1、 . =.-=. ,., “al_ _._.-NATIONAL ADVISORYCOMMITTEEFOR AERONAUTICSTECHNICALLmlqcopyA METHOD FOR PREDICTING LIFT INCREMENTS DUE TO FLAPDEFLECTION AT LOW ANGLES 03 ATTACK ININCOMPRESSIBLE FLOWBy John G. Lowry and Edward C. Pol.hamusLangley Aeronautical LaboratoryLangley Field, Va.WashingtonJanuary 195
2、7Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-G-,. .-487NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS*-. TECHNICAL NOTE 3911“-.A METHOD FOR PREDICTING LIFT INCREMENTSDUE TO FLAPDEFLECTIONAT LOW ANGLES OF ATTACK ININCOMPRESSIBLEFLOWBy John G. Larry en
3、d Edward C. pOhS211USSHYA method is presented for estimating the lift due to flap deflectionat low angles of attack in incompressibleflow. lh this method provisionis made for the use of incremental section-liftdata for estimating theeffectivenessof hh-lift flaps. The method is applicable to swept wi
4、ngsof any aspect ratio or taper ratio. The present method differs from%. other current methods mainly in its ease of application and its moregeneral application. Also included is a simplifiedmethod of estimatingthe lift-curve slope throughout the subsonic speed range.a71a15INTRODUCTIONAlthough sever
5、al methods are currently avaibble for estimating theeffectivenessof flaps on wings of various plan forms (for examplerefs. 1 to 4), they are generally restricted to small flap deflections;and furthermore each method has certain reservations in its application.For example reference 1, which is a semi
6、enrpiricalapproach, is limitedto specificwing plan forms and flap-chord ratios within the range ofexperimentaldata used as well as to small flap deflections. In addition,both references 1 and 2 may require considerablemanipulation to obtainvalues for a particular plan form.The present method attempt
7、s to combine the various existing methods into a simple procedure that has more general applications than any one .of them alone. Section lift data are used as a basis of the calculations,and this approach provides a means of estimating the increments of liftdue to high-lift flaps at large deflectio
8、ns.a71.X8-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-,. , 2 NAC!ATN 3911SYMBOISA%-bbfCLACLCLcL5 =cCfCzAclc2aKbKcMa(%)CLaspect ratiosection lift-curve slope, per radianwing spanflap spanthree-dimensionallift coefficientincrement of three-dimensio
9、nallift coefficientdue to flapdeflectionthree-dimensionallift-curve slope, per degZJ(constant a)wing chordflap chordtwo-dimensionalsection-liftcoefficientincrement of section-liftcoefficientdue to flap deflectionsection lift-curve slope, per degflap-span factor (ratioof partial-span-flaplift coeffic
10、ientto full-span-flaplift coefficient), (ACL)partial spsm(ACL)full SPSJIflap-chord factor (ratioof three-dimensionalflap-effectivenessparameter to two-dimensionalflap-effectivenessparameter),(%)cL/(%)czMach numberangle of attack, degthree-dimensionalflap-effectivenessparameter at constant lift“w.Pro
11、vided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3911 3d-0 (qj)cz two-dimensionalflap-effectivenessparameter at constant lift“6 flap deflection normal to hinge line, deg5 flap deflection streamwise, tan 5 = tan 5 cos , degA angle of sweep, degAh
12、sweep of hinge line, degJc/2 sweep of half-chord line, degfJc/4 sweep of quarter-chordline, degA taper ratioSubscript:eff effective*DEVEH3PMENT OF METHODOne reason for developing the present method is to provide a meansof estimating the lift increment of high-lift flaps. The method is there-fore bas
13、ed on the use of a section lift increment Act, either theoreti-cal or experimental. The basic concept used inACL = Ck (c+= 8KbSince it is desired to use either a theoreticalof Acz in the method and sinceAcl = CZa (UJC7 multiplying the right-hand side of equation (1)givesthe method is(1)or an eqerime
14、ntal valueby A and flap deflection in the streamdirection 51 is used, since this plane is used for measuring the angle ofattack. Several investigatorshave proposed that the section data shouldbe referred normal to some sweep line since this conceptwouldbe inagreementwith that used in the simple swee
15、p theory. For airfoils in therange where the profile has a negligible effect on section characteristics(thinwith small trailing-edgeangle), the two methods give identicalresults for constant-percent-chordflaps on relatively untaperedwings.For highly taperedwings the present method somewhat simplifie
16、s the-.4difficulties,with regard to flap-chord ratios in the vicinity of theroot and tip, that are encountered in the simple sweep theory. In viewof this simplificationand the fact that wings of current interest arerelatively thin, the use of section data relative to the airplane centerline is belie
17、ved to be warranted. Since the values of Act are the basisof the method, the final results will be only as accurate as the sectiondata; thereforeuse of experimentaldata is advisablewhen such areavaiable.The aerodynamicAerodynamic duction Factorinductionfactor C! if a. differs appreciably from 2x, th
18、e term should be com-chputed from equation (3)by using the most appropriate value of a.0 available. The choice of A=/2 rather than the more commonly usedhowever, figure 9 shows that when the curves are made symmetricalby useof the half-chord line for the sweep reference, relatively little dis-placem
19、ent due to taper ratio occurs. Also, in the modified lifting-linemethods such as the Weissinger method, taper effects are dependent uponthe sweep and the relative position of both the quarter-chordline(bound-vortexlocation) and the three-quarter-chordline (boundary-condition location). This fact sug
20、gests the possibility that wirigshaving the ssme sweep of the intermediateor half-chord line might beless affectedby taper than those having some other common sweep line.Accuracy of MethodThe preceding results indicate that equation (A2) may be applicableto all plan forms, providing the sweep of the
21、 half-chord line is used.Use of A42 results in the following expression for the lift-curveslope:Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACATN 3911Dividing both sides by A and letting a. equal 2Z gives thefollowing expression:(%) M+o = 2X
22、A7)which indicates that % is a unique function of AA In orderCos M=O.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-0!Figure 2.-Sweep of half-chord line, degNomographAspect rath, Afor converting quarter-chod sweep angles to.i .,half-chord78sweep an
23、gles., .“,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3911Figure 3.-.2 4 .6 .8Variation of span factor Kb with flap span for inboardLoflaps.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
24、0/2F%mre 4 Spm factor for flaps other tk inboodLoflaps a71-.*,.f! b.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3911 19-.,.,.*. “Figure 5.- Variation0 .2 .6 .82 3 4 5 6 7 B 9-/0Aof flap-chord factor with (%)CZ smd aspect ratio.-,. .,-Prov
25、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-20 NACA TN 3911.,.8C.6CI I(From fig 5 (.“.,“Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-a71a15 a15a13.7.6,5.3.2./oFigure 7.-0 .04Variation ofedgeFs!3.08
26、 ./2 ./6 .20CfTflap-effectivenesspsrameter withangle approximately10; M S 0.2;.24 .28 .32 ,36control-chordratio. Averageflap deflection, lOO.gotrailing- NrProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-22 NACA TN 39110nAaf A g APlo/ff flop 10 0 1Dou
27、ble - slotted fbp 60” 40 .4/Double - slotted fhp 60 4/0 07.*=A .:/to63.72.3 /-.o .2 4 .6 .8 /.0Es fimufed A CL1Figure 8.- Correlation of experimentaland estimated ValUeS of ML.u= OO; M 0.4. “*Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-) .(.-.0.5
28、04Ia71a13 ; /4=!5A=Lo- /l=o. ./ 1 .03 - ,02 -.0/ -0 a I 1 I I J. , “ .I I I i i-60 -40-200204060 -60 -40Sweep of quarter- chord line, oeg Sweep(a) A = 1.5.Figure 9.- Variation of with sweep; Weissingez-20 0 20 40 60of half -chord Iine, oeg15-petitmethod.Provided by IHSNot for ResaleNo reproduction
29、or networking permitted without license from IHS-,-,- J=L5A=/o- Ao/.(25-.05-04 -.03 -.02 -.0/ -0 A I I/I-60 -W -20 0 20 40 60 -60 -40 -20 0 20 40 60Sweep of quarter-chord /inel deg Sweep of ha/f-chord line, deg(b) A = 3.o.Figure 9.- Concluded. gr,ta71“ . .-, ,. ,Provided by IHSNot for ResaleNo repro
30、duction or networking permitted without license from IHS-,-,-. ./4 l% Method Ret0 Krienes /427 Fa/kner /5.020 -4/” Falkner /5.3/ 55 Falher /695 43” M/Hhopp 17.0/6 - A_/0 Falkner /5Eq v 45 Fi71kffer /5.0/2 -v.008 -.c04 -0 I 1 1 1 1 1 1 I I I 1 10/23456 789/0/2A/cos Avp.%a AFigure 10.- Variation of wi
31、thA as determined by severalmethods. a. = 2x; M = O.Cos AProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.032.028024.020ca .0/6A.0/2.008,0040.; .*o / 234567 8 9Akos Aq2c%Figure H. - Variation of Awith in incompressibleCos&/2, .4b“ ,n)(h/0 / /2flow.Pr
32、ovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, .NACA TN 3911(cL.)M(%=)M=O“y-o /0Figure 12. - Ratio of20 30 40 50 60 70 80 90Sweep, of half-chord Iine, cfegcompressibleto incompressiblelift-curve slopesfor subsonic speeds.-.Provided by IHSNot for Res
33、aleNo reproduction or networking permitted without license from IHS-,-,-28 NACA TN 3911.Sweep of half-chord /ine,degFigure 12. - Continued.L.w.?:,#-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 3911 29=“ .w4*,*- *(%)M(CL=)M=O2.5242.3222./20/,918/.716/5/413L21./, o 10 20 30 40 50 GO 70 BO 90Sweep of half-chord line, degFigure 12.- Concluded.NACA -Langley Field, VJ.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
