1、4(.I-.,!1.,WT. DOGNATIONAL ADVISORY COMMHTEEFOR A.ERONAU IICSTECHNICAL NOTENo.13)3.A TRANSONIC PROPELLER OF TRIANGULAR PLAN FORMBy Herbert S.RibnerLangleyMemorial AeronauticalLaboratoryLangleyField,Va.v!WashingtoiiMay 1947P .*- .I-USINESS,SCIENCEmoreextendedsignificancein appendixB;yrop-ulsiveeffici
2、encypreemre ,.massdensityof airflightvelocityradiusof pro.lerdiameterof propeller(baseof isoscelestriangle)bladBchordof yropellerlootbladechordof propeller(heightof isoscelestri-sngle)pitchof propeller-mileadmmce-dismeterratio (V/nD)JN nomsl forceQT thrustProvided by IHSNot for ResaleNo reproduction
3、 or networking permitted without license from IHS-,-,-NACATNYIYal%sNo.1303.forceparallelto y-axismomentof inertiaacuteanglebetweenx-sxisandbladesectionangleof .MtackSubscriptsandcoefficient(Drag/qS)areasuperscripts:L.E. measuredat leadingedge, .T.E. measuredat trailingedees duetOn duetof duetoP duet
4、oi idealsuctionnomuilforce“skinfrictionpressureR “ resultantWt weightedTHEORYFoRFLATHAN FORMThe theorythatis developedhereini.gderivedfromthetheoryof two-dimensional”flowspresentedin reference1. Thepresenttreatmentfortherotatintriangle,as thatof reference1 forthetriangleat an angleof attack,appliest
5、o thelimitingcondi-tionof verylowaspectratio. TheLimitationson aspectratioarediscussedin the sectionentitled“AspectratiotandinappendixA. .Reference1 pointsout thatthefl.ow.abouta pointedairfoilof verylow aspectratiomay be consideredtwodimensionalwhenviewedin crosssectionsperpendicularto thedirection
6、ofmotion.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.4 NACATN No,1303Considerk longflattriangukrairfoilmovingpointforemostandrotatingaboutthe -, ,.,. . . . . . . . . . . , :.:.:;:+,:,T;.:-,=:,: “. .”v: - . . . . . . . -:., : ., -: . . ,. -y, . .
7、 . :., .-. . -. . -.-.e. . -”,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,NACATN NO a71 1303 7.for thethrustoftheuntwistedpropeller.Thisvalue,in whichtheprofiledragisneglected,is called.the idealthrust. The idealthrustis thusindependentof forrd
8、epeedao longas equation(7)is applicable.Applicabilityis limitetito therangeof smalllocalangleof attack,orhighvaluesof V/KDOEfficiency.-The idealefficiencyof theflattriangularpro-peller(thatis,the”efficiency”tithprofiladragneglected)isThe insertionofequations(5)and (7)givesa valueof 1/2,or50 percent.
9、 It is shownhereinafterthattheaddition.of a suitabletwistallowsa peakidealefficiencyof 100percent. /Origin of thethrust.-The wakeof an ordinarypropellerbehaves “likea twistedribbonmovingaxiallyrearward.Backwa?xlmamentumis impazzedto theairwith the s . .:.,;, ,-: , , . , .:, .,. . . ., - :- - .-:;:,.
10、 - ?, 2 . .:-, -,:.tj,+.-. ,. ,-, ,. /.-. . . . . . . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-MACA.TNOo 1303 9“The powerinputminusthewalce”powershouldequaltheusefulpoweras follows:m.ru6t pow it iSIIDapproximtdy() Jmy l-p/D,.(lo)The ccmresp
11、ondingvelocitycomponentfortheflatplanformis oy. . Torqw.- AccorUngto theforegoingdiscussion,theslighttwistedplanform(pitch,p) rotatingwithangularvelocitymexhibitsthesme two-dimensional-flowpatternat a section xas a fistplanformrotatingtithangularvelocityapproxl-()Jmately 1- . The pressuredlstriution
12、forthe slightlyPbtwistedpl,j, -,.;+,:.; :,.:. .,-: .,-. -.-. - -. -.,-,. :“,.-.:.,;j+(t):+-(zj.,.may be pactly -(B4). . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN NO.1303Implicitd.ifferent : ,. :+-. . . ,:. 7 .1, ,.-+-.“:;+.-.,7:X,. , ,
13、- : .:.”; - ,:“:-.,. -.?. . . . ,- .:-. . . .,. . :-., .,.+ . ,.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NAC!ATN NO.1303 25The substitutionofeqlt?.ons(B7)and (B8)in equatio(B4)givestheexcesspresspreaa .Al?= w2(a + b)28/2c2e-2(*22q- )(Sinh25 Co
14、s27,- a +b)2e-45 (B9)JThe excesspressureforceonan elementof surfaceof theellipticcylinderof unitlengthin theaxialdirection(x-direction)hasa caaponentparallelto they-axisofamountAt the surfaceof”thecyltider(,=,.),Y= ccoahOcosq=acos q 1(B1O)Therefore. =Substitutingequation(B9)intoequatim (B1.1)with $
15、= go,eliminatinggo and c by meansof equations(BIO),and evaluatingJgives( 2ab2(a+b)2 2(a-b)2 sin22- )1COS 29 -(a-b)2 b cos dqa2-2a.F=-8(a2sin2V+ b2 co82q)(B12)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-lWMA NO.1303a26m ”b) thisIs approximatelyfYo
16、2a%(2ein22q- 1) cosq dqdF=-8(a2sin2q+ b2)The integralfromthemiddleofthebottomsurfacearoundtherightedgeto themiddleofthetopsurfaceis.and(B13)This givesthe suctionrotatingflatplateofperunitlenh actingat the edgesof asemiwidtha.Provided by IHSNot for ResaleNo reproduction or networking permitted withou
17、t license from IHS-,-,-.,“ . IUTEGMTIONOFOFJ?orpurpoeesofsideredthe limiting- -AhlmMtic . ., . . . . .! ,.-,. .,lmEsmREmovERmm N-To AlmsWAKE OF _ ,-.calculationtheflat-ribbon%Msemay be con-formCd? ellinticcvlinderas +ileminoraxisShrhlkS to zero. Tus,the excesso theocalprespwe overthe “streamWesaureo
18、derivedIn apexix,B“*s;.applicablelikewisehere. “ . . .-,.In anypiane x = Constant,p“nlemetof areainthe coordi-nate C,q is givenby J d d where J is theJacobiandefinedafterequation(B6). The excespressurefce on thlaelementofareais. . .Substitutingfor AP fromequation(B9)gfves1al?= (I+ (E+ *c2e.2g )sin22
19、q-sinh 2E coa27 -(a+b) e 1243aga?8= fm2(a+b)2 28,.(cl)The exoesspressureforceonthe entireplane x = Constant is .obtainedby integratingfrom O to 2SX in andfrom 30 to ain g, where = definestheboundaryof the ellipticcyl.jmr.The integrationves ,.-dgoF=&c2(a+3)2e c -&-4301(a+ b)2 2 (C2)Provided by IHSNot
20、 for ResaleNo reproduction or networking permitted without license from IHS-,-,-28 NACA NO. 1303 The ldmitof thisexpressionas the ellipticcylindershrinlmintoa flatribbon (+o, )!3.+0, c-a isalim F= 24- ag+oSincethe semiwid.th.a of theflat-rilbonwakeis one-halftheriiameterD of thetrianglethisis(C3).wh
21、i.ohisinagreement&th equation“(7).Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.lTACA NO. 1303 29,.AJ?PENDIXDcoMPom OF REsumNT VEWCITYNURMKLTOLZMDINGIWGEOFTWISD3DTRIANGLEINSCREWM3TIONThe twistedtrianglemay bedefinedthin itsenvelopeconer=cx1.by the
22、screwsurfacei92=CxAn elamentofthe edgenaybe expressedbyis a unitvectorinthedirectioniere 1 a unitvecta in thedirectionof increasingvectoralong x. Thu3 .of increasingr, 31 ise, and? is aunit= Tlcl + 1rc2+ 3by equations(Dl)and (D2).L-et= be a vectorlyingtithe surfacethe edgewithpositivesenseoutward. Itmaytriplevectarproduct(m),.-andperpendiculartobe obtainedby the”.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
