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I.~ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WAlR'LTI ME REPORT ORIGINALLY ISSUED August 1944 as Advance Confidential report IABD5 EiECT ON HELICOPTEl PEIFOR MACE OF MODIFICATIONS IN PROFILEIDAG CEARACTEISTICS OF EOTORBLADE AIRFOIL SECTIONS By F. B. Gustafeon Langley Memorial Aeronautical Langley Field, Va. Laboratory WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre viously held under a security status but are now unclassified. Some of these reports were not tech nically edited. All have been reproduced without change in order to expedite general distribution. DOCUMENTS DEPARTMENT T. ?6 L~b i ;. . ~3~5~1~~1; . Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/effectonhelicopt001ang * z . .ACA ACR T'o. LIHO5 COCIIFTD ':.TAL IATIOiAL A VISCFY COl.! ITTEE FR AE"RCiA.UT CS ;.DVA'CE CO PTDEiTTAL REPORT EF'FE .JT CII MHELIC F P LE FE :FI'R .i:CE F' Hl,' DIFI:. I IC i3 TIJ F':;'FILEDFAG CHALRATE RI.'T'iCS. CF R''TCR3.L EE AIRFICI SE TIC. IS .y F'. E. Gus'i::fson Pcrfora'r'n:nce c a I, tion ar': ]:rs. s tei fo o a t ;:i '.l helicopter rot.or in wl;vicih three t;,l:e ci 9irIoil se Lio:n vwere success ivel, used. T ttyp' renres rted .re the rough ccn'c e t ioncal, tlih s.ro',tlh c:.'V rLntlcrL al, an:i the laminarflow or I c~wdrE secti ins aS dev~ ljLd for hell ccpter us The pe rf r'?rrance it.m? oc:ered i e ittr thrust for fixed p. e'r in !'overin,., rLan.e sad enduran.e at cruising sp ed.J, and pc.AC : re:iu.ireJ at a rielit reiy high forward spe.e;,. Cot.:,urs sno~ ,I g she conditions of operation ernc..ountcre.: b;: thie b aile sec"ti.c.n ar.d '.vwe i tin J ci rves sh owviing the relIat i:e irl.r'op f.t ,rce cf the var'Lous section angles o7 attck fo spoecifie. piet :nL 'itions are included as *n a J in: thei i ter:re:a ti:. of the re sult . The calcul nations indic :te D tha t th1e Lie f a sr .c'th conventional sc t.on. r ill result in r3crl:ed cerfranrce g.ins throughout the ii ht r nse. Definite, thnu.h stialler, add.ti t io al ,ai;n in takeoff ei:'ht and in range artn: endLurre E'i," be re .izsci by th ie uis of a low drag section. AC. hi i'c,'Ar spe.ds or at moderate frrward speeds and hi ig las:irigs ho.G'verr, losses are indicated for the lovw,lraig sctions in c'_,ntr: t vilth} the smooth convent io nal se:ctions. It is di.monstr. 'ited that, if these losses a:re t tLe avoided, the low i:'e' ,tectiDrns must be des.i:ned to avoid the extirene rise In drc cocffi cient at the hi, ir angles of attack wtiich is cnar!iter istic of the lowdr; sections now available fcr 'ue in helicopters. CC, F IDENTIAL 2 COFFIDEiTTIAL NACA ACR No. L4H05 INTRODUCTION It is generally recognized that an important part of the power required to operate a helicopter is absorbed by the profile drag of the blade elements; consequently, considerable interest has been shown in the possibility of using laminarflow, or lowdrag, airfoil sections in helicopter rotors. A recent report (reference 1) described the characteristics of several lowdrag sections that were developed especially for use in helicopters. Pre vious lowdrag sections had either excessive pitching moment coefficients or low drag only at extremely low lift coefficients. The sections of reference 1 were designed to give the maximum liftdrag ratio (L/D)max obtainable with zero pitchingmoment coefficient, over an appropriate range of Reynolds number. In order to indicate the magnitude of the performance gains that might result from the use of the new sections and to provide a guide for the development of additional sections, an analysis has been made for several condi tions of flight for a helicopter of assumed character istics. The method of analysis used for hovering flight differs considerably from that used for forward flight. The results for the two flight conditions accordingly are presented separately. Material that is not essential to the analysis but provides substantial aid in under standing the results has been incorporated in an appendix. SYMBOLS R rotorblade radius b number of blades c blade chord r radius of blade element r x R 6 pitch angle of blade element 01 difference between hub and tip pitch angles (posi tive when tip angle is greater) CONFIDENTIAL IIACA ACOR io. L[HC05 COc'lTDEIT.IAL 3 0c. blale pitch angle at x = 0.75 Q rotor angular velocityy, radians per se.o,.nd V forward sp.Ded Ij tipspeed ratio aV .. G eagle of &ttac:: cf rotor disk C2.R speed of axIal rlow tihru.ug rotor cdil positivee upward) ao section nc ,i le of attack.: (absclutQ) Cd section pr:filedrs 'i efficient CL section lift c'effic ie.t a slope of lift coefficient as.inst section arnile of a ttac (r a d i n mr 3s u re a solidity; ratio of tocal blade are to sweptdisl: area r (bC , T rctor thrust Cm thrust coeff icienrt (  \ F'^ TTni4/ C, torque coefficient (Rotor torque . t  P power Cp pover coefficient (t ft p r inut CL lift coefficient (Rotor 1i ft ap angle of attack of blade ele,.ient from. zero lift aR angle of attack of blade element at tip uTRF, velo ity component at blade clement perpendicular to blade span and parallel to rotor disk p.QR velocity component st blade element perpendicular to blade span and to UTQR CONFIDENTIAL NACA ACR No. LHo05 p = tanI1  uT 'V blade azimuth angle measured from down wind in direction of rotation S gross weight, pounds /S rotor disk loadlnF, pounds per square foot f parasitedrag area, square feet p air density Subscripts: i induced o profile HOVERING FLIGHT In order to indicate the effect of variation in air foil section drag characteristics on the useful loyd that can be carried, the rotor thrust developed by a fixed shaft power was calculated for an assumed helicopter rotor in which three different types of airf:'il section were successively used. The calculations were, in each case, carried out for a series of blade pitch settings. Sample Helicopter Rotor The sample helicopter was assumed to be in hovering flight at sea level. The rotor characteristics vwere taken to be as follows: Rotor radius, feet . 20 Solidity . . O.07 Blade plan form .... ...... .Rectangular Blade twist . . cne Power available at rotor, horsepower ... 20 COFI TDENITIAL CONFIDENTIAL IUACA ACR ITo. L+H05 Airfoil Sectcin Characteristics The UACA 51H.5 section was chosen as representa tive of the new lorvldra sections of reference 1. The NI'ACA 2501 section, for which data are also given in reference 1, was inciuded to permit comrrparison v vith a smooth conventional section. In c;'..der to permit compari son with a c conventional section in a condition believed to be typical of presentday r'oors, a "rouIogh" con'ren tional section was included; the dra cu :rve for, this section is a composite of data fr.lc vrarioufs soir'ces. The curves cf profiledrag coefficient against angle of attack. used for the three sections are shown in fig ure 1. These curv are e repres.rtative .o:f ,eynol, ds numbers corresp.ondi.ng to the o:.t.r psrt of the rotor disk, in which most of the profiledrg losses occur. As is shown in the appendix the Reynolos nntumer, IMach number, and angles of yavw encountered b; the rotor blade vary considerably over the rotor disi:. :.o attempt wvas made to modify the curves o ffi.ure 1 to a lci.j for these variations? tthe analysis is thus a coI:parison of drag curves representative of certain types of airfoil section rather than cf specific sections. The profiledrag values available for high angles of attack were incomplete, esTsciali for the IIACA 5H15.5 section. The drag data of r.fer rce 1 reach an angle of attach,: of 15 for the iAC, t53' 15 section and of 10 for the IC A 3'H15.5 section. The follvwng relation, which is based l1rely on a composite f all the data for high angles of attack of reference 1, was used to extend these data as neces.siry: Acdo = 0.25 IcZ' cI) where acd increment in profiledrag coefficient atve value at upper end of straightline portion of lift c r. ve c7' lift coefficient as given by extension of straight line portion of lift curve This method gives results that agree with the available values for high angles of attack for the lowdrag sections of reference 1 within about 20 percent. It is also in CONFIDENTIAL COTNFIDEITT TAL 6 COTFID.ETIAL NACA ACR No. L4HO5 approximate agreement with drag data for other airfoils at angles of attack beyond the stall. The slope of the airfoil section lift curve was taken as 5.85 throughout the analysis. Method of Calculation of Thrust for Fixed Horsepower Thrust. The rotor thrust T is [2 T = CTPTrA! or, for the assumed rotor, T = ll95CT2 (1) The value of CT for a given blade pitch setting may be obtained from equation (14) of reference 2, which may be written 2 A5 a\2 A5 2a CT = a2a + + 2 25 L5222 L \ 62;i where A = +4 a In order to obtain an expression for t, the power required and the power available may be equated as P = 260 hp = pTR52 Cqi 0 + p1T5Q2 CQo I5 hence, S= 26o ( 2) V3.46(cq + Co) Induced torque coefficient. The value of Ci for a given pitch setting may be obtained by using the CON FIDENT IAL :!ACA ACR LC:iO5 CO.F':DZ:ITIAL 7 fiFur3ofmerit equati on ,o .rferncrCce 2, which ma'; te w.ri tteni ;:= 0o707 hence , ./2 Val..:ues of 1'. f' a: i7 ,r i ".i :. .. .' ? cf 1 itch :'a1, c obtai d fr..,, fi e 17 o ._er. The f'ct:r in th ab.ve cqi .i... .7 I r t .f 1 /2 a n re a;' rice'. 2 E in,:: .... '.. 3 u i: t", ," e finii.t t .. ..f LT a:i C in rf:'er:: vh reads p is used in the def'nij ions t lro  t. :e ; . t r:p..rt. 1 'P .file tor .e :effi: t. In n ,i:rC t:, cbti: n the *desi i '.r ,valu es o o.. for a ra curve oi arbit rn,'," r.,ri, it is nicezas.r, fit to culccu.te tn_ in:noux angle of fI'lo. at a Jer, es :.f r:..ii fo, =...: t.e specified .tch anilz. :ias calc'.;. L cn w ; :... r:7 r.i.ns f eque ta. (1 ) of ref :. .. ch.. ; i .. rit r 2 8 1 . ''iere an u?/ard inlnnrin.li r: of t;h; flow is associated v..'i u: ",sitive v i;]l..V=s of C; 0h(.: P (0.751 o.:,5 + 4l.Uex 'The a, les of atrac!: are thei. o'ai.n.ed from the rletion S= 9 + Sinle curves of ..e3 olf at.tck aain:lt fraction of radl ius are shown in figure 2. COI:FIDE::TIAL NACA ACR No. LLH05 The torque coefficient per foot of radius can then be cdx2 be obtained from the expression . The torque 2TrTR2 coefficient for the entire rotor is then readily obtained by graphical integration. After both CQi and Co 'are obtained, equation (2) may be solved for Q and equation (1) may then be solved for T. Results of Hovering Analysis Rotor thrust was calculated for a range of pitch angle from 70 to 210. The results are shown in figure 5. Curves for zero profile drag and for the still more ideal case of zero profile drag together with uniform induced velocity have been included for comparison. The maximum section angle of attack, that is, at the blade tip, is indicated in figure 3 along with the blade pitch. At the higher pitch angles, the slope of the airfoil lift curves falls off and the calculated thrust values are optimistic. These portions of the curves have been drawn as dashed lines. Discussion of Results of Hovering Analysis It is apparent from figure 3 that, within the range of tip speed corresponding to present practice, the rela tive merit of the three sections being considered remains virtually fixed. A change from the rough conventional section to the smooth NACA 25015 section results in an increase in rotor thrust of more than 300 pounds. Changing from the smooth NACA 25015 section to the smooth NACA 3H13.5 section results in a further increase of approximately 200 pounds. It is noteworthy that only about 500 pounds more could be gained if the profile drag could be made zero. The calculated values of maximum available thrust shown in figure 5 are greater than the gross weight assumed in the forwardflight analysis. The lower gross weight was assumed because, in a practicable machine, the ability to hover at altitude and the ability to take off with an overload are considered desirable features, CC1I IDEIiT IAL C Oi FTDEI'T IAL '',A ,.C P : O. LL C,5 COITFITDETTTAL C'R7',..D FLI .1GHT cf the1 various e .r: .rrmiLn. c ace cbca ct rist 1ics assocI. ted viitr forward fiijlit, .r':ge and endurance seer:i of r.eate:t interest at the ores :nt_ tim. C.I J il: 1A con ot f r nF ze1; r e. uriice at pa rrticals s1.. e (. aprc": mately tt for' minimrirm po.er) cc nse :iue cntly Vere nad for a samL, S he licopF ter in ,hich the tlire C.irfDil s.c tions prev ou.  de..cr ibed w.ver use: .z.cce :.si'vel . fuel iead :' ,1) percent C:i' T. rjs v. i:t was s su,ned in such :cse. T e pc'.'er a' b by ll i es other than the rcto.r, i ncludin. c1. in .fa?.ns andi toru,:. compera tirt g de'. . :, '." s ]i .. :! for :, isu. ing a hor se'ower hour, f.nic i s n. pr ma t'ly tc 20 .er nt higher than the rior:'.al v' a n. f r cru.L i; n pCw.I BecaJ.se of the irre1i.Lr s1qe Uf the dri a curve rcr the lc,drag a ir cil, n. L ,ti:?. L tre..i.tr:,rnts of the ro,trr. prcnfildr:."g l ses, sucih as th ht o.f rt er:.nce 5, were Sa1.1plee 1lic opt c r ani .JT,' ,, L:n it ions The s in.ple h: licopter v."aZ 2 su:ared to b, in l:v1l fligh. at sea 1:,T. 1 and t: i.e r': tiii nd. r the fol lowing conduit ics : Forward specd e t r. s.ond . . 0 'Miles : rc h .our . . '. Rot, or tip p ed, feet r s c . 00 Tipsp,, ed r.ti . . 0.2 The geomietr ic c ciractzris tcs t ssmLed caere eas fcllowvs : Rotor r adius, feet . 20 Disk lo'ding, pounds per s1'juere foot . 2.5 Gross weight, pounds . 140 Blade plan form . Rectangular Blade twist . . one Solidity . . 0.07 Parasitedrag area, square feet . 15 CCI FIDT'T RL NACA ACR No. L4Hi05 Except where otherwise indicated, the foregoing assumptions apply to all results presented for forward flight. It will be noted that the geometric character istics assumed for the rotor are the same as those used in the hovering analysis. Method of Analysis The power absorbed by the rotor may be considered as the sum of the power required to overcome the parasite drag, the induced drag, and the rotorblade profile drag. The power required to overcome the parasite drag is 1 V P = 2pVf5 9 2P 550 = 16.6 horsepower which is considered to be constant. The horsepower required to overcome the induced drag is P = a L i 550 As explained in reference 3, the induced D/L is simply CL/4,. Because the change in weight is small, the use of the average weight is considered permissible, and the average induced power is then 8o Pi = 0.0735 x 2980 x 6 550 = 55.9 horsepower The calculation of profiledrag losses is much more complex and is described in some detail. Calculation of s3ngl.s of attack. Any graphical treatment of profiledrag losses recui'es knowledge of blade section angle of attack at various points on the rotor disk. In order to calculate the angle of attack of a blade element at any given point, it is necessary first to calculate the required blade pitch, the inflow velocity, and the blade flapping coefficients. The pitch and the inflow velocity were determined by means of the analysis described in reference 4. This analysis CC F IDETIAL CONFIDENTIAL '..CA A "1~ o. LHO.5 C OIIFDEI'TIAL 11 e::tends the an.alysi of reference 5 by the addito'.n of a sparaTimeter tha t rrreents tne shaft Cpv.cer su.:lied to the rc'tcr. The flapping coefficirents were then deter mrined by e.qu tions (1 ) t (o (") of ref rerce n . in determining, the itch:! and inflo,,. v'eioc.it, it was necessarytr to esti:nmte the r.otor: prc f iledrag losses. This est i:.tion i. 4as a ccmrplishEd b use of a s"e. ifi airfcil drtag curve as repreentd by a po'' ser1ieLs. The drag cur'.e u;se:. corresponds to that e:i loyed in tie example of referer.ce ?, but the r~ultitr: values of rtor ;c filc dra N w frCe cecreased a:'LIt 10 i3 ...er.ccnt to provide a better appr' xi.i a ticn o th1 cIr.?teri tics of the Si::.:.oth Secti ons in ~:' ins ,ere in trhe ore; en t scudy. In a strict Sa:e, a d.1iff rent c:. tir.stio'n of pitch and Ii[low'. ve.1 ior;, should be d ter mrin d for each sect,ion, p. rti _iarly for th: r':u71h1 ::'nvnt iOucnal section, because of the dli _ference in rqu ired power input ; how ever, the effects cf such c gnnges in Lhe co m'ation 0 pitch and inflow velocity are nr.El ibe e:c:t in cases in which the retreatin.' tipsection nles become hig:i enough, to produce ece:sive :.ra's. TI effect of n extreme change in pce r inpout an. in the r Eu ltinn corcbi nation of p. tch arni' i.iflo21 velccity m riy rr.c ted by referring to the e:.i.pl:oi given in the e ppendix: this example co:pre s the roror profile dry losses tZ.1 hen 15 square feet of p .ra itedreg aIrea ani:'. zer'o artas. ite drag a rea :e, su cess 'ely assum..d at : relatively hih forward scee .. The nori.mal and tangent i.1 conpcnents of velocity relative to s b.ladc element uer? obtained from the fol lo in, expression, v.hich :ae mo:ifications of equa tions ( ) and (9) of Ireerence h: li = + x up = 2 + {x 'A whe re K1 = 1 sin f 1 I i 1 K2 = + al + pa~c +pa cos j+ 23 sin + t ipa cos 21 1 1 1 + 2kbi sin 24 +2. a2 cos 35 +7pb2 sin 5W COIJFI P TDE TIAL NACA ACR No. 4HJ05 K3 = bi cos al sin + 2b2 cos 24 2a2 sin 2* and ao, al, a2, bl, and b2 represent coefficients in the Fourier series expressing the blade flapping motion. In reference 6 the angle of attack of an element ar is shown to be equal to 0 + tan1 U. In the present UT analysis, the tangent was assumed equal to the angle in radians; hence, the angle in degrees is ar = 57.35( + Values of a, were calculated at every 100 azimuth and at intervals of 0.1R over the blade radius, so that values were provided at a total of 360 points on the rotor disk. Profiledrag power loss. The rate of profiledrag energy dissipation for a blade element of unit length is the product of the drag and the relative velocity, or 1 uTU R uTQR Po pP) bccdo C S cos cp/ Cd cos p For the conditions of operation covered by the present analysis, a negligible error is introduced by the omis sion of cos p and the profiledrag power loss per foot of radius becomes o= puTnR) be cd By using the assumed values of solidity, blade radius, and tip speed, there is obtained in footpounds per second per foot of radius PO = 554,000uTcdo (5) In order to obtain the total power for a given airfoil, the drag coefficient corresponding to the calculated angle of attack at each point in the disk is used succes sively in equation (3). The details of the integration of the 360 values are omitted. CO FIDE iTT AL CONFIDENTIAL .CA 'C3 "o. 4I,.H' Co I irEiTTI T_.L 15 Tr order to obtain curves of pr.ofiled: g p1c. r loss aga inst wei Yt, '~.ic. ul1'. toi s of an.!.i of att.ck ;fni: energy loss '.re a:re ied. oLut 'or e ViiLes of gross weight. Tei r it in curves are shev.wn in f iure 4. T''he "aulues for tae r.u.rh air ,'c ,il cot1 3 ined a,Il':tic'lly are included for c.;:'ericcr.n viLth t!he '. lues obtained r.' i, l.l In order t: c c nit uL)ch I 'al .ul." ticn: the drc a curve of fiL ur 'or tr e ,: U 5ij .irfIoil 'a mai'e t. ,i .e, u. to an an:rl of stt'ci: :f h('' ti!e S ,Jie I"fr; as thEst . the exI.,mple SYiven in .efe'rnc? 5 t: cI .:rdi t e re, however, increa. s d p:.rc nt in crj.e,' to m:. the e.s ir 3d allov.ance for sufi : ce i' ughnt ess. Val.l' ,. D.,'L obtL ined as desc r ibed in r frre nc, c co.ullo th.l ": us.j.d after' bF ing i ncr.easd '; 2' e rE:ft. C. lc'. U, ti o f , n K. rai .L n c :. E ; usi.g thie 3"..: e rd .fil dr. is in horsepower, as given by % i u e L, for th.. r.:e .f w ii.t i ro 510 topounds c Dti a.ra. total rotor dirag looses f',or e c;. airfoil SE', ic .i '" [ ,v i u. ted. as follows: .. Airfoil Dr.ag. losses 's, (hp) Parasi te Induced Pr.cfile Total 2;ounch SIrmooth convenrtion.l I!ACA 2d0 .? I 53. I ~ ~ ' ' 1,' .3 t h 15 i. ,.C,. 3h1 .5 "'.9 c!ii., 7C.5 By assuming. a Sp i ifi : ful 1o.su:irtion Of. 0.5 pound per rotor horsepY..:.'erhour, ti' valuis of r an'e and endurance are c. s follows : irTfoil riRouh Srnuoth Smoothl c onvent Ional :IACA .2015 IIACA 5H1.5 Range, miles Endurance hours U23 5.8 i7.5 ?.5 S.1 NACA ACR No. 14H05 HighSpeed Condition As an indication of the effect of tipspeed ratio on the relative merit of the airfoil sections, calcula tions were made for the sample helicopter at a tipspeed ratio of 0.5. The corresponding forward speed becomes 120 feet per second, or about 80 miles per hour; all other assumptions are as previously given. The drag losses then are as follows: Airfoil Drag Rough Smooth Smooth losses conventional NACA 25015 NACA 5H13.5 (hp) Parasite 56.0 56.0 56.0 Induced 25.0 25.0 2. Profile 67.5 35.5 54.5 Total 148.5 1145 155.5 The high profiledrag loss for the lowdrag section results from the high drag values above the lowdrag notch; this point is demonstrated in the appendix. Discussion of Results of ForwardFlight Analysis It is apparent from figure 4' that the relative merit of the airfoils depends on the loading used. Certain aspects of the comparison are brought out more clearly by plotting the profile draglift ratio (D/L)o instead of power loss. Figure 5 shows this factor plotted against the loading factor 2Cm/ia, which is more general than but is proportional to weight or loading. It is evident that the optimum (D/L)0 occurs at a considerably lower loading for the NACA 3H15.5 sec tion than for the NACA 25015 section. Although a relatively small portion of the rotor disk is affected, it should be pointed out that the assumption of constant liftcurve slope is not strictly valid at the high loadln s and at [ = 0.5. The calcu lations for the NACA 5H135 section, in particular, are increasingly optimistic as these conditions are reached. CC:J' T TIAL CONFIDENTIAL I'AC\ 'AC o. LE4 05 CO,. HIC LUSIO S [ Thel effect of modi'fications in the airfoil section drag characteristics, as indicated b:r .he the oretical performance enalysis made 2for the sample helicopter, may be s.uimari.zed as follows: 1. Tne use of the section characters t ics taken as representative of a smooth :;.onf veti ona section instead of those t.i.l:en as representative of a rou;n conventional section resulted in an increase orf .~ :.::i:nmately 9 percent in the rotor thr;ust availa":'l with fixed shist po'er in hovering, an increase ,of f per"cen..it in ruan2L. and endurance (with equal fuel load) at cruising s:.peed, and a reaction of 25 percent in the po.oer requiH'e, at a relatively high forward speed ('.O mph; tipJi, ied rstio, C.3j. 2. The use of the section characteristics taken as representative of the lcAdra airfooils of' IACA CS Ho. 5115 instesd of t"ose fi ti smoozch conventional section resulted in a furtl.Lr increase of approximately 5 percent in the rotor thrust available witiit fixed shaft power in hovering snd an a.lditional increase of 10 per cent in rEn.e anda endurance at cruising speed: however, at the highspeed. condition, 5r in crease of. approxima tely 18 percent in the .po'er rs quired wJ.s indicated. 5. If the losses show n for the lowvdraR section at high speeds and at moderate speeds and high loadings are to be avoided, the lowdra2 section ;imut be designed to prevent the extreme rise in dr;a. oefficient at the hifgh'er rnzles :f attac': exhibited hb the lo 'drag sections of I;ACA CE !!o. 5112 . Langley Memorial Aeronautical Laboratory National Advisory Co.nrittee for Aeronautics Langley Field, Va. C O FIDET:IT IAL COPITIDEliTIAL NACA ACR No. T1O05 APFPE DIX CONDITIONS OF OPERATION ENCO;N;TERED BY THE BLADE SECTION AND EFFECT OF VARIATIONS IN ASSUMPTIONS Contours of angle of attack and power loss. In order to make the reason for the results obtained in the forward flight analysis more evident, contours of angle of attack and power loss were prepared. The source of the values of section angle of attack has already been sufficiently explained. In order to show the relative importance of a given increment in drag coefficient in the different parts of the rotor disk, the expression previously given for power loss per foot of radius was modified by dividing by the area of the annulus at the appropriate radius; the resulting expression for the power loss in footpounds per second per square foot of disk area for a profiledrag coefficient of 0.01 is UT5 P = 26.60 u 0 x Contours for the set of conditions initially assumed are shown in figure 6(a). Figure 6(b) shows the effect on the contours of increasing the assumed value of solidity. Changes in loading produce similar effects, since the higher solidity is com~narable with lower loading. Contours for the original solidity but for p = 0.5 (V z 80 mph) instead of p = 0.2 (V = 55 mph) are shown in figure 7. Weighting curves. The contours in figures 6 and 7 indicate that a given increment of profile coeffi cient is more important at low than at hic:. section angles of attack. It is difficult, however, to judge the significance of certain factors for example, the abrupt rise in drag coefficient at high sngles of attack shown for the ITA"A 3H15.5 section (fig. 1). In order to permit more rapid quantitative judgement of such factors, the data may be combined for the two sets of contours into a single curve showing the relative ir:por tance of different parts of the curve of airfoil section profiledrag coefficient against section angle of attack. This weighting curve is designed to show the amount by COI'F LEPT IAL COUFIDESTITTAL T ACh ACR No. L4i HOS which the power consuLned in overcoming the profile drag of all the blade elements operating at any particular angle of attack is increased if the airfoil section drag coefficient corresponding to that angle of attack is increased by some convenient increment, for example, O.C1. Such a curve has the further merit of permitting rapid calculation of total rower for ain airfcil section; it is necessary; only to multiply the oridinates of the curve of profiledrag coefficient against angle of attack charac teristic of the airfoil section by the ordinates of the weighting curve and obtain the area unLder the resulting curve. In order to obtain such a weighting curve, the range (or ranges) of aziir.uth angle ('in1 to 2) through which a given range of angle cf attack (Car to ar2) was maintained was determined for a ie.en radius by using a plot of angle of attack : against azimuth angle for that radius. The nrocess was repeated for successive ranges of angle of attack until the entire circumference was, accounted for. The apDoro riare average value of UT for each range of azimuth angle was then read from a plot of UT5 against azimuth angle. Ordinates for the weighting cure for the specified radius were then obtained by means of the expression for the energy aer second per degree angle of attack uer foot of radius 1 '1 1 pbc cc uTp R3 2 5 0 a 2 oar where uT5 is the average value of UT5 for the range from )l to '2. It was found that increments of angle of attack of 0.20 provided amnle detail in the final curve. The process was repeated at intervals of 0.1R over the blade radius. The resulting weighting curves for representative radii and the overall weighting curve obtained by a summation of the curves at the various radii are shown in figure 8 for u = 0.2. Values of power obtained by use of the curve of figure 8 and other values obtained from each of a number of other weighting curves were checked against corresponding values obtained by the more laborious pointbypoint method already described, and the answers agree within 0.5 horsepower. C nNPTDFNT TAL C CITrF DE T IAL NACA ACR 1:o. 14105 In order to permit ready application of the weighting curves to rotors differing from the sample rotor in chord, radius, or airfoil section and likewise to rotors oper ating at different tip speeds and altitudes, the curves have been plotted in nondimensional form. The use of the curves for calculation of the profiledrag loss for a particular rotor and a particular airfoil section involves the following steps: (1) Multiply the ordinates of the weighting curve by the ordinates of the curve for airfoil section profile drag coefficient (2) .iltiply the resulting ordinates by 100 to allow for the fa t tha the weightingcurve ordinates were given for do = 0.01 (5) Obtain the area under the resulting curve and thus obtain the total value of CGp/ (U) Multiply the value of Cp/o by the factor 550 Steps (2) and (4) may of course be combined; the factor for the sample rotor is then 100 x 0.07 x 0.002378 x (20)3 x n x (20)5 6 = 2.43 x 10 550 Effect of variations in helicopter characteristics and flight conditions. The weighting curves provide a convenient means for indicating the effect of changes in assumptions on the airfoil requirements. The effects of tipspeed ratio, loading, solidity, blade twist, and power input are thus indicated in figure 9. Corresponding profiledrag losses for the drag curves under considera tion are given in table I. Source of losses indicated for lowdrag airfoil. Comparison of the weighting curves of figure 9 with the profiledrag curves of figure 1 shows that, for the conditions in which the lowdrag airfoil shows losses instead of gains, these losses result from the extremely high values of profiledrag coefficient at the high angles CON FI DENT IAL CONFIDENTIAL I'ACA .ACR Ho. LcH05 of attack. The point is brought cut more clearly in fig ur;e 10, which shows the u'.ves th;t result from multi plyig c s o the drag curves of ur 1 by the corresponding we'ihtin: urves of figure ''(a) for i = 0.5. Pre] iminary results (unpublisled.) of additional low drag airfoils intended to reduce these losses at hi g angles cf actack. indicate Lh'ct zonrsiderable f.pror'&ss mray be expected. Conditions of cpe ration i2gnordr in an,lys is. S ime lif ing a szsunlptii ons ior proc :.i' e 1hic'; have been used in the analysis but hvE'. nut been discussed an.d 'aii& be suspected cf endang;r'inr the. siiJ.it of the comipari sons made, include: (1; Use of scticaly meli suedJ s action ctar.:acter istics with nc alilo':n'ce for .ff' cts dico to iotaeton (2) Assiumptlon of uniform inflow velocity (forward flight analysis only) (35 Use of section charactri. t.Le corrsponding to a single Reynclds numiber an a inerle Ta'ich n, umriber ,s applying at all points on th rtotor dis;: (4) liHelect cf effect of angles ofr a. n section characteristics Past experience indic ates thu t airfcil sections used in rotating blades exhibit clarcteristics similar to their statically measured section characteristics. P s sible effects on thl chs racteristics of the lowdrag sections are conjectural. The effect ?f rucnunifor.ity ofi inflc'. velocity was examined in reference 6, an it was concluded that the net effect on the rctor forces was secondary. The method of analysis used '.would permit study of items (5) and (j), or even inclusion of the effects in the analysis if such were deemed desirable and if suffi cient section data were available. Although the data at hand are insufficient to penrit complete calculations, it is of interest to note the magnitude of the variations of Reynolds number, Phach rumblrr, and angle of :Iaw. COIGF IDEJiT IAL C OI! F IDE'TT IA L NACA ACR No. L4H05 The Reynolds number, which was taken as approxi mately 3 x 10 in choosing the drag curves, actually varies from 0 to 4.5 x 10 in a typical case. The value 2.8 x 106 corresponds to the mean value at x = 0.75 when the number of blades is taken as three. Figure 11 shows the variation of Reynolds number over the rotor disk for two tipspeed ratios. Radial components of velocity are ignored. Comparison with figures 6 and 7 indicates the regions in which the greatest differences might result if the drag curves were varied with Reynolds number. The contours of figure 11 may also be used in esti mating Mach numbers. For this purpose, the values shown on the contours should be multiplied by 0.000014QR. For the sample rotor in forward flight, OR = 400; hence, the :':i.h number is approximately equal to the value shown on the appropriate contour line times 0.0056. For = 0.2, the maximum tip Mach number is thus 0.42 at S= 900 and the minimum is 0.28 at V = 270. The variation of angle of yaw over the rotor disk at a tipspeed ratio of 0.2 is shown in figure 12. The same contours can also be applied to any value of p, above 0.2 by placing a new outer boundary at a radius equal to 0.2/k times the original radius; the tip circle for p = 0.4 has been drawn in as an example. It is of interest to note that the regions which appear in figures 6 and 7 to be the most critical that is, the region of high power loss per unit drag coefficient on the advancing side and the region in which tip stalling is approached on the retreating side include relatively low angles of yaw. COiTFIDENT=W CONFIDENTIAL T'.CA ._ CR iTo. L.FIOS REFEElEICES 1. T'eLervii, Heal: Tets ii the Il:CA Tw'orimenricnal Lo r !Turbulence Tur nneil of Airfoil Secti iorns Desicnaed to Hav'e Sinuall Pitchin ri i',m rits and hjich Lif'tDr.a ;. tis. Ji.LCA CS 'Io. 511,, iA 3. . 2. I:ni .ht 'int .r.er and He FRalph : Statc thrustt An'i .'si .of t W U Lit 'tir.: Al"sa e ew U/IlCA 'THI lio. 2' lY37. 3. Baily, F. J. Jr. A .imrplil d T'hc.:oretical ine thod of D'eter.,,i.,inr t : Chari tc .r is tics ,f a Liftingt Rotor in c.r.wa d FI.it. i s ; .. Cer F. 71., i'7i. 4. aPIl ].., F. J., Jr. sar Gu3st s.n. F. F.: Charts for Es tim i aL ion of the Chis.c ti:ist ics of a Helicopter Rotor inr Forviary J F'li' lt. I p.ofile DragLift Ratio for Untwiste.j RictDanuler Bla.des. II.CA ACR io. LHC7, 1?<4. 5. Wh tle; Johin E..: An A'al ytic and E:.per imetnt1 3tudry of the Eff'ect of Feriodic Blade Ti''ist on the Thrust, Torque3, a :, Fi ,ppin '..otion of in utogiro ic tor. il. p:.. n. 591, l?17 u. Wheat iy, John E . : nr. t .e ody.akriilc ni lysi. of the Autogir ao Rotor iwiitlh a Coiimprison betn'een Calculated and Exeriimental Fresults. Ii'.LCA Rep. F!,. 437, 1 35. COF'?IDEI TIAL CO'FIDET l' TtL I.AC.A ;C Fo. Li.HO5 CCl T r 2iT IT L C/) E < " r'3 C, C' E C' I2 CI1 C HU C). I I O 0 r  i _ c.1E S S^ rr I * rri I I 0 : .. , .I . . ; .  5 .   SI 1 , 1 r Ci) i.i *l' T S ..I ,, u"' , .  ) I11 I. i u c 'I. 'I IU C_. *I. I 4 1 C J i I K 1 ""I I "' _  ' * I 4 ____________ 4_'1 * ***] *7 S ':: .l r,,?\  ** * i ,t, COI'FITDEi!T I.''L  'I r J I "' i . I I ..i I , 4 ' I i i0C I C ' .... ""' ,' r ,N ,, ;i rCJ CJ C'.~ C'.~C1 CC". u~ C' ~I r~j I J~i CT ic ,.I C1] N CN 4i o CL 4, 0 O II o o ;: 0 i* 41 ) C) cr, '4  i )I O 4H o 0 ' I ^ "C' 0 r c, c ~ ~ ~ ~2__ __ ~ _ _ I r ri ".C CR "o. LHC 5 '. L '. 4 ,., 1 I0 1:., :1 D., , ,J 1I. o r  I ,II I * I. I . E'' * II K E;   C T ., 'T, .I L r,~ , ^ I, I 1r1 , 3 ' I,, I4 L 1 ;j CI 01P FT" lT L NACA ACR No. L4H05 ,b .049 .07 I CONFIDENTIAL Fig. 1 CONFIDENTIAL Section anqle of a//acK (abs), cr deq F/ are APofiledraq curves used in the analysis. NACA ACR No. L4H05 20 NATIONAL AD ISORY S_ MMITTEE FOR A RONAUTI I Pitc angle, 8 (deg) _/ ....~t.9.  c 0 .2 rQ .6 .8 /O L Frmcf/on of vdJc/s, x Figure Z. ection /7ngl/e of attecK for three pAich hetfings. Jamp/ helicopter rotor /n hovering f//hht CONFIDENTIAL Fig. 2 CONFIDENTIAL NACA ACR No. L4H05 Of 1 I I II1 I I.I [IJIJ1I1 I I I 1 I 300 340 380 420 460 500 '40 S90 620 Tip speed, fps Figure 3. Rotor thrust For 260 slwft horsepower. Sarin hel/copeer in hovering Flght. CONFIDENTIAL CON:IjF IDENTICAL Fig. 3 NACA ACR No. L4H05" 2A Z40 2800 3200 Gross weight, /1 Airfoil 3600 Met wsh conwmtalul Grqp Rouyh conventional Arnl nooth #/A 3HS.5 Grap mooth NAt 23015 Grap NATIONAL ADVISORY COMMITTEE FOR AERONAUTIS 4000 Figure 4.Rjter ,orofiledray Ioss for a range of gross weight. Sample hehcopter; j,=42. ic. 2 14 / .7 R 2 & 5 2. 8 .036 /' I v /I. Pitch angle, 0 Omox at tip W/3 (tb/af) Airfoil Rough conventioand  Rough conventional Smnooth AA CA 3H135 /Smodth NACA 2390/ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS CONFIDENTIAL .040 Figure 6. Roatr ptof/1 dratlft ratlo as affected by loading. Sample hehcopter rotbr j.=O. . 460 f40 ti 0 1 /IQ thod ico/ ica/ /7 1.9 S.1 .ozl Methled Graphqcx AnGewco/ Graphical GrqA*cal @rvap'UcGI/  h ..JLL & L .0 OZ 28 .032 ZCr/ra S S,' wool 90 45 8 / ,/ *  L Figs. 4,5 CONFIDENTIAL 0 NACA ACR tlo. L4H05 Power lose (ftlb/sec/sq ft/O.Oicao) (a) Original solidity; X = 0.0385; Angle of attack (deg) 6 = 90; 0= 0.07; NATIONAL ADVISORY COMMFIFEE FOR AERONAUTICS (b) Increased solidity; X = 0.0350; 8 = 70; c= 0.10; Figure 6. Contours of power loss and angle of helicopter rotor and for an alternate rotor solidity and lower pitch. V = 55 miles per A = 2.5 pounds per square foot. S attack for sample with higher hour; I 0.2; CONFIDENTIAL S= 0.0321. oa 2CT oa = 0.0225. CONFIDENT. TIAL Fig. Fa,b Fig. 7 NACA ACR No. L4H05 0 0 I s 0L 00d 0 0 I gl o O4 o C, ; E4 420 1 i=) o : 4 1, o 0 : o ~~e o 00 0 V  4 I lci 40 Os SI i I S\ i, / / +, * 0 4 0a +7 +~ I $40 cuH go I I oI 4 NACA ACR No. L4H05 /.t OrO ~~lb Sectin atile of attack, or,,de Figure 6. Weghtng curves for reoresentatrve rwd, and for entire rcr. Sampl helicopter rotor; /O.B; 6 =9;9A= 0.038S. CONFIDENTIAL COiFI DEN TI AL Fig. 8 NACA ACR No. L4H05 I I I i I p LCO. R e9" A= o0.0385 6 u= 0 o K  N's PMMM I FOR O RONM cs_ S Z 4 6 10 / /4 A/ Section angle of attack w)., deg (a) Effect of tipspeedratw. W/,S=2.5;o'=0.07 4,=Of CCN :FIDENTIAL Figre 9. The effect of mnous changes in the qperni g coramfes Pd~geome~ rc characteristics assumed For hes saprLe vrota as shown hb the correspo mi/ weighting curves. CCNFIDENTIAL Fig. 9a 5x CONF IFDNTI AL 6 = 7" A= 0.03/0 2 W/12. I e =19 A=0.0385 4  9 A0.0469 NAT AL A VSORY S OMMI I E FOR Ai RONAI CS 0  A a M I_ IA 0 Secetir avgle of aftac, 0, dray IH I'r IU (b) Effect of loading. .0.2O a=a07oj =0. Figure 9. Continued. 1(3 NACA ACR No. L4HOG f CONFIDENTIAL NACAACR No. L4H05 6 4 2. 0 O 6 24 2. e= 9" A=003=5' 9= 7' A0.036L S IIA1NAL A ISORY SMM I FOR ENA ICS 0 4 6 6 0 I Section angle of attack, w.C, de (c) effect of solidity. 4~=&. W/S=Z.5 ,=0. Figure 9. Conmnued CONFIDENTIAL L( I.M t i l l f i l l l l i l i l l :=  Fig. 9c CONFIDENTIAL NACA ACR No. L4HOF. ,. 4.' 1 I l (s / A= 00680 4== O 0 4 6 /o 72 14, 16 Section argle of oatacrts, dae (d) Effect of blade twis*. A/ 0.3; WA,=2.5 OS0.07. NATIONAL ADMVSORY SCOMITUU FOR AEDOMAInIC iramsmedraq area 5" fs ,= /ao" A 'e.0680 I lul llE Sween angle ofttacmk deg (e) Effect of redaucton u# rewred power mt. 2i 3; W/S I ,s .=B6 Figure 9. Concluded. CONFIDENTIAL Fig. 9d,e CONFIDENTIAL Fig. 10 NACA ACR No. L4H05 _____s y o*\ 0 "j .IJ  .I " So ' z 0 o o 2 'I ... r I i I rri I , CV V I ____ __, ________ zLL ^ ^ ^ ^ o S>q 6ap/44 NACA ACF No. L4H05 Fig. 11 0 (a s o .. a a *r Ao r 0* t 0 *S 4 dW / H Owe 0 0 d r rr 2w d NACA ACR No. L4H05 Direction of flight Direction of rotation NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS Figure 12. Contours of rotorblade angle of yaw for A = 0.2. Angles shown are in degrees. Contours may be used for any tipspeed ratio p above 0.2 by placing a new rotor boundary (x = 1.0) at a radius equal to 0.2/& times the radius of the boundary shown for i = 0.2. As an example, the boundary for L = 0.4 has been drawn in. CONFIDENTIAL Fig. 12 CONFIDENTIAL UNIVERSITY OF FLORIDA 3 1262 08104 982 6 I ~.'Er.SiTY CF FLCFJDA DOCUMENTS DEPART MENT 120 MARSTCON SCIENCE LIBRARY ,:0. BOX 117011 \ .iAll 4JJ'JiLE, FL 326117011 USA \ 