1、d“ .-.-._ t: -LNATIONAL ADVISORY COMMITTEEFOR AERONAUTICSTECHNICAL NOTE.No. 1175-.LIFTDNG-SURI?ACE -THEORY ASPECT-RATIO CORRECTION TO THELIFT AND HINGE -MOMENT PARAMETERS FOR FULL-SPAN :.ELEVATORS ON HORIZONTAL TAIL SURFACESBy Robert S.Swanson and StewartM. Canda.11 -“.- .Langley Memorial Aeronautic
2、alLaboratory .Langley Field,Va.WashingtonFebruary, 1947. .-. . ._. . -, . . _ _ . . .,. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NATICJNALADVISOKY COMMITTEE FOR AERONAUTICSTECHNICAL NOTE NO. 1175IZFTING-SURFACE-THEORY ASPECT-WTIO CORRECTIONS T
3、O THEAND RINGE-MOMENT PMUMEWERS FOR FULL-SPANELEVATORS ON HORIZONTAL TAIL SURFACESRobert S. Swanson and Stewart M. CratiallSUMMARYA limited number of lifting-surface-theory solutionsfor wings with chowise loadings resulting from singleofattack, parabolic-arc camber, and flap deflection arenow availa
4、ble. These solutions were studied with thepurpose of determining methods of extrapolating theresults in such a way that they could be used to deter-mine lifting-surface-theory values ofthe aspect-ratiocorrections to the lift and hinge-moment parameters forboth angle-of-attack and+flap-deflection-typ
5、e loadingthat could be used to predict the dwaracteristtcs ofhorizontal tail surfaces from section data with sufficientaccuracy for engineering purposes. Suoh a method wasdevised for horizontal tail surfaces with full-spanelevators. In spite of the fact that the tlmx?y involvedis rather complex, the
6、 method is simple to apply, andmay be applied without any knowledge of lifting-surfacetheOrysA comparison of experimental finite-span and section.values and of the estimated values of the lift andhinze-moment Parameters for three horizontal tail surfaceswas”rnade to povide an eerimentalmethod sugges
7、ted.INTRODUCTIONverification of the. One OS the problems for which lifting-line theohas proved inadequate (see reference 1) is that of esti-a71 mating the hinge-moment parameters of finite-span controlProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2
8、 NACA TN No. 1175surfaces from section data. In reference 1 for whicheertmental data were available for three casessatisfactory additional aspect-ratio corrections to thehinge moments of ailerons caused by ohordwise loadingdue to angle of attaok could be dete?nninedby means oflifting-surface theory.
9、Since the publication of refereme 1, considerablymore seotion and finite-span (tail surfaoes and ailerons)hinge-moment data have beoome available, and In all easesthe slope of the hinge-moment curve against angle ofattack (measured at small angles of attack) could bepredioted with satisfactory aocur
10、acy from the sectiondata by means of the ltfthg-surfaoe-theo aspect-ratiooorreotions. Although the lifting-surface-theory aspeot-rati.ocorrections were determined from a linear tieoryand thus apply only to the range of angles Or attaok nearzero, they are extremely valuable for defng the stiok-fome g
11、radient for the important high-speed ease ati arenecessary for estlmath.g the stiok-free stabilitycharaoteri.sties.No lifting-surface-theory soluttons were available,however, for wings with chordwise loading due to flapdeflection. In order to obtain at least one such solution,an electromagnetic-anal
12、ogy model (reference 2) of anelliptic wing of aspect ratio 3, with the chordwiseloading corresponding to that ot a O.-chord plain flapin two-dimensional flow, was constricted and tested(reference 3). In order to check the aspect-ratio correc-tions, determined from the results of the tests on theelec
13、tromagnetic-analogy model, a semispan wing of thesame plan form, same flap-chord ratio, and of theNACA o(X)9 airfoil section was constructed and testedin the Langley 4,-by 6-foot verttoal tunnel.!l!heresultsof these tests are reported in referqnce 4.As will be shown (see Experimental Verificationll)
14、the wind-tunnel tests provided a satisfactory check ofthe lifting-surface-theory aspect-ratio corrections bothto the variation of hinge-moment coefficients with respectto angle of attack and to flap deflection.Lifting-surface theory appeared to provide an accuratemethod of predicting finite-span cha
15、racteristics from .a71Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACA TN No. 1175section data. It might, however, be msny years beforesufficient lifting-surface-theory results will beavailable to determine the corrections for any PIWform or fla
16、p-chord ratio because so many variables areinvolved. The lifting-surface-theory aspect-ratio cor-rections were determined for elliptic wings; howeverythey apparently could also be applied to unswept wings of other plan forms (see reference 1), even to therectangular wing as indicated by the data of
17、reference 5.That iS, the hinge-moment slopes near zero angle of attackand zero flap deflection wezepredicted satisfactorilyfor the rectangular wing of aspect ratio 3 by use oftheoretical results for the elliptic wing of aspectratio 3.3The effect of the chord of the flap on the lifting-surface-theory
18、 aspect-ratio corrections was still to bedetermined; therefore, an electromagnetic-analogyrn”delof an elliptic wing of aspect ratio 3 with ellipticchordwise as well as elliptic spanwise loading (approxi-mately circular camber) (reference 3) and an ellip%icwing of aspect-ratio 6 simulating a steady r
19、oll were alsotesced(reference 6). A study of lifting-surface-theoryresults available (elliptic wings of aspect ratio.z withangle-of-attack loading, 0.5-chord-flap loading, andparabolic-arc camber and an elliptic wing of aspectratio 6 with angle-of-attack loading and steady-rollloading) was made and
20、certain c.onsisten.tiesin theresults were observed. From these observations. themethods of extending the results so that they wouldprovide lifting-surface-theory aspect-ratio correctionsOT satisfactory accuracy for engineering purposes werebelieved to be practical for horizontal tail surfs-ces“ “of
21、any flap-chord ratio, of aspect ratios from about 2to ?,and with almost any plan form provided that thedihedral, taper, and sweep are not excessive. Insufficientlifting-surace-theory data are available, however, topredict the variation of hinge moments with elevatordeflections for part-span elevator
22、s.The actual method of determining lift and hinge-moment parameters from section data is presented hereinin a fairly simple form in llApplicationof Method.lThe theoretical development of aspect-ratio correctionsto lift and hinge-moment parameters for elliptic wingswith constant-percentage-chord, ful
23、l-span flaps and themethods used to extend these corrections to other pianforms are given in tDevelopmentof Method.tlProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-4 NACA TN No. 1175 .A comparison of the available experimental l?inite-spar.and secti
24、on values and of the estimated values oflift and hinge-moment parameters is made for three horiz-ontal tail surfaces and is presented in the section“Experimental VerificationlSYMBOLS .-( )Section liftsection lift coefficient , qcCzCLcuLifitail lift coefficient qscsec ion hinge-moment coefficient)Sec
25、tion Mnge momentqcezelevator hinge-moment coeficient():;:n)dynamic pressure *Q+a71p.aa.mass density of air, slugs per cubic footangle of attack, degrees ,angle of attack.for two-dimensional.flow,degrees .effective angle of attack, degreesinduced angle “ofattack, degreesratio of maximum ordinate of-a
26、 t in p rabolic-(Jzmaxarc airfoil to its semichord c/ induced parabolic-arc emberordinate of thin parabolic-arc airfoilelevator deflection, degreestab deflecti.on,degrees Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No: 1175 5aspect ratio
27、(b2/S)taper ratiowWwvr maxaoNACA TN No. 1175 “.“increment *trailing-edge angle$ degreesvertical component of induced velocityvertical component of induced velocity resultinfrom trtillng vorticesfree-stream velocitycirculation around tail center sectionsection lift-curve slope(.)acCza =- da0 r),p,ut(
28、:%),= I(a)cz.-.a.* .-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACA TN No. 1175 7()achCha = aa 5,P,(5*The subscripts outside the parenthesis indtcate thefactors held constant in determining the psrameter.Lifting-surface-theory parameters deter
29、mined fromlifting-surface-theory solutions of elliptic wings withtwo-dimensional chordwise loadings (these parameters ,jare discussed when they appear in the report):.,ACLSCCLinduced angle of attack at thecjift CoeffiQ.-chord linecient *.induced streamline-curvature lift coefficientper unit section
30、lift coefficient($”($%6+-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 NACA TN No. 1175 .induced streamline-curvature hinge-momentcoefficient per unit s;tion lift-coefficientc2)2kJo0(%(5Yd(*)Subscripts:LL lifting-line theory :LS lifting-surface t
31、heory gS.v averagemsx maximumf, 5 flap-type chordwise oad$ngb balancea angle-of-attack-type chordwise loadingSc streamline curvature :P parabolic-arc camber chodwise loadinge elevator or effectivet tab811 elliptic2 determined from two-dimensional loadingconditionA“PPLICATIONO PGENERAL METHODMETHODTh
32、e section lift parameters (ca, ct? andconsequently (Wct) and section linge-moment-parameters(ch and ch6) are assumed available for the airfoila-.*-.-.-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN No. 1175 . 9sections and flap arrangement o
33、f the horizontal tail atthe Reynolds number, Mach number, and turbulence condi-tions of the finite-span-horizontal tail. The methodaccounts for first-order compressibility effects,provided that the section values of the lift and hinge-moment parameters are determined at the proper valueof Mach numbe
34、r,LIFTThe Parsmeter cLaThe slope of the curve of lift coefficient plottedagainst singleof attack at small angles of attack maybe found from figure 1. The slope CLa is given as a function of the aspect ratio A and the “slopeof thesection lift curve Czaw Effectiveness parameter ()% CL The value of the
35、 finite-span effectivenessparameter U% CL ()is found from the section values a czin two steps (from figs. 2 and 3) if the horizontal taildoes not have constant-percentage-chord elevators. - Theeffectiveness of elevators that have variable value of1)the section effectiveness parameter CC5 is found by
36、 aC-L- CAamechanical integration of the parameter. “/Aajm=presented in figure 2 as indicated by the followingformula: The values of a( ) are plotted against the valueC+I CzOf ctiAajm= forallpoints * along t.e elevator _ -span, The area under the curve is equal to )ab cLL”Provided by IHSNot for Resal
37、eNo reproduction or networking permitted without license from IHS-,-,-10 NACA TN No. 1175 .If ()a has a constant value along the elevatorspan c1O%fJ = ()%()LLLThe corrected lifting-surface-theory value ofl(a)CLis estimated from figure 3. The procedure is to estimatethe average value of cc/c over the
38、elevator span anddetermine the value of1W.Q()from figure 3. This% cZLSratio is multiplied by the value of (a)CLLL determinedfrom the curves of figure 2 or byThe ParameterThe slope cL of the curve.-the section value ()ab CLcLof lift coefficientplotted against elevator deflection for small values ofel
39、evator deflection is equal to the product of CLaand ()a CLY which were found previously; that 1s,.HINGE MOMENTSThe Tal?ameter Chu(2) .The slope Cha of the curve of:hinge-moment coeffi-cient plotted against sngle of attack at.small angles ofattack may be found with satisfactory accuracy from thefollo
40、wing equation: a71. J-Cha = (“h)ava-(%)L+cha)c(3)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.uNACA TN No. 1175In fi ure 4 are presented values of the parameter(i/ha.e .(;) (4) ()Chb(1)aeValues of are given in fiure 8 a71aeel LSThe parametOr ChaT
41、he slope Ch5 of the curve ofhinge-moment coeffi-oieilt plotted against”elevator deflection at small valuesof elevator deflection may be found with satisfactoryaccuracy from the following equation:where values of ()ch6 may be averaged by eye if chav 6varies only a small amount or by the following equ
42、ationif it varies considerably1beh()chb ()c, ce”da= beav _ 2 6 b/2beoThe induced-angle-of-attack parameter (./)ai 6 S may(6):; determined from figure for_thS_averagevaluece/C.The following integral is used,for the evaluationof ()cha avo*. .-*Provided by IHSNot for ResaleNo reproduction or networking
43、 permitted without license from IHS-,-,-NACA TN No. 1175Values of the parameter (.i/.iel,)LL may be determinedfrom figure 9. Values of the streamline-curvaturecorrection (“%) ., may be determined from figures ,6, and 7 by use of an average value of cc/c over theelevator spancThe Parsmeter Ch6tThe as
44、pect-ratio corrections for partial-span tabsare usually smaller than for full-span tabs. Ananalytical method of calculating the corrections isnot available but, according to the data presented inreference 7, an average reduction factor of O.0 issatisfactory; that is(8)where the integration need be m
45、ade only across the spanof the tab.For full-span tabs the aspect-ratio correction isa little larger and may be computed more accurately byuse of the following approximatimo The ssme reductionin th3 vdUe of cha caused by aspect ratio (last .two terms of equation (5) may be assumed to apply tochat pro
46、vided that it is multiplied by the ratio ofthe tab-lift effectiveness ()at (37 to the elevator-“lift effectiveness () Thus,% Ct” ()aatCL() ()atct = Chat-av + . ()Ch() 1+h at least this case wouldrequire a different layout of the horseshoe vorticesand, therefore, different tables for use in the calcu
47、la-tions. Also, the calculation of hinge-moment aspect-ratio corrections is considerably more critical than the”- +calculation of the lift-curve slope. Falknerls resultsfor the lift-curve slope are also presented in figure 10. .Provided by IHSNot for ResaleNo reproduction or networking permitted wit
48、hout license from IHS-,-,-16 NACA TN No. 1175Semigraphical SolutionsReference 12 presents a semigraphical method ofdetermining the downwash for any continuous distributionof vortices in a plane such as a liftlngsurfice. Someof the results obtained by this method are summarizedin figure 11.Electromagnetic-Analogy SolutionsThe electromagnetic-analogy metho
