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2. A des.i-gnaaaon systen was then devised, ktlerein the first digit inaicates the rax-inum canber j.:r t of chorC. t'he second d.igit indicates the locaiion of naxj:nmr ca,nberin lenalls of the chord length, and t}le last two dj,gits inAnca.ie the maximur.l thick-ness 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,totethal 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 airfoilswas 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 int"!re designation systqn, included conditj,ons of "stardard roughness',. si:nulaled splitflaps 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 GernranGo 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 cores-pond closely lo that for those wing sections, and is given by the fo.l1c'\ring equatj"on:

t t =* (.2s69 x\ -.126 x -.351 x2 + .2843 xl -.:ois x1 )

where t is tire rnaxjrnmr urickness expressed as a fraction of the chcrd. rn practice.lhe ordinate schedule for the 20t thi.ck section (0020) is detennined frcrn this fonn-ula, a-nd then the ordinate schedule for the other t^hicknesses is deterrdned by scal-ing tie 0020 ordinates d:j-rectly up or do\,,'tr !o the d.esired thickness.

For the canber schedu]-e, a family of paraboric curves { mean l-ines) was develop€d,designated as mean Lines 62 *]rough 67, indicating that the maximun canber of 6t ofchord was localed at the 20, 30, 40,50, 60, and 70 per cenl chord position. Thisgave a selection of forward l0aded (52-64), mid-1oaded (55), and alt toaced (66&57)nean Lj-nes. For less camb:r, the basic 5t mean lines are si-rply scal-ed do{dn dj-recl-ly t'o the new va1ue.

N.nr tie ba:;ic tllickress forms and the carnber schedules were cqnbined accordingto the "I'IACA" method, shcn^,T in figure 111-l belcrvr, r"tri-ch turts out lo be a faultyrnetirod, and t.h-is was o'jle of the rajor ,rristakes af th,: llAq{ resea:r:chers. }4ore onlhat later ' ]n a:]y event. the 4 digit "arrfoil-s,' so obtained 1"€re tesred. and sincethe advantages cf forr"erd loading had been demonstrated previously, the most prac-tical of lirese airfoils used the 64 mean llne, lvhi-ch ptaiea ure *u*:-,* canber at{09 af chord ( NACA x4xr), These airfoils, in spite of tileir shortccrrlings, r*ere wide-ly used on popular airplanes of the day, such as Cessna (241-2), f,usccnrie and Aeronca(4412). and seabee (4415), etc.

B- liACA,?-dicir Airfoils. Fo]-lc'\ring the 4-di9i! airfoil r.rork, }.{AsA conducted a testprogram i.:r the early 1930's to see j-f zero pitching rTn:rents coul,d be acbj-eved oncanbered ar:foils by using lead:-ng edge droop al-one, rather Lhan using a convent:i"on-al camber schedule. ( Read Addendum *1 below. "Understind.:irg ei-rfoils,', for a d.is-cussion of the relationshi"p betueen C1, d. and en in canbered a.d tutca,,nbered air-foils). zero p-itching nsnents on ca.nbered airfoils had been achieved earJier byrefleci.ng the airfoil trailing edge, as on the M-6 and 2R11,2 ai:foi1s, bui thisr€thod has :he d-isadvantage of reducing the na:<irnLrn rift toefficient, T'ire ns, testairfoils, using leading edge droop al,one, becalre knourr as the ,'S-digit" ser.ies.In doing these tests. NACA shared the general fascinatj"cn of t!:at era for zeropitching nsnent arrfoils, without critically evaluati-ng the need for t-t.j,s feature,and without q,rantifying the effssts of dj-fferences in airfoil cln on ajrcraft per-fonnance.

The only airfoils of any conseguence i-n th-is series are th€ 230)c{ airfoils,represented by the ubiquitous 230f2 airfoil, r,irrch is 12* t-!dck, and has l.BtCleadirg edge droop forward of the 15t chord posiiion. The ai-rfoil- has no other cam-ber. and tire rean line is perfeeCly straight frcxn ,l_5C to the trail,ing edge.The tii-ckness d:rst-ributi-on for ai-l of the 5digit airfoi-ls ( 0012 etc ) is the saneas for all" of lhe 4digit airfo.|ls. The saqe faulty LIACA nethcd of ccrnbining tlr-i-ck*

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4industry, especially considering the fact that these aj-rp.Lanes are in a Reynokls nunr-ber range that is especial.ly favorable for lanrinar flow aj-rfoirs. Furthernpre, theconstant 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, withno drag penalty. a well-proven technique that was used in the prior (turbuleni)airfoils. Ttris mean line is designed to hold constant pressure ( therefore constantverocity) back to only 50t of chord, which is the practical lilrlt for larninar flo.ranyway, and then it tapers the J-oading linearly to zero at the trailing edge. Foranyone acquainted with the t{AcA airfoil design methods, and wirring to derive theironrn airfoirs, ttris seerns to offer the "best of both r"orlds", that is, low Gn as wel,ras ro^r drag corpared to the publisbed "base line" 6-series airfoi.l-s, v,'l-rich haverelatively high On due to nid-loading. In fact, Cessna did just that, by derivingand using the unpublished I'lAcA 64Mr5(a=0.5) for the root.. ;nd the ,rnputri=n.a naca64A412(a=0.5) for the tip, of the Model 2L0 ,,Centurion', wing.

spite of the potentiat l:erforrnance jmprovernent that could be nade by usinglanirnr flo* wings. they have never gained wide acceptance in the cA fierd. I'rostsnarl light planes continue to use the 4-digit and s-digit turbutent airfoils, andthe great nrajority of light twins, and even ccrmuter transports, use tl,e obsoteteand dangerous 5-digit airfoils, a horrible mis-nntch considering the consequencesof sharp-stall airfoils in an engine-out situation, The I.lAcA 6-ieries airfoils areoften avoided, since they have gained a reputation of being "kilrer airfoils. withsharP stall characteristics and 1ow naximum lift coefficients, as r.,eII as re]ativelyhigh pitching nErnent co€fficients. Read on. and you wi.rl see that this unfortunatesituation has nothing at alr to do with the fact that these airfoirs are lanrinarflovrtype 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 acamber schedule to form a cambered airfoil. An obvious rnistake in t}Ie |IACA airfoildevelogrent ,nprk was the method used for ccxnbining the thickness distribution ord-inates with the camber ordj-nates. There are trno wiys to do this, the right way andthe wrong way. von l'lises discusses both methcds in reference z, uut unf6rtunalelyhe does not indicate a clear preference for one or the other, The first (correctJmetrod 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 rollinga. circle of ever-changing radius aLong a curved nrean- line, top and bottcm, and thenthe area swept by the rorling circle beccnres the airfoil shape. This method. sho/rnon figr:re rrr-r belovr, is quite curplicated mathernaticarly, rrtlich ironi-calry nny bethe reason that |lAcA picked it. unfortunatety, it leads to a distortion at the read-ing edge, h,hich is tben $rcthed by the so-carled "srope and radius" method for for-nting tbe reading edge - rhis taulty prccess is used on all l|AcA airfoils. un-fortunaLely, this has the bad effect of super-erevating the leading edge above theoriginar chord rine. Figure rrr-r sho^'s an exanpre- with ttre NACA ;4ls-airfoir theleading edge is lifted .486c above the original chord line, creating a new rnean lineaborre the originar rean line. Tbis de-carnbers the airfoir, as a funition of the air-foil thickness, as shovrn by figure 5. As a result, the thinner t.lACA ail:foil-s haverDre camber, and thus m3re lift, than the thicker ones. this nlay explain McA,sfascination with thinner airfoirs, especially for wing tips- anittrer nlistake. seeMdendum Nurnber 2 belo^,. l^lorse yet, the incorrect rnetir"a "r ccnbining ordinatesfrattens the initial slope of the rnean line, and this detracts frun ine row-speedperfornance of the airfoil. But NACA never investigated this effect.

Figure 2 shcnrs the beneficiar effect of using the correct rnethod of ordinateccrnbination on a typicar }{AcA airfoir, the ubiquitous }.IACA 64-212. when tbe correctmethod is used to form the airfoil, redesignated 64-zrzc I the stall is softenedappreciabry ' and the naxirnr.rn lift coeffi-cient with and without flaps is raisedsrightl-yf ccnpared to the originar airfoil. Accordingly, the "dirdt addirion"rnethod of ordinate ccnrbinaLion is used airfoils.

5B. l"'lean Lines. Eigure 3 sha^is the wide variety of rnean rines that have been used inllAcA'/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-Load-ed nean ]ines (x4xx-see figure 1) with naximum carnber at 40t of cho;d, since it waskaown 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 forwardloaded 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 air-foi-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(rFryred to the drag coeffj.cient (cd) has never been studied nor guantified by NACA orNASA- Horv can one intelligentty desigrn airfo.j-ls wj-thout knc,v,ring this relationshipuFor 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 @? rsit al-1-irportant, or just a nicetyz Do he need zelo qn?

- -Tb. ans\"€r these guestions, ,,.E investigated the drag that is caused by airfoil On,

and derived a formula ( figure 8) for calcuLating this ',tr:m arag,,, or drag associatedwith 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,

'nle- arrivl at a icorrected,, dragcefficient, Cd', which can nc'$r be used directl-y for ccnparing candidate airfoilsfor a given application.

-eriefly, the problen arises due to the fact that the center of pressure of cam-bered airfoil-s npves aft frcrn the c/4 position as the angle of attaci decreases- seefigure 7- This causes an. aircraft nosedown pitching nc.rint at higher speeds thatmust be rea*ed b1r negative Iift in tie horizontal tail. Remqnber that Lhe aj-rcraftcG 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,onof vertical forces on the airplane must be zero. Ttlis additional increnrent of wingl-ift also creates an incre{rent of induced drag. Add these tr,,D additional drag incie-rnents (wing and tail) togetber, and r,,e have trim drag. l.totlce frcrn figure g tlat thetrim drag coefficient for the very high-on }{AsA GAw iirtoil= is approiirnateJ,y 20 dragc€unts at cruise for an application having a design rift coefficient of 0,2. whenthis is added to the section &ag coefficient of 53 drag c€unts, re obtain a correct-ed drag coefficient of 73 drag counts. This renders the t.{AsA GA!,1 airfoiLs unsatis-factory, 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 anecessity for general aviation airfoi-ls. Hoirever, it is not necessary to go to theridicu.Lous extrenE of the ill-advised 5-digit airfoil test progran {;airt6its f,rrri.,gthe nExrmum camber unusuaIy far for^rard" ). In short. it is- noi necessary to havezelo qlt, nor is it necessary to reduce on to the point !^'l)ere other vital perfonrnncecharacteristics of the airfoil. are curprcndsed. rhe IrAcA S-digj-t airfoil,s' achj-eved1"t9 Gn, by! the price pa.id ( sharp stau) is unacceptabl-e. th&efore the S-digit air-foiLs should not be used,

therefore, '.,e

have selectd the IiACA (a=0.5) nean line to be the basis for theuniversal family_ of only 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 NACA64-2I2C airfoil. produces 64-212(a=.5)C. Figure 2 shorr"s that this results in a widerlarLilar 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 irportantparirEter 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 ttlisoversi-ght. I{e have found t}rat the initial slope should ne a nLin:mum of 12 degreesfor any airfoil, thus our GA-2 nean line inccrlnrates .3* drop, and the GA_3 rneanline has .2t leading edge droop- see Appendix ir. ne effeceiv;ess of the drmp

6can be seen in the perfornance of airfoiL C.A j7- .2, which has a much softer stall-,ar even wider laminar bucket, Io/r On, and yet higher Clmax with flaps, with no dragpenalty. as shcl'Ir on figure 2. For this reason, all cA airfoi.l-s can be described as" lc'e/ pitching nsnent, soft-stal-l- airfoils". In fact, rTt3re]-y by selecting a GA air-foi.I, an aircraft designer can be assu-red tlEt the pitching nsnent coefficient hasbeen held as lc",r as practical, short of degrading other perforrnance features of theairfoil, thus for the rna jority of cases a trim drag analysis is not required. Hor-ever, in ext.:rslE cases, such as a very high perfornance application with the designl-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. SinceforHard loadj.ng increases the velocity ratio slightly in the forward half of the air-foil canpared to nrid-foading, the critical Mach nunber fo! these airfoi-l-s is degradedslightly. Ho\^rever, this occurs in the 580 MPH range, far above our needs, hence thisis of no concern to us.

C. Thickness Distributions. For our ce arrfoils. only ninor changes have been madeto ffibutions. The cA thicknes; distributions are listed inAppendix I belcr,/. For the turbul-ent airfoils (cA 30), the GA 30A015 shape is ident-icaf to NACA 0015. Hot^rever, this strape has a slightLy convex, or "boat-tailed" after-bcdy, rrtrich is rather unusual. Therefore, we have generated an alternate tu-rbulentshape, GA 30-01,5. with a strai.ght afterbcdy, that reduces the prof.ile drag frcrn 75drag counts Lo 72 drag counts, with no structural disadvantage. One concern here, hov,l-ever' is the change in the tlaj,ling edge angle, h'hich affects aiLeron effecti-veness-see figure 9. Since the trailing edge angl-e is reduced in cA 30-015, the control-effectiveness nny be slightl-y }ess tlnn wj-th GA 30A015. Hs,Eve.r, the trailing edgeangLe 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 thecA 30-)oor airfoils.

For the GA 35 and GA 37 larninar shapes. no changes were nEde to the }IACA 63alld 64 series shapes. which are conservatj.ve, utilita.rj.an l-arni,nar sections, havingwide lamrnar buckets. Thj-s alloers airplanes with these thickness distrlbutions to op-erate 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 countscarpared to sqne other so-calJ-ed "superior, lore-drag " lam:-nar thickness distrib-utj,ons that have been develo@ since, ard the drag penalty is a snrall- price to payfor 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, Taeprofil,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, whichhas a poorl-y designed, straight afterbody (high drag ) and should not be used, W1ththe point of nraxirm:m thickness ncved aft to the 403 chord position, the design of thepressure recovery section krc.rEs critical, and a straight afterbody is no longersuitabLe, due to the unaccaptable drag penalty. Accordingly, l,ve settl-ed on a reducedcusp 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 no-cusp shape, with a drag penalty of .Iess than 2 drag counts.

ttotice that the basic thickness distribution for the c"1 thi-ckness distributionsj-s I5S thick, and then the 12t and 18* thicknesses a-re scaled proportionately upor dorn frorn the 15t thick shape. this is a departure frcrn the NACA schen-- for theirlandnar thj-ckness distributions, wherein unique syrnretrical shapes have been calculat-ed and published for eacb thickness, and these shapes are not guj-te exact nruJ-tiplesof each other. The difference is very srnal,J-, ho^'ever, and does not affect a-irfoilperforTnance, therefore ue have ignored it to si.nplify the process of generating fan-il,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

7drag ratio is probably closer to 13? or l4B thick, for any airfoil systern. Sirplyput, 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 ccrm-only used. Ordinates for these shapes are l-isted in standard I.IACA tabLes ( refer-ence 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 rnerelya-fGrino o-ng of-test sanples tJ:lat r,prt included in IIACA' s wind tunnel tests , and arethus incfipl"ete. In contrast, the GA airfoil ordinate tables. Appendix III| are accnplete 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 "cookbook" of airfoils fron \,tdch to choose,

MSA's official position i-s that a ccnprehensive catalog or " cookbook" of air-foil-s is not necessary, and suggests that a unigue airfoil- should be custorn-designedfor each and every nan airplane, one that "exacely fits the specificati-on for the ne\.rairplane", otherwise ttle lErforlnance of the nevr airplane will be ccnprqltised. Thisis, 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 perfonn-ance 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 noother 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 ratherselect frcrn a good catalog of standardized designs rather th,an take a chance on acustcm airfoil.

NACATS thj-nking. evident frcrn reading reference L, was that "custcrn" I{ACA air-foj-ls could be s)mthesized using l{ACA's data and nethods. In other hDrds, IIACA assundtlnt a designer coul-d select a particular thickness distribution and a camber profilefrcrn tlle text ' and then ccrnbine thern by the I'IACA rethod, to obtaj,n the desired custcrnairfoil, just as cessna did for the !'todeL 210 wing desigm. This is probabry t-trc reasonthat I.IACA was content to publish test data a1one, rather tllan to publish actual- cata-logs of airplane arrfoi.l-s. Hot,rever, to thus s)mthesize custam NACA airfoi-1s is adauntj-ng task, beyond the capabiJ-ity (or pa.tience ) of the average designer'. Further rdue to the nfstakes and onissions in the NACA work, the airfoils vDuld still be lessthan ideal. For example, Cessna,s airfoils for the lbdel 210, r,,trile a step in therj-ght direction, do not contain leading edge droop, and the ordinates are ccrnbinedincorrectly. 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 assum-tion 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 topof 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-onllas 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-nsteada curve defined by a series of discrete points.

co],uru''s #2 and Jl3 of the ordinate tables are the thickness distribution (sym-nEtrical shape ) and tbe nean rine, respectivery, frcrn which the tirree airfoj,rs 1neach table are fornred. corunm #2 and +3 are listed for reference only. they are aLsousable 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, thenadd col-unn *3 to obtain the desired aj-rfoil,E. Aerodvnandc Characteristics of winq Sections. The aerodynaninc characterj-stics ofeach 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 6ndLlion, corresponding approx-i:rateJ-y to stal1 conditions and cruise conditions re-spectively for tlpical light airplanes. The characteristics of the 188 thick wingsections 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 charac-teristics of the "cusp" t)pe sesLions are not sho^rn, horever: they are approxirnatelythe sare as the "no-cusp" shapes, wi,th 2 drag counts less drag. Sree figure 14.

8Tbe 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. Theprjjnary perf orrnance degradation is ]-oss of lajrlnar f J-o,r', causing a substantial in-crease in profile drag, and there is also scan-- Loss of nraxirm:rn 1j-ft coefficient aswel-l-. Ttre data r-s for roughness conditj-on !=4, b'trich is approxirnately equj-valent tothe NACA " stEndald rouglmess" condition used in their tests. According to referenceI' this is eguivalent to a wing ",,e11 contanrinated with bugs". Ho+rever, the concensusis that the ''standard rouglmess" lrrposed in the I{ACA tests is unusually severe, andis not likely to be encounlered in actual alrcraft service. F\rrther, due to the super-j-or leading edge shape of the cA airfoils, the perfonnance degradation of GA airfoilsdue 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 rnuchexperinentat raork has been done in wind tunnels with high-lift devices (see referenceIf chapter 8), there is no readj-l-y available ccmputer program ttlat can accuratel"ypredict airfoii- section perfornence with flaps, due to the ccrnplicated flc,ld patternsin the flap systsn. AccordingJ.y, very littl-e data is presented herein for GA wingswith flaps, except for figure 2, which illustrates the principLe that cA a.irfoi]-shave significantLy better fl-ap effectiveness, that j-s, increase of nraximum lift co-efficient with a given flap system, due to the cumulative effect of the cA jjrprove-rpnts, 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 withflaps, for cA airfoj-ls. For large, ,,e11 desi-gned f1aps, the greatest expectable fac-tor 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, theClrex with sirrple flaps coul-d be as higb as 2.4, slotted flaps as high as 3.2, andFo/rler fl,aps as high as 4.0. ltese are section (2 dilrensional ) coefficients, andappropriate reduction must be made for ttrree-dinensional effests. AIso, they a.re theestirnated nnxirnum values for the best fl.rp systens, whereas existing production flapsysters 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 scflEguidelines for selection of [Erticular airfoils for given applications.A. Effect of Series. Figure 13 shc'vts the general performance differences betrr€enthe tulbulent GA 30 series and the laninar cA 35, 37, and 40 series. The GA 30airfoils are tie rrc)st @nservative, and are atrPropriate for l-or-po\^rered, cub typeairplanes. GA 35 ai-rfoil-s are I'entry level" Larmnar flor airfoils, and are suitablefor airplanes .Like the thorp T-18, at least when nndestly Fc ^rered

as in the orig-inal desi.grn. GA 37 airfoils are general, purtrDse lanLinar florr' airfoils, to be used ona wide lange of ajrplanes. cA 40 airfoils are for onl"y ttle nDst soplListicated, highperfoFMnce designs, such as the Glassair or White Lightning, where rninjmr.un dragat high speed is a strong reguirenent. they reguire the rcst accuracy in nEnufac-ture to reafize their lc^d drag potential. ALso, the lanr-inar buckets on the cA 40airfoils are the narroa€st of a-11 the C,A series, so the wing mrst be designed care-fu11y to insure tlEt tie airplane is olnrating witlr-in the laninar bucket Lrnder alff light cuditions.B. Effect of Cusps. Figrr:re 14 sho{rg the effest. of afterbcdy susps ofl airfoil per-fornance. Although both "cusp" ard "no-cusp" airfoiLs are presented herein, for tbegreat majority of applications tlle "no-cusp" airfoils are preferred. Ttre main reasonis to irrprove aileron effectiveness, as liel-I as to si:rplify fa.brication. the t)p-ical drag i-ncrease (.0002) is usually insignificant. For appU,cations such as sail-pl-anes and mtor-saj.1ers, r.here nLinirm-un drag is ijrportant, and especially with thick-er airfoils, the "cusp" type a:-rfoils can be used. Ho\aever, with the "cusp" t)?eairfoils, specj.al "fat" aileron designs ttBt trave increased trailing edge angfesshould be used, to obtain acceptable aileron effectiveness.

IC. Effect of Canber. Fiqure .I5 shoe/s the effect of different camber levels onGA airfoiL perforlnance - Of c-ourse. the main reason for using camber in the firstpl-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 tonEet the design reguire(ents. See Addendun #l for a discussion of the effects ofincreased On due to camber. In any event, l-arge, effestive flaps are the key to hi-ghaircraft lElforrnance, for they Fernlit the use of 1c{.Er cambered sections and re-duced wing alea r ard tlds results in higher top speed. Accordingly I a good air-plane design shouLd star! with the fl-aps, and then tJIe rest of the airplane shoutdbe designed around the flaps. tn general, the tcffer camber levels are used with high-er powered airplanes ard/or with large, effective flaps, while the higher carnberIeveLs 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 air-plane ' 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, thecA 37A415 coufd be used, but not the 37A61-5. this concern is especially irrPortantwith 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 statedabove, the tiinner ai-rfoils have narrc,hEr laniinar buckets, thus shou.Ld be used caut-iously' nrreherncre, the starl tends t be ress soft with the thinner airfoils. inspite ofthickness is so srall, the nrin n-rn arrfoil ttrickness to be used for npst laflLinarflcrvr apprications is l5t. see Adderdun *2 for a discussion of the effects 6f usingairfoiLs that are too thin, especial].y at tie wing tips.

E. Effect of Reynolds Nunber. the design Relmolds nunber can affest the choice ofairfoil-. For exars)le, frcrn figure 17 notice t-Llat the lam-nar bucket narrc'vrsconsiderably at fligher Reynolds nunbers, since l-arninar flol is tErder to ach-ieve asRe)nolds nunber increases. Iherefore, for tdgher Reynolds nr.rnlcer applications, thick-er airfoils and/or lover canbered airfoils nay be nec.essary to insure that tie air-plane is operating within the bucket at top sFed. @nversely, at 1*/ Rqmolds ntmrbers, cljnax drops off considerably, thus additional camber, andlor addi tj-onal thick-ness, and,/or nore wing area ftry be ne€ded ccfipared to a tligher Re)mol-ds nunber apP-lication, for the safiE take-off/Iandi-ng sIE€d. For exarpl-e, the BD-5 has a stal1 Rey-nolds nunber of Less than 1 miuion, and uses a DJACA 64-212 airfoil for the r@tsestion- a terribLe choice for such a lor Relmol-ds nwnber, resultj-ng il nany need-l-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 insailplanes. a phencnenon kncnn as " larrinar separation br:bbles " follcrqEd by turbuLentre-attachfiEnt near the erxi of the laminar run, may occur, on the top anVor thebottdn 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 sur-face 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 normalattached turbul-ent flov'r, avoidr,ng the separation. Ttris subject is beyond the scopeof this book, ard is nornally not a problern for @ airfoils, ltdch are forrerardIoaded and thus iEve littfe camber in the afterbody, and tiis reduces the curv-ature 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 laninarseparation bubbles. Afso. tlre laninar separation bubbl-e probl€m is nagrnified as thepoint of rna:cirm-rn airfoil thickness is noved farther aft, that is, beyond .40C, inr^hich case radical cusps are regui:ed for satisfactory pressure recovery, and thisleads to separatj.on. "@" airfoils, especially the no-cusP shapes, do not have thisproblem, for there a-re no GA airfoil-s with linax beyond .40c.

101n 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 occur-ing in ttre first place. with the basic airfoil shape. This requ.ires thin, lctw cam-bered. a:-rfoi]-s, wr-th ltnax forward of -40c, utith no cusps. Hoi",ever, this is not Prac-tical for sailplanes, for exanple, so the alternate solution is to 90 ahead and usethe 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 tur-bulator tapes located top and bottcrn near the end of the Lanrinar nrn, to keep theflc'vi attached. Ttre drag of tJIe turbufator tapes is less than the drag that vnuldotherw.ise occur frcm the laminar separation bubbles ' so everl,one is happy -

ror exceedingly Io.J Relmolds numbels, such as with very slow, indoor, smallrubber bancl po"ered nndel-s . the f lc'vr is I00t l-anr-inar. Ib irprove l=rforflEnce. atrip wire is often placed spanwise in fron! of the leading edge, to make sure thatthe flctor over the enti-re rring is turbulent.

F. Applications. GA airfoils are currently being used on a wide range of applicationsFron-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 theSkystar "K.itfox" and the Ultravia "Pelican". All experi:renters who have substitutedcA ailfoils for the original aj-rfoils on their hq€builts have reported performancejrprovernents. 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 pre-dicted perfonnance data is tr.io-dfiEnsional data,Iike wind tunnel data, that is. rtis idealized data for a wing of infillite aspest ratio. fte data rnay be clrrected forthree-dlrensional. effests, that is, correstd for wing aspect ratio, using nethodsdescrlbed in standard aeronautj-cal teJrts. For exarple, in detenn-ining a suitabl-eangle of incidence for a particular alrfoil on a gj.ven airpJ.ane. tJ.is usually neansadding approxi:nately I to I degree angle of attack to obtain the design lj-ft coeffic-ient ( average ) over the entire wing, dependj-ng on the aspest ratio. A higher astEctsratio 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 deter-nine 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 de-grees- Nov/, since an aspecE ratio of 5 is a fairly Lorr nwrber, add I degree for three-dinensj-onal effects, and set the wing on the fuselage at ar algle of incidence of +Ldegree to the fuselage reference U-ne. Ttris nethcd should be accurate enough for rostca5e5.

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 approx-jrnate 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 approxirrntedesign lift c-oefficient of this airfoil is .3, so this apl=ars to fi.t \del1 enoughwit.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 probablynot suitEble for tJ.e application, or the estlnated cruising speed of the airplane rnaybe opt]Jru,stj-c.

6. CEMPT'TER PROGFAM ACCURACY.

the ccnputer program used to generate the Predj-cted performance data of APpen-

d1x 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 onlyrrclldesigned airfoiLs such as ,,GA" ai-rfoils, that have slrpoth, contj,nuous neanU5es, 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

11it cannot fol.Lod the ccnplicated effests of premature setE-ration bubbles at higherangles of attick ccrnrpn in those aj-rfoiJ,s. But htro wants to use poorly-designedairfoils 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 isguite good, all tfrings considered, and is a credit to Dr. Eppler. The programappea-rs to be especiarl-y accurate i-n predicting laninar/turbulent phencmena, separ-ation 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 appearsto be in ttle pitching nrnent coefficient, btrich tbe program overstates by at least30t. For thi-s reason, as absolute data, t}le ccnputer re-sults shouLd be used cautiousLy. Ho\rEver, for ccnparative purposes, such as shqn'non figure 2, the program is exc€.]Ient.

The program appears to be cal"ibrated for best accuracy for airfoil thi-cknessesof 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.re16. 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 thisiI his book. reference (9), and suggests that, due to the lijn-itaLions of wind tunneltesting, especr-a]-l-y the change in the ratio of aijfoif cross-section area to thetunnel tlEoat size witi different ailfoil thicknesses, Ferhaps his qxrputer dat! isfipre accurate than wird tr.mnel data. In any event, lrE suggest that \r,hen ccf{Eringthe perfornence of different airfoils with the cc(puter prcgram, one shoul-d usethe sanE airfoil- tldckness for both airfoils being c.crpared,

the Eppler prcgram has a routine for sirurlating the !=rforrnance of an aj-rfoi1witi sjrpl-e flaps. Ho,$ever, tlre predicbed performanc€ is wildly opti-rdstic crcnparedto wind tunnel data, because the program of necessi-ty, wfien the flap chord and de-fl,eqtion are inputted, drav,,s a ccnpletely new, idealized airfoil tlrat is unreal-istically snEothed so that the nenesis of the prcglan ( prenature flc'gr separation )

will not occur. Furtherlrl3re, tlle program caffiot begix to sjmulate the cffplicatedflo\^' 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 thisshortcurfng, ho$€ver, the flap routine is valuable for predicting relative differencesof flap trerfornunce betrcen sj:nilar airfoils, as shGln on figure Z, Another use forthe flap routine is to predist On vs clnax for a given flap systern. In otherrnords, if a sirple flap systen yields a Clnax of 3.0 b}/ the prograrn, then the repDntdOn will be reasonably acsurate for a flap systern with tbat CLlnax, even though it naytake 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[)ressibilityeffects. treaLing the airflorr as bei-ng inccnpressible. Ilo€ver. this effect is sonlinor as to be insignificant, for the flight regi.res of typical-,light general aviationair planes. For exanple, the tdlng ]oading of a Piper cub, 1*/ft', yields an aEeragepressure dj.fference of only 7 */ft-/L44 = .05 psi betr"Een the top and bottcrn surf-aces, Ccc$Ered to the atjrDspherj.c pressure of 14.7 psia, this arEunts to a pressuredifference of only 0.3t, For higher perfonrEnce airplanes, such as a Bonanza with awing loading of 20 */ft', ttre difference is sLill Iess than 1?. thus, the assrnptiontbat the flovi is ilccnrSrressi-b1e is not bad.

ltre Eppler program for perfornance a''alysis calcufates ve.l-ocity ratios acrossthe aj.rfoil at each algle of attack, top and bottqr surfaces, then arints these ve1-ocity ratios (Foint velocity divided by free stream verocity ) in tairurar and graphicform. AJ-ternativery. it will calcurate and print out pressure ratios across the air-foir- then, the program catculates boundary layer data for each angle of attack atspecified Reynolds numbers, including coefficienls of 1ift, drag, and pitching nrcnrent' the turburent area. ani the separated a-rea. Ttrese values are also printed outin tabul-ar form, arld in a "boundary rayer swnary ptot". A salrple analysis print-outis shorr'n on figures 24-I thru 24-4.

12Several- 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 lalninarbucket 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" inverse" rethod, whereby idealized velocity dj-agrams are first calculated, and thenairfoil top and bottcm surface ordinates are ca.l-sul,ated frcm the velocity data. Thatis OK, but the Fossibil-ity exists of "creating a nonster", such as the very recentNASA NLF(I)-OII5F alrfoi], discussed in Addendun No. 5 bel-or^r. lbis is less likelyto 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€tiodwas used to design the airfoil, and the final perfonrEnce figures a-re the only thingthat caunts. Thus both nEthods are valid. Any airfoil, even if hand-sketched, can bebroken dov'rn into a symrEtrical thickness distribution and a camber profile (neanIine). and much can be learned about the airfoil- by inspeccing and analizj-ng thesetllo 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 thefaulty 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 leadingedge ipproxirmtaly tt to 1? of chord length. The rpthod for designing these "droopedleiOing- 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 neanIine, r,,e calculate the ordinates for the bottcm surface.

Ttre perfornrance analysis for this cuffed alrfoil shclts a draratic jnprovenpntin ttre stall ccrnpared tso the original 64-212, as r.vell- as a slightly wider lan.inarbucket- see figure 26. A-Iso shorvn is the perforrnance of an uPIEr sulface nbdificationproFosed by Hicks et aL at NASA An€s. Ttlis cutes the sharp staff ' but it also revertsthe 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 theNACA s-digit airfoils, like the ?3012' which already llave too much leadj-ng edgedroop, 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 agen-cy's responsibiiities were e4xnded !o include national space Projects as r"eII asthe old-line aeronautj.ca.l, Prolests. Ttre total budget is currently about 14 bi]liondo.llars yearly, of whi-ch about 1.2 billion is refated tg "aeronautics" projects, afairly cpnstant arpunt yearLy. Ho$Ever, over the past Several decades, '.Jork relatedto @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 thesporadic release of several randcrn airfoils. These have usual-ly been the brain-child-ren of particul-ar NASA individuals, rather than any c,oncerted effort, and have beendisappointmmts.A. N;\SA GAI,t-j- . In l-974, the NASA GA!.J-I and GAVFz "Whitc6nb" airfoils ( later designatedEtlFb'qffi 15(I)-041-3) vere released. Ttrese airfoil-s are characterized by a largeIeadrng 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 leadrngedge has a droop of about .75tC, npre than it ne€ds to give the airfoil its soft stalfchiracceristic. -

Ttre 1c'vr profile drag i-s enhanced by the pronounced cusp in the afier-

13body, and the blunt trailing edge, The brorst feature by far, hcturever, is the aft-loaded camber profj-Ie- an outrageous nListake for an airfoil that was touted to bea general avj-ation panacea. This gives the airfoil a pitching rTDrnent coeffic.rentthree tijnes as high as it ne€ds !o be for the alrpunt of canber in the airfoil-, andthis produces very high Lrjr drag, rendering the airfoil unsuitabLe for genera.l av-iation 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" (MvancedTechnoLogy Light 1\,rin ) project in 1974, r"trlch turned out to be a disaster, perfor-nance-wise. The project was dccrned to failure frcrn the beginningdue to the seLectionof 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 blun-der. The spoj.lers for rol.l- controL \rere also unsatisfactory, experiencing controlreversal at ]ow and mediurn deflections. Nothing new was Learned by using a LongersPan. tapered wing- these effects had been kno\^'n for decades. This merely contam-inated 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]ectengineer never even bothered to hrite a final report on the projecc, but he got pro-ncted any,ray. He no, has a top position at NASA Langley. In retrospect, I.iA.sA forgotthat their function is to c.onduct basic aeronautical R&D, not to "shcwr the industrythat they are \,rrong, and this is the proper way to build a GA 1i9ht twin". Ttris isan example of hhat can happen if R&D is not rnarket driven, bub is directed by irre-sponsible 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- horesin 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-ang-J-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 shcunon figure 6. This reduces the aft loading scmewhat. reducing Gn and trim drag, butthe airfoil refiEins a rrr-ish-nash.B. MSA NLF(1)-02I5F Airfoil. This airfoil, due to Scnrers, and descriH in ReferenceT was a$n- oilg'inaTlt as a sailplane airfoil. thus it has too much carnber in itfor typical porrered airplane applications. Accordingly, the trailing edge must. bereflexed approxjrraCely l0 degrees as shc'vn on figure 29, for powered airplanes, Evenwith the reflex, high aileron hinge rrnents (stiff ailerons ) renEin, so a ccnrncn re-r^prk is to make the ailerons and f laps f lat-bottqned, as shc^,,'n on f i.gure 29 , tosalvage Che airfoil. Of course, the better solution to the problen j.s sjrply to de-sign an airfoil witl- less camber in it in the first place.

Anothe! strange feature of this airfoil is the canber "diP' "a .60C, as shc'vznon fj-gure 3. This is an attefipt to move the trans.itj-on point aft, extendj-ng the larn-inar run to reduce profi.Ie drag, which it does. Hcrvrever, the fallacy here is that thenegative carnber at .60C causes negative lift, and this causes nore ( induced ) dragthan 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 carnberprofiles for general avj,ation airfoils, See the "GA" camber profiles in A5pendix IIfor a conparison,

C. I{ASA NLF(1)-04I4F Airfoil. this airfoil, figure 30, due to viken, was envisionedas a very lo* drag lamjnar flovr airfoil for high-pornrered, high perforrEnce generalaviation airplanes. the Foint of rnaxinum thickness on the airfoj-l is at .45C, and thenraximum camber, c.entrally loaded, is approxirnately 2.53c. This makes the airfoilccnpa.rable to the }IACA 65-414 airfoil , Unlike the }IACA airfoil, hodever, the t\T,F air-foil has enough J.eading edge droop, approxjrrately .353C, to give the airfoil decentslc'vr speed perforfiEnce.

Realizing that the price pa..id for locating the nraxi:rn:m thickness so far aft isa 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' atvalious typical v€ights and speeds encounterd in aircraft service. lttis Proved to bedifficult and jrpractical. and the net wlng drag turned out to be nlf,re than antic-ipated. The scheme was t]"ug considered to be unsatisfactory for the intended appli-cation. This is an example of a "single design point" airfoil.

ltotice frdn figure 30 that the -7 degree cruise flap setting, necessary to reducethe rnaximum carnber frcnr 2\\C to IEC for Cruise. cleates a region of negative carnberat .85C. This causes a dlag penalty, simil-ar to what hE have seen prevj'ously fronref)-exrng the tlailing edge of the NLF(1)-02L5 airfoil ( ccrnblned with the canber dj-Pat .60C). reducing the efficiency of the airfoil. As before, the better choice wouldbe to desj,gn the airfoil witlr less canrber (NLF(1)-02I4), to keep tJ-e airfoil clean atcruise- in short, a conventioal design approach. Ho^Iever, the airfoil ltoufd still bea single point design. Accordj.ngfy, our concLusion is tllat the point of maximum air-foiL 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 suc-cessfully on the Nernesis Formula I racer. this is a very special application' a"single point" airplane, and thj-s suPporEs our concLusion that the airfoil is un-satisfactory for mcst general, aviat.ion aPplications.

It is interesting to note that I'JASA's Cessna 210 flight test progran for thisairfoil, repofted in liAsA Tl,1 85788, was simi.Iar to the Poorly designed "ATLIT" flighttest progran descrj-bed above. On the Cessna 2I0, the span Iras increased frdn 39 ft-to 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 toshov,/ that they can design airplanes better than the priroe rnanufaceurer, ratber thanbej-ng satrsfied with doing Iegitirnate research r\,ork. At }east, in both cases, llAsAproved 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 traibngedges, 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. Soyou 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 usezero-o'o airfoils, thus GA airfoils are not suitabl-e. nlrttrer, due to pitch stabilityconcerns. flaps cannot be used on flying wings. Ttrus, due to these tr.rc design con-straints, the perforrr€nce of any flying wing airplane wiU be nrediocre ccmpared toan egually sophrsticated canventional airplane.C. Canard Airplanes. This configuration has sinilar design constraints. Fl,aps cannotbe used on the nEin wing. llrther, the forward surface rl[l.rst al\.Jays be rll3re heavi].yloaded than the main wing, so tlEt the carlard wilL alvays stall first. Since thernain wing can never be allo*ed to stall. it never reaches its nexjmum lift coeffic-ient, and j-s thus relatively inefficient. Ttrerefore, due to these tlro design con-straints (no flaps. no-sta1l nrain wing), t}Ie canard configuration can never be asefficient as an equally sophisticated conventionaL ccnfiguration. Flrther, sincefull--stall landings are not possible, landing sPeeds are relatively higher than forcanrlxrable conventional airplanes.D, Three-surface lirplanes. control surfaces placed in the taiL have longer rsrentarrns 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-r-foils, hc,wevlr. ajre soft-stall- airfo1ls, htlich n*ans that lead-ing edge separationis not a problern, hence slots and slatsS cannot offer much jfiprovement. Ttlere aretv,o exceplions, honEver. First, in the case of novable slats that nDVe out fldn t]1eleading edge and increase the wing ;rrea I rrDre lift wil-l result srmply frcm the in-crease of iing "r.u. Secondly. leading edge sl-ats contribute a positive (nose up)pitching nterrent that can help offset the l-arge negative pitchj"ng nEnent due to large-traiung

edge flaps. In spite of tiese tDtential advantages of leading edge devices,with C,e airioils, the prir.nry effort at lift aug[rEntation should be \,rith effectivetrailing edge f1aps.

F. Case Study, Rutan Canards, Figure 3I sho\ns that Rutan used fhe GAwt-l airfoil scaledE 6TA{-rhick"==-?6;-6-ari-Eze. Ttre cAw-l airfoil, however, \^rith its high Gn,

has a considerable center of pressule travel, contributing to Pitch stabi-lity Prob-terns. Accord.ingly, for the successor l-ong-Eze, Rutan chose a forward Ioaded ( 1q"erGn, Io,.rer c.P. tjcavel ) airfoil to j:nprove pitch stabil-ity. Ho^'ever ' The Long-Ezeairfoil is a turbufent airfoif- vrby? with such a 1ar9e, lightly loaded nain wing, thenatural choice Seenls tso be a fs"r Gn, soft stall laminar flonr wing. I donrt have anans!',er to t].is puzzle.

16Postscript

As stated in the Introductsion above, tJre original NACA airfoils \,{ere never in-tended for astual airplane use, and, according.Ly, "GA Airfoils" has been erittento address this need. tn retrospect, one must ask why NASA, in the forty-odd yearssince 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 havebeen needlessly wasted, because llA.SA failed to address this problernz They certain-ly must have recognized the need, so why dj-dn't they acc? vitry did they fail to putan end to the lrlaLh that the I,IACA airfoifs were astual airplane airfoils, and whydidn't they admit 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 hardto believe, ho,i/ever, in vielr of the astroncndcal budget tllat l.IAsA is bl-essed wi-theach year to pay for talent and facilities.

Another possible er<planation is that, by the innEdlate Fost-I4MI era, the Unitedstates had achieved undisputed rrcrld-wide suprsnacy in aviation affairs, in spiteof the "good advice" frcrn NACA, and we enjoy this nLmber one position to this day.Accordrngly, NASA could have felt that there was little ne€d to do additional aviationR&D hDrk, nor to reviev the old lrork, so they "lested on their oars", So then thequestion arises, lrhy wasn't f,lASA's furding cut off at that point? And why has theirfunding continued yearl-y to ttris day? After al-I, the agency was set up origj-nalJ-yto subsid.ize an infant industry, which aeronautics r,ras in the 1920's. But U.S. avi-ation is no\^r not only a matu.re industqr, but it enjoys a runarrday position of $,orldsuprsrEcy ! To c.ontinue to subsidize this industry with federal funds, at the expenseof starving deserving infant industries of the I990's, rnakes no sense h'hatever.

zurthenrcre, a nore basi-c, philosophical concern exists, In a free society, onemust al\./ays be on guard against excessive centraL planning, in rhich decisions re-gardj-ng all-ocation of productj-on resources are nade by bureauclatic guesstinEtes,rather ttran econcrn-ic realities. R&D !$crk is a legitinate production expense. and fallsin this sarE category, and rnrst be hel-d in check by the realj.ties of rnarket econcrnics -For this reason, r{re must always be suspicious of gove!:rurEnt R&D as opposd to prj-vateseccor R&D. Since the U.S. aviation industry is ncrvr undoubrtedly nlatu-re, they areunguestionably able to do their ovm R&D 'aork, in the norrnal course of their business.For this reason, the aviation R&D budget of NASA should be terninated ifinediately.And let's not be rlLisl-ead b,y those vrho !,Duld argue that it is necessar!. to continueNASA's aviation R&D to insure tllat ttle U.S. aviation industry rnaintains its positionof leadership. That is a specious argrLrrEnt, and ignores the reatities of li:rdtedfederal funds. ltard choices have to be made j-n washington, but fortunately this isan easy one. llreher. Let's not confuse the i-ssue by clairning that tIASA's rdork isvital for nati.ona.I defense. Ttre rnilitary can cronduct thei-r crvn R&D, under their q'mbudget. Accountability for governrEnt spending insists on th-is.

l,lo one will be hurt j-f the NAS|C aviation R&D shop is closed, and the U.S. Tax-pa.yer wi-l1 be eteFraLly grateful. In fact. nor is a good tijrE to terninate this Fed-eral jobs prcgram. the currently bocning air transport i-ndustry can easily absorbthe "out-placed" 1=rsonnel resul-ting fron "dosm-sizing" f.lASA. Now is the tjjle to act.Aviation R&D should be rnarket-driven bry Adam $nith's "invisible hand" of free enter-prise, not subject. to politics and bureaucratic r^trjms.

17

LIST OF REFERE}JCES

l. Abbott, I.H., and Von Doenhoff, A.E., "Theory of wing sections,Dover Publications. NYc, 1959. Available fron the EAA b@kstore,Oshkosh WI 54903-3086. Publication +2I-37f77.

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" 'NASA conference hrbLication +2085, Ms,A Langley R.c., 1979.

4. Prouty, R.w., "Helicopter Aerodynamics".

5. Eppler, R., and Scnprs, D., ''A ccrnputer Program for the Design andAnalysis of l.ow speed Airfoil-s", !&qsA N80-29254, NASA Iangley R.C., 1980.

6. Sawyer, R.D., 'A Program for Designing and Analyzing Airfoils, Airfoil II".Airware. P.o. Box 295, Canton Cf 06019, 1985.

7. Saners. D., "Design arld ExperijTEntal Results for a Flapped Natural LanrinarFlo,r Airfoil for General Aviation Applications, |IASA 1P #1865, NASA lang-ley R.C. , June 1981.

8. 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.

9. Eppler, R.. "Alrfoi] Design and Data', u. of stuttgart, springer-verlagNYC, 1990.

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. KII'FOX SPEEDSTERWirh 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 udleadin! edge.ngrreeing xllo*\ il top sleed oi 5lintes ir\ rornxl rtlll \peed. oilerinf ntarimunreiljcjcncy and sllcl-\'. The Specdstcr refre\cnls aarl spo pe bnnrncc ;rnd lnluL :r, .r prirc r'rrr r.rrrlflorrl. Worid renown lerobaljc pilorJinr F.! klin dcnto rtralcd thc Spe.dster xl O\hKosh 9l ardsrve ll rale reriews, crlljng il".'\ lrcrl jiltjr llj$hne. I $dnl onel '

33

itA3OJ-i,tz-

?e,acen]

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

Dear Mr. Ribicq

I arn intleed using thc GA 30ll-315 airf,oil on lhe Peliean < ll" > and wo arc vcry happy l:ithir-

Jcan-Iicnf Lepage,P.ling^Presidont

soN€{\Rl

From lhe Soneror Newslefer

FLETCHER BURNS REPORTS ON HIS SONERAI II WITH RIBLETT AIRFOIT( '\e /.r' a7 1

The wings ore thjcker thon normai ofter o beni\ring on my woy lo Oshkosh (which ls onotherstory). i corne up wlth o 15% ihicker oirioil lromHorry Riblett ond I love ll. I don't ihink it slowed medown ol qll. l've sondboQced them down to I G's

uAci (l -ztz)stolic wiihoul a wrinkle. Thick€r ls strongerl This is ogenerol oviotion oirfoll not o pylon roce oirfoll. iilcnd! muclr softer now. climbs belter wlih lwocbocrd cnd lhe roll rcle reolly improved (oihoughi.i didn'i need ta).

hh 31 fr3t5

€ A n Technicot counselor News 7

f t&uR€ l1JAt/ tqss'

A New Wing for theProtech PT-z AirPlane

ln Januarv oi 1993 Ken Fogers called me and iold me thathe was disaopo nted with the perlo'mance ol his SubaruLeoacv oowered Protech PT'2 (see Conlacll isslre t11 ioren;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 replacementlor hio'r-li+t 'Cub" type applications and Ken wondered if itmiqhinot 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 coulddo to "patch ..:p" the oid wtag Acco'dingly Ken sent thedetails bf the old wing io me, and I made a perlormance

analvsis usino the NASA "Eppler' code(pR6f trt, com-nercialized for PC use as'Aidoilit" Tni. ir a simole code, but il qives e\cel'e4tresulls, especialiy concerning laminar,turbulenitransition, llow separation, elc.

The analvsis showed that the existrng airfoil has

a separition problem on the botlom suriacenear the nose at high speed and also a similarproblem on the top sudace at 70 percent o{ thechord at allspeeds. This agreed with Ken s flightlest experience with the airplane, which showeda low cruise speed, high landing speed' andpoor rale of climb. Accordingly, lsuggested weattack the top surface problem first by installingan array oi vorlex generators (VT) along lheentire span al .70 C, in an atiempi to'Yill in" theseparation problem in the "low spot' there,which he did. These VGs are simple, smallpieces 01 bent sheei metal, glued to the wingsur{ace at a slight angle to the slipstream, andcan oflen cure separation probiems.

?1 t!t {+

l'!5rlf Sibaetf

415 Ribtett Lane

W,-lrninglon t€ 198t8paz) 994 0479

however, Ken iell ihat in lhe long run it would be betler forhim 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-613.5airfoil.

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 curvethat of the old wing it was necessary to decrease lhe angleof incidence ot the new wing, and also the existing horizontalslabilizer, by 4 degrees-

Comparison ot the original PT-2 and new 6A 3oU-613.5tldoils, Note lhe localion of the vortex generalo.s apptiedio ths original wing to promote lurbulenl llow.

Evidently the problem was quite severe, howeve., since Kenreponed that the vGs helped only a little bit, especially inprodr.rcrng sl ghtly bener aileron control, a slight imorovementin rate rn cl mb. and better handling at cruise speed. Overall,

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

Ken flew the airplane in August 1994 and reported theseresults:

Sefore AfterCruise speed 85MPH 100MPHTop speed 90 11oStall speed-no flaps 6tr65 45St3ll speed-w/rlaps and power 50'55 35Rat€ ol climb(FPM) 5m "betterl"

In addition, Ken reports that the siall is vary genlle andpredictable, and that the handling characterislics are bettetat all spesds. An unexpected benelil is that the engine oil

temperalure now run 15 degrees cooler, due no doubt to thereduced drag of the new wing!

Ken is alrue experimenter and is lo be congratuiated lor hisperseverance and "can do" atlitude. He says, ''lt it ain't-righl,ix it". t would be glad to furnish details oi the new airloil oryou can simply reler to Contact! issue #'1 1. For details of thenew wing consiruction I suggest you contact Ken Rogers at1450 Konnowac Pass Road, Moxee WA 98936, or call himat {3€A 248-1a13. HB{t1 flAs.(A' A p{{t tqq,

CONTACT! lssue 2s pase 17r'.'.ltLlu(x LU

T//////{//////////"/,i/.{f{{/,/722727t121T2fl,777717121711V./zl%7774&7277721Vk

35Aircrrft Performance Prediction (see a_tso figure 2l)

Aircraft pcrformancc can bc cstimated from wind tunncl (compurer) data usingformulas from standard tcxlbooks, which wc will summarizc below. Thcrs arc thrcedimensionlcss cocfficicnls of pcrformancc dctcrmincd for cach anglc of sltack as

follows:Ct = wing lift coefficientCa = winS drag cocfficicntC6 = wing momenl cocflicient

From thcse. quantitative valucs of lifi, drag, and pitching momcnt can bc calculatedas follows:

L = lifr = Clal Sw V2, pounds

D = drag = ta* Sw v2, pounds

M = pirching iooment = C.f 2 S* V2 C, foot pounds

wberc: p= mass dcnsity of standard air =

Sw = wing arca, square fcEtV = airspeed, fectlsccondC = wing MAC (avcragc chord), fcer

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

Thc tcrm p n Vz appears in all thrcc basic formulas, and is somctimcs known as

"dyaamic pressurc", q, pounds/ft2.

Notc that thc pitching momcnt (in wind tunncl tcsts) could be mcasurcd about anyrefcrencc 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 mcasuredand cootrollcd. Although Rn can bc dctermincd cxactly, for practical purposcs it canbe 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 ofapprorimately 3.6 x 106 (3.6 million), somctimcs writtcn as 3.6E6. As wing chord andspccd decrcase, so does Rn, and performance drops slightly. Pcrformancc dropsrapidly bclow R-n=5E5.

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

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

Usc a "wing cfficiency" factor =.85 for non-uniform span loading.FrcuRe L l

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1. (-l(:)1 - 98f,.994 .978,-9A4 .969.97? .939.9=9 .947.946 .936.9:? .923. 91 5 .9Ct7

. B?Cr . BEl4

eo

1. :iib1.:Etr

1.411.\-4r/1.418I . 4?rJ

r . 4271.4f,=1.44f,

r.47A1. . 4691,4=A1-4t4

l. ict c|

. 11{)

. f,(16

.462

. al l

.lJ.Jc'

- 9C)7

- 94t-t

.964

. 9Bi

.998

1 . (:)(:r9

L (r{)?- 989

r.4671i

4

6. 5€471.619

18

191 .7?C,

)

:r

1

1

Cr

. r:l

5{)1.i)i:r1.7=1-

, 8061 .O1 . 9()f,1.9E}5?f,?. t-t47?4

:. {i66:161 - 8C)4i71 . rt47.679

-<)

f,(r.14trl1. r7B.4?t--l ?.344-'.4

f,5.7 19

f,b.7 Bt:l

a7

. cr.Jof,9

4C).9C)7

,1, I,91(:|4:.9c,7

4f,. g{:)g

44.91{r.9Q9

46.9(r5

47. 499

4B. 893

49. sB5

5(r-976.460

c)4465

c)49f,C)

r:r5{rC}6.767

1

1

(j(:)5

{t731 c)il

1Sir,1'{ )( I

C)f,

t74

.87770cr()o

.87 67gc)c)o

, E7S8C)()cl0

, A7 CrB5oc|o

, 8669 C)(:xlC)

- €}5995()O{.846

Crl

o?c)lo1c)tl

()C)

4 {)(:} C)(r

45C)C)0.El62

5(:r{j(:r(l.El64

13C)743109764f-)85773

FthuRe t+'L

114IRFtrIL,all5UNA

8.4-)O 1{:r. C)1:rNXELATIVE TO THE52 1 . {:)(:r{)()O.445 . Bi9

1 5. r li:);/, TH I CI,INESS

40. (:'(:) DEGREES DEFLEI

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

Vo. Fgg1 StftEA.\ y'eLa.tfu

- (:)tl7. FLAF'

-1.(r[r . ()(:] 1.(:){r !. ()(l :i. {:x_} 4.(:}(l 6.(iC1? . (:r{:r 14 . ()il 1o . (J{:r 18. il(:,

Y VELOCITY DISTRIBUTIONS FOR THE AEOVE ANGLES OF ATTACF

5E - 858 . A57 .856?4 . Ar5 .8r-)gI nurler I Drta - 2-?6-19!A

hA t1 43tS

V

l.oo; ,s x/c

SUT4HARY AIRFOIL1 af,l5 ANGLE OF ATTACIT1 FELATM T0 THE trHORD LINEALFHAO : 2.79 DEGREES* INDICATES BLIBELE ANALOG LONGER THAN . {)f,{]

R = ?OCICIC)OO HU =: R = 6l:)O(l{)C){:} MU =.1

CD. crr]34. CrO?g. ol:t64

CD. (ittf,7, (tct?7. (i064

CD, (:rcr4 (:)

. C){)25, ()a-t65

CD. o(r4=. oo2f,. 0.-166

CD. rJa_r46. c,c) 1g. oa-t64

CD. of-r49. (r(r16. c)o63

CD. C)(r57.c)o12

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

CD. (-){rf,f,. Qtr!4. c\:t37

CD, C)4r=5. c)o22. ctct17

CD- oof,B, r-)Ol1. c)c)s8

CD. oQ40, QC) l9. oc)59

CD- oo45, oo 1B. C)C)64

CD. cxlB4. C)CtlS. t (t97

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

CL = .142 CD =cH = -.t)529

2 S TUREI S SEF- 573f, . (jtlaj(-).5845 . OCI{-)C)

cN = _,(:,559

? S TURE S sEF. SASS , (J{rctr-).3723 . Cr()OC)

CL = ,f,6? CD =cM = _.._1589

2 S TURB S SEP.=97t . OOOC). 557r-) , C){rCrO

CL = .472 CD =CM = _.1:)619

? 5 TURB 5 sEP.6t.t67 , OC)OO. =4?A . OCIC)O

CL = .5El2 CD =CM = -. o55O

2 S TURE 5 SEP. E49t . r-lOOCr.3772 , OOC,()

CL = .692 CD =Cl4 = -. C)681

2 S TURF S sEP.9476 . .r 196_ 3756 . (rO.-)O

cL = ,89? CD =CM = -. O696

ALF.HA = _1_Cro DEGREES1S TURET S SEPUF PEF , 5{j45 - C,C)O{:|LEIIER .5865 . OO(IOTOTAL CL = .142 CD -cM = -. ('529

ALF.HA = , {II1 DEGREESl STURB S SEPUF'PER .517E1 -O{)(){rLOWER .541C) . (:lcx:r{:}TOTAL cL = .25? CD =CH = -. (1559

ALPHA = 1, O(r DEGREESl STURE S SEPUFFER ,5f,49 . (){:)(l{:lt-OltEF .424(.t . C)C)(-r(rTOTAL CL = .362 CD =Ctl = -,{l=B?ALF,HA = ?, (rr_r DEGREESl STURE 5 SEFUF'PER .549f, . OOC){}LOU]ER .3Ct77 . ._)r)OC'TOTAL CL = .477 CD =

CM = -.('619ALF'HA = f,. C)Cr DEGREES1S TURB S SEPUF'PER ,565C' , Cr(,()C)LOWEF ,3734 . ()ClC)CrTOTAL CL = ,5AA CD =

CH = _, {:)69()

ALFHA = 4,Cr{' DEGREESr STURE S sEPUF.FER .=794 . CrOC)trLOWER .3777 . {)O{iOToTAL CL = .692 CD =Cl4 = --(t681

ALFHA = 6. O(r DEGREESl STURE S SEPUFFER .6Ct7t - {tc).-){rLOhIEF .24:E - CIOC)()TOTAL CL = .912 CD =Cl4 = --8t744

CHORD LINE, r_)(:){)a_){:}

Ftduae a4'3

SUMI,IARY AIRFOIL af,l5ALFHA{I = ?. :9 DEGREES* INDICATES BUEELE ANALOG

R = 2(r{:)O(:,rf(j HU

LONGE R

ANGLE OF ATTACIi:

THAN . (:,f,O

R = 6l:)(:)(:)0(-r( )

RELATIVE TO THE

MU=3

41CHORD LINE

ALPHA =1

UPF.ERLONEF

TOTAL

ALFHA = IUPPERLOTJEF

TOTAL

ALPHA = IUF,F'ERLOUIEF

TOTAL

ALFHA =1

UF.PERLOUJEF

TOTAL

ALFHA = IUF,PERLONER

TtrTAL

ALFHA =1

UPFERLOWER

TOTAL

CL

1(J.c

CL

1.

CL

14,1.CL

16.

trL

18.s1.CL

S TURE S SEF, 9812 . Cr4L9.296L , (rcr)(r

cL = 1,._)86 CD =CM = -. C)699

S TURE S SEF1, O167 . (:)822

. 2081 - (]{:,{_x:rcL = 1.?52 CD =CM = -.Cr631

CD. a-) 1 (rE. Qcr 10.(:r115

CD. (11 f,6. C)CrC)7. c) 14f,

O ,@< .tro ,at{LD

This rLrn made on "-26-1994At 1;,3E: 48.77

2 S TIJRB S SEF CD1. (,1E}6 . 1294 . C)16f,.1196 . (:r(rC)C) . {Xr{:}SCL = 1.4(lO CD = ,.-1169

CM = -. OEB6

2 S TUREI S SEF CDI.t)797 .1gB(r .t:r!97. (r69C) . {)Orjrl , O()(-)4cL = 1.52? CD = .Q?(:rl

CM = -. C)5Of,

? 5 TURE S SEF CD1, C)?10 .2545 . O2f,9

. (Ja-)oa-) , ()()r-'a-) . otlll?cL = 1.619 CD = . C)241CM = -. (:)4?6

? 5 TURE S SEF CD1.C):S5 . f,f,l2 . Ct297_ ()o(:)f-) . o{x)o . (lcr{]?

CL = 1.6€l? trD = .(t299CH = -, Of,7(l0 Detr - Z-?s-lr9{'

3-i A3t{

Ct'tr

-a,lo- o,o9

C){] DETUFBCr23{r(lalt)o

DH

G

^L

-

KG Atlo------ R: 6x roe

6A

!,i

cLl.o

.6z0 .ol.s

*lc = o6--9

, o3o .os f.s t o

to zo

Run tirne was

f taueez4-+

! ------ |

t\

aUtro

t)o]J!otro

Jx+$:

?3i

I

o oota "J ^/| - €aroool' r' I

co.

q

o

a

o€Joo+'

a

I

Noao?

ctL0l€ L€

43

IliJ-lt .l

-|-3-

I

,,t.it

:I

89

tF

a

z

{

I

T

I

Ir,

!tlr(

{-ts ':.

ri!!<

TJia5t.l;l{5r€

'1 <J3t!t\

9l * 2!t ;il .s:t ^!l ,-' r'3l j i.1 " J-

:l t:El: Iil 'iil o iil " .:3l : .sl iiti:

oE.-l

LH rd

:l.liltl

C)

IEt

o

!r0c.lF

l,l

C'l

NI!.'t

.rJ

or+

3\

a

l.16

.r.J 0)

lorJ

()

6rol-ci .tJ

!F d 5-.{J-+Jlro

r.{ {,O'EUFr

o.'Jl!c u q-.r

OiEO'.{!O.]J +J

a.

J

'*

'{i\i

..l

'?r i

-i

o

60.J

Iaoo)

d\t'

44NASn an (w)-l ArAtrarr- fus (')- o+rrl

t_

2

,5

t.o.9.8.3.2,l

U

.t

-.t

-.?; A.5.6.7r/c

lq'r4 Figr.rre l.- Section shape for NASA GA(w)-1 airfoil. (r1% rr'rrc<J

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 air-

.{$ !, !q!- HHilH$ flUlf,tl0ll

craft - 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 lateralcontrol. Wind tunnel tests with models have indicated that the netv airfoil will provide inqqelq! of90 oer cgnt in range,80 ocr-,cent in the single+ngine-rate+f+limb, 30 oer-ce?t in maximum lift,g9_gg. c_elt-tgup and jgpzullt in cruise speed. Although the rving is being built by Pipera;E install€d on a Seneca, NASA spokesmen emphasired that the program is designed to provide amore efficient wing for a wide range of generil aviation aircralt, not iust the Seneca. A full flightresr program will be conducted at NASA's Langley, Va., research facility after initial flights are

" AT u, r' fAcLtec-

CAr4B€A-'/- ..-

-/-

__=iIj

I

:I

><--I

I

completed in Florida.

rruftG Ln

c/}-!)

:l1.-,jI

I-.1ca"!O-u

IUio

J.rJtu..)o

:t-JP

--!s!

l' ILt L6

k-1

,--

?

tbJ

.t\Ju

I)Lva

.-3..11,

tc

q"5..t ---

o\3

*

oc.'

Jx

\h

lr.

1o*) ''

{1

.9r0

x

t-

Ctr- ? 4

ata0!)tl+

,",1()

CJ

CJ!!

00orrd6

d^!!r

ortr0)7

+.l '.r']JoUOa,OX\r CJCr*

o.,16

1]U6Cl'n!

Jstt

€

u-.

t,

tJ-,".

,

._:il

uJ

i'*q- ltt'2

o47

oF

I

t-- -'|-\

I --l, ,-

\-- /

]4l'.aG

o

c

do

- o-I'

,

:t-

U

Ntlot\4

L!|,.J

eq{

=-

OF+olz()$Eotr!c

,e&.-l lr .4C'ocrrd- ood)0)> cE0l rd..,i'4Cc o,ootrkrd .,i @'

dFr3 r'd.co!6JICErdlO..l.,t lr o,lJ 16

6-o-q'{-r O

"Efrd!_t. .,t- u).'.a 5 q)F tlt J)EOd.-rl{o

"lIt (u-.{'-{ ! O,

,dEOOc o,od .d -.1! r-l _co'sFro0J.!oo._;.1_Eu|r otr lr ..1

_-l O .lJt{ : .-itori o-co{Jo.6COqr

0,.1a'c+l

E tiq'l.!tt..{ id O

E'A{d >..1or lr l]OOJId!>>

J€

\9lt

qcllrt

t

jrc

ou,r

nJf,rlJ

w

t-

l!Lt\TJlr

{

l.t&uE€- 30

48t'l-'1o T*,.( iJA cA 4 D'611- ANp t g|Air ArrFcret

oLD-E_L_AgEqlr

JEof6 t ao&>

:

II

I

I

4.O

s

L(

I'o

l

Lo!6_E+€ fie ^J

(r/6

t.EtA

NLF(') - d?r5 F

Lor':cr - 6?5 ( 'l'L ge-\

NASA L!(t)-6+18

VARr E+F

( crau-r ,rr.o'r'el)

.-o I /C_ ,o

APPnDIX I - Bas.rc Thickness Forms. 49

T - 84stL a*rc<lveSS Foems ( synretrical- shapes . l5t thick)A ' "cusp' TrPe 7 Atc<+v€ss D tsrRrgurrorts

GA 30 Aotl

(nrRca oors)'

GA 3s-Ots

INACA Ll-ot5)

, QA 31- 615

(,vncn 6+ -arr)

o lo ?.o go ao ta Lo .ro go qo nc

llote- For thicknesses other tllan l5t, these sba[Es nEy be sca]ed d-irectlyup or dcnnr to the desired thickness.

f I6LJAE -L-I

-

GA 4o-ots .

{lncn al-ors)

a - BAsrc THrcKt.]gsl FoRmS ( symrEtrical shapes, 158

50thick )

TF tc <ru Es s. otsTRtgullarJs

Y = TRANsttT ror'), R =6xtoL

shapes may be scaled directfy

B. PREFe-RR 1-,7 'fuo Cus P

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

6A 30-o rs

GA 35AOl5

(ueca ut aors)

6A 37nots

(NAcn 61 Ao rs)

CrA 4oAots

Frh T'L

APPNDIX rA - ctrso Tv.pe Thickness Distributions (GA 30A, 35-' 37-' 40-)

Feb 94sta0.000. 250,50o.75L .252 .505.007 .50

10.0015.0020.0025. 0030. o035.0040,0045.0050.oo55,0060.0065.OO70. oo75.0080,0085.O090.0095.00

100.00

Feb 94sta0.00o -250.50u. ta1 .252.505.007.50

10.00L5.oo20.0025.OO30.0035.OO40.0045.0050. o055.0060.0065.0070. o075. OO

80.0085.0090.0095.00

0 015Ord

0. o001.090

1.8562-3673 .2644,4435.2505.8536.6817,1727.4277 .5027.436

6.9766.5186. ie15.7045.1664.5803.9503.2792 .5661.8101.008o.158

63-015ord

0. o00o.a75I .204L452I .8742.6103.6484 .4275.0556 - 0116 .6937.L557.42I7.5007 .3467.O996 .6656.1085.4534 .72I3.9343.1192.3101.5410.852o.300o.000

63AO15ord

0.0000.a75L .2031.44S1.8442 .5793.5184 .3A24.9975.9425.6197.O91,7 .3447 .4967.4357 .2L56.8586 .3875.8205.L734,4683.73I2 .99L2.252I .5L2o -772

54-01-5ord

0.0000.8651,2081.456r.4422 .5283.5044 .2404 .4425.7856.4806 .9457 .3797.4427.4737 .2246.8106 .2665.6204.8954.1,133 -2962.472L.6770.9500.3460. ooo

644015ord

o. o000.8551.l-931,436r.8152.508J.4774 .2024 -7995.7326 .4236.9267 -2707 .4637 .4877,3136.9745 .5L75.9565.3114 . 6003 .8473,0842 .3211.558o.795n - o??

65-015ord

0.000o.830L .7241.356r.7022 .3243 .2453.959

5 - s046 .2236.764

7 -3967.49A7 - 4277 .1686.7206 . 1.185.4034.6003.7442.858L .9771.144o-42A0.000

51

APPENDTX rB - I,Io Cusp ltlickness Distributions (GA 30-, 35A, 37A, 40A)

30-o15ord

0.0001.090r .5271,8562 .3673 .2644 .4435.2505.8536.5817.1727.4277 ,5027.4407 .2657.0006.6556 .2405,7555.1904.5403.8173.0532.290L .527o.753

4 04015ord

0.0000.830I.L24t_.356I -7022 -3243 -2453.9594 .5555.5046 -2236.7647.L527 .3967 - 4947 .4277 .1686 -7206.1185.4034 .6003.7442.8852.0651.2900.600n. nnn Ft6 T-3

52APPENDIX II - l4ean Lines ( camber profiles)

Feb 94sta0. ooo .250.50o.75r.252-505.007.50

L0.0015.0020.0025.0030.0035.0040. o045.0050.0055.0050. o065.0070.0075.0080,0085.0090.0095.00

lo0,00

canberGA-20.0000.0600.1160.169o -2630.450o.715o .8921.023L .244I .420r .5571.663r.737t-.780r.7921.764I .672L .537L.3741,,1890.991o.7930.5950.3960.198o. o00

CamberGA- 3o.0000.063o. t-20o.770o.2750.5000.8521. tL81.3351.6831- 9582-r732 .3402.4572 .5242 .5432 .4992 .3682-L7aI -9471.685t . 4041. L230.843o .5620,281o. ooo

CamberGA-40.0000. o820.1 52o .2L30.323o.570o.9701 .307L ,5972.Q46?.4732.7763.0103.!75J.Zb93 .2963.2343.0652.8182 .5t92.180L .8L71.4541.090o-727o.363o.000

camberGA-60. o000.L12o .207o ,29L0.441o.777r .323L.7A22-17A2 .4443.3723 -7A64. t- 044 .3294,4584.4944.4104.L?93.8433.4352.9732-4741.982L .4870.9910.496o. ooo

9- cAt oEA ?2. F.Le t

bA .|CA,J L,,\r65 arvD TJACA t^€A^f Lt'|/et - Co'Jaa'1ttt1- /ec..'.7 fyk

trocr-@ '2t*L.__.1..

A.nla*. UE^tt r-J

r.e-z tlliA (^.|at!.1,r4 t"E D16' t ,1.1 :L C ,(lc7-S't'q. e.c.c?.to :1. e .es cL .ao oh e.(tc-

- a1.'5' -"

As:*A

\\r Fta

Ix/L ro .L 2.tah-

53I

,_a

.t

c<

o

0)E+J

o88.fo (,1

alJ.-r o(to.ri k

]Jlr..r o..1^'HY'

6J

iElg

lulE

\

i\

+l

J

;l

APPmDIX rII - Airfoil- ordinates._--

t J-:t

6*

?g: !.rr. :'f t-

\!;

!oiz

IIII

tE

2

oo' dd

h

L)

!I48,

)6

f!+

\l

2

cl r+l tsl'a[czl l

2

OJ

Ed,c.-t

Fl

o'.c,/1,

c)+)I

-9CO

oI

II

?..l 9t{

1*uII I

!!g

!Ug!o

tIl.ltroc

dt

0,]J|!

fcJtrllo

)-t!!r-Of,..i)Ll

+J

8.Iirrd ..ll'' .i

lJl o ptJI O Udjtc c)!J l! !.tr I L, .-iol..r dulcfl'.glo cIrl-c c.r I rJ .-l

gle Ecl'nrJl 11

ele Esl.r B*[Henlo r,E[e 3

eta fr

gifrE=2 zii- 3^

,o;E= il -Elr 4F ,9 E d c:5 6 0-- -, i dHiS:g F o> -. xI E 5;;E;

f .iFtRedaf I F=rq3x.;. ; E E E E ;:: 5 c€. a.l

9 o< -u:5i E .9o -.i I!-! s >r <'a s';t! | aZE' Aii i I= E Er

i:I E Eii:€;ii ; EE€ E:!!t i i s:;€tli ;€Es,iIa- -. Cl-r.,l3$ a StEEB

F{'5'o!Il.

oI

'z

UzeI

s

II31ta,

5ig=i5S5t8tlrrl

9a

a

.

gigi II

t e333:

sEe g

I

IPilFErt88

;3t tI

IE:r ra!t tIli

tFSFB

OG

sollct

ao1)=_o.-l!.lJoo

ri \'

f- li'rfd

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tuOo

aizz\ot'>

+OFEcoi

F

Bl ^ol t)cl Fi

dl 6

EI :., 6

El p

el #jl u

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Hl s4!tEIotrl

EI

n

84ql

lrlnat

$.P

iE

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!haT

glt

!,)s

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LN-1roo

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.-l|!o!

l.lqIJItrU

o.l-,)

caard

0)

!0)ol16

ooard

4-.13a

]Jt1o

a!n0,

U

-c!OJu'a6

a.t

o.t)

o

otl6

o0)_c.u

OJr-.tl[Uo]JI8I0).lJ

2

1ou.

E

\tvvIF

*l{t

cE

U)

+JocrttctIo

1

)o$I(

(

t ll

I

\i\r\Fnf,-7

E-ct)+,o

lr)

u')

Feb 94sta0.00o .250.50o.75

2 .505.007 -50

10.00L5, o020 - oo25.0030.0035.0040. oo45.0050. o055.0060.o065. O070. o075.0080.0085.0090.0095.00

100. o0

Feb 94sta0.00

o-50o -75L .252 .505. OO

7.5010.oo15.O020.0025.0030. o035.0040.0045.0050.0055.0060.0065.0070.0075.OO80.0085. O090. o095.00

100.00

30-015ord

0.0001.090

r.8562 .3673.2684 .4435 .2505.8536.6817.I727 - 4277 .5027 .4407 .2657. O006.6556 .2405.7555.1904.5403.81-73.0532 .290L -527o.?630.000

0 015Ord

o.000t-. o90

L,8562 .3673 .2684.4435.2505.8536,6817.1727.4277 .5027.4367 .2546.9766.6186.191R ?nas.1664.5803,9503,2792-5661.8101.008o. L58

CamberGA- 20.0000.0600.1,160.1690.2630.450o.715o.8921.023L-244L .4201.5571.663r.7371 .780L.?92L.764L.6721.537L.3741.1890.991o.7930,5950.3960. r980.000

camberGA- 20.0000.0600.1160,1690.2630.4500.7150.8921.023L -2441.4201 .5571,663r -7371.?801.792I.764L.672! .537L.3741.1,890.991o.7930.5950.3960,198o. o00

30-2L2upper lowero.000 0.000o -9J2 -0.8121.338 -1,.1061.654 -1.3162-L57 -l-.6313. 064 -2.1644.269 -2.A395.O92 -3.3085.705 -3.6596.589 -4.101?.rsa -4 . 3187 .499 -4,3857 .665 -4.3397 .689 -4.2r57 .592 -4.O32? .392 -3.8087.088 -3.5606.664 -3.3206.L47 -3.0675.526 -2.7744.82L -2.4434.045 -2,0633.235 -1 .6492.427 -l -2371.618 -O.4260.808 -O - 4120.000 0.000

3042r2upper lower0.000 0.o000.932 -0.81-21.338 -1,106r-.654 -1.316?.L57 -1,631.3 .064 -2.L644.269 -2 .8395.O92 -3.3085.705 -3.6596. s89 -4.1017.158 -4.3187 .499 -4.3857.565 -4.3397.6A6 -4 -2r27.583 -4 -O237.373 -3.7A97 .O5A -3.5306.625 -3.2816. 100 -3 . 0265. so7 -2.7594.853 -2-4754. 151 -2.L693.415 -1.8302.64A -1,4581.844 -L.O521,004 -o . 6080.126 -0.126

30-215upper lowero.000 0.0001.150 -L.0301.543 -1.4112,O25 -1.6872.630 -2.1o43 .718 -2.8185. 158 -3.7246.L42 -4.3586.a76 -4.8307.925 -5.4378.592 -5.7528.984 -5 . 8709.165 -5.8399.L77 -5.7039.045 -5.485a.792 -5.2088.419 -4.8917.9L2 -4.5647.292 -4.2I46.564 -3.8165.729 -3.3514.808 -2.4263,846 -2.2602.885 -1 . 6951.923 -1.131o.961 -0.5650.000 0.000

3 0A2 t-5upper lower0.000 0.0001 .150 -1.0301.643 -1.4112.O25 -1.6872,630 -2,1.043.71S -2. Sl.85.158 -1 -7 2a6 -t42 -4. 3586.876 -4.8307.925 -5.4378.592 -5.7528.984 -5.8709,1.65 -5.8399.]-73 -5.6999. O34 -5.47 4I . 768 -5 . 1848.382 -4.8547.A63 -4.5197 ,24r -4.16?6. 540 -3.7925.769 -3.3914.94r -2,9594.072 -2.4463.16L -L.97L2.206 -1 .4141.206 -0.81,0o.158 -O.158

5530-21-8

upper lower0.000 0. o001.368 -L. ?441.948 -L,7L62.396 -2.0583.103 -2.5774.372 -3.4726.O47 - 4 .6177,r92 -5.408LO47 -6. O019.26L -6,77i

10.026 -7 . L86t 0.469 -7 ,35510.665 -7 .33910.665 -7.r9L10.498 -6,93810.192 -6.6089.750 -6 .2229.160 -5.8168.443 -5.3697 .602 -4.8546.637 -4,2595.57r -3.5894 -457 -2.A7r3.343 -2.1532.?2e -1.4361.114 -0.7180.000 0.000

3 0A218upper lower0. o00 0,0001.368 -r .2441.948 -!.7L62.396 -2.0s83.103 -2 .5774.372 -3.4726.O47 -4 - 6177.L92 -5.408a.o47 -6. 0019.26L -6.773

10.026 -7.La610 .469 -7. 35510.665 -7.33910.660 -7 .LA610.485 -6.92510.163 -6 .57 99.706 -6.1789.101 -5.7578.382 -5.3087.573 -4 . A256.685 -4 .3075.731 -3.7494.72a -3.r423,674 -2.4442.568 -I .77 61.408 -1. OL20.190 -0.190

Fta f,-3

Feb 96sta0.00o.250.500.75L .252.505. OO

7.5010. o015. O020. o025.0030.0035.0040.0045. O050,0055.0060.0065.0070.0075. O080.0085. O090.0095. O0

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Feb 96Sta0.00o .250.50o.75

2.505. OO

7 .5010 . o015.0020.0025.0030.o035.O040 . o045.O050. oo55. OO

50.0065.0070.0075. OO

80.0085. OO

90.0095.00

100.00

30-015Ord

0.0001.090| .5271.8562 .3673 -26a4 .443s.2505.8536,6817.L727.42?7 -5027 .4407 .2657.0006.5556 .240

5.1904 - 5403.8173.0532 .290r-527o.763o. ooo

0 015ord

o.0001. O90L .5271.8562 .3673.2684.4435.2505.8536.5817.1727.4277 .502?.4367 .2546.9766.6186.1915.7045.1654.5803.9503.2792 .5661.8101.0080. t 58

CamberGA-30. o000.0630.1200.170o.2750.5000.8521.1181.3351.6831.9582.L732.3402-4572 .5242-5432 .4992.3642.L74L .9471.6851.404L.L230.8430.5620.2810. oo0

canberGA-3o.0000. 0630.1200.170o.2750.500o.8521. t l-81.3351.5831.9582.r73?.3402.4572 .5242-5432.4992.3682.r74L .947t-.6851.4041.1230.8430.562o.281o.000

30-312upper lower0.000 0.0000.935 -0.809I.342 -1.1021.655 -1.3l-52 -169 -1. .6193.114 -2.!L44 .406 -2,7025.318 -3.0826.Or7 -3,3477 .O2A -3 .6627 .696 -3.7AO8.115 -3.769a.J42 -3.6628,409 -3.4958.336 -3.2888.143 -3.O577.823 -2 .4257.360 -2.6246 .782 -2.4266 . O99 -2.2055,3r7 -r ,9474.458 -1.6503.565 -1.3192.675 -0.989r.7a4 -0.6600.891 -O.3290.000 0.000

3 0A31,2upper lor.ver0. o00 0.0000.935 -0.809r.342 -1.1021.655 -1 .3152,t69 -1.6193.114 -2.rL44.406 -2.7025.318 -3. Oa26.017 -3.3477.O28 -3.6627,696 -3.7808,115 -3.7694.142 -3 .6628.406 -3 .4928,J27 -3.279a.L24 -3.0387.793 -2.7957.32:I -2.5856 .7 4r -2. 3856. O80 -2 . 1865.349 -L.9'794.564 -L.7563 .7 46 -1.5002.A96 -1.2102.010 -o.8861.087 -O.5250.126 -0.126

30-315upper lotrero.000 0. oo01.153 -L . O27r.647 -r .4072.026 -1.6862,642 -2.O923.768 -2 -7 6e5.295 -3.5916.368 -4.r327.1.88 -4. s188.364 -4.9949,130 -5 .2L49.600 -5.2549.842 -5.!629 .897 -4.9839.789 -4.74L9 ,543 -4 .4579.154 -4.1568.608 -3.8727 .933 -3.5777.L37 -3.2436.225 -2.8555,22r -2.4L34,L76 -1.9303.133 -r-4472.089 -O.965t.044 -0.4820,000 0.000

30A315upper lower0.000 0.0001.153 -L.O27L,647 -I.4072.026 -1.6862.642 -2 -O923.764 -? -7685.295 -3.5916.364 -4.L327.l-88 -4.51-88.364 -4.9989.130 -5 -2L49.600 -5.?549.842 -5.1629.893 -4.9799.778 -4.7309.519 -4.4339.LL7 -4.1198.559 -3.8237 .AA2 -3.5257.113 -3.2t96.265 -2.8955. 354 -2.5464 .402 -2. 1563.409 -L.7 232.372 -I .248L.249 -O .7 270.158 -O.158

5630-318

upper Iower0. oo0 0.000L,37L -L.2451.952 -L -7122.397 -2. O573.115 -2.5654.422 -3.4226.184 -4.4807 .4I8 -5. 18 28.359 -5.6899.700 -6.334

L0.564 -6 . 64811.085 -5,73911 .342 -6 .66211. 385 -6,47Lrr.242 -6.19410.943 -5 . 85710.485 -5 .4879.856 -5.l-209.084 -4 -7 288.175 - 4 .2477 .L31 -3.?635.984 -3.1764,747 -2.54I3.591 -1.9052.394 -1.270L.r97 -0.6350.000 0.000

3 0A318upper lower0 . o00 0.0001. 371 -L ,245r.952 -L.7L22-397 -2 . O573.115 -2 ,5654.422 -3.4226.144 -4.4807 .4]-4 -5. 1828.359 -5.6899.700 -6.334

10.564 -6.64811.085 -6.739LL.342 -6 .66211.380 -6.466IL.229 -6,18110.914 -5.82810.441 -5 -443

9 -797 -5. 06 t-9.O23 -4.6678.146 -4 -2527 .]-8I -3.8116 -L44 -3.336s.058 -2.8123.922 -2.2362,734 -1 .6101.491 -O.9290. 190 -0.190FrE trr -4

Feb 94Sta0.000.250,50o.?5

2 .50s.007 -50

10. o015.0020. o025.0030. 0035.O040.0045.OO50. o055. OO60. oo65. O070.o075. O080.0085. OO

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Feb 94stao. o0o .250.50o.75L .252.505. O07.50

10. o015.0020.0025.0030.o035.0040.o045. O050,0055. OO

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80.0085.0090. o095.O0

100. oo

30-o15ord

o. o001.090L .5?71.8562 .3673.2684.4435.2505.8536.6817.172

7 .5027.4407 .2657.0006.6556 -2405.7555.1904.5403.8173.0532 .290L .527o.763o.000

0 015ord

o,0001.090r .5271.8562.3673 . 2684-44J5.2505.8536.6817.1727.4277 .5027.4J67 .2546 -9766.6186.1915.7045.1664.5803.9503.2792 .5561.8101.008o.158

carnberGA- 40.000o.082o.r52o.2l-30.3230.570o.9701.307L.5972.0862.4732.7763 .0103.1753 -2693 .2963.2343.0652.8r-82 .5L92.1801.8171.454r.090o.7270.3630. o00

canberGA-40. oo00.0820.152o.2L30.3230.5700.970I .307L .5972.0462-4732.7763.01-03 -r753 .2693 .2963.2343.0652.8182 .5L92.1801.81-71.4541.O90o.7270.3630.000

30-412upper lower0.000 0. o00o.954 -O .790L.374 -1.0701.698 -r.2722.2I7 -1 .57r3 , r- 84 -2.O444.524 -2 .5445-507 -2.A936 -279 -3 .0857 .43L -3.2598.211 -3 . 2658.718 -3.l_659.Or2 -2 -9929 .L27 -2.7779.081 -2 -5438.896 -2.304I . 558 -2.0908. O57 -L.9277,422 -I.7866.67L -1.6335. 8t- 2 -L.4524 -A7 L -L .2373.896 -0.9882.922 -O.7 421.949 -O.495o .971 -O .2470.000 0.000

30A412upper lower0.000 0.000o.954 -0.790L-374 -1. O701,698 -r .27 22.2t7 -1.5713.1.84 -2.0444.524 -2.5445.507 -2 .8916.279 -3. O857 .43L -3 .2598.211 -3 .2658.718 -3.1669.0t 2 -2 ,9929 .LZ4 -2 .77 49.O72 -2.534a -477 -2.2458.528 -2 . 0608.018 -1,8887 .3AL -L .7 456.652 -1.5145.844 -1,4844.977 -1.3434.077 -1.1693.143 -0.9632-I75 -O.72!1. L69 -0.4430 . 126 -O.126

30-415upper lowero.000 0. o00r.172 -1.0081.679 -L .3752.O69 -l-.6432.690 -2.O443 .8 3B -2 .6985.413 -3.4736.557 -3.9437 .450 -4.2568.767 -4.5959.645 -4.699

10.203 -4 . 651l-o. 512 -4 .49210. 615 -4 .26510.534 -3.99610.296 -3.7049. BB9 -3 .42t9.305 -3.175s.573 -2.9377-709 -2.6716.720 -2.3605.534 -2.0004.507 -L. 5993.380 -1,2002.254 -0.800).-L26 -0.400o.000 0.000

3 044 15upper Lowero.000 0.000L.L7? -1. O081.679 -1.3752.069 -1.64 32.690 -2. 0443.838 -2.6985.413 -3.4736.557 -3.9437 .450 -4.2564.767 -4.5959.645 -4.699

10.203 -4.65110.512 -4 .49210.611 -4,261l0,523 -3.985LO .27 2 -3.6809.852 -3.3S49.256 -3 - 1268.522 -2 - 8867.645 -2.6476.760 -2.4005.767 -2.1334.733 -1.8253 .656 -I.4? 62.537 -t- . O831.37I- -O.6450.158 -0.158

573 0-418

upper lower0.000 0 . 0001.390 -t.2261.984 -1.6802.440 -2.0143 . 163 -2.5L74.492 -3 .3526,302 -4.3627 .607 -4,9938.62r -5.427

10.103 -5.931r.1.079 -6.1-3311.688 -6.13612.Ot2 -5.99212.103 -5 -753LL.9A7 -5.44911.696 -5.104rL.220 -4 .? 5210.553 -4 - 4239.724 -4.088B-747 -3.7097 .62a -3.2686.397 -2 -7 635.118 -2.2103.B38 -1.6582,559 -1.105t.279 -0.5530.o00 0.000

30A418upper Iower0, o00 0. o001.390 -I.2261.984 -1.68O2.440 -2 . 0I43 .163 -2.5I74 -492 -3.3526.302 -4.3627 .607 -4.9938. 621 -5.427

10.103 -5.9311I.079 -6.13311.688 -6.136L2 -OL? -5 .99 212.098 -5.748IL.974 -5.436Lr.667 -5. 07s11.176 -4 .70810.494 -4.3649.663 -4,O278.718 -3.6807.676 -3_3166.557 -2.9235.389 -2.4814 . t 69 -1.9892.899 -1.4451.573 -0.847o.190 -o.190

Fl41 [l- S

Feb 94stao.00

0.500 ,75

2 .505,007 .50

10.0015.0020.0025.0030.0035.O040.0045. O050.0055. O060.0065. OO70. 0075.0080.0085.0090.0095.00

100. oo

Feb 94stao.000.250.50o.75

2 .505. O0

10.0015.0020. o025.0030.0035.O040.o045.0050.0055. O060 . o065.0070.o075.OO80. o085.0090.0095.00

100 . o0

30-0lsOrd

0.0001.0907 .5271 . 8562 .3673 .2644.4435.2505.8536,6817 -L727.4277 .5027,4407 .2657.0006,6556 .2405.7555.1904.540

3.0532 .290r .527o.763o.000

0 015ord

o.0001.O90|-527l-.8562 .3673.2684.4435.2505.8536.6817.!72

7 .5027.4367 .2546.9766.6186.1915.7045.1664.5803.9503 .2792 .5661.8L01.008o. 158

camberGA-6o. ooo0.112o.207o . 291-0.441o.7771.323r.7az?.L742.8443 -3723.7464.1044 .3294.4584.4944,4104.L793,8433,4352.9732.474r,.982L.4470.9910.496o. oo0

camberGA-60. oo00.112o .207o -29L0.441o.7771.323L.7422.L782.4443 -3723.7864.1044 .3294.4584.4944.4104.L793.843

2.9732 .4741.982L .4470.991,o .496o.o00

30-6r2upper fow€r0.000 0.000o - 984 -O.760L.429 -1 .015L.776 -1.1942.335 -1.4533.391 -I.8374.877 -2.23t5.982 -2 .4!86,860 -2 . 5048.189 -2.50]-9.110 -2 -3669-72A -2.156

10.106 -1.89810,281 -L -623to.270 -1.35410.094 -1.106

9 -7 34 -O.9149-L7L -O.8138.447 -O.76r7 -587 -O .7 t76. 605 -O.6595.532 -O -5764 .424 -O.4603.31-9 -O. 3452.2r3 -0.2 311.106 -0 . 1140.000 0.000

3 0A612upper lower0.000 0.000o.984 -O.760r.429 -1.015r.776 -1.1942.335 -1.4533. 391 -L.A374.a77 -2.2315.9A2 -2 -4L86.860 -2.5048.1-89 -2.5019.110 -2.3669 -724 -2.L56

10.105 -1.8981o.278 -r.62010.261 -1.34510.075 -1.087

9 .704 -O.8849.132 -O-7748. 406 -O -7207.568 -0.6986.637 -O.6915.638 -O-6824.605 -0.5413. s40 -0.5662.439 -O - 4571.302 -0 . 310o .].26 -0. 12 6

30-61supper lower0.000 0.000I.202 -O.978),.? 34 -1.3202.L47 -1.5652.808 -L ,9264.045 -2.49L5.766 -3 . r207 .O32 -3 .4688.031 -3 .6759.525 -3.437

10.544 -3,80011.213 -3.64111.606 -3.398LL.769 -3.111tr-72f -2 -ao71 1.494 -2.50611.065 -2.24510 - 419 -2.O6L9. 598 -I -9I28.625 -L7557.513 -r.5676.295 -l-.3395.035 -1,0713.777 -0 . 8032.518 -0.5361.259 -O .2670.000 0.000

30A515upper loerer0.000 0.000L.202 -O,9781_.734 -1.3202.L47 -1.5652.808 -L.9254.045 -2.49I5.766 -3.1207 -O32 -3.4688.031 -3.6759.525 -3.837

10.544 -3 .800LI.2L3 -3.64111.606 -3.3981.1 . 765 -3 . LO7rI.712 -2.79611.470 -2.48211.028 -2.2051"o.370 -2.oL29.547 -1.8618.601 -\.73L7.553 -!.6076.424 -!.4725.261 -]-.2974.053 -1.0792.801 -0.8191.504 -0.5120.158 -O.158

5830-518

upper lower0.000 0.000L.420 -1 . 1962.O39 -L.6252.518 -1.9363. 281 -2 ,3994.699 -3 .1456.655 -4 . 0098. 082 -4 .5189.202 -4.A46

10.861 -5.L7311,978 -5 -234L2.694 -5.t2613.106 -4.89813 .257 -4 . s9913,176 -4.260L2.894 -3 - 90612.396 -3 .57 6lL.667 -3.309IO.749 -3.0639.663 -2.7938.421 -2.4'757. O58 -2 -LO25.646 -1.6824-235 -1,-2612.423 -0. 841r -4L2 -O.4200.000 0.000

3 04618upper lower0.000 0.0001.420 -1.1962.039 -t -6252.518 -1.9363 .281 -2 -3994 -699 -3.1456.655 -4 . 0098. O82 -4.5189 -202 -4.845

10.86L -5.17311.978 -5.23412 .698 -5.12613.106 -4.898L3.252 -4.59413.163 -4.24'l12 .865 -J -a771't 'lq1 -1 R11

11.608 -3. ?5010.688 -3 .0029.634 -2 -7648.469 -2 .5237 -2tA -2.2625.9L7 -1.9534.566 -r-.5923.163 -1 .1811.706 -O.7L4o.190 -0.190

Ftq fft -{,

Feb 94Sta0. o0o .250.50o.751.252.505.007 .50

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Feb 94sta0.000.250.50o.75

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90.0095.00

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0.000o.8751.204I-4621.8782.6103.6484 - 4275.0556.0116.693

7.4217.500? -3A67 -O996.6655.l-os5.4534.72I3.9343.1192.31-01.5410.852o-300o.000

63A015ord

0.000o.4751.2031.4481.8442.5793.61-84.3424 .9975 .9426.6197 -O9L7.3847.4967.4357 .21 56.8586 .3875.8205 .I714.4683.7312.991) )qaI -5!2o.7720.032

CamberGA-20. o000.0600.11-50.169o .2630.450o.7L5o.8921.023r .2441.420

1.663r-7371.780t -?921,.7641_.672r-537r.3741.1890.991,o.7930.5950.3960.198o. oo0

caltrberGA-2o.oo00.0600.1160.169o -2630.450o -7L50.8921.023r .244L.420

1.663t.7371.780L -792r.764L .672r .537r-3741.1890.991o -793o-595o.396o.1980 - 000

35-212upper l-ower0.000 0.0000,760 -0.640r.o79 -O.4471.339 -1.001r.765 -1.2392.538 -1.6383.633 -2.?O34.434 -2.6505.067 -3.O216.053 -3.5656.774 -3.9347.zAL -4.L6?7 ,600 -4 .27 4? .737 -4.2637 .6A9 -4.L297.47L -3 -8877 .0S6 -3.5686.558 -3 .2L45. 899 -2.4255. 151 -2.4034, 336 -1.9583.486 -1.5042.64r -1.0551.828 -0.6381..078 -o.2460.438 -0. 04 2o.000 0.000

3 5A21.2upper lowero.000 0.000o.760 -o.6401.078 -0.846L -327 -0.9891.738 -L.2r22.5L3 -1.6133.609 -2. r794.398 -2.6t45.021 -2.9755.998 -3.5106.71_5 -3.8757 .230 -4 . 1l- 67 .570 -4.2447.734 -4.2607.72A -4.1687.564 -3.980? .250 -3.7226.742 -3.4386.193 -3.1195.512 -2.7644.763 -2.3A53 .976 -1.9943.186 -1 .6002-397 -r.2071.606 -O.814o.816 -O.4200. 026 -0.025

35-215upper .Iower0.000 0.000o.935 -0.8151.320 -1. O881.631 -7 .2932 - I4)- -1.6153 - 060 -2 .I504.363 -2.9335.319 -3.53s6.078 -4.O327.255 -4 .7 678.113 -5.273a -7L2 -5.5989.084 -5 -7549 -237 -5 .7 639 . 166 -5.6068.891 -5.307I .429 -4.90L7 -7AO -4.4366.990 -3,9166.095 -3 -3475.123 -2 -7 454.110 -2.t243.103 -1.5172 -t36 -O.946L.248 -0.456o.498 -0. t-o20.000 0.000

3542r5upper lower0.000 0.0000.935 -0.8151.319 -1.087I.6L7 -t.2792 -to7 -1.5813.029 -2.L294.333 -2.9035-274 -3.4906.020 -3.9747 .1_86 -4 , 6988.039 -5.1998.648 -5 . 5349.O47 -5.72L9.233 -5.7599.215 -5,6559.OO7 -5.423a -622 -5.0948. O59 -4 .7!57 .357 -4.2836.547 -3.7995. 657 -3 -2794.722 -2 .7 403.?84 -2,1982.847 -L.6571.908 -1.116o-970 -o.574o.032 -0. o32

5935-218

upper lower0,000 0.000t-.110 -o. 990l-.561 -t.329l_.923 -1.5852.5I7 -1.9913.542 -2.6A25.093 -3.6636.204 -4.4207.089 -5. O438 .457 -5.9699.452 -6 -6t2

10.143 -7 -O2910.568 -7.242LO -737 -7 -26310.643 -7.08310.311 -6 -7 27

9 -762 -6.2349. OO2 -5. 5588.081 -5.0077.OJg -4.29r5.910 -3 ,5324.734 -2 .7 523 - 565 -r.9792.444 -t.2541.418 -O .6260.558 -0.1620.000 0.000

3 542L8upper lower0.000 0.0001 - 1r- 0 -0.9901.560 -1.3281.907 -1.5692 - 476 -1- 9503 .545 -2 -6455 -O57 -3.6276.150 -4 -3667 .Otg -4.9734.374 -5.8869.363 -6 -523

10 . 066 -6 .95210.524 -7.198LO.732 -7 .25A10.702 -7 .I4210 .450 -6.8669.994 -6.4669.336 -5.9928.521 -5.4477.582 -4.5346-551 -4.1735-468 -3 . 4864.382 -2.7963.297 -2.IO72.2IO -1, ,418I.I24 -O.728o - 038 -0 - o38trt6 IIf --7

Feb 96Sta0. o0o.25o.50o.?51.25? .505.007 .50

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0. o000.875r .2031,4481..8442.5793.6184.3824 -9975.9426.6197.O9r7 .3447 .4967.4357 .2L56.8586 .3475.8205.1734.4683.73L2.9912 .252L.512o.7720,032

camberGA-3o.000o.063o.1200.170o .2750.5000,852l- . 1181,3351.6831.9582-L732.3402.4572 .5242 .543t aao2. 3682-r78L.9471.6851.404r-r230.8430.5620,281o.000

camberGA- 3o.000o.0630.120o.1704,2750.500o .4521.1181.3351-.6831,9582.r732.3402 .4572 .5242 ,5432 .4992.f642-17At.9471.6851.4041.1230.843o .5620.2810.000

35- 3 t2upper logrer0. o00 0.000o.763 -O .6371.083 -0.8431.340 -1.000L.777 -r.2272.588 -1.5883.770 -2.0664.660 -2.4245-379 -2.7096.492 -3.1267 .3L2 -3.3967 .A97 -3.551a.277 -3 .5978.457 -3 . 5438.433 -3.385a.222 -3.136?.a3L -2.A337 .254 -2.5186.540 -2.r445.724 -!..8304.832 -L.4623.899 -1 ,091?.97L -O.7252.076 -0.390)-.244 -0.1200,521 0.0410.000 0 . 000

3 5A312upper lowero.000 0.000o -763 -O ,6371.082 -O .842L-328 -0.988I.750 -1,.2002.563 -l-.563f -746 -2,O424.624 -2. 3485.333 -2.6636.437 -3.0717 .253 -3.3377.846 -3.500a -247 -3.5678.454 -3 . 5408.472 -3 .4248 . 315 -3 .2297.985 -2.9477.478 -2 ,7 426.834 -2 - 4786. O85 -2.r9r5.259 -1.8894.389 -1 . 5813 .515 -L -2702.545 -0.959L.772 -0.5480.899 -O -337o.026 -0.026

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a.476 -3 -7 407 .63L -3.2756.668 -2 .77 45.519 -2.2494.523 -1 .7153,433 -t.1872.3A4 -O,6981.41.4 -0. 2900.581 -O . 0190.000 0. 000

3 5A315upper lower0.000 0. 0000.938 -O.812L.J23 -1,0831.618 -r.27a2.LL9 -1.5693 .079 -2.0794.470 -2,7665.500 -3.2646.332 -3 .6627 .625 -4.2594.577 -4.6619.264 -4.9189.724 -5,0449.953 -5.0399.959 -4 . 9119.?54 -4.6729.357 -4.3598.755 -4.0197.99A -3 .6427 .I20 -3.2266. t 53 -2 -743E 1 'r A -1 1.t.7

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6035-318

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10.759 -6 , 413Lr.?45 -6.565rL.457 -6,54311 . 387 -6.33911. O62 -5,976lo .497 -5.4999.698 -4,9624.722 -4.3667 .612 -3.7I45.406 -3.0365.r47 -2.3393 .895 -1,6492.692 -1. O061 .584 -0.4600.641 -0, 0790.000 0.000

35A318upper lower0. o00 0.000r,l-13 -0.9871.554 -r.3241.908 -1.5682.448 -1- 9383.595 -2.5955.194 -3.4906.376 -4.1407 .33r -4.66L8.813 -5.4479 ,901 -5.985

10.682 -6.336t-1.201. -6-52I11.452 -6.53811.446 -6.39811, 201 -6.115IO.729 -5.73Ll-0. o32 -5.296

9 -L62 -4.8068.155 -4.26I7 .O47 -3 .6775.881 -3.0734.7L2 -2.4663.545 -1.8592.376 -I .252L.207 -o.645o.038 -0 . 038Fta fr- g

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6 3A015ord

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camberGA-40.0000.0820.1520.21-30.3230.5700. 9701.307I-5972.0852.473.2,7763.0103,1753 .2693 .2963 ,2343.0652.8182.5192.180L .8I7I.4541.090o.7270.363o - oo0

35- 412upper lowero. ooo 0.000o.782 -0.618l-.l-15 -0.8111.383 -0.956)..a26 -L -I?92.658 -1.5183.889 -1.9484.848 -2.2355.641 -2.44?6.894 -2.7237.827 -2.8428.500 -?.9488.946 -2.9279.L75 -2.8259.r7a -2 .640a.975 -2.3448.556 -2.0987.95L -r -8?27. 181 -L.5446.296 -L.2585.327 -o.9674.3r2 -0.6783.302 -0.3942.323 -O . L421,408 0. O450.603 0 , r230.oo0 0.000

35A412upper lower0. ooo 0.000o.7a2 -0.618r,.114 -O.811.t.372 -0.945r,799 -r -I522.633 -1.4933 .865 -r.9244.8L2 -2 . L995, 595 -2.4006.839 -2.6647.76A -2.8228.449 -2.4968.9L7 -2 ,8949.L7L -2.4229.2L7 .-2 .6799.068 -2.4768.720 -2.2528.174 -2.0457.474 -1.8386.657 -1.6195.755 -1 .3944.802 -1 . 1683.847 -0.9392.892 -0.7111.936 -0,483o.981 -O .2540.026 -0.026

35-415upper lower0.000 0.000o.957 -O.793l-. 356 -l-,0521.575 -r.2492.20L -1.5553 .180 -2.O404.618 -2.6785.734 -3.1206.652 -3 .458a.o97 -3.9259.166 -4.2209.931 -4.379

10,431 -4.411r.0.675 -4.32510.65s -4.II7.1 0. 395 -3.8039.899 -3.4319.L73 -3 - O43a.27L -2,6357.240 -2.2026.114 -L.7544.936 -1.3023 -764 -0.8562 -63r -0 .451t.579 -0.1250.663 0.063o-oo0 0,000

35A4L5upper lower0. ooo 0.0000.957 -O.7931.355 -1.0511.661 -r -2352.167 -L.sZL3.149 -2 -OO94 - 588 -2 -6445.689 -3 .0756.594 -3 ,4008.028 -3.8569 -O92 -4.1469.467 -4.315

L0.394 -4.37410,671 -4.32L10.704 -4.L6610.511 -3.91910.092 -3 .6249.452 -3.3228.638 -3.0027 -692 -2.6546.644 -2 -2485.548 -1.9144.445 -r -5373 -342 -I -L622-239 -0.7851.135 -0.4090.032 -0.032

6135-418

upper ]ov,rer0. oo0 0.000]- r32 -0.968t.597 -L .2931.968 -1.5412.577 -1.9303.702 -2 ,5625. 348 -3 .4076.61"9 -4.0067 -663 -4.4699.299 -5.128

10.504 -5.559L1.362 -5.81011.91 5 -5 . 89612 -1_75 -5. 825L2.L32 -5.594l,1 . 814 -5 .223tr.232 -4.76410.3 94 -4 .2659.362 -3.7258.184 -3.1466.901 -2.54L5.560 -r.9264.226 -1 .3182.940 -O.759r,7 49 -O.296o.723 0.0030.000 0.000

3 5A418upper loster0.000 0.000L -I32 -0. 9681.595 -L.2921.951 -L.5242-536 -1.8a93 .665 -2.525

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10.416 -5.47011.286 -5.73311.870 -5.851L2.t70 -5.42L12.191 -5.65311.954 -5. 362rL.464 -4,996LO -729 -4.6009.802 -4.1668.727 -3.6897 .542 -3.1816.294 -2 .6605.043 -2.1353.?93 -1 .6122 -54r -L .0881.290 -0.563o.038 -0.038Fh ltr-c

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camberGA-60. o000.112o .207o .29Io.44ro.7771.323t -7422.L742 .844

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35-6t2upper Iower0.000 0.0000.812 -O.5881 . 170 -o.756I-.461 -0.879t-.943 -1.0612.865 -1.3114 -24L -1 .5955 -324 -L.7606.222 -1.8667.653 -1,.9658.726 -L.9429.51O -1.938

10.041 -1.83310.329 -L-67L10.367 -1.451LO.r73 -1.1859.742 -o.9229. 065 -O.70?L205 -0.5197.?r2 -O .3426.r20 -0.1744.973 -O.0173.830 0.1342.720 A -254L.673 0.309o -736 0.256o. 000 0.000

3 5461 2upper lowero - oo0 0 .0000.812 -0.588t-.169 -O -755I.449 -O.8671.916 -L.0342.A40 -L - 2464.2L7 -L.57t5.288 -r.7246.176 -1. S207 .59A -1.9108.667 -L.9239.459 -1.887

10.011 -1.80310. 326 -1 . 66810 . 406 -1.49010.266 -L.278

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3 5 -615upper lower0.000 0.000o.987 -O -7631.411 -O -9971.7 53 -1.1712.319 -1 .4373.3A7 -1,.8334.97L -2.3256.209 -2.6457.233 -2.8778.855 -3.L67

10 . 055 -1.32110.941 -3.369r,1.525 -3.3L711.829 -3.17111.844 -2.92811.593 -2.60511.075 -2.255to.2a7 -\.9299.296 -1.6108.156 -1.2866.907 -O.9615.597 -0.6414.292 -0. 3283 .028 -0.0541.843 0.139o-796 0. 196o. 000 0.000

354615upper l-oeter0.000 0.0000.987 -O.7631 .4LO -O.996r.739 -r.L572.285 -1.4033.356 -1 . 8024.94L -2 .2956.J.64 -2.6007 -r75 -2.81,9a.7a6 -3.0989 .991 -3.247

LO.B77 -3.30511.488 -3 . 28011.825 -3.1671 1 001 -1 01t

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6235-618

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10.057 -4.36911 .404 -4 . 660L2.372 -4.80013.009 -4.80113.329 -4.67r13.321 -4.40513.O1-3 -4-O2512.408 -3 . 58811.509 -3.15L10.387 -2 -7079.100 -2 .2307 .694 -l .7 486.22L -r .2654.754 -0.7903.336 -0.3622.OL3 -0.031o.856 0.135o.000 0.000

35A618upper lower0. o00 0.0001.162 -0.9381.651 -L.2372.O29 -r.4472.654 -I .7723 -A72 -2 . 3185.665 -3.019? .o40 -3 -476a.174 -3.8189.9?4 - 4 .2A6

1t-.315 -4.571_12.295 -4.723t2.965 -4.75713 -324 -4.66613.380 -4.464L3.I52 -4.16412.640 -3,82011.843 -3.485LO.A27 -3 .1419.643 -2.7738.335 -2.3896.955 -1.9995.571 -I - 6074 .189 -1.2152.805 -O-823t.422 -0.4300. 038 -o.038Frt:l GL- to

Feb 94sta0.000,250,50o,75r ,252. s05. o07.50

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carnberGA-20.0000.0600.1160.1690.2630.4500.715o .4921.O23I .244L .420L .5571.663L .7171.780L.792t.764r.672r.537!.3741.1890.991o.7930.595o.3960.198o - oo0

37 -2I2upper Iorter0.000 0.000o.752 -O.6321.082 -0.8s01.334 -0.9961.737 -L.2lL2.472 -I.5723 . 518 -2. O884.?a4 -2.5004.A97 -2.45]-5.A72 -3.3846.604 -3.7647 -r45 -4,0317.518 -4 . r927 .723 -4.2497 .758 -4.1987.57L -3.9a77 .2L2 -3.6846.685 -3.341,6.033 -2.9595.290 -2.5424-479 -2.1013.62A -1.6462.77L -1 ,185r.937 -O .7 471,156 -0.364o.475 -O.O790. o00 0.000

37 A2L2upper lower0.000 0.000o.744 -O -6241.070 -0.8381.318 -0 - 9801 . 71s -1 .1892.455 -1.5563.497 -2.0674-254 -2.4704.862 -2 -8L65.830 -3.3426.558 -3.7187.098 -3 . 9847 .47 9 -4.1537 .707 -4.2337 .770 -4.21_O7 .642 -4,0587 .346 -3.81,86.886 -3.5426.302 -3.2285.523 -2.4754.859 -2.49L4.069 -2.O473.260 -r .67 42.452 -r.262I.642 -0.8500.834 -0.438o. o26 -o.026

37 -215upper lower0. o00 0. o00o.925 -0.805L.324 -L . O92L.625 -l .2872.105 -L.5792.97A -2.O744.2r9 -2.7495.L32 -3.3485.865 -3.81-97 .O29 -4.54L7 .900 -5.0608.542 -5.4288.982 -s.6s69.219 -5.7459 -253 -5,6939 . 016 -5.4328.574 -5.0467 .934 -4.5947 .L57 -4.0836.269 -3.52I5.302 -2.9244.247 -2.3053.265 -L .67 92.272 -1..0821.346 -0,554o.544 -0.1480.000 0.000

37 A2J,5upper lower0 .000 0.0000,915 -0.7951.309 -L -O77t.605 -L.2672-O78 -1 . 5522-958 -2.0584-r92 -2 -7625. O94 -3 .31-O5.422 -3 .77 66.976 -4.4887 -443 -5. O038.483 -5 . 3698.933 -5.6079. 200 -5.7269.267 -5.7079.105 -5.521a.742 -5 .2L48.189 -4.8457.493 -4,4L96.685 -3.9375-7a9 -3.4114.838 -2.8563.877 -2.29I2.9L6 -r.726t -954 -1,.t 620.993 -O.5970.032 -o.032

63Jt-zL6

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10.446 -7 .I2010.715 -7 -241LO.74A -7.1-8810.461- -6.4779.936 -6.4089.19r -5 .8478.281 -5 - 2077 .248 -4.5006.r25 -3 .7 474.946 -2.9643.759 -2.r732.607 -r,4L71.536 -O.7 440.613 -O.2r70.000 0.000

37 A2rAupper lower0.000 0.0001.086 -0.9651.548 -1 - 316r -492 -r.5542.44r -1.9153.460 -2.5504.887 -3 .4575.934 -4 - 1506.742 -4.7364.r22 -5.6349.L?A -6.2889.868 -6.754

t 0.387 -7 -O6L10.693 -7 .2r910.764 -7 .20410 . 568 -6,984r0.138 -6.6109.492 -6.1488.684 -5.61.07.747 -4.9996.709 -4.3315,607 -3 .6254.494 -2. q083.380 -2-1902.266 -L.47 4r.L52 -O.7560. 038 -o.038Ftq ][-rr

Feb 96Sta0.00o .250.50o.751.252.505. O07.50

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camberGA- 30,0000.0630,1200.170o.275o.5000.8521.118t-.3351.6831.9582.L732.3402.45?2 .5242 .5432.4992.3682.L78r .94?1.685r-4041.1230.843o.5620.281o. o00

CarnberGA- 30.000o.063o.1200.1 70o.?750.500o.8521.118r.3351.6831.9582.L732 -3402-4572 .5242 .5432-4992.3682-778L -9471.6851",4041.123o.843o -5620.281o - ooo

37 -3L2upper lower0.000 0.000o.755 -O.629l-,086 -o.8461.335 -0.995L,749 -1.1992.522 -r -5223 .655 -1.9514.51-0 -2.2745.209 -2.5396.311 -2.9457.L42 -3 -2267 -7 6L -3.4158.195 -3.5158.443 -3 . 5298.502 -3.454a.322 -3.2367 .9 47 -2.9497.38L -2 .6456.674 -2.3185.863 -1.9594.975 -1.6054 .041 -L.2333. t- 01 -o.8552.ras -0.499I.322 -0.1980 . 558 0.0040.000 0.000

37 A3L2upper lower0 .000 0.000o.747 -0.621L.07 4 -0.8341.319 -O -979r.727 -r.L772.506 -1 . 5063.634 -1.9304 - 480 -2 ,2445.l-74 -2 . 5046.269 -2 .9037 .096 -3.1807 .714 -3.3688. 156 -3 .476a -427 -3.5138.514 -3.4658.393 -3.3078.081 -3.O837.542 -2.8466.943 -2.5876.196 -2.3025. 365 -1 .9954 -442 -L .67 43.590 -1.3442-700 -1 .0141.808 -0.684o.9r7 -0. 355o.026 -0. o26

37-315upper lower0.000 0,0000.928 -0.802L.324 -1. O881.625 -l-.2862.r17 -L5673.028 -2 , O2a4.356 -2.6525.358 -3 .I226.L77 -3 . 50?7 .46A -4,lO28.438 -4.5229.158 -4.AL29.659 -4.9799.939 -5.0259.997 -4.9499.767 -4 . 6819,309 -4.3118.634 -3.8987 .79A -3 .4426 -442 -2.9445 -79A -2.42A4.700 -1.8923.595 -1.3492.520 -O.8341.512 -0.388o.6?7 -O.0550.000 0.000

37A315upper Iower0.000 0.000o.918 -o.7921.313 -1-0731.606 -r.2662.090 -1 . 5403. O08 -2. O084.329 -2.6255.320 -3. O846.134 -3.4647 -4L5 -4.0498.381 -4.4659.099 -4.7539.510 -4.9309.920 -5.006

10.011 -4.9639.856 -4.7709.477 -4.4798.885 -4.L498.1.34 -3.7787 -25a -3.3646,285 -2.9155.251 -2.4434.207 -1.9613.164 -!.4742 .],20 -0 . 9961.076 -0.5140.032 -0. o32

6437-318

upper I o$ter0 . o00 0.0001.101 -A.9751.570 -1.330L9L7 -L .5772.4A5 -l-.9353.534 -2 .5345.057 -3.3536.206 -3.9707 .r45 -4.4758.625 -5 -2599,734 -5.818

10.555 -6.20911.123 -6.4431l-.435 -6.521II . 492 -6 .444r1_.212 -6 . L2610,671 -5 .67 39.887 -5.151a,922 -4.5667 .A2L -3.9276.62L -3.2515.359 -2.551-4. O89 -1.8432.855 -1.169L.702 -O.5780.596 -0.134o. o00 0 . o00

3 7A3 18upper lower0.000 0.0001.089 -O.9631..552 -1.3121.893 -1.5532.453 -1.9033.510 -2.510s.024 -3 .3206. L60 -3 .9247 .O94 -4.4248.561 -5. 1959.666 -5.750

10.484 -6.138l-1.054 -6. 38411.413 -6.4991.1.508 -6,46011.319 -6 .23310.873 -5.87510.1,88 -5.4529.325 -4.9698.320 -4 .4267 .205 -3.8356,020 -3.2124.824 -2.57A3.628 -I .9422.432 -1 . 308r.235 -O -6730. 038 -o. 03IFta fl- t?

Feb 94sta0. o00.250.50o.751.252.505.007 -50

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I .6770,950o.346o.000

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o.000o.8551. L931.4361.8152.5083-4774 .2024.7995 -7326-4236 -9267 .2707.4537.4877 ,3r36.9746.5175.9565.3114.5003.A473 .0842 -32r1.5580.795o.032

canberGA-40.0000.0820.152

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CamberGA-40.0000.0820.1520.213

0.570o.9701.3071 .5972.0862.4732.7763.010J . 1,7 53 .2693 .2963.2J43.0652.8182 .5L92.1801.817I .4541.090o.7270.3630,000

37 - 412upper lowero.000 0.000o.?74 -O.6101.118 -0.8151.378 -0.951-!.797 -1. L502.592 -1.4533.773 -1.8334.699 -2.0855.471 -2 .27 66.7L4 -2.542-7 .657 -2 .7 rr8.354 -2,8r2s.865 -?.A469.160 -2.8119.248 -2.7099.O75 -2.4448.6A2 -2 .2r4a.o77 -l-.9487.314 -L6745. 435 -L.3975,47r -1.1104 .454 -0.8203 .431 -O -5242.432 -O.251,L.4A7 -0.033o.640 0,087o. 000 0.000

37 A4L2upper lower0.000 0.o00o.766 -O.6021,106 -0.803!.362 -0.935t.775 -1.1292 .57 6 -r - 43'73 .752 - l- . 8114.668 -2.055s.436 -2.2426.67r -2 . 5007.6Lr -2 -6668.317 -2 -7 648.826 -2.8069. 145 -2 .7969.259 -2 .7 209.146 -2 .5558.816 -2 .344a.27a -2 . L497.583 -!,9476.76A -1.7305.860 -1 .5004. 895 -L.2643.92L -1.0132 -947 -A.7661.973 -O -5200.999 -O .27 3o . 026 -o.025

3? - 4r5upper Iower0 .000 0.000o .947 -0.783L. 360 -1. O561.669 -L .2432.165 -1.5193.098 -1.9584.47 4 -2 .5345.547 -2 .9336.439 -3,245? -a?1 -3 .6998.953 -4.0079.76r -4.209

10.329 -4 , 30910.557 -4.307to.742 -4.20410.520 -3 -92410. o44 -3 .57 69.331 -3.2018. 438 -2.4O27.4!4 -2 .3? 66,293 -1.9335.1L3 -L.4793.926 -1.01-82.767 -0.587L.677 -O .223o.709 0. o170.000 0.000

3 74415upper Iower0.000 0. 000o,937 -O.7731.345 -1.041r.649 -L.2232.138 -L .4923 .078 -t-.9384.447 -2.5075. 509 -2.8955.396 -3.2027.818 -3.6468.896 -3.9509.702 -4.150

10.280 -4 .2601o.638 -4.28810.756 - 4 .2IA10.609 -4 .01710.212 -3 ,7 449.582 -3 .4528.774 -3 .1387 .830 -2.7926,780 -2.4205.664 -2.0304.538 -1.6303.411 -1.2312.245 -0.8311.158 -O - 4320.032 -0.032

6537 - 4L8

upper lower0. oo0 0.000l-.120 -0.9561.601 -r .2941.961 -1".5342.534 -1.8873.603 -2 - 4645 -175 -3.2356 , 395 -3 .7817 .40A -4 .2139.028 -4.856

10.249 -5 - 30311 . 1s8 -5.606LI .792 -5.773L2.L53 -5.80412.237 -5.69811.964 -5 .37 3

11.406 -4 . 93810. 584 -4 .4559.562 -3.9268.393 -3.3557.IL6 -2.7555.772 -2.1384.420 -1 . 5133.103 -O -922L.867 -O.413o -779 -O. O52o.000 0.000

37A418upper lower0.000 0.0001.108 -0.9441.583 -t-.2801.937 -1.5102.501 -1.8553 .579 -2.4405.143 -3 .2026.349 -3.7367 .356 -4.]-628.964 -4.793

10.1 80 -5.23511.088 *s.s35rI.734 -5.7!412,130 -5.781L?.254 -5.715L2.O7L -5.48011,608 -5.14010.885 -4 .7 569.965 -4 -3298.892 -3.8547 -700 -3.3406.434 -?.7995.155 -2 -24'l3.476 -1 .6952.596 -1.1431.317 -0,5910,038 -o. o38

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Feb 94sta0. 00o .250.50o-75L .252 .505. O07.50

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64AO15ord

0.0000.8551.193L.4361.8152.5083.4774 .2024.799

6.4236.9267.2707 .4637.4877.3136 -9746 .5L75.9565,3114.6003 .4473,0842 .32rl-.558o.7950.032

c arnbe rGA- 60.0000.112o .2070.2910.441o.777t ,323r.742

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CanberGA-60.0000.112o .2070 - 2910.44r-o.7771.323L.7422-17A2 .444

3.7864.1044 .3294.4584.4944.4104 -r793.8433.4352.973

t -942r .4870.991o.496o.o00

31-612upper lower0.000 0.0000.804 -0.5801.173 -O.7591.456 -O .47 41.915 -1.0332.799 -r .2454.L26 -1.4805.L74 -1.6106.O52 -1,6967.472 -L.7848.556 -1.81"29 .37 4 -1.8029.959 -r -75r

10.315 -r -65710.436 -1.520LO.273 -1.2859.858 -1.0389.L92 -0.8348.339 -0.6537.35! -0.4816.26f -o.31-75.115 -0.1593,960 0 - O042.A29 0.145r.75I O.23Lo.773 0.2L90.000 0.000

37 A6t2upper lower0.000 0.000o.796 -O.5721.161 -O.7 4?1-440 -0.8581.893 -1.011

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4 .105 -r,4595.144 -1.5806.017 -1..6617.430 -! .7 428.51_0 -L ,7 669 .327 -r.7559.920 -r.7L2

10.299 -1.64110.448 -1.53210.344 -1 .3569.992 -l -17 29-393 -1.O3s8. 608 -O -9227 .6A4 -0.8146.6s3 -O -7 075.556 -0.6004.449 -0.4853.344 -0.3702.237 -O .2551.132 -0 . r40o. o25 -O .026

37-6L5upper lolter0.000 0.000o.977 -0.75J1.415 -1.001I .7 47 -1 .1652.2A3 -1.4013.305 -L-75r4.827 -2 . 1816 -O22 -2 .4547.O20 -2.664a.629 -2.94L9 .852 -3.108

LO.77l -3.1991_L . 423 -3 .2L5l"i-.811 -3.153t-1.931 -3.015t-1.7l_8 -2.730LL.220 -2 .40010.445 -2 . O87

9 -463 -L.7778,330 -1 . 4607. 086 -1 . 1405.774 -O.8184.454 -O.4903 .164 -O.1901 ,941 0.041o.a42 0,1500.000 0.000

37A615upper lower0.000 0. oo0o.967 -O.7 431.400 -0.986L.727 -1.1452-256 -r .37 43.285 -L.73r4.800 -2.L545 . 984 -2 .4206.977 -2 .62La.576 -2.8889.795 -3.051

LO.7L2 -3. L40rL.374 -3.166rr.792 -3.13411.945 -1 .O2911..807 -2.4L911 . 388 -2.56810.696 -2.3389.799 -2.1134.746 -r.8767 .573 -L.6276.325 -1,3695.066 -1 . 1023.808 -O.8342.549 -O.5671,291 -O.299o. 032 -o. o32

6637-618

upper lower0.000 0.0001.150 -0.926r.657 -L.2432. O38 -1.4562.65L -I .7693.811 -2-2575.528 -2.4826.870 -3.3067.988 -3.6329 .7A6 -4,098

11.148 -4.40412.168 -4 . 596t2.aa? -4 .67 913.307 -4 -649L3 -426 -4.51013.163 -4.L7512-542 -3.7621l-.698 -3.34010,587 -2.90r9.309 -2 - 4397.909 -1.9636.433 -L.4774.944 -0.9843.499 -0.5252.131 -0.1490.911 0.0810.000 0.000

3 7A6l-8upper lower0,000 0. 0001.138 -0.91 41.639 -L -2252 . O'1,4 -t - 4322.619 -L -? 373.747 -2.2335. 495 -2 -8496.424 -3 .2607.937 -3.5819.722 -4.O34

11.080 -4,33612.o97 -4.525L2.824 -4 .62013.285 -4.62713.442 -4.52611 -270 -4.242L2.7A4 -3.96411.999 -3.64110.990 -3 . 3049.808 -2 - 9388.493 -2.5477.O94 -2.1385.683 -L.7L94,272 -1 . 2982.86L -0.8791.450 -O.4580,038 -0.038FtLl f:f- - lll-

Feb 94Sta0-000.250 .50o.75

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camberGA-20.0000. o60o.116o.169o.2630.4500.7150.8921.023r .244L-420L ,5571.663I .737L.7AOL.792I.764I-672L .537L.3741.1890.9910.7930.5950.3960. 1980. o00

canberGA-20.0000.0500.1160.169o .2630.4500.715o .8921. O23L .244L,4201.5571.663r.7371.780L.792r.764L .6721.517L.J741.1890.991o.7930.5950.396o.1980.000

40-2I2upper lower0.000 0.000o.724 -0. 604l-.015 -0.783I.254 -0.916L .625 -r,0992.309 -1.4093.311 -1.8814.059 -2.2754.667 -2.62L5.647 -3.1596.398 -3.5586.968 -3.8547 .3e5 -4.0597.654 -4.1S07.77A -4.2187.734 -4.1,507 .498 -3.9707 -O48 -3.7046.431 -3.3575.696 -2.9484.869 -2.49L3.986 -2.OO43.O79 -1,4932.L?7 -O.9871.311 -0.5190 . 540 -0,1440, o00 0.000

40}.2r2upper lower0 ,000 0.000o.724 -0.6041.015 -0.783t.254 -0.916L.625 -1.0992.309 -1 . 4091.31L -1-.8814. O59 -2.27 54.667 -2,62)-5.647 -3.1596.398 -3.5586.968 -3 . 8547 . 385 -4. O597 .654 -4.1807 .77A -4.2r47 -734 -4,1507 .49A -3.9707.O4A -3.7046.431 -3,3575.596 -2.9444 .869 -2.49L3.985 -2.0043.101 -1.5152.247 -1 .057I.428 -O.6360 .678 -O.2420.000 0.000

40-2L5upper Iower0.000 0.0000.890 -o.770L.240 -1.0081.525 -T.LA7r..965 -1.4392.774 -L.87 43.960 -2.5304.851 -3.0675.578 -3.5326.?48 -4 -2607.643 -4.8038.321 -5.207I .81s -5.4899.133 -5 . 6599.27a -5.7I89.2r9 -5.6358 -932 -5.4048.392 -5.0487,655 -4. s816.777 -4.O295.789 -3.4114.735 -2.7 533.651 -2.06s2.572 -L.342l- . 540 -o.7 4Ao.626 -0,2300,000 0.o00

4042l-5upper lowero.000 0,0000 - 890 -o .770r.240 -1,0081.525 -1 .1871..965 -1 .4392 .77 4 -t.47 43 . 960 -Z,5304.851 -3.0675 -57a -3.5326.?44 -4.2607 .643 -4.803a - 321 -5.2078.815 -5,4899.133 -5.6599.27A -5.7189 .2L9 -5.6358.932 -5.404a.392 -5.0487 .655 -4.5816.777 -4.O295.789 -3.411-4.735 -2.7533.678 -2.O922 .650 -t - 4701.685 -0 .894o.798 -0.4020.000 0.000

6740-2),4

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10.245 -6.9r910.612 -7.l-38to.77a -7 .2).410.704 -7 .L?Ol-0. 366 -6.838

9 .736 -6 .192LA79 -5.8057.859 -5.1106.709 -4.3315.444 -3 .5024.223 -2 .6372.967 -L.777L.769 -O .977o.7L2 -0.3160.000 0.000

4 0A218upper lower0.000 0.0001 .056 -0.9361.465 -1.233L.796 -1, . 4582.305 -!.7793 -219 -2.3394.609 -3 .]-795.643 -3 . 8596.489 -4 .4437 .A49 -5.3618.888 -6. 0489.674 -6.560

ro.245 -6.91910. 6l- 2 -7.138LO.77A -7 -2LB10.704 -7.L2010.366 -6.8389.736 -6 -3928.A79 -5.8057.858 -5.1106.709 -4. 3 315.484 -3 . 5024.255 -2 -6693.07X -1.883r.944 -1 . 1520.918 -O ,522o.000 0 .000Frcr 5x-tr

Feb 95

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camberGA- 3o.000o.o630.1200.170o.275o. 5000.8521.1181.3351.6831.9582.L732 .3402 .4572 .5242 .5432.4992 .3682 - 1,7IL .9471.6851.404r-.1230.843o .5620.2810. oo0

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? -rL OO

2 .168?-17AL .9471.6851.4041.1230.843o .5620.2810. oo0

40- 3 r2upper Lowero.000 0. oo0o.727 -O.6011. 019 -O.779L.255 -0.915L.637 -1. O872.J59 -1,3593 .448 -L.7 444,2A5 -2 . O494.979 -2 .3096.086 -2 .7 206.936 -3.0207 .584 -3.2388,062 -3 ,3828.374 -3,460a.522 -3.4748.485 -3.399a.233 -3 .2357 .744 -3.0087.072 -2 -7 L66.269 -2-3755.365 -1 . 9954.399 -1.5913.409 -1. L632.425 -O.7J9I -477 -0.3530.623 -0.0610.000 0.000

4 0A312upper lower0.000 0.000o.727 -0.601t- . 021 -o .777L.255 -0.915L.637 -1.0872.359 -1. 3593 .448 -t.7 444-285 -2 -O494.979 -2 -3096.086 -2.7206.936 -3 . 0207 .5A4 -3.2388.062 -3.382a.374 -3.460a.522 -3-4748.485 -3.3998.233 -3.2357.744 -3. O087.O72 -2.7166.269 -2 .17 55.365 -1.9954.399 -1.591,3.431 -1.1852.495 -0.8091.594 -0.470o.76L -0,1990.000 0,000

40-315upper lower0.000 0.0000.893 -O.767r,244 -1.0047.526 -1.186L.977 -t.4272.824 -r.4244 -O97 -2.3935.O77 -2. A4L5.890 -3 .2207,IA7 -3.8218.181 -4.265a.937 -4.5919 .492 -4. 8129.853 -4.939

LO.O22 -4.97 49.970 -4.8849 -667 -4.6699.088 -4 -3524.296 -3.9407 .350 -3.4566.285 -2.9155. 148 -2 -3403.981 -L.?352.420 -1.134L.706 -O.582o.709 -o -L470 . 000 0 - o00

4 04315upper lorrer0.000 0.0000.893 -O.757L.246 -1.002L-526 -1.186L.977 -I .4272-424 -L.8244.O97 -2.3935.O77 -2 , A4L5 . 890 -3 .2207 -LA7 -3,8218.t81. -4.2654.937 -4 .5919.492 - 4 .8I29,853 -4,939

LO.O22 -4.9749.970 -4.8849.667 -4,6699.088 -4 .3524.296 -3.9407 -350 -3.4566.285 -2.9155.148 -2,3404.008 -r.7622.908 -L.2221.852 -O.7240.881 -0.3190.000 0 . o00

6840-318

upper lower0.000 0.000t-.059 -0.9331.469 -1.229I.797 -r.4572.3L7 -L ,7 671.2A9 -2 .2894.746 -3,O425.869 -3.5336. 801 -4.1318.288 -4.9229 .426 -5. 510

10.290 -s.944ro.922 -6.242LL.332 -6.418rr.522 -6 .47 41L.455 -6.36911. 101 -6.10310.432 -5.6969.520 -5.1648.431 -4,5377 .205 -3.8355.897 -3. O894.553 -2 .30?3.215 -L .5291.935 -0,81to -?95 -0.2330.000 0.000

4 0A318upper 1o$rero.000 0. ooo1.059 -0.933L.47I -r .227L.797 -L - 4572 -3L7 -L.7673.249 -2.2A94-746 -3.0425,869 -3.6336.801 -4.1318.288 -4 -9229.426 -5.5L0

t 0.290 -5.944LO.922 -6 .24211.332 -6,418LL.522 -6.47 411.455 -6 . 36911.101 -6.103l-0,432 -5.6969.520 -5.1648 . 4 31 -4 .53'l7 -205 -3.8355-897 -3 . 0894.585 -2 -1393.32L -t-.5352.1L0 -0 . 9861.001- -0 . 4390.000 0.000

FlCr E- lb

Feb 94

0. o00.250. s0o-75L .252.505.007.50

L0.0015.O020.0025.0030.0035.O040.0045.OO50 - 0055.0060. o065.O070. oo75. OO80.0085.0090.0095.00

100.00

Feb 94Sta0.00o .250.50o,75)-.23

5. O07.50

10.0015.0020. o025. O030.0035. O040.0045. O050. o055.0060.0065.0070.0075.00s0. o085. OO

90.0095.00

100.00

65-01sord

0.0000.830L. L241.356L.7022.3243 .2453.959

6.7647.L527 .3967 .4987.4277 .1,686.7206,1185.4034.6003.7442.858L.9771.1440,4280. oo0

4 04015ord

0.000o.830L.T241.3561, .7 02

3.9594.5555.5046 .2236.7647 .r527 .3967.49A7.4277 .L6A6.7206.1185.4034.6003.744t oaR

2.0651.2900.600o.o00

canberGA-40.0000.082o.L52o.2130.3230.570o.9701.307L.5972.0862.4732.7763,0103.1753 .2693 - 296

3 - 0652.8182-5r92.1801.817r.4541.090o.7270.3630,000

camberGA-40.0000.0820.l-52o,2130.3230.5700,9?01.307L.5972.086

2.7763. Ol-03.r753-2693.2963 .2343.0652.8182 .5L92.1801.817

1.090o.727o.363o - 000

40- 4]-2upper lower0. o00 0.000o.746 -0.5821 , 051 -o.7 47L,298 -0.8711.685 -1.0382.429 -L.2493.566 -L.6264 .47 4 -1.8605.24L -2.O476.489 -2.3187 .45). -2.5068. 188 -2.6358 .73t -2.7L29.091 -2.7 429.268 -? -7299.237 -2.6468.968 -2.5008.441 -2.3117.713 -2.O766.841 -1.8035.860 -1 . 5004.A12 -1 .1783.740 -O.8332.672 -0.49rr.642 -0.1880.706 0.021o. o00 0.000

4 0A4 12upper lower0,000 0.000o.746 -0. s821. O51 -O .7471.298 -O.87t1.685 -1,.0382.429 -1 .2893 .566 -L.6264.474 -L.8605.24L -2.O476.489 -2.3L87.45r -2.5068.188 -2 .6358.731 -2,7]-29.091 -2.7 429-268 -2.7299 -2J7 -2 .6468.968 -2.5008.441 -2,3LL7 .7L3 -2 .07 66.841 -1.8035.860 -1 . 5004.4L2 -L.1783.762 -0,8542.742 -O .562L.759 -O.30so.843 -0.1170.000 0.000

40-415upper lower0.000 0.000o-9I2 -O.7 48L.276 -O ,97 21.569 -1 .1432-O25 -L .3792 -894 -t.7544 -2L5 -2.2755.266 -2 .6526.r52 -2.9587.590 -3.4188.696 -3.7509.540 -3 . 988

10.162 -4.I4210.571 -4.22Lto -767 -4 -229LO.723 -4.13110.402 -3.9349.745 -3.6558.936 -3.3007 .922 -2.8846.780 -2.4205 - 561 -L .9274.3L2 -1.4043 .067 -0.8871 .871 -O.4I7o.79L -0.065o,000 0.000

40A415upper lower0 .000 0.000o.912 -O .7 487.276 -O.9721.559 -1.1432.O25 -1.3792.494 -L.7544.2I5 -2 -2755.266 -2.6526 .152 -2.958?.590 -3.4188.696 -3.7509.540 -3 - 9a8

10.162 -4.I4210.57t -4.22rIO,767 -4.229LO.723 -4.13110.402 -3.9349.785 -3.6558.936 -3.3007.922 -2.AA46.7AO -2.4205,561 -I.9274.339 -1.,4313 . l-55 -O .97 52.Or7 -0. 5630.963 -O.2370. oo0 0 . 000

6940-418

upper lower0-ooo o.ooo1. 078 -0.9141.501 -L . r971.841 -1.4142 -366 -r.7L93.359 -2 .2r94 .864 -2.9246.058 -3 ,4447 .063 -3.8698.690 -4.51 99.940 -4 .995

r0.893 -5.34011.592 -5.57312.050 -5 - 701L2.267 -5 -7 2At2.204 -5.6L711.836 -5.36811- t-29 -4 -99910.160 -4 .523

9. OO3 -3 .9657.700 -3.3406.310 -2 .67 64.883 -t .97 63.463 -]-.2822.100 -0,646o.877 -0.1500 - 000 0. ooo

404418upper losrer0.000 0.0001.078 -0.9141.501 -1.1971.841 -r,.4142-366 -L.7r93.359 -2.2L94 -864 -2 ,9246. O5a -3 .4447 .063 -3.8698.690 -4.5J.99.940 -4.995

10.893 -5.34011.592 -5.57312.050 -5.701-12.267 -5.7?812.208 -5.61711.836 -5.36811.129 -4.99910,160 -4 - s239.003 -3.9657.700 -3.3406.310 -2 .67 64.916 -2.0083 .568 -1.3882.275 -0.82L1,083 -0.3570. o00 0.000Fth E-rl

Jul 94Sta0. o0o -250.50o.75r .252.505.007 .50

10,0015. OO

20.0025.0030.0035.0040.0045.0050. o055.0060,0065.0070.0075.0080.0085.0090.0095.00

1.00.00

JUI 94Sta0. o0

0.50o,75

2,505. O07,50

10.0015.0020.0025.0030,0035.0040.0045.0050. o055. O060,0065.0070.0075.0080.0085. O090.o095. O0

100.00

6 5- 015ord

0.0000.830T .I24J-.3561.702

3.?453.9594.5555.504

6.7647 -]-527 .3967.4987,4277.t6A6.7206.1L85,4034.6003.7442.8581.9771.144o.4240.000

40AOl-5Ord

o. oo00.830L.L241.3561, .7 022 .3243 .2453.959

6 .2236.764

7 -3967 .494

7.1686.7206.1185 - 4034.6003.7442.8852. 0651.2900.6000. oo0

canberGA- 60,0000.112o.207o .29L0.441o.7771.323I.7A22.I782.A443.3723.7864.1044 .3294.4584,4944.4104.L793.8433.4352 -9732.4741.982L-487o.9910.4960.000

Carnber 40A612cA-6 upper lower0.oo0 0.o00 0.0000.112 0 -776 -0.552o.207 1.106 -O.6920 .291 t.376 -O.7940.441 l-.803 -O.921o .777 2.636 -1.0821.323 3.919 -1-.273L.7A2 4.949 -1.3852.r7a 5.A22 -1.4662.844 7.247 -1.5591.372 8.350 -1 .6063.7a6 9.L97 -L.6254.104 9.826 -1 . 6184.329 rO.246 -1.5884.458 10.456 -1.5404 -494 10.436 -1.4484.4LO 10.144 -L.3244 .L79 9 - s55 -L -L973.843 8.737 -1.051,3.435 7.757 -0.8872.973 6.653 -O -7072.47A 5.473 -0.517r.9a2 4.290 -O.326L-4A7 3-139 -O.1650.99L 2.O23 -0.0410.496 0 .976 0.016o-ooo 0.oo0 0.000

40-6L2upper lower0.o00 0.000o.776 -0.5521.106 -O.6927.376 -O.7941,803 -O.9?r2 .636 -1. O823 . 91.9 -L .27 34.949 -1.3855.A22 -1.466?.247 -1.5598.350 -1.6069 . ).97 -L .6259.A26 -1.618

IO.246 -1.58810.456 -t .54010.436 -1.44810.144 -L.3249.555 -L.L97B -73? -1.0517.757 -0.8876.653 -O.7075 -473 -0.5174 .26a -0.3043.069 -0.0951.906 0.0760.838 0.154o.ooo o.000

4 0- 615upper lo(rer0.000 0.000o.942 -0.71,81 . 3 31 -O ,9),?7.647 -1.06s2.L43 -t .26r3.101 -L .5474,568 -I .9?25.7 4I -2, r776.733 -2.3778. 348 -2 -6609,595 -2.851

10.550 -2.97Al,t.256 -3. O48II .725 -3.06711 . 956 -3,04011. 921 -2.93311 .578 -2.75810.899 -2.54r9.961 -2 .27 58.838 -1 . 9687,573 -r -6276.222 -L - 2664.840 -O.8763.454 -0.4902,135 -0.153o,924 0. 0680.000 0.000

4 0A51- 5upper lowero. o00 0 - oooo.942 -0.7181.331. -0.9177.647 -1.0652.L43 -1.2613.10t -I.5474.568 -L,9225,74L -2.r776.733 -2.3778.348 -2 . 6509.595 -2.851

10.550 -2.97811 . 256 -3.048tL.725 -3 -06711.955 -3.04011.921 -2.93311.578 -2 -75A10.899 -2.54L9.961. -2.2758.838 -1.9687 -573 -t.6275.222 -L.2664.867 -0,9033.552 -O.5782.24r -0.2991. 096 -0.1040.000 0. 000

7040-618

upper lower0 .000 0. o001.108 -0.884I .556 -1.1421. s1g -1 .3362.443 -1.6013.566 -2.O]-25.2r7 -? .57 r6.533 -2 .9697 .644 -3.2889.449 -3.76I

1.0.840 -4,09611.903 -4.33112-646 -4 - 47413.204 -4.54613.456 -4.540t3.406 -4.41"8t 3.012 -4.L9212.243 -3.88511.185 -3.4999.919 -3.0498.493 -2 -5476 .97I -2. 0155.472 -1.4483.859 -0.8852.364 -0.3821.010 -0,0l-80.000 0.000

4 0A61Supper Iovrer0. o00 0. o001.108 -0.8841,.556 -I.I421.918 -1.3362.443 -1.60L3.566 -2.OI2

6.533 -2.9697 -644 -3.2889.449 -3.76\

10.840 -4.09611.903 -4.33112.686 -4.47A13.204 -4.54613 .455 -4 .54013.406 -4.41813-O12 -4.I92L2 -243 -3 .88511.185 -3.4999.919 -3.0498.493 -2.5476.97I -2.0155.444 -1.4803.965 -0.9912.539 -0.5571.216 -O .2240,000 0. o00

Ftq ff-t9

Feb 94Stao.00o .250.500.75r .252 .505.007,50

10. o015. OO

20.0025.0030.0035. OO

40.0045.0050,0055.0060,0065.0070.0075. OO

80.0085.0090.0095. O0

100.00

HIGH LIFT AIRFOII,S

3 0- 015Ord

o.0001.0901 .5271".8562 .3671-2644 - 4435.2505.8536.681-7.L727 - 4277 -5027.4407 .2557.0006.6556 .2405.7555. 1904.5403 -AL73.0s32 .290r .527o.7630.000

( see also fi-gure III-6)30-61-3.5

upper lowero.000 0.0001.093 -0 .4691 . 581 -'t . 1671.961 -L.3?92.57L -1.6893 - 7L8 -2.L645.322 -2 .6? 66.507 -2.9437.446 -3.0908.857 -3.1699 -A27 -3 .083

LO - 470 -2 .898l-o.856 -2 -64411. O25 -2.36710.997 -2.080ao -794 -1- 80610.400 -1.5809.795 -L .4379.O23 -L.3378.106 -r.2367 -O59 -1.1 135.913 -O.9574.730 -O -7663.548 -O .57 42.365 -0.3831.183 -O.l-91o. ooo 0.000

30-515upper lower0.000 0,000L.202 -O.978L.734 -1 . 3202.L47 -1.5652.808 -t.9264.O45 -2.49L5-766 -3 -1207 .O32 -3.4588.031 -1 .6759.525 -3.837

10.544 -3.800l-r.213 -3 .64111.606 -3.398L1 -7 69 -3 . 11r,Lt-723 -2.80711.494 -2 . 50611. 065 -2.24510.419 -2.061

9 .598 -)- -9r28.625 -r.7557 .573 -I .56?6.295 -1.3395.035 -1.0713.777 -O.8032.518 -0.536r.259 -O -2670.000 0.000

( ccfiputer anafysis, forCI max-no flaPs

r tao

,t*r.'707

r .6771A))

degrees

7130-616.5

upper Iower0.000 0.000l-.311 -1.08?1.887 -L.473

-1 ?(1

3.045 -2 . L634.372 -2.8185.210 -3.5647 -557 -3.993a.615 -4 .260

10.193 -4.50511.261 -4.5L711.956 -4.38412.356 -4. 148t-2.513 -3 . 85512,450 -3 .53312.L94 -3.206lL.73! -2.91111.043 -2 .645IO.L74 -2.4889.I44 -2 .27 47 .967 -2.O2r6.677 -r .7 2L5. 340 -t.3764.006 -1.0322.67L -0.6891.335 -0.343o. ooo o. ooo

canberGA- 60. o00O.LI2o .2070.2910.441o.777r .323I -7422.L742.8443 -3723.7864.1044.3294.4584.4944.41-04 -r793.8433-4352.9732.478L.982I .4470.9910.4960. o00

Table l - Predicted Performance Sumarv curparison only )

Cl max-Vf laPs*R=2H

3.62

3. 14

3.02

3.07

lirfoil

cA30 -613.5NACA 4415 ( I93I )

NACA 4412 ( 1931)

usA 35B (1923 )

clark Y (1924 )

*Flap condition:

On c/4R=6M

-. r05

-.125- 1'ra

--114-. lll

deflecci.on=25

Cd rninR=61'{

.0058

.0073

.0070

.0071

.0072

Cflag. 20 .

FIAUR€ fi.|1

72C LA55r( * rCrF{- LrFr A rRFatLS ( F oa. (o

^^?ARtso N a^iry)

NA CA 4 4I'

FlQvP,€ fl,--zo

73APPENDIX IV - Aerodynanric Characteristics of wing Sections '

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ADDE 'Jl-.ri'r LrUi'rEER l 93Underst€.ndinq lirf oils

Or, '' nverythj-ng you always wanted to knolr about airfoils but \,rere afraid toask'r, for fear of feeling stupid, perhaps. Donrt feel bad- there are scme confusingaspecLs about airfoil perfonrErce, and a surprising nw cer of stupid airfoil designmistakes have been rnade in the past by people who should have knoarr better. 9're willpoint out a ferr of these, but the prirnary purtrEse of this artsicle is to "get backto basics" so that you can better understand the nain causes and effests of subsonicairfoiL 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 eachof these at the guarter-chord Foint to receive an axle, and then nDunt then (oneat a tinE ) in a wind turlnel such that tbey are free to pivot on this ax1e, and thenbLcn on thern. The airfoil is then tested at various angl-es of attack (C ) frcrn zeroto about 18 or 20 degrees, plus and minus, in one degree j-ncrenents, and lift anddrag are recErded at each angle of attack. Lift and drag are easy to visualize, rneas-ured in pounds, aqtsj-ng at the pivot point. Lift is neasured perp€ndicular to theair strean, and drag is nEasured parallel to the air stream. The }ift and drag valuesat 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 clversus Cd to obtain tne "Iift curves " sho,in on figure 3. the Cl vs Cd cr.rrve issFnr€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 increasesas angle of attack increases, due to "induced" drag, or drag due to lift. As tieangle of attack increases bq/orld about 15 degrees, the lift begins to decrease asf 1ov, separation occurs on ttle top surface, @inrling at tie trailing edge. ttrisarea of separated flonr progresses forward frcn ttle trailing edge as the angle ofattack increases, causing further loss of lift, and large increases of drag, until-the airfoil evenlual-Iy "stalls".

i,ie are not finished with or:r !.rind turnel fieasurenEnts, ho^Jever. on scarE arrforlsthe 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,sonrcunt a sprjng scale at the trailing edge of the airfoil (see figr:re 1) to neasurethe pitclling nrnent in foot-pounds about the quareer-chord point. A nosedorrrnpitching tendency is, by convention, a negative pitchj-ng firctrent. !,ie nc'v, convert thepitching roxrEnt ( sprillg scale reading tj:res .75c) at each angle of attack to adi: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 mcflEntcoefficient curve, qn^ /d vs alfa (figure 3) for these tvro syrrr€trical airfoils, wesee 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 ) passes directly through the guarter-chordpoint. Inde€d, the center of Iift for anv s}'nretrical airfoil. is always at the quarL-er-chord point, regardless of tie angle of attack. ltrus, this point has special sig-nificance, r*rich is the reason tbat we picked it for the ncunting point for windtunnel tests in the first p],ace. the explarEtion for this phenc.rEnon is beyond thescolE 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 anysynrnstrical 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 inFnaturiFinraisturbed staie is laninar, that is, in layers. rf you ncve yourhand slor,ly in fron\ of you, holizontally, tie air renains in layers, and your handpasses ttrrough snrcQy with mimmun drag, without disturbing the layers. Tlr-is isknorn as " la,rLinar flor.r". If you rrpve your hand rapidly enough, or if your hald isrough enough, tire flow over your hand wil-L "trip" to turbulent flor*, rrrhich has rprethan twice as m uch drag as lanjrnr flow. Ttre reguirerent for .Larnj-nar flo\^' is thatthe flcrvr over the surface should not be accelerated beyond cerbain lirn-its in anyd.irestion- fore and aft, sideways, or verticalLy- tlEt is, we need c\onstant velocj-ty

94

fl-op over the surface. If the flov/ has tripped to turbulent, \,vre need only to slct/doh/n to the point h'here the acce.leratj-on lirlits are not exceeded, and the fLc'vr willonce agaj-n revert jrnrEdiately to tanr-inar.

!€ se€ that the 64A015 shape has a region of lovr drag betvJeen -4 and +4 de-grees angle of attack. this lo.r-drag region is knov,'n as the lanr-inar bucket. BeyondI 4 deqrees, rr)St of the laninar flow is lost, and tl.e ftor over the entire wingbeocrrEs turbulent. Iaminar flovr is easiest to maintain near the front of the air-foil vtrrere tie pressure gradient is highest ( "ncst favorable" ) , and is hardest tomaintain beyond the thj-ckest part of the wing. Accordingly, t].e " Ia.runar" shapeshave been desigrned for constant velocity flov,r over the wing at cruise, and the thick-est part of the wing llas been IIEved as far aft as prasticable, to maxjrize the ]-arn-inar run. The net resuLt is that the laninar section has approxirnately 20t lessdrag at cnise tllan the ccnparable turbulent sestion, a sigrmficant FerforlrEnceadvantage.

ScnE recentients than the I{ACA 6-series shaFes. but tleir larlinar buckets are carrespondinglynarroi,er. They camot tolerate nuch change in angle of attack without tripping toturbul-ent flc'r.r. At higher Reynolds nunbers (higher speeds, larger airplanes ) larninarflorr is npre dj.fficult to maintain an!4Jay, so ttle bucket becqres even narrcr,\Erwith 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 bucketwidth 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, orwing curvature.cambered Airfoil Performance. If rre take t-ire tr€ synrEtrical shapes d,iscussed

"!o"e, ""E,ffi'EA-ij@ in the nr-idd.Ie, r.rc obtain the tvp canrnerea airfoilsshonn in figure 2. The camber schedule is carefully designed, and is called the

reference (A). The canber schedule for GA37A3I5 is a nr:dification of another neanl-ine frcrn reference (A), and is especially designed for lanr-inar flctor. The maxjjrrlrncanlcer 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.Tparingwith fi$Ee 3, the first thing we notice is that canber produces a sigmficant in-crease of naximum 1ift, with no change in crui-se drag. Second, tfie stafl becc.rEssofter, that is, the top of t}le lift curve is flatter, and lift continues to bedeveloped at higher angles of attack than with the uncanbered airfoils. This isprirnarily a function of the inj-tial slope of the rEan line ( slope at .25tC), an irn-portant paraleter for good sloH-speed performance. this inj-tial nrgan line slopehas been optirlized at about 15 degrees ,rn a1l "GA' airfoiLs, correcting an unfortun-ate crnission in the NACA r€rk. Ttre third thing that we notice is ttrat canrberingIifts the vrhole performance curve (Cl vs cd) vertically upmrds into a nrre usablerange 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 pcnerto v,eight ratj.os. AII other a.irplanes olErate above this point: for exajrPle, IrpstIight GA airplanes operate at cruise lift coeffj.cients betrreen c1=.2 and .4. I€ seetiat 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 beingcentered 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 , renainhgccnfortably 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 thepitch-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 incln. Ttlus, a pitchijlg nsrEnt is ttre prj,ce lie pay for carbering tie airfoi], and itrequires us to invesligate tie effects of On on airpJ-ane perforrnanc.e so that ue c€ndesign our airfoils intelligentl-y.

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95Ttjfi Draq. As shovrn on fj-gure 5, the center of lift (center of pressure ) for carnberedairfoils does not alr^rays remain at the nragic guarter-chord point. It does so at thestal]", but as the angle of attack decreases, the center of lift IIEves reandard. Butsince ne must always locate tie aircraft C.G. at or near the stall c.P, , sothat tie nose of the airp.Iane will drop at the stall, the wing lift vector at cruisef or carnbered airf oi.Is is af t of the r,,Eight vesEor, and the airplane has a nose-dc'rrnpitching tendency. The fix? I,fe put a horizontal taj.l surface on the airplane to reactthe pitching nE(IEnt, holding the tail dcr.n. But as tle l-eamed earlier, negative l-iftin ttre tail surface produces induced drag' *hich adds to the wing d!ag. Retrernberalso that for every pound of negative lift in the tail, an additional pound of li-ftmust 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 wingmust generate 1040* total lift. Ttris additional 40+ of fift, above hhat rapuld berequired for our sl4flretrical airfoil, also creates induced drag. so vte see that t.rjmdrag, or t}le drag associated r,rith trjJrrLing out the pitchlng nEnent of a canberedairfoil, has trrc cc([Dnents- the induced drag of the tail, and the additional dragof the wing in producing an increnent of lift egual to tie tail doum-load. For ourtr,.E canbered airfoils, fi-gure 5 shcr*s that the trim drag at cruise is appro).ijnate1y5-8 drag counts, which is about I0S of the sectsion drag coeffici-ent, and addl-tiveto it. conclusion? Unless e€ can shctur at .Ieast lot i.ncrease in rnaximum lift frdllcambering the airfoil, it isn't r.Jorth it. Ifappi]-y, the increase in Clnax for ourairfoils is about 30t, considelably greater thEn the drag increase of 10t, so klehave 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 inon on airpJ-ane perfornance when ccrnparing airfoils. vse also see that it behooves us,when designing subsonic (1ight cA) airfoi-ls, to keep the On as lcnr as possi-ble, otherthings belng egual. Using srmth, forward-loaded nean lines, and using only as rnuchcamber as necessary, does ttris. This is a rrErjor critj-cism of the l|A6A 6-series air-foils. which are nid-loaded, and tie infanpus N&sA GAIAI (I^5-1) airfoils, which areaft 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 usinga long tail length, at least three wj,ng chord lengths long. A high aspeqt. ratiohorizontal tail. surface also helps. Anot-Ller effestive technigue is to have a r,,eightshift to the rear at cruise, follcwirg the C.P. shift to the rear. Retracting thelanding 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- equaUyjnportant. the effect of airfoil- On on airplane performance mtst be quantified andnot 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 de-signs, to rnillinrize Gr. It is not necessarl' to reduce t].e airfoil On cc(pletely tozero, rrrhich r,.,a.s done with the }.lAcA sdigit (230rc<) airfoils,at tlle unfortunate costof degrad"ing safety, but onl,y to keep the On as lcnr as praclicable, other thingsbeing equal.Disclaj-ner. Ttris paper is adnittedly a sfuplified explanation of airfoil lnrformanceand design. For exafiple. wind tunnel force neasursnents are now ccnnrcnly taken withpressure rakes rather than old-fashioned spring scales- Al-so, for satisfactoryhorizontal aircraft stability, it is not necessary tiat the taiL lift coefficientbe negaLive, nelely ttlat it be l"ess than the wing l-ift cefficient, provided thatthe nuny olher factors affecting horizont-al stability contribute in a favorable(stabilizing) direst:-on. Hou,ever, at slo\^' ftight, which is norrnally the lrrcst crit-ical conditron for longitudinal stabj,lity, the center of pressure of any airfoilapproaches 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 /95Ha.rry Riblett, 416 Rilelett Iane, wilrLington DE 19808 302/994-0479

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ADDSNDUM NLD4BER 2-99

Deslgn ltotes for Tapered wings

!,lhen designing a taperd wing airplane, the designer is faced with certain choiees.including:

1. !,lhat airfoil secbions should be used for the root and tip sections, especial-Iyconcernj-ng [Er cent thickness?

2. Hctur much t\,rist (washout ) should be put in the wing to protect the wingtips frcrnprenEture 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 taP-ered 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 tabulatedtest results . D/pj-cal performance curves are a.Lso sholnm on figr:re I. l.Iote the sketch ofthe initiat stalf dlstributions predicted by l.lACA for "restangular, tapered, and sr,€pt-back wings". This sketch is especially botherscme, since it il.l.ustrates the NACA con-cl-usion that "rectangular wings stall first at the wing roots ' and tapered !,.rings stallfirst at tl-e wing tips"- hence, supposedly, rather drastic llEilsures are needed, suchas use of considerabl-e rrrashout, or use of sections with rore camber at the tips, andthen even nrcre uashout, to ccrnbat these "bad tip sta1l characteristics" of taperedwings. The bothe.nscrre aspect is that the planform differences betrnteen the straight andtapered wilgs are not so great as to account logically for the n'Erked differences inthe location of initial stall reported by I{ACA. Neverthel-ess, generations of aeronaut-ical- students have been conditioned to accept these resuLts as gospel, and to desiginaccordingly. ltre ccnnonly acceptd washout recqrrrEndation is about 3 degrees, in spiteof 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 ar@t thj,ckness of l5t, f68, 18t, or 20t to a tip tiickness of only 91, in additionto the planform taper. The nexc to last specimen uses a 23013/43010 ccnbination. that ilnrrre canrber at the ( thinner ) tip- all t}.e rest have the same canlDer, root ard tip. onl-ythe l-ast specirren has the sanE per cent thickness at the root and tip, IZt, but it usesan odd (eUiptical) planform. Evidently. l.lACA ( erroneously ) assurEd that the preferredway 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 variablesccrnlcined. 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, htrichhas an odd planform that further contaninates the data. In fact, if they had tested a2415/2415 sampLe for exanple, with 2/I planform _taper ratio, they reoul.d have foundtllat the initial- statl, distribution is the sane]for a straight rectangular Hing, thatis, benign. Further, if they had tested a straj-ght pLanform wing with a per cent thick-ness change frcm root to tip, they rrculd have seen the locaLion of the illilral stalfshrft to the wj-ng tips. thus. c.ontrary to NACA'S conclusj-on, the spanwise location ofthe rnitial stal1 j-s pri:narily a function ot the per cent thickness change frcrn root totip, 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'Sdesign of the tapered sestions was a rnf,nunEntal mistake.

UnforEunately, follcrvring NACA'S psr exarple, a r.hoLe generation of tapered wingairplanes was built with wing tips that r^,ere t@ thin. Fign:re 4, c€urtesy of I'lr. ceorgeCopland 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 tlreseccnrrDn airplanes. It is also interesting to note that a fe!e, of tie nore sucessful air-planes (P-38, P-5I, Dc-3, Eonanza ) did not fall for the trap of using 9t thict( tj-p sec-tions, but used 12t tip sestions, contrar)' to I,IACATS reccnnendation. l.lote a.l-so that thePi,per PA-2+ cc.manche, desigrned i.n 1954, rrras a historically si-gnj,ficant airpfane, forit "broke the ncld" by using only planform taFer with no [E! cent thickness taper, with

100no 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€echncdels (see frgure 6) continue to be buj-lt with thln wing tips, unnecessarily causingcontrol prob.l-etns and ccrnprcrnising safety. 'Itle 23015/23009 cc.nbination is especiallyj-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 carnberprofil-e has a discontinuity (ki-nk) in at at 158 chord- Tl-ris causes the airfLsd. athigher angles of attack, to selErate at that point, resulling in a separation bubbl-e onthe 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 toact 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 yearsthj-s airfoj,r was touted as "lnving the best of both r,rorlds", but ttre disadvantage is adangerously sharp stall. As the angl-e of attack increases further, the Pattached sec-tion gets shorter and shorter unti.I the separation bubbl-e suddenly expands to cover theentire top surface. resufting in a sudden toss of lift. This is bad enough on singreengine airplanes, but on twin engine airplanes with one engine out the airprane miyslap-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 beenused to rmprove this situation, as shc,wn on fign:re 6. the vc's are instaued at l-0t ofchord ' just before the discontinuity at 158 of chord. They function by creati-ng a thi-ckturbulent ( energj-zed ) boundary layer i-nrnediately aft of ttre VG's, preventing ttie =epar-ation bubb.Le frcrn formrng. Ttrj-s forces the flo,.r into an even rpre frl-gUy ca.nereO snape(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 thevc's' but overal'L this is a very good guick fix, uproving safety. of course the bette.rsolution, next ti.file around, is to use nDdern soft-sta}l airfoils not subiecL to theseparation 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 plan-form. This slrcirnen has the Lrighest CLmax (I.8I) of any tested, and is aclordingiy oftencited as proof of tlle " inherentLy superiority" of the Lltiptical planform over t-l-re uni-forrnly tapered planforms. I{ote, ho^rever, that this specijnen enjoyi tro distj-nct advan-tages over the other specjrEns- it has a unique high-fift secLion (4412), and in additionit has the same per cent ttrickness root and tip, l-2s, htlich is, as r,,,e have seen, theoptimun thi-ckness in terms of best L/D. In vierrr of this, we vDnder if the legenda-qrrnystique of the ellipti,cal planform is justified.

Regarding planform taper ratio. it is r+et1 to renrenrber tllat a ve4/ short tip chordreans a 1on' Reynords nlrnber at tlre tip, and ai-rfoil section performanci drops ofi atJ.c&r Re)mords nurnbers, ltlus it i-s best not to taper the wings tcro much. cccntcn taperratios go frcm about 3/2 to 2/I. Snal-Ier tip chords rEan $naller tip losses, but alsolq.€r ttn, as stated above, Of course a higher taper ratio (2/l) alsi tras a structuraladvantage ' since it pernLits a greater spar depttr at the root for a given per cent rootthickness, other things being equa1. Alternativery, a higher taper iatio may permituse 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. ForLaminar wings, notice that uEre is litt1e difference in L,zD beer*een ]2t and l5t thicksections, thus r5t thick tip sections are preferred. rf thj,s is done, and if nrcdernsections 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 additionalcanber at the tips is not needed, nor is vring twist. A flapped section starls at aloler angle of attack than the sanE sesti-on unflapped, ana tfris in itsel,f provides pro-tegtion 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 useof soft staLl airfoils, so tllat assynretrical- lift c-onditions are unlikely to develop.ttarry Riblett - 4/I8/I994

101NA CA TRP€(t:D uJlA/6 Tesrj

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clssNA3l0voRIEXGENrRAToRs tJAcA tsatg R'k,r, A)ecry.2tool YtPBoundary l-ayer Research and The Twin Cessna Flyers have

teamed up tro bftig e3rly model Cessns 310 ownels the advaltagesvodex generaton afford. Afier Boundary Layer Research @LR)developed the kits for the Cessna 3 1 0 &rough the 3 i 0F, BLR aadThe Twb Cessna Flyers came to an a€reement granring The TwinCessna 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 thedevelopment of new products. while it pisces the marketingefforts witi a.n organization thar has dirccr conuct with over 7000twin Cessna opemtors,

Inslallation of the kit can reduce Vmc bv as much as 20mpftiiii?s by inodel. Handling characreristics are dramaticaiiyimproved. Low speeds conrol response remains positi\'c. rhetendency for the controls to become mushy is eiiminared. In

fact, VC equipped aircralt rnaintain full aileron controlresponse all the way *uough a stall.

The kits consist of a series of small aluminum exrusioos rhatare attached to the lpper lading edge of &e wings, !p bo& sidesof the venical fin, and there are two srrakes which are atlachedoo the outtroard side ofthe ergine raceiles. Over simpiified. thevonex 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 thusthe saall is deiayed alld actually becomes much more dociiewhen it does occur. Amazingly, this is all done with a kit tharadds 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 thesekjls conract: Th6 Twin Cessna Ryen ar (800) 825-5310.

ArR &oaR€st AUGUST 1SS4 27

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(Irl/JtlI995)Tandnq trre sharp stal] of Lhe NACA 23012 A.irfoil

nar"v niurett 1 07/il6 Rib'en Lane

Wilmington, DE 1980830?934-0479

Srnnnarv. This paper discusses t'.r) methods tllat carl be used to soften the notoriousl-yl-narp staff of the neCA 23012 airfoil, that is, use of vortex generators, or alter-nativeJ-y an upper surface build-up (reprofiling). l€ also discuss the nechani-sm ofthe stail on ttris airfoil, and explain wlly additional leading edge droop is ineffect-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 .

NACA aducted a series of tests on airfoils related to the 4-di-git airfoils ( salrethickness distribution), but with the rnaxjmum camber placed unusually far forward.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 keptreasonably 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 ubiqui-tous and infanrcus I'IACA 23012 airfoiL. It is l2t thick, with Peak camber of 1.8tcIocated at the l-5tc position, rather ttEn tl]e usual 40tC Fosieion us€d on nDst of thepozufax 4-digit airfoi-ls Q4I2, 44L2,4415, etc-). the nean line aft of .I5c is astraight 1ine, thus the only camber in tl:-is airfoil is in the first 15t of the chordlength. Accordingly, rrie can describe the airfoil as bejlg the DiACA 0012 sYrlretricalsecaion 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 factrenains 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 Pitch-ing nErrcnt coefficient (Gn). Fr:rther, sirtce there is no negative canber jn the air-foil, the nEximun lift c,'cefficient Eemains high and the induced drag is loi^r, cdrparedto the best knorvn previous zermn airfoil-, l'4ax ltur)l('s 1924 |+6. The [&-6 achievedzero 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 trail-ing edge of the airfoil ( figure 9). this, hokever increases total induc€d drag, andreduces Clnax. the carnber profile of the !F6 in the first 60tC is conventional ' ho\^r-

ever, so the M-6 des have a nice. soft stall-wind 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,LEda nEderately high Clmdx, very lol Gn, and Cd no greater than the 0012 syrnetricalsection. NACA pronounced this airfoil to be "markedly superior to l€ll-knovm andcc6rpnLy 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 tod.issuss, and that i-s its domfall. thrs was noted briefly in Table II Airfoil Dataof 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 driventwini with one engine out these aj-rfoils are especially letha1, causing accidentssuch as described in figure 2. In fasE, sharp stall airfoils are the rnaior reasonthat cA light twin fatality rates ironically exceed the fatality rates of GA ]ightsingles. [,le will not achieve true twin-engine reliability in prop-dri-ven twinsuntit h,e get rid of these sharp-sta1I airfoils. ProP.driven twins are ljjrlited byIateral cont.rol authority near vtIE due to the effect of a "blovtn surface" aft of theoperating engine - with shatp-stal-l airfoils, sudden unccnmanded and uncontrollabl-eupsets 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 ' 'erealize tlEt NACA, as soon as they learned of the bad stalL characteristic of thesdlgit airfoils, shoul-d have terafnated the project. Accepting the sharp stallrnerely 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-ecamber in t-ire Ieading edge, and those with too much cafiber in the leading edge.

Exarp.l-es of tJre fj-rst group incluae nDSt synrnetrical sections, and l-olv-carnbered air-ioi:"! such as ttre- l-ater 11gcA 64-212, These airfoils experience ccnPlete and

suoa* rlo', separation frcm the very leading edge at the stall-, and they can usuallyG-i-pt"""O by adding a sITEIl anpun! of leading edge d"rmP ' Arrf oils of the second

108

group. ircluding ?3OI2, experj-ence ccnpl-ete flo* sepa.ration on t}re toP su-rface at thestall, frcm a poj.nt near the end of the leading edge droop, that is, at about .l2Cin 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 asubstantial decrease of angle of attack ( wrth considerable altitude Ioss ) beforeattached flc'vr can be re-established.

Arrfoils of tfre second group cannot be irnproved by adai ng leading edge drrcp,since they al-ready have too much droop. For exanple ' adding npre droop to the 230]2airfoil results in t}Ie 33012 or 43012 ai.rfoils, and these have stall- characteristicsas bad as or vrorse t-lnn the 23012, frcm wird tunnel data ( check it out)- I'itut is re-quired is to ease the cransition frcrn the leading edge droop to the rest of the rleanIine, reducing the discontinuity in the nean line at tbat point- one effecLive andproven rrEthod is to install a cqnplete span-wise array of vortex generators on thetop surface at alout .10c, (Fiq. 3, delered). Ttlese function by fi11in9 in the "lowsFot" on the wing dch/nstrean of the vcrs with a thickened boundary layer of energizedturbulent ai-r. discouraging flol separation. Ttris fix is cheap and effective, andshould be reguired on all twin-engine prop cqnnuters using 5-digit airfoil-s, whichis the nrajority of the fle€t. AIso. don't forget that that single enging airplaneswith 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-dmaterj.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 thisnethod. l,lotice that the secej.on drag astuafly decreases, in spite of ttre increasedsestj-on thickness, due to the prcnption of Iaminar flovr. Furttrer, the zero-lift Gnrenains about the saITE, so top speed is unaffected. Ttris nerr profi-le could alsobe used to nlcdj-fy existing t@.Ling on production airplanes. Of c-ourse, t}le bettersoluti"on aerodlmarnically is to discard the ?3012 airfoil crcrTplete.l-y, and use a rndernlol.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 leadingedge droop, tius the tlc State/l{AsA fj:< on the "Venture" airplane (figure 8) is apoor solution lo the prob.Len. I suspect that any jjrprovenent of the stall in this caseis nereJ-y the result of the consj-derable aerodlmaruc twist that was introdticed intothe wing by this fix, delaying the tip stal-l. Horever, tll]is causes a considerableloss 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 withtwice 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 isFred l^Jeike's " Etcoupe" ( NACA 43013), holrever on this arrplane the elevator travel, isljrnited so that the stall angle of attack can never be reached, Still, the 43013 wasa 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 acrash occurred at Roselar,en, Indiana kitling a1I 68 people on board, a direct resultof the NACA 4301X airfoj.Is used on that airplane ( figure I0). As confirned by sub-sequent 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 stallcharactseristic of the airfoil, this caused an unccnnanded, uncontrollable roll-overand irrec'cverabl.e dive. Ttre ice ridge forms at the very spot on the airfoil- \rtrerea pronouncd suction peak exists ( figure 7), since here the tsrperature depressionfrcm adr-abatic expansion and cooling is the greatest. The ice ridge is aggravated bytlre strange ptacglrent of the vortsex generators on the ATR 72 wing. The "fi;<", longerde-icer bcots, is nrerely a bandage, for the basic probJ-ern rguins. Ivlodern c-onstant-velocity 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

despo calcu,latioos. Tbe simple meenJi_oc rirloilsgste erceptioDolly lor+. pitcbiag DoDeDts, soElesb!,t,l9*". th- the theorelical vaiues bss€d on the mearliae. BotI the rueasured aod theorelicsj curves for tlesimple mean-line air{oi.ls are given in fgrLre t6-_- TJre anolysis of ihese chorts o'Dd the" dstr of tobleIJ shor that tbe reflesed !-irfoils, altbouqh co[rDlr.irsfnror.rbl-r s.itb otber ref ered airfoiis, uJ;;J;;;the simple meaali-oc uitt"ils_ f*tf,.r.o"r1il"

^r'-foils corerirg r range of carn ber locations lorro,rdot 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€ -.-_tio"forms. These airlofu harbg rhe same ""-tJ;tloD but difl'erent Des'!.li-ue foras possess aooroxi-

ntrtel_v tbe same lift and drag characteristics.' Theangle of zero lift and the pitchirg moment, lo"r"""r,are quite di{fereut. .Especio.llv notevrortby is the venr0uch loEer pitchiag moment produced b-. tbe airfoilsreported herein.

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

109<.),

terlstics over well-knorrn and commonl,r used s.irfoils o,lhrs clo.ss. Ir hos a hish ma_rimum hft and a 1",lor

moheDt- Furrbermore, the niainum drng isprocticrll_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 thcneed, of 'nan5 -applicarions ,"q"fiog a

"figl,iJ-"'cam_bered section of modernte thicl:ness f,uring"a ,er_, loupitchiDg 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.

1. JTobs, ETlDel li., Itard, f,eooerb E., rDd pi.Etrenon,Robert trt,: Tbr Cbr,r!,.!.ristics ot ?g R.Irted -UrfoiiScctioD! 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.risticrof tbe N. A. C. A- 230f2 Airfoil from T.!ts i.D tb. Iult-*dl TO. I'erirble-Dcasitr Tuoaele. !. R. .No. SJO,N. a. c- A-, t935.

AEFENENCES

TABIJ II._AIRFOII, DAT-A.

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rol.2 a5 u 23

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UPPFR SURFACE REPRO TIUFl^JAcA

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4.47i

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11.658

11.47811-611

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7.3o, L- u p

3. oO 4. OO E- O.ABOVE ANGLES OF ATTACF:

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115

Ttris is qarbage

NORTH CAROLINASTATE UNIVERSITY -:

._:r

@,r:a:

ENHANCED WING DESIGN FOR STALL DEPARTURE RESISTANCE

I THE HIGH .ASPECT RANO WIiIGWhile prcviding significant bsn€fits in cruis€ andclimb, the higfi aspect ratio wing ,"qrir"i *i"design considaralion at stali ol.j" to rt Jinconsistencies in rhs grow{h ot irs muttipL siilcells.

. STALL STFIPS

Stall strips ar€ widsly us€d to force inboardseparation b€tors the stall celts fully develop.However, the r€sutting aircraft pitch_do*n firiisth€ useable litt ot the wing.

.. THE LEADING EOGE OBOOP

The design philosophybehind rh€ NaSh teadingedge droop is to provid€ a'passive" davice whichdelays th€ outboadseparation well beycnd thepoint at which it wouldnormally occur. This isachieved by th€ introductionot increas€d leading edgecamb€r and theaugmentation ol the energywithin the boundary layercrealed by a vortex whichtorms at the discontinuouswing/droop intsrs€ctiori. Th6net result ii increased stalldepartur€ rssistanc€ due tothe improv€d.. roll damping .and predictable pitch break . -

ti' r+'

t'.' ta' tfri'Stall Pattem w h hboaftf Sla[ Strips

Vonex

ffiSeparated Flor

- LE. Droop

Basic Wi.E

Leadlrp Rtge Orcop Aorodynamics

.'tt,tlo= (t--

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. Acomput€r codg was developed tomathemalically defina, iterat€, and optimizea leading' edge €xtension ot lhe ctrnentairloil s€ction. Minimizing the cruisedragpenalty whil€ increasing tho stall anglo otattack ar€ the primary designconsiderations.

Ouestair Venlura Droop/Slol D€siEn

. TEST FESULTS

Wind tunnel data indicat€s that the adclition ot lh€sewing enhancements provides more useable litt lhanthe industry-standard stall strips while draslicallysoftening tho slall break Subsequent flight tostshave further demonstrated th€ departure r€sistancool ths conti

116

O THE VENTURE DROOP/SLOT DESIGN

Designed at North Carolina State Universityancl wind tunn€l tested at NASA Langtey, theOuestair Venture modifications reprssent auniqu€ blending ot a€rodynarnic concepts. Aconservative droop is coupled with a pair ofchordwise leading edge slots. The slotsgonerate additional vortices which act toprovent the progr€ssion of the primary stacell. Thus, the combination of stots anddroops allow more ol the wing to attainanached flow to high€r angtes of anack

Modiflad V€nturo Stall Pattem

Cut}r til d.tennh.d math.fndi:d cquarbne[ach tloinl

Porc.nt dtoop

Pcrcenl rxienrionlorer anach point

Liadirg Edg. Olaop oesbn O.scriprbn

t.5

1.0

0.5

0.0

-0.5

-1.0

* 8:sclinr

-+ oloops E Slotr

.0Fl.ps - 15 d.gr.

't.5

1.0

05

0.0

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117

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Lorgcr deicer prevcnts fiorrnotion ol iccforwond of the oilerons. Neorly 20O oircrafi in l.lortfi Arnericqn seryice crl c.hod-uled to b. retofitted by June l.

y' c At en e1€N€t<A|te' t.€ R'oa€ g,.qCCaSR€'ttt's 7oiJ6&. g(4s5,{s ?64<

this yeo'lo iest oiher turboproppoworodregionol oircroh. The chiel gool will bo todetermine their susceptibiliry ond reoctionto tho effects of freezing drizzle ond freez-ing roio, Solvono soid. H6 expeds fh€ t 5ring to be compleied before the stqrt of ic"lng seosoa.

IHE FAA'S IR NSpOIT Airc.oft Dir€crorotsond SmollAirplone Directorsts will be .e:ponsible for solecting test poro.neiors andprepr:ring progroms to conduct the ex"penm€nrs. Aiiho,rgh n-fl;ghl r€siing s;Ti-lo. lo thot or Edworos AFB wjli be p6r-forned, :one tests con b€ done in windtunoels, he soid. Toilplone icing olso willba explorod os porl of o seporoie but keyprogroo, occording to Solvono.

In oddition to $ese reshicfions, fhe FAAis preporiog o.othe. oi,worthinss5 dir€c-live iniended rc) inpose rew .esnoinis uplontight operc ons wj'h'ne reoesigned do-icers, Solvono soid. He expecls the di"rective to be irsued this rnon$.

Despiie tho .ew deicer ond pleos fromAIR officiols, lho FAA losl week refvsedlo removo reshjclions trnposed in Jonuof/of{eciing fligtrt operotions of the ATR42ond Alt72. PiloB musr continee b observethe limitotions o$er $e deicers ore fitedto tl,e qtrcroh. lhese include:I Requi.ing pilob b moniitr cackpit 5idowindows for o r.rnique ice occr€rion thot irrdicdres Feezing roin hos been encounJered.I proh;b;';rg. J5e of floos when holoingrn rctng condttrons ond rBquirirg inm€_diore disengogonen. o[ ourop;lot in ffe€z-rno dflzzla 0r rdrn

otlention wss poid lo ice occuhulotionwith lhe ffop5 ot l5 deg. At $ot 5eting,ice wos qble lc occrete oft of tho originoldoicar. When *e flcps wore rekocted, theoirflow obove the wing wqr disruptcd,chonging oileron hing6 moment dromdti-colly. With the new doicer, no odve.se eFfects occurred becouse rhe ice ridga foiled

ATR officiols expect io cornpleto ret.o-fitting new wing deicers on ATR42s ondATRZ2s byJune l ---.o deodline esbblirhedby tho FAA in Jonuory.

As o resvh ol $e ATR occident, FAA of-r;c;ols ho'e norilied U.S. ond foreign oir-lrome monu{octurers t"qr Ae ogenc/ pions

1;Pa',-ee)\

74oue tqt-

I'n/oo^o- t--f 6 "t;a ' u ec

3eP aa ar r oil

'10c

5€paa'

,tk t Leoving flops oep oyed lf .hey ore ex-teoded ,n {reoz.ng dr,zzle o. roin. a

AVIAi]ON WIEK & SPACE T€CllNOtOCY,/March 27, 1995 35

U.S. APPROVESNEW ATR DEICEREDWARD I-I. PI"I'LTIPSAVASHINGTON

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

vasligoting icing chorocteristics of otherturboprop reglonol oircroit lqter tilis year.

Cedifjcotion of 6e deicer lqst week oc-curred bllowing four montirs of FAA 9ud/ond evoluotion of "oll ovoiloble lechnicoldoto" by tho ogoncy ond it: French coun-terpod, rhe Djreclor Genemie de l'Avio-lion Civile, Doniol Solvono, spociolorsis-icat 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 chord-oeorly twice the oreo lornerly protocledogoinsl ic6 occumulotion. Flight t6sts co+ducted or Edwords AFB, Colif., eorl;e. rhismon$ indicob ihe deicer preventr formo-oo olon ice ridge forword of the cilerons.A U.A. Alt aORCE KC-135 tqnksr

equipped wifi wobr sproy equipmenl deluged th6 ATRZ2 ir q series ol rosrs rhor in-cluded wotar dropleb vp io 200 micronsin diomet€r. Ths deicers funcioned proFerly 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 tohove coused o loss of loteroi conrrol thorled to tho crosh of on Americoo EogleATR72-21A naor Roselown, lnd., in 5c-rober. Thot oircroft wos llying o holdingpore.n w;rh flops or l5 deg. ihen the oc-cident occurred,

During the testr ot Edwords AFB in De-csmber ond ogotn this month, porticulor

t .t ,l1t dce.wq <to

118

(A1R72 uses NACA 430fX airfoils )

-,-^.-

A t(ta)v,^r^ Atv\^N rFF ,----r.'.4

.",. o

ADDM{DUM NLIMBER 4119

An Upper Surface winq Re-profile for the BD-5

the BtF5 airplanes as originally designed have a,,elL docunented, undesirablesharp 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 sectionat the wing root. Ttlis ai-rfoil is l-ow-cambered and onty 12t thick, wtrich largeJ-yaccounts for its lcrw naximr,rn lj-ft ccefficient and aLso the the sharp loss of l-iftat the stall, folloled by a hysteresis loop during stall recover,y. That is, theang.le of attack mlst be decreased considerably in order to obtaln fl-c,v/ re-attach'1entafter 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 wilddelErture . Other f actois cutri-bute to the probletn, such as the extrenely lc'v/ Relnoldsnunber of this ajrplane at the stal-l, less then Il mil]ion. AII- in all-, tie airfoalselection 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 theBD-5 staLL lErfornence. For eJ{anE)l-e, BD l"Licro Technologies offer dr@ped leading edgenose ribs ( and ot-|rer cqQonents ) for wings tbat are still under cronstruction. Forccnpleted airplanes, ho,tever, seve-ral, nEticds of re'profiling the wing shatrE havebeen used witn good resu.lts. Seti Arderson has nodified hrs rel-l--knom BD-5 with anulper forl ard surface re-profile of his crldn desigrn, extsending back to approxirrately40t of chord on the top surface, aJld ti-is h3s been fl-yjjlg for several- years withexcellent results. 'Ihis npdrfication is mini-rral and relatively s jrrpfe, and, Iikeotfler 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 pro-file to a turbulent seceion, resufting in a slight drag increase. this is only anr-inor orsadvantage, and is of lj-tlle conceln, considering the nnrked inprove<rent inflight safety tllat results,

Anothe.r schene for utr4=r surface re-profiJ-ing is shown on the attached sketch,dalLed II/20/92- In this schenE the cqpl"ete up[Er surface is built up frcrn the lead-ing edge to the flap,/ai.l,eron yELI lip, at approxjratefy 80t of chord. The flaps andail.erons regui-re no nadrfication and are re-used as j,s. A-lso, the exrsting tip sest-ion, NACA 64-218, hrldle inprovable, has acceptable stal} perforrnance due to itsI88 thickness. 1trus, a re-profi.l,e tenplate j-s furnished for tJre wing root only, andthe re-profil-e br:ild-up feathers out to nothing at the wing Lip, arld at the }eadingedge ard at the flaplaileron r+e1l lip. I'4a)dnu.[n hrild-up, at the root, is I inchadditiona-l ttrickness.

The "GA" re-profile irproves tne alJ--i-nportant leading edge prof iJ-e, adds aSlnall amcunt of thrckness and camber, and mcves the loading fonsard slightly sothat 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 flcwto approxlrately nid-chord, preserving larn-irnr flqr ( ard lcrvr drag). CG l-ijltits forthe ai.rpl-ane are not affected.

Flight experienc-e with this nrcdification has been excelLent. A typical exanpleis the attached report frcrn Bobble Parcr of Odessa, Texas.

Another option for BD-5 projects under eonstrucb.j-on j-s sirnply to assernble thewings as designed, and then re-profile the top surface befor€ ffigbt-

In the interest of rrProving flight safety, I offer a ful-l-size tsrplatedrawing tori lq1o to crf,ver the cost of printing and naiting.8/16/1995

Harry Rr.bleft, EAA *295764I5 RibLett Ianewi.Lrli.ngton DE 19808 302/994-O479

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8/LL/s{Harry Riblett416 Rr-blett I-anewikilington DE 19808

Dear }tarry:Like I told you, I \"pu.l-d let you kno\^' ho^'the (top surface ) scahr-on wing air-

foil 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-ikean ErcoulE, kind of "mushing" like. lbp end, the s'aflE- no loss there. The warm daytake-off d"istance was 2500 ft, and is no,r about 1600 ft. I stiU hold it dcldn untilI get about 85 MPH, ard then lift off. HcrA,ever, I novJ notice that the accelerationis 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 isshoruer. 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 thewing 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 thefirst layer lengthwise, and the seoond layer 90 degrees to the first, and finishedoff with tr.D coats of polyester, I then reinforced the leading edge with t\nlc layersof fine hre-ave 3-inch glass tape, staggered, wtdch extended back about 2 inchesfrcrn 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. Theairplane enpty Height was 467 lbs, ard is ncr^' 471 lbs, so the rebork added only4 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 Hondaengine 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 ttleED-5 neb.€rk n€rJsletter.

ADDE{DI}I II\J},IBER 5 123A 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 anarticle 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 itturns out, the airfoil- was designed by Herr Doktor Richard Eppler, and I have corres-ponded with hjil about it. Ttre airfoil and its nrean l-ine ( canber profile) are shotnnon figure 1. After plotting these, I saw notiing frightening about the thickness dis-tribution, 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-ikethe 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 air-forl. al,so due to Eppler, As hE have seen previously. this area of negative lift ex-tends the lan:inar n:n slightly ( hence the npniker "natural " Iaminar flc,w ), hoereverthe negative lift produced by the camber dip resufts in a loss of efficiency, a pointthat I suspect Dr. Eppl"er has not c.onsidered.

3, Pronounced aft camber appears in the airfoil fran .65C rearward, and I suspecteda rel"atively high pltching lrraftEnt coefficient (Gn) as a resu],t. Ttris also',Duld prob-abfy cause high aileron hinge lrErents (stiff ailerons), a.Ithough thj-s rould probablybe hard to prove without flight tests.

A canputer perforrnance analysis confirned ny fea.rs about this airfoil, espec-j"ally the sharp staU at 13 degrees ang]-e of attack, accordingly, in an attenpt totrack 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 thepoint of naxj.rn:m thickness is at .42C rather th,an .40C. the new airfoil uses the un-offensive Eppler thickness distribution frcrn M,F(1)-0115, and cqnbines it with theproven GA-2 rean l-ine frcrn "GA Airfoils". This should give us a direct cdnparisonof 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 cheIErforrEnce of NASA Nf,F(I)-01f5, including a soft stall rather than a sharp sta.I1, awider laminar bucket, and a 30-401 reduction of pitching nr:nr=nt coefficient. The pro-file drag ' as expested, is the sane, since both airfoils use tie sanre thj,ckness dis-tribution. Ttre obvj-ous concLusion is thac the rean Iine of D.IASA NL!'( 1) -0],15 is poorlydesigned.

If an even wj-der laminar bucket is desired for oFerational flexibility, GA 4OA2I5rnay be used, but the tlade-off is a slightly higher profile drag coefficient. See. fj-g-ure 3.

In spite of the ind-icated superiority of GA 42E-2I5, Dr. Eppler does not tike1t, because it was not designed by the rEdern "inverse" rnethod for designing air-foifs.

You be the judge.

Harry Riblett416 Riblett Ianewilnlington DE 19808

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2/8/L996National Ttans portation Safety Board490 f'Enfant Plaza Eastwashington 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 unfor-tunate. for that is the key to the puzzle. Ttterefore. f arn enclosing additional datashowing that the cause of the ice rj-dge, r*rich caused the accident, is due to ananc.rEly of the l,lACA 430xx airfoil, that is, a pronounced negative pressule peak atthe 9t chord position, exactfy where tJ.e ice ridge forms. l4ore conventional. airfoilsdo 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'IACALangley on "airfoils having the camber unusuaLly far: forw-ard", Ilere].y to see \{hateffects the exErso-. forvard loading would have on airfoil perforrnance- hopefully. lovtpitching nrnent coefficients, Figure 2 shov/s the forward loading scheduJ-e, and ccm-pares it to a rbre conventionaL. unifoqnJ-y loaded ai-rfoil, the NACA 54-415, used onthe Fokker F-27 'Friendship". the theorcical pressure profiles predicced by I{ACAfor 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 performanceanalysrs, figure G, confj,rms the predicted profiJ-es.

Ttre results of t.t.e 1935 NACA wind tunnel tests, figure 5, shoh/ that the arrfoiLncnent 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- evertested 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 gener-ally disappointj-ng resutts. espe.cially on propdrlven twins.

The ice ridge forms at the negative pressure peak (.09C) because that is hrherethe adiabatic cooling is the greatest. Thls is analagous to ice formation in thetbloat of a carburetor. In fact, tie top surface of an airplane wing is sirplya one-sided venturi. Etcrn that point onrrrar:ds, further conjecture as to the exacteffect 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 theice ridge to form at that point, and that dovrned the airplane. Ttrerefore, the IIACA430)0( airfoil is at fault.

Accordingly, there nuy be scnre nerit for the FAA to ban airplanes usi-ng thel,lACA 430:o< airfoils frcrn flying jrr freezing rain and &izzle ( figr:re I), but notall turboProp regional airliners should be so banned. To issue a blanket prohibitionis 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.

Harry Riblett416 Ribtett Lane

Wilmington DE j9€093o'r-lat1$ -D +71

128

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

In the j.nterest of rmproving flight safety,

Harry Rib,.e* 11",^" [hAW--,lCC: Venc]-.

Mr. Dan Salvano, FAA, Washington DC 2059I!4r. Tbny Broderick, FAA, I,fasfLj.ngton DC Zg59ll4r. Andtehr CebuJ,a, v.p., Gov't &rndustry Affairs, National Ai! Ttansportati,on Assn.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 TURBOPROPSIN FREEZING RAIN, DRIZZI.EIDWARD H. PHIIIIPS/WASHINGTON

f iting on unsofe condition rot coveredLr by curranl certificotron rules, the FAAplon3 lo issue qn oirworlhir€ss directiveoy Moy lo.b;dding vrrtuol,y oll tu,bop'oppowered regionol oirline oircroh hom fly-rng rn heezinq roin ond drizzle.

The direclve wil' orohibit dl l€osr l8 dii-lererl.oircroh, inctud,ng oll turboproo re-glonol konspods rn U S. servrce. from operot;ng in freezing roin ond drizzle 6yomend,ng eoch oircroh's opprov€d A;.-plone Fl:gh,Ma.luoi, soid Don p. Solvono,monoger of the FAA's Rotorcroh Dires"lorote, Ft. Worth. fhe FM hos set Mor. Zos lhe deodline For rece ving commenls,ond ":s very.eluctont" to exiind the com-rrenrperiod 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. Dornisr228/328. Embroer EM& I 20, Soob340/20O0 series, Foictlild 5A226/227o'rd Eeechcrofi Model 99 senes, 820O ond

r vUU serier. l lese o rcroti neel rc nq cer-lilicolion cnterio unde. Aooendix C of Pon25 o{ tire Federol Avrolion Regulolions.

The di,ective would require chongeslo lhe Airplone Flighr Monuol thor wouid:I P.ohibit u5e of the oirtopiiot when ice

ured for Moy 68 rn Soringfield, Vo. (eytopics 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;d-rng on eorly worning ro p'lots The ,rs€ olorrsrde vrsuol cues olso w ll be discussed,Solvsno soid.

"\ /e ore 1or expeoing ro moke ony oe-ciorarrons obour teez.ng ro,n ond orrzzleoher rhe neetrrg concjuoes." ou'Florrici-ponrs wjll be encoJroged ro openly d s.cLsg lh€ isrue Fom o" operarronol rio.ro-po'qt, occording ro Sorvono. He expe<fsthe Russion deleqar,on ro p.o'rde,mpor.bnt doto on Feez:ng prec p ohon becou!6of their extensrve llyrng experienco in s+.vsr€ weother cgnditoru.

The FAA s drrectrve esrentiolly will moleoll rurbop'op regronol oircroh ;equol-

byprohib;fing flight in fteozinq roin ond dr,1-zle, rcid Alorn Brodin. p.esrdent o[ mor.k6ting for Aoro lnr6rnotionol R6gionql{AlR) Morkotrng lnc. AIR is o sol€s con-3orlium o[ $6 lormer ATR, Jehtraom ondAvro cornponie:.

Brodin roid the snlirs U-S. flcd of no{slion 158 AlX4? ood ATRZ2 oircrslr howbeen litttd with lorgol wing deicers o: wall

os ;ce evidence probes mounted ouisideol'he copro,n's *,ndow Tne probe is de-signed b occrete ice ord serve os o vjsuojcr.Le lhot lhe oircroh l.os encounrered ic-ing conditions lor which it is not cerrifi"coted, Brodin soid.

The FAA rs sr'rl corducring speciolground6ored rests desiqned io oere.,nin€which regionol .ronspo s ore su5cepriblelo conl.ol problemg Under severe icirgcondit;ons. In.llighf,e5,rng \,srro o specro,ly modihed U S. A,l. Foice NKt-t3SAlonker oircrah is ovoiloble lor monr.rfqc.lurers, bul the FAA ir, not mondo no itsese. Solvono soid.

OPERATION Of Th! TANKtt ir fundedthrough Fiscol I996, "but we hove nogvorontees beyond thi: yeor" thot theuniquo orrcroh will romoin op€.dtionol,Soi"ono soid. ll cosh monufocturors qbcu{$250,0OO ro $5OO,O0g ro chqaer $chonker for ;cing tosts.

ln oddition ro rh€ ATR72-20O, qn Erh-broer EMBI20 Brosilio ir the onfy otb6r 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 baderived ftom groundbored rcs*ng, Scl"v{lno so.c,. I

hes lormed oh of the wing deicers, or wlrcnon unusuol joterol 'rim conoilon exisls.I Require rhot ol' ice hghts be ope.ot,veprio. b flighl into ;cing conditions oi nigltl,

'rrespectjve ol exceptionr contoined in o

Frodrculo' orrcrolt'! Mosler Min;mum Equ prnenl Lirt.I -'mil use oi flops ond forb;d use of tneouroprlor it ice is ooserved forming oft oflhe wrng jg;6sp5.

ln qdditron, fi6 di!6clive mondoies rhotpilols use opgroved orocedures to;mmediolely exit freezrnq i,izzle or.ojn condi-

tions ond tho.hey moke evey eftn o orcdinodvenently flyrng rnlb such reqions

Tre c,ouA ot.rt ocnon stem-s hom ihec,oslr o[ on Americon Eogle AIR72.2OOor Roseldwn, tnd Iawd,Sf Nov I4, I994.p. 28; Nov. 7. 199A. p.361. Ahhoughrhe U S N,ot,o1ot T'onsporrorion Soie-vEoord hos not determin€d rhe probobl!couse ol rhe occidenr. onolys;s Indrcotes,ho'on ce r dge fo,med oh of .ns w;pgde.cers, coL:srng o.oprd rol onC suose-q,renr loss of control by the tlignt c'ewlAw&sT )o^ 2, 1c95. P 28).

fi,Af ACCIOENT hos not only rejnlo.cedconce.r obou he donqer o[ lreezino roinord o-:2.? e. bur hos fo,ied rhe FAA ri cotside'exponding furprendix C of Porr 25 boyond ;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 conoperote iolery in *oter droplers hovingon overogo d;ometer ol 2O5O l"nic.ans.The diomoler of dropreh .n.ount6rod bylhe Amerrcon Eogte ATR72 probobiy ex-ccod.d 200 hicro4s, occordinq to thaNTSE

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

AVIATION WEE( & SPACE lEcHNotocy/fcbrvory S. 1996 37

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About the Author

Harry Riblett, 64 , EM#2957 6, j-s a llechanical Engineerrecently retired froo Hercules Inc. in Wilnington, Delaware. He

holds a Commercial ASEL pilotrs license, and has been active lnsport avi-ation and EAA activities for many years, He is an ex-president of }illmington Chapter #?4Q ana is cuEently a chapterTechnical Advlsor. He has buj.1t two homebuilt airplanes, a Star-duster 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 fold-ing 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 iBmediat-ly following WV-II. Harry served as a Reservist Radar Officer/Air ControLler on a USN cruiser during the Korean War. He sub-sequently worked a dozen or so years uith civilian coEpaniesmanufacturing, testing, and installing aircraft runway arrest-ing gears.

His interest in airfoil design prompted him to visit NASA

langley j.n 1985 to encourage them to develop a EoderD aerles ofairfoils specifically d€signed for General Avlation alrcraft.nisappointed pith NASATS near total lack of enthusiasB for sucha project, he returned horoe, bought a computer, developed hisown GAtr series of airfoils, and published his book, rrGA Airfoils-a Catalog of Airfoils for GeneraL Aviation Use't.

Harry and his wj.fe Jo-Ana never Diss going to the annualOshkosh Convention, have three chj-ldren (Allen, Gail and Mark),and sjx grand-children. Allen is an.active "Stardustertr pilot,and the others give flmoral supportrr.

June 1994

Harry Riblett415 Riblett LaneWilmington, Delaware 19808

n2/994-s479

ADDENDUM t'lo. 7 133Aircraft 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]l ]! yer" rtlat sinpJ-e, but it isn't, Aircraft longitudinal stability, and the aJtCG liJrdt, depend on many factors, and the parUicul-ar airfoil belng used is onlyone factor affecting the ploblern.

9i:g !;.Flvrnq Winq Airplanes. l,et,s bregin by looking at the npst sj:rrcle case, allyrng wrng. As Ln any airpLane, thD conditions mlst be satisfied, tt]al is, itT::, b. sta!.ica]]r stabre, and it arso must be dvnarnicaLlv stabt;: i;trc stalirityIrErely reguires that the cG be located in rine r,ritrr tne ritt vecbo!. ttnt is, at thecenter of pressure of the. arrplane. so tlrat the airplane ( unai,sturb& i ,iff tfyleveL. Since rer cannot shift q.t" cG fore and aft in f1ight, ,r. th;;;;r; need, for$"-llt*n ving airplane, an airfoir h,hose cp does nor itt""g" p"sid"" is ttre angr,eot attack changes, but._ramins. at the ,,nugic' quarce!-chord p"l"t. itri., bry def_rlrltron ' is a "zero cq" aiJfoir ' which neans that tre airfoil rust be either syn-fiEtrical (uncanbered), o., if canber is used in the alrfoil sestion, trr" t

":.tingedge rm:st be ref]exed sufficiently to achieve zero On. In prastice, the trai]jngedge reflex can be changed slightry to trim out sfilali chairges in cc location, butonLy veqr srnalJ- changes can tre ha'dled. l^ie descrih:e this ,'balanceO,' c€rdi,ti-on' bysaying tl)at the srrn of the nrnents arFut the cG must be zero, for any steady st-atefight clcndition.T*9". stEbility, on the o-ther han:, involves tl* rate of chanqe of the ns,.ents about urc cG, follorr'ing a disturbance frfir trifined ffgrrEl G-oe aynan;.ca[y

stable ' the disturbed airplane must scrrEhoe, develop a net nirent about Lhe cg cointerto the direcLion of the d.istulbance. that is, a nei stabilizing ncrent, so tilat theairplane will tend t-o return to its trirrrEd attitude and speed. Notice that the fiyingwins.315glang has precior.ls littr-e fiechanism to develop thii restoring rnxrEnt. onepossibirity is to Locate the cG beneath the rrring as shou', so that ,^,hen . no=e upd'isturbance ocflrrs, for. .,€np_Ie. the "pendurlm 6rr.ce" of the cG noving forward wirlterd to bring the nose back d"',*' to ttrl trre origi'ar Fositi.on - Another nDle cqft.-pricated_possLbility is to use elestronic sensors to detece the drresti-on and nrag-nitude of the disturban:e, so. that ?Fpropriate accuation signals can be generatedfor {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 seriousdesigrn restristions. First, zero pit-ning -nr.tent airfoils nust be used,'and tl,eseare gcnparatively inefficient in terrns of vD. second, no flaps can be used on theairplane, for there is no tair. to reast the cqsiderabl" noi"Ic,^,l,- pit"Lg n'-r=.,t

fT th. flaps are deployed. accordilgJ.y, landj.ng and take-off "p".il" -. reratvelyhigh. curpared t! a simirar oonventiorni airprani with flaps. tt La.

-ti," cc rangeof tne ai..plane is veqr ri,',itq, restricting the- utili-ty "i tn" .iir.".. A fl-yingwilg airplane doesnrt have to drag around a fuselage an& a tail, hr;-th; price pa.idfor this suFposed advantage is tco high.

=: F.;ql!Iq*$$]angs..- rn a carrrd configr:rarion, $E have rl^lc !,rings operating inEarrd€m, It r.E load the airplane per the ar.tached sketch, with the CC Sit f6nrara ofthe aft wrng c/4 pint, rre see that the forr{drd wing produces AO lb. "i-fj.tt, .rrda. posiri-re nE''Ent of 80Q fr-1b5 about tie cc. sirnilfuiy, th"-r;;;; prcduces J"6Q

+5-"1_rll!,,"rd a negarive nErent of 80Q ft-Ibs about- the cc. rtrerer6rl, the totar:::"_I_:t.{] ]r)s, equalrng thg h919lt of the airplane. and rhe surn of the positiveand negatJ.ve fiEflEnts about tle cG is zero. Thus ttre resultant rift vecto! passesthrough the CG, and the airplane is statically stable.. If re novr apply a I degree nose-up distuibance to the ajrplane, for exatrq>l-er,vith a sudden stick noveneni, or L-ith i .o=*-up gust load, the'picture changes, Sj-ncethe srope of the li-ft curve for any airfoil is'approxirrutery o.i ah;;" -ot

cr ro,each one-degree change of angre of attack, the ci- of the fona; *iog'"iir increasefrcrn CI=.4 to CI=.5, w^.r-ich iJ a li.ft increase of onl-y Z5t, wtdle the -C.L of the rearwi-ng will increase frcrn c1=.2 to cf=.3, a li-ft inqrease of 50t. Ttris is the key toachievrng dynamic stabirity. ccrnpleting tlre anarysis. the rift of the for$ra.rd wing

134i-ncreases frqn 8e to l.oe {you're welccne), ar'd the li-ft of the rear wing increasesfrcnr I6Q Eo to 24e, for a totaL resulranL lift of 34e lbs. But since the *eight ofthe ai-lprane is stiu onry 24e lbs, the first thing we notice is tlEt ure aiiplane90es 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 transitioialconditj-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 thatre 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, "*t u" fonardfuselage area, f!:.ctlon in the conrroi.s, ard sti.ci-free ( destabiirrinoJ, -."a

"tafusel-aEe area ard stick-fjled (stabilj.zing), as qEII ". p."p.:.f"i-J1j'ar*,"""n

effects - These a-re not incruded in tne adve sinple anarysi;, -b"l .h" !iir,"rpr"=JTtarl F.r: sane. As tong as the cG is f orvrard of

' tire aj-rilan" ,

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-n ,rt .i-poi.rt , unet stabirizing rEcEnt will -resurt after a disturbance. rn our anarysis, negr-estingthe iesser factors rentroned above, the neutra] point is the CG I;;d;" ul *1rr"nthe Ci of both r./ings is tne salrE.

Fram the above r.le .n """. that the prumry reguir€(ent for arly tal:Id.en wrng3rrplane regarding dlnaruc l61l+av i.s itnr ti'r" r"..r*ra wing nust. be n,"i" i,rgi:.yloaded than the rear wjng. In .aaitio.,, tfre tor,rraia wing musi

"Lr,rays st ii beforethe rea:: wing, so that the -nose of the arlplane wilJ- dr-p at ttre siau. rather thanche reverse. In Lr1e case. of. L1e gllard aLrplane, Lir-is neans that the nrain wi.ng cannever reach its nra:<irun lif c coef fj-cient, btrich spells inefficienry and relatively

tt-igh ianding sFeds. E\rthe!,. it neans titat f]aps'cannoc be useci on the main winglof a canard arrpJ'ane - A further resEErcrion is trrat a car:.ard airprane shour-d not beflared on randing, since a starr of ttre forvard wing approaching touchdo^'n is rikeryto cause a sudden nose drop.

+ +If - convent+onal Ailprare. A convenrionat aj.r-orane (taif in the rear ) is arso: -1"* wlng arrplane, so:-r obeys the san= rul-es for stab.i.Iity as stated a.bove.The horizontaL tail surface. hcrdsver, unlike a canard, is c^rl.d on to produce al-ift in either direction, up or. dc'ern. Accordi-nsly, e" usual practice is to cunpro-mj,;e, and use a syrnEtrical sect-ion for the tail'surfaces. =u!n -" tn. nrce o:ao:-2.yldgh has a good VD ralio and decent ttlickness. By using a ,"f"tiu"fy farge, ,^Effdesigned tail. hE can achieve a wi-de cc range. ttrii is a desi-rab.r,e a"'=ign 6oi""eiu",for instance in a c'h-in-class. airplane, enrrinci,ng the utirity ot tire airprane by per-ni-tti-ng considerabre flocibiJ,ity ir't roaoittg. By r,\,ay of irlu-stration, r.Li= *r- in"an arrpJ,ane wj-th a main wing area of g0 sqit, aid a horizontal tail a-rea of z0 sqft,:: i:B of rhe rnaln '"ring area. Trr-is i.s srigntry n.re tt'n the rur.e of thunb of r5-2ogor cne wrng area, used on srnalle:: airplanes. No./ suppose orlr airplane uses a wingsection with a pitching nErrent of OrF-0.04, and suppose the desj-gn li-ft coefficientat cruise is Cldes=0.z. Referring to the attached @ chart, r.e s& tUt t]le maj-nwing @ is at .45c at cnris€.

- rf r"e load t-rre airplane with the cc at tt'is sa,.E poi.nt,,45c (aft cc lir{dt), the airprane wirr be staLic;J.ly stable, aj}i the lifi coerfi-cientof the tair' wir..r, be zero. lt.,rLher, be see that this i-s arso a aynarnicaiif =a"ri"condi-tion. since the Lift coefficient of the rear wing (tail) i; ro'"rer iian the trftcoefficient of thefonrnrd r,iing. lJe a-l,so nolice tlar trris is a parLrcul-arlv effj.cient

".nfiguration, since there is no wastefur- tai,l dcnn-road. ,iud-;J;-Jiir'rr ti,eCG 'r,ere placed farther forr"and, -or if, ure pitching nsrEnt coefftcrent of .rr" ,*g."ere greater , or both. For exarpr-e , -if the ai4>rar,' used the r.rAsA GAIFI ai.rf oir , withIts gYtr€geous pitcLinE ntrEnt coeffj.cient of do-O . f Z. the c' of ttre nain wing r_oufabe off the chare, and a c-onsiderable ( and rEsteful ) tail dcr"n-load muld L requjredto trjrn Lhe airptane.

alext vre check to rnake sure the tair- does not starl before the main wing. At thesta]-l, our wing airfoil has a C]rrEx of I.8. and the G> of the main wi-ng nov6s fonrardat or very close to tlE c/4 positron, as a1l ai-rfoils do. with ttre cc it .asc, ,,. =.=that the required Eil lift coefficient will be +0.5r for "t t,." "t"l ity.

-rt is rswit-t:-i' the range of our IEC-A 63A012 tail section. even at the relatively icnr p.eynolds

nunber and lcwJ aspect rario cc(Ifrlf,n for tail surfaces, and re are satisfied that thetail wirl not starl before t}Ie nraj.n wing. vJe also note that the taiL cJ. is consj.derablv

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

9ie are not finished yet. hodever. Before r,re can be satisfied tt)at this is asafe aft CG limit, r,{e mlst also investigate the spin recoverff properties of theairpLane at th-is CG location. ltris involves a lthole nevJ set of paranEters, beyondthe scope of tlai.s tEper.

It is interesting to note, as shoiml b'y lhe exafipIe above. that a srnal] anEuntof pitcllixg trErEnt c€€fficient in an airfoil can actually tre helpful in ach.ievinga wider CG range, Thus the zer*r airfoi.Ls tlEt NACA developed in the s-digit. studiesserve 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 theyneed to be, are equalfy ill-advised.

Holv shall rrE ans\re! tfle question posed in the first Paragraph above? The corleqEansrrer 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 recov-er!. characteri-stics of gre a:irplane a.re satisfaqeory. " I{o\a€ver, this is difficultto calsulate pEior to flight tests, therefore a c€nservative pracLice with sj-rpleairi planes is to ignore tie infLuence of t-he tail on the position of the airplane'sneutral 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 unLilflight tests can be done to Fossilcly extend the CG range. RenEnber. horever, t-tlatthe CG peniulun effect rrrks for us on high wj.ng aj-rplanes, but r^orks against uson low wing airplanes. thus, for Io^, wing airplanes, 23-25tC is often used as theaft CE ljmit prior !o f1ight tests.

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ADDNiDUM NTI4BER 8 137Vortex C,enerator Kits

This paper discusses the highly effective vortex generator kits that are avaj-l-able to lolver stall speeds and inprove lcrvr-speed controllability, especialLy onprop-driven twins with one engine out. the subject was discussed at scrne length inmy papers "Design Notes for Tapered [iings", and "Tanr.ing the Sharp Statl of t]e NACA2301-2 Airfoil". !'Je also elaborate on an artj.cle concerning lAcro-Dynandcs Inc VGkits printed in the January 1996 issue of "Arr Progress', magazine, and we stronglyreccnrrend 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 install-ed on the top surface of the ping. across the entire wlngspan, at the fOg chord pos-ition. the second array is instarled as crose as possj-b]e to the l-eading edge of therudder, both sides. In ssrE cases, this second set is instaued near th6 triiungedge of Lhe fin. The prirE y effect. of the vc's is to i,ncrease the trrickness ofthe bounciary rayer doenstream of the vc,s. thus, they increase the effective thick-ness of the wing, just as if "gon6.' r*ere appl_ied to the top surface. And since theadded thrckness is al-.l on the top surface oi the wing, this causes an uF.rard shj-ftof the airfoil mean line, that is, an increase of wing carnber. Both the increasedthickness and the increased carnber result in a higher rnaximurn lift coefficient forthe wing' l"bre urportantry, hcr.€ver. these vc's, when placed at the ,rOc positionon 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 theseairfoil-s have at the .15C Position. This el-minates the fl-c'vi separation that occursat that point at high angles of attack. l,Ji-thout the frorr, selErati.on, the stalr be-cdr'es soft and gentre. and this is the key to good aileron i"=ponse. even with oneengine 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.cha]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-ect-ed rudder. without vc's, the si:rp1e hinged rudders used on nlfst of today,s lighttwi'ns llave terribl-e flovr separati.on at the hinge rine, tl.us high drag, ihen oneengine 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 iredon't need.

r'-nus ' the vc's a.re very effective band-ards that address the poor wing and taildesigns that are used 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, andI5t 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 thefauLt of the FAA t1,'pe cerLificate systern, for the re-cerEification costs associatedvrith najor design changes effectj.vel-y freezes t].e design. Thus rne are forever v€ddedto 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 ofperhaps trno years ) the tl,?e certificates of at1 prop--driven twins that cannot showa unc lo,rer thEn the normal stal1 speed of tl'e a-irplane. Ttren the arended typecertificate for the rnproved "no \.trc" nrcdel shoul-d be issued follo,ring a sinpiefl-j-ght denpnstration. wj.thout the prohibitiveLy expensj-ve "normFl-" c"itificallonprocedure. 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 nothave with today's obsolete, garbage airplanes.

Harry Riblert - 5/Li /1996

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