r

8.896 9.990 10.759 Lr.?45 rL.457 11 . 387 11. .

lower

0.000 -O.987 -1..325

O62

lo .497

9.698 4.722 7 .612 5.406 5.r47 3 .895 2.692 1 .584 0.641 0.000

-5.530 -6.074

-6 , 413

-6.565 -6,543 -6.339 -5,976 -5.499 -4,962 -4.366

-3.7I4

-3.036 -2.339 -1,649 -1. O06 -0.460 -0, 079 0.000

35A318

upper 0. o00 r,l-13 1.554 1.908 2.448 3.595 5.194 6.376 7 .33r 8.813 9 ,901 10.682 t-1.201. 11.452 11.446 11, 201 IO.729 l-0. o32 9 -L62 8.155 7 .O47 5.881 4.7L2 3.545 2.376 L.207 o.038

lower

0.000

-0.987

-r.324

-1.568 -1- 938 -2.595 -3.490 -4.140 -4.66L -5.447 -5.985 -6.336

-6-52I

-6.538 -6.398 -6.115 -5.73L -5.296 -4.806

-4.26I

-3 .677

-3.073 -2.466 -1.859 -I .252 -o.645 -0 . 038

Fta fr-

g

61 Peb 94

sta

0.00 o

.25

0,50 o.75 L .25

63-015 Ord 0.000 0.875 r .204 L -462 1.878 2 . 6L0 3 .644

5.00 7 .50

4.427 5.055 6.011 6.693 7.t-55

10. o0

15.00 20.00 25.00 30.00

7

7.500 7.346 7.O99 6.665 6.108 5.453

35. OO 40. oo

45.00

50. o0 55. O0

60.00 65.00 70.00 75.00 80.00 85.00 90.00 95.00 1 00.00

Feb 94 Sta 0.00 u-z> 0.50 o-75 L .25 2.50 5.00 7 .50

10. o0

15.00 20. oo

25.00 30.00 35.00 40.00 45.00 50.00 55,00 60.00 65.OO

70.00 75-00 80.00

85.O0

90.o0 95.00

100. oo

.42r

4.72r 3.934 3.L19 2.310

GA-4

o.000 0.082 o -152 0.213 o .323 o.570 0.970 1.307 r .597 2. 086

2-473 2.776 3. O10 3-1-75

.269 .296 3 -234

3

J

3 . O65

2.8L8 2.519 2-180 7

.4t7

0.852 0.300 0.000

l--454 1.090 o.727 0.363 0.000

3A015

camber

1.541,

6

Canber

ord

0. o00

0.875 1.203 L,448 1.844 2.579 3.61S 4.997 5.942 6.619 7.O9'1, 7 .344 7 - 496 7 .435

7 -2L5

6.858 6

.3A7

5,820 5.L73 4 .468 2 .991

r .512 o

-772

0.032

GA-4

0.000 0.082 0.152 0.21-3

0.323 0.570 0. 970

1.307

I-597

2.085 2.473 .2,776 3.010 3,175 3 .269 3 .296 3 ,234 3.065 2.818 2.519 2.180 L .8I7 I.454

1.090 o.727 0.363 o-

oo0

35- 412

upper o. ooo o.782 l-.l-15 1.383 )..a26 2.658 3.889 4.848 5.641 6.894 7.827 8.500 8.946 9.L75 9.r7a a.975 8.556 7.95L 7. 181 6.296 5.327 4.3r2 3.302 2.323 1,408 0.603 0.oo0

lower 0.000 -0.618 -0.811 -0.956 -L -I?9 -1.518 -1.948 -2.235 -2.44? -2.723 -2.842 -?.948 -2.927 -2.825 -2 .640 -2.344 -2.098

-r

-8?2

-L.544 -L.258 -o.967 -0.678 -0.394

-O . L42 0. O45

r23 0.000 0,

35A412

upper lower 0. ooo 0.000 o.7a2 -0.618 r,.114 -O.811 .t.372 -0.945 r,799 -r -I52 2.633 -1.493 3 .865 -r.924 4.8L2 -2 . L99 5, 595 -2.400 6.839 -2.664 7.76A -2.822 8.449 -2.496 8.9L7 -2 ,894 9.L7L -2.422 9.2L7 .-2 .679 9.068 -2.476 8.720 -2.252 8.174 -2.045 7.474 -1.838 6.657 -1.619 5.755 -1 .394 4.802 -1 . 168 3.847 -0.939 2.892 -0.711 1.936 -0,483 o.981 -O .254 0.026 -0.026

35-415

upper 0.000 o.957 l-. 356 1.575 2.20L 3 .180 4.618 5.734 6.652 a.o97 9.166 9.931 10,431 r.0.675 10.65s .1 0. 395 9.899 9.L73 a.27L 7.240 6.114 4.936 3 -764 2 -63r t.579 0.663

o-oo0

lower 0.000 -O.793 -l-,052

-r.249

-1.555 -2.O40 -2.678 -3.120 -3 .458

-3.925 -4.220 -4.379 -4.411 -4.325 -4.II7 -3.803 -3.431 -3

- O43

-2,635 -2.202 -L.754 -1.302 -0.856 -0 .451

-0.125 0.063 0,000

35A4L5

upper 0. ooo 0.957 1.355 1.661 2.167 3.149 4 - 588 5.689 6.594 8.028 9 -O92 9.467 L0.394 10,671 10.704 10.511 10.092 9.452 8.638 7 -692 6.644 5.548 4.445 3 -342 2-239 1.135 0.032

lower 0.000 -O.793 -1.051

-r -235

-L.sZL -2 -OO9 -2 -644 -3 .075 -3 ,400

-3.856 -4.146 -4.315 -4.374 -4.32L -4.L66 -3.919

-3 .624

-3.322 -3.002 -2.654 -2 -248 -1.914

-r -537 -I -L62 -0.785 -0.409 -0.032

35-418

upper 0. oo0 ]- r32 t.597 1.968 2.577 3.702 5. 348 6.61"9 7 -663 9.299 10.504 L1.362 11.91 5

]ov,rer

0.000 -0.968

-L .293

-1.541 -1.930

-2 ,562 -3 .407

-4.006 -4.469 -5.128 -5.559 -5.810 -5 . 896

-1_75 -5. 825 L2.L32 -5.594 12

l,1 . 814 -5 .223

tr.232 10.3 94 9.362 8.184 6.901 5.560 4.226 2.940 r,7 49 o.723 0.000 3

-3.725 -3.146 -2.54L

-r.926

-1 .318 -O.759

-O.296 0.003 0.000

5A418

upper 0.000 L -I32 1.595 1.951 2-536 3 .665

6.565 .594 9 .2L6 10.416 11.286 11.870 L2.t70 12.191 11.954 rL.464 LO -729 9.802 8.727 7 .542 6.294 5.043 3.?93 2 -54r 1.290 o.038 7

-4.764

-4 .265

loster 0.000 -0. 968

-L.292 -L.524 -1.8a9 -2.525 --r

1_rl

-3 -952 -4.399 -5. O45 -5.470 -5.733 -5.851 -5.42L -5.653 -5. 362 -4,996 -4.600 -4.166 -3.689 -3.181 -2 .660 -2.135 -1 .612 -L .088

-0.563 -0.038

Fh ltr-c

62 JUI

94

63-015

cam.ber GA-6

0. o0

o.000 o.875 I -204

0.000 0.112 o .207

1.878 2.610 3.648 4.427 5.055 6.011 6.693 7 .L55

0.441

Sta

o.75

.25 2.50

L

5.

OO

7.50 10.00 15.00 20.00 25.00 30.00

ord

r-462

40.o0

35.O0

7.500 7.346

45.

OO

7 -O99

50.00

55. 00 60. oo

65.00 70.00 75.

O0

80.00 85. O0 90. o0 95. O0 100. o0

JUI

6.665 6.108 5 .453 4.72L 3.934 3.119 2 ,3rA 1.541 0.852 o.300 o.000

94

63A015

Sta 0.00

o. oo0

o.50 o

-75

2 .50 5.00

7 .50 10. o0

l-5 . oo

20.00 25.00 30.00 35.00 40.00 45.00 50.00 55. O0 60.o0 65.00 70.00 75. O0 80.00 85.00 90.00 95.00 100 . o0

ord

o.875 1.203 1.448 1.844 3.618 4.382 4 .997 5.942 6,619 7.O9r 7.344 7 .496 7 .435 6.858 6 ,347 5.820 5.L73 4.468 3.73L 2 .99L 2 .252 o.772 0.032

o

-777

L.323

t.7a2

2.178 2.844 3.372 3.746 4.104 4.329 4.458 4 .494 4.410 4.L79 3.843 3.435 2.973 2-478

r-942

I .447 0.991 0.496 0.000

camber GA-6 0. o00

0.112 o o

.207

.29I o.44r

o.777 1.323 t -742 2.L74 2 .844 3.746 4.104 4 .329 4.458 4 .494 4.410

4.r79

3.843 3.435 2.973 2.478 1.982 L .447 0.991 0,496 o. o00

35-6t2 upper Iower 0.000 0.000 0.812 -O.588 1 . 170 -o.756 I-.461 -0.879 t-.943 -1.061 2.865 -1.311 4 -24L -1 .595 5 -324 -L.760 6.222 -1.866 7.653 -1,.965 8.726 -L.942 9.51O -1.938 10.041 -1.833 10.329 -L-67L 10.367 -1.451 LO.r73 -1.185 9.742 -o.922 9. 065 -O.70? L205 -0.519 7.?r2 -O .342 6.r20 -0.174 4.973 -O.017 3.830 0.134 2.720 A -254 L.673 0.309 0.256 o -736 o. 000 0.000 3

5461 2

upper lower o - oo0 0 .000 0.812 -0.588 t-.169 -O -755 I.449 -O.867 1.916 -L.034 2.A40 -L - 246 4.2L7 -L.57t 5.288 -r.724 6.176 -1. S20 7 .59A -1.910 8.667 -L.923 9.459 -1.887 10.011 -1.803 10. 326 -1 . 668 10 . 406 -1.490 10.266 -L.278 9 .896 -r -076 9.289 -0.931 8.499 -0.813 7.573 -0.703 6.547 -0.601 5.463 -0.507 4.375 -0.411 3 -289 -0.315 2.20r -0,219 1.11-4 -O.r22 0.026 -0. 026

35

-615

upper 0.000 o.987 1.411 1.7 53 2.319 3.3A7 4.97L 6.209 7.233 8.855 10 . 055 10.941 r,1.525 11.829 11.844 11.593 11.075 to.2a7 9.296 8.156 6.907 5.597 4.292 3 .028 1.843 o-796 o. 000

lower

0.000

-O -763 -O -997

-1.171

-1 .437 -1,.833

-2.325 -2.645 -2.877 -3.L67 -1.321 -3.369 -3.3L7 -3.171 -2.928 -2.605 -2.255 -\.929 -1.610 -1.286 -O.961

-0.641 -0. 328 -0.054 0.139

0. 196

0.000

354615 upper l-oeter

0.000 0.000 0.987 -O.763 1 .4LO -O.996 r.739 -r.L57 2.285 -1.403 3.356 -1 . 802 4.94L -2 .295 6.J.64 -2.600 7 -r75 -2.81,9 a.7a6 -3.098 9 .991 -3.247 LO.B77 -3.305 11.488 -3 . 280 11.825 -3.167 11

001

L1.709 LL.268 10-566 9.663 8.608 7.44r 6.209 4 -973 3.739 2.503 1.268 0.032

-1

01t

-2 ,7 2L -2 - 448 -2 -204

-L.97? -1.738 -1.495 -1.2s3 -1. O09

-O -765

-O,52L -O .27 6

-0.032

35-618

upper Iower 0.000 0.000 L.162 -O.938 r.652 -1.238 2.O45 -1.463 2,695 -1.813 3 .909 -2.355 5.701 -3 .055 7 -O94 -3.530 8.244 -3.888 10.057 -4.369 11 .404 -4 . 660 L2.372 -4.800 13.009 -4.801 13.329 -4.67r 13.321 -4.405 13.O1-3 -4-O25 12.408 -3 . 588 11.509 -3.15L 10.387 -2 -707 9.100 -2 .230 7 .694 -l .7 48 6.22L -r .265 4.754 -0.790 3.336 -0.362 2.OL3 -0.031 o.856 0.135 o.000 0.000 35A618

upper lower 0. o00 0.000 1.162 -0.938 1.651 -L.237 2.O29 -r.447 2.654 -I .772 3 -A72 -2 . 318 5.665 -3.019 ? .o40 -3 -476 a.174 -3.818 9.9?4 - 4 .2A6 1t-.315 -4.571_ 12.295 -4.723 t2.965 -4.757 13 -324 -4.666 13.380 -4.464 L3.I52 -4.164 12.640 -3,820 11.843 -3.485 LO.A27 -3 .141 9.643 -2.773 8.335 -2.389 6.955 -1.999 5.571 -I - 607 4 .189 -1.215 2.805 -O-823 t.422 -0.430 0. 038 -o.038 Frt:l GL- to

Feb

94

sta

0.00 0,25 0,50 o,75 r ,25 2. s0 5. o0

7.50 l"0.oo 15. O0 20. o0

25.00 30,00 35,00 40.00 45.00 50.00 55.00 60.00 65.00 70.00 75 -OO

80.00 85-00

90. o0

95.00 100.00

Feb

64-01-5

ord

0.000 0.865 1.208 1.456 L.842 2 .528 3.504 4,240 4 .842 5.745 6,480 6.985 7

.3t9

7.482 7 -224

6.810 6 .266 5 .620 4,895 4.113 3 .296 2-472 I .6?7 0.950 0. 346 0.000

94

644015 Ord

o. o0 o .25

0.000 0.855 1.193 1,436 1.81s 2,508 3 .477 4 .202 4 .799

sta

0.50 o-75

2.50

5.

O0

7.50 10.00 15.00 20.o0 25.

O0

30.00 35.00

40. o0 45. O0

50.o0 55.00 60. o0

65.00

70. o0 75.OO

80,00 85.00 90. o0

95.00 100.00

6.42J 6 .926 7.270 7.463 7.447 7.313 6,974 6

.5r7

5.956 5.311 4,600 3 .847 2

-32r

1.558 0.795 o.032

camber cA- 2

0.000 0,060 0.116 0.169 o .263 0.450 0 . 71,5 o .492

t-.023 L -244 1

.420

r .557 l, .663 1.

.7 37

1.780

r.792 r.764 L.672 ! .537 L-3?4 1.

189

0.991 o,793 0.595 o.396 o.198 o.000 carnber GA-2

0.000 0.060 0.116 0.169 0.263 0.450 0.715 o .492 1.O23

I .244 L .420 L .557 1.663 L .717 1.780 L.792

t.764 r.672 r.537

!.374

1.189 0.991 o.793 0.595 o.396 0.198 o-

oo0

37 -2I2 upper Iorter 0.000 0.000 o.752 -O.632 1.082 -0.8s0 1.334 -0.996 1.737 -L.2lL 2.472 -I.572 3 . 518 -2. O88 4.?a4 -2.500 4.A97 -2.45]5.A72 -3.384 6.604 -3.764 7 -r45 -4,031 7.518 -4 . r92 7 .723 -4.249 7 .758 -4.198 7.57L -3.9a7 7 .2L2 -3.684 6.685 -3.341, 6.033 -2.959 5.290 -2.542 4-479 -2.101 3.62A -1.646 2.77L -1 ,185 r.937 -O .7 47 1,156 -0.364 o.475 -O.O79 0. o00 0.000 37

A2L2

upper 0.000 o.744 1.070 1.318 1 . 71s 2.455 3.497 4-254 4.862 5.830 6.558 7.098 7 .47 9 7 .707 7 .770 7 .642 7 .346 6.886 6.302 5.523 4.859 4.069 3.260 2.452 I.642 0.834 o.

o26

37

-215 lower

upper 0. o00 o.925 L.324 L.625 2.105 2.97A 4.2r9 5.L32 5.865 7 .O29 7 .900 8.542

0. o00

-0.805

-L . O92 -l .287

-L.579 -2.O74 -2.749 -3.348 -3.81-9

-4.54L -5.060 -5.428

8.982 -s.6s6 9.219 9 -253 9 . 016 8.574 7 .934 7 .L57 6.269 5.302 4.247 3.265 2.272 1.346 o.544 0.000

-5.745 -5,693 -5.432 -5.046 -4.594 -4.083

-3.52I -2.924 -2.305 -L .67 9 -1..082

-0,554 -0.148

0.000

37 A2J,5

lower

0.000 -O -624

-0.838

-0 - 980 -1 .189

-1.556 -2.067 -2.470 -2 -8L6 -3.342 -3.718 -3 . 984

-4.153 -4.233 -4.21_O

-4,058

-3.81,8

-3.542 -3.228 -2.475 -2.49L -2.O47

-r -r.262

.67 4

-0.850 -0.438 -o.026

upper 0 .000 0,915 1.309 t.605 2-O78 2-958 4-r92 5. O94 5.422 6.976 7 -443 8.483 8.933 9. 200 9.267 9.105 a.742 8.189 7.493 6.685 5-7a9 4.838 3.877 2.9L6 t -954 0.993 0.032

lower 0.000 -0.795 -L -O77

-L.267

-1 . 552

-2.058

-2 -762 -3 .31-O -3 .77 6

-4.488 -5. O03

-5 . 369

-5.607 -5.726 -5.707 -5.521 -5 .2L4 -4.845 -4,4L9 -3.937 -3.411 -2.856

-2.29I -r.726

-1,.t 62 -O.597 -o.032

Jt-zL6

upper 0.000 1.098 1.566 1.916 2.473 3 .4A4 4,920 5.980 6,833 8.186 9.196 9 -939 10.446 10.715 LO.74A 10.4619.936 9.19r 8.281 7 .248 6.r25 4.946 3.759 2.607 1.536 0.613 0.000 37

63 lower 0,000 -O.974

-1,.334

-L.578

-l ,947 -2.584 -3.490

-4.196 -4.787 -5.698 -6 . f56 -6.825

-7 .I20 -7 -241 -7.1-88

-6.477 -6.408

-5 .847 -5 - 207

-4.500

-3 .7 47

-2.964 -2.r73 -r,4L7 -O.7 44

-O.2r7 0.000

A2rA

upper 0.000 1.086 1.548 r -492 2.44r 3.460 4.887 5.934 6.742 4.r22 9.L?A 9.868 t 0.387 10.693 10.764 10 . 568 r0.138 9.492 8.684 7.747 6.709 5,607 4.494 3.380 2.266 r.L52 0. 038

lower 0.000 -0.965 -1 - 316

-r.554

-1.915 -2.550

-3 .457 -4 - 150

-4.736 -5.634 -6.288 -6.754 -7 -O6L -7 .2r9 -7 .204 -6,984 -6.610 -6.148 -5.61.0 -4.999 -4.331 -3 .625

-2. q08 -2-190 -L.47 4 -O.756 -o.038

Ftq ][-rr

64 Feb

96

Sta 0.00 o .25 0.50 o.75 1.25 2.50

64-015

ord

o. oo0 0.865 1..208 1.456

t .442

20.00 25.00 30.00

.524 3.504 4 .240 4 .442 5.785 6.480 6.985 7 .3L9

OO

7 - 4A2

5.

O0

7.50 10.00 15.

35.

O0

40.oo 45-00 50.00 55.00 60. o0 65. O0 70. o0

75.00 80. o0

85.00 90.o0 95-O0 100. o0

feb

2

.224 6.810 tr. ltrt) 5.620 7

4,895 4.113 3 .296 2.472

I .677

0,950 0. 346 0. o00

camber GA- 3

0,000 0.063 0,120 0.170 o.275 o.500 0.852 1.118 t-.335 1.683 1.958 2.L73 2.340 2.45? 2 .524 2 .543 2.499 2.368 2.L78 r .94? 1.685

r-404

1.123 0.843 o.562 0.281 o. o00

96

644015

Carnber GA- 3

o. o0

0. o00

0.000 o.063 o.120

sta

0.25 0.50 0.75 L .25 2.50 5.

OO

7 .50 10.o0

r.5 . o0

20, o0 25. O0

30.o0

35.O0

40.00 45-O0 50. o0 55. O0

50.00 65.00 70.00

75 -OO 80. o0

85.00 90, o0

95.00 100 . o0

ord

0.855 1.193 1.436 1 . 81.5

2.508 3 4 4

.477

.202 .799 5.732 6.423 6 .926 7 .270 7.463 7.447 7 .3L3 6,978

0.1 70

o.?75 0.500 o.852 1.118

r.335

5.956

1.683 1.958 2.L73 2 -340 2-457 2 .524 2 .543 2-499 2.368 2-778

5.31-1

L -947

6

.5L7

4,600 3.A47 3. O84

.32L 1.558 o.795 0.032 2

1.685

1",404

1.123 o.843 o -562 0.281 o-

ooo

37

-3L2

upper 0.000 o.755 l-,086 1.335 L,749 2.522 3 .655 4.51-0 5.209 6.311 7.L42 7 -7 6L 8.195 8.443 8.502 a.322 7 .9 47 7.38L 6.674 5.863 4.975 4 .041 3. t- 01

2.ras I.322 0 . 558 0.000

lower 0.000

-O.629

-o.846 -0.995 -1.199

-r -522 -1.951 -2.274 -2.539 -2.945 -3 -226

-3.415 -3.515

-3 . 529

-3.454 -3.236 -2.949 -2 .645 -2.318 -1.959 -1.605 -L.233 -o.855 -0.499 -0.198 0.004 0.000

37 A3L2

upper lower 0.000 0 .000 o.747 -0.621 L.07 4 -0.834 1.319 -O -979 r.727 -r.L77 2.506 -1 . 506 3.634 -1.930 4 - 480 -2 ,244 5.l-74 -2 . 504 6.269 -2 .903 7 .096 -3.180 7 .714 -3.368 8. 156 -3 .476 a -427 -3.513 8.514 -3.465 8.393 -3.307 8.081 -3.O83 7.542 -2.846 6.943 -2.587 6.196 -2.302 5. 365 -1 .995 4 -442 -L .67 4 3.590 -1.344 2-700 -1 .014 1.808 -0.684 o.9r7 -0. 355 o.026 -0. o26

37-315

upper 0.000 0.928 L.324 1.625 2.r17 3.028 4.356 5.358 6.L77 7 .46A 8.438 9.158 9.659 9.939 9.997 9.767 9,309 8.634 7 .79A 6 -442 5 -79A 4.700 3.595 2.520 1.512 o.6?7 0.000

lower

0,000

-0.802 -1. O88 -l-.286 -L567

-2 , O2a

-2.652 -3 .I22 -3 . 50?

-4,lO2 -4.522 -4.AL2 -4.979 -5.025 -4.949 -4 . 681

-4.311 -3.898 -3 .442 -2.944 -2.42A -1.892 -1.349 -O.834

-0.388 -O.055 0.000

37A315

upper 0.000 o.918 1.313 1.606 2.090 3. O08 4.329 5.320 6.134 7 -4L5 8.381 9.099 9.510 9.920 10.011 9.856 9.477 8.885 8.1.34 7 -25a 6,285 5.251 4.207 3.164 2 .],20 1.076 0.032

Iower 0.000 -o.792 -1-073

-r.266

-1 . 540

-2. O08 -2.625 -3. O84 -3.464 -4.049 -4.465 -4.753 -4.930 -5.006 -4.963 -4.770 -4.479 -4.L49 -3.778 -3.364 -2.915 -2.443 -1.961 -!.474 -0 . 996

-0.514 -0. o32

37-318

upper 0 . o00 1.101 1.570 L9L7 2.4A5 3.534 5.057 6.206 7 .r45 8.625 9,734 10.555 11.123 1l-.435 II . 492 r1_.212 10,671 9.887 a,922 7 .A2L 6.62L 5.359 4. O89 2.855 L.702 0.596 o. o00 3

I o$ter

0.000 -A.975 -1.330 -L .577

-l-.935 -2 .534 -3.353 -3.970 -4.475 -5 -259 -5.818 -6.209 -6.443 -6.521 -6 .444 -6 . L26 -5 .67 3

-5.151 -4.566 -3.927 -3.251 -2.551-

-1.843 -1.169

-O.578

-0.134 0.

o00

7A3 18

upper 0.000 1.089 1..552 1.893 2.453 3.510 s.024 6. L60 7 .O94 8.561 9.666 10.484 l-1.054 11.413 1.1.508 11.319 10.873 10.1,88 9.325 8.320 7 .205 6,020 4.824 3.628 2.432 r.235 0. 038

lower 0.000

-O.963

-1.312 -1.553 -1.903 -2.510 -3 .320 -3 .924 -4.424 -5. 195 -5.750 -6.138 -6. 384 -6.499 -6,460 -6 .233 -5.875 -5.452 -4.969 -4 .426 -3.835 -3.212 -2.57A -I .942

-1 . 308 -O -673

-o. 03I

Fta fl- t?

65 Feb 94

sta

64-01-5

ord

0.000 0.865 1.208 L.456 1 .842 2 .52e 3.504 4 .240 4.842 5.785 5.480 6.985

0. o0

0.25 0.50 o.75 1.25 2.50 5.00 7 -50

10.o0 r5. o0 20.00 25.00 30.00

7 7

35-OO

40.00 45. O0 50.00

.224 6.810 6 .266 5.620 7

65.00

70. o0

75.00 80.00 85.00 90.00 95.00 100. o0 94

sta

0.00 o .25 0.50 o.75

.482

7 -473

55. O0 60. o0

Feb

.3r9

6

50.00 55,00 60.00 65.

O0

70.00 75.00 80. o0

85.00 90.00 95.00 100.00

t.597

2.085 2.473 2.776 3.010 3.175 3 .269 3.?96 3 .234 3.065 2 . 81,8

1.090 o -727 0.363 0,000

4A015

Camber GA-4

ord o.000 o.855 1. L93

7

25.00 30.oo

.323 0.570 0.970 L.307 o

I .677 0,950 o.346 o.000

45.OO

15. OO 20. o0

0.000 0.082 0.152

2.519 2.180 1.817

35.O0 40. oo

2 .50 5.00 7 .50 10.00

GA-4

4.895 4.113 3 .296

1.436 1.815 2.508 3-477 4 .202 4.799 5 -732 6-423 6 -926 7 .270 7.453 7.487

I .25

canber

,3r3

6.974 6.517 5.956 5.311 4.500 3.A47 3 .084

-32r 1.558 0.795 o.032 2

r.454

0.000 0.082 0.152 0.213

0.570 o.970 1.307 1

.597

2.086 2.473 2.776 3.010 J . 1,7 5

.269 3 .296 3.2J4 3.065 2.818 2 .5L9 2.180 1.817 I .454 1.090 o.727 0.363 0,000

3

37

- 412

upper o.000 o.?74 1.118 1.378 !.797 2.592 3.773 4.699 5.471 6.7L4 -7

lower

0.000 -O.610

-0.815

-0.951-

-1. L50 -1.453 -1.833 -2.085 -2 .27

6

-2.542

.657 -2 .7 rr 8.354 -2,8r2 s.865 -?.A46 9.160 -2.811 9.248 -2.709 9.O75 -2.444 8.6A2 -2 .2r4 a.o77 -l-.948 7.314 -L674 5. 435 -L.397 5,47r -1.110 4 .454 -0.820 3 .431 -O -524 2.432 -O.251, L.4A7 -0.033 o.640 0,087 o. 000 0.000 37

A4L2

upper 0.000 o.766 1,106 !.362 t.775 2 .57 6 3 .752 4.668 s.436 6.67r 7.6Lr 8.317 8.826 9. 145 9.259 9.146 8.816 a.27a 7.583 6.76A 5.860 4. 895 3.92L 2 -947 1.973 0.999 o . 026

3

lower

0.o00 -O.602

-0.803 -0.935 -1.129

-r

- 43'7

- l- . 811

-2.055 -2.242

-2 . 500 -2 -666 -2 -7 64

-2.806 -2 .796 -2 -2 -2 -2

3?

.7 20

.555 .344 . L49

-!,947

-1.730

-1 .500

-L.264 -1.013 -A.766 -O -520 -O .27 3

-o.025

- 4r5

upper 0 .000 o .947 L. 360 1.669 2.165 3.098 4.47 4 5.547 6.439 ? -a?1 8.953 9.76r 10.329 10.557 to.742 10.520 10. o44 9.331 8. 438 7.4!4 6,293 5.1L3 3.926 2.767 L.677 o.709 0.000

Iower 0.000 -0.783 -1. O56 -L .243 -1.519 -1.958 -2 .534 -2 .933 -3,245 -3 .699 -4.007 -4.209 -4 , 309 -4.307 -4.204 -3 -924 -3 .57

6

-2 .3?

6

-3.201 -2.4O2 -1.933 -L.479 -1.01-8

-0.587 -O .223 0. o17

0.000

74415

upper 0.000 o,937 1.345 r.649 2.138 3 .078 4.447 5. 509 5.396 7.818 8.896 9.702 10.280 1o.638 10.756 10.609 10.212 9.582 8.774 7 .830 6,780 5.664 4.538 3.411 2.245 1.158 0.032

Iower 0. 000

-O.773

-1.041 -L.223 -L .492 -t-.938 -2.507 -2.895 -3.202 -3.646 -3.950 -4.150 -4 .260

-4.288 - 4 .2IA

-4 .017 -3 ,7 44 -3 .452 -3 .138

-2.792 -2.420 -2.030 -1.630 -1.231 -0.831

-O - 432

-0.032

37

- 4L8

upper 0. oo0 l-.120 1.601 1.961 2.534 3.603 5 -175 6 , 395 7 .40A 9.028 10.249 11 . 1s8 LI .792 L2.L53 12.237 11.964 11.406 10. 584 9.562 8.393 7.IL6 5.772 4.420 3.103 L.867 o -779 o.000

lower 0.000 -0.956 -r .294 -1".534

-1.887

-2 - 464

-3.235

-3 .781 -4 .213

-4.856

-5 - 303

-5.606 -5.773 -5.804 -5.698

-5 .37 3 -4 . 938 -4 .455

-3.926 -3.355 -2.755 -2.138

-1 . 513 -O -922 -O.413 -O. O52

0.000

37A418

upper 0.000 1.108 1.583 1.937 2.501 3 .579 5.143 6.349 7 .356 8.964 10.1 80 11.088 rI.734 12,130 L?.254 L2.O7L 11,608 10.885 9.965 8.892 7 -700 6.434 5.155 3.476 2.596 1.317 0,038

lower 0.000 -0.944 -t-.280 -1.510

-1.855 -2.440

-3 .202

-3.736 -4.]-62 -4.793 -5.235 *s.s35 -5.7!4 -5.781 -5.715 -5.480 -5.140

-4 .7 56 -4 -329

-3.854 -3.340 -?.799 -2 -24'l -1 .695

-1.143 -0,591 -o. o38

Flq -S-r3

66 Feb 94

sta

0. 00 o .25

0.50 o-75 L .25 2

.50

5.

O0

7.50 l-0,00 15.00 20.00 25.00 30. o0

35.00 40.00 45.00 50,00 55.

O0

60.00 65. OO 70. o0 75.O0 80. oo 85. OO 90. oo 95. O0

l-00.00

Feb 94 Sta 0.00 0.50 o.75 2

.50

5. O0 7 ,50

10.00 15.00 20.o0 25.00 30.00 35.00 40.00 45.00 50.00 55.00 60.00 55.

O0

70.00 75-00 80.00 85.00 90.00 95.00 100.00

64-O15

ord

0. oo0

0.865 1.208

r.456 I .442

.528 3.504 4 .240 4 .442 5.785 6.480 6.985 7.319 2

7-

482

7.473 7 .224 6.8t 0

6 -266

5.620 4.895 4.113 3 ,296 2.472 L .677 0,950 0.346

c arnbe

r

GA- 6

0.000 0.112 o .207 0.291 0.441 o.777 t ,323

r.742 2.444 3.372 3.786 4. Lo4 4 .3?9

4,458 4.494 4.41-0

4,L79 3.843 3.435 2.973 2.474 1.982

r.4a7

o. o00

0.991 o .496 0.000

64AO15

Canber

ord

0.000 0.855 1.193 L.436 1.815 2.508 3.477 4 .202 4.799

GA-6

0.000 0.112 o

291

0.44ro.777 1.323

L.742 2-17A

2

6.423 6.926 7.270 7 .463 7.487 7.313

.207

0-

.444

6 -974

3.786 4.104 4 .329 4.458 4.494 4.410

6

4

.5L7

-r79

5.956 5,311 4.600

3.843 3.435 2.973

.447 3,084

t

3 2

.32r

l-.558

o.795 0.032

-942 r .487 0.991

o.496 o.o00

31-612

upper 0.000 0.804 1.173 1.456 1.915 2.799 4.L26 5.L74 6.O52 7.472 8.556 9 .37 4 9.959 10.315 10.436 LO.273 9.858 9.L92 8.339 7.35! 6.26f 5.115 3,960 2.A29 r.75I o.773 0.000 37

lower

0.000

-0.580 -O.759 -O .47 4

-1.033 -r .245 -1.480 -1.610 -1,696 -L.784 -1.81"2

-1.802 -r -75r

-r

-657

-1.520 -1.285 -1.038 -0.834 -0.653 -0.481

-o.31-7

-0.159

0 - O04

0.145

O.23L

0.2L9 0.000

A6t2

upper lower 0.000 0.000 o.796 -O.572 1.161 -O.7 4? 1-440 -0.858 1.893 -1.011 .105 5.144 6.017 7.430 8.51_0 9 .327 9.920 10.299 10.448 10.344 9.992 9-393 8. 608 7 .6A4 6.6s3 5.556 4.449 3.344 2.237 1.132 o. o25 4

-1

1',to

-r,459

-1.580

-1..661

-!

.7 42

-L ,7 66

-r.755 -r.7L2

-1.641 -1.532

-1 .356

-l

-17 2

-1.O3s

-O -922

-0.814

-O -7 07

-0.600 -0.485 -0.370 -O .255 -0 . r40 -O .026

37-6L5

upper 0.000 o.977 1.415 I .7 47 2.2A3 3.305 4.827 6 -O22 7.O20 a.629 9 .852 LO.77l 1_L . 423 l"i-.811 t-1.931 t-1.7l_8 LL.220 10.445 9 -463 8,330 7. 086 5.774 4.454 3 .164 1 ,941 o.a42 0.000

lolter

0.000

-0.75J -1.001 -1 .165

-1.401

-L-75r

-2 . 181 -2 .454

-2.664 -2.94L -3.108 -3.199

-3 .2L5

-3.153 -3.015 -2.730 -2 .400 -2 . O87

-L.777

-1 . 460 -1 . 140 -O.818 -O.490 -O.190

0.041 0,150 0.000

37A615

upper 0.000 o.967 1.400 L.727 2-256 3.285 4.800 5 . 984 6.977 a.576 9.795 LO.7L2 rL.374

rr.792

11.945 11..807 11 . 388 10.696 9.799 4.746 7 .573 6.325 5.066 3.808 2.549 1,291 o. 032

lower

0. oo0 -O.7 43

-0.986 -1.145

-r .37 4 -L.73r -2.L54

-2 .420 -2 .62L

-2.888 -3.051 -3. L40 -3.166 -3.134

-1 .O29

-2.4L9 -2.568 -2.338 -2.113 -r.876 -L.627 -1,369 -1 . 102 -O.834 -O.567 -O.299

-o. o32

37-618

upper 0.000 1.150 r.657 2. O38 2.65L 3.811 5.528 6.870 7.988 9 .7A6 11.148 12.168 t2.aa? 13.307 L3 -426 13.163 12-542 1l-.698 10,587 9.309 7.909 6.433 4.944 3.499 2.131 0.911 0.000 3

lower

0.000

-0.926 -L.243 -1.456 -I .769 -2-257 -2.482 -3.306 -3.632 -4,098 -4.404

-4 . 596 -4 .67 9 -4 -649

-4.510 -4.L75 -3.762 -3.340

-2.90r

-2 - 439

-1.963 -L.477 -0.984 -0.525 -0.149

0.081 0.000

7A6l-8

upper lower 0,000 0. 000 1.138 -0.91 4 1.639 -L -225 2 . O'1,4 -t - 432 2.619 -L -? 37 3.747 -2.233 5. 495 -2 -849 6.424 -3 .260 7.937 -3.581 9.722 -4.O34 11.080 -4,336 12.o97 -4.525 L2.824 -4 .620 13.285 -4.627 13.442 -4.526 11 -270 -4.242 L2.7A4 -3.964 11.999 -3.641 10.990 -3 . 304 9.808 -2 - 938 8.493 -2.547 7.O94 -2.138 5.683 -L.7L9 4,272 -1 . 298 2.86L -0.879 1.450 -O.458 0,038 -0.038 FtLl f:f- - lll-

67 Feb

94

Sta 0-00 0.25 0 .50

65-O15 Ord 0 . 000

0.830 I . )-24 1.356 T.702

o.75 .50 5.00 2

3.245 3.959 4.555 5.504

7.50 10. oo

15.00 20.00 25.00 30.00 35.00 40.00

6 -223

6-764

7.r52

70. o0

.396 7 .494 7,427 7.L68 6.720 6.l-l-8 5.403 4.600

75 -OO 80. oo

3 .'7 44 2 - 858

45.

O0

55.

O0

7

50.00 60.00 65.00

85.

I .9'77

OO

1.144 0.428 0.000

90.00 95.00 100.00

Feb 94 Sta o.00

.25 0.50 o-75

o

2

.50

5.O0 7

.50

10. o0 15. O0 20. o0

25.00 30.00 35.00 40.00 45,

O0

50.00 55.00 60. o0 65. O0

70.00

75.O0 80. o0 85. O0

90,00 95.

O0

100 . o0

4

04015

ord

0.000 0,830 1.124 1.356

!.702

.324 .245 3.959 4.555 5.504 6-223 6 -764 2 3

.396 7 .494 7

.427 7 .16A 7

6,720 6.118 5.403 4.600 3.744

2,AA5 2 -065 t .290

0.500 0.000

camber GA-2

0.000 0. o60

o.116 o.169 o.263 0.450 0.715 0.892 1.023 r .244 L-420 L ,557 1.663 I .737 L.7AO

L.792

I.764 I-672 L

.537

L.374 1.189 0.991 0.793 0.595 0.396 0. 198

0. o00

canber GA-2

0.000 0.050 0.116 0.169 o .263 0.450 0.715 o .892 1. O23

.244 L,420 1.557 1.663 L

r.737

1.780 L.792

r.764

.672 1.517 L.J74 1.189 0.991 o.793 0.595 0.396 o.198 0.000 L

40-2I2 lower 0.000 -0. 604 -0.783 -0.916

upper 0.000 o.724 l-.015 I.254 L .625 2.309 3.311 4.059 4.667 5.647 6.398 6.968 7 .3e5 7.654 7.77A 7.734 7 .498 7 -O48 6.431 5.696 4.869 3.986 3.O79 2.L?7 1.311 0 . 540 0, o00

-r,099

-1.409 -1.881 -2.275 -2.62L -3.159 -3.558 -3.854 -4.059 -4.1S0 -4.218 -4.1,50

-3.970 -3.704 -3.357 -2.948 -2.49L -2.OO4

-1,493

-O.987

-0.519 -0,144 0.000

40}.2r2

upper 0 ,000 o.724 1.015 t.254 L.625 2.309 1.31L 4. O59 4.667 5.647 6.398 6.968 7 . 385 7 .654 7 .77A 7 -734 7 .49A 7.O4A 6.431 5.596 4 .869 3.985 3.101 2.247 I.428 0 .678 0.000

lower 0.000 -0.604 -0.783 -0.916 -1.099

-1 . 409 -1-.881

-2.27 5 -2,62)-3.159 -3.558 -3 . 854

-4. O59 -4.180

-4.2r4

-4,150 -3.970 -3.704 -3,357 -2.944 -2.49L -2.004 -1.515 -1 .057 -O.636

-O.242 0.000

40-2L5 Iower 0.000

upper 0.000 0.890 L.240 1.525 r..965 2.774 3.960 4.851 5.578 6.?48 7.643 8.321 I .81s 9.133 9.27a 9.2r9 8 -932 8.392 7,655 6.777 5.789 4.735 3.651 2.572 l- . 540 o.626 0,000

-o.770 -1.008 -T.LA7 -1.439 -L.87 4 -2.530 -3.067 -3.532 -4 -260 -4.803 -5.207 -5.489 -5 . 659

-5.7I8

-5.635 -5.404 -5.048 -4. s81 -4.O29

-3.411 -2.7 53 -2.06s -L.342 -o.7 4A -0,230 0.o00

4042l-5

upper o.000 0 - 890 r.240 1.525 1..965 2 .77 4 3 . 960 4.851 5 -57a 6.?44 7 .643 a - 321 8.815 9.133 9.27A 9 .2L9 8.932 a.392 7 .655 6.777 5.789 4.735 3.678 2 .650 1.685 o.798 0.000

4

lower

0,000 -o .770

-1,008

-1 .187 -1 .439

-t.47

4

-Z,530 -3.067 -3.532 -4.260 -4.803 -5.207 -5,489 -5.659 -5.718 -5.635 -5.404 -5.048 -4.581 -4.O29 -3.411-

-2.753

-2.O92

-t

40-2),4

upper 0.000 1. 056 1.465 L.796 2.305 3 - 2f9 4.609 5.643 6.489 ? .849 8.888 9 .67 4 10.245 10.612 to.77a 10.704 l-0. 366 9 .736 LA79 7.859 6.709 5.444 4.223 2.967 L.769 o.7L2 0.000

- 470

-0 .894

-0.402

0.000

lower 0.000 -0.936 -1, 23 3 -l-.4s8 -L.779 -2.339 -3.L79 -3.859 -4 - 443

-5.351 -6.048 -6.560

-6.9r9

-7.l-38

-7 .2).4

-7 .L?O -6.838 -6 .192

-5.805 -5.110 -4.331

-3 .502 -2 .637 -L.777 -O .977

-0.316 0.000

0A218

upper lower 0.000 0.000 1 .056 -0.936 1.465 -1.233 L.796 -1, . 458 2.305 -!.779 3 -219 -2.339 4.609 -3 .]-79 5.643 -3 . 859 6.489 -4 .443 7 .A49 -5.361 8.888 -6. 048 9.674 -6.560 ro.245 -6.919 10. 6l- 2 -7.138 LO.77A -7 -2LB 10.704 -7.L20 10.366 -6.838 9.736 -6 -392 8.A79 -5.805 7.858 -5.110 6.709 -4. 3 31 5.484 -3 . 502 4.255 -2 -669 3.07X -1.883 r.944 -1 . 152 0.918 -O ,522 o.000 0 .000

Frcr 5x-tr

68 Feb

95

0. o0 n ?q

0.50 o.75 I .25 2.50 5.00 7 .50

10. oo 15.00 20.00 25,00 30.o0 35. O0 40. o0 45. O0 50.00 55.00 60 - o0

65.

O0

70.00 75.00 80.00 85.00 90,00 95.00

65-Or5

ord

0.000 0.830

|.r24

1.356

t.702

.324 .245 3,959 4.555 5.504 6.?23 6.764 7,L52 7 .396 7.494 7.427 7.L68 6.720 6.118 5.403 4.600 2 3

3

.7 44

.458 L.977 1.144 o.424 2

100. o0

o. 000

Feb 96

404015

sta

0. o0

.25 0.50 o.75 r .25 2.50 o

5. O0 7 .50

10.00 15.00

20. o0 25. O0

30.00 35.00 40.00 45.

O0

50.00 55.00 60.00 65.00 70. o0 75.OO

80.00 85.00 90. o0 95. O0 1,00 . oo

ord 0.000 o.830

7.r24 1.356 J.

.7 02

.324 3.?45 3.959 2

5.504 6 .223 6 -764 7 7

.I52

.396 7.498 7.427 7.L68 6-720 6.118 5.403 4.600 3.744 2

.885

2.065 1.290 o.500 o. ooo

camber GA-

3

o.000 o.o63 0.120 0.170 o.275 o. 500 0.852 1.118 1.335 1.683 1.958 2.L73 2 .340 2 .457 2 .524 2 .543 2.499 2 .368 2 - 1,7I L .947

1.685 1.404 r-.123 0.843 o .562 0.281 0. oo0

canber GA-3 0. oo0

0.063

o.r22 0,1.70

o.275 0.500 o.852 1.118 1.335 1.683 1.958 2.L73 ?-340 ? .457 2 .524 ? 2

-rL

OO

.168

?-17A L .947 1.685 1.404 1.123 0.843 o .562 0.281

0. oo0

40-315

40- 3 r2

upper o.000 o.727 1. 019 L.255 L.637 2.J59 3 .448 4,2A5 4.979 6.086 6.936 7 .584 8,062 8.374 a.522 8.485 a.233 7 .744 7.072 6.269 5.365 4.399 3.409 2.425 I -477 0.623 0.000 4

Lower 0. oo0

-O.601 -O.779

-0.915 -1. O87 -1,359 -L.7 44

-2 . O49 -2 .309 -2 .7 20

-3.020 -3.238 -3 ,382 -3,460 -3.474 -3.399 -3 .235

-3.008

-2 -7 L6

-2-375

-1 . 995

-1.591 -1. L63 -O.7J9 -0.353 -0.061 0.000

0A312

upper 0.000 o.727 t- . 021 L.255 L.637 2.359 3 .448 4-285 4.979 6.086 6.936 7 .5A4 8.062 a.374 a.522 8.485 8.233 7.744 7.O72 6.269 5.365 4.399 3.431 2.495 1.594 o.76L 0.000

4

lower

0.000

-0.601

-o .777

-0.915 -1.087 -1. 359

-t.7

upper 0.000 0.893 r,244 7.526 L.977 2.824 4 -O97 5.O77 5.890 7,IA7 8.181 a.937 9 .492 9.853 LO.O22 9.970 9 -667 9.088 4.296 7 .350 6.285 5. 148 3.981 2.420 L.706 o.709 0 . 000

44

-2 -O49 -2 -309 -2.720 -3 . 020

-3.238 -3.382 -3.460 -3-474 -3.399 -3.235 -3. O08 -2.716 -2 .17

5

-1.995

-1.591,

-1.185 -0.809 -0.470 -0,199

0,000

lower

0.000 -O.767

-1.004 -1.186

-t.427 -r.424

-2.393 -2. A4L -3 .220 -3.821 -4.265 -4.591 -4. 812 -4.939 -4.97 4 -4.884 -4.669 -4 -352 -3.940 -3.456 -2.915 -2 -340 -L.?35 -1.134 -O.582 -o -L47 0-

o00

04315

upper 0.000 0.893 L.246 L-526 L.977 2-424 4.O97 5.O77 5 . 890 7 -LA7 8.t81. 4.937 9.492 9,853 LO.O22 9.970 9.667 9.088 4.296 7 -350 6.285 5.148 4.008 2.908 1.852 0.881 0.000

lorrer

0.000 -O.757

-1.002 -1.186

-I -L.824 .427

-2.393

-2 , A4L -3 .220

-3,821 -4.265 -4 .591

-

4

.8I2

-4,939 -4.974 -4.884 -4,669 -4 .352 -3.940 -3.456 -2.915 -2,340

-r.762

-L.222 -O.724 -0.319 0.

o00

40-318

upper 0.000 t-.059 1.469 I.797 2.3L7 1.2A9 4.746 5.869 6. 801 8.288 9 .426 10.290 ro.922 LL.332

lower 0.000 -0.933 -1.229

-r.457

-L ,7 67 -2 .289 -3,O42

-3.533 -4.131 -4.922 -5. 510 -s.944

-6.242

-6.418 -6 .47 4 1L.455 -6.369 11. 101 -6.103

rr.522 10.432 9.520 8.431 7 .205 5.897 4.553 3.215 1.935 o -?95 0.000 4

-5.696 -5.164 -4,537 -3.835 -3. O89

-2 .30? -L .529

-0,81t

-0.233 0.000

0A318 1o$rer 0. ooo

upper o.000 1.059 L.47I L.797 2 -3L7 3.249 4-746 5,869 6.801 8.288 9.426 t 0.290 LO.922 11.332 LL.522 11.455 11.101 l-0,432 9.520 8 . 4 31 7 -205 5-897 4.585 3.32L 2.1L0 1.0010.000

-0.933

-r .227

-L - 457

-L.767 -2.2A9 -3.042 -3.633 -4.131 -4 -922 -5.5L0 -5.944 -6 .242 -6,418 -6.47 4 -6 . 369

-6.103 -5.696 -5.164 -4 .53'l -3.835 -3 . 089

-2 -139 -t-.535

-0 . 986 -0 . 439 0.000 FlCr E- lb

69 Feb

94

65-01s

ord 0.000

0. o0

0.25

0.830 L. L24 1.356 L.702 2.324 3 .245 3.959

0. s0

o-75 L .25 2.50 5.00 7.50 L0.00 15.O0

20.00 25.00 30.00

6.764 7.L52 7 .396 7 .498 7.427

35.O0

40.00 45.OO 50 - 00

7

55.00

80.00 85.00 90.00 95.00 100.00

Feb

94

4

35.

.7 02

O0

O0

40.00 45. O0 50. o0

55.00 60.00 65.00 70.00 75.00 s0. o0 85. OO 90.00

95.00 100.00

3-

065

2.818

2-5r9

2.180 1.817

r.454

camber

1,

30.00

296

04015

)-.23

20. o0 25. O0

3-

0. oo0

ord 0.000 o.830 L.T24 1.356

7.50 10.00 15.00

0.000 0.082 o.L52 o.213 0.323 0.570 o.970 1.307 L.597 2.086 2.473 2.776 3,010 3.175 3 .269

1.090 o.727 0.363 0,000

Sta 0.00 o .25 0.50 o,75

5.

GA-4

.1,68

6.720 6,118 5.403 4.600 3.744 2.858 L.977 1.144 0,428

60. o0 65.O0 70. oo 75. OO

canber

3.959 4.555 5.504 6 .223

GA-4

0.000 0.082 0.l-52 o,213 0.323 0.570 0,9?0 1.307 L.597 2.086

6.764

2.776

7 7

3. Ol-0

.r52

.396 7.49A 7.427 7

.L6A

6.720 6.118 5.403 4.600 3.744 t

oaR

2.065 1.290 0.600 o.o00

3.r75

3-269 3.296 3 .234 3.065 2.818 2 .5L9 2.180 1.817 1.090 o.727 o.363 o-

000

40- 4]-2

upper 0. o00 o.746 1 , 051 L,298 1.685 2.429 3.566 4 .47 4 5.24L 6.489 7 .45). 8. 188 8 .73t 9.091 9.268 9.237 8.968 8.441 7.713 6.841 5.860 4.A12 3.740 2.672 r.642 0.706 o. o00 4

-2.O47

-2.318 -2.506 -2.635 -2.7L2 -2.7 42 -? -729

-2.646 -2.500 -2.311

-2.O76 -1.803 -1 . 500 -1 .178 -O.833

-0.49r

-0.188 0.021 0.000

0A4 12

upper 0,000

o.746

O51 1.298 1.685 2.429 3 .566 4.474 5.24L 6.489 7.45r 8.188 8.731 9.091 9-268 9 -2J7 8.968 8.441 7 .7L3 6.841 5.860 4.4L2 3.762 2.742 L.759 o.843 0.000 1.

lower 0.000 -0.582 -o.7 47 -0.871 -1.038 -L.249 -L.626 -1.860

lower 0.000 -0. s82 -O .747

-O.87t

-1,.038 -1 .289

-L.626 -L.860 -2.O47

-2.3L8 -2.506 -2 .635 -2,7]-2 -2.7 42 -2.729 -2 .646 -2.500 -2,3LL -2 .07

6

-1.803 -1 . 500 -L.178 -0,854 -O .562 -O.30s -0.117 0.000

40-415

upper 0.000 o-9I2 L.276 1.569 2-O25 2 -894 4 -2L5 5.266 6.r52 7.590 8.696 9.540 10.162 10.571 to -767 LO.723 10.402 9.745 8.936 7 .922 6.780 5 - 561 4.3L2 3 .067 1 .871 o.79L o,000

lower 0.000

-O.7 48 -O ,97 2 -1 .143

-L .379

-t.754

-2.275 -2 .652 -2.958 -3.418 -3.750 -3 . 988

-4.I42 -4.22L

-4 -229 -4.131 -3.934 -3.655 -3.300 -2.884 -2.420 -L .927

-1.404 -0.887 -O.4I7 -0.065 0.000

40A415

upper 0 .000 o.912 7.276 1.559 2.O25 2.494 4.2I5 5.266 6 .152 ?.590 8.696 9.540 10.162 10.57t IO,767 LO.723 10.402 9.785 8.936 7.922 6.7AO 5,561 4.339 3 . l-55 2.Or7 0.963 0. oo0

lower

0.000

-O .7 48

-O.972

-1.143 -1.379 -L.754

-2 -275

-2.652 -2.958 -3.418 -3.750 -3 - 9a8

-4.I42 -4.22r

-4.229 -4.131 -3.934 -3.655 -3.300 -2.AA4 -2.420

-I.927

-1.,431

-O .97 5 -0. 563

-O.237 0.

000

40-418

upper

lower o.ooo 1. 078 -0.914 1.501 -L . r97 1.841 -1.414

0-ooo

-366 3.359 4 .864 6.058 7 .063 8.690 9.940 r0.893 11.592 12.050 L2.267 t2.204 11.836 11- t-29 10.160 9. OO3 7.700 6.310 4.883 3.463 2.100 o.877 0 - 000 2

-r.7L9

-2 .2r9

-2.924

-3 ,444 -3.869 -4.51 9 -4 .995

-5.340 -5.573

-5 - 701 -5 -7 2A

-5.6L7 -5.368 -4 -999

-4 .523 -3 .965

-3.340 -2 .67

-t

6

.97 6

-]-.282 -0,646 -0.150 0. ooo

404418

upper 0.000 1.078 1.501 1.841 2-366 3.359 4 -864 6. O5a 7 .063 8.690 9.940 10.893 11.592 12.050 12.267 12.208 11.836 11.129 10,160 9.003 7.700 6.310 4.916 3 .568 2.275 1,083 0. o00

losrer 0.000 -0.914

-1.197 -r,.414 -L.7r9 -2.2L9

-2 ,924 -3 .444

-3.869 -4.5J.9

-4.995 -5.340 -5.573 -5.701-

-5.7?8 -5.617 -5.368 -4.999

-4 - s23

-3.965 -3.340

-2 .67 6

-2.008 -1.388 -0.82L -0.357 0.000

Fth E-rl

70 Jul

94

Sta

0. o0 o -25

0.50 o.75 r .25 2.50 5.00 7 .50 10,00 15.

OO

20.00 25.00 30.00 35.00 40.00 45.00 50. o0

55.00 60,00 65.00 70.00 75.00 80.00 85.00 90.00 95.00 1.00.00

JUI

94

Sta 0. o0

0.50 o,75

6

5- 015

ord 0.000 0.830 T

J-.356

1.702

3.?45 3.959 4.555 5.504 6.764 7 -]-52 7 .396 7.498 7,427 7.t6A 6.720 6.1L8

5,403 4.600 3.744 2.858 1.977 1.144 o.424 0.000 40AOl-5

Ord o. oo0

0.830 L.L24 1.356 1,

2,50 5.

O0

7,50 10.00 15.00 20.00 25.00 30,00 35.00 40.00 45.00 50. o0 55. O0

60,00 65.00 70.00 75.00 80.00 85.

.I24

.7 02

.324 .245 3.959 2 3

6

.223

6.764 7 -396 7

.494

7.168 6.720 6.118 5-

403

4.600 3.744 2.885

O0

2. 065

90.o0

1.290 0.600 0. oo0

95. O0 100.00

canber

40-6L2

4

0- 615

0.076 0.154 o.000

upper 0.000 o.942 1 . 3 31 7.647 2.L43 3.101 4,568 5.7 4I 6.733 8. 348 9,595 10.550 l,t.256 II .725 11 . 956 11. 921 11 .578 10.899 9.961 8.838 7,573 6.222 4.840 3.454 2,135 o,924 0.000

40A612 Carnber upper lower cA-6 0.oo0 0.o00 0.000 0.112 0 -776 -0.552 o.207 1.106 -O.692 0 .291 t.376 -O.794 0.441 l-.803 -O.921 o .777 2.636 -1.082 1.323 3.919 -1-.273 L.7A2 4.949 -1.385 2.r7a 5.A22 -1.466 2.844 7.247 -1.559 1.372 8.350 -1 .606 3.7a6 9.L97 -L.625 4.104 9.826 -1 . 618 4.329 rO.246 -1.588 4.458 10.456 -1.540 4 -494 10.436 -1.448 4.4LO 10.144 -L.324 4 .L79 9 - s55 -L -L97 3.843 8.737 -1.051, 3.435 7.757 -0.887 2.973 6.653 -O -707 2.47A 5.473 -0.517 r.9a2 4.290 -O.326 L-4A7 3-139 -O.165 0.99L 2.O23 -0.041 0.496 0 .976 0.016 o-ooo 0.oo0 0.000

upper o. o00 o.942 1.331. 7.647 2.L43 3.10t 4.568 5,74L 6.733 8.348 9.595 10.550 11 . 256 tL.725 11.955 11.921 11.578 10.899 9.961. 8.838 7 -573 5.222 4.867 3.552 2.24r 1. 096 0.000

GA- 6

0,000 0.112 o.207 o .29L 0.441 o.777 1.323

I.7A2

2.I78

2.A44 3.372 3.786 4.104 4 .329 4.458 4,494 4.410 4.L79 3.843 3.435 2 -973

2.474 1.982

L-487 o.991 0.496 0.000

upper 0.o00 o.776 1.106 7.376 1,803 2 .636 3 . 91.9 4.949 5.A22 ?.247 8.350 9 . ).97 9.A26 IO.246 10.456 10.436 10.144 9.555 B -73? 7.757 6.653 5 -473 4 .26a 3.069 1.906 0.838 o.ooo

lower

0.000

-0.552 -O.692 -O.794 -O.9?r -1. O82 -L .27

3

-1.385 -1.466 -1.559 -1.606 -L .625 -1.618 -1.588

-t .540

-1.448 -L.324 -L.L97 -1.051 -0.887 -O.707

-0.517 -0.304 -0.095

4

lo(rer

0.000 -0.71,8 -O ,9),?

-1.06s -t .26r -L .547 -I .9?2 -2, r77

-2.377 -2 -660 -2.851 -2.97A -3. O48 -3.067 -3,040 -2.933 -2.758

-2.54r

-2 .27 5 -1 . 968 -r -627 -L - 266 -O.876

-0.490 -0.153 0. 068

0.000

0A51- 5

upper 0 .000 1.108 I .556 1. s1g 2.443 3.566

ooo

-0.718 -0.917 -1.065 -1.261

-I.547

-L,922

-2.r77

-2.377

-2 . 650

-2.851 -2.978 -3.048 -3 -067

-3.040 -2.933

-2 -75A

-2.54L -2.275 -1.968

-t.627 -L.266

-0,903

-O.578

-0.299 -0.104

0. 000

lower

0. o00

-0.884 -1.142

-1 .336

-1.601

-2.O]-2 -? .57 r 6.533 -2 .969

5.2r7

.644 9.449 1.0.840 11.903 12-646 13.204 13.456 t3.406 t 3.012 12.243 11.185 9.919 8.493 6 .97I 5.472 3.859 2.364 1.010 0.000 7

4

lower

0-

40-618

-3.288 -3.76I -4,096 -4.331

-4 - 474

-4.546 -4.540 -4.41"8

-4.L92 -3.885 -3.499 -3.049 -2 -547 -2. 015 -1.448 -0.885 -0.382 -0,0l-8 0.000

0A61S

upper 0. o00 1.108 1,.556 1.918 2.443 3.566

6.533 7 -644 9.449 10.840 11.903 12.686 13.204 13 .455 13.406 13-O12 L2 -243 11.185 9.919 8.493 6.97I 5.444 3.965 2.539 1.216 0,000

Iovrer 0. o00

-0.884

-I.I42

-1.336 -1.60L

-2.OI2 -2.969 -3.288 -3.76\ -4.096 -4.331 -4.47A -4.546

-4 .540

-4.418

-4.I92

-3 .885

-3.499 -3.049 -2.547 -2.015 -1.480 -0.991 -0.557 -O

.224

0. o00

Ftq ff-t9

LIFT AIRFOII,S 3 0- 015 canber GA- 6 Ord 0. o00 o.000

HIGH

Feb 94 Sta o.00 o .25 0.50 0.75 r .25 2 .50 5.00 7,50 10. o0 15. OO

20.00 25.00 30.00 35.

OO

40.00 45.00 50,00 55.00 60,00 65.00 70.00 75. OO 80.00 85.00 90.00 95. O0 100.00

Table l

1.090 1 .527 1".856

.367 1-264

2

4-

443

5.250 5.853 6.681-

7.L72 7-

427

7 -502

7.440 7 .255 7.000 6.655 6 .240 5.755 5. 190

4.540 3

-AL7

3.0s3 2 .290 r .527 o.763 0.000

-

(

see also fi-gure

O.LI2

.207 0.291 0.441 o.777 r .323 I -742 2.L74 2.844 3 -372 3.786 4.104 4.329 4.458 4.494 o

4.41-0 4

-r79

3.843 3-435 2.973 2.478 L.982 I .447 0.991 0.496 0. o00

30-61-3.5

upper o.000 1.093 1 . 581 1.961 2.57L 3 - 7L8 5.322 6.507 7.446 8.857 9 -A27 LO - 470 l-o.856 11. O25 10.997 ao -794 10.400 9.795 9.O23 8.106 7 -O59 5.913 4.730 3.548 2.365 1.183 o. ooo

lower

0.000 -0 .469 -'t . 167 -L.3?9

-1.689 -2.L64

-2 .6? 6

-2.943 -3.090 -3.169

-3 .083 -2 .898 -2 -644 -2.367 -2.080 -1- 806 -1.580 -L .437 -L.337

-r.236

-1.1

13

-O.957 -O -766 -O .57 4

-0.383 -O.l-91 0.000

30-515

upper 0.000 L.202 L.734 2.L47 2.808 4.O45 5-766 7 .O32 8.031 9.525 10.544 l-r.213 11.606 L1 -7 69 Lt-723 11.494 11. 065 10.419 9 .598 8.625 7 .573 6.295 5.035 3.777 2.518 r.259 0.000

lower 0,000 -O.978 -1 . 320 -1.565

-t.926 -2.49L -3 -120

-3.458 -1 .675 -3.837 -3.800 -3 .641

-3.398

-3 . 11r,

-2.807

-2 . 506

-2.245 -2.061 -)- -9r2 -r.755 -I .56? -1.339 -1.071 -O.803

-0.536

-O -267

0.000

30-616.5

upper Iower 0.000 0.000 l-.311 -1.08? 1.887 -L.473 ?(1 3.045 4.372 5.210 7 -557 a.615 10.193 11.261 11.956 12.356 t-2.513 12,450 12.L94 lL.73! 11.043 IO.L74 9.I44 7 .967 6.677 5. 340 4.006 2.67L 1.335 o.

ooo

-1

-2 . L63

-2.818 -3.564 -3.993 -4 .260 -4.505 -4.5L7 -4.384 -4. 148 -3 . 855 -3 .533

-3.206 -2.911

-2 .645

-2.488

-2 .27 4

-2.O2r -r .7 2L -t.376 -1.032 -0.689 -0.343 o. ooo

Predicted Performance Sumarv ( ccfiputer anafysis, for curparison only ) Cl max-Vf laPs* CI max-no flaPs On c/4 Cd rnin

lirfoil

R=61'{

R=6M

cA30 -613.5

.0058

4415 NACA 4412 usA 35B clark Y NACA

71

III-6)

R=2H

r tao

3.62

(

I93I

)

.0073

-. r05 -.125

(

1931)

.0070

-

1'ra

r.'707

3. 14

,t*

(1923

)

.0071

--114

r .677

3.02

(1924

)

.0072

-. lll

1A))

3.07

*Flap condition: Cflag.

20 .

deflecci.on=25 degrees

FIAUR€

fi.|1

C

LA55r(

*

rCrF{-

LrFr A rRFatLS

(

F

oa. (o ^^?ARtso N a^iry)

72

NA CA 4 4I'

FlQvP,€ fl,--zo

APPENDIX

IV -

Aerodynanric

Characteristics of wing Sections '

A FPelv olx

73

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lirf oils Or, '' nverythj-ng you always wanted to knolr about airfoils but \,rere afraid to ask'r, for fear of feeling stupid, perhaps. Donrt feel bad- there are scme confusing aspecLs about airfoil perfonrErce, and a surprising nw cer of stupid airfoil design mistakes have been rnade in the past by people who should have knoarr better. 9're will point out a ferr of these, but the prirnary purtrEse of this artsicle is to "get back to basics" so that you can better understand the nain causes and effests of subsonic airfoiL trErfol:IrEnce, SwrrEtrical Airf oil Perfornance. l,ie ' 1l start r./ith a sinpl-e case of b^'o syllnEtrical uncambered ) airfoi.Is, I5s thj-ck, sho,.rn on figure 1. The first of these "basic thick" ness foms", NACA 0015, is considered a "turbulent flor^r" shape, while the second, lrAcA 5rtA0I5. developed later, is a "la$inar flovi" type shape. we dril,l a hole in each of these at the guarter-chord Foint to receive an axle, and then nDunt then (one at a tinE ) in a wind turlnel such that tbey are free to pivot on this ax1e, and then bLcn on thern. The airfoil is then tested at various angl-es of attack (C ) frcrn zero to about 18 or 20 degrees, plus and minus, in one degree j-ncrenents, and lift and drag are recErded at each angle of attack. Lift and drag are easy to visualize, rneasured in pounds, aqtsj-ng at the pivot point. Lift is neasured perp€ndicular to the air strean, and drag is nEasured parallel to the air stream. The }ift and drag values at each angle of attack are nohr converted to dirrensionLess perfomance coefficients, CJ- and cd, consi-dering t}Ie wing area, air density, and ai-r speed. lie nexts plot cl versus Cd to obtain tne "Iift curves " sho,in on figure 3. the Cl vs Cd cr.rrve is sFnr€trical about alfa = 0, r*rhere Cl- = 0, since the airfoil itself is s1'nnetrical. the zero-lift drag is called "profile" cf " form" drag, and the total drag increases as angle of attack increases, due to "induced" drag, or drag due to lift. As tie angle of attack increases bq/orld about 15 degrees, the lift begins to decrease as f 1ov, separation occurs on ttle top surface, @inrling at tie trailing edge. ttris area of separated flonr progresses forward frcn ttle trailing edge as the angle of attack increases, causing further loss of lift, and large increases of drag, untilthe airfoil evenlual-Iy "stalls". i,ie are not finished with or:r !.rind turnel fieasurenEnts, ho^Jever. on scarE arrforls the lift and drag are not exasll-y centered on the guarter-chold point, t}lat is, the "center of pressure" may be sdrF distanc€ forward or aft of the guarter-chord point, and tlre airfoil terds to rotate about the pivot point. For this reason, rrE [ust al,so nrcunt a sprjng scale at the trailing edge of the airfoil (see figr:re 1) to neasure the pitclling nrnent in foot-pounds about the quareer-chord point. A nosedorrrn pitching tendency is, by convention, a negative pitchj-ng firctrent. !,ie nc'v, convert the pitching roxrEnt sprillg scale reading tj:res .75c) at each angle of attack to a di:rensionless croefficient, On, sirnilar to Cl and Cd, by considering the wing area, air density, ai-r velocity, and also chord lengrttr. vihen r,,e plot the p.itching mcflEnt coefficient curve, qn^ /d vs alfa (figure 3) for these tvro syrrr€trical airfoils, we see tiat ttre On is zei6'for any angle of attack up to the sta].l point, ttEt is, the center of l-ift center of pressure ) es directly through the guarter-chord point. Inde€d, the center of Iift for anv s}'nretrical airfoil. is always at the quarLer-chord point, regardless of tie angle of attack. ltrus, this point has special significance, r*rich is the reason tbat we picked it for the ncunting point for wind tunnel tests in the first p],ace. the explarEtion for this phenc.rEnon is beyond the scolE of this article, which is anotler my of saying tbat I don ' t kncr^, ra,hy it j-s . Regaldless, the pitch-ing ncnent cefficient about the guarter-chord Foint for any synrnstrical airfoil is always zero. Ianiner F1crd. the next thing to look at j,s landnar f.l-or./. The ai-r alf aror.rnd us in FnaturiFinraisturbed staie is laninar, that is, in layers. rf you ncve your hand slor,ly in fron\ of you, holizontally, tie air renains in layers, and your hand es ttrrough snrcQy with mimmun drag, without disturbing the layers. Tlr-is is knorn as " la,rLinar flor.r". If you rrpve your hand rapidly enough, or if your hald is rough enough, tire flow over your hand wil-L "trip" to turbulent flor*, rrrhich has rpre than twice as m uch drag as lanjrnr flow. Ttre reguirerent for .Larnj-nar flo\^' is that the flcrvr over the surface should not be accelerated beyond cerbain lirn-its in any d.irestion- fore and aft, sideways, or verticalLy- tlEt is, we need c\onstant velocj-ty Underst€.ndinq

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94 If the flov/ has tripped to turbulent, \,vre need only to slct/ point the acce.leratj-on lirlits are not exceeded, and the fLc'vr will to the h'here doh/n once agaj-n revert jrnrEdiately to tanr-inar. !€ se€ that the 64A015 shape has a region of lovr drag betvJeen -4 and +4 degrees angle of attack. this lo.r-drag region is knov,'n as the lanr-inar bucket. Beyond I 4 deqrees, rr)St of the laninar flow is lost, and tl.e ftor over the entire wing beocrrEs turbulent. Iaminar flovr is easiest to maintain near the front of the airfoil vtrrere tie pressure gradient is highest ( "ncst favorable" ) , and is hardest to maintain beyond the thj-ckest part of the wing. Accordingly, t].e " Ia.runar" shapes have been desigrned for constant velocity flov,r over the wing at cruise, and the thickest part of the wing llas been IIEved as far aft as prasticable, to maxjrize the ]-arninar run. The net resuLt is that the laninar section has approxirnately 20t less drag at cnise tllan the ccnparable turbulent sestion, a sigrmficant FerforlrEnce fl-op over the surface.

advantage.

ScnE recent I{ACA

ients than the

6-series shaFes. but tleir larlinar buckets are carrespondingly narroi,er. They camot tolerate nuch change in angle of attack without tripping to turbul-ent flc'r.r. At higher Reynolds nunbers (higher speeds, larger airplanes ) larninar florr is npre dj.fficult to maintain an!4Jay, so ttle bucket becqres even narrcr,\Er with these airfoils, wtrich rnakes ti€fn jjrpractical for nrany applications. A1l in all, tbe NrcA 6-series tllickness distrj-butions are not bad, having a ccmfortable bucket width and depth, perndtti-ng wing twist if desrred, cl"jjnb at relatively slo,r speed, etc. withouC running out of the bucket. So nuJch for synrretrical shapes. turbulent ard lan$-rtar. |lexb ccrrEs canrber, or wing curvature.

Airfoil Performance. If rre take t-ire tr€ synrEtrical shapes d,iscussed in the nr-idd.Ie, r.rc obtain the tvp canrnerea airfoils "!o"e, ""E,ffi'EA-ij@ shonn in figure 2. The camber schedule is carefully designed, and is called the cambered

reference (A). The canber schedule for GA37A3I5 is a nr:dification of another nean l-ine frcrn reference (A), and is especially designed for lanr-inar flctor. The maxjjrrlrn canlcer in each ai-rfoil i-s about tl:le saIIE. Also. both ajrfoils are forwarded loaded, that is, the maximrm camber is located forh,.ard of the airfoiJ- rnid-point. at a.bout .40C.

The perfonnance curves for these tlrtc airfoils is shornn on figure 4. Cc.Tparing with fi$Ee 3, the first thing we notice is that canber produces a sigmficant increase of naximum 1ift, with no change in crui-se drag. Second, tfie stafl becc.rEs softer, that is, the top of t}le lift curve is flatter, and lift continues to be developed at higher angles of attack than with the uncanbered airfoils. This is prirnarily a function of the inj-tial slope of the rEan line ( slope at .25tC), an irnportant paraleter for good sloH-speed performance. this inj-tial nrgan line slope has been optirlized at about 15 degrees ,rn a1l "GA' airfoiLs, correcting an unfortunate crnission in the NACA r€rk. Ttre third thing that we notice is ttrat canrbering Iifts the vrhole performance curve (Cl vs cd) vertically upmrds into a nrre usable range of CI, with no increase irt drag. Airfoil perfornance is neaningless belo* C1=.15, except for a few ve-ry high performance airplanes with extrenely high pcner to v,eight ratj.os. AII other a.irplanes olErate above this point: for exajrPle, Irpst Iight GA airplanes operate at cruise lift coeffj.cients betrreen c1=.2 and .4. I€ see tiat our cambered aj-rfoil- perforrnance curves, and especial"Iy the lan-inar bucket. are nohr centered vertlcally on ttre desigrn lift coefficient (C1=.3) instead of being centered on Cf=0. thus the top edge of the larnina-r bucket is raised to nearly C1=.8, i.€f I into the cljjlib range. the bottcrn edge of the bucket is at Cl-=0 , renainhg ccnfortably belov, tie lo,"est operating CI nrini:rn:rn of C1=.I5. A11 good stuff. ltrere is one big disadvantage caused by the camber, ho\rever. tlctice that the pitch-ing nsrcnt coefficient is no longer zero, but is Or=-.05 for both airfoj,ls. Increasing the camber, or rpving the loading aft, both result in an increase in cln. Ttlus, a pitchijlg nsrEnt is ttre prj,ce lie pay for carbering tie airfoi], and it requires us to invesligate tie effects of On on airpJ-ane perforrnanc.e so that ue c€n design our airfoils intelligentl-y. ']

95 Ttjfi Draq. As shovrn on fj-gure 5, the center of lift (center of pressure ) for carnbered airfoils does not alr^rays remain at the nragic guarter-chord point. It does so at the stal]", but as the angle of attack decreases, the center of lift IIEves reandard. But the stall c.P, , so since ne must always locate tie aircraft C.G. at or near that tie nose of the airp.Iane will drop at the stall, the wing lift vector at cruise f or carnbered airf oi.Is is af t of the r,,Eight vesEor, and the airplane has a nose-dc'rrn pitching tendency. The fix? I,fe put a horizontal taj.l surface on the airplane to react the pitching nE(IEnt, holding the tail dcr.n. But as tle l-eamed earlier, negative l-ift in ttre tail surface produces induced drag' *hich adds to the wing d!ag. Retrernber also that for every pound of negative lift in the tail, an additional pound of li-ft must be generatd by the wing so tllat the swnnation of vertical- forces rernains zero. For exarple, if the airplane r.ireigls 1000# and the tail do^,n-load is 40*, the wing must generate 1040* total lift. Ttris additional 40+ of fift, above hhat rapuld be required for our sl4flretrical airfoil, also creates induced drag. so vte see that t.rjm drag, or t}le drag associated r,rith trjJrrLing out the pitchlng nEnent of a canbered airfoil, has trrc cc([Dnents- the induced drag of the tail, and the additional drag of the wing in producing an increnent of lift egual to tie tail doum-load. For our tr,.E canbered airfoils, fi-gure 5 shcr*s that the trim drag at cruise is appro).ijnate1y 5-8 drag counts, which is about I0S of the sectsion drag coeffici-ent, and addl-tive to it. conclusion? Unless e€ can shctur at .Ieast lot i.ncrease in rnaximum lift frdll cambering the airfoil, it isn't r.Jorth it. Ifappi]-y, the increase in Clnax for our airfoils is about 30t, considelably greater thEn the drag increase of 10t, so kle have a balgain. But thr-s is not always tj€ case, especially with aft-loaded 3irfoils, so t}te bigger lesson j-s that r*e should always consider the effect of oj fferences in on on airpJ-ane perfornance when ccrnparing airfoils. vse also see that it behooves us, when deg subsonic (1ight cA) airfoi-ls, to keep the On as lcnr as possi-ble, other things belng egual. Using srmth, forward-loaded nean lines, and using only as rnuch camber as necessary, does ttris. This is a rrErjor critj-cism of the l|A6A 6-series airfoils. which are nid-loaded, and tie infanpus N&sA GAIAI (I^5-1) airfoils, which are aft loaded I an j-nexcusable mistake. Don't use thern. For ccnparison, OrF-.05 is lovr, CrF-,10 is h-igh, and the Gn of the f.ASA GAI., airfoils (npre than -.I5) is outrageous. Ttrere are other th-ings that can be done to ninirtrize trim drag, such as using a long tail length, at least three wj,ng chord lengths long. A high aspeqt. ratio horizontal tail. surface also helps. Anot-Ller effestive technigue is to have a r,,eight shift to the rear at cruise, follcwirg the C.P. shift to the rear. Retracting the landing gear to the rear does this, as on tie Iancair rV and the Cessna 210. Sunnarv. ltrere are thre€ crefficients of airfoil lErfolnEnce- CI, Cd, and Cm- equaUy jnportant. the effect of airfoil- On on airplane performance mtst be quantified and not neglected in desigrning airfoils. orrly forr,€rd-loaded nean lines, such as the NACA (0.5) nean line of reference (A), should be used for csrnon subsonic C.A airfo.il designs, to rnillinrize Gr. It is not necessarl' to reduce t].e airfoil On cc(pletely to zero, rrrhich r,.,a.s done with the }.lAcA sdigit (230rc<) airfoils,at tlle unfortunate cost of degrad"ing safety, but onl,y to keep the On as lcnr as praclicable, other things

being equal. Disclaj-ner. Ttris paper is adnittedly a sfuplified explanation of airfoil lnrformance and design. For exafiple. wind tunnel force neasursnents are now ccnnrcnly taken with pressure rakes rather than old-fashioned spring scales- Al-so, for satisfactory horizontal aircraft stability, it is not necessary tiat the taiL lift coefficient be negaLive, nelely ttlat it be l"ess than the wing l-ift cefficient, provided that the nuny olher factors affecting horizont-al stability contribute in a favorable (stabilizing) direst:-on. Hou,ever, at slo\^' ftight, which is norrnally the lrrcst critical conditron for longitudinal stabj,lity, the center of pressure of any airfoil approaches tne C/4 point, and tie c.onclusions presented herein regarding "trjm drag" or drag associated with trinning out t].e wing Qn, are not invalid. Revised 5/I7 /95 Ha.rry Riblett, 416 Rilelett Iane, wilrLington DE 19808 302/994-0479

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Deslgn ltotes !,lhen deg

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Tapered wings

a taperd wing airplane, the designer is faced with certain choiees.

airfoil secbions should be used for the root and tip sections, especial-Iy [Er cent thickness? 2. Hctur much t\,rist (washout ) should be put in the wing to protect the wingtips frcrn prenEture stall, and to preserve ail-eron c.ontrol tlEoughout the stall? 3. !,lhat taper ratio and what aspest ratio sbou.l-d be used? Hj-storically, designers have teen guided (at least partj-ally ) by a series of taPered wing tests conductsed on turbulent secti-ons at NACA I-angley in the rn-id-1930's. Figure I sho\ds a tabulat.ion of the strEcurEns used during these tests, and the tabulated test results . D/pj-cal performance curves are a.Lso sholnm on figr:re I. l.Iote the sketch of the initiat stalf dlstributions predicted by l.lACA for "restangular, tapered, and sr,€ptback wings". This sketch is especially botherscme, since it il.l.ustrates the NACA concl-usion that "rectangular wings stall first at the wing roots and tapered !,.rings stall ' first at tl-e wing tips"- hence, supposedly, rather drastic llEilsures are needed, such as use of considerabl-e rrrashout, or use of sections with rore camber at the tips, and then even nrcre uashout, to ccrnbat these "bad tip sta1l characteristics" of tapered wings. The bothe.nscrre aspect is that the planform differences betrnteen the straight and tapered wilgs are not so great as to logically for the n'Erked differences in the location of initial stall reported by I{ACA. Neverthel-ess, generations of aeronautical- students have been conditioned to accept these resuLts as gospel, and to desigin accordingly. ltre ccnnonly acceptd washout recqrrrEndation is about 3 degrees, in spite of the fact. that twist reduces t}le overalL efficiency of ttle wing. !et's look a Iittle cJ.oser at the test s1=cimens used in the IiACA tests, hodever. Incredulous.l-y, of t].e 22 specj:rens tested, a1I but tLlc tEve a t thickness taper frsn a r@t thj,ckness of l5t, f68, 18t, or 20t to a tip tiickness of only 91, in addition to the planform taper. The nexc to last specimen uses a 23013/43010 ccnbination. that il nrrre canrber at the thinner ) tip- all t}.e rest have the same canlDer, root ard tip. onl-y the l-ast specirren has the sanE per cent thickness at the root and tip, IZt, but it uses an odd (eUiptical) planform. Evidently. l.lACA ( erroneously ) assurEd that the preferred way to build a tapered wing is to taper both the pladorm and the per cent thickness, and unfortunately the test results are contarninated by the effest of these tr.ra variables ccrnlcined. casting considerabfe doubt on the conclusions. It is curj-ous (and unexplained' tllat NACA never dj.d test the tHo variables separately, except for sarple #22, htrich has an odd planform that further contaninates the data. In fact, if they had tested a 2415/2415 sampLe for exanple, with 2/I planform _taper ratio, they reoul.d have found tllat the initial- statl, distribution is the sane]for a straight rectangular Hing, that is, benign. Further, if they had tested a straj-ght pLanform wing with a per cent thickness change frcm root to tip, they rrculd have seen the locaLion of the illilral stalf shrft to the wj-ng tips. thus. c.ontrary to NACA'S conclusj-on, the spanwise location of the rnitial stal1 j-s pri:narily a function ot the per cent thickness change frcrn root to tip, and is not due to the planform taper. Prmf of thrs is shor*n on figures 2 and 3. Itote that the thj-n (9t) tip sestions stall about 3 degrees ear.l-ier than the thicker /raot) sections, for both the 24>o< and the 23olo( sections. Flrther, the mlst efficient 'secLion thickness in tenns of naximum L/D is LzZ, as shom by figure 7. Therefore, there is absolutely no reason ever to use a tip thickness Iess than 12*, and NACA'S design of the tapered sestions was a rnf,nunEntal mistake. UnforEunately, follcrvring NACA'S psr exarple, a r.hoLe generation of tapered wing airplanes was built with wing tips that r^,ere t@ thin. Fign:re 4, c€urtesy of I'lr. ceorge Copland of Duncan, OK, is a partial listing of representative planes frcn the I930's, 1940's, and 1950's. Note tJee ill-advised use of 9t thick tip sections on nany of tlrese ccnrrDn airplanes. It is also interesting to note that a fe!e, of tie nore sucessful airplanes (P-38, P-5I, Dc-3, Eonanza ) did not fall for the trap of using 9t thict( tj-p sections, but used 12t tip sestions, contrar)' to I,IACATS reccnnendation. l.lote a.l-so that the Pi,per PA-2+ cc.manche, desigrned i.n 1954, rrras a historically si-gnj,ficant airpfane, for it "broke the ncld" by using only planform taFer with no [E! cent thickness taper, with 1. !,lhat concernj-ng

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100 no washout in the wi-ngs. The resul-t was a very docile ai4ll-ane, Unfortunately, hor"ever, too rnany nndern airpJ-anes. such as the Venture, Malibl, and high-perfornEnce E€ech ncdels (see frgure 6) continue to be buj-lt with thln wing tips, unnecessarily causing control prob.l-etns and ccrnprcrnising safety. 'Itle 23015/23009 cc.nbination is especially j-11-advised, due to the additional problsn of sha-rp statl cha-racterj-stics of the 230)0( airfoil-s. Figure 3 sholrs the mechanisn of this sharp, dangerous sLalJ-. The 230xx carnber profil-e has a discontinuity (ki-nk) in at at 158 chord- Tl-ris causes the airfLsd. at higher angles of attack, to selErate at that point, resulling in a separation bubbl-e on the top sLrrface. foU-c'\^Ed by reattach(Ent before the no.nnal trailing edge separation. The added thickness of this separation bubbfe on the top of the wing causes the wing to act as if it were thicker and nrere ir-ighly canbered (high li-ft) at high angles of attack, i-n spite of the re.l-atively lovr gecnEtIic camber of the section. At lc,v, angles of attack, the bubble disappears, and the section leverts to its lop--drag profile. For many years thj-s airfoj,r was touted as "lnving the best of both r,rorlds", but ttre disadvantage is a dangerously sharp stall. As the angl-e of attack increases further, the Pattached section gets shorter and shorter unti.I the separation bubbl-e suddenly expands to cover the entire top surface. resufting in a sudden toss of lift. This is bad enough on singre engine airplanes, but on twin engine airplanes with one engine out the airprane miy slap-ro1l suddenly and unc€ntro.Llably into the dead engine, if the speed drops tcrl lorr(King Air crash € l,filmington 5/2/93, Fig 5 del) Recent1y. vortex gen;rators have been used to rmprove this situation, as shc,wn on fign:re 6. the vc's are instaued at l-0t of chord just before the discontinuity at 158 of chord. They function by creati-ng a thi-ck ' ( energj-zed turbulent ) boundary layer i-nrnediately aft of ttre VG's, preventing ttie ation bubb.Le frcrn formrng. Ttrj-s forces the flo,.r into an even rpre frl-gUy ca.nereO=eparsnape (nore lift) than with the bubble. wi,thout tlrc disadvantage of the bubbl; ( sharp stalfi. Ttre Price is a slightly ]-orarer cruj.se speed due to the srnall- anrcunt of drag frcrn the vc's' but overal'L this is a very good guick fix, uproving safety. of course the bette.r solution, next ti.file around, is to use nDdern soft-sta}l airfoils not subiecL to the separation bubbl-e probl€rn. Also rerernber that the vc's are not a parurcea for aI} air-

foils' but rather a sg=cific crutch for the poor features of the 230>o< airfoiLs. one finaL ccflnrent is needed regarding l{AcA sarple *22, with the erliptical planform. This slrcirnen has the Lrighest CLmax (I.8I) of any tested, and is aclordingiy often cited as proof of tlle " inherentLy superiority" of the Lltiptical planform over t-l-re uniforrnly tapered planforms. I{ote, ho^rever, that this specijnen enjoyi tro distj-nct advantages over the other specjrEns- it has a unique high-fift secLion (4412), and in addition it has the same per cent ttrickness root and tip, l-2s, htlich is, as r,,,e have seen, the optimun thi-ckness in of best L/D. In vierrr of this, we vDnder if the legenda-qr rnystique of the ellipti,cal planform is justified. Regarding planform taper ratio. it is r+et1 to renrenrber tllat a ve4/ short tip chord reans a 1on' Reynords nlrnber at tlre tip, and ai-rfoil section performanci drops ofi at J.c&r Re)mords nurnbers, ltlus it i-s best not to taper the wings tcro much. cccntcn taper ratios go frcm about 3/2 to 2/I. Snal-Ier tip chords rEan $naller tip losses, but also lq.€r ttn, as stated above, Of course a higher taper ratio (2/l) alsi tras a structural advantage since it pernLits a greater spar depttr at the root for a given per cent root thickness,' other things being equa1. Alternativery, a higher taper iatio may permit use of a lo"rer per cent root thi.ckness (15t vs lgt) for letter i/n**. Regarding aspect ratio, the hj.gher the better, Ijnlited only by structural- consid_ eraLions . AsIEct. ratios betr.reen 6 and l0 .rre ccnnErn for porered- aiforan".. rn sunnary I for turbul-ent wings, the cips should not be Less than lzt thick. For Laminar wings, notice that uEre is litt1e difference in L,zD beer*een ]2t and l5t thick sections, thus r5t thick tip sections are preferred. rf thj,s is done, and if nrcdern sections such as GA airfoi.l-s are used that have forward road-ing and lead:-ng edge dr@p, the tip sta11 probrsn is eurrlinated, or at least, is greatly reduced. use of additional canber at the tips is not needed, nor is vring twist. A flapped section starls at a loler angle of attack than the sanE sesti-on unflapped, ana tfris in itsel,f provides protegtion against tip stall-s. For twin engine airplanes, to herp the engine-5ut situafion, the above recqlnEndations are especially applicable, particularly with regard to the use of soft staLl airfoils, so tllat assynretrical- lift c-onditions are unlikely to develop. ttarry Riblett - 4/I8/I994

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clssNA3l0voRIEXGENrRAToRs tJAcA Boundary l-ayer Research and The Twin Cessna Flyers have teamed up tro bftig e3rly model Cessns 310 ownels the advaltages vodex generaton afford. Afier Boundary Layer Research @LR) developed the kits for the Cessna 3 1 0 &rough the 3 i 0F, BLR aad The Twb Cessna Flyers came to an a€reement granring The Twin

fact, VC equipped aircralt rnaintain full aileron control response all the way *uough a stall. The kits consist of a series of small aluminum exrusioos rhat are attached to the lpper lading edge of &e wings, !p bo& sides of the venical fin, and there are two srrakes which are atlached oo the outtroard side ofthe ergine raceiles. Over simpiified. the vonex generators "re-energize" &e airflow over the con0.ol sur, faces at low speeds aod high angles ofattack, and whefl the air, cnft yaws, $'hich increases the angle of attack of the vefiical fia. This "re-energizing" causes the airflow to remain attacbed thus the saall is deiayed alld actually becomes much more dociie when it does occur. Amazingly, this is all done with a kit thar adds less than one pound !o the weight of the aircraft. Kits are available for rhe Cassna: 310, 310A, 3108, 310C, 310D,3i08. and 310F. For more information regarding these kjls conract: Th6 Twin Cessna Ryen ar (800) 825-5310.

Cessna Flyers the €xclusiye marketing rights for the kits. According to Bob Desroche, PrcSidenr of BLR, the rclationship is "a perfect rnarch" in that it allows BLR ro concentrale on the development of new products. while it pisces the marketing efforts witi a.n organization thar has dirccr conuct with over 7000 twin Cessna opemtors, Inslallation of the kit can reduce Vmc bv as much as 20

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nar"v niurett 1 07 IIO. 3 /il6 Rib'en Lane Wilmington, DE 19808 (Irl/JtlI995)Tandnq trre sharp stal] of Lhe NACA 23012 A.irfoil 30?934-0479 the notoriousl-y soften carl be used to tllat t'.r) methods paper discusses Srnnnarv. This generators, or alterof vortex is, use that airfoil, neCA 23012 l-narpstaff of the of (reprofiling). nechani-sm the discuss l€ also build-up an upper surface nativeJ-y droop is ineffectedge leading wlly additional and explain airfoil, on ttris the stail tive for i:rproving the stall on this airfoi-I. Discussion. In the mid-I930 ' s, follorn'ing tie r.prk on the 4digit airfoif series . ( salre NACA aducted a series of tests on airfoils related to the 4-di-git airfoils placed far forward. unusually camber rnaxjmum the thickness distribution), but with The ob ject of the tests r,,ras to see if the aj-rfoil Gn cDuld be reduced to zero, Iartdch is not a necessity for conventional, airplares any'\r'Jay, as long as the GIl is kept reasonably lcrhr by nEderately fo4rard loading. Anyhc'vr, these " zero on" airfoils !,rere designed ana esiea, and the nrcst widely used of these 5digit airfoils is the ubiquitous and infanrcus I'IACA 23012 airfoiL. It is l2t thick, with Peak camber of 1.8tc Iocated at the l-5tc position, rather ttEn tl]e usual 40tC Fosieion us€d on nDst of the pozufax 4-digit airfoi-ls Q4I2, 44L2,4415, etc-). the nean line aft of .I5c is a straight 1ine, thus the only camber in tl:-is airfoil is in the first 15t of the chord length. Accordingly, rrie can describe the airfoil as bejlg the DiACA 0012 sYrlretrical secaion wj,th the first 15t bent do,mward5 (lc:ding edge droop ) approxirrrately 1-8t. Actually, the effective drmp is only about l.4t due to the faulty "slope and radius" nrethod of leadil]g edge design used on all of tjte I'IACA airfoi.l's , ho/,,ever the fact renains that the camber profi,le of this airfoiL consists of leading edge drmp only, with no conventional camber. the result of tJris is an airfoil- with near-zero Pitching nErrcnt coefficient (Gn). Fr:rther, sirtce there is no negative canber jn the airfoil, the nEximun lift c,'cefficient Eemains high and the induced drag is loi^r, cdrpared to the best knorvn previous zermn airfoil-, l'4ax ltur)l('s 1924 |+6. The [&-6 achieved zero cln by reflexing ( negative carrber ) the nean line frcrn .60c to the trailing edge, effectj,vely kj,lling the nosedcnn pitching nE(Ient by applying a dcarnload on the trailing edge of the airfoil ( figure 9). this, hokever increases total induc€d drag, and reduces Clnax. the carnber profile of the !F6 in the first 60tC is conventional ' ho\^rever, so the M-6 des have a nice. soft stallwind tunnel- test results of the "ns^," zero-on ai-rfoit, 23012' are sr.nrnarized in t{AcA IR *537 of l{Ey 7 , 1935 (see figure I). Based on the faets ttlat 2301-2 shc,LEd a nEderately high Clmdx, very lol Gn, and Cd no greater than the 0012 syrnetrical section. NACA pronounced this airfoil to be "markedly superior to l€ll-knovm and cc6rpnLy uSed sectj-ons',, and reccnnended its wide usage in glorn'ing telrn5. HouJever, the airfoil has a terrible sh;rFstall characEeristic. wtlich MCA TR#537 failed to d.issuss, and that i-s its domfall. thrs was noted briefly in Table II Airfoil Data of IR #537, So IIACA knevr of the existence of the sha-rp staU, ard chose to ignore it. SlErp sta11 airfoj,ls are bad enough on single engine airplanes, but on prop driven twini with one engine out these aj-rfoils are especially letha1, causing accidents such as described in figure 2. In fasE, sharp stall airfoils are the rnaior reason that cA light twin fatality rates ironically exceed the fatality rates of GA ]ight singles. [,le will not achieve true twin-engine reliability in prop-dri-ven twins untit h,e get rid of these sharp-sta1I airfoils. ProP.driven twins are ljjrlited by Iateral cont.rol authority near vtIE due to the effect of a "blovtn surface" aft of the operating engine - with shatp-stal-l airfoils, sudden unccnmanded and uncontrollabl-e upsets occur at relatively high vlo'lc. with soft-stal,I airfoils, vtlc is much ]o$,er, and in addition the roll tendency is control,lable. Knq,'/ing wllat r.,e knod today ' 'e realize tlEt NACA, as soon as they learned of the bad stalL characteristic of the sdlgit airfoils, shoul-d have terafnated the project. Accepting the sharp stall rnerely to achieve zero Gn was a Poor trade-off. There are t\^D tl/pes of airfoils that have sharp statlsr tllose with too u,tt.l-e camber in t-ire Ieading edge, and those with too much cafiber in the leading edge. airExarp.l-es of tJre fj-rst group incluae nDSt synrnetrical sections, and l-olv-carnbered and such as ttre- l-ater 11gcA 64-212, These airfoils experience ccnPlete ioi:"! separation frcm the very leading edge at the stall-, and they can usually rlo', suoa* G-i-pt"""O by adding a sITEIl anpun! of leading edge d"rmP ' Arrf oils of the second ADDn{DUI'1

108 group. ircluding ?3OI2, experj-ence ccnpl-ete flo* sepa.ration on t}re toP su-rface at the stall, frcm a poj.nt near the end of the leading edge droop, that is, at about .l2C in the case of the 23012. the resul-t is the sane. horever- a shaq) loss of 1ift, usually acccnpanj-ed by loss of lateral control, and a hysteresis loop reguiring a substantial decrease of angle of attack ( wrth considerable altitude Ioss ) before attached flc'vr can be re-established. Arrfoils of tfre second group cannot be irnproved by adai ng leading edge drr, since they al-ready have too much droop. For exanple ' adding npre droop to the 230]2 airfoil results in t}Ie 33012 or 43012 ai.rfoils, and these have stall- characteristics as bad as or vrorse t-lnn the 23012, frcm wird tunnel data ( check it out)- I'itut is required is to ease the cransition frcrn the leading edge droop to the rest of the rlean Iine, reducing the discontinuity in the nean line at tbat point- one effecLive and proven rrEthod is to install a cqnplete span-wise array of vortex generators on the top surface at alout .10c, (Fiq. 3, delered). Ttlese function by fi11in9 in the "low sFot" on the wing dch/nstrean of the vcrs with a thickened boundary layer of energized turbulent ai-r. discouraging flol separation. Ttris fix is cheap and effective, and should be reguired on all twin-engine prop cqnnuters using 5-digit airfoil-s, which is the nrajority of the fle€t. AIso. don't forget that that single enging airplanes with 5-digit airfoils can benefit frcrn tj:-is as rrell. Another possi-ble way of acccrplishing ttrc sane fix is to reprofile the wings, filling rn tie lor,r sFot aft of the leading edge droop on the top surface with soli-d materj.al such as foam and glass. This is quite cqrrrDn on experinental (hcnebuilt ) aj.rplanes, wi-th both nptal and ccrPosite wj-ngs. Fign:res 4, 5, and 6 describe this nethod. l,lotice that the secej.on drag astuafly decreases, in spite of ttre increased sestj-on thickness, due to the prcnption of Iaminar flovr. Furttrer, the zero-lift Gn renains about the saITE, so top speed is unaffected. Ttris nerr profi-le could also be used to nlcdj-fy existing [email protected] on production airplanes. Of c-ourse, t}le better soluti"on aerodlmarnically is to discard the ?3012 airfoil crcrTplete.l-y, and use a rndern lol.F-gn, soft-stall airfoil, such as a "cA" airfoj-l. As stated above. the I{ACA s-digit sestions cannot be inproved by adding leading edge droop, tius the tlc State/l{AsA fj:< on the "Venture" airplane (figure 8) is a poor solution lo the prob.Len. I suspect that any jjrprovenent of the stall in this case is nereJ-y the result of the consj-derable aerodlmaruc twist that was introdticed into the wing by this fix, delaying the tip stal-l. Horever, tll]is causes a considerable loss of efficiency at high spce d, and aLso raises the ]anding speed of the airplane, so it is not a good solution to the problsn. 4301X Airfoil-s. The NACA 4301X airfoils are the sarrE as the 2301x airfoi.Is, but with twice as rm:ch leading edge droop ( figure 9). The stall is as bad as, or tanrse thar. the 230IX airfoils. Fortunately, the 4301x airfoils are rarely used. one exception is Fred l^Jeike's " Etcoupe" ( NACA 43013), holrever on this arrplane the elevator travel, is ljrnited so that the stall angle of attack can never be reached, Still, the 43013 was a strange choice for this airplane. Anotier airplane that uses the 4301X airfoiLs is the Ftench ATR-72 twin turbo"prop c:cnmuter. and tlEt story does not tEve such a happy ending. In october 1994 a crash occurred at Roselar,en, Indiana kitling a1I 68 people on board, a direct result of the NACA 4301X airfoj.Is used on that airplane ( figure I0). As confirned by subsequent in-flight spray tests a 3,/4 inch high j-ce ridge forms on the top surface at .09c, forfidng a very effective' spoiler. vffren ccrnbined with the already terrible stall charactseristic of the airfoil, this caused an unccnnanded, uncontrollable roll-over and irrec'cverabl.e dive. Ttre ice ridge forms at the very spot on the airfoil- \rtrere a pronouncd suction peak exists ( figure 7), since here the tsrperature depression frcm adr-abatic expansion and cooling is the greatest. The ice ridge is aggravated by tlre strange ptacglrent of the vortsex generators on the ATR 72 wing. The "fi;<", longer de-icer bcots, is nrerely a bandage, for the basic probJ-ern rguins. Ivlodern c-onstantvelocity airfoils do not have this suction peak, nor the problan. Conculsions. Ttrese interirn fixes should be used until the t'IAcA 5-diqit ai-rfoil-s cbn

(

}IACA TR

109

r.b.

537 ) ITRTOILS ILII'L\G ?EX I.A..XITU){ C.{.I(BEA ST-OSI]ALI,Y FI..R FORW,I.ND

despo calcu,latioos. Tbe simple meenJi_oc rirloils gste erceptioDolly lor+. pitcbiag DoDeDts, soElesb!,t,

l9*". th- the theorelical vaiues bss€d on the mear liae. BotI the rueasured aod theorelicsj curves for tle

simple mean-line air{oi.ls are given in fgrLre t6TJre anolysis of ihese chorts o'Dd the" dstr of toble _IJ shor that tbe reflesed !-irfoils, altbouqh co[rDlr.irs fnror.rbl-r s.itb otber ref ered airfoiis, uJ;;J;;; the simple meaali-oc uitt"ils_ f*tf,.r.o"r1il" foils corerirg r range of carn ber locations lorro,rd ^r'ot Dormal positions possess improved characreristics-{ con:parison of tbe N. A. C. A. 24 012 ,ittr the -\. -.1'. C. A. 2912 i-Ddicates the differea""s'tba; y;

attributed to tb€ dif€r€nce betweeD th€ forms. These airlofu harbg rhe same -.-_tio" tloD but difl'erent Des'!.li-ue foras possess ""-tJ; aooroxi-

<.),

terlstics over well-knorrn and commonl,r used s.irfoils o, lhrs clo.ss. Ir hos a hish ma_rimum hft and a lor 1", moheDt- Furrbermore, the niainum drng is procticrll_v o,s los as thst of tbe correspondiag sji,Betrjcal oirJoil, the r*. J. C. -{. 0012. I!gre.9e^neraU5, other secrions of tbis gtoup- sucb as , the N. .'1. C- A. 2lOt2 aad 29012 baringL e.cn loou, pitching moment thllc tbe g30l?, sbo'uld supply thc need, of 'nan5 -applicarions ,"q"fiog a "figl,iJ-"'cam_ bered section of modernte thicl:ness f,uring"a ,er_, lou pitchiDg EoDeDt-

LexcLsr ME}ronl,'l AERoliAvrrcal, Lesonaron):, N.r.:rotr-e.r- ApvtsorI Conyrrrrr ron _A.unoraurrcs, Ler;cr,er firr,n, 1-e., trlay 7, f $i.

ntrtel_v tbe same lift and drag characteristics.' The angle of zero lift and the pitchirg moment, lo"r"""r, are quite di{fereut. .Especio.llv notevrortby is the ven r0uch loEer pitchiag moment produced b-. tbe airfoils reported herein.

AEFENENCES

ETlDel li., Itard,

1. JTobs,

f,eooerb E., rDd pi.Etrenon,

Robert trt,: Tbr Cbr,r!,.!.ristics ot ?g R.Irted -Urfoii ScctioD! froE T€srs i-b rbc !'t!iEble",Deasit-" Wiaa tumd. T. R. \o. 460, li. -{. C- -{., 1933. 2. J^cob6, Easroao \., lDd _{bbott, Ira, E.: Tbe .\. C. A. Vtiable'Deo:ity lfild Truael. T. R. r-o. 416, -{. C. ;., -\-.

1932.

-{.

3. Jrcobs, LstEaD li,, rod Cl.af, \fillirm C.: Ch.rict.risticr of tbe N. A. C. A- 230f2 Airfoil from T.!ts i.D tb. IultI'erirble-Dcasitr Tuoaele. !. R. .No. SJO, *dl N. a. TO. c- A-, t935.

TABIJ II._AIRFOII, I

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irr

g ,t

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= -

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r De I "* -o,i$*-.ffijgr6 _ I

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tl

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DAT-A.

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Ei!

\

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!9

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u

23

0.t9 6.25 Il

ao

16

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r0 ir ro _-,1

6.26 12 z. l.A l2 2i

;; ilg;.i$f;''"t{r .Dord 1.5o.d &5 r i,a. ro,D,o8 !!. cr,ltD,u.. or r!. E-!riD.. itif t-or ot i-r. rrccr o l-afi,m

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13,937- THrct{NESs

, oC, DEGREES DEFLET

oO

OO E- O. ABOVE ANGLES OF ATTACF: 3.

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NORTH CAROLINA STATE UNIVERSITY

@,r:a :

ENHANCED WING DESIGN FOR STALL DEPARTURE RESISTANCE

I

THE HIGH .ASPECT RANO WIiIG

While prcviding significant bsn€fits in cruis€ and climb, the higfi aspect ratio wing ,"qrir"i

design considaralion

*i" at stali ol.j" to rt J

inconsistencies in rhs grow{h ot irs muttipL cells.

ti'

siil

.

STALL STFIPS

Stall strips ar€ widsly us€d

t'.'

ta'

tfri'

r+'

to force inboard

separation b€tors the stall celts fully develop. However, the r€sutting aircraft pitch_do*n firiis th€ useable litt ot the wing.

Stall Pattem w h hboaftf Sla[ Strips

.. THE LEADING EOGE OBOOP The design philosophy behind rh€ NaSh teading edge droop is to provid€ a

'ive" davice

which

delays th€ outboad separation well beycnd the point at which it would normally occur. This is

Vonex Separated

Flor

ffi

achieved by th€ introduction ot increas€d leading edge camb€r and the augmentation ol the energy within the boundary layer crealed by a vortex which Basic Wi.E torms at the discontinuous wing/droop intsrs€ctiori. Th6 net result ii increased stall Leadlrp Rtge Orcop Aorodynamics departur€ rssistanc€ due to the improv€d.. roll damping . and predictable pitch break . -

-

.'tt,tlo=

LE. Droop

(t--

116 O

THE LEADING EDGE DROOP DESIGN PFOCESS

Sinca l€ading edge droops are rctrcFtitted, th€ design process musl accout tor th€ aerodynamics of the €xisling wing. A comput€r codg was developed to mathemalically defina, iterat€, and optimize a leading' edge €xtension ot lhe ctrnent airloil s€ction. Minimizing the cruisedrag penalty whil€ increasing tho stall anglo ot

attack ar€ the primary

Cut}r til d.tennh.d

math.fndi:d cquarbn e[ach tloinl

Porc.nt dtoop

Pcrcenl rxienrion

design

lorer

anach point

Liadirg Edg. Olaop oesbn O.scriprbn

considerations.

O THE VENTURE DROOP/SLOT DESIGN Designed at North Carolina State University ancl wind tunn€l tested at NASA Langtey, the Ouestair Venture modifications reprssent a uniqu€ blending ot a€rodynarnic concepts. A

conservative droop is coupled with a pair of chordwise leading edge slots. The slots gonerate additional vortices which act to provent the progr€ssion of the primary sta cell. Thus, the combination of stots and droops allow more ol the wing to attain anached flow to high€r angtes of anack Ouestair Venlura Droop/Slol D€siEn

.

TEST FESULTS

Wind tunnel data indicat€s that the adclition ot lh€se wing enhancements provides more useable litt lhan the industry-standard stall strips while draslically softening tho slall break Subsequent flight tosts have further demonstrated th€ departure r€sistanco ol ths conti

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U.S. APPROVES

(A1R72 uses NACA 430fX

)

Lorgcr deicer prevcnts fiorrnotion ol icc forwond of the oilerons. Neorly 20O oir crafi in l.lortfi Arnericqn seryice crl c.hoduled to b. retofitted by June l.

NEW ATR DEICER EDWARD I-I. PI"I'LTIPSAVASHINGTON

f I

airfoils

he FAA hos oooroved o new deic6r for ATR honspods ond plqns ro begin irF

vasligoting icing chorocteristics of other turboprop reglonol oircroit lqter tilis year. Cedifjcotion of 6e deicer lqst week occurred bllowing four montirs of FAA 9ud/

ond evoluotion of "oll ovoiloble lechnicol doto" by tho ogoncy ond it: French counterpod, rhe Djreclor Genemie de l'Aviolion Civile, Doniol Solvono, spociolorsisicat or FAA's Aircroft C6dificotion S€rvico, soid. llose doit iicluded flight tssts in nq$ urol ond orrificiol j.ing conditions. The enlorged deicer cove.s up to i 2.5% of lhe wing's meon oerodynomic chordoeorly twice the oreo lornerly protocled ogoinsl ic6 occumulotion. Flight t6sts co+ ducted or Edwords AFB, Colif., eorl;e. rhis mon$ indicob ihe deicer preventr formooo olon ice ridge forword of the cilerons. A U.A. Alt aORCE KC-135 tqnksr equipped wifi wobr sproy equipmenl del uged th6 ATRZ2 ir q series ol rosrs rhor included wotar dropleb vp io 200 microns in diomet€r. Ths deicers funcioned proF erly with ffops retrocted ond with flops ex-

rended ro

l5 deg.--o

setiing normolly

{rsod in holding pott6hs,

A similor r;dgc ol rce is su.rpected to hove coused o loss of loteroi conrrol thor led to tho crosh of on Americoo Eogle ATR72-21A naor Roselown, lnd., in 5crober. Thot oircroft wos llying o holding pore.n w;rh flops or l5 deg. ihen the occident occurred, During the testr ot Edwords AFB in Decsmber ond ogotn this month, porticulor t

.t ,l1t y'

otlention wss poid lo ice occuhulotion with lhe ffop5 ot l5 deg. At $ot 5eting, ice wos qble lc occrete oft of tho originol doicar. When

en

fls wore rekocted, the

chonging oileron hing6 moment dromdticolly. With the new doicer, no odve.se eF fects occurred becouse rhe ice ridga foiled ATR officiols expect io cornpleto ret.o-

fitting new wing deicers on ATR42s ond ATRZ2s byJune l ---.o deodline esbblirhed by tho FAA in Jonuory. As o resvh ol $e ATR occident, FAA of-

r;c;ols ho'e norilied U.S. ond foreign oirlrome monu{octurers t"qr Ae ogenc/ pions

dce.wq

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oirflow obove the wing wqr disruptcd,

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regionol oircroh. The chiel gool will bo to determine their susceptibiliry ond reoction to tho effects of freezing drizzle ond freezing roio, Solvono soid. H6 expeds fh€ t 5r ing to be compleied before the stqrt of ic" lng seosoa. IHE FAA'S IR NSpOIT Airc.oft Dir€crorots ond SmollAirplone Directorsts will be .e :ponsible for solecting test poro.neiors and prepr:ring progroms to conduct the ex" penm€nrs. Aiiho,rgh n-fl;ghl r€siing s;Tilo. lo thot or Edworos AFB wjli be p6rforned, :one tests con b€ done in wind tunoels, he soid. Toilplone icing olso will ba explorod os porl of o seporoie but key progroo, occording to Solvono. In oddition to $ese reshicfions, fhe FAA is preporiog o.othe. oi,worthinss5 dir€clive iniended

rc)

inpose rew .esnoinis uplon

tight operc ons wj'h'ne reoesigned doicers, Solvono soid. He expecls the di" rective to be irsued this rnon$. Despiie tho .ew deicer ond pleos from AIR officiols, lho FAA losl week refvsed lo removo reshjclions trnposed in Jonuof/

of{eciing fligtrt operotions of the ATR42

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ond Alt72. PiloB musr continee b observe the limitotions o$er $e deicers ore fited to tl,e qtrcroh. lhese include: Requi.ing pilob b moniitr cackpit 5ido windows for o r.rnique ice occr€rion thot irr

t

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dicdres Feezing roin hos been encounJered. proh;b;';rg. J5e of floos when holoing

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rn rctng condttrons ond rBquirirg inm€_ diore disengogonen. o[ ourop;lot in ffe€zrno dflzzla 0r rdrn t Leoving flops oep oyed lf .hey ore exteoded ,n {reoz.ng dr,zzle o. roin. a AVIAi]ON WIEK & SPACE T€CllNOtOCY,/March 27,

1995

35

119

ADDM{DUM NLIMBER 4

An Upper Surface winq Re-profile for the BD-5 the BtF5 airplanes as originally designed have a,,elL docunented, undesirable sharp stall characLeristic that has caused nlrnerous accidents, many of thern fatal. the rEin cause of the problem is the use of the infanous IIACA 64-212 airfoil section at the wing root. Ttlis ai-rfoil is l-ow-cambered and onty 12t thick, wtrich largeJ-y s for its lcrw naximr,rn lj-ft ccefficient and aLso the the sharp loss of l-ift

at the stall, folloled by a hysteresis loop during stall recover,y. That is, the ang.le of attack mlst be decreased considerably in order to obtaln fl-c,v/ re-attach'1ent after stall- separation has occured, usually with a cqsiderabfe loss of altitude. Al-so. the stalf is often acsc.rFanied by loss 6f lateral c.ontrof, resulting in a wild delErture . Other f actois cutri-bute to the probletn, such as the extrenely lc'v/ Relnolds nunber of this ajrplane at the stal-l, less then Il mil]ion. AII- in all-, tie airfoal selection was especially pcor for thj,s appU.cation I and this is inexcusable. Short. of a ccnplete tring re-design, various nEtnods are availa-ble to irqxove the BD-5 staLL lErfornence. For eJ{anE)l-e, BD l"Licro Technologies offer dr@ped leading edge nose ribs and ot-|rer cqQonents ) for wings tbat are still under cronstruction. For ccnpleted airplanes, ho,tever, seve-ral, nEticds of re'profiling the wing shatrE have (

witn good resu.lts. Seti Arderson has nodified hrs rel-l--knom BD-5 with an ulper forl ard surface re-profile of his crldn desigrn, extsending back to approxirrately 40t of chord on the top surface, aJld ti-is h3s been fl-yjjlg for several- years with excellent results. 'Ihis npdrfication is mini-rral and relatively s jrrpfe, and, Iike otfler upper surface build-up schenes, stiffens the upper skin to prevent wrink-Iing. Unfortunately, hordever, this partial re-profiling essential-Iy reverts tt.e wing profile to a turbulent seceion, resufting in a slight drag increase. this is only a nr-inor orsadvantage, and is of lj-tlle conceln, considering the nnrked inprove
additiona-l ttrickness.

The "GA" re-profile irproves tne alJ--i-nportant leading edge prof iJ-e, adds a Slnall amcunt of thrckness and camber, and mcves the loading fonsard slightly so that tl€ pitching nEnEnt coefficien! is not affecced. ltre result is a softer stall, higher nraxi.mm lif t cef f icient with ajld h'j-thout f laps , and a wider larninar bucket, In addj,tion, the new profi-le has been designed to nailltain c-onstant velocity flcw to approxlrately nid-chord, preserving larn-irnr flqr ( ard lcrvr drag). CG l-ijltits for the ai.rpl-ane are not affected. Flight experienc-e with this nrcdification has been excelLent. A typical exanple is the attached report frcrn Bobble Parcr of Odessa, Texas. Another option for BD-5 projects under eonstrucb.j-on j-s sirnply to assernble the wings as designed, and then re-profile the top surface befor€ ffigbtIn the interest of rrProving flight safety, I offer a ful-l-size tsrplate drawing tori lq1o to crf,ver the cost of printing and naiting. 8/16/1995

Harry Rr.bleft, EAA *29576 4I5 RibLett Iane wi.Lrli.ngton DE 19808

302/994-O479

Note. The attached standard table of ordinates can be used to generate the profile BD-5 root terq)late ( 31 inch chord) , or for any airplane using the IrAcA 64-212

for-Tle

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Harry Riblett 416 Rr-blett I-ane wikilington DE 19808 Dear }tarry: Like I told you, I \"pu.l-d let you kno\^' ho^'the (top surface ) scahr-on wing airfoil re{iork calrE out (on my BD-58). It lceEred nv stall sFed f rcm 80 MpH to 67MPH. The stal-I .is nq^, sc(ethj-ng .l-ike an ErcoulE, kind of "mushing" like. lbp end, the s'aflE- no loss there. The warm day take-off d"istance was 2500 ft, and is no,r about 1600 ft. I stiU hold it dcldn until I get about 85 MPH, ard then lift off. HcrA,ever, I novJ notice that the acceleration is guicker frcrn 60 to 85 MPH tban it used to be. probably because the wing is no$/ generating nrcre lift on tlle take-off ro11 than before, thus the take--off ro11 is shoruer. TjnE to rotatj-on is nour only 16 seconds e 1600 ft, with OAT € 86 degrees, density altitude 6200 ft. Our airport is at 3000 ft.ASL. For the rer,rork, I left t}le wings on the ship, and cleaaed the top surface of the wing of aII paint, to the bare ah:nr-inun, and scrubbed this with APX. I used 2 l-b. dersi-ty fcElrjl, I/2 in thrck, cqvered with tr.ro layels of glass cloth. I put on the first layer lengthwise, and the seoond layer 90 degrees to the first, and finished off with tr.D coats of polyester, I then reinforced the leading edge with t\nlc layers of fine hre-ave 3-inch glass tape, staggered, wtdch extended back about 2 inches frcrn the leading edge on the loler surface. Itle tota.L cost of all Irlateria,]-s t|as $105.00 frdn wicks Aircraft, and it t@k re 44 hours to put it al,L together. The airplane enpty Height was 467 lbs, ard is ncr^' 471 lbs, so the rebork added only 4 lbs to the enpty ,reight. t"ly ship is a BD-SBDH, s/N 19, N-6782F, '.rtrich I built myself. It has the standald ( non-stretched ) body fength. the wing spa.n is 2L\ ft. It has a non-turbo Honda engine wi-t]. a 46x66 H€y prop. It has Matco wheels and disc brakes. Thanks again,

ltarry-

Etlb FarnEr

P.S. I also riirote to Rich Perki-ns and gave him aU the i.rfo and pish.ures for ttle ED-5 neb.€rk n€rJsletter.

ADDE{DI}I II\J},IBER

123

5

A

critique of the

I\ASA N'I;F(I)-0115

eirfoi]

The Ju.l-y- August 1995 issue of the "Journa.L of Aircraft" (AIAA) contains an article by SeJ-ig, I{aughfiEr. and Sc(rers, that presents a unew NASA" arrfoil, NLF(f)0II5, a "Natural l-a.rr-inar Flovr AirfoiL for General Aviation Applications". As it turns out, the airfoil- was designed by Herr Doktor Richard Eppler, and I have corresponded with hjil about it. Ttre airfoil and its nrean l-ine ( canber profile) are shotnn on figure 1. After plotting these, I saw notiing frightening about the thickness distribution, although the point of rnaximun utickness I-s relatively far aft at '42C, but I was concerned about ttrree things in the nean li-ne: .1, ltle nose of the airfoil contains excessive leading edge droop, scnewhat l-ike the NACA 230L5 airfoil, vrhich has a sharp stal] due to excessive J-eading edge droop. Therefore, I suspected that NLF(1)-0115 nEy have a siJrdlar sharp sta1I. 2. A dj-p appears in the canrber profile at .60C, sinr-ilar to the NLF(I)-0215F airforl. al,so due to Eppler, As hE have seen previously. this area of negative lift extends the lan:inar n:n slightly hence the npniker "natural " Iaminar flc,w ), hoerever the negative lift produced by the camber dip resufts in a loss of efficiency, a point that I suspect Dr. Eppl"er has not c.onsidered. 3, Pronounced aft camber appears in the airfoil fran .65C rearward, and I suspected a rel"atively high pltching lrraftEnt coefficient (Gn) as a resu],t. Ttris also',Duld probabfy cause high aileron hinge lrErents (stiff ailerons), a.Ithough thj-s rould probably be hard to prove without flight tests. A canputer perforrnance analysis confirned ny fea.rs about this airfoil, especj"ally the sharp staU at 13 degrees ang]-e of attack, accordingly, in an attenpt to track dob/n the cause of the por performance, I designed a ner,r, airfoil- for ccnpar:ison, c,A 42E-215, figure 2. Ttris new airfoil looks like cA 40A21,5 on figure 1, except the point of naxj.rn:m thickness is at .42C rather th,an .40C. the new airfoil uses the unoffensive Eppler thickness distribution frcrn M,F(1)-0115, and cqnbines it with the proven GA-2 rean l-ine frcrn "GA Airfoils". This should give us a direct cdnparison of the efficacy of the Eppler mean line versus the GA-2 nean 1ine. Figure 3 shcrys that the perfornunce of GA 42E-2I5 is indeed superior to che IErforrEnce of NASA Nf,F(I)-01f5, including a soft stall rather than a sharp sta.I1, a wider laminar bucket, and a 30-401 reduction of pitching nr:nr=nt coefficient. The profile drag as expested, is the sane, since both airfoils use tie sanre thj,ckness distribution. ' Ttre obvj-ous concLusion is thac the rean Iine of D.IASA NL!'( 1) -0],15 is poorly (

designed. If an even wj-der laminar bucket

rnay be used,

ure 3.

is desired for oFerational flexibility, GA 4OA2I5 but the tlade-off is a slightly higher profile drag coefficient. See. fj-g-

In spite of the ind-icated superiority of GA 42E-2I5, Dr. Eppler does not tike 1t, because it was not designed by the rEdern "inverse" rnethod for deg airfoifs. You be

the judge.

Harry Riblett 416

Riblett

Iane

wilnlington DE 19808 2/L4/r996

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Harry Riblett 416 Ribtett Lane Wilmington DE j9€09

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2/8/L996

National Ttans portation Safety Board 490 f'Enfant Plaza East

washington DC 20 594 Attn: Mr. John Clark, Chief, VehicLe perfonnance Divi-sion Subject: tuneri.can Eagle ATR-72 crash at Roselawn Indiana LO/31/1994 Dear Mr. Clark:

Ity letier xo you 9/7/95 explaj,nd ,ahy the ice ridge on the ATR-72 wing, wtrich was t-lle jfiediate cause of loss of contro.l , formed at exact.Ly the 9t chord position. In you response Ietter I/25/1996 you ignored this point ccnp-letely, which is unfortunate. for that is the key to the puzzle. Ttterefore. f arn enclosing additional data showing that the cause of the ice rj-dge, r*rich caused the accident, is due to an anc.rEly of the l,lACA 430xx airfoil, that is, a pronounced negative pressule peak at the 9t chord position, exactfy where tJ.e ice ridge forms. l4ore conventional. airfoils do not have this problern. Ttlerefore, t}re accident r,Jas caused by the p@rl-y designed, unusual, and fortunately rarely used, }IACA 430)0( airfoils used on this airpLane. This il.l-conceived airfoil design was part of a test prograrn conducted by I'IACA Langley on "airfoils having the camber unusuaLly far: forw-ard", Ilere].y to see \{hat effects the exErso-. forvard loading would have on airfoil perforrnance- hopefully. lovt pitching nrnent coefficients, Figure 2 shov/s the forward loading scheduJ-e, and ccmpares it to a rbre conventionaL. unifoqnJ-y loaded ai-rfoil, the NACA 54-415, used on the Fokker F-27 'Friendship". the theorcical pressure profiles predicced by I{ACA for these airfoils, figure 4, shol't€ a pronounced Feak at .09C for the 430xx airfoil, ard no peak whatever for the 64*41-5 aj-rfoil. The actual pressure distributions (velocity ratj-o curves ) for these trno airfoils obtaj.ned by ccnputer performance analysrs, figure G, confj,rms the predicted profiJ-es. Ttre results of t.t.e 1935 NACA wind tunnel tests, figure 5, shoh/ that the arrfoiL ncnent coeffici.ent ( unrelated to the Roseladn acci.dent ) is indeed loev, as anticipated. However. the sharp and dangerous starl on these aj,rfoj-ls. as bad as any airfoil- ever tested by NACA, is unaccepta-ble, therefo;c the tests must be considered a failure. UnforEunately, ihese test airfoils canE to be used on actual" aj-lpl,anes, r.riti generally disappointj-ng resutts. espe.cially on propdrlven twins. The ice ridge forms at the negative pressure peak (.09C) because that is hrhere the adiabatic cooling is the greatest. Thls is analagous to ice formation in the

tbloat of a carburetor. In fact, tie top surface of an airplane wing is sirply a one-sided venturi. Etcrn that point onrrrar:ds, further conjecture as to the exact effect the ice ridge had on wing performance, aileron hinge nErnents, etc, a-re rrDot. The point is, the unusual pressure peak on the 430xx airfoi,ls at .09c caused the ice ridge to form at that point, and that dovrned the airplane. Ttrerefore, the IIACA 430)0(

airfoil is at fault.

scnre nerit for the FAA to ban airplanes usi-ng the airfoils frcrn flying jrr freezing rain and &izzle ( figr:re I), but not all turboProp regional airliners should be so banned. To issue a blanket prohibition is heavy-handed, irperialistic, arxi ignores the fasts in the case. For confirriEtion of this airfoil data, check lrrith scrrEone other than: -[{ASA, h,ho is responsible for the idiotic 430:o< airfoil; -ATR (AIR), wlro made t}re trListake of ch@sing this airfoil for their airplanes; -FAA, hrho made the nistake of certifying the ATR airplane with this airfoil on it.

Accordingly, there nuy be

l,lACA 430:o<

128 .By copy of this letter' r request FAA'S Mr. salvano to incrude this letter as a public ccmEnt in the docket rega_rding this accident, and also to include at in the FAA'S tcing symposium schedu.ted for May 6-8 at Springfield. VA.

In the j.nterest of rmproving flight safety, Harry

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Mr. Dan Salvano, FAA, Washington DC 2059I !4r. Tbny Broderick, FAA, I,fasfLj.ngton DC Zg59l l4r. Andtehr CebuJ,a, v.p., Gov't &rndustry Affairs, National Ai! Ttansportati,on Mr. walt colernan. president, Regional Airline Assn. 1"1r. Edwa.rd Phifl-ips. Al,ieST. !"tashington DC 20005

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FAA TO BAN TURBOPROPS IN FREEZING RAIN, DRIZZI.E IDWARD H. PHIIIIPS/WASHINGTON

iting on unsofe condition rot covered by curranl certificotron rules, the FAA plon3 lo issue qn oirworlhir€ss directive oy Moy lo.b;dding vrrtuol,y oll tu,bop'op powered regionol oirline oircroh hom flyrng rn heezinq roin ond drizzle.

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The direclve wil' orohibit dl l€osr l8 diilererl.oircroh, inctud,ng oll turboproo reglonol konspods rn U S. servrce. from op erot;ng in freezing roin ond drizzle 6y omend,ng eoch oircroh's opprov€d A;.-

r vUU serier. l lese o rcroti neel rc nq cerlilicolion cnterio unde. Aooendix C of Pon

25 o{ tire Federol Avrolion Regulolions. The di,ective would require chonges

lo lhe Airplone Flighr Monuol thor wouid: P.ohibit u5e of the oirtopiiot when ice

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Require rhot ol' ice hghts be ope.ot,ve b flighl into ;cing conditions oi nigltl, ol exceptionr contoined in o 'rrespectjve orrcrolt'! Mosler Min;mum Equ p Frodrculo' rnenl Lirt. I -'mil use oi flops ond forb;d use of tne ouroprlor it ice is ooserved forming oft of lhe wrng jg;6sp5. ln qdditron, fi6 di!6clive mondoies rhot

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pilols use opgroved orocedures to;mme diolely exit freezrnq i,izzle or.ojn condi-

plone Fl:gh,Ma.luoi, soid Don p. Solvono,

monoger of the FAA's Rotorcroh Dires" lorote, Ft. Worth. fhe FM hos set Mor. Z os lhe deodline For rece ving commenls, ond ":s very.eluctont" to exiind the comrrenrperiod beyond.l"or dote. he soid. Ai.c.ofi chiefly offeded bv fie directive :nclude ti€ Jehheom 31/4i ArRA2/lZ, , de Hovillond DHC.7,/DHC-8. Dornisr

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Tre c,ouA ot.rt ocnon stem-s hom ihe c,oslr o[ on Americon Eogle AIR72.2OO or Roseldwn, tnd Iawd,Sf Nov I4, I994. p. 28; Nov. 7. 199A. p.361. Ahhough

rhe U S N,ot,o1ot T'onsporrorion Soie-v Eoord hos not determin€d rhe probobl! couse ol rhe occidenr. onolys;s Indrcotes ,ho'on ce r dge fo,med oh of .ns w;pg de.cers, coL:srng o.oprd rol onC suoseq,renr loss of control by the tlignt c'ew lAw&sT )o^ 2, 1c95. P 28). fi,Af ACCIOENT hos not only rejnlo.ced conce.r obou he donqer o[ lreezino roin

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side'exponding furprendix C of Porr 25 bo yond ;t! cunent b'eodr$. Port 25 qowm: cenif rcohon ol -ronspon Coiegory;i.croh.

Exrstrng'69J'otions requirc monufoc-

turafs to domonsi.otc thol on qircrofi con

operote iolery in *oter droplers hoving on overogo d;ometer ol 2O5O l"nic.ans. The diomoler of dropreh .n.ount6rod by lhe Amerrcon Eogte ATR72 probobiy exccod.d 200 hicro4s, occordinq to tha NTSE

To iaorn more obout fraezing driz:le ond ro;n, lh6 FAA is plonn;ng on rnrsmo lionol icing !ympor;um currendy scheci-

ured for Moy 68 rn Soringfield, Vo. (ey topics lo be discussed rncir.de how teez.

ing roin ond driz.zle should be definad,

oroblems ogsocrored wrrh forecosrrng jrs presence ond deveioprrent ol oclvonced .ce de'ecl'on sysle.as copoble of prov;drng on eorly worning ro p'lots The ,rs€ ol orrsrde vrsuol cues olso w ll be discussed, Solvsno soid. "\ /e ore 1or expeoing ro moke ony oeciorarrons obour teez.ng ro,n ond orrzzle oher rhe neetrrg concjuoes." ou'Florrici-

ponrs wjll be encoJroged ro openly d s. cLsg lh€ isrue Fom o" operarronol rio.ropo'qt, occording ro Sorvono. He expe
k6ting for Aoro lnr6rnotionol R6gionql {AlR) Morkotrng lnc. AIR is o sol€s con3orlium o[ $6 lormer ATR, Jehtraom ond Avro cornponie:. Brodin roid the snlirs U-S. flcd of no{s lion 158 AlX4? ood ATRZ2 oircrslr how been litttd with lorgol wing deicers o: wall

os ;ce evidence probes mounted ouiside ol'he copro,n's *,ndow Tne probe is designed b occrete ice ord serve os o vjsuoj cr.Le lhot lhe oircroh l.os encounrered icing conditions lor which it is not cerrifi" coted, Brodin soid. The FAA rs sr'rl corducring speciol ground6ored rests desiqned io oere.,nin€ which regionol .ronspo s ore su5ceprible lo conl.ol problemg Under severe icirg condit;ons. In.llighf,e5,rng \,srro o spe cro,ly modihed U S. A,l. Foice NKt-t3SA lonker oircrah is ovoiloble lor monr.rfqc. lurers, bul the FAA ir, not mondo no its ese. Solvono soid. OPERATION Of Th! TANKtt ir funded through Fiscol I996, "but we hove no

gvorontees beyond thi: yeor" thot the uniquo orrcroh will romoin op€.dtionol, Soi"ono soid. ll cosh monufocturors qbcu{ $250,0OO ro $5OO,O0g ro chqaer $c honker for ;cing tosts. ln oddition ro rh€ ATR72-20O, qn Erhbroer EMBI20 Brosilio ir the onfy otb 6r rsgionsl oircroft thot hos flown b+ h;nd rh. NKC-135A'. Th6 in-flighr tosr!

Proyid. q 'criticol doto point' lor morr !,[octur6r5 ond rhc FAA ihqr connot ba derived ftom groundbored rcs*ng, Scl" v{lno

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132 About the Author

6, j-s a llechanical Engineer recently retired froo Hercules Inc. in Wilnington, Delaware. He holds a Commercial ASEL pilotrs license, and has been active ln sport avi-ation and EAA activities for many years, He is an expresident of }illmington Chapter #?4Q ana is cuEently a chapter Harry Riblett,

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Technical Advlsor. He has buj.1t two homebuilt airplanes, a Starduster II and a CUBy, flies both regularly, and is working on a (nearly finished) single seat original design, as yet unnamed. The new project is a high-winC ,50Lb. pusher, tricycle gear, wlth folding wings, and j.s of typical ICubI construction. Harry got his early interest in aviation from his father, who operated a G.L flight school at l{j,1trj.ngton airport iBmediatly following WV-II. Harry served as a Reservist Radar Officer/ Air ControLler on a USN cruiser during the Korean War. He subsequently worked a dozen or so years uith civilian coEpanies manufacturing, testing, and installing aircraft runway arresting gears. His interest in airfoil design prompted him to visit NASA langley j.n 1985 to encourage them to develop a EoderD aerles of airfoils specifically d€signed for General Avlation alrcraft. nisappointed pith NASATS near total lack of enthusiasB for such a project, he returned horoe, bought a computer, developed his own GAtr series of airfoils, and published his book, rrGA Airfoilsa Catalog of Airfoils for GeneraL Aviation Use't. Harry and his wj.fe Jo-Ana never Diss going to the annual Oshkosh Convention, have three chj-ldren (Allen, Gail and Mark), and sjx grand-children. Allen is an.active "Stardustertr pilot, and the others give flmoral rr.

June

1994

Harry Riblett 415

Riblett

Lane

Wilmington, Delaware n2/994-s479

19808

ADDENDUM

t'lo.

133

7

Aircraft Srabili-tv - lri.plified is surprising hor9 lIEry builders ask this question - ,'I am using arrfoil (XyZ) on my airplane. hhat shou.Ld I use for ttre itt CG lirrlit? " It \.Duld be nice yer" rtlat sinpJ-e, but it isn't, Aircraft longitudinal stability, and the aJt ]l ]! CG liJrdt, depend on many factors, and the parUicul-ar airfoil belng used is only one factor affecting the ploblern. !;.Flvrnq Winq Airplanes. l,et,s bregin by looking at the npst sj:rrcle case, a 9i:g llyrng wrng. As Ln any airpLane, thD conditions mlst be satisfied, tt]al is, it b. sta!.ica]]r and stabre, it arso must dvnarnicaLlv be stabt;: i;trc stalirity T::, reguires that the cG be located IrErely in rine r,ritrr tne ritt vecbo!. ttnt is, at the center of pressure of the. arrplane. so tlrat the airplane unai,sturb& ,iff tfy leveL. Since rer cannot shift q.t" cG fore and aft in f1ight, ,r. th;;;;r;i need, for ving airplane, an airfoir does nor itt""g" p"sid"" ttre angr,e $"-llt*n ot attack changes, but._ramins. at theh,hose ,,nugic' quarce!-chord p"l"t. itri.,isbry rlrltron is a "zero cq" aiJfoir which neans that tre airfoil rust be eitherdef_ syn' fiEtrical' (uncanbered), o., if canber is used in the alrfoil sestion, trr" t edge rm:st be ref]exed sufficiently to achieve zero On. In prastice, the ":.ting trai]jng edge reflex can be changed slightry to trim out sfilali chairges in cc location, onLy veqr srnalJ- changes can tre ha'dled. l^ie descrih:e this ,'balanceO,' c€rdi,ti-on' but by saying tl)at the srrn of the nrnents arFut the cG must be zero, for any steady st-ate fight clcndition. on the o-ther han:, involves tl* rate of chanqe of the ns,. T*9".urcstEbility, ents about cG, follorr'ing a disturbance frfir trifined ffgrrEl G-oe aynan;.ca[y stable the disturbed airplane must scrrEhoe, develop a net nirent about cg cointer to the' direcLion of the d.istulbance. that is, a nei stabilizing ncrent,Lhe so tilat the airplane will tend t-o return to its trirrrEd attitude and speed. Notice that the wins.315glang has precior.ls littr-e fiechanism to develop thii restoring rnxrEnt. onefiying possibirity is to Locate the cG beneath the rrring as shou', so that ,^,hen . no=e d'isturbance ocflrrs, for. .,€np_Ie. the "pendurlm 6rr.ce" of the cG noving forwardup terd to bring the nose back d"',*' to ttrl trre origi'ar Fositi.on - Another nDle cqft.-wirl pricated_possLbility is to use elestronic sensors to detece the drresti-on and nragnitude of the disturban:e, so. that ?Fpropriate accuation signals can be generated for {e elevons, to produce the needii rLtoring rurlent a.bout tfle CG. Frcm ti:-is \.E can see. t,.at flying wing arrpranes invorve scne fai-rry serious desigrn restristions. First, zero pit-ning -nr.tent airfoils nust be used,'and tl,ese are gcnparatively inefficient in terrns of vD. second, no flaps can be used on the airplane, for there is no tair. to reast the cqsiderabl" noi"Ic,^,l,- pit"Lg n'-r=.,t th. flaps are deployed. accordilgJ.y, landj.ng and take-off fT -ti," -. ccreratvely high. curpared t! a simirar oonventiorni airprani with flaps. tt"p".il" La. range of tne ai..plane is veqr ri,',itq, restricting the- utili-ty tn" .iir.".. A fl-ying wilg airplane doesnrt have to drag around a fuselage an& "i a tail, hr;-th; price pa.id for this suFposed advantage is tco high. (

rn a carrrd configr:rarion, $E have rl^lc !,rings operating in per the ar.tached sketch, with the CC Sit f6nrara of the =: aft wrng c/4 pint, rre see that the forr{drd wing produces AO lb. .rrd a. posiri-re nE''Ent of 80Q fr-1b5 about tie cc. sirnilfuiy, th"-r;;;; "i-fj.tt, prcduces J"6Q a negarive nErent of 80Q ft-Ibs about- the cc. rtrerer6rl, the totar +5-"1_rll!,,"rd ]r)s, equalrng thg h919lt of the airplane. and rhe surn of the positive :::"_I_:t.{] and negatJ.ve fiEflEnts about tle cG is zero. Thus ttre resultant rift vecto! es through the CG, and the airplane is statically stable. . If re novr apply a I degree nose-up distuibance to the ajrplane, for exatrq>l-e r,vith a sudden stick noveneni, or L-ith i .o=*-up gust load, the'picture changes, the srope of the li-ft curve for any airfoil is'approxirrutery o.i ah;;" -ot cr ro,Sj-nce each one-degree change of angre of attack, the ci- of the fona; *iog'"iir increase frcrn CI=.4 to CI=.5, w^.r-ich iJ a li.ft increase of onl-y Z5t, wtdle the -C.L of the rear wi-ng will increase frcrn c1=.2 to cf=.3, a li-ft inqrease of 50t. Ttris is the key to achievrng dynamic stabirity. ccrnpleting tlre anarysis. the rift of the for$ra.rd wing

F.;ql!Iq*$$]angs..Earrd€m, It r.E load the airplane

134 i-ncreases frqn 8e to l.oe {you're welccne), ar'd the li-ft of the rear wing increases frcnr I6Q Eo to 24e, for a totaL resulranL lift of 34e lbs. But since the *eight of the ai-lprane is stiu onry 24e lbs, the first thing we notice is tlEt ure aiiplane 90es up' lto\,{, taking rEflents dbout the cc, q€ see L\at the resultant e is no longe! aligned with the cG, nhich first of all neans tlrat the a-irDlane is in a transitioial conditj-on. Ttle net *t=l!_"l the airplane alout the cc is nor,r negative ( nose d.s,nn ) , and anEunts to (34e tbs)(0.6 ft)=20.4a ft-lbs. This is ttre stabiiizing nE(IEnt that re a-re looki-ng f or , to bring the nose back dor.,n tsnard th" ;i;; atl-tude Ttrere a-re othe! lesser factors that af fest dynamc stal iiv, u" fonard fuselage area, f!:.ctlon in the conrroi.s, ard sti.ci-free ( destabiirrinoJ, "*t -."a fusel-aEe area ard stick-fjled (stabilj.zing), as qEII "ta p."p.:.f"i-J1j'ar*,"""n -b"l ". effects - These a-re not incruded in tne adve sinple anarysi;, .h" !iir,"rpr"= sane. As tong as the cG is f orvrard of ' tire aj-rilan" , -n ,rt .i-poi.rt JTtarl F.r: ,u net stabirizing rEcEnt will after a disturbance. rn our" anarysis, negr-esting -resurt the iesser factors rentroned above, the neutra] point is the CG I;;d;" ul *1rr"n the Ci of both r./ings is tne salrE. Fram the above r.le .n """. that the prumry reguir€(ent for arly tal:Id.en wrng regarding dlnaruc i.s itnr ti'r" r"..r*ra wing nust. be n,"i" i,rgi:.y 3rrplane loaded than the rear wjng. l61l+av In .aaitio.,, tfre tor,rraia wing musi st ii before the rea:: wing, so that the "Lr,rays of the arlplane wilJ- dr-p at ttre siau. rather -nose che reverse. In Lr1e case. of. L1e gllard aLrplane, Lir-is neans that the nrain wi.ng than can never reach its nra: rar,' used the r.rAsA GAIFI ai.rf oir , with -if the of pitcLinE ntrEnt gYtr€geous coeffj.cient do-O . f Z. the c' of ttre nain wing r_oufa Its off the chare, and a c-onsiderable ( be and rEsteful ) tail dcr"n-load muld L requjred to trjrn Lhe airptane. alext vre check to rnake sure the tair- does not starl before the main wing. At the sta]-l, our wing airfoil has a C]rrEx of I.8. and the G> of the main wi-ng nov6s fonrard at or very close to tlE c/4 positron, as a1l ai-rfoils do. with ttre cc it .asc, ,,. -rt that the required Eil lift coefficient will be +0.5r for t,." ity. is rs=.= wit-t:-i' the range of our IEC-A 63A012 tail section. even at the "t relatively "t"l p.eynolds icnr nunber and lcwJ aspect rario cc(Ifrlf,n for tail surfaces, and re are satisfied that the tail wirl not starl before t}Ie nraj.n wing. vJe also note that the taiL cJ. is consj.derablv

135 less tfnr the wing cl, so this condj-tj-on is dynamically sta-ble as r",e)'l. lte proF ably ',,ouldn't have been able to prove out this aft CC liJrrit with a gnalLer, PoorLy designed tail, such as the flat tails of tubular construccion ccflncn to l"ight aj"rplanes.

9ie are not finished yet. hodever. Before r,re can be satisfied tt)at this is a safe aft CG limit, r,{e mlst also investigate the spin recoverff properties of the airpLane at th-is CG location. ltris involves a lthole nevJ set of paranEters, beyond the scope of tlai.s tEper. It is interesting to note, as shoiml b'y lhe exafipIe above. that a srnal] anEunt of pitcllixg trErEnt c€€fficient in an airfoil can actually tre helpful in ach.ieving a wider CG range, Thus the zer*r airfoi.Ls tlEt NACA developed in the s-digit. studies serve no useful- pu4)ose, at least in c€nventional- airplanes. At the other extrenE, the later I.IASA GAvFt ard -2 aq16i1s , rrl'rich have gfl values 3 ti.nes larger than they need to be, are equalfy ill-advised. Holv shall rrE ans\re! tfle question posed in the first Paragraph above? The corleqE ansrrer is "ltle aft CG lijrdt shDuLd be slightly forviard of the aircraft neutral poijlt. provided the tarl does noE stall before the nE-in wing, and provided the spin recover!. characteri-stics of gre a:irplane a.re satisfaqeory. " I{o\a€ver, this is difficult to calsulate pEior to flight tests, therefore a c€nservative pracLice with sj-rple airi planes is to ignore tie infLuence of t-he tail on the position of the airplane's neutral Foint, arld sirply put the aft CG lirnit at or near the i,'i:tg A.C., tllat is, at a[proxijrately 25-30i of chord. This seerns to be a safe practice. at least unLil flight tests can be done to Fossilcly extend the CG range. RenEnber. horever, t-tlat the CG peniulun effect rrrks for us on high wj.ng aj-rplanes, but r^orks against us on low wing airplanes. thus, for Io^, wing airplanes, 23-25tC is often used as the

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Vortex C,enerator Kits This paper discusses the highly effective vortex generator kits that are avaj-lable to lolver stall speeds and inprove lcrvr-speed controllability, especialLy on prop-driven twins with one engine out. the subject was discussed at scrne length in my papers "Design Notes for Tapered [iings", and "Tanr.ing the Sharp Statl of t]e NACA 2301-2 Airfoil". !'Je also elaborate on an artj.cle concerning lAcro-Dynandcs Inc VG kits printed in the January 1996 issue of "Arr Progress', magazine, and we strongly reccnrrend that anyone interested in the subject should read that exceLlent article. The vG kj-ts basically contain tr4o sets of vorEex generators. one set j-s installed on the top surface of the ping. across the entire wlngspan, at the fOg chord position. the second array is instarled as crose as possj-b]e to the l-eading edge of the rudder, both sides. In ssrE cases, this second set is instaued near th6 triiung edge of Lhe fin. The prirE y effect. of the vc's is to i,ncrease the trrickness of the bounciary rayer doenstream of the vc,s. thus, they increase the effective thickness of the wing, just as if "gon6.' r*ere appl_ied to the top surface. And since the added thrckness is al-.l on the top surface oi the wing, this causes an uF.rard shj-ft of the airfoil mean line, that is, an increase of wing carnber. Both the increased thickness and the increased carnber result in a higher rnaximurn lift coefficient for the wing' l"bre urportantry, hcr.€ver. these vc's, when placed at the ,rOc position on the I.IACA 2301x airfoils that are used on npst GA liaht twins, el-iminate or at .least soften the needless and troublesare discontinuity in the rnean li-ne tlrat these airfoil-s have at the .15C Position. This el-minates the fl-c'vi separation that occurs at that point at high angles of attack. l,Ji-thout the frorr, selErati.on, the stalr becdr'es soft and gentre. and this is the key to good aileron i"=ponse. even with one engine out. Ttrus, for the 2301x airfoiLs, the vc's give rnproved controJ-J-abirity ( eh-mination of \nrc ) as \nelf as a higher C]nax, ,direreas on the Cube and Charnps, \.!trj.ch a]ready have soft-stalr airfoils, the prinary effect is sinply an increase in clnax. The rudder VG's reduce fls^, separation on the 1o,l pressure side of the defl-ected rudder. without vc's, the si:rp1e hinged rudders used on nlfst of today,s light twi'ns llave terribl-e flovr separati.on at the hinge rine, tl.us high drag, ihen one engine quits ard hard rudder opposite the dead engine is applied to iold headrng. In this condj-tion, the rudder beccnes a large, effective drag bra-te, just what ire

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r'-nus the vc's a.re very effective band-ards that address the poor wing and tail ' are used designs that on today's Iight tvrins (and ccnrnuter twlns ai well). Of course, the better approach is to design and build the planes properly in tbe first p1ace, Three things are required, at1 withi-n current tectnorogy: (l) soft stalr airioil-s, such as "GA" airfoi-rs (2) t'ting tips ar least l2t thick ior turbulent airfoirs, and I5t thick for lani,nar flol airfoils, and (3) Low drag. effective rudder designs, such as the articulated rudder used on the USAF C-I7. Hhy does Vlichi-ta continue to build this trash, htlen \i€ knov, better? It,s the fauLt of the FAA t1,'pe cerLificate systern, for the re-cerEification costs associated vrith najor design changes effectj.vel-y freezes t].e design. Thus rne are forever v€dded to 40 and 50 year-ord technology. to the detrirent of aafety, Ttris must be changed. Ttre first thing that FAA shoul-d do is to rescind ( after a suitable grace period of perhaps trno years ) the tl,?e certificates of at1 prop--driven twins that cannot show a unc lo,rer thEn the normal stal1 speed of tl'e a-irplane. Ttren the arended type certificate for the rnproved "no \.trc" nrcdel shoul-d be issued follo,ring a sinpie fl-j-ght denpnstration. wj.thout the prohibitiveLy expensj-ve "normFl-" c"itificallon procedure. Imported airplanes t"ouJ-d have to me€t the sanE perfornEnce reguirenents. VJj-th that, 'ne',^ould at last tEve true twin-engine reliability, whrch we do not have with today's obsolete, garbage airplanes.

Harry Riblert

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5/Li /1996

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