1、REPORT No. 648DESIGN CHARTS FOR PREDICTING DOWNWASHANGLES AND WAKE CHARACTERISTICS BEHINDPLAIN AND FLAPPED WINGSBy ABE SILVERSTEIN and S. KATZOFFLangley Memorial Aeronautical Laboratory111 ():_4-3!_- IProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-N
2、ATIONAL ADVISORY COMMITTEE FOR AERONAUTICSHEADQUARTERS, NAVY BUILDING, WASHINGTON, D. C.LABORATORIES, LANGLEY FIELD, VA.Created by act of Congress approved March 3, 1915, for the supervision and direction of the scientificstudy of the problems of flight (U. S. Code, Title 50, Sec. 151). Its membersh
3、ip was increased to 15 byact approved March 2, 1929. The members are appointed by the President, and serve as such withoutcompensation.JOSEPH S. AMES, Ph. D., Chairman,Baltimore, Md.I)AVID W. TAYLOR, D. Eng., Vice Chairman,Washington, D. C.WII.LIS RAY GREGt;, So. D., Chairman, Exeeuti_e Commillee,Ch
4、ief, United States Weather Bureau.WILLIAM P. MACCRACKEN, J. D., Vice (hairman, ExecutiveCommittee,Washington, D. C.CIIARLES G. ABBOT, So. D.,Secretary, Smithsonian Institution.LYMAN J. BRIGGS, Ph. D.,Director, National Bureau of Standards.ARTHUR B. COOK, Rear Admiral, United States Navy,Chief, Burea
5、u of Aeronautics, Navy Department.HARRY F. GUGGENHEIM, M. A.,Port Washington, Long Island, N. Y.SYDNEY M. KRAUS, Captain, United States Navy,Bureau of Aeronautics, Navy Department.CHARLES A. LINDBERGH, LL.D.,New York City.DENIS MULLIGAN, J. S. D.,Director of Air Commerce, Department of Commerce.AUGU
6、STINE W. ROBINS, Brigadier General, United StatesArmy,Chief Mat6riel Division, Air Corps, Wright Field,Dayton, Ohio.EDWARD P. WARNER, Sc. D.,Greenwich, Conn.OSCAR WESTOVER, Major General, United States Army,Chief of Air Corps, War Department.ORVILLE WRIGHT, Sc. D.,Dayton, Ohio.GEORGE W. LEWIS, Direc
7、tor of Aeronautical ResearchJOlIN F. VICTORY, SecretaryHENRY J. E. REID, Engineer-in-Charge, Langley Memorial Aeronautical Laboratory, Langley Field, Va.JOHN J. IDE, Technical Assistant in Europe, Paris, FranceTECHNICAL COMMITTEESAERODYNAMICS AIRCRAFT STRUCTURESPOWER PLANTS FOR AIRCRAFT AIRCRAFT ACC
8、IDENTSAIRCRAFT MATERIALS INVENTIONS AND DESIGNSCoordination of Research Needs of Military and Civil AviationPreparation of Research ProgramsAllocation of ProblemsPrevention of DuplicationConsideration of InventionsLANGLEY MEMORIAL AERONAUTICAL LABORATORYLANGLEY FIELD, VA.Unified conduct, for all age
9、ncies, ofscientific research on the fundamentalproblems of flight.OFFICE OF AERONAUTICAL INTELI,IGENCEWASHINGTON, D. C.Collection, classification, compilation,and dissemination of scientific and tech-nical information on aeronautics.Provided by IHSNot for ResaleNo reproduction or networking permitte
10、d without license from IHS-,-,-REPORT No. 648DESIGN CHARTS FOR PREDICTING DOWNWASH ANGLES AND WAKECHARACTERISTICS BEHIND PLAIN AND FLAPPED WINGSl_, +I+I: _II+I,:RSTEIN altd _. I_+,TZOFFSUMMARYl+,quatiol_s aml desigl_ c/torts are given for predictingthe doumwash al+gles a_(1 the wake charachristics .
11、forpower-off eoT+ditio_+s behimt plain and flapped wings oJthe types used in modern desig_ practice. The dou,mrashcharts cover the cases of elliptical wings amt wil_gs of taperratios 1, 2, 3, aTM 5, with aspect ratios of 6, 9, arid 12,hadr_g flaps em, eri_g O, gO, 70, aTM 100 ereel_t of the,_pa_. Cu
12、rves of the spa_ load distributio_+s for all thesecases are i*wluded. Data o_ the lift aml tile drag qflaplJed airfoil secti+ms aml curces for fiI_di,_g the coldribu-tion of the flap to the total wb_g lljt .for diff_re?it types offlap al_dJor the entire ra,ge of flap spans are ah.o ineluded.The wake
13、 width, and the distribution of dyrmmie pressureacross the wake are given in terms of the profile-dra 9 eo-eflieiel_t and the distance behind the whig. A method ofestimating the wake position is olso give_+.The equatlons and the charts are based on theory thathas been show_t ia a previous report to
14、be in a.qreemeT_t withexperime_ t.INTRODUCTIONIn a recent paper (reference 1) methods are developedfor predicting t,L“7 t)c,? 2c 3 _tI_q:j?I22qB2“ _ rQq. l , C. _kJ_ (jCo 9.3/Q) C-_ C3_(, LJ,L sC )wF._,“ (/f -_Ir, L“c_s,i(b-c3 _i%c_ t% - _,(f3 _ _J fi o,)ql22C2 (:,c_Jif/iIi1i_-:kk_k;,ttc-, r_L“Lb_.
15、COChc5c13cL L.ul d_.t24k.k3-z,ITI,i I iII4 o _o “q5 t-: _ ck. t. . ; - c3_3_9I,tt/1,71“_ _!t% cb (3_“q/a_3%_f3tk3cL_Q_o _%Q-t-._3dr_2._ggc,_ 72“C3 dLq)_t_-.: c3q/a a(b,_._ _- Q)-.l 1034_39-3I%_bq/aaQ_ _-_ck_ gc_LL:E_.k /_ggcuLDt.- hq*:“i-! _ _ .C3etjtn4 - _ql_ a(2)Q3 . _._- - Q3 -d11Provided by IHSN
16、ot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 REPORT NO. 848-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSL :r iI1f/_Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-DESIGN CHARTS FOR PREDICTING DOWNWASH ANGLES AND
17、 WAKE CHARACTERISTICS 13i-tiL%COI_b_/_u(kllYO(/5“tUfL)tt.l,.i A! ! /1_Jilt,.io9 c,_ “2. _+ , “b._ %_(3k_C3 -_%5i _g_ %L, qb t. r.)7, Q5_3%-_g.;amIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 REPORT NO. 648-NATIONAL ADVISORY COMMITTEE FOR AERONA
18、UTICSLI I.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I)ESI(_N CttARTS FOR PI_It,:DCTI_,(I )OYN_VA_tl ANGLk,. AND WAI_E (_.IIAILA, CTIi:I_ISTi(S .,_CO“oQL%CtO?“NgclIProvided by IHSNot for ResaleNo reproduction or networking permitted without lice
19、nse from IHS-,-,-16 REPORT NO. 648-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICSProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-DESIGNCHARTSFORPREDICTINGDOWNWASHANGLESAN) WAKECIIARACTERISTICS 17F. itq5 q5, (:) qJ b/ kD ) _1)i%UDd_/L.la_ 4ua_Jad iLI/Od
20、p joel,- _/t_b,c o% “*_Uver the t,dl.The correction facttte(1 in tigure 21for all eases.METHODS (iF APPLICATIONDownwash, plain wings. Tim downwash at the tailof an a.irplane with a wing haviil/lieither twist nor a flapis obtained from the ehllrts 7iron in ti/ure_ 1 t.o 15 inthe foliowin 7 lllll:llll
21、el;.2 .3 .41. For each angle of atttlek under consi(|erlttion, tindthe |onTit.udinal dist, ailee x of the elevlttor=liin_e axisfronl the qull.rter-ehord point of the 1oo section qndtile. vertical distlulee m of-the hinge axis from the trail-ing edge, (it“ wake oriTin. (onsi(ler m ( tm neTa.tive ifth
22、e linTe ,i.xis lies below the lrliilin 7 edTe.7. Find t|le (owliwilrll (lisphleement 1t. of the wllkecenter lille li.t (listitlice .r from tile u/rter-clior(t poinlby multipiyiilK the value lit. dislnnee x on tim eorre-spondili 7 disl)hicemelit chart by the lift eoeltlcienl (L.Provided by IHSNot for
23、 ResaleNo reproduction or networking permitted without license from IHS-,-,-22 REPORT NO. 648-NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS3. Locate the point (x, Im+hl) on thc downwash-contour chart and multiply the corresponding down-wash angle by the lift coefficient and by the correctionfactor of
24、figure 21.Downwash, flapped wings.-For an airplane withflaps down, it is first necessary to separate the lift co-efficient into two parts. The part CL. is the lift coeffi-cient at the particular angle of attack, with flaps up.The part CL I is the increase, at the particular angle ofattack, on loweri
25、ng the flap; it may be obtained by theuse of figures 19 and 20. Derivation of the downwashproceeds in the following manner:l. Find the longitudinal distance x of the hinge axisfrom the quarter-chord point of the root section, andthe vertical distance m of the hinge axis from the wakeorigin. The wake
26、 origin in this case is not the trailingedge but a point below the trailing edge, as previouslyexplained. (See equation (4).)2. Find the contribution h_ of the plain wing to thedownward displacement of the wake center line at dis-tance x from the quarter-chord point by multiplying thevalue on the co
27、rresponding displacement chart (plainw_ing), at distance x, by CL_.3. Find the contribution h2 of the flap to the down-ward displacement by multiplying the value on thecorresponding displacement chart (flap), at distance x,by CL r4. Locate the point , Im+h,+h21) on the contourcharts for the plain wi
28、ng and for the flap; multiply thecorresponding downwash angles, respectively, by CL_and CL r and by the correction factors of figure 21 andadd in order to get the desired downwash.This procedure completes the computation of thedownwash, except for the wake effect, which increasesthe downwash above t
29、he wake center line and decreasesthe downwash below it. The amount of this correctionwill be discussed in the next section. There are twoother reasons, previously mentioned, for making stillfurther corrections, seldom exceeding 0.5 , positiveabove the wake and negative below it. Interference ofthe f
30、uselage, the nacelles, and the wing-fuselage junc-tures is only partly predictable; however, for the modernairplane with efficient wing-fuselage junctures andstreamline fuselages, it is likely to be of small im-portance.For wings or for flap spans other than those coveredby the charts, a linear inte
31、rpolation is usually permis-sible. For a wing with appreciable aerodynamic twist,the downwash due to the twist will have to be computedfrom the span load distribution at C_.-0 and appliedas an additive correction. Dihedral and sweepbackmay be neglected.WAKE CHARTS AND FORMULASThe center line of the
32、wake coincides with the centerline of the trailing vortex sheet; hence no new data arerequired for locating it. The wake half-width, inchord lengths, is given by the formula_ = 0.68c,_0! _(_+ 0.15)_ _ (5)in which _ is in chord lengths. It will be noted that theunit of length in this and the other wa
33、ke equations isthe chord rather than the sere,span. Curves of thisequation are plotted in figure 22 for different valuesof the parameter c_0.o o / 2 3Di._tonce from ;rE., _ ,chord lengihsFII;IrRE 22. -Relstinn between wake width and distance from trailin_ edge._-= 0.6S_aol/l(6+0,15) 1/2The maximum l
34、oss of dynamic pressure in the wakeoccurs at the wake center and its value _ i_ given by theforinula2.42Cd0_ (6)6+0.3Curves of this equation are plotted in figure 23 for dif-ferent values of the parameter cd0- The distribution ofdynamic pressure within the wake is given by the equa-tion, =cos t 77 (
35、7)which is plotted in figure 24.The effect of the wake on the downwash in and nearit is negligible for low profile-drag coefficients as, forexample, in the case of plain wings at low angles ofattack. It must, however, be taken into account forwings with high-drag flaps and it may be approximatelyPro
36、vided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-DESIGN CIIARTS FOR PREDICTING DOWNWASH ANGLES AND WAKE CHARACTERISTICS 23computed for such cases, as exphtined in reference 1.Results of some of these conqmtations are shown inl.Ii0 / 2 3 dD_fonce from r_,
37、 _ ,chord lengths,I(;):l_E 2:C |_.elatioll between nlaxinltlm oss Of dynanlic pressure ill the _ake _Lilddistance from the trailing e,lge.2 4o_ tl+, _ d0/,_+().3Ltp,J ll,IJIH , _t ;il i_tioll ,)f ,13 rt;_rllit _)1_,_11113 IH_q lJ.i_l-i:q_ Ilq x,t,_tl,.4,.,7_ irzOtigme 25. Figure 25 (t) shows the c()
38、mputed effectat the ut)per edge of tile w,tke for three distances behindthe trailing edge; at the lower edge of the wake, it is thesame ill magnitude but opposite in sign. The effectdiminishes with distance from the wake; for points only:t short distance outside the wake (i. e., for the mostusual ta
39、il positions), however it, is nearly equal t() that_-3_o_. / g_./ .2profNe-_r_ coefficient, c-_o_i- )-:- f- (b)-./ .e .3 .5Oistonce from w_le ce_#et- /me, _,chord length(a) At the upper edge of the wake.(b) Within the wake.FIGUICE 25.-Wake effect on downwash. The clIcets are equal, bllt or opposite
40、sign,below the wake center.at the wake edge near it. Figure 25 (b) shows sometypical variations of the effect within the wake.In order to facilitate the application of the precedingequations, which involve c_0, some section profile-dragcLJ2420/6/2- .08040I Flop tvpe c./c A_PFo/I th_ckne55- PIo_nonds
41、pht 0.2|-i0., c t I “ .2 .2 ,j i ,l-d , L.-d-x/ernolotrfo/I .2l I ./ “ _ )“ iI0 20 30 40 50 _0 /0Flop onqle, d, , de 9.I“II;I!IIE 2G. -Section i,rofih,-(lrat: (_oellieicllts for (lillerent llal)S.eoelficients for the different flaps are presented in figure26. These do.ttt apply particularly in the h
42、igher liftrange, about 3 to 4 below the stall. They were col-lected mainly from N. A. C. A. results and fromreference 5.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-24 REPOIT NO. 648- NATIONAl, ADVISOIRY COMMITTI,:E FOR AEIONAI;TI(SEXAMPLE OF APPL
43、ICATION TO DESIGNFor purposes of illustration, some spccinwn calcula-tions will be made for a nlidwing monoplane (fig. 27).The wing is of aspect rlttio 9, taper ratio 3 : 1, and has lsplit tlap of 0.70b si)an and 0.20c chord. This case iscovered by figure 8. The tail span is 0.3b.The ease of the air
44、plane with flaps up will be con-sidered first. It will be _lSSumed that, when the air-plane is operating at the attitude shown in figure 27 (a),_o,4“ ern=.02 b/2 edge- “Wc,/Te ,c)m _-./3b/2 -_(a) Flap up.(b) Flap down.(c) Flap down, tail in the wake.FI;URE 271-lllustration for the si)ecilncn calcula
45、tions of downwash anti wake.the lift coefficient C_. is 0.9. The steps outlined underMethods of Application are as follows:1. x-0.68 b/2. m-O.O1 b/2.2. The downward displacement of the trailing vortexsheet at x=0.68 b/2 is, for CL-1.0, 0.05 b/2, so tluith=0.9X0.05=0.045 b/2.3. Reference to the downw
46、ash-contour .chart showsthat the downwash at point (x, Ira-i-hi), or (0.68, 0.04),for CL= 1.0 is 5.6 . Multiplying by Cr (0.9) and by tilecorrection factor of figure 21 (0.95) gives, for thedownwash,_=0.9X0.95X 5.6_4.8 The center of the wake passes mq h. semispans I)elowthe hinge axis, as shown, and
47、 its half-widttl ,-at thispoint is obtained from tim section l)rofile-dnlg cocflicien t(assulne cao=O.Ol5 ) anti the distance behind the trailingedge (-1.29c), where c may be taken as the “lot chord.By equation (5) or figure 22,_=0.68X0.015_“_X 1.44_=0.1 chordThe edges of the wake are shown in the f
48、igure.The tail lies outside the wake and, inasmuch astim wake is too slight to affect, the downwash, it requiresno further consideration.The airplane at the same attitude, with flaps down,8I=60 , is shown in figure 27(b). From figure 20,kc, is seen to be 1.13 (assuming the wing thickness to|)e 0.12c); from figure 19, CLI/Ac_ is 0.67, so that CLI-0.76. Tlle contribution of the plain
