1、/,.NATIONALADVISORYCOMMITTEEFOR AERONAUTICSTECHNICAL NOTENo. 1732CALCULATED EFFECTS OF GEOMETRIC DIHEDRAL ON THELOW-SPEED ROLLING DERIVATIVES OF SWEPT WINGS5T W J. QueQo and Bgron M. JaquetLangley Aeronautical LaboratoryLangley Field, Va.wry=washing-km .October 1948,$ i/,r ,-. .A./ !-, .-IIJ;- +Pro
2、vided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.,0144714NATIONAL AIl% however, the relations presentedare belleved to be reasonably reliable for w3ngs of taper ratio as lowas O.q.Some comparisonsare made between cal.cullatedand arperimentalvalumof the
3、rollin however, the effects ofgeometric dihedral genem13y have been neglected. The analysis presentedin reference 1 for the stability derivatives of swept wings did notinclude the effects of geometric dihedral.,but the methods presentedtherein can be adapted to include dihedral.effects. The method o
4、freference 1 was extended in reference 2 in order to determine the effectiof geometric dihedral on the rollhg moment due to sidesUp and on therolling moment due to yaj a similar method of anslysis is used hereinto detemine the effects of geometric dihedral -therefore,equation (14) can be writtenas(2
5、8) The rate of cWm.ge of pequation (1.8) with respectIwith dihedral engle is found by differantiattngto r; therefore,acyp 0.=3C7P,+0 .therefore equation (21)reduces to.(24)% therefore,for positive dihedral the tail contrilnrtionto theairplane Czp would decrease as the angle of attack increases. This
6、effect shoulil.be small unless the tail area is quite large relative tothe wing area.Lateral force.- Geomrbric for small dihedral angles z hasno appreciable effect on the change in m cued by dihedral, butfor larger dihedral angles (grea*r thsn *IOo) the distance z affects()Acy Pr appreciably. Whethe
7、r (% becomes more positive or morePnegative with increase in z depends onthesiof z tidr.Yatig mment. - Geom9tric dihedral causes an Increment in yawingmment due to rolling which is almost independent of lift coefficient(equation (21). The increment is very small and probably WCUM benegligible as a c
8、ontributionto the values of C% of a complete airplene.Comparison of lEzperimentaland.Calculated Resultsme data offigure 6 ticate that the methcxiof ction pre-sented herein can be used to predict values of IClp quite accurately at . - .- - . . . . . . .Provided by IHSNot for ResaleNo reproduction or
9、networking permitted without license from IHS-,-,-12 NACA NO. 1732low and mode?.%e lHt coefficientsbut that the application of thetheory is less reliable at the higher lift coefficients. This differenceletween calculatedand expetd values is p due to the factthat the experimentalwalues of %p vary wit
10、h Hft coefficient;whereas,theory indicates that Czp is Wependent of lift coefficient.Figure 8 indicates that the theory overest=tes the effects ofgeometric diheclrs2 on % Sna Cym at low lift coefficientsand undezestimates the effects at high Hft coefficients. For the wing used inthis tivestition, th
11、e Calculatedvalues of the p arsmeters acy r ot(equation () ) ti a% ar (equati (25)are apprte= e- todthe average experimentalvalues of the same parameters.cOrwIammGREwKKsAn apyrm3mate theory has been used to derive equations to indicatethe effects of geometric dihedral.on the rolllnn parameters of sw
12、eptwingsa71 Although the equationspresented were derived specificallyforuntapend wings, the reljtionspresented beueved t6 be reasbreable for w3ngs of taper =tios as low as O.The theo 3ndicates that lateral force due to roltig shows awked change with geometric W= “ej tit Yam moment due torolliqg is a
13、lmost hdependent of geometric dihedral, and that damng inroH can be changed appreciably if the dihedral ane is lsrge and thedisplacement of the rollhg axis from the wing-root-chord line ismoderate or large.Corupari.sons_betweencalculatedand experhmmtal values of theroJUg derivativesfor an untapered
14、45 swept%ack*g of aspectratio 2.61 hambggeometric dihedral angles from -20 to 10 indicatethat the calcuhted values are fairly rellable over the low- and moderate-Uf t-coefficient ranges.Iangley Aeronautical LaboratoryNationsl Advisory Conmitteefor Aertics .Ia.ngleyField, Va., A-t 24, 19. + ., - -. ,
15、 .”Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACA NO. 17321ImFERENm131. Toll.,ThUMM A., and Queijo, M. J.: Approximate Relations and Chartsfor Low-speed Stability Derivatives of Swept Ws. NACA TNNO. 1581, 1948.2. Queijo, M. J., and Jaquet, B
16、yron M.: Investigation of Effects ofGeometric Dihedxal on Low-speed Static Stability and Yaw3ngCharacteristics of an Untapered 45 Sweptbaok-WingModel of Aspectmtio 2.61. WA TN NO. 1668, 1948. ,J. _. = . - -.- -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from
17、IHS-,-,-14.I NACA TN NO. 1732.7%!Yz v ./ A%/Lp .tL.-E=”figure b System of stabihty ems. Arrowsjndcufe podwe direcfion of forcesmornen?$ ond unguhr dizpkmcmets. -. -.:,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA NO. 1732 15wewgeometryamws. .
18、 - . .-. _m. The. _ . . _ _ . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-I0I:60P m,I I I I I712“1I,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA NO. 1732 17I . t 1%1 .1 I 1-rr a+7 I I_
19、 1 . . . .(CL./7JJ -. .2X. PJ$oO42w Pp-+,. b/2“o.3-1.z0.-60 -+0 -20 20 +0Dhedral mg%J rJ deg - 42)/7gure +- Churt showing cu/cu/ufedvdue- - .-. -.- - - - -.- - -. -Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-18 JVACATN No. 1732%“.8 +t7I I 1. .1-1
20、1.1-. - . . ,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA NO. 1732Cp.0(a)CL=(),tEXper/rnCOiW- -CakuMcd2-I=ELLE19)1Fjyure 6.- Compandon ofcalculated va/Utm offe# Reynolds-. . . . _ . mmber= LI x #!. - = .Provided by IHSNot for ResaleNo reprod
21、uction or networking permitted without license from IHS-,-,-20CyP%poNACA NO. 1732.6 .- . Q.2 .: #-.6.4 v-20 “/0 o 10lMwhz/ uogk= degCnp W% dihedrai angle. A= 2.6/;A= 4s. . - . .r, -. . -.,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.NACA NO a71 1732 21acyp cdcukvtx?23xE-0 L. .l/&-.0F)gure 8.-.8“=s=COmparw7 or OperlmemW and. . . . - - . -. . - - . _ -. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
