NASA NACA-TR-819-1945 Formulas for propellers in yaw and charts of the side-force derivative《偏航螺旋桨和侧向力导数图表的公式》.pdf

1、NATIONAL TECHNICAL_IN_FIELD,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NOTICETHIS DOCUMENT HAS BEEN REPRODUCEDFROM THE BEST COPY FURNISHED US BYTHE

2、 SPONSORING AGENCY. ALTHOUGH ITIS RECOGNIZED THAT CERTAIN PORTIONSARE ILLEGIBLE, IT IS BEING RELEASEDIN THE INTEREST OF MAKING AVAILABLEAS MUCH “INFORMATION AS POSSIBLE.!| -0“-aProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT No. 819FORMULAS FO

3、R PROPELLERS IN YAW AND CHARTSOF THE SIDE-FORCE DERIVATIVEBy HERBERT S. RIBNERLangley Memorial Aeronautical LaboratoryLangley Field, Va.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-National Advisory Committee for AeronauticsHeadfuarters, 1500 New

4、Hampshire Avenue NW., Washington _5, D. C.Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientific studyof the problems of flight (U. S. Code, title 49, sec. 241). Its membership was increased to 15 by act approvedMarch 2, 1929. The members are appointed

5、 by the President, and serve as such without compensation.JEROME C. HUNSAEER, So. D., Cambridge, ._Iass ChairmanLVMAN J. BRINGS, Ph.D., Vice Chairman, Director, NationalBureau (f Standards.C_ARLES G. ABsor, Sc. D., Vice Chairman, Ezecutive Committee,Secretary, Smithsont_n Institution.HEsRv H. ARNOLD

6、, General, United States Army, CommandingGeneral, Army Air Forces, War Department.WIr.LrAM A. M. BURDEN, Assistant Secretary of Commerce forAeronautics.VANNEVAI_ BUSH, Se. D., Director, Office of Scientific Researchand Development, Washington, D. C.WILr.ZA u F. DuRAsI), Ph.D., Stanford University, C

7、alifornia.OLIVER P. ECHOLS, Major General, United States Army, Chiefof Materiel, Maintenance,.and Distribution, Army Air Forces,War Department.ACnREY W. FiT(:n, Vice Admiral. United States Navy, DeputyChief of Naval Operations (Air). Navy Department.WmLIAM LITTLEWOOD, M. E., Jackson tIeights, Long I

8、sland,N.Y.FRANCIS W. REICHELDERFER, So. D., Chief, United StatesWeather Bureau.LAWRENCE B. RWHARDSON, Rear Admiral, United States Navy,Assistant Chief, Bureau of Aeronautics, Navy Department.EDwAav WARNER, SC. D., Civil Aeronautics Board, Wa._hington,D.C.OaVtLLE WRInHT, So. D., Dayton. Ohio.THEO_OE_

9、- P. WRW,_T, Sc. D., Administrator of Civil Aero-nautics, Department of Commerce.Gr.oao_t W. L_-wls, Se. D., Director of Aeronautical ResearchJoss F. VietORT, LL. M., Secretary.HEART J. E. REIn, So. D., Engineer-in-Charge, Langley Memorial Aeronautical Lal3oratory, Langley Field, Vs.Smvrt J. DEFRANC

10、E, B. S., Engineer-in-Charge, Ames Aeronantical Laboratory, Moffett Field, Calif.EDWARD R. S_ARP, LL.B., Manager, Aircraft Engine Research Laboratory, Cleveland Airport, Cleveland, OhioCARLTON KgMPER, B. S., Executive Engineer, Aircraft EnginetResearch Laboratory, Cleveland Airport, Cleveland, OhioT

11、ECHNICAL COMMITTEESAERODYNAMICS OPERATINO PRORLEMSPOWER PLANTS FOR AIRCRArI MATERIALS RtlSEARCII COORDINATIftNAIRCRA l_rCONSTRUCTIONCoordination of Research Needs of Military anti C/nit .4t, latlonPreparation of Research ProqratnsAllocation of ProblemsPrevention of DuplicationLANGLEY MEMOWIAL AERONA

12、UTICAL LABORATORY AMES AERONAUTICAL LASNRATNRYLangley Field, Vs. Moff(,It Fh,ld, Calif.AIRCRAFT ENnINE RESEARCH I,AnORATORY, Clevelaad Airport, Cleveland, OhioConduct, under unified control, for all aoencies, of scientific research on the fundamental problems of flightOFIqCE OF AERONAUTICAL NTELLInE

13、NCE, Wcries of (harts for the estimation of the rate of change of)repeller side force with angle of yaw. Although the formulaew_oped by Harris and Olauert in references l and 2 andliscussed in reference 3, which expresses the side force in,-aw in terms of coefficients for the unyawed propeller, isai

14、rly _atisfactory, there has been no adequate formula based)timarily on the geometry of the propeller blades. Anmpublishi,d analysis has resulted in such a formula. The_asi(“ assumptions are similar to those of the vortex theoryor the uninclined propeller when the Goldstein correctionor finite number

15、 of blades is omitted. Comparison with ammber of experimental results has indicated that the ac-_zracy of :i= IO percent obtainable by the analytical methods of the order obtained by the uncorrected vortex theory“or the unin(tined propeller.Tlw formula developed in the analysis and given hereinhas t

16、wcn us(,d to l)reparc a series of charts giving the rate of7_057_-48change of side-force coefficient with angle of yaw as a func-tion of the advance-diameter ratio V/nD; the blade angleand solidity are parameters; the charts cover both singleand dual rotation. The computations were made for tworepre

17、sentative propellers, the Hamilton Standard 3155-6and the NACA 10-3062-045. ,_eans are given for inter-polating for other propellers.In order to make the present report complete in itself andto make the charts more intel_gible, formulas for the side-force and pitching-moment derivatives are given at

18、 theoutset with an explanatory text. The other propellerstability derivatives with respect to yaw are zero.For the purpose of expediting the publication of the charts,the derivation of the formulas has been omitted from thepresent paper. There is included herein, however, a graphthat shows a compari

19、son of the theoretical values with theexperimental data of Lesley, Worley, and Moy (reference 4).SYMBOLSThe formulas of the present report refer to a system ofbody axes. For single-rotating propellers, the origin is atthe intersection of the axis of rotation and the plane of rota-tion; for dual-rota

20、ting propellers, the origin is on the axis ofrotation halfway between the planes of rotation of the frontand rear propellers. The X-axis is coincident with the axisof rotation and is directed forward; the Y-axis is directed tothe right; and the Z-axis is directed downwaM. The sym-bols are defined as

21、 follows:D propeller diameterR tip radiusr radius to any blade elementS disk area (TrD_/4)x fraction of tip rtuius (r/R)x0 minimum fraction of tip radius at which shank bladesections develop lift (taken as 0.2)x_ ratio of spinner radius to tip radiusB number of bla_Pof zero fhrusf I-.40 35 I.16.4 B

22、1.2 t.6 _0 2._ 2.8 3.2V/,=DFIGU ag 13.-Side-force derlvatlve for dual-rotating NACA propeller t0-3062-045 with spinner. Six blades; -0.247.3.6 4.0.24.Eo./6.12,O80 .0 _ o_z$_ thru.,B of“ 0.75R Experimentol Colculofed(d.q)/6.6 0ZO.6 “_24.6 028.6 V.o. llll0 .2 .4 .6 .8 /.o 1.2 1.4 /.6 1.8V.l=,-k-d.|“I_

23、,_ 1_.: 14.-Olnl_Lri.a.t of :tlc.izLh. _TI_ _,x|a,liln.nl_t| _ida_5_rre dl,rivltLivcs or two-blade model prolm|h,r. Ctlr%e._ :tr. t,rmitl:ttec, txt_l*g or _= I(kl; , :_! i_in! wh.n, .bvt.Us _lal|irlg of_l|al.(q_ Ck_Lll_. _,xlx!lJm,gltl_l ch=t_, fr_)llrl roft,r(,nPi. 4.Provided by IHSNot for ResaleNo

24、 reproduction or networking permitted without license from IHS-,-,-12 REPORT NO. S Ig-NATIONAL ADVISORY COM.MITTEE FOR AERO_XAUTICSCONCLUDING REMARKSEquations for propellers in yaw and charts of the side-forcederivative have been given herein for single- and dual-rotating propellers in terms of a si

25、de-area index and adynamic-pressure factor, which is a function of the inflowfactor. The study of these equations indicates that they areconsistent with the following physical interpretation: In de-veloping side force, the propeller acts like a fin of which thearea is the projected side area of tile

26、 propeller, the effectiveaspect ratio is of the order of 8, and the effective dynamicpressure is roughly that at the propeller disk as augmente,by the inflow. The variation of the inflow velocity, forfixed-pitch propeller, accounts for most of the variation oside-force with advance-diameter ratio.LA

27、NGLEY MEMORIAL AERONAtTICAL LABORATORY,NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS,LANGLEY FIELD, VA., April 7, 1948.APPENDIXGauss rule forapproximate integration may be expressedby the relationwhere x,toz.are certainabscissasand P, toP. areGausscoefficients.For the integralsof the presentreport,fiv

28、eordinatesarefound tobe sufficienttodetermine Cr,withinI percent. For zo taken as 0.2 and z.+_taken as I,theappropriate values arext = 0.238 Pl = 0.095x2=0.385 P2=0.191x,=0.600 /3=0.228x4=0.815 P_=0.191x5=0.963 P_ = 0.095f :bAs an example, the integral _ sin ;30dx which occursin It may be evaluated

29、as(b/D)o._5, sin _oo._(b/D) o.23,_sin _o_.a3sa+ 0.191 (b/D)o.75,0.005 (b/D)o._3,+0.228 (b/D)o_, sin flogs00,+0.191 (b/D)o.s,s, sin _,o.s,._R(b/D)o.na “ (b/D)_ T_t_(b/D)o._,_,-1 0.095 ib/D)o.7sR sin _%._._,_b/D has been written for its equivalent bb_=_where (b/D)o.7_l,in recognition of the practice o

30、f using b/D as the plau-formvariable.REFERENCES1. Harris. R. G.: Forces on a Propeller Due to Sideslip. R. , 5.No. 427, British A. C. A., 1918.2. Glauert, H.: The Stability Derivatives of an Air, crew. R. & ._.No. 642, British A. C. A., 1919.3. Goett, Harry J., and Pass, H. R.: Effect of Propeller O

31、peratioa o_the Pitching Moments of Single-Engine Monoplanes. NACAACR, May 1941.4. Lesley, E. P., Worley, George F., and Moy, Stanley: Air Prop,.lh*r.in Yaw. NACA Rep. No. 597, 1937.5. Munk, Max *.: Fundamentals of Fluid Dynamics for AircraftDesigners. The Ronald Press Co., 1929, p. 79.6. Runckel, Ja

32、ck F.: The Effect of Pitch on Force and ._o|ne_t Char-acteristics of Full-Scale Propelers of Five Soiidides. NACAARR, June 1942.7. Biermann, David, and Hartman, Edwin P.: Tests of Two Ft_ll-Scale Propellers with Different Pi_ch Distribudon._. at Bla,b.A,gles _ip to 60 . NACA Rel). No. 65_, 1939.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-