1、 -* . - . . A . -.RESEARCH MEMORANDUMIiIXPERINKENTAL DETERMINATION AT SUBSONICSPEEDS OF TEE OSCILLATORY AND STATIC LATERAL STABILITYDERIVATIVES OF A SERIES OF DELTA WTNGS WITHLEADING-EDGE SWXEP FROM 30 TO 86.5By William LetkoLangley Aeronautical LaboratoryLangley Field, Va.NATIONAL ADVISORY COMMITTE
2、EFOR AERONAUTICSWASHINGTONApril 12, 1957Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARYKAFB,NM.NACA RM L57u + #C% andCz - cl. for the 82.5 wing are very large and of oppositesign tor,u 13,uthose of the other wings. !Ihi*comparison was ma
3、de for one frequency andamplitude of oscillation. The results of the static tests showed thatthe static lateral stability deriative the motion was a combinationof yawing and sideslipping and provided te combination derivatvesCn - Cn. cl - cl. Cn + k2Cn. and: _Czr,u B,U.) r,u p,o + k2C.B,(D r,u B,(L)
4、 r,u.where k is the reduced frequency parameter S%cm pitching-moment coefficient, /qSbCn yawtng-moment coefficient, Mz/qSbFL lift dProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM L57A30. FD drag (approximate)* Fy lateral force% rolling moment
5、% pitching momentM yawing momenta angle of attack, degb span, ftP angle of sideslip, radians or deg3Pfi=zPo amplitude of sideslip, dega71, E mean aerodynamic chord, ftk ubreduced frequency parameter,. mu! circular frequency of oscillation, radisns/sec+ angle of yaw, radians or deg$. above an angle o
6、f attick of about 10 the curvesdiverge and the value of the parameter at 30 is close to zero for the600 wing, about -0.4 for the 75 wing, and about -0.7 for the 82.5 ng.In order to show the effect of frequency on the parameterclp,lm+ cl. cross plots of figures 11 and 12 were made for a numberr,oProv
7、ided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-8 tmmmmm NACA RM L57A30of angles of attack and are presented in figures 13 and 14. Generallyfor the low angles of attack presented there is only a small effect ofrequency n Czp,u + k2C1. for both the 82.5 a
8、nd 75 wings. Atr,u .the higher angles of attack, there appears to be no consistent effectof frequency, although for the 75 wing the values of Clp,a + k2C,0become more negative with an increase in frequency.ige Uiations f C%,u+k2CJ$ with amplitude were obtainedat the high angles for both wings (figs:
9、 15 and 16), and the changeswere usually greater for the 82.5 wing.-Directional stability.- The variation of the directional stabilityarmter Cnp,u+k C%,u with angle of.attack for_the 82.5 and75 wings is given in figures 17 and 18 for different values of the and for an amplitude .reduced frequency pa
10、rameter 2V of t6.Figure 17 shows that for all frequencies the parameter is small andnegative at zero angle of attack for the 2.5 tiw-becomes more nega-tive with angle of attack up to about 20, after 20 becomes less nega-tive, and at angles of attack above 400 the values of the parameterbecome positi
11、ve. The value of the parameter at 0 gle of attack forthe 75 wing is zero or a small negative value, depending on the fre-quency. (See fig. 18.) At some small positive angle the parameterassumes a small positive value which is more or less constant up toabout 300 angle of attack; above 30 angle of at
12、tack) however) thevslues Of Cnp,u + k2C%,0 become negative. Also shown in figures 17and 18 are the static values of P (per radiem) which can be comparedwith the oscillatory values of % + k2Cn:,u. The comparison shows,as was noted for Cl, that the static values of CnB for both wingsexhibit the same t
13、rend with angle of attack as is shown by the oscil-latory derivatives. A comparison of the variation of cn, + k Cn,mwith angle of attack for the 600, 75, and 82.50 wings for a reducedfrequency of about 0.066 and an smrplitude. of t6 is shown infigure 35(a).rBoth the 600 and 75 wings have small posit
14、ive yalues of the deriva-tive at smll angles of attack UP to about 10, whereas the 82.5 _nghas relatively large negative values indicating directional instability.At an angle of attack of about 22, the 75 wing stiil has a small posi- .tive value, snd the 600 wing has a positive value about 1: times
15、that ofthe 75 wing while the 82.5 wing has a ge negative value whfch % 4about 5 times that of the 600 wing. nProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM L57A30 +.the!lhevariation of Cnp,u + k2,u th82.50 wing is irresr even at OO angle9how
16、ever, a lsrge change n the parsmeter occurred between 2 and4 amplitude for 40 and 50 angles of attack where the values of theparameter changed from a positive to a negative value.Rolling moment,due to yawing.- The variation with angle of attackof the rolling moment due to yating Cz - cl”r,u p,co for
17、 the 82.5o and 75 wings is given in figures 23 and 24.For the 82.5 wing, the variation with singleof attack is nonlinear,. the values being positive In the low-angle-of-attack range and becominglarge negative vslues above about 22 and becoming positive or tendingto become positive at sngles of attac
18、k above 30. For the low frequencies,the values of c - CL. for the 75 wing are negative in the low-r,u p,uangle-of-attack range while at the higher frequencies the values areS and positive. At angles of attack above about 30, the veriationbecomes extremely nonlinear for the three lower frequencies an
19、d thevslues of the parameterattack.Fig-me 35(b) showsthe 82.50, 750, and 600and f6 amplitude. Thesmall difference in theare positive in the range around 40 angle ofa comparison of thevalues of Cz - cl= forrpv :$0.066delta wings for a reduced frequencyfigure shows that, even though there is only aval
20、ues of Czr.a - Czb,a for the three wings atlow angles of attack, there is a lsrgedifferece in the angle-of-attackrange above 24 and at a angle of attack of 30 increasing the sweep ofthe leading edge from 600 to 82.5 chsmges the value of the parameterfrom 2.8 to -2.6.The effects of frequency on the p
21、arameter Czr,m - C2”J3,u)are shownx in figures 2 and 26 which ue cross plots of figures 23 and 24, respec-tively. The 82.5 wing shows less vaiation of the parameter with. - *Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-10 NACA RM L37A30frequency i
22、n the low-angle-of-attack range than does the 750 wing. Atsthe high angles of attack the effects of frequency or the value ofcr - c.for both wings are considerably greater them at thep,w 7thelower angles of attack.The variation of Czr - cl. with amplitude for both wings is9 p,ushown in figures 27 an
23、d 28; The figures show that smplltude has a large _effect on the magnitude of the parameter for the 82.5-wing at allangles of attack shown except 0 angle of attack. FOC the 75 wing, amuch smaller effect of emplftude can be noted in fi”e 28.Damping in yaw.- Tne variation with angle of attack of the d
24、amping-in-yaw parameter Cnr,u - Cnb,a for the 82.3 and 75 wings is givenin figures 29 and . The damping in yaw for the 82.5 wing is zeroor slightly negative up to about 10 angle of attack and becomes morenegative up to about 20, but after 20 the variationwith angle ofattack is irregil_arand depends
25、on frequency. For the 75 wing (fig. 30),the value of the parameter is zero or nearly zero to about 20; after20 the values become large and negative up to about 40 and then tendto become less negative. Figure 3(b) shows a com arisen of the varia- - x“ion f C%,a - cn,u for the 600, 75, and 82.5 winge.
26、 For allthree wings, C%,u - Cnp,o is nearly zero in the low-angle-of-attack. .range, as was expected, and the values become more negative at higherangles of attack. In the range mound 20 angle of attack, the 82.5 winghas the greatest negative values.Figures 31 and 32 show the variation with frequenc
27、y offor the 82.5 and 75 wings for several angles of attack andof ?6. For both wings at low angles of attack, the effects% -c”r,m np,uan amplitudeof frequencyare small. The effect of frequency is extremely large and erratic forthe 82.5 wing at 30 and 40 but for the 75 wing the variation isextremely l
28、arge only for an angle of attack,of 40. Similarly, theeffect of amplitude is large only at the higher angles of attack pre-sented and generally the largest changes in the parameter occur in therange from between 2 smd 4 in amplitude for both the 82.50 and75 wings. (See figs. 33 and 34.)CONCLUSIONSTh
29、e static lateral stability of six delta wings wms determinedat subsonic speeds and, in addition, two of the wings with 82.5 and Y75 sweep of the leading edge were oscillated in yaw about the -percentpoint of the root chord in order to determine the effects of frequency wProvided by IHSNot for Resale
30、No reproduction or networking permitted without license from IHS-,-,-NACA RM L37A30 11and amplitude on the combination lateral stability derivatives resultingfrom this motion. The results of this investigation indicate the fol-lowing conclusions:1. The results of the oscillation tests showed that la
31、rge changesin the derivatives occurred with chsnges of frequency and amplitude atthe high angles of attack for the 82.5 and 7P delta wings. For the = 0.066 the largest changes in thereduced frequency parameter Vderivatives with smplitude generally occurred at low values of amplitude.2. Comparison of
32、 the variation with angle of attack of the oscil-latory derivatives obtained with the 82.50 and 75 wing with those of a600 wing of another investigation showed that,large differences in theoscillatory derivatives are generally obtained at the higher angles ofattack and that the values of the combina
33、tion oscillatory deriva-tives Cn,u + 2C%,0 and cZr,u - CZB,U for the 82.5 wing are verylarge and of opposite sign to those of the other wings. This comparisonwas made for one frequency and amplitude of oscillation.3. The results of the static tests showed that the static lateralstability derivatives
34、 followed trends which were similar to those ofother investigations.Lmgley Aeronautical Laboratory,National Advisory Committee for Aeronautics,Langley Field, Vs., January 7, 1957.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACA RM L57A30.REFER
35、ENCES.1. Csmpbel.1, John P., and Woodling, Carroll H.: Calculated Effects ofthe Lateral Acceleration Derivatives on the Dyn-iimicLateralstabilim of a IMta-Wing Airphe. NACA RM L54K26, 1955.2. campbell, John P., Johnson, Joseph L. Jr., and Hewes Donald E.:hw.speed Study of the Effect of Itrequencyon
36、the StabilityDerivatives of Wings Oscillating in Yaw With Particular Referenceto IH.ghAngle-of-Attack Conditions. NACA RM L55H05 1955.3. Fisher, Lewis R.: Experimental Determination of the Effects ofI?requency and Amplitude on the Iateral Stability Derivatives fora Delta, a Swept, and an Unswept Win
37、g Oscillating in Yaw.NACA RM L56KL9, 1956.4. Queijo, M. J., Fletcher, Herman S., Marple, C. G., and Hughes, F. M“:Preliminary Measurements of the Aerodynamic Yawing Derivatives ofa Triangular, a Swept, and an Unswept Wtig perfog pure yawOscillations, With a Description of the Instrumentation Fmploye
38、d.NACA RM L55LJ-4,1956. 1!5. Tosti, Louis P.: Low-Speed Static Stability and Damping-in-RollCharacteristics of Some Swept and Unswept Low-Aspect-Ratio Wings.NACA 1468, 1947.6. McKinney, wion O., Jr., and make, Hubert M.: Flight acter-istics at Law Speed of Delta-Wing ?bdels. NACA RM L7K07, I-948.r.P
39、rovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA RM L57A30.*13.TABLE IGEOMETRIC CHARACTERISTICS OF SIX DELTA WINGSwing1 2 3 4 5 6Aspect ratio . . . . . . . . . . . 0.25 0.53 1.07 2.31 4.0 6.93Leading-edge sweep angle, deg . . %.5 82.5 75 60 45 30D
40、ihedral angle, deg . . . . . . . 0 0 0 0 0 0!hdst, deg . . . . . . . . . . . 0 0 0 0 0 0Airfoil section . . . . . . . . . Flat Flat Flat Flat Flat Flatplate plate plate plate plate plateArea, sh in. . . . . 114 207.4 335.8 561.2 703.2 405.9Span, in. . . . . . . . . . . . . 6 10.45 18.97 36.00 53.03
41、53.03Wan aerodynamic chord, in. . . . 32.00 26.46 23.60 20.79 17.68 10.21Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-14 NACA RM L57A30FvFDI/See?ron A -AzFigure 1.- System of stabilitymoments, andaxes. Arrows indicate-= displacements .positive for
42、ces,“d”.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, * *EccentrlFigme 2 Sketch of oscil.latton-in-yoxepmemt.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-f % .A;, ,“,N. * “ u,F_re 3.- Photograp
43、h of oscillation-in-yaw eqzlpment. ,; +1 = “*$.+ f ,$L-9W44on top of tunnel test section.i3-SilProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, * .(a) 82.5 delta wing. L-91.176Figure 4.- Photograph of mod.elain tunnel.Provided by IHSNot for ResaleNo
44、 reproduction or networking permitted without license from IHS-,-,-(b) 75 d,gta i%.L91J77FiWe 4.- Concled.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-, *r .,CliWIM leadng eag6 4L .e!w24 -1 T Beveled48 mmwfngfWfrg 4wtng 2Wing5.I MxbWfg ,mntr Orwk?
45、r kdlng and side.orce characteristicof the 75 delta wing.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA FM L57A30 25j&Q.Figure Il.- Variation with angle of attack of the effective dihedralparaneter for the 82.50 delta wing measured during oscil
46、lation.V. = *6”o .018.032z.066A .31L 152-82&o.V-4 0 4 8 12 fL9 Po 24 28 3.2 3Li 40 44 48 52.4eofaftmj GC,degFigure 12.- Variation with sngle of attack of the effective dihedralparameter for the 75 delta wing measured during oscillation.q. = ?6.Provided by IHSNot for ResaleNo reproduction or networki
47、ng permitted without license from IHS-,-,-iiX&2V 4*a75 10020A 30Figure 13.- Variation with frequency pexameter Figure 14.- Variation with frequency parameter ofof the effective dihedral ammeter for the the effective dihedral parameter for the 7582.5 delta wing. o= 16$ delta wing. *O = 6.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.Figure 15,- variationeffective dihedral82.5 delta wi.4687&with aDIPtll& Ofparawt
