1、NATIONAL ADVISORY COMMITTEEFOR AERONAUTICSTECHNICALNOTENo. 1581APPROXIMATE RELATIONS AND CHARTS FOR LOW-SPEEDSTABILITY DERIVATIVES OF SWEPT WINGSBy Thomas A. Toll and M. J. QueijoLangley Memorial Aeronautical Laboratoryw!Washingtonmy 1948. . . . . . . ).-. . . . . . . . . . . . . . . . . _Provided b
2、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-. TECHLIBRARYKAFB,NMCIJL14!IL4“.-,ERRATANACA TN No. 1581APPROXIMATE RELUCIONS AND CHARTS F LOW-SHIEDSTKBIZJ71?YDERIV al?SWQZC WINGSBy Thomas A. Toll end M. J. CeijoMay 1948I?age 15, equatim at bottom of page: The
3、 second term within the2 ACILparentheses shouldbe - .Page 19:AaPage 20,be +;Page 22,Witmn1A COB Awyatim () and (35) should%? ( A+8 coBAc%= 1+d cos A A+4COEAbe replaced by the followlng:%2 ( ,2A+8 COBAC2R I-c/LCOB A 1- )t )Pv tan A -#A+4 COBAline 5: The sign of the secondthat isterm within the4+2 A+2
4、COSAa71 .* tan A.b/2 A+4COSA)second line of equation atthe brackets should beNACA- LauglegField,Vangle between plane of symmetq andlocal air-stieam direction at quarter-chordline of anysection,radiansangle of attack, radians unless qecified differentlyangle of attack, measured between ylme of wing a
5、nd componentof veloci normal to wing quarter-chordlineincrementalchange in angle of attack, caused by rolling, atmy spanwise stationugle between Z-=is cuuivector representingprhary forcecoefficient Cl (or cl)sngle of sweep or skew of()32aspect ratio ( ch-tqer ratio i )Root chorddihedral angle, radie
6、nswing quarter-chordline, degreeseffective edge-velocitycorrectionfactor for 13fteffective edge-velocitycorrectionfactor for rolling moment,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN NO. l 5qc2Ta.wing-tip helix anglelateral flight-path c
7、urvaturelongitudinalf13ght-p these correctionfactors may be applied to experi-mental or rigorous theoreticalvalues of the derivativesfor unswept wingsand exe consideredto be reasonably reliable for wings having taper ratiosas low as 0.5. The approxhmte theory indicates that certain derivativeexist o
8、nly for wings with sweep. Such derivativesdirectly by the approximate theory.In order to account for induction effects, itfamiliar expression (from liftim.g-linetheory) forattack of unswept ellipticfigs=gmust be evaluatedis assumed that thethe induced .mgle of(1)is also applicable to swept wings and
9、 that the same expressionmay beused to dete?mine the local induced angle at my sectionprovided thelocal section lift coefficient,rather than the wing lift coefficient,is substitutedin eqmtion (l). This procedure amounts to a reductionin the two-dimensionallift load by a factor that remahs constant a
10、longa semispanof the wing. Although the assumption regarding the localinduced ane of attack is lmown to be inaccurate,the consistentappli-cation of this assmption to loth swept ma unswept wings is expected toyield reasonablyreliable correctionfactors for the effects of sweep.The effects of sweep on
11、the distributionof loading are, of course,neglected in the strip-theorytreatment. The present method, therefore,can be expected to account only for the geometric effects of sweep.Certain lWtations of the present simplifiedtreatmenthave beenolserved experimentally. For example,when the sweep angle is
12、 referredto the wing quarter-chordline, the wing lift-curve slope is found todecrease somewhatmore rapidly with sweepforwardthan with sweepback,particularlyfor highly taperedwings. fithough such _ therefore, theis sly(5)By substitutingequation (3) in equation (9), the lift-curve slopeobtained from a
13、n adaptation of lifting-line theory is found to be givenbyAcos Ac whereas, equation (8) overestimatesthe effects of sweep emd equation (9) Underestimatesthe effects of sweey.At aspect ratios approaching zero, results obtained either by Mutterperlsmethod or by equation (7) are in agreementwith Jones
14、theory (reference4).Induced.ara.- The induced bag of a swept wing is, to the firstorder,Substituting the expressionforgives,asa direct consequence of2C2COS A (lo)C2 (equation (4) in equation (10)the basic assmption that the inducedangle-of attack is give= by equation (1), the fo-Uowing equation:CL2C
15、Di A. (n)Equation (U.) indicates that, to a first approximation, the induced dragis independent of sweep. Some effects of sweep on the induced dragwould, of course, be eected because of changes in the load distributionwhich are not consideredin the present.method. Theoreticalresultspresented in refe
16、rence 3 for the induced drag of swept wings are in fairagreementwith equation (n), and,therefore, some support is given to thepresent assumptionregarding the induced angle of attack.SideslippingFlightFor a constant-chordswept wing in sideslip,according to striptheo the distribution of load is unifor
17、m over”each panel, although themaitude of the load on the left panel is differentfrom that on theright panel. As in the case of straightflight, therefore, the componentsof the total load on each panel may be representedfor conveniencebyvectors located at the centers of pressure of the panels.1 . . .
18、_ . . . . . _ _.-. . . .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-12 NACA TN No. 1581.The pmel loads are altered by sidesli%ecause of the effect ofsideslip on the veloci componentsncrmal to the quarter-chordlines ofthe panels and on the angles
19、of attackwith respect to the no-l-velocity .components. The component of veloci normal to the quarter-chordlineof the left wing psmel of a swept wing is altered due to sideslipby thefactor COS(A + P) , snd the angle of attack tiUthrespect to the normslcos Aveloci component is altered by the reciproc
20、al of the sam(C,L-C,Ry (26)After substitutionin equation (26) of the values of c1 and cRgiven by equatiom (22) and (23), the strip-theoryvalu of the derivativeof rolling moment due to rolling is found to be1AC08Ac1 =-gAy4coAPwhich can be rewritten in a form similar to that of equation (7); thatis,Cz
21、p = (A + 4)COS A()A+4coa Acz HO (7)The equationfor Cl actually should contain additional terms dependentDon the angle of attak and the center-of-gravi location. Such termsgenerallyare small, however, and are thereforeneglected in the presentapproximate tieatient.Lateral force.-ven byCy.$ 12rowhereTh
22、e coefficient of lateral force due to rolling isFrom equatiou (22) to (25) and from the approximaterelation between aand. CL as given by equation (6) for a. equal to 2ti, it can be shownthat+4cos A .24 C2Aor(36)(37)Lateral force.-ven byThe coefficientof lateral.force due to yawing is(38)wheresin A8L .aCOS(A + PI)andlWom equations (34) (35)J2cfc%-+-A+,cosA+( therefore, the product AEemay be calculatedfor the same range. -. .- .Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-
