légcsavar kísérletek

5/28/2018 lgcsavar ksrletek

1/143

N TION L DVISORY COMMITTEEOR ERON UTICS

TECHNIC L NOTENo. 834

C SETHE INFLUENCE OF BLADE WIDTH DISTRIBUTION

ON P R O P E L L E R C H A R A C T E N S T I C SBy E l l i o t t G. R ei d

S t a n fo r d U n i v e r s i t y

Wash ing tonMarch 949


2/143

NACA TN No 1834TABLE OF C o r n s

PageL5uImmYNTRODUCTION

MODELS PPARATUS AND TECHNIQUE

ZDUCTION OF DATA

ISCUSSIONesults of Force Testsesults of Wake Surveysnalysis of Influenc e of Width D is tr ib ut io nndependence of Blade Elementsi t c h D i s t r i b u t io n and Prof i le s

ONCLUSIONS

ables 1 7 ~ o r c e est ~ a t a )ables 8 14 wake Survey ~ a t a )

i e


3/143

NATIONAL ADVISORY C O W = FOR AEZIONAUTICS

THE INFLUENCE OF BLD&K~M H DISTRIBUTIONON PROPEIUZ CHARACTEHTSTICS

By E l l i o t t G. Reid

SUMMARY

Combined force nd wake survey t e s t s on three-b lade model pro-p e l l e r s have been made i n th e Guggenheim Aeronau tic Lab orato ry ofS tanford Univer s i ty to determine the e f f e c t s o f b lade-wid th d i s t r i -bution upon c o n s t a n t - s p e d e f f i c i e n c y c h a r a c t e r i s t i c s .

The blades of the v arious models di ff er ed widely i n plan form buta l l incorporated the same p i t ch d i s t r ib u t i on nd were of such wid thsa s t o make t h e i r a c t i v i t y f a c t o r s e qu al ; a s r e s u l t , a l l t h e model^exh ib i t ed subs t an t i a l ly ide n t i ca l power-absorp tion cap ac i t i es a t equa lp i t c h s e t t i n g s .The force t e s t re su l t s show tha t th e envelope ef f ic ienc y curvesfo r the s evera l types of b lades d i f f e r apprec iab ly on ly t advancer a t i o s l e s s t ha n 1 .0 and gr ea ter than 3 .0; i n those ranges the envelopee f f i c i en c i e s o f t h e b e s t o f t h e t ape r ed b l ad es a r e s l i g h t l y i n f e r i o r t o

thoso of bla des c har act eriz ed by approximate uni form ity of width. Onthe ot her hand, the constant-speed eff ici en cy curves 7 vs. v / ~ z o r f i x e dvalues of Cp diverge sub s tan t i a l ly as the advance r a t io s a re r educedbelow the value s a t which the maximum ef f i c i enc ies occur . A t these reducedadvance r a t io s , and a t a l l va lues of power coe f f i c i en t equa l t o o r g rea t e rthan 0.1, S lades t apered from broad r oo t s t o narrow t ip s a t t a ined g rea te ref f ic i en cie s than did those of r e l a t iv el y uniform width. However, a t powerco eff ic i en ts appreciably le ss than 0 .1 , the untapered blades were found t obe somewhat more e ff ic ie n t than tapered ones a t a l l advance ra t i o s .Simil ar , and only s l ig h tl y smaller , d iffer enc es of constant-speedef fi ci en cy were found when th e c ontinuously tapere d blades were repla cedby a compromise type i n which th e ro ot width was reduced t o a p ra c ti c a ll yacceptable value.

Analys is of the t hr us t and torque grading curves ind icat es th atthe more ef f i c ie n t oper ation of the ta pered blades a t reduced advancer a t i o s i s the r e su l t of r ed i s t r ib u t io n of losin which augments theprop ortion of th e t o t a l power input absorbed by th e inboard elementswhich continue t o funct io n ef f i c i en t l y a s th e outboard e lements approachand ex ceed t h e i r s t a l l i n g an g le s . While the sp ec if ic zause of th ein fe r io r i t y o f the t apered b lades a t smal l power coef f i c i e n t s i s note n t i r e l y c l e a r , it i s app ar en t t h a t t h i s i n f e r i o r i t y m ig ht be reduced


4/143

2 N C TN No. 1834

i f not e liminated by d iminishing the th ickness of th e inboard sec-t i on s of the tapered b lades which was unnecessar ily gr eat as a r es ul t ofthe use of geometr ically simil r pr of i l e s a t equal ra d i i i n models o fdi f f er en t p lan forms.

n inc ide nta l re su l t of fundamental ~ l ign if ica nce oncerns the theoryof blad e -element independence De spit e it s previous apparent ver i f ica t ionby the re su l t s of experiments i n which only the p i t ch d is t r i bu t io n wasvar ied , the theory i s de fi n i te ly not substant ia ted by the wake surveydata obtained with t he prese nt models of various plan forms.Corre la t ion of r es ul ts from t h i s inv est ig at ion with those of precedingstud ies ind icate s t ha t the incorporat ion of h ighly cambered pro f i l es

i n p rope l lo r b lades i s genera l ly undesirable and th a t the so-cal ledenvelope p i t ch d i s t r i bu t i on does not possess the mer i ts predic ted byex t rapo la t ion of p rev ious te s t re su l t s .

INTRODUCTION

The or ig in of the. pr ese nt in ve st ig at io n may be of more than usua lin teres t because it i l lu s t ra te s so c lea r l y the pe rvers ive tendency o faccep ted p rac t ices t o in f i l t ra t e a f i e l d of knowledge and , a s the re su l tof long usage, t o achieve the undeserved s t a t us of fea tur es of sc ie nt i f i -ca l l y proven meri t .I n 1943, th e wr i te r ca l le d a t te n t i on t o c e r t a in marked d i f fe rences

between th e constant--speed ef fi ci en cy curves f o r two model pro pe ll er s~ ~ h i c h ,n h i s op in ion , d i f fe r ed s ig n i f ica n t l y on ly i n the p lan fo rms ofth e ir b lades . The minor inf luence genera l ly ascr ibed t o t h i s designparameter le d t o vigorous contrwvlrsy over th e ch ief cause of thediff eren ces but t h i s , i n th e end, proved inconclu sive. However, th ed is cu ss io n d i d s er ve t o e s t a b l i s h t h e r a t h e r s t a r t l i n g f a c t t h a t , a f t e r40 years of su ccessful screw propulsion of a irp lan es, the e ff ec ts ofblade-width d i s t r i bu t i on upon propel ler ch ar ac te r i s t ic s remained sub-s t a n t i a l l y unlsnown. Thus, both the plan f o m i n general use and thebasic concept of width d i s t r i bu t i on as an unimportant design factor wereseen t o have gained unwarranted acceptanceRecognition of t h i s lac k of fundamental inform ation, and of th e

p os s ib il i t y of improvement by means hit h er to unexplored, le d t o th e studydescribed i n th i s repor t . This inve st ig at io n was co~lducted nder thesponsorship and with the financial assistance of the National AdvisoryCommittee f o r Aeronautics.s ex is ti ng information on the su bjec t of plan-form influence i sla r gel y th at der ived from t e s t s of f ixed-pi tch models ( re ferencest o 8) and i s fu r the r complica ted by va r ia t ion of th e ac t iv i t y fac to r i n


5/143

NACA TN No. 1834

a l l cases, the present exploratory program had t o be based, i n the main,upon such inferences as could be drawn from the single aforementionedcomparison. n that case, two model propellers characterized by practi-c a l ly ide n t i c a l a c t iv i ty f a c to r s and barely distinguishable efficiencyenvelopes exh ibit ed marked di fference s of constant-speed ef fi ci en cyrl a t p = ~ o m t a n t ) t reduced advance ra t io s . The one which developedthe greater effi cien cies i n th i s range had blades i n which the width ofthe intermediate portion was subs tan tial ly greater than th at of ei th erroot or tip, whereas the width of the inferior blades was much more nearlyuniform. Upon th e bas is of thes e few fa c ts , th e models described i n theprese nt paper were designed t o enable exp lor atio n of th e ef f e c t s of con-tinuous taper from ro ot t o t i p and those of ta pe r from an intermediatest a ti o n toward both extremities.

disc area, square feet r r ~ ~ / 4 )diameter, feett i p r ad iu s, f e e tradius of element, f ee t see als o defi niti on of a. )radius r a t i o r h )width chord) of element, f e e tm a x i m thickn ess of element, f e e t

pi tc h angle of element, degrees ref eren ce chord)pitch angle of element, degrees reference l i f t ax is)pi tc h angle of t i p element, degrees

angle of yaw, degrees

veloci ty, f ee t per secondlip stream velo city , f e e t per second

a x ia l component of Vstangential component of Vscoef fici ent of induced ax ia l vel ocit y note: + a = r


6/143

NACA TN No. 1834

a i r densi ty , s lugs per cubic footr e l a t i v e a i r density (p/po)

S.P. s t a t i c p l a t e pressure d if ference , pounds per square foo t(q 1 046 s.F.)q p@/2 qw pw2/2 E qw/qEl 2 succ essi ve approximations of

n ro ta ti v e speed, r evol utio ns per secondv / n ~ advance ra t io V/S J

Po s t a t i c p r es s we a t upstre am face , pcnmds per quar re f o o t

P s t a t i c p r e s s u re a t downstream fa ce , pounds per squase fo o t.LP inc rease of s t a t i c pressure, p o ~ ~ ser square foot pl po)P to t o t a l p re ss ur e in undistu rbed stream, pounds per square foo tPt l t o t a l p re ss ur e a t dam stre am face, pounds per square foot;*pt increase of t o t a l pressure, pounds per square fo ot kt pto)AP1, AP2 successi ve ap pr ox ha ti on s of P

pu t o t a l pyessure on upstream1 tub e of yaw head, pam ds persquare footpa t o t a l pr es su re on downstream1 tub e of yaw head, pcr~Jldspersquaxe footp~ yaw-head pres sure di ffe ren ce , pounds per squ are fo ot (P, Pd)

with refersence t o tan gen tia l vel oci ty normally imparted to slipstream .


7/143

NACA T No. 1834

ap valu e of -Pyo i n und istur bed streamK yaw-head constant (K = pv/sin 2

T thrust, poundstorque, pound-feet

P pwier input, f at-pmnds per second

TO i n t egrated th r us t coeff i c i en t2

sp inner th rus t coef f i c i en t(~ bs o l u t e a lues ; spi nner t h ru s t i s act ual ly negat ive. )

CT th r u s t co ef fi ci en t (T/pn2D4) CT = C T ~ mT)c~ torq ue coeff ic ie nt 2 (Q/Pn2D9 f = l * ( d C Q / ~ ~ )0.15C~ p w e r coe ffi cie nt (P/pn3D5) (cp = zrrcQ)Il ef f ic iency ( c ~ v / c ~ ~ D )

dT th r u s t of a l l elements a t radi us r po~mdsdQ torq ue of a l l elements a t rad ius r pound-feetIle ef fi ci en cy of element

A.F. a c t i v i t y f a c t o r

%pper l i m it nominal; inte gra t ion extended t o include en ti re are aenclosed by curve.


8/143

NACA T No. 1834

Seven +blade, adju stab l4-pit ch, mtal, model propellers of 2.80-footdiameter were designed and cons truc ted fo r use i n th i s inves t iga t ion . Ofthese, six (models o 6) di f f er only i n plan form, that is they haveide nt i c a l d i s t r ibu t ions of p i t ch and t h e i r p r o f il e s a t e qu al r a d i i a r egeometrically similar. Because the profi les and p i t ch d i s t r i bu t i on i nco r-porated i n these models differg somewhat, f r o m any previously testedunder s b i l a r condit ions, the tr an si t i on type, model 7, which di f fersfrom model 6 only i n prof i l es , wa s added t o th e se r i e s t o enable corre-l a t i on of t he p r esent t e s t r e s u l t s wi t h t hose of p r ev i a s i nves t iga t ions .Examples of all six p lan f o r m m e i l l u s t r a t ed by photograph ( f i g . 1 ) .The ra d i a l d i s t r ibu t ions of b lade width fo r models 1 t o 5 wereobtained by systematic dis to rt io n of one quadrant of an el l i ps e. 3 Thebasic blad-idth curves4 of fi g ur e 2 a r e defined by th e equation?

i n which coe- l (rD) . The var ious a d e l s ar e characterized by t h sfol luw ing va lue s of th e exponents and c:

The ac tua l blad-idth c m e s fo r models o 5 ( f ig . 3) were obtainedby multip lying the ordin ates of each of t he ba sic width curves by theconstant required t o make the corresponding ac t i vi ty f ac to r equal t o92.4 which i s the value of tha t quant i ty fo r the conventional plankorm incorparated i n model 6 he ac t i vi ty fa cto rs were equal ized wi thth e object of insuring, inso far as i s poss ible by the use of a simpledes ign cr it er io n , equ al abso rption of power by th e se ve ra l models ilndercomparable conditions of operation. The a rb it ra ry di st ri b u ti dn of widthi n model 6 i s a l s o i l l u s t r a t e d b y f i g u r e 3.

3The el l ipse w a s se lec ted as a basis only because it can be s o conven-ien t ly modif ied t o y ie ld t aper ch arac ter i s t i cs of the des i r ed v&rie ty .'~ n e q u a l sc al es have been used t o enELmce th e resemblance between t h ebas ic nd ac tu al width curves.h e n s and c 0, (1) becomes th e equat ion of a c i r c l e bu t t h eintroduction of an ar bi t ra ry constant t o obtain normal widthr a t i o s t r a n s f o r m i t i n t o t h a t of an e l l i p s e .but lo zsed f o r model 7; previously incorporated i n the mem3ers of t he

U nd %se ries of references 9 and 10.


9/143

NACA T No. 1834With,reference t o the var ious width dist r ibu t ions, the fol lowingfe atu re s ar e noteworthy:

(a) 'The se v er it y of continuous taper diminishes progressivelyfrom model 1 o model 3.(b) Model 3 i s of more ne ar ly uniform width nd has a broadert i p than th e conventional model 6 (Note, hawever, t h a t th e out-board portion of model 6 i s wider than the shank.)(c ) The t i p s of models 1 4 nd a re more sev erely tapered thanthose of the other models and differences between the width distr i-but ions f or these three ar e l a rge ly confined t o the inner por t ions ofth e blades.The thickness nd pi tc h dist r ibu t ion s f o r models 1 o 6 are def ined

by f igure 4; NACA l h e r i e s p ro fi l e s of 0 7 desi gn l i f t coe f f ic i en t havebeen' incorporated throughout th e len gth s of th ese b lades.M d e l 7 i s dist inguished f r o a n model 6 only by differences betweent he i r p r o f i l e s . Those of model 7 m e i den t i ca l wi th the ones used fo rt he U- nd E-series blad es of refere nces and 10, th a t i s l k e r i e st i p s and roots are separated by a cen tral por t ion i n which Clarkprof i l es a re incmpora ted . The thickness- and p i t c k d i s t r i b u t i o ncur ves f o r md e l 7 w i l l be found i n f ig ur e 4The p i t ch d i s t r ibu t ion fo r a l l seven models i s the so-cal ledenvelope type; th e equation of th e t w i s t curve i s

The curve s o def ine d i s the envelope of the t w i s t curves(pt pTt against x) for a l l pro pe ller s of uniform design pi tch.During te s ts , th e hubs of a l l models were enclosed within a spinnerof th e form shown i n fig ur e nd the aper tures fo r th e blades weresealed by clo sely f i t t e d masks.

APPARATUS ND TECHNIQUE

The expe rim en ta l work, which wa s conducted i n th e 7.3-foot windtun nel of Stanford s Guggenheim ~ e r o n a u tc Laborat m y (reference 11)cons is t ed i n m king r ou t i ne f o r ce t e s t s nd complete surveys of thewakes of a l l seven models, each of which wa s tested, successively, a t


10/143

8 NACA T No. 1834

six pi tch angles . The force nd s l ips t ream pressure o b se rv a t iw werenzde sFmu1tanemsl.y.Models were d ri ve n by th e customary pr ope ll er dynamometer ref er-ence l l ) , which w a s improved, p ri or t o th e presen t te s t s , by some refine-ment of i t s shrouding and by the subst i tut ion of automatic e lec tr icbalances f o r the manually operated ones previously used f o r th ru st andtorque measurementThe character nd ge ne ral arrangement of th e wake survey appa ratu si s i l l u s t r a t e d by f i gu r e s 5 t o 8. The combined total-head nd yaw tubeswere i n s t a l l e d i n 3 r a d i a l rows of 1 0 tu be s each; ow extended ve rt i-ca l l y ab0t.e the pro pel le r sh af t while th e other 2 were symmstricallyarranged a t angles of 45 below the horizontal . Corresponding tubes ofeach row were located a t equa l r ad ia l d i s tances from t he s ha f t axis andthe t i p s o f all tub es were 0.0m behind th e plane of th e blade axes.Recognit ion of the extreme sen s i t i v i t y of survey-determined thrystand torqu e t o nonuniformity of th e dynamic and t o t a l p r es s ur e s of t heundis turbed s tream? indica ted the d e~ t i ra b i l i ty f carrying the re f in-ment of f r e e s t r e a m c ha r a c t e r i s t i c s t o t he l i m i t of pr a c t i c a b i l i t y andthen minjmizing the er ro rs due t o res id ua l nonuniformity by averagingmult iple observat ions of the s l ips t ream pressures a t each radius.Reads stment of th e de ns it y of return-passage ssre ens nd ins ta l -l a t i o n of a boundary- layer-remo~al device a t th e t i p of the entrancede flector. r e su l ted i n small, but worth while, improvements i n ve lo ci tyand tot,al-head di st ri bu ti on s a t the t e s t sec t ion . The ~ ~ X ~ M U Uvari-a t i on of t he c i rcumferen t ia l averages of t he t o t a l heads a t e ightpoints on each of a se r ie s of concent r ic c i rc l e s having ra d i i of 4.5t o 22.5 inches w a s reduced t o 20.006q, while corresponding v ar ia ti o nof the dynasnlc pressure w a s even smal ler outs ide th e 8. 5i nc h radiu swhich appeared t o t e th e l i m it of spinner inf luenceO8 Three banks ofyaw heads were then installed and interconnected a s explained i n thefollowing paragraph; t h i s mrangement enabled dir ec t recording of theaverages of th e slip str eam pressur ea t orrespo rding po.i_nts of th re er a d i a l l i n e s . The banks were spaced a t angular intervals of 135O, go0,and 135O t o pre clude simul taneou s impingement of t h e wakes of two rnore b la de s upon th e s urv ey i n s t m n t s .Ninety small copper tu be s 0.090 in., O.D.; 0.030 in., I .D.)

t ransmit ted the presw nes f r om th e yaw heads t o a multiple manifoldf ig . 7) which co nsi ste d of t h i r t y four-way connections. The t h r e e t ube s

7 ~ i ~ c u ~ ~ e an re fe rence 10.8~ etw een a d i i of 8.5 and 4.5 inches, q i nc rea ses by 2 5 percent.


11/143

NACA T No. 1834communicating with corresponding elem3nts of th e t h ree yaw heads a t eachra di us were interconnec ted a t th e manifold and the average press.De w a st ransmi tt ed to a si n g le column of th e rec ord ing manometer by a t ub eattached t o the remaining branch ~f each f o p w a y connection.

The yaw- and total-head tubes used i n the se t e s t s are, themselves,th e re s u l t s of soclewhat exten sive resear ch. In reference 10, thefa i lu re o f coiiventional shielded total-head tube s t o func tion sat isf act o-rily behind a st a l l e d model was ten ta t i ve ly ascribed, a f t e r strobcz-scopic otservat ion of the behavior of wool tu f t s , t o periodic inter-rup tion of continuous flow throcgh th e s hi el ds due t o the occurrenceof v ery l ar g e ang les of yaw i n th e highly turb ule nt wakes of t he blades.t w a s al s o suspected th a t t he range of angle of yaw with in which suchtubes give re l i ab le indicat ions of t o t a l head might be appreciablyreduced by f luctu at io ns of veloc i ty , even i n th e absence of di re ct i on alvar i a t ions . The ta s k of d eveloping a total-head tube su bs tan tia l lyf r e e of t he se de fe ct s throughout t he range of a ngle of yaw between-20 and 90 was th ere f or e undertaken and, a t t h e same time, improve-ment of th e cal ibr at io n cha rac ter i s t ic s of the previously used type ofyaw head w a s sought. The most s ign i f i can t res u l t s of t h i s a ux i l i a r ystu dy m e summaf.ized as f allows

Tests of a shie lded total-head tube o conventional type showedt ha t , i n flow pu l sa t ing a t a frequency comparable t o th a t of t hepassage of blad es during model te s ts , the ra ng e 9 wi thi n whichPt/q = 1.0 was reduced from th e steady-flow va lue of f60 t o one of250 . However, th e e f f e c t of such pu lsa tio n upon the valu es ofa t which pt/q = 0 was fomd t o be prac t i ca l ly neg l ig ib le .

No ma ter ial improvemant was ef fe ct ed by al te r in g e it h e r the s iz e ofthe length-diameter r a t i o of a sh ie ld of conventional ven tur i form. 011th e other hand, the use of a highly cambered pr of i l e f o r the ve nturi w : ~(type B, f i g . 9 ) w a s found t o be d ef i n i t e ly benef i c i a l .b c h more su bs ta nt ia l improvements were ef fe ct ed by th e use ofasymmetric sh ie ld s which, although un sui tab le fo r so m purposes, a r een t i re ly sat i sf ac to ry fo r propel ler wake surveys because th e lo ca l anglesof yaw which occur within the po si t iv e range of t o t a l th ru st a t t a i nla rg e valu es of only one sense 9 The f i r s t unsymmetric types i nv est i-gat ed were n ~ d erom co~ivent iona l en tur i sh ie ld s by c u t t ing of f t h e i rends obliquely and the n restorling smoothness of th e i nt e rn a l contours

by hand-filing. The improved ch ar ac te ri st ic s obtained by tru nca tingboth ends a t angles of TO0 with respec t t o the ax i s a re shown in f ig ure 9(type c , but th e mechanical d if f ic u l t y of a ccur ately dt lpl icat ing such~ t symmetric s h ie ld discouraged i t s adoption. t was recognized that9True everywhere except a t t h e bo-undizry o t h e slipstream and erroneous

th er e only when th e t i p elements produce considerab le negativ e th ru st .


12/143

10 NACA T No. 1834

substantially identical characteristics might be obtained by obliqueorienta tion of spmmtrica1l.y shielded total-head element with r e f e ~ence t o the xis of t he yaw head but t he proba bi li ty of consequentadverse eff ec ts upon th e ca li br at io n of th e yaw head i t s e l f lllade t h i salternative seem unattractive.

A s t m l t a n e o u ~ olutio n of the problems of interference ndrep rod uci bili ty was fi n al ly found i n th e half-venturi shie ld which i sdesignated as type D i n f i v e 9. Sudh shields are readily dupli-cated by using formed reamers t o shape complete ven tu ri s which ar ethen milled off t o th e i r planes of symmetry, nd they exercise noappreciable inFluence on th e di re ct io n of flaw a t th e ti p s of t he yawtubes. Moreover, they were found t o possess th e be st c al ib ra ti onch ar ac te ri st ic s of any type tes te d. The curve f o r type D shown i nf igure 9 i s applicable t o an iso la ted total-head tube of t h i s form,but th e r el at iv el y s li gh t adverse eff ec ts of combination with the yawhead may be seen i n f igure 10 where the ca l ib ra t ion c m e s fo r t he cowpl et e prototype instrument ar e reproduced. The intr odu ctio n of pi tchangles as great s flo0 had no perceptible effect upon the totalpressu re cali br ati on , but, a t negative angles of yaw, th e device i ssomewhat se ns it iv e t o changes of loc atio n of th e shi eld with respec tt o the to ta l-pressure orif ice .

lznprovement upon the ca li br at io n ch ar ac te ri st ic s of th e yaw headsused i n previous wake surveys (reference 10) wa s sought through fu rt he rstudy of t i p form. The e f f e c t s of bevel angle, diameter of bore, andwidth of f l a t a t th e mouth of th e bore were Investigated r at he r thoroughlyand although no sp ect acular improvement was ef fe ct ed , some be ne fi ts wereobtained by changes of bevel and bore. Det ails of th e farm of t i p incorpo-ra te d i n th e present yaw heads a re given i n figu re 10 where the corre-sponding calibration curve i s compared with that of the older type.A s th e r es u l t of un sat isf ac to ry experience with yaw heads whichconsisted, essentially, of three sm ll st ee l tubes soldered together,th e much more su bs ta nt ia l design shown i n fi gu re 10 was adopted f o r t h i sinvestigation. The photograph ( f i g 11) i l l u s t r a t e s how the sep arat elyfabr ica ted t ips nd sh ie ld a re accurate ly loca ted by a j i v o h i n e d ,so li d brass body i n t o which they and th e thr ee pressure li ne s a re sweated.The body i s l i gh tl y pressed i nto the s tou t s te e l tube s tem and securedby a s e t screw. A shoulder on th e stem r e s t s upon a spot-faced su rfacea t th e mouth of a hole reamsd through th e w lls of th e supporting tube

t o insure correc t lo cati on of t he assembly; collapse of t he s lo tt ed endof th e stem under pressur e of th e anchm ing nut i s prevented by plug.Although t h i s constr uction involved considerable p rec isio n work, tproved eminently sat is fa ct m y; no disturbance of th e del ica te pressurebalance of the yaw hsads wa s detected during the entire investigation.The technique of re cording th e wake survey da ta con sisted i nphotographing the multiple manometer with 3 m l l i m e t e r camera. naddi tion t o to ta l- and yaw-head pre ssures, a pressur e di ff er en ce ofprecise ly known magnitude and one proporti onal t o the Qm mi c pressu re


13/143

NACA TN No. 1834

of t h e wind s tre am were imposed u p o ~ anometer columns a i i recorded i neach photogaph so th at th e records would be sel f-suff ic ient , th at isen t i re ly determinate wi thout refe rence t o th e manometer l iq uid densi ty .linprovements i n illu mi na tio n nd the use of a fae t l ens permi t t edrecording on Microf i l e f i l m a t l/50-second exposure wit h f 2.8 ap ert ure ;negatives characterized by high contrast nd shmp meniscus de fin i t i onwere th us obtained. Such recorm dswarranted fu rt he r refinement of t heproject ion-measuring equipmnt described i n referen ce 10; a micrometerscrew, equipped wi th d i re ch re d i ng , geared c o ~ n te r s a s subs t i t u t edf o r th e previously used vernier-read sca les . The over-al .1 r e s u l t ofth es s improvements was t o enable th e s cal ing of pressure recor ds t obe repeated with an accuracy of kO 001q when q 10 pounds persquare foot and with inversely proport ionate accuracy a t smaller valuesof q.

Percept ible interf eren ce e ff ec ts due t o the presence of the wakesurvey apparatus were sh am t o be nonexistent by fa rc e te s t s made beforeand a f t e r i t s i n s t a l l a t i o n .

T ST PROGE?AM

n accordance with reg ula r Stamford pract ice, th e model pro pel ler sof t h i s se r i e s were t es t ed a t fix ed ro ta t i ve speeds and th e advancer a t i o w a s va rie d by changing th e airs pe ed. Each modolL was te a te d a tthe fo l lowing p i t ch se t t ings and rotat ive speeds:

Speed, rpm 2100 2100 1740 1470 1056 7

The a irs pe ed s ranged from approximately 90 mil es p er hour down t olowest values a t which s ign i f ic ant for ce readings could be obtained.Since the maximim h c h number a t ta in ed by the t i p e lements w a s approxi-mately 0.3, t he e f fe c t s of compress ibi li t y upon the t e s t res u l t s a reconsidered t o be negligible.A s has been customary i n the p ast , two complete for ce t e s t s

coils isting of 1 0 t o 24 s e t s of obs erva tions ) were made a t each bladese t t i ng a id the advance ra t i os u t i l i z ed i n one t e s t were s taggered wi threference t o those of the other . Wake s urvey d a ta were recordedsimultaneously wit h each observatiorl of f or ce d at a duri ng one of eachpa i r of t e s t s . The number of manometer records so made was unneces-sarily large, but i t w a s thus insured th a t th e l im ited number requiredt o i l l us t r a t e s i gn i f i c an t var i a t io ns of b l ade load ing would be ava i l ab lefo r reduct ion t o numerical and graph i ca l fo rm . These records wereCBoxlinal blad e ang les a t 0.75R; ref er enc e, chord.


14/143

12 NACA T No. 1834se lec ted by refe rence t o the fo rce te s t cumes; th e i r number va r iedfrom 6, when th e pi tc h s s t t i n g was 12O, t o 14 when 60,

REDUCTION OF DATA

The for ce t e s t d at a have been reduced t o th e usu al nondimensiomlforms

and

I n th e i r eva lua tion, the only correc t ions appl ied were those requiredt o ad jus t the messixred t hr us ts t o t he values which would have prevailedhad th e pressure on th e back of th e spinner been exactly equal t o thes t a t i c pres sure of th e wind stream. The valu es of these corre.ztions(of neg l igi ble consequence except i n the case of high pi tch se t t in gsand la rge a d m c e ra t io s ) were de te rmined by calculations based on pres-sure observations.The constan-dspeed ef fi ci en cy cu rves were co nstructed i n accordancewith the method described in reference nd i l l u s t r a t e d by f i gu r e 27

of t ha t r epor t.The wake survey reco rd s were tran spo sed from photographic t onumerical form by means of the improved projectiozwmasuring appmatusor ig ina l l y desc ribed i n re fe rence 10 . This equipment enables directtab ula tio n of th e s l ips tream pressures i n terms of dynamic pressure,t h a t is PT1, r a t h e r th an Ptl, i s read d i re c t ly f rom the pro jec ted

record, These data, tog ethe r with th e re s u lt s of f ree-s trem yaw-and tota l -head ca l ib ra t io ns , suf f ic e f o r th e evalua t ion of e lementarytorque nd th ru st co efficien5s by use of th e formilas

Complete de ri va tio ns of th ese equations ar e given in referenc e 10.


15/143

N C T No. 1834 13

For th e ev alu atio n of dcQ/dx, th e experime ntally determined va lue sof y were cor rec ted by deductiori of th e small amounts of yaw-head-pressure unbalance recorded dur ing f i n a l cal ib rat ions i n the undisturbedstream. These correct ions, i n th e cases of all bu t one of the groi:ps ofth re e heads, corresponded t o an average misaljneaent of less than 0.1'and were accepted as pra ct ic al ly unavoidable because th ei r e l iminat ionwould have required prohibitively laborious adjustment

I n connection with th e eva luation of dcT/dx, at te nt io n i s ca l l edt o t he f a c t t h a t P i s l e s s t h a n AFT, t he increase of to t a l pressurecaused by the propeller, and t h a t i t s value m a t be deduced from th a t oft he l a t t e r by aux i l i my ca l cu l a t ions ll n reference 10, th e di f ference

was approximated by assuming t h a t t he induced a x i a l inf low ve loc ity whichwould correspond t o uniform di st r i bu ti on of th e mea~tured o t a l th ru stprevailed a t a l l poin ts of the prop eller disE. n the present calcu-l a t i ons , E i s evaluated by a process of suc cess ive approximationswherein the a x i a l inf law veloci ty i s deduced from loc al , ra th er thanaverage, values. This nethod i s out l ined as follows.I n appendix I of reference 10 it i s shown that

Since the values of y and K a r e known, th e dete rmina tion of r(or 1/4r2) enables the evalu ation of E. (1t should be noted thatr a and th at a i s the ax ia l inf low fa cto r . ) The rela t ion shi pbetween r and h fur nis he s th e key t o th e problem; it i s derivedas fol lows.

By equat ing the al te rna t ive expr6ssions fo r the th ru st of the bladee l e ~ e n t s t a given radius

This refinement of previous pa c t i c e was introduced i n refere nce 10;the d i f f erence E (equation 5 ) ) re p ~ e s e n ts he dynamic pressurewhich co~-respo;?ds o th e ta ng en ti al v el oc it y of th e s1ips.trea.m ju stbehind the propeller.


16/143

INACA TN No. 1834

d

th e thrust-producing pres sure dif fer en ce may be expressed as

~p 2p a(1 a 9whence

2a a ap/2p (10)

Introduci% AP /q ' & l ~ / p ~ ~ ,quatian (10) becomes

Theref ore

Se lec t ing the poa i t ive s ign so tha t r > when AP > 0,

and

Thus th e lo c a l value of 1fir2 i s seen t o be f u l l y determined by th atof AF The method of ev al ua ting AP by succ es sive app roximat ions cannow be described i n d et a il .Taking an expe rim ent ally determined va lue of APT as a rough

appox i m t i on o f AP the correeponding value of 1/4r2 i s obtainedfrom a curve of 1/4r2 ag ai ns t AP prepared by use of equation (14).Int roducing th i s value in to equation 6 ) , along with t he experimental lydetermined value of Py for the same stat ion, a f i r s t approximationof E (i.e., E ~ )s obtained. Sub tract ion of l from yieldsthe f i r s t r e a l approximat ion of LIP ( i e , A P ) ~h~ process is nowrepeated by using aP1 f o r determina tion of a second approximationof 1/4r2; E2 i s then obtained by use of equation (6) and subt ractedfrom .QT t o o bt ai n 4 In a l l bu t cas es which involve ve ry unusua lvalues of APT and Py, subsequent repet i t ions of the process yieldvalues of AP indist ingui shab le fr on th at of AP2. The method is ,ac tua l ly , no t near ly so l ab or i ms as might be in fe r red f ro n i t s


17/143

NACA T No. 1834 15de sc ri pt io n because th e lac k of nec ess ity f o r even a second approximationcan fre que ntl y be determined by inepection.

A sample record nd the corresponding computation sheet, which arereproduced as f igu res 12 and 13, r e spec t ive ly , i l lu s t ra te the reduc t ionof a complete s e t of wake m v e y da ta fo r a si ng le conditiorl of operation.The da ta read from th e photographic record a r e the values of PT1, PU,nd PD' The va lu es of PTO (which vasy s l i g h t l y w it h q) nd those

of a y ar e obtained from th e re s u l ts of free-stream cal ibr ati ons . Thevalues of CTO and Cg ( loxer r i g ht corner of computation she et) ar eobta ined by in te gra t io n of the t hr us t nd torque grading curves. Forcomparison of the t k m s t coe ffi cie nt determined by dl re ct (dynammeter)measurement with that deduced from a wake survey, CTO must be reducedby the am~untaT ecause m e y s gi ve no m i c a t i o n of sp in ne r drag 12

The ch m ac te ri st ic s of th e seven models, as establ ished by rou tin efo rce te s t s , a re shown i n f igu re s 14 t o 20; each of the se logarithmiccha r t s dep ic t s the cha ra c te r i s t i c s of one model a t s i x p i tch se t t in gs .The corresponding numerical data w i l l be found i n tab les o 7.Wake survey re su l t s a re presented i n the f o r m of th ru s t and torquegrading curves. Each of t he c har ts (f i gs. . 2 l t o 32) contains th e curvesf o r models o 6 a t a s ing le p i tch se t t ing ; f igu re s 33 nd 34 pressnt

s im ila r d a ta fo r model 7, the t r an s i t i on model which d if fe rs f rom th eo th er s i n bl ad e p r o f i l e s . In t h e i n t e r e s t of c l a r i t y , t h e d e f in i t i v epo in ts ar e shown on only two s e t s of curves but the se examples (f ig s. 25and 26) may ser ve t o emphasize th e f a c t t h a t th e grading curves have beenfaithfully drawn through a l l p lo t ted po in t s nd a re , the refo re , no t t obe in terpre ted as f ai re d r e s u l ts . S in ce t h e s c a le of t he s e c b t s i snecessa r i ly small and because th e da ta a re be lieved t o be of pot ent ia lvalue fo r th e analysis of vasiaus propelle r problems, numerical re s u l tsa r e a l s o p re se nt ed i n t a b l e s 8 t o 14DISCUSSION

The recognized ef fe ct of so li di ty upcn the constant-speed eff ici enc ych ar ac te ri st ic s of pro pelle rs made the prin cip al problem of designingb la de s f u r t h e pr es en t e x p e r k n t s that of in su ri ng th a t t h e moCels ofvarious plan forms would absorb substantially equal amounts of po$er underspeci f ied opera t ing condi tions. The se l ec t ion of equa l i ty of the ac tP > i ty'*Fo~ discussion of corre ction nd exper imenta l da ta re la t i ve t o drag ofth e spinner used i n these t es ts , see reference 10, appendix 111


18/143

16 NACA TN No. 1834f a c t o r s as a design cr i t e ri o n a.ppeared t o be reasonably well jus t if ie dby empirical data and, as no more dependable one wa s known, th e bla dewidths were adjusted upon that basis.

The measure of su cces s achieved i s i l l u s t r a t ed by f igu re 35 i nwhich the power co ef fic ien ts at ta in ed by models 1 o 6, under conditionsapproximating those fo r maximum efficiency,13 have been plot ted againstpi tch angle. In order t o avoid confusion, only th e most widely sepa-ra te d curves a re shown; th e positi ons of th e intermediate ones a r eindicated by the coordinates tabulated on the C h a r t As t h e d u e sof Cp d i f f e r by l e s s t han 10 percent a t all but +,he lowest p it chse t t i ng , it i s bel ieved th at effect ive sol idi ty 1 ' as measured by powerabsorpt ion a t maximum eff ic iency has bean equalized t o n ex ten t whichprecludes the ascribing of ny major difference between the character-i s t i c s of th e various models t o t h i s saurce. Thus blad-idth d is tr i -bution must be accepted as th e primary, i f not exclusive, cause of anyconsequentia l var ia t i on of p ropert ies revealed by the te s t res ul t s .

Examination nd ana lys i s of the t e s t da ta may well be prefaced bycomparison of th e re s u l ts of f or ce t e s t s and wake surveys. Whereasre la t i ve ly sa t i s fa cto ry agreement between for ce and survey t e s t s hasbeen obtained i n previous work involving pro pe ller s of small and moderatepi tch (references 10 and 12) , t he on y surveys which have been made ofth e wakes of high p i tc h models l e f t much t o be d esire d (see f ig s. l2t o 19, reference 10) In fact, under conditions of fully stalled ope*a t i o n a t high pi t ch se t t in gs, th e disagreement wa s so se r ious that eventhe qua l i ta t ive s igni f icance of the corresponding thrus t and torquegrading curves appoared doubtful. In th e present instance, improveapparatus nd te chnique y i e l d t he g ra t i fy i ng r e s u l t s i l l u s t r a t ed byfig ur es 36 t o 38; these cha rts pe rt ain t o the extremes of the plan-forms e r i e s and include one va ri at i on of' pro fi le , th at is i n model 7.

It w i l l be se en t h a t th e power c oe ff ic ie nt s determined by wakesurveys are in excel lent agreement wi th fo rce t e s t r es ul t s under a l lcondit ions and th a t such discrepanc ies of t hr us t a do occur are ofr e l a t i v e l y small magnitude and a re confined t o the lowest ranges ofadvance ra t i os . With reference t o th e thr us t discrepancies, exami-nat ion w i l l revea l that except in the case of model 7, the systematicdevi at ion which occurs a t low advance ra t io s with sm all and mediumpi tc h angles disappears when the se t t in g i s i ncreased t o 4 8 O and 60 .This obvimxsly precludes asc rip t io n of the e rr or s t o blade st al l in g;th e i r probable source is indicated by the fol lowing tabulat ion.1 3 ~ h e lot ted values of C p a re tho se a t which the experimental curvesof Cp against v / ~ D i n t e r s e c t th e s t r a i g h t l i n e 1 1 which appearson each of the logari thmic cha rts (f igs . 14 t o 1 9 ). This i s t heLine I m ed i n ana ly s i s of th e res ul t s presented in references 9and 10; i t clo sel y approximates the locus, i n the v / ~ D , p plane, ofthe points of maximum constant-speed efficiency a f l / a ~= 0 ) f o rpropel lers wi th three blades of a ct iv i t y fact or 92.4. ( s ee f i g . Dreference 9. )


19/143

NACA TN 30. 1834

M XIMUM F EF3XCTTCTE TOTAL PRESSUIiEAT MINIMUM ADTCWCE RATIOS OF WPXE SUIiV YS

Since th e values of AF2 m e id en ti ca l with those of the lo ca lFroude thrus t coeff ic ients (cT1 T / ~ A , i t i s c l e a r t h a t t h ediscernable errors of thrust determination occur i n conJunction wi thh igh s t a t i c p ressu res in , and severe contrac t ion of, the s l ips tream.It may prove di f f i c u l t t o elimin ate wake survey er ro rs under suchconditions as these.

The cause of th e th ru st discrepancy i n th e case of model 7 a t t h e60' setting is as yet, undetermined. S ince t he re ~ lu l t s o r model 6exh ib i t a similar pec uli ari ty, plan form, ra th er than pro file , wouldappear t o be i n so4w way re sp ow ib le but th e be tt er agreement obtainedwith model 5 , which also has =row blade shanks, has th us far balkeda l l atte mpts a t analysis. With these l imited a ld re la t ively minorexceptions, the agreement between for ce and survey t e s t r e m l t s i s seent o be of such qu al ity as t o warrant confident acceptance of th e wakedata.

Results of Force TestsIden t i f i ca t i on of the e ff ec ts of varying the d is t r i bu t io n of b ladewidth i s bes t begun by examining th e fixed.-pitch ch ar ac te ri st ic si l l us tr a t ed by f i p e s 14 t o 19.14 One co ns is te nt d if fe re nc e betweonthe propertien of' conventional nd taperen 'blades is appment a t t h e

ou ts et . The curv es of CT and Cp agains t Q / ~ D for the taperedblades (models 1 2, 4, and 5 r i s e t o h ig he r v alue s b efore f l a t t e n in goff and remain higher a t reduced advance r a t i o 3 than do the correspondi~-2curves f o r t he b lade s of more nea rl y uniform width (models 3 and 6 .It w i l l a ls o be no ted tha t th e CT curveo f o r models 3 and 6 t t h ehigher pi.t;cli se tt in gs ar e di stin gui she d by more p~omin entpeaks, and byaeeper valle ys ad jacen t there to, tha n a re th e corresporlding ctuzpes f o rth e apered blades.1 4Nobe t h a t model 7 i s excluded from these comparisorm because i t s bladepro f i le s d i f fe r from those of m de ls 1 o 6.


20/143

NACA No. 1834

When the eff icie ncy curves f o r equal pi tc h s et t i ng s a re compared,th e uniformity of t h e ir peak values can h w d ly f a i l t o b e s u rp r is in gi n view of th e s ub st an tia l diff ere nc es of power- and t h r u s k u r v e f o r mjus t notea. Such uniformity, however, does not cha rac ter ize th e shapesof th e ef fic ien cy curves f o r th e vari ous models. The ty p ic a l change ofform which r e s u lt s from th e introd uctio n of pronomced tap er i s besti l l u s t r a t e d by t h e c urves f o r n ~ d e l s and 6 a t t h e 60 se t t ing ; thee leva t ion and s t ra igh ten ing of the l e f t s ide of the curve i n the caseof model w i l l be apparent upon inspe ction of f ig ur es 4 and 19.

Some fu rt he r diffe renc es which m e not apparent i n the logari thm icchar ts are brought out by the Cartesian plo ts (f ig . 39) . There it w i l lbe seen th at , i n th e unsta l led range, th e s lopes of the curves of CTand Cp against Q/ID a r e almost imperce ptibly affe cte d by changes ofplan form. On th e other hand, th e sep ara t ion of th e curves ind ica tes amarked ef fe ct of blade-width di st ri bu ti on on th e values of th e advancera t i o a t which Cp and CT would become zero. Th is e f f ec t, comple telyneglected i n designing the blade s f o r equ al power absorption, i s suf f i -c i en t t o account fo r p ra c t i ca l l y a l l of t he d i f f erences i l l u s t r a t ed b y ,f i w e 35.

The cause of the aforementioned separation i s readily deduced fromth e th ru st (or torque) grading curves. Reference t o f igure s 21 t o 32s.hows th a t th e angl es of a tt a ck of th e ou ter elements w i l l be negative,nd those of t he inner ones posi t ive, when th e to t a l th ru st i s zero.l?

Consider, now, a model wi th blade s of uniform width o pera ting a t t headvance r a t i o fo r zero t o t a l t h ru s t . I f blade a re a were taken from th eneighborhood of th e t i p s and an equivalent amo~mtadded near the roots,the equality of positive and negative thrust components would bedestroyed, th e t o t a l thr u st would become posi t ive , and an increase ofadvance r a t i o would be requi red t o re-es tab l i sh the i n i t i a l condition ofequil ibr ium. The tapered blades there fore a t t a in zero thr us t and torquea t la rg er advance r a t i o s tha n the ones of uniform width when both typ eshave equal pi tc h se t t i ng s at x 0.75. Lest it be suspected that these par ati on of t he curves f o r models 3 and 6 i s i ncons i s t en t wi th th i sexplanation, the reader i s r e f er r e d t o f i g u r e 3 where it w i l l be seenthat model 6 i s ac tua l ly d i s t ingui shed by s l igh t reverse t aper , t ha t isth e average width of th e outer ha lf of the blade i s grea ter than t ha t ofthe inner one.

k s p it e of a l l the diffe renc es which have been pointed out above, iti s shown i n f i gu r e 4 th at the eff icie nc y envelopes fo r models o 6 areappreciably sepaxated on y a t very l a rge and very small advance rat ios.( In order t o avoid confusion i n t h i s char t , only thove curves whichdefine the upper and lower limits of t h e group a r e shown; numbered aux-i l i a r y l i n e s iden tif y th e poait ions of the others.) The maximum ordin atesAn unavo idable consequence of tho- us e of t h e envelope t w i s t curve.


21/143

NACA T No. 1834 19

of all six curves are between 0.85 and 0.86. Since there is reason tobelieve that more nearly complete coincidence would have resulted ifa more conventional pitch distribution had been incorporated in thesemodels, it is hardly surprising that the results of early propellertests -which were appraised almost exclusively upon the basis of maxi-mum efficiencies were interpreted as indicating that blade-widthdistribution had an inconsequential effect upon propulsive efficiency.

In striking contrast to the envelope curves, figures 41 to 45reveal very substantial effects of plan-form variation upon constant-speed efficiency. In each of these charts, curves for model 6 are repro--duced as a basis for comparisons. It will be seen at once that, as inthe case which gave rise to this investigation, the effects of b ladewidth distribution are confined to advance ratios less than those formaximum efficiency and that their magnitude increases with that of thePower coefficient* At Cp 0.05, the smallest value for whichefficiency curves have been constructed, model 3 is very slightlysuperior to model 6 whereas all the others are somewhat inferior. Atlarger power coefficients, the efficiencies of models and 6 are practi-cally indistinguishable. However, at Cp 0.10 the beneficial effectsof taper are clearly apparent and, as Cp continues to increase, thetapered blades models 1, 2, 4, ar-d 5 exhibit increasing superiorityover the conventional type throughout the ranges of reduced advanceratios. These divergences between corresponding constant-speed efficiencycurves are the more notable because the peaks of corresponding curves arepractically indistinguishable except in the case of the smallest powercoefficient.

Of the four models which are superior to the conventional one, itwill be noted that two models 1 and 2 have blades which taper con-tinuously from root to tip, while those of the other pair models 4and 5) are of the doubly tapered type, that is, their widths diminishfrom intermediate stations toward both root and tip. It will, therefore,be of interest to identify the better plan form of each type. By con-paring the curves in figure 41 with those of figure 42, the efficienciesof model 1 ill be found to exceed those of model 2; a similar comparisonof figure 44 with figure 45 will establish the superiority of model 4over model 5. It thus.appears that the wider blade of each type is themore efficient.16In order to summarize the most significant results of the forcetests, typical constant-speed efficiency curves for models 1 and 4 have

161t is, of course, equally true to say that the one with the narrowertip, the more severe taper, or the broader root is the better; thenumber of models included in the present series was insufficient toenable positive identification of the most influential plan-formcharacteristic.


22/143

20 NACA TN No. 1834

been superimposed upon corresponding curves for madel 6 in figure 46An auxiliary logarithmic scale has been placed alongside the curves forCp 0 5 to enable convenient appraisal of the advantages of one typeover another. Its use is illustrated by the dotted lines which show that,at Cp 0 5 and V ~ D 1.5, the replacement of model 6 y model 1or 4 ould have the result of augmenting the efficiency and availabletkust horsepower by one--third or one-fourth, respectively. Althoughthe advantages of the tapered plan f orm diminish as the power coeffi-cient becomes smaller, it is worth noting that they are still apparentat advance ratios less than 0 6 when f is only 0 10 Another featureworthy of note is the substantial para1 elism of corresponding efficiencycurves in the range of small advance ratios; as the coordinates of thechart are logarithmic, such parallelism implies the maintenance of aconstant relative superiority throughout the take-off and low-speedclimbing ranges.

When the foregoing results are viewed from the standpoint of practi-cal applicability, it appears almost certain that the root width ofmodel 1 will be considered prohibitively great for incorporation in amodern constantdpeed propeller. On the other hand, this objection isnot applicable to model 4 which clo~ely pproaches the performance ofm~ d e l ~urthermore t would appear reasonable to anticipate thatfurther development of plan f orm characterized by limited root widthswill lead to substantial reproduction, if not improvement, of the charac-teristics of model 1 In this connection, attention is called to theilnnecessarily great thickness of the inner sections of the heavily taperedblades. Corresponding elements of models 1 to 6 were made geometri,callysimilar with the object of reducing the number of variables capable ofinfluencing the test results; however, it should be duly noted that thepractically allowable reductions of thickness in the cases of the taperedblades would certainly have beneficial effects upon their performancecharacteristics. Consequently, the merits of these unorthodox plan formshave been demonstrated under a handicap which would not have to beaccepted in practice.

Results of Wake SurveysWhile the consequences of varying the distribution of blade widthare clearly shown by the force test results, the underlying causes ofthese effects are to be found only by analysis of the wake survey data,

which were recorded with that principal objective in view. However,since the present surveys are considerably more comprehensive than anymade heretofore, it would appear appropriate to preface the analysis bysome comments upon the general character of the results of this majorphaae of the investigation.A birdts ye view of the principal effects of advance ratio andpitch setting upon the distributions of thrust and torque over blades


23/143

NACA TN No. 834 21

of conventional plan form may be obtained by inspection of figures 33and 34, which contain the grading curves for model 7.l7 Perhaps themost noteworthy feature of these charts is the marked similarity betweenthe forms of corresponding thrust and torque curves for the largeradvance ratios, that is, those for completely unstalled operation. Theadvent of stalling is indicated by the disappearance of similaritybetween correspanding curves and is most marked in the outer portion ofthe blade. In this connection, it will be noted that there is a generaltendenzy for the torque curves to expand radially, that is, to have sub-stantial positive values at, and even beyond, x 1 0 as the advanceratio is reduced at the higher pitch settings. By comparison, it willbe seen that the corresponding tendency on the part of the thrust curvesis relatively slight.

At their inner ends, the slopes of both the thrust and torquecurves increase as the advance ratio diminishes nd it is worth noticingthat the increase continues even after the tips stall. The usual out-ward displacement of the peaks of the grading curves with the increaseof pitch setting and decrease of advance ratio will be observed; it is,of course, most apparent in the curves for small pitch settings whichare characterized by considerable regions of negative thrust near thetips. The tall, narrow peaks at the tips of a few of the torque curvesare seen to be associated with negative thrust on the outer portionsof the blades; it is believed that they indicate the existence ofsharp discontinuities of tangential velocity at corresponding radii.

A particularly noteworthy feature of the grading curves formodel 7 is the irregularity of their forms in the neighborhood ofx 0.8 . As a transition from Clark Y to NACA 16-series profilesoccurs there, the irregularity of the curves is ascribed to the changeof section.Turning now to the grading curves for models 1 to 6 figs. 21

to 32), it may facilitate interpretation to keep in mind the fact thatthe curves for models 3 and 6 which have blades of nearly uniformwidth appear at the right-hand side of each chart, whereas those formodels 1 and which have the narrowest tips are shown on the left.The characteristic effects of plan-form variation upon the radialdistributions of thrust and torque are illustrated very clearly byfigures 27 and 28, which correspond to a pitch setting of 370. BYscanning the charts from left to right, it will be seen that the curves2articularly those for large advance ratios) are modified in quali-tative accordance with the variations of blade width. The peaks of thecurves and the centers of gravity of the areas which they enclose areshifted toward the tips as the width of the inner portion of the blade

17~rading urves for all six of the related models models 1 to 6at a single pitch setting appear in each of the preceding chartsfigs. 2 1 t o 3 2 . This arrangement was chosen to facilitatevisualization of the effects of plan-form variations under compar-able conditions of operation.


24/143

22 NACA T No. 1834is diminished and that of the tip increased. The shapes of the curvesare even more radically altered at reduced advance ratios. While thephenomenon of stalling appears to have a relatively small effect uponthe division of the total torque between inner and outer portions ofthe blades, a masked influence upon the corresponding distributions ofthrust will be observed. The result is an augmentatian of the dissimi-larity between the grading curves for blades of canventional and taperedforms

Inspection of the charts for other blade angles reveals that thephenomena associated with stalling tend to disappear as the pitch settingis reduced and to become accentuated as it is increased. It will beapparent, however, that, in the absence of stalling, the character ofthe modifications of thrust and torque distribution caused by changes ofplan form is not seriously influenced by pitch setting. These twofeatures are emphasized to call attention to their consistency with theresults of the force tests, that is, the influences of blade-widthdistribution are confined to advance ratios less than those at whichmaximum efficiency is attained and they increase with power coefficient.

Analysis of Influence of Width DistributionThe conditions under which substantial differences between theconstant-speed efficiency characteristics of the various blades occur canbe identified by noting, in figures 41 to 45, the largest values of v/nDat which such differences are apparent at given values of Cp andthen locating the corresponding points (v/nD, Cp) on the fixed-pitch

performance charts (figs. 4 to 19 . When this is done, it will be seenthat constant-9peed efficiency divergence accompanies or follows -butnever precedes the sharp changes of slope of the curvet; of Cp wainst~ / z l ~hich occur as the advance ratio is reduced.s the flattening of the Cp curves is caused by progressivestalling of the blades, it is evident that variations of plan form mightinfluence the performance characteristics by altering the radial extentof stalling under given operating conditions, by redistributing the loadingin such fashion as to alter the consequences of the stalling of a givenportion of the blade, or by a conibination of the two effects. Appraisalof these possibilities is facilitated by consideratian of the definitionof the efficiency of a blade element

This indicates that, at any given advance ratio, the relative efficienciesof the elements of a blade are directly proportional to the ratios ofcorresponding ordinates of the appropriate thrust and torque grading curves.


25/143

NACA TN No. 1834 3In the light of this index, the previously mentioned similarity betweenthe thrust and torque grading curves for large advance ratios and thecontrasting lack of resemblance between those for small ones becomehighly significant because the dissimilarities are of such characterthat marked reductions of efficiency over the outer portions of theblades are clearly indicated. An unmistakable example of such indicationwill be found in the grading curves for model 6 t the 37O pitch setting(figs. 27 and 28).

If it is now tentatively assumed that the outer elements of all theblades experience comparable reductions of efficiency as stallingprogresses with reduction of the advance ratio and that their inboardelements operate at approximately equal, and much higher, efficiencies,it is clear the blades in which the inner, more efficient, elementsabsorb the larger fraction of the total torque input will develop thegreater total thrust and higher over-all efficiency. In order to testthe validity of this hypothesis, the radial distributions of torque andefficiency for blades of various plan forms must be examined under com-parable conditions of operation.

A case in which large differences of constant-speed fficiency areknown to develop at reduced advance ratios has been chosen for illustra-tive analysis. In figure 47 curves of dC dx and 7, against x forQmodels 1 4 and 6 at pitch settings of 60 have been plotted for threeoperating conditions. The curves of the upper pair of charts in thisfigure correspond, as closely as the recorded data permit, to the can-ditions under which maximum efficiency is attained by each model. Thoseof the middle charts correspond to advance ratios which approximate 0.8of those for maximum efficiency, while the lower pair depict the distri-butions which prevail at approximately 0. ~(7-)

A general reduction of efficiency with decrease of advance ratiois evident in the differences between the upper and middle sets of effi-ciency curves but it will be noticed that the curve for each model has beendepressed almost uniformly. However, the further loss of efficiency whichoccurs with reduction of the advance ratio to o . ~ J ( ~ ~ ~ )s seen to behighly nonuniform and, although the curves for the three models deviatemore under this condition than at the larger advance ratios, all arecharacterized by serious reductions of efficiency over the outer portionsof the blades and by relatively slight ones over the inner parts.

When these efficiency curves are interpreted in conjunction with thecorresponding ones of torque distribution, the principal reason for thesuperiority of the tapered blades (models and 4 at reduced advance ratiosbecomes unmistakable. With the tapered blades, a relatively large portionof the power input (total torque) is absorbed and converted into thrustat relatively high efficiency by the inboard elements, whereas, withblades of nearly uniform width, the fraction of the input absorbed by theefficient inner elements is much smaller and that inefficiently utilizedby the stalled outboard elements is correspondingly augmented.


26/143

24 NACA TN No. 1834Charts similar to figure 47 have been prepared for the sane modelsat smaller pitch settings but are not reproduced herein because theymerely illustrate, in diminishing degree, the relationships brought out

most clearly by the curves for the 60 blade angle. Whether due to theimproved accuracy of survey under those conditions or to other causes,the curves of elementary efficiency for the lower pitches are lessirregular and more nearly coincident than the 60 ones. Furthermore, itshould not escape notice that the curves of figure 47 are not strictlycomparable because models 1 and 4 re characterized by somewhat largerpower coefficients at maximum efficiency with the 60 pitch setting thanis model 6. Therefore, equalization of the power coefficients andadvance ratios at which comparisons are made would bring the efficiencycurves into closer coincidence than that illustrated by figure 47.Thus the suggested hypothesis based on redistribution of loadinghas been qualitatively confirmed and it would appear to be useful as an

approximate quantitative Vasis for predictian of the probable effects ofother plan-form variations.

1ndepe.ndence f Blade Eleme.ntsThe independence of blade elements predicted by Glauert reference 13)has been substantially verified, insofar as the variation of pitch distri-bution is concerned, by the results of two previous investigations refer-ences 10 and 14). However, in discussing the results presented inreference 10 the writer expressed doubt that similar canfirmation wouldbe obtained if plan form, rather than pitch distribution, were varied.Data obtained in the present experiments have therefore been examinedwith that question in mind and some comparative curves which appearsignificant are presented in figure 48.The widths of the blades of models 1, 2, and 6, as may be seen infigure 3, are equal when x is slightly greater than 0.80. The valuesof the thrust coefficients for these elements of equal chord have beenread from the correspanding thrust grading curves and are plotted againstadvance ratio in the upper chart of figure 48. It will be seen that thecurves for these identical elements of the three models of different planform exhibit consistent differences. The analogous curves in the lowerchart of figure 48 indicate the existence of even larger discrepancies inthe case of comparable elements of models 3 and 4. It will be noted that

the separations of the curves are greatest at the smallest pitch settings;for that reason, and because of their greater irregularity, results forthe larger pitch settings are not included.The forces on other pairs of identical elements located at smallerdistances from the axis than those of figure 48 have been compared and,as might be expected, the discrepancies are generally s~mewhat ess thanthose for the outboard elements.No entirely satisfying explanation of the discrepancies revealed byfigure 48 has yet been evolved. It is evident that, under identical


27/143

NACA T No. 1834 5conditions of operation, the outer elements of tapered blades developsmaller thrusts than do the corresponding ones of blades in which thewidth is nearly uniform. This, it will be noted, is the reverse ofthe relationship between the total thrust coefficients for the sameblades. see fig 39. The possibility that the discrepancies originatein differences of pitch setting is thus excluded. But since directanalogy with monoplane wings would lead to the expectation of larger,rather than smaller, forces on an outboard element of the tapered blade,the explanation of these results must await further analysis.

The net result of this critical examination is, however, unmistakable.The principle of independence is seen to be inapplicable at least to theouter elements of blades which have different pl n fomna.

Pitch Distribution and ProfilesThe envelope pitch distribution incorporated in the models usedfor the present experiments was selected on the basis of the extra-polations summarized in figure 39 of reference 9. The expected charac-teristics were realized under some conditions of operation but not underothers.Models designated 0.4E, 0.6~,nd 0.8~ave been tested previouslyreference 9); the designations indicate that the twist curves of theseblades have ordinates 0.4, 0.6, and 0.8 times those of the envelopetwist curve defined by equation 2). Model 7, the transition model ofthe present series, is the 1.OE meniber of that family. The effects ofthis further increase of blade twist are illustrated by figures 49 and 50.Figure 49 shows that the maximum ordinate of the efficiency envelopefor model 7 1.0~)s, in accordance with expectations, somewhat greaterthan that of model 0.8~,ut the extent of the depression of the left-hand portion of the curve is surprisingly great. These characteristicsare reflected in the constant-speed efficiency curves of figure 50 whereanother, and unexpected, shortcoming of model 7 is revealed. This is theserious loss of efficiency which occurs when the advance ratio is reducedat large power coefficients. Reference to figure 39, reference 9, willshow that the efficiency of a 1.OE model at CP = 0.5 and V ~ D= 1.71was expected to be approximately 54 percent; the value actually realizedunder these conditions is only about 44 percent. It thus appears thatblades of both uniform design pitch and envelope types suffer severe

losses of efficiency under the conditions associated with climb at highpower when the pitch distribution is such as to make the geometric angleof attack very nearly uniform over the entire length of the blade. To besure, the constant-speed efficiency curve for model 7 degenerates rathersuddenly as Cp increases from 0.4 to 0.5 but the relationship betweenthe two families of curves in figure 50 leaves no question that, exceptfor a slight advantage of peak efficiency, model 7 with its 1.OE pitchdistribution, is generally inferior to model 0.8~.


28/143

NACA T No. 1834

Figure 51 illustrates the results of replacing the Clark Y andsmall design li t coefficient) 16-series profiles of model 718 by the

16-series profiles of 0.7 design lift coefficient which characterizemodels 1 to 6. It is apparent without detailed examinatian that thischange neutralizes the greater part of the adverse effect produced byadoption of the envelope pitch distribution, but it is also evident thatuse of the more highly cambered profiles has reduced the maximum efficien-cies attained at all power coefficients. As the loss of peak efficiencyis most serious at small power coefficients and as the divergence ofcorresponding curves increases with the advance ratio in all cases, itwould appear almost certain that excessive profile drag at small liftcoefficients is the source of this undesirable effect.

Consideration of the foregoing results leads to the canclusian thatthe twist incorporated in these models was too great to yield optimumcharacteristics and that m e of approximately 0 8 ~ orm is most suitablefor the blades of constant-speed propellers which are to be utilized overwide ranges of power coefficient and advance ratio. Further, it wouldappear that the use of such highly cambered profiles should be avoidedunless it is absolutely essential to the suppression of shock stallingin heavily loaded propellers.

It appears possible that the preceding considerations m y have createdthe impressian that the inferior pitch distribution and high-cauiber pro-files of the models used for these experiment3 have enhanced the oppor-tunities for demonstration of the potential benefits of plan-form modifi-cation. The reader who entertains such misgivings may quickly dispel themby comparing the constant-speed efficiency curves of model 6 ith thoseof model 0 8E figs. 50 and 51) he will find them incansequentiallydifferent except in peak height. Thus, the characteristics of the conven-tional type used as a basis of comparison throughout this discussion arenot appreciably inferior, as regards efficiency at reduced advance ratios,to those of one characterized by more suitable profiles and a better pitchdistribution. In view of this fact, most of the superiority, at reducedadvance ratios, of the constant-epeed efficiency curves for models 1 and 4over those of model 0 8 ~ figs. 41 44 and 50) can only be ascribed tothe influence of blade-nidth distribution.

The most important result of combined force and wake survey tests onthree-blade model propellers is the demonstration that blade-width distri-bution has a marked influence on the constant-speed efficiency character-istics of propellers.18~1so ncorporated in all members of the E-eeries.


29/143

NACA TN No. 1834The envelope efficiency curves for the types of blades tested differappreciably only at advance ratios less than 1.0 and greater than 3.0;in those ranges, the envelope efficiencies of the relatively straightblades are slightly superior to those of the tapered ones. However, theconstant-speed efficiency curves diverge substantially as the advanceratios are reduced below the values at which maximum efficiencies occur.At these reduced advance ratios, and at all values of power coefficientequal to or greater than 0.1 blades tapered from broad roots to narrowtips attained greater efficiencies t h m did those of relatively uniformwidth. At power coefficients appreciably less than 0.1 untapered bladeswere found to be somewhat more efficient than tapered ones at all advanceratios. Similar, and only slightly smaller, differences of constant-speed efficiency occurred when the continuously tapered blades werereplaced by a more practical type characterized by a considerable reduc-tion of width close to the root.

The more efficient operatian of the tapered blades at reducedadvance ratios is ascribed to a redistribution of loading which servesto minimize the absorption of power by the outer elements which becomevery inefficient as they stall and to correspondingly augment the frac-tion of input which is efficiently converted into thrust by the unstalled,inboard elements.n incidental result of fundamental importance is the failure ofthe present wake survey data to confirm the theory of blade-element inde--pendence. It is noted that apparent verification has been accomplishedby previous experiments in which only pitch distribution, rather thanplan form, was varied.

Correlation of the present results with those of preceding studiesindicates that highly cambered profiles are not generally suitable forpropeller blades and that the so-called envelope pitch distributionis inferior to one derived therefrom by proportionate reduction of theangles of twist.

Stanford UniversityStanford University, Calif., May 25, 946


30/143

REFERENCES

NACA No. 1834

1. Watts, Henry C.: The Design of Screw Pr op ell ers f o r Airc raf t.Longmans, Green and Co. London), 1920, p 71.2. Durand, W F., and Le sle y, E. P.: Experimental Research on AirPrope l le r s , V NACARep. No. 141 1922.3. Munk, Max M : Notes an Pr op el le r Design-IT: General Proceeding i nDesign. NACA TIT No. 96, 1922.4 Weick, Fre d E.: A i r c r a f t P ro pel le r Design. McGraw-3illBook Co.,

In c 930, pp. 116-117.5 Glauert , H.: Airplane Pro pel lers . Vol. IV of Aerodynamic Theory,div. L, ch. I. sec . 3 W F. Durand, ed., J u l i u s Sp rin ger~ e r l i n ) , 935, p. 176.6 Lock, C. N. H. and Bateman, H.: Wind Tunnel Tests of High PitchAirscrews. Part 11. Va ria tia ns of Blade Width and Blade Section .

R. M No. 1729, B r i t i s h A.R.C. 1936.7. Hartman, Edwin P., and Biermmn, David: The Aerodynamic Charac-t e r i s t i c s of Four Ful l -Scale Pro pel le rs Having Differen t PlanForms. mACA Rep. No. 643, 1938.8. Von Mises, Rich ard : Theory of F l i g h t . McGraw-Hill Book Co.,

Inc 945 p. 294.9 . Re id , E l l io t t G. : Studies of Blade Shank Form and Pitch Distr ibutionfor ConstantSpeed Propel le rs . NACA TN No. 947, 1945.

10 . Reid, E l l io t t G.: Wake Studies of Eight Model Propellers. NACATN NO . 1040, 1946.

11. Lesley, E. P.: Tandem A i r Prope l le r s . NACA TN No. 689, 1939.12. Stickle, George W : Measurement of t he Di ff er en ti al and To talThrust and Torque of S ix Full-S cale Adjustable-Pitch Pro pel lers .

NACA Rep. No. 421, 1932.13. Glauert, H.: The Elements of Ae ro fo il and Airscrew Theory. Univ.Press cambridge), 1926, pp. 211-212.14 . Lock, C. N. H. Bateman, H. and Townend, H. C. H.: Experimentst o Veri fy t h e Independence of th e Elements of an Airscrew B lade.

R. 9 M NO. 953, Br i t ish A.R.C. 1924.


31/143

NACA TN No 834TABU 1. FORCE TEST DATA; MODEL 1

600 . 7 5 ~e s t E 1

V / ~ D3.7243.5803 4733.3013.1623.0042.8662 7152.5822.4192.2812.1361.9931.856I.. 7061.5501.4251.2841.1481.001.871-733

Tes t E 2v/m

3.8043.6643.5083.3573.2193.0782.9362.7942.6482.4912.3492.2212.0781.9381.7961.6481.5031.3641.2151.074927-792

Po 75R 48

c~0.7766.8318.86518973.88638553.8332,8140.7978-7777

7473715769306753.6702.6746.6743.6773-67366763.6708.6700

C~0.7396-7950.8446,8902.8907.8679.8404.82O6.8043.786O

.7626-7335-7053.6818.6727-6707.6727.67206717.6721731.6666

Test E-3

C~0.151117561903.2127.2194.2224.2261-22952319.2251

.2134.20221917.1848.1837.1836.1838.18521855.1870.1862.1865

2.7082.6432.5292.4252.32 ;2.2272.121

T e s t

0.725.756.764.782.783.781.778.765.751.TOO.651.603.551.508.468.422.388.351.316.277.242.204

C~0.1390.1608.I827.2061.2163.2215.2245-2307-2329.2288

,2210209519751897.1852.184 7.18621859.1866la1.1886.1896

2.5852.4852.3732.2762.1712.0701.963

70.715.741759777.782.7867q4.785.7670725

.681.634582539.494,454.416377338300.260.225

0.1811.2084.2577.3021.34823913,4196

0.2366.27563252-3718.406g.4223.4230

0.04420573. a 1 71035.1252.1464.1682

0.660.727.801.831.836.833.850

0.0726.ogoo,1141,1388.15891739.1807

0.794.811,833,850.848.852.836


32/143

30 NACA TN No. 1834

\

T A B U 1. FORCE TEST DATA; MODEL 1- Continued

0 7 5 ~ 37O

I0.788.821.844.856.852.843.836.830.812.788,757.6go.636573519.472.421378325277

v / n ~1.7861.7021.6341.5701.4941.4151.3481 2771.2041.1241 [email protected],694.617555-477.407

T e s t E 6v / n ~

1.8061.7411.6701.6001.5261.4521.3861.3121.2311.1601.0881.016.g41.86596725655584513437

.3870 7 270

Teat E-5CP

0.1140,142816331930.2198.2381.2443.244g.2468.25002563.2640,27022779-2837,29143015.309131583236

CP0.102512731513.1802.PO93.2332.2430.2444.2447.24762507.2587.2671.2728.2808.2878.29603047.3122.32043245

T e s t E-7

CT0.0503.0689.0844. lo52.1254.1418.15161591.166517531839.1884.1888. lgo41934,1981.2056.2103.2149.2204

1.2931.2321.1691.1081.037.980

917857*794732675.613552.4go.4243723 6

Te s t E-8

C~0.0426058707530954.11761369.148g.1560.162617071783.1861.1894.188119151959.2017.2078. e l 25.2182

.2210

1.2471.1871.1261.0641.008947

.885.819759699639.582519459398334

I0.751.802.831.847857.852.84g-837.818.800774731.667596543493.446398349.298.264

0.0434.0648.08070990.11871332.1454.1504.1510.1498.1506.15161558.1617.1714.1784.1866

0.057207450937.UOg-12591394.14841499.14go1497.1512.152515771655,1740.1814

0.02070397.056107490952.1122,12911397.1.466,1526.1593.16721759.1822.1861.18801919

0.618.754,813.838.832.825.814796771.746.714,676.623552.460392.314

0.0339.0512.0694.0874. lo43.12141354.1440.1502.1568.1648. l?og-17941855.1866.1892

0.739.816833839835..825.807787.765732.696.652.590.514.428.348


33/143

NACA T No. 1834

T BU 1. FORCE TEST DATA; MODEL Concluded

Test E 9 Test E 10

0.75R 12Tes t E 11 Test E 12


34/143

NACA T N o 834

TABLE . ORCE TEST DATA; MODEL

T e s t D 1 Te s t

T e s t D 3 T e s t D 4


35/143

NACA T NO 1834 33TWICE 2. FORCE TEST DATA; MODEL 2 C o n t i n u e d

T e s t D-5 T e s t D 6

T e s t De s t D-7

o .0546074900930o 1.124801374.142801435.1434.1434.1447.1471152301583.1656.1728

o .0321.0512.068800873.lo42.1209.1326*I393.1454.1516J583.16510169591739.17621787


36/143

N C TN No. 834

TAB= 2. FOR E TEST DATA; MODEL Concluded

T e s t D 11

T e s t D

T e s t D 12

T e s t D 10


37/143

N C T NO 834 5

TABU3 3 FORCE TESP DATA; MODEL 3

T e s t G 1 T e s t G 2

T e s t 6 3


38/143

6 NACA TN NO 834TABU 3. FORCE TEST DATA; MODEL 3 C o n t i n u e d

T e s t G j T e s t G 6

T e s t T e s t G0.0376 0.0179.0560 003497~ 7 4 8 . 0 5 2 1


39/143

NACA TN NO. 1834 37

TABLF: 3. FORCE TEST DATA; MODEL 3 Concluded

T e s t G 9 T e s t G 10

Tes t0.02440297.034290379.0420.04440459.0466.Oh @

0475

T e s t 6 1 2


40/143

NACA TN No 1834TABLE 4.- FORCE TEST DATA; MODEL 4

Po 7~ = 60'

T e s t C-1TInD

3.7133 5523.4023%2683 013009782.8352.6932 5772.4422.2912.1131.9761.8236991 5591.4191.2781.136987.86871.9

Tes t C 4V/IID

3.6583 a4773 a3453.2003 -0522-90?2 7762.6302.490-3492.1982.0641.9121.7731.6311.4871.3481.2051.064.920792

0 7% = 48'

C~

0 7655.&9608659-871.808439.811379027735.7618749419067916577.6416.6416.6381.6441.6421.6431.6502.6552-6513

P

0.7842-8408-8737.8584.82297994.78227627.75137327.6923.670365056457.6423.6451.6468.6440.6502.65376557

Test C-3

C~

0.1572.1805.2022.2139.2152.2165.2198.2228.2229.2185.20662 9 0 0.1812J 7 4 6-1737J71901743.1670.1665.I705-1738~ 7 6 4

Tes t C 4

I

0.762773794.802798795789-776754.712.658591.544.496.460.420.384332.29459.230195

C~0.1641.l904,2109.21382159.2193.2213.224o.2225.21291974.1867.17941751J734.1753*I755-1657.1698A744.1764

0. 729.816.830.849.846.850

2.6342.5402.4322.3352.2322 3 6

0 77078708070797.801797785772*737.683.6285750527.481.440.404.366.310.278.245.213

2.6552.6002.5072.4002 3052.202

0.19742199.26273071e3538.3913

0.05520657.0841.lo50.1290.1521

0.2033.2483953.33&-3771.4027

0.7420775.&3.821.841-859

0.05630797.lo08.12292 4 3 0.1602


41/143

NACA T N o . 1834 9TP BLE 4. FORCE TEST DATA MODEL 4 C o n t i n u e d

T e s T e s t c-6

T e s t C-7 T e s t c-8


42/143

N C T No 834

TABLE 4. FORCE TEST DATA; MODEL 4 C o n c l u d e d

T e s t C 9 T e s t C 10

T e s t C 11 T e a t C 12


43/143

N C T No 1834 41

T es t F-1 Tes t F 2

T es t F 4es t0.1238.1678

.2342-2913.3201365638753906391639453998

.4067.4069.4066.4088.4150-4253-4335.4413.448404551-45964679

F-30.0293.0436

0737.loo0.11451390-1557.1642.17.1784.18511899.1864.I828.I824

.18431873.19021923-1932195319581985


44/143

42 N C TI? No 1834TABLE 5.- FORCE TEST DATA; MODEL 5 Continued

0.75~ 37OT e s t F-5

v/m1.7791.704

T e s t F 6v / ~

1.7981.7341.6611.5911.5151.4421.3711.2921 2221.1581.0851 012.940.866794.720.647.576.5100435,341

0.75~ 27O

c~0.0884

I201

C~0 08021077.1386.16921957.2174.2219.2229.2269-2305-2375.24522547.2616267527502855,2931300330583129

r e s t F-7

C~0.035705591.630 .1506

T e s t F 8

0.718-79307710987,1195-.13411398,146815571637172517721770.1786.182018591903.1g44.1984.2018

c~0.03040479.06760903.llOg.l2901375

1439.15181587.1680.1748-177617751790.18281881.192119581991.2029

1.5521.4831.4061 3371.2621.1891.1191.046973899.827756.683.611.541.469397

1.2391 1771.1251.0631 000936875.812754693633572513.454394332

1.2851.2231.1601.0981.039.976.914.854793730.669.610.546.486.424372.2g4

.834.847.854.852,840.826.808.782.743.688.618558505.452.402354305.258

9

0.682771.810.84g859.856.850.834.818.797767.72l655588531479.426378333.283221

.1811.20742212.2226.2244.2290.2341.2427-25072575.2646.2724.2808.28go29703047.3102

0 012203070497.0696.08691055.1209.1285.1342.I409.1485.1561.1634.16921727.I748.1784

0.0320.05160733.0921.lo88.1244.13461377.135513651387.141g.14671530.1611.1685.1766

0.488.728.787.830.829,828.821797785754.716.671.608537455.386297

0.0468.0696.0851.lo43.12071317.13601358.13661385.1406.14621505-1576.16521729

0.02530459.0624.0820loo1.1160.1262.1318.138614571533.1620.166617191739.1762

0.670776.825.836.829.824.812788765729.6go.634.568495.415338


45/143

NACA m No. 1834

T BLE 5 FORCE TEST DATA; MODEL 5 Concluded

0 . 7 5 ~ l g OT e s t F + l

0 . 7 5 ~ 1 2

Test F-10

T e s t F-11 T e s t F-12


46/143

NACA T No 834TABLE 6. FORCE TEST DATA; MODEL 6

0 755 = 60'

v m

3.6953 ,5773.4283 -2793.1233.0092.8632.7212 5752.4252.2892.1452.0011.8361.7141.5641.4141.2881.1401.016.858.714

v m

3.6033.4483.3033.1613.0292.8862.7492.6062.4512.3092.1782.0361.8971.7601.6131.4731.3351.1831.060.904775

c~0.6553.71167538.7619.7401.7189.7021.-6879.6813.6774

.6528.61735850.5641559956325650.5762-5909-5940596359870 75 = 48'

T e s t B 4C~

0.6988.751.8.7641.7400.71786990.6914.684367346583

.6247.5882.56465557558455945701.58165859,58695897

Tes t B-1c~

0.130915471757.1867.I928.19281955.1982.20251977.1831.16271495139813901357.13211363.I416.1448.I476.1492

T e s t B-3

0.739*779.800,805,814,808.797.783.766,709.641.567.511.456.425.378330.304.273.248.212.178

C~0.1501-1727-1875.1889.1902.lg40.1981.20171991.1849

1679.1508.1416U 6 71363.1318-1333.1381.I419.14441459

T e s t B-4

0.77307-92.811.807.803.801.788.7680725.649585.522.4760433394347.312.281257.222.192

2.5392.4602.3282.2262.1422.0381.9341.8271.7301.6335291.4311.3331.2311.1321.040945-843743.641534

2.6232.5882.4902.3862 .2952.1862.0781.9841.8921.789

-599

0.0414.0485.0684.0876.1103135015031595,1642.1717571794-1737.1687.1642.1634.1650.1650.1667.1694-17251770.1803

0.1562.1736.2152.2586.30163491.368637093709*3709-3748.381238233856.3826,386439043956.4016.41134197043034373

0.695.723.7918O 8.839.845.847.853.838.823789.745

-674.606-553.506.460.414370327.287.246,211

0.19162390.2846-332236353710.3708-3708.37053769.3824.3841.38283825386539423991,40804157.4262.4362

0 ~ 5 6 7,0782.lo15.1267.I4521552.1617.16771723.1782.1762,17081657.1629.16401659.1669.1686171317511798

0.751.805.830.848855853843.826.805772705.636577.524.480.438395.348306.263.220


47/143

NACA TN No 1834 45TABLE 6- FORCE TEST DATA; MO EL 6 Continued

0 7 37O

~ n d

1.8021.7301.6501.5911 4971 4351.363I 961.2171.1501.0631.002.928-861789715.643573.494.429378

Tes t ~bV m

1.7441.6751.6101.5421.4691.3961.3261.2501.1771.1071.037.961893.819749-677.605537.466392

Tes tCP

0.0696.0960.12701513.1813.2031.2107.2123.2150.2176.22222 2 9 7,2348.'i41624952587,264302707.2762.2809= 2839

Po 7c3 27'

CP

0.0941,1169.1400.16861939.209O.2104.el25.2138.2185.2260.2319.2381-2453-2533.2618.2678.272092773.2837

B-5CT

0,0240.041g,0643.o800. lo24,1212.1312,1381.1448.15201583,1637.1631,1627.1634,166616931727175517751797

T e s t B-7

9

0.552.756.835.841.846.856.849.843.820.803.757,714.645579517.460.412.366.314.2710239

T e s t ~ 8

CT0.04010555.07210931.1119.1272.1341.I409.1476.1546.1620.16411633.1632.1652.1683170917371759.1791

0.507.697.788.822.831.832.824.809.782756719.672.605523.445.380,290

9

0.743795.830.851.848.850.845.829.813783743.680.612-545.488435.386343.296.248

0.590753791.827.834.832820.812.771.741699.641.564.485.419334

0.0102.0272.0445.06240792.0980.1132.1209,126613291392.145415071531.I5481572.1621

1.2721.2111.1491.0881.029.967907

.846,784.726.665.608.546.484.421.366.286

0.017703470507.0684.0872. lo601173.1241.12981359.1419.1486.1524.1542.1564.1604

1.2461.1871.1271.0631.002939879

.838755695,637577,514455399.326

0.0282.o472.0650.0826.og801139,1246.1264.12672 7 6.1288.1316.1361.1416.146415131597

0.03740547.07220879. lo48.1196.1258.1265.1271.1274.1294-1338.1388.1446.14911565


48/143

NACA T No. 1834TAI3I;E 6. FORCE TEST DNA3 MODEL 6 C o n c l u d e d

T e s t B 13 T e s t 3-14

0 7 ~ l g OT e s t B 9 T e s t B 10


49/143

N C TN Wo. 834

TABLE 7. FORCE TEST DATA; MODEL 7

e s t A-3 T e s t A 4

Tes t A-1V / ~ D

3.6173 4973 3423.2063.0602.9222 7712.6282.4852 3432.1942.03818931 756I 131.4931.3521.2101.062.914787

T e s t A SQ/a

3.6773.5633.4083.2653.1132.9922.8402.6992.5462.4172.2892.1341.9581.8241.6771.5521.4211.2771.133998.862707

Cp0.62146497.6641679569096957.69606932.6 P6325

5785551553585368.5408554557115850583459055922

C~0.6423639065706756.68686956.6g646958.6904.6634

.6092669.54165348535654435674.571205833-58745928918

c~0.1353.149415951715.1810.1920.I9711991.18981557

1356.1201.1145.1136.1147.1183.I243.1288.13211391.1432

c~0.1292.14441569.16841790.18go1947199119771797

1495.1301.11601136.1131.I157.1232.126613121353.l422.I436

l

0.788.804.803.809.802.806.7850755.692.577.514.444.405.372.342-319.2g4.266.240.215.lgO


50/143

48 NACA TN No 1834TmL 7.- FORCE TEST DATA MODEL 7 Continued

Tea Test

Test A-7 Test1.283 .0 247 .0112 .582 1.236 .03681.221 .0444 .0278 .765 1.178 05431.163 .0606 -0433 .831 1.116 07071.102 -0758 0589 .856 1.060 -08371.040 0905 0749 .861 996 0972975 lo31 0899 .850 936 1075.914 .1111 .lo18 837 -875 .1132.853 1159 .1109 .816 .814 .1183793 .1209 .1202 .788 756 .1211731 .1237 1279 -756 695 .I ?673 .1263 1352 .720 635 .1265.611 .1300 .1407 .661 573 91336549 1379 .1429 569 513 .1421.489 1477 1439 .476 .456 1493.428 .1546 .I481 .410 392 1570.367 .1625 1531 .346 343 .1629,316 .1678 .1562 .294


51/143

NACA TN N o . 1834.

T BLE 7. FORC E TE ST DAYA; MODEL 7 C o n c l u d e d

T e s t A T e s t A-10

9

T e s t A-11 T e s t A-12


52/143

N C TN No 834

T BLE 8. W K E SURVEY DATA; MODEL


53/143

NACA TN N o . 1834

TABU? 8.- W XE SURVEY D N A ; MODEL 1- Con t i n u e d

xCTxd Qxd Qxc ~x

T h r u s tndt o r q u e

0.702

C Td x

0.20.35.48.60.71.81.89.951.001.05

0.022.082.135.163.162.125.071.022-.002-.002

0.810

dcTx

0.003oil.01g.022.022.017011= 005001.oo1

0.015.056.og6.116. l o8.073.029-.oo5-.005- OOI

0.856

dC

0 002.008.014.017.017.012.006.oo3.oolo

0.012.045.078.egg.081.480.008-.016-.004-.002

0 9090.002.oo7.0120 5.014.oog.oo4.002.003o

0.005.034.060.069.053. o l g-.018-.036-.006-.003

0.311.604

0.001.oo6.ox0.012ole.006.ool0.004o

0.041. I19.189.

Documents

légcsavar kísérletek