1、REPORT No. 703DESIGN CHARTS RELATING TO THE STALLING OF TAPERED WINGSBy H. A. SOULfiand R. F. ANDERSONSUMMARYAs an aid in airplane design, charts have been pre-pared to show the eects oj wing taper, thickness ratio,and Reynolds number on the spanwi.se location oj theinitial stalling point. Means of
2、improving poor stallingcharacteristics resulting jrom certain combinations ojthe variables have al-so been considaed; additional jiguresMu.strate the injkmce oj camber increase to the wing tips,washout, central sharp leading edges, and wing-tip slotson the stalling characteristics. Data are included
3、 jromwhich the drag increases resulting from the wse oj thesemeans can be computed. The application oj the data toa specijic problem is Wu.#rated by an example.INTRODUCTIONIn the investigation of the stalling of wings, a knowl-edge of the spmnvise location of the initial stall and ofthe susceptibili
4、ty to stalling of the tips is importantbecause of the connection of these two factors with lossof damping in roll. A method of calculating the pointalong the span of tapered wings where stalling shouldbegin was given in references 1 and 2. In a later report(reference 3), the method of references 1 a
5、nd 2 wasapplied to an investigation of the optimum design oftapered wings, tip stalling being considered.The present paper extends the previous work to asurvey of tapered wings to determine the manner inwhich the sparnvise location of the initial stall varieswithin the range of wing parameters cover
6、ed by currentdesign practice. For the guidance of designers, theresults are presented in the form of charts for threeReynolds numbers, corresponding to three airplanesizes with wings having various taper ratios and roohthickness ratios. As in reference 3, the basic airfoilsections are the NACA 230 s
7、eries. The wings werewithout flaps and had no sweep.The various means considered of moving the stallingpoint inward were: increase of the percentage of camberof the airfoil sections from root to tip, washout, centralsharp leading edges, and leading-edge tip slots. Theeffect of these methods of reduc
8、ing the susceptibilityof tip stalling on airplane performance is discussed.The use of the charts is illustrated by an example.CALCULATION AND PRESENTATION OF THE DATACONDITIONS FOI?THE CALCULATIONSAU the charts were obtained for unflapped wingshaving straight taper and rounded tips, as shown infigur
9、e 1, except for two special cases of a wing with astraight center section that will be discussed later.The taper ratio r is defined as c,jct, where ct and c. areshown in figure 1. Taper ratios of 1,2, and 5 were used.FracfionsemisponFIGUREI.Typical plan form and thichmessvariations.The increase in c
10、amber of the aixfoil sections from rootto tip, when present, was linear. The camber is givenas a percentage of the chord but will be referred tosimply as “camber.” Washout, when used, was alsolinear and was aerodynamic (angular difference be-tween the zero-lift +rections of the root and the tipsecti
11、ons). The NACA 230 series of airfoil sectionswas assumed for the wings without camber increase.For the cases with camber increase, the NACA230 series sections were used at the root and theNACA 43oo9 section was used at the tips. Theroot thickness ratios were 0.12, 0.15, 0.18, and 0.21;513Provided by
12、 IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,- - - .- .- .514 REPORT NO. 703NATIONAL ADVISORY COMIVIITIEEFOR AERONAUTICSthe tip thickness ratio was always 0.09. The thick-ness ratio is the maximum thickness t divided by thechord c. For all cases, the variatio
13、n of the actualthickness along the span was linear. Typical varia-tions of thiclmess and thickness ratio are shown infigure 1.Three values of Reynolds numbers (4,000,000,8,000,000, and 14,000,000), corresponding to the stall-ing speeds (without flaps) of three sizes of airplane,were considered. The
14、Reynolds number was basedon the mean chord, S/b. Typical airplanes correspond-ing to the thee ReynolhXtwist distribution.coefficient Clbthat is independent of the wing lift codfi-cient. Figure 3 gives section lift coefficients CZb10forwings with 10 washout at CL= O. The effect of twistis directly pr
15、oportional to the angle of twist and, forother values of the angle of twist G!Ctbisgiven M c1clb=lo b,.where c is in degrees and is negative for washout. Inthe general case, the section lift coefficient c1 may bewrittenCl=cla-hlbWhen there is no twist, of course CZ= CZ.Figures 2 and 3 are based on v
16、alues from reference 1.The data in reference 1 can be used to determine thesection lift coefficients for combinations of taper andaspect ratios other than shown in figures 2 and 3.STALLING CHARTSThe calculated point along the span at which stallingshould start is given in figures 4 and 5 for what ma
17、y becalled basic wings, that is, plain vvings without washoutor other means of moving the stalling point inward.The data are given for the three taper ratios, the fourroot thickness ratios, and the three Reynolds numbers.Provided by IHSNot for ResaleNo reproduction or networking permitted without li
18、cense from IHS-,-,-DESIGN CHARTS RELATING TO THE STALLG OF TAPERED WINGS 5151.1.1.1.1.,.* - - _- I I/ - -/ “ .x . - :.M - - .-cz,“ y. 4 -;.18s/.2, ! ! , I I I I I I II I I I I I I I I I“HttHttt1.4/.21.01.61.41.2/.OO .2 .4 .6 .8 0 .2 .4 .6 .8 0 .2 .4 .6 .8 1.0Frocfion semispon(a) Average Reynolds nnm
19、ber, 4,000,000. (b) Average Reynolds number, 8,000,000. (c) Average Reynolds number, 14,080,000.FIGURE4.Diatribution of ct and ct= over aemiapan. NACA 230series airfoila: tip thickness ratio, 0.09.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.516
20、REPORT NO. 703NATIONAL ADVISORY COiWMIIWTEE FOR AERONAUTICSl I Root thicknessrdiolrFIQUBE5.Effect of tsper on the location of the Wdfiig point. prstio, 0.09.thicknessThe curves of cl=given in figure 4 show the mnximumlift coefficients of the individual nirfoil sections. I?oreach airfoil section and
21、Reynolds number, czaz wasfound fromczmaz=(cJrnaz),d+ AcJ mazThe (c,a=) values, for the standard effective Rey-Stdnolds number of 8,200,000 used in variable-density-tunnel tests, were obtained from reference 4. Thevalues of Aczaz, which correct clu= to the Reynoldsnumber of the particular section, we
22、re obtained fromreference 5.The lift coefficients c1 for each section along the spanwere obtained from figure 2 for a value of Csdnt I I CL, IcombeC IVACA r=2 5 cum benVA CA Y-=2 57-ltJcoLso” “”23018-23009 comber IVACA r.2 5-lncreosing 55combenflACA I +1+-t-lncreosingCOmberlJACA I IW-H-lncreosingcom
23、be NACA23i18iq30YI”5f-4? Z3018-b3009 /.631.52 23018-43009 1.641.58111111 1111111.521.33 11 230/8-3009 1.621.47 2301-83009i.64 L:Frucfion semis-pun(a)AversgeReynolds number, 4,0CC,0011. (b) -kvemge Remolds number, 8,1XW133. (c) Aversge Reynolds number, 14,0C0,000.FIGURE6.Effect of finesr percentage e
24、smber inerese from root to tip.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-DESIGNsummarized in figure 5, which.CHARTS RELATING TO THE STALLING OF TAPERED WINGS 517shows the variation ofthe stalling point with I/r. Although only the NACA230 series
25、 airfoil sections were used, the locationof the stalling point should be nearly the same forcommonly used sections.The rate at which the c1 and the Czna=curves separateis believed to be an added indication of the natureof the stall. The dif?ierence between the curves is themargin between the actual
26、lift coefficient and the stallinglift coefficient of the sections. Where the margin issmall, a slight disturbance may produce that is,the zero-lift directions of the root and the tip sectionsare parallel. As the angle of zero lift of the NACAc Wcrshouf,-z. cL- ti. w1.53 - 2% + 1.59 “”-+t-1 I 5 = Clm
27、a1,6 / - - -.- /-=- .#- / -C,mer / .a., -.,.“ N-f,” h., ,. /I x u. . ./ / . / /. -1.4 / /./ / / ,/ /“ .-! C*/ -./ %-” 1.2 .!l 1 I I I I I I . 1 l 1- s 2I,z -c,-. J -(a) (b) (c)l.oQ- 1 .2 .4 .6 .8 0 .2 .4 .6 .8 0 .2 .4 .6 .8 1.0Frocfion semispun(n) Average Reynolds number, 4,000,000. (b) Average Reyn
28、olds munber, 8,000,000. (c) Avcmge Remolds number, 14,00+3,000.FIGUEE7.Effect of linear washout. Corrskmt esmber; NACA 2301S-23009sections.407300 ”4134Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.518 REPORT NO. 703NATIONAII ADVISORY COMMITTEE FOR
29、 AERONAUTICS43009 is 2.4 and that of the NACA 23018 is 1.2, a geometric washout of 1.2 must be used toproduce zero aerodynamic washout.The effect of linear aerodamic washout on the c1margin is shown in figure 7 for the same conditions usedfor the wings with camber increase. The CZmm valuesare the sa
30、me as for the cases with constant camber butvalues from figures 2 and 3 have been combined toobtain the tangent c1 curves for the given angles ofaerodynamic washout. The effect of combined in-crease of camber and washout may be inferred from thecurves showing the separate effects (figs. 6 and 7).The
31、 two methods considered thus far of moving theinitial stall inboard consist in making a gradual changeof margin. An abrupt change caused by the effect on2.1 I I II slot/.9c.wsshout, l%O; constsnt camber;A,ACA Olg weight of 1 pound - lbPower - P horsepower (metric) - - horsepower-r hpSpeed - v kilome
32、ters per hour _ kph miles perhour - mphmeters per second- reps feet per second- fpsw(7mIPss.GbcAv!zLDDoD,D.c2. GENERAL SYMBOLSWeight=mg v Kinematic viscosityStandard acceleration of gravity =9.80665 m/s2 p Density (mass per unit voIume)or 32.1740 ft/sec2 Standard density of dry air, 0.12497 kg-m-s a
33、t 15 CMass=; and 760 mm; or 0.002378 lb-ft-4 sec2Specific weight of “standard” air, 1.2255 kg/m2 orMoment “of inertia =mk2. (Indicate axis of 0.07651 lb/cu ftradius of gyration k by proper subscript.)Coefficient of viscosity3.AERODYNAMIC SYMBOLSAreaArea of wingGapSpanChordAspect ratio, True air spee
34、dDynamic pressure, 4J72Q!2R4Lift, absolute coefficient Cz=qsDrag, absolute coefficient C=E aqs eProfile drag, absolute coefficient C.O=$ QwInduced drag, absolute coefficient C.,=% aaParasite drag, absolute coefficient C%= YCross-wind force, absolute coefficient Cc=Angle of setting of wings (relative
35、 to thrust line)Angle of stabilizer setting (relative to thrustline)Resultant momentResultant angular velocityReynolds number, p where 1is a linear dimen-sion (e.g., for an airfoil of 1.0 ft chord, 100 mph,standard pressure at 15 C, the correspondingReynolds number is 935,4oo; or for an airfoilof 1.
36、0 m chord, 100 reps, the correspondingReynolds number is 6,865,000)Angle of attackAngle of downwashAngle of attack, infinite aspect ratioAngle of attack, inducedAngle of attack, absolute (measured from zero-Iift position)Flight-path angleProvided by IHSNot for ResaleNo reproduction or networking per
37、mitted without license from IHS-,-,-“ /zPositive directions of axes and angles (forces and moments) are shown by arrow-sAxis IForce(parallelDesignation sb- to axis)symbolLongitudinal - X xLateral - YNormal - z zMoment about axisIIDesignation sb- Positivedirection.Rolling - L YzPitw rAbsolute ceflici
38、ents of moment bgle of set of control surface (relative to neutralC,=F8 c+ Cn=i$ position), & (Indicate surface by proper subscript.)(rolling) (pitching) (yawiig)4. PROPELLER SYMBOLSD, DiameterP? Geometric pitch P, Power, absolute coefficient Cp=Dp/D, Pitch ratiov, (7.,d57ZInflow velocity Speed-powe
39、r coefficient= zv,Slipstream velocity ?, EfficiencyRevolutions per second, r.p.s.T, Thrust, absolute coefficient C,=-& n,a,()Effective helix angle=t-1 &Q, QTorque, absolute coefficient CQ=a5. NUMERICAL RELATIONS1 hp. =76.04 kg-m/s= 550 fklb.lsec. 1 lb. =0.4536 kg.1 metric horsepower= 1.0132 hp. 1 kg=2.2046 lb.1 m.p.h. =0.4470 m.p.s. 1 mi.=1,609.35 m=5,280 ft.1 m.p.s.=2.2369 m.p.h. 1 m=3.2808 ft.oProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
