Formulas for Prope 00 Lang

7/30/2019 Formulas for Prope 00 Lang

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ARR No. 3E19

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

WARTIME REPORTORIGINALLY ISSUEDMay 19U3 a8

Advance Restricted Report 3E19

FOEMULAS FOR PROPELLERS UH YAW AND CHARTSOF .THE SIDE-FORCE DERIVATIVE

By Herbert S. Rilmer

Leaigley Memorial Aeronautical LaboratoryLengley Field, Va.

WASHINGTONNACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution ofadvance research results to am authorized group requiring them for the war effort. They were pre-viously held under a security status but are now unclassified. Some of these reports were not tech-nically edited. All have been reproduced without change in order to expedite general distribution.

L - 217


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:^^ 9^r q 7r^b"S"7SHATIOIIAL ADVISORY COMMITTEE FOR AERONAUTICS

ADVAITCE RESTRICTED REPORT

FORMULAS FOR PROPELLERS lU YAW AlID CHARTSOF THE SIDE-FORCE DERIVATIVE

By Her"bert S. Ri'tiner

SUMMARY

General formulas are given for propellers for therate of change of sideforce coefficient v;ith angle ofyaw and for the rate of change of p it chingaoinent coef-ficient with angle of yav;. Charts of the sideforce de-rivative are given for tv?o propellers of different planform. The chart? cover solidities of tv;o to six 'bladesand sinful e and dual rotation. The blade angles rangefrom 15 or 20 to 50.The equations, and the charts computed from the equa-tions, are hased on an unpuhlished analysis, v;hich incor-porates factors not adequately covered in previously puhlished v;ork and gives good agreement v/ith experiment over

a v;ide range of operating conditions. A study of theequations indicates that they are consistent with the follevying physical interpretation: In developing side force,the Tpropeller acts like a fin of vfhich the area is theprojected side area of the propeller, the effective aspectratio is of the order of 8, and the effective dynamicpressure is roughly that at the propeller disk as augmented"by the inflow. The variation of the inflow velocity, fora fixedpitch propeller, accounts for most of the varia-tion of side force with advancedi am et er ratio,

The charts may he applied to obtain the rate of changeof normalforce coefficient with angle of attack of theaxis of rotation if proper account is taken of the upv/ashor downwash from the wing.

IJTTRODUCTIOH

There has "been a need in sta"bility analyses for asystematic series of charts for the estimation of the rate


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of chan^je of propsller side force ';ith an^le o^ ya.\i. Althori.^h the formula developed 'b^ Harris and Gl'-j-uert inreferences 1 and 3 and 'liscassed in reference 3, whichexpresses the side force in vav; in ternis of coefficientsfor the unyavied propeller, is fairly satisfactory, therehas 1:00:1 no adea^uabe formula hased priia.arily on thegeDactry of the propeller "blades. An unpublished anp.lysishas resulted in such a formula.. -he hasic assumjjt ionsare sir.iilar to thof.e of tl: e --orter: theory for the uninclined propeller when the Goldstein correction for finitenuraoer of bl-..des is onitted. Ccnparison v.'ith a nuraherof e;:per ir. snt ,1 resrlts has indicated that the a,c3ura.c"of "10 percent ootainaolc hy the analytical nethod is ofthe order ohtrined oy the uncorrected -rorter-: theor;'' forthe v.ninclined propeller.'"

The fcrnula, developed in the analysis and given'herein. ha3 been \iced to prep-'.re a series of charts givingthe rate of change of sideforce coefficient vrith angleof yavr as a function of the advancediaaet er ratio V/nll;the "blade angle and soiiaity are parameters; the chartscovc-r "both single imddual rots^tionv' !ihe cor.putat ions'were riad'e fo?r tv/o representative propellers , the- HamiltonStandard" S155-6 and the ITAGA 10-3bc2-045". " Means are givenfor int "erp olat ing for other pr ojieller's .-

In crder to nake the present report complete in it-self and to raJ:e the chitrts j.;ore intelligible, forniula,sfor the sideforce and },it chingnonent" der ivat iv'es aregiven at the ov.tset v.'ith an e:cplanatcrv text. x'he otherpropellur stal:^ility derivatives v/ith respect to ya'-.r arezor c?or the purpose of expediting the' purl icat ion of thecharts J- the derivation of the forinv.las has "been ouitted

froit: the present paper. There is included herein, hove-'-er,a graph that sho^-;s a cor.pari~on of the theoretical valueswith the experimental data of Lesley, '/'orley, and Hoy( refer once 4) .

SYIOOLS

i'he for-ivilas of the present report refer to, a systemof- "body axes. Jov singlerotat ing propellers, the originis at the intersection of the axis of rotation and the


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plane of rotation; for diia-lr ot at ing propeller?., theorigin is on the axis of rotation halfv;ay "between theplanes of rotation of the front s.ncl rear propeller;?.The S aicis is coincident vrith the a"is of rotation andis directed forward; the Y a:cis is directed to the right;and. the 3 a::cis is directed dov;nv;ard. She synods aredefined as follows:DRrS

XXo

BId

a

3o

P

CCffi

propeller diaaetertip radiusradiv.s to any Made eleraentdisk area (ttD""/4)fraction of t i^p radius ( r /3 )nini:n,LLrn fraction of tip radiius at which shanlc "blade

f-.cctions develOT) lift (taken as G.2)ratio of spinner ro.dius to tip rs.di^isniinber of "blades"bla-de section chordsolidity at 0.75H 4B Z' Id

1~ V'-'TT \ \. \I) y . 7 5 E

"bD. ade angle to zerolift chord"lolade a,nE_-le to reference chord, measured at 0,75Hstation, degress

an^le oi yaw, raaianso.n.jle of attack of thrust a;cis, radians

Y freestream velocityq free st roan dynamic pressure (l/2pV^)a inflow factor


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A

f(a)

Cr,

arvial velocity at ijropeller disk [V( 1 + a)jho-" I .. ^ . (1 + a) -H (1 + 2a)^ I(1I act or I { J. + a; lL

. 1 + (1 + Sa)"' -

thrust coefi'iciont ( thrunt /pn^D )iciont ( thrust /pT^D^- or Gt/'T^)

rZ

M

cm'.^,.

n,

Icr,

ka

I.

rotational speed, revolutions per secondr,c".v a:i c od i s.n c t er rati "> ( " /iiI' )effective heli:-: an/:::le

^tan ' L Va/'(2 ;Tnr r^lipstr eam rotational velocitjOjTside force (lod^ a:'es)normal f or ccpitcliinr noment (nod?,'- caxes)side--force cerivative: rate of chan^^e of sideforce

coefficient v/ith angle of yaw [ ( 5 Y /c>i.';/qS ' ]p it chingElement derivative: rate of change of

t) it chingrr. Oiiient coefficient v;ith angle of ya--r[(3ll/H')/qD3']

r,vera,";c sloiie of section lift curve per radian( taken as 0.9 5 X 2-.')

spinner factorf idewash fact orconstant in the equa.ticn for hss i d 0ar e a ind e :c

defined "hj equation (2a) (zero for dualr otat ingpropellersIs integral defined oy equation (SId)


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Ig integral defined hy equation (2c)m defined Tdj eqxiation (Sa)Su'oc cr ipt s :0.75?. measLired at the 0.75E station (x '.75)

POHHULASP.ate of Change of SideForce Coefficient with Angle

of Yaw for DualHot at ing Propeller

The nature of the fcr;nulf,s for the sideforce de-rivatives nahes it simpler to present the formula forthe dus.lr ot at ing propeller first. For a dualr ot at ingpropeller, the sideforce derivative is

Cvi'^^ hiJM ^ -kgf( B.)al^qS 1 + hacrl. (1)wherethe sipinner factor kg ~ 1.14the s i d e w a 3 h factor k g^ ~ o . 4the inflow factor a ~

the qfactor f(a) =

=- (-v^ 1 + ST^/rr - l)/2(1 + a)[(l + a) + (1 + 2a )^]

1 + (1 + 2a) (la)

the solidity at 0.7'oR a 4B / h^OTT \ L y 0.7 bH1

the sidearea inde" I ]_ = 3/4 itio / ( "o/'bo .75 H ^ ^ ^^^ ^o '^"'^"0

md I^, f(a), kg, and k^ are discussed in detail later.


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Sidearea inde:: -i-~ ^J^c product ctI^^ is proportioncil to the area projected "by the "blades on a planethrough the propeller a:îs. This area nay "be called theprojected side area of the propeller. "he significantfactor 1 3^ hcs Deen termed "the sidearea index"; ais the solidity at the 0.75S station. In equation (l),!cg_crlj^ is alv/ays snail in comparison v;ith unity, v;iththe result that CY*\i; is appr oicinat ely proportional tocrl^ and hence to the projected side area of the pro-peller. The factor l/(l + '^'-aP'^x) ^^ây be regarded asa correction for aspect ratio.

If graphical integration is inconvenient, the side-area inde:: I ]_ nay oe evaluated auite sir.ip)ly and v;ithsufficient accuracy "by Gauss' rule for appro::imate inte-gration (reference 5), v/hich ordinarily reqûires fewerordinates than Sinpson's rule for the same accuracy.Dete.ilc are given in the appendix.

1h e q 1 a ct or f ( a ) . By the definition of a , thee-pr ession T( 1 + a) is the axial v/ind velocity at thepropeller disk. Accordingly, (l + a)''q is the dynamicpressure at the propeller disk. Ihe value of f(a,)q isonly slightly less tha:; (l + a)^q for moderate inflov/s.Ecuaticn (l) shoTS , t'lerefore, that the side force for agiven angle of yaw is roughly proportional to the dynamicpressure at the prcpeixer disk as augmented hy the inflow.A chart of the va,riation of f ( a) v;ith Tq is given inf i gur el.

j'p inner i act or If the r^ropeller is i^rovided\;ith a spinner in comhination vrith a 1 iquidco oled na-celle, the cir cunf er ent ial component of the side v/ind dueto yaw is consider ahl;- increased in the region of the"blade ch?,nk3 'This circumstance increases the side force"by a f actor kg v:hich is closely given ~Qir

K1 + '

-' -(r-E/x)'" ( 0/D0.75H )sin 3o ^''--^

/ (Vô,(lb)

7 5pjsin 3q d:


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xirhere xg is the1,5

tio of the spinner radius to the tiprali-CLS and K is a ccnstant which is appr oxi'Uit ely 0,90for a nacelle finep.e5s ratio of 6 and 1.00 for a finenessr?.tio of infinity. Por the spinners of presentday usa~;e,

is o: le order of 1.14 0.04A sir.ilar effect undouht edly occurs v:hen spinnersare used v/ith air cooled nacelles, "out the estimation ofkg is aore difficult. It is recoanended that the factor1.14 "be u s e dS i d e \ra sh factor -. g^

due to t-ie side\;a,sh of the slipstrean is accounted forTd7 the sidev.'ash fa-ctor l-g_ and "by the deviation off(a) fror. the value (l + a)'". IHie accurate expressionfor

. The reduction of side force

-â IS

+ P,-}.)'"^r.l ^ 2

( o/h . 7 5?. ) s in p o is 0.4.

E e nu ire d a c cur p. cy , --S an d To the de;ree invrhich conparison with erristini^ experiments est ablisliesthe accuracy ahout ilO j-ercent of the sideforceformulas, it is sufficiently acciirate to use the meanvaln.e 0.4 for >"a and, for the usual sirê spinner( X3 = O.ln), 1,14 for kg.

Phystudy ofof t:le 3data fort i n r- ?3 "^^pr et at iacts lilcar e a ofar e a prof r 1 ata z in uth;

sical interpre t at i onequations (l)

id ear e a index I , an d._^ o]2 el ler in yav: . A

and ( 2 ) in 1 i gh t of the d i s cu s sl-t i'x e Qf a, c t r i ( a ) , v;J- ""representative proxjellers, sho--:s that the eqû

e consistent with the following physical inter-n: In develcpinf; side force in yav;, the prope

a fin of v/hich the area is the projected sidthe propeller. (The projected side area is th.iected ly the "blades on a plane through the axion. i''or t-;o or one "blade, this area varies v"but the text refers to the average value, v/hi

ionith

Hereeisithch


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is given to a close approximation by onehalf the nunberof olades tiass the area projected by a single blade on aplane containing the blade center line and the axis ofrotation.) iThis equivalent fin ma;- v/ith small error beregarded as situated in the inflow at the propeller diskand subject to the ccr r osponding auf!;mented dynamic pres-sure, 'J:he variation of inflov? velocity therefore acccLintsfor Liort he variation of side force v;ith advance-d i px\ 1 er ratio, for a f i :: edp i t cri propeller.

is!' J.

less VIZ

The effective aspect ratio of the projected side areaof the order of tv.-c thirds the geometric aspect ratio

rotiition. The effective aspect ratio is much-single than v.ith dual r otat ion ; the smaller as-pect ratio accounts for a reduction in the side force,v/hich for the nix ulade Hamilton Standai'd propeller cl55varies from 4 perceiit at p = 55 to 24 percent at P = 15A mean val"ae of the effective aspect ratio for sin.^le ,anddualrot at inf; propellers of present-day usage is 8.

3.a,t e of Chan;e of SideForce Coefficient vfith Angleof Yaw for S ingl eH ot at in; Propeller

Por a c in^:l er 1 at in^: propeller, the sideforceder ivat ive is

Cylii

SY/o'i> kf(a)al,Ii/( ^1 - ^') + r_^ai. (3)

The definitions of eouation (l) still apply and

v.'h er e

A = V .";;a alp + 2 ac-( 1 + al^ )

(2a)

T =I ^0

1/ (b/bo.-7 5R -OS p^ xd:

cosrT) COS x^dx(2b)

(2c)


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3, s theA i''a:nilv cf appr oxirr.at e curves of It are given in fig-ure 2 a^ functions of V/nD, ^^'ith the solidity apararaetaro T'hc curves are applica"ble for "blaclsettings at a given value of V / nD in the range in vrhichthe Dlades are not stalled. The data of figure 2 werecompiited for a definite "propeller, Hajnilton Sta.ndard 31556,cut Ji'.aj'' 'oe applied to any other propeller \;ith negligililserror in Cyi,. The variation of 3a/n v.'ith T isgiven 1 1 ,e:ur e c^

The terra A is positive over the operating range ofthe propeller in flight and is roughly onetenth of Ij_oComparison of eriLiation (s) for single rotation V'ith equa-tion (l) for dual ro-ation s'lo-'s tha.t the effect of posi-tive A is a reduction in Gvi that is, a singlerotating propeller experiences less side force inthan t!ie corresponding dualr ot at ing propeller. 'a''.'

'^'nsfor l0V7duct iond i s k loa.du c e s thpone ntof y av.f.suit antload ingspen s ate.

its av er ag e is 15 p or c e nt . The fact that the asyrnuetryred-action in side force in yaw reaches 241 ad e an gl e c.

is explained oyding, which for the singler ot at ing propolle pitching moment due to yaw, also inducesf flovi- tending to reduce the effect of thePor dr.alr ot at ing propellers, there is noasj-jviinotry o a cause the as yH:.ie tries of the diof the two sections arc so dis'oosed as to

2:1 e r c e nth e r eof

er proa CO.::angler eskcoa

Rate of Change of Pitching Homentv/ith Angle of Yo^v

3?or a du.alr ot at ing propeller, the p it chin gmomentderivative is ai:pr or.ii/.at ely zero for the reason previouslymentioned. ?or a s inglerotating propeller, this deriva-tive is given "by

"h.^hll/c'i' kgf(a)iaqDS' " 1 + k^^ad. (3)

whore the -.oositive sign is to "be taken for a righthandpropeller and the negative sign, for a lefthand propeller.


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10

The definitions prcviouslj- given arc applicable here andCTI3 + ?.J ~in = rrz -rv- (3a)3(1+ crl3 )

S IDIl-F OH CE CH AP. TS

J'oi-Kulas (1) and (2) have been used to compute aserie.?. of charts of the sideforce derivative

^Y'^^' - ~irf~

This derivative, otherwise interpretectvfice the .area of an equivalent fin osratio divided by the disk area.

is approximatelyaverage aspect

for e.solidibladeE am i 1r icalthe 0.h a s aand ad i s t r i

a enrangf c r ~ion 3aboueonv; i ;lr ountut i

ch ar t t- the V p,r i a t i n ofe anf:l3S and a'pplies

.VCGe c f b 1 a dThere is a series ofs. One blade forir; is

v;i th Vto a definitecharts for each of tvro

a CO nv ent-ion al t yj) e ,

/nD

tandard 51556, v'ith a plan form almost synr.ctt the maxiE-am chord, which is at appr ovir^at elystation. The other blade form, ITACA 1 0-3063-0 45 ,, alTiOst uuif orra chord out to the 0,75?. stationded tip section. The plan forms and pitchons for tJie tv;o propellers are shown in figure 4-,

Hami lton Sta.ndard prop ell cr 315 56 , The char t s offifi;o.res 5 to 9 appl-- to Hamilton Standard propeller 31556,Fig-aros 5, 6, 7, and 8 are for the two-, three, four,and t'. ixblade s ingl er ot at ing propellers, respectively.Figure 9 in for a si:-:blade dualr ot at ing propeller. Thesolidity g varies from 0,061 for the t\/oblade propellerto 0,1S2 for the si:-:blade xr oueller s .

A 1 i-'V.idcoded nacelle of fineness ratio 6 vras tSsuracd and the spinner diameter v;as taken as 0,164 timesthe propeller diameter in determining the spinner factorkg. The averat,'c value of kg, v/hich depends slightly on:ho blade-an^.le setting, is about 1.125. ' i : aluesignifies that, en the average, 12. o percent has been addedto the values v/hich v.'ould be obtained in the absence of as-D inner


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11

-2 ixsod in tho computations wereoôtaincd irom figures S4 and 35 of referonce S for tho25 p.nd 45 "blade angles and '-'crc int erpolfit ed for theother I'ladc -.Ufvlcs v'ith the aid of lifure 15 of refer-ence ?.

iiMi: prop eller 10-5055-045,- The charts of figures10 to 13 apply to I'lACA pr opell or 10-3062-045. Pigurcra 10,11, r:xd 12 arc for the tv-o , three, and fourblade singleroto.tin-v; propellers, r e sr)C ct ively . Figure 13 is for asixI'lade dualr ot at i r.fr propeller. The solidity a variesfro.-u 0.0325 for the tv.ro-olade propeller to 0.2-17 for thesix clad e prop oiler.

The sp inner-nac ell e proportions were taken the sameas for Ilauilton Standard propeller 31556, and tho corre-sponding avcrn,^-ô valiie of the spinner factor hg is 1.15.

The values of Tp used in the coniput at i ons veroohtained from unpubl isli ed cxp er fe. ent al carves for thethree- "blade s ingle r ot at ing propeller. The cxirves vrereextrapolated for fcv/er "blcades o,nd for xore blades andfor dual rotation with the aid of figures 24 and 26 ofreference Go It is "Ijelieved that the errors in ^yi ,introduced hy errors in tlic extrapolation are vfithin 2or 5 Tjcrcent.

C onipar is on viith ^'^v er imen t . It gur c 14 p r e s en t s t h evariation of the sideforce derivati%'e v/ith advancediaraeter ratio for tl.ie two"blade model propeller of refer-ence 4. Curver. computed from the fornulas of the presentreport are plotted '-ith the experimental valîes.

In t erp 1 at i c n f o :: 'c 1 ad sh a]'' e 'in d s ol idity . "hecomputations show that, within the usual range, "blade tviristhas a relatively s'nn.11 effect on Cvi..,. The three in-portant- wpar-'mc t cr 3 are solidity, "olade angle at 0.753., and plan form,for a given Y/nD. The charts for .a given ;plan form maybe interpolated line,arly from the charted values for varia-tions of solidity cr and olade angle P,

"he det era inat i on of Cy',i, for plan forms "betv;ecnthose of hamiiton Standard prorjeller 31556 and FACApropeller 103062045 would be expected to require adoLible interpolation, one for solidity, because the two


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IP.

propellers aro not chsxted at the same solidities, anda second cue for plan form. A simpler proccdv.rc rGGultsfro;.: tliG f ollO'-.'in>r considerations:

Poi- a given solidity, it is found that the plan foraof ^he ITACA propeller 103063-045 yields aeout 13 percentffi-jro si.lc force than does the plan foru of th 3 HamiltonStandard propeller ?1556 at the same V/r.D. The factor1,13 holds v/iTihin 2 or 3 percent near the line of zerothrust although the error increases to ahout 6 percent atlov/ T/n3 and hi^h thrust. "o this accuracy the side-force coefficient for a propeller of a given plan fornazid solidity a - 0-091, for ci-ample, could ha estii'iatGdfrom the a ~ 0.091 chart of Hamilton Sta.ndard propeller3155G hy co.v.pc-r in.'?; the f:iven plan form '-/ith the plan formsof Eainilton Standard 3155G and iJAOA 10oCo2 045 propellersin figiirc 4 and increasing the ordina,te3 from the cha.rt h;'the apipropriate fraction of 13 percent. In making the plan-f orm compar i s on , most ght should he f?;iven the root sec-tions of the "olado. If the solidity a does not corre-spond to that cf one of the cha,rts, tv;o charts of differente saiwe propeller aay he interpolated linearly.olidity for the

u o o 1 c I s for propellers i n p i t ch , - cnar tsv;ith pit ch 3uus trate of ch an gethrus t axi s, ifflov: at th e propt aken into a ccouv/ing, Dy mul tipl

ituted for ya,;: can oe uced to ohtain thef ncrinal force vith angle of .'ttack ofthe influence of the wing on the angle ofoiler is included. 'The upv;ash can oeLt, the 'ororseller in front of theying the value of Cyt,,, now interpreted/

ls / ocr,rp hy 1 plus the rate of change withanglo of a J. J.,1/ U ackPCHer hy th v; ith e fa c 1 r s hou 1of att aclc of thehy the M i ng.

of the angle of upvash indiiced at the pro-ng. If the propeller is "celiind the v;ing,d he 1 minus the rate of change with angleangle of downwash induced at the -nro-Doller

COUCIUDIFG- HSIIASKS

3nuo,tions for propellers in yav; and charts o:sideforce derivative have oeen given herein for singleand dualr otat ing propellers in terms of a sidearea indexand a d7,-n


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i:3

mi.thaiint

. V.' .ctor. Tho rtud7 of tl'.oso eauationsth .r c ons 1 r7' cnt '.v'itli the following pli:

.rpr ct at ion : In devolopinfi- side lorcG, thoactsap ather oui n

'in of r.'hich ths area is thi r oj ocof the propeller, the effective aspect ratand the effective dynamic prcsGu.

nt odti

oraer oz cf;'hly -hat at tho propeller dish &,s augraelov.r. I'hc variation of the inflov; velocich iorcpeller, accounts for most of tho v;itforce v/ i t h .adv an c gd i aa ot e r ratio. ia

d i c atf: icalpr opeted' si i nre isby t

1 -: at ion

esHeridcof

hefixe dof side

Lan^-lc,7 Meinorial Aer on a'at ical Laooratory,ilational Advicory Cor.mittec for Aeronautics,La:T.j;ley Tield, Ta.

APPZiir IX

Gauss' rule for approximate integration may bee:cpr cs s .id by tliC relation

f (:Od:c ~ P.f(yi) + P2i'(:c.) + . . . + Pn? ( :',,)whor c Z X-.1 t a in ab f. c i 6 s as and P , to Pj_ w v.- ._%i ill' u l; ...i. .- J-ii '^ u ; u J. ;3 13 ti.o c'-.'ii'^ j, -^ u u i" pare G-a-ass' coefficients. For the integrals of thr, presentreport, five ordinatcs c:


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14

IA s ,ur, c X as: i'. 1 e , t h o i :: t c ::;r r.l / ( '- / -which o^cT.rs! ir. l^ Eay be cvaliiat ccl as

.75r.)3in Po d:

^^"-^A''c .areP.. o s i n P n ^ -^+0.19 1-^p-^/3)o..:;e5H -nin 3,

\ f^ / - / .600?,^ _ . ( b /it ) o a 1 5 ?-( -r- /: ^ _ ^ con"" ( "n/")^ --. '^0,315

J-n nc ."^ , a v O,^o.vsH

vncr ct/D

ha? hcGn r-^'ittcn for its ''r it iv.?,lcnt"b/bj^Tj;^ ill r ucoj:;?! i'b ion oi' th 3 practice of uning b/Das t>..c -ijI-t-f ori?. variable.


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15

HSITEHEIICIS

1, Harrin, 3., fe , : Forcon on a Fx-opcllor L j o to Sido3l:.p. R. :j I:. 2io. 427, 3ritiF:h A.C.A,, 1918.

2. G-lauort , H . : The StaDilit;^ D sr ivr t i-rcjs of an lirscrcvH,. & M. I'd. 642, British A.C.A. , 1919.

3, G-cctt, Kn.rry J., r-nd Prss, H. H.: Iffect of PropollorOperation on the Pitchinc MoniantG of 3 in.f^l eSnginoHonoplanos. ITAC A A.G.2., May 194]..4, Lesley, B. F., Worley, Goorge F., and I'.oy , StanloytAir Propjll3T-s in law. 3ev. Fo. 5? 7, ITACA, IS 37.5, Mtink, Ke.x II,: Fundaiuent al s of Fl-aid Dynair^icc forAircraft Fesi:5ners, "he Sonald Press Co., 1S39,

-n "O6 . E V.n c 1: G 1 , J .^ c;k Jho Effect of Fitch on For. arc

of FivG Solidities. i"ACA A.H.F., June 1942.7, Ficrrriann, David, and Hfirh;an, Edwin P.; Tests of TwoFullScale Propellers v/ith F^ifforcnt Pitch Distri

'butions, at Blade Aiz.


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ITAGA li.-s. 1,2

?.0

/ !

/' "\" r ! H h-- r !

i

I

j

i

1.0 1.4 1.8 ?.0

Figure 1.- VaricJotion of .|-factor f(a) with T:^. 1^ = Cq]/ (v/nD)^.


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KA?A

.8 i.O 1.2 1.4 l.S 1.3 ?.0

Figure 3.- 'variation of Pa/rr with T^ T,. = C'l/ i'j/nD)^

1.2 r T"L I ! I ! iI

HACA propeller 10-3052-0-5>'^i iI , I 1 1 w 1 1__j;r_. L

in

o

Hpmilton StauiardproTDeller 31b:3-r

pip.b

II

I ^

,^_Wbo.75R --^-

i--h-f..-._4-V--V-

V"

iI ITACA propeller 10-3002-045, 3 =- 13.2'^ at O.VdH ' U

! I '/I P/D,,1' i.^-.

I i

I I

_HairJ.lt oxi_' btaridard _pr^3peller__31ot)-G, 3 - 2D^at 0.7oH -j"'

I I I ! _'.J L.1 .3X - v/r

T.7'

3.0

2.0p/d1.0

.y 1.0

Figiare 4.- Plan forins and pitcli iibtri-^-'j.tions of IJAQA iO-SO^c-04o


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HACA.40

,3?

?i^S. 5,'^

.S4!

.08t

1

1

.,

1

1

i

1 i

!

1

1

1i Â .~r] 11 1

i

i

1

11

Ii

1

j1 O'r,^ U_j__^ tt,' -' 1 Soo' 1\^ M-J .(- >l \ -'\- -" iO'^ -430 - -; 1^ " T 35-1 1 ~^..}.'.".] : "xno, 1s ^'-^~f~i: Scî 1 1.-;- ..\

I int=~ 8 ^ io' at J. V;;

I

^-!

! i

5 OT Z -!

ru I1

Sti

; 1

1 1

1.? 1.^ ?.0 ?.4 ?.b 3,?7/nD

4.0

Fiirure o.- Slie-force ieriv'ttive for sinsle-roto tins Fairiilton Stsr.iardprooeller 315o-" with spinner. Two blaies, S, 0.0--1.

.08

OL

B ^ lo'-' at O.VoRj-ine of zero tnrust "T" ..._L..

J L. O 1.? 1.6 ?.0 P.i ?.VnD 3.? 3.6 4.0

Jieâre 6.- Sile-force derivative for i?in^le-rotatine Hamilton Standardpropeller 3165-6 witn soinner. Three l^lades, cr, 0.0^1.


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1 . 1 . Sv/nD

?. 3.2 o.'^ 4.0Fisrare V._ Siie-force ierivative for sini?le-rntatinj?' Hamiltori Staniariprapeller Slob-o with spinner. Fo-ur blades, o', 0.1?1.

4.0

?inire 8.- Siie-force Ierivative for single-rotating Hamilton Staniaripropeller 31o5-'^ witn spinner. Six blaies, a', O.is?.


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ui:-A.

. B 3.? 3.-^ 4.0

i'i^^ire b.- Siie-force ierivgti"''e for iu'^.l-rJt^ti1? Familton St-niaripropeller "^loj-P --vitli Kpinner. 3i" lr;lai.es, o'. 'i.lPP.

v/aD) .


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Fiffej-force dorivativo for sin^lo-rotating flACA propeller


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'ifir.s. 13,14

.8 1.2Vr/nD

2.4 ?.8 3.2 3.6 4.0

Fit]xirt=! 13.- :jiie-force derivativa for di;al-i-otating ilAOA prone] lur10-3032-045 with spinner. Six Dlaies, a, 0.247.

I

.1':

OY I

.12

.OS

.04

"T"T"I -I |_Sat0.7oR iSxperimental Calc-alated -J^ _ (i;-:)

0..= L\I 24. D23." V ^ -

-r

J ,u--i

I

l._ L

rfmtmm^^^^-^,-r^r.^--.L-

1-- i-^Llni4^-

of zero thrust

.8 1.0 1.2 1.4 1.6J = '^/nD 1.8Fi^re 14.- Comparison of calc^alatcd and oxperincntal side-forcederivatives for tv/o-tlade raoiel propeller. Curves ar!


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UNIVERSITY OF FLORIDA

3 1262 08106 520 2

UNIVEBSnV OF FLORIDA

SSra 33611-7011 US.

Documents

Formulas for Prope 00 Lang