1、!J. ._ . J _,-,-f-TF - 7.-_/NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSREPORT No. 721DETERMINATION OFCONTROL-SURFACE CHARACTERISTICS FROMNACA PLAIN-FLAP AND TAB DATA,- .AiBy MILTON B. AMES, Jr. snd RICHARD I. SEARS_J, fI REPRODUCEDBYNATIONAL TECHNICALi INFORMATION SERVICE$. DEPARTMENTOFCOMMERCE. Sm._
2、F|ELg.v_ _61-2“,;1941 |, wProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-AERONAUTIC SYMBOLSI. FUNDAMENTAL AND DERIVED UNITSWg771IS8.0bcAVqLDDoD_D,6Metric English Symbol jn Unit Abbrevia- Abbrevia-tion Unit tionLeP, gt_ j / meter m foot (or mile) ft
3、(or mi)|Time t second . s second (or hour) . see (or hr)Force F weight of I kilogram kg weight of Ipound IbPower . P horsepower(metric) . horsepower . hp/kilometersper hour kph miles per hour . mph-Speed . 12“ (meters per second raps feetper second fp_2. GENERAL SYMBOLSWeight _mg - “ Kinematic visco
4、sityStandard acceleration of gravity= 9.80665 m/s 2 p Density (mare per unit volume)or 32.1740 ft/sec 2 Standard density of dry air, 0.12497 k,-m-*-s: atM_t,_s_= I_f_.“ and 760 mm; or 0.002378 lb-ft- see _0 Specific weight of “standard“ air, 1.2255 kg/_Moment of ineriia=mkL (Indicate axis of 0.0765l
5、ib/cultradius of gyrs tion/c by proper subscript.)Coefficient of viscosity “8. AERODYNAMIC SYMBOLSArea i., Angle of setting of wings (relative to ihruslAr_a _f wing i, Angle of stabilizer setting (relative to lGap line)Span Q Resultant momentChord fl Resultant anguhlr vcocityAspect r_tin, b:_ R Reyn
6、olds number, p_Wwhere I is _ linear ,ITrue :lir ._pccd sion (e.g., for an airfoil of 1.0 ft chord, t001 ._ standard pressure at 15 C, the eorrespo_Dynrgni_ pressure, _p_ Reynolds number is 935,400; or for an _,Lifl, absolute _oofficient C_=L-_ of 1.0 m chord, 100 mps, the correspolq_ Reynolds number
7、 is 6,865,000)c, _ D a Angle of attackDrag, ab_lute coefficient ,_o _ _ Angle of downwashProfile ragp absolute ao Angle of attack, infinite aspect ratiocoefficientCffi=q a, Angle of attack, inducedIndue, q drag, absolute coefficient CvtzD-_ a. Angle of attack, absolute (measured fromlift position)C
8、,D, Flight-path anglePara_:,te drag, absolute coefficient _ _ 36Cross-wind force, absolute eoetficient G#=-_2626 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NOTICETHIS DOCUMENT HAS BEEN REPRODUCEDFROM THE BEST COPY FURNISHED US BYTHE SPONSORING A
9、GENCY. ALTHOUGH ITIS RECOGNIZED THAT CERTAIN PORTIONSARE ILLEGIBLE, IT IS BEING RELEASEDIN THE INTEREST OF MAKING AVAILABLEAS MUCH INFORMATION AS POSSIBLE.SProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction o
10、r networking permitted without license from IHS-,-,-ERRATANATIONAL ADVISORY COMMITTEE FOR AERONAUTICSREPORT NO. 721DETERMINATION OF CONTROL-SURFACE CHARACTERISTICS FROMNACA PLAIN-FLAP AND TAB DATAPage 7, column 2, llne 17: the parameter should read:instead of-_-_/Sf, 8t f,StPage 7, figure 4: ordinat
11、e scale should be designated “r“.Page 8, column 2, table, lines l? and 18 under “Definition“should read:Assumed ratio of tab chord to horizontal-tail chord. pa_e _i0, figure S: Aet value should be 4.5 instead of 4.2.iif!Provided by IHSNot for ResaleNo reproduction or networking permitted without lic
12、ense from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT No. 721DETERMINATION OFCONTROL-SURFACE CHARACTERISTICS FROMNACA PLAIN-FLAP AND TAB DATABy MILTON B. AMES, Jr. and RICHARD I. SEARSLangley Memorial Aeronautical LaboratoryProvide
13、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSHF.ADQUARTERB, NAVY BUILDING, WASHINGTON, D. C.(jreated by act of Congress approved March 3, 1915, for the supervision and direction of the scientific study of the pr
14、oblemsof flight (U. S. Code, Title 50, Sec. 151). Its membership was increased to 15 by act approved March 2, 1929.appointed by the President, and serve as such without compensation.V_yz_vAa Bus_. So. D Chairman,Washington, D. C._,F.olmz _. Mr.An, Sc. D., lricc Chairman,Washington, D. C.CH_a_S G_LBm
15、Yr, Sc. D.,Secretary. Smithsonian Institution.l_z_aY 1:I. AJ_o_. 3Iajor General, United States Army,Deputy Chief of Staff, Chief of the Air Cor1_, WarDepartment.GEOROE H. But“r, Major General, United States Army,Acting Chief of the Air Corps, War Department.I,Z_AX J. BRIOGS, Ph. D.,Director, Nationa
16、l Bureau of ._tandards.Do_AI.n H. Co_Z_OtZ.T, B. S.,Administrator of Civil Aeronautics.The members areRosF_rr E. Domm_, 3L S.,Pittsburgh, Pa.Rosr_wr H. Htz_c_zacr, A. BAssistant Secretary of Commerce.J_oM_ C. HUNSAK_, Se. D.,Cambridge, Mass.S_r_r _. KRAUS, Captain, United States Navy,Bureau of Aeron
17、autics, Navy Department.Fxamcm W. R_c_.vimzr_, So. D.,Chief, United States Weather Bureau._ToHzq 3. Towns, Rear Admiral, United States Navy.Chief, Bureau of Aeronautics, Navy Department.Evw_ WAL,_, Sc. D.,Washington, D. C.Olnrn.zJc Wale_, SC. D.,Dayton, Ohio.Gto_g W. Lzwzs, Director of Aerofl_utZcal
18、 ResearcA S. PAOT, $o_mgro_, Coordinator of ResearchJouzq F. V_c-roa_r, georeta_lH_r _. E. RIley, F,ngineer.in-_harge, Langley Memorial Aeronautical Laboratory, LangleyFteld, Va.S_ J. Dr.F_zqcr_ F,ngi_eer-4tt-G_harge, Ames Aeronautical Laboratory, Moffett Field, _aZi_.AEROD_NAMIC_POWER PLANT9 FOR AI
19、RCRAFTAIRCRAr_ MATERIALSTECHNICAL COMMITTEESAIRCRA_r STRUCTURESAIRCRAFT ACCIDENTSINVENTIONS AND DESIGNSCoordination of Re._earoh Needs of Military and _tv_i A_iatio_Preparation of Research ProframsAllocation of ProblemsFiegentian of Duplication_oflsideration of nveflttonsLANGLEY MEMORIAL AERONAUTICA
20、L LABORATORY_rAMES AERONAUTICAL LABORATORYLANGLEY FIELD, VA. MOFFETT FIELD, CALIF.Conduct, under unified control, for all agencies, of scientific research on the fundame,tai problems of flight.OFFICE OF AERONAUTICAL INTELLIGENCEWASHINGTON, D. C.Collection, classification, compilation, aml disseminat
21、ion ofscientific and technca| inf,rmalion -r_ :ter, n:tutlcsProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REPORT No. 721DETERMINATION OF CONTROL-SURFACE CHARACTERISTICS FROM NACAPLAIN-FLAP AND TAB DATABy MILTON B.AuES,JR.and R_CRXnDI.SzARsSUMMARYTh
22、e data -from pre_ious NACA pressure-distribution_nvestigations o,f plain flaps and tabs _oith sealed gapshave been analyzed and are presented in this paper in a-form readily applicable to the problems el control-surfacedesign. The ezperimentally determined variation of aero-dynamic parameters ,with
23、flap chord and tab chord are._ven in chart form and comparisons are ma) (- ).1)0:_2)(-0.+_7) (-+1.007+;)-11.4_Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 REPORT NO. 721-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSThe corresponding flap deflecti
24、on required to maintain equilibrium may be computed from equation (6).Thus for the example cited-_ F(-o._4) 7_/,%-o, = _I_ - (- 1.2)+ (-o.06) (_1.4)j =-3.1 When the tab 6 used as a balancblg tab, the free-floating angle of the flap may be computed from equation(7). For the example cited_/=K_/+_,o, w
25、hen _,_-1 and N=-0.5Thus, when as=- 1.2 ,(-0.093) (0.054) (- 1.2) + - (-0.093) (0.054) (-0.06) + (-0.O03211 (1!*/_e_p _= - (-0.093) (0.054) (-0.67) + (-0.0076) + (-0.5)- (- 0.093) (0.054) (-0.06) + (-0.0032) _0,27 OThe corresponding normal-force coefficient of the tail is determined by equation (8).
26、 Thus for _hc exampleunder considerationC_,ch/.o) =0.054 (- 1.2) - (-0.67) (0.27) - (-0.06)1 + (-0.5) (0.27) =- -0.05The rate of change of free-floating angle with angle of attack may be calculated from equation (9). Thus,_ = (-o.09_)(0.054)i)a/C,r, - (-0.093) (0.054)(-0.67) + (-0.0076) + (-0.5)- (-
27、0.093)(0.054) (-0.06) + (-0.0032)-0“546Similarly the slope of the lift curve for the tail with controls free is found from c_luation (10).(-_a_)c,r = (0.054) I-(-0.67)+ (-0.5)(-0.06)(-0.546) =0.035APPLICATION OF DATA TO VERTICAL TAILS AND AILERONSThis entire procedure may be used equally well to cal
28、culate rudder size, with the obvious moditicatiou ofsubstituting yawing-moment coefficients for pitching-moment coefficients anti sidewash for downwash incalculating the normal-force coefficient required.The section parameters presented in this report may also be used to compute aileron characterist
29、ics by meansof the method outlined in reference 14.LANGLEY MEMORIAL _ERONAUTICAL LABORATORY,NATIONAL ADVISORY COMMITTEE FOR AERONAUTIC,_,LANGL_,Y FXV.LD, VA., December 30, IM_O.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-APPENDIX AEQUATIONS OF TH
30、E THIN.AIRFOIL THEORYIDENTIFICATION OF PARAMETER8The conversion of the equations for the aerodynamiccharacteristics of a finite airfoil based on the thin-airfoil theory (references 1, 2, and 3) from the oldBritish system of .aerodynamic coeiiicieuts to the stand-ard NACA form and the use of symbols
31、for the param-eters, or slopes, in these equations has led to some mis-understanding as to the identity of these parameters.The purpose of this analysis is to clarify the identity ofthe parameters and to distinguish between the onesthat are sometimes confused because of a similarity inform. In addit
32、ion, a summary of the relations is givenwhereby otber useful parameters not presented in fig-ures 1 and 2 may be computed from these data.IfC, =/, (,_,_I,_,)it follows that(“v=_ _-I“ _t _tT _)_t twhich is identical toac._ bC_ - bc.vd C._r-“_“_a d a “t“ _ T7 d_ t q“-_-/ d_ ,_-_ _ /Likewise ifit follo
33、ws thatand ifThenC=/ (CN,_,_,)d _ _C_t _Cht bC_tJ,= b-_.dC.,.+ -_t d_/+-_ d_,or, if it is considered thatbC_t bC+_ 5C_t .Because, according to the thin-airhfil theory, a linearrelationship exists among the variables C_, C_/, (-,., a, $_,and $, the total differential in the foregoing equationsmay be
34、replaced by the variable. Because no changein circulation is involved, (_-_._- is identical with oot/ Ctt,Jt5_),.,t; etc. The subscripts indicate the variablesheld constant when the partial differential is taken.The equations now become tav,t /$t,_t _xt f /e.,_ tarot /c.Ateta t ova t _caf_t=/-_-/ a.
35、+/-_-r-. / $_+1 .-:_z_ _, (4)These equations are of the same form as those pre-sented in references 2, 3, and 5. By comparison it ispossible to define the various constants of the equationsin these references in terms of the variables involved.The following table of corresponding symbols has becnpre
36、pared for future reference. The parameters fromreferences 2 and 3 are, for obvious reasons, expressedin tcrms of the old British system of coefficients; theangles were measured in radians; the pitching momentwas measured about the airfoil nose.ParalnctcrbCsi)a _,_(oc_be.,_ be._ _t/c,_i)c.,be_ _f,_,N
37、ACA system !of coef-ficientsRefer-ence 5- HOld British system of eve/fie;eatsReference 2 Reference 3f1_ a_l II4-m-bt- X, or - Xt- h. or - X$1-T- m, or - mt- e_o or - _- b, or - bt,_-b, or -b_,_13Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 REPO
38、RT NO. 721-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSSUMMARY OF RELATIONSHIPSThe slopes summarized iu the following equationsare useful for design purposes and may be computedwith the aid of the charts of figures 1 and 2.9a“(gcv _:gcv _: J _, 9a 5,9a 1_, , be./5,. _, aa/, _,Provided by IHSNot for R
39、esaleNo reproduction or networking permitted without license from IHS-,-,-APPENDIX BDEVELOPMENT OF FORMULAS FOR TRIM, BALANCE, AND FREE-CONTROL CONDITIONSFor an airfoil with a flap and a trimming tab, the formula for the tab deflection required to trim, where fortrim Ch I is 0, was developed in the
40、following manner.From tile thin-airfoil theory (see appen(ILx A)C.v / SCv 5a ba 8c,= _v+(._7)., _,_/-=J _, (:),1, Oft J., afaf, $1S.lve for 3/in equation (1):_,=_L k _- ), k _- J,.,t ,JBecause Chs-0 to trim, equation (3) may be equated to 0. Solve for _tw%-01 and obtain5e_t _t_,_,.o,=- (_,) (._, _)_
41、I/.,L,f (.N for the condition when C,_0 is substituted for Cs in equation (la), _ will become _,.h .0). Now equa-tions (la) and (3a) m_y be equated ant! “he res_.itant expression may be solved fi)t“ St to trim _c%-01.(._“4 7, ,J ,5,%.o,= L _-_/, ,. .,(_“) (_,_,) (_)_I 1.,8,In this form, the tab detl
42、eetion to trim may be determined by direct substitution of tim wdm,s for theparameters as given in the data for this report.The flap deflection with tiw tab s_,t to trim may be dctermim,d from equation (Is), which, when eonlbim,dand rewritten, becomes“(“):(d_ /_-+(_)*.“_(“_) (0)ki_j/eL,Ik _)a iv,L,T
43、he equations for an airfoil lind a flap with a hahmcing tab were derived as h)llows:For a balancing tab, St isJOD, so that _,-K_Iz+_, where K is a constant for a linear variatiou of _ with_z, and Se is the initial tab setting. Therefore equations (I) aml (3) become_C_A _ _ (Ka_+a,.).Jand(_,:(_.,_,_,
44、 C.vt /_e,“ I _e,_t-*,-),2 _t-_;),.,(r,_,_ _l/Lt,fl , .,Wil,h controls flve, Cht=O Itlid t,qllill,illlt (;i) lll!ellnil,_t, _, I_,_,Revise equation (1) by changing (_ to (?_w_f-“) and slibstitute _sie, s.,_ h)r _t; IlSe, this exprl,_sion for (.v(e_t.,)in the foregoing relation, and the tlal)angD for
45、 control-free comlition b_,conms15Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-16 REPORT NO. 721-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS- - as+ - - - _, + “_, a,oI t_.),t _), L t_.),t _),t_ ,)_ , t ,)_ J I51,.e,._ -_ /ac,;_ 15C_ Ib- /b% _.J- 1
46、5% /bC_ lba 15% 11 (7). _ _ _ _ +- + + - t_g,)l,.ht()a);t.,._r)e, t_l)l, KLt_.),t_.J,t_,).,t_,)_.,_The equationforthe normal-forcecoefficientwith freecontrolsis obtainedby substitutingthe free-floating flap deflection from equation (7) into equation (1). ThusC_ bC_ _a a, b-By the actual substitution
47、 of the right-hand member of equation (7), this eq.ation may be written asba _)a _)ak_.),.,t_),.,.=.+L-t-a.),.,t_),.,t_,),+t_,),20ia%_ i_C_, ib, 1_% +I- IS% /bC,_ 1_,_ Is% (Sa)-t,-_.),.,t._),.,t._,),.,+t_,),.%-t._),.,t,_),.,t_),.,+t_),By the differentiation of equation (7) with respect to a, _f,obeing a constant, the stabilizing factor becomes(_q P%=_ _,/a,._, _a/I,.I,If equation (8) is differentiated with respe(,t to a, the slope of the normal-force (o(,ffieien
