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ory ignores the induced drag and mutualinterference effect between adjacent wing sections. As a result, the strip theory prediction becomes increasingly erroneous as the w7ing aspect ratio becomes smaller. For such configurations, the following Datcod relation can be used: (Clp)W=(P~ ),,=o(~)((C~C)) )/rad (4.576) In Eq. (4.576), it is assumed that the angle of attack is in the linear range or CL -. awa and the effect of drag force on the rolling moment is ignored. The parameter (Cip)r/(Cip)r = o is given by the following relation:7 where (Cip)r = (1 _ 2z'sin F +3zz sinl F)/rad (4.577) (Czp)r =o z' = 2z,y (4.578) b Here, zw is the vertical distance between the center of gravity and the wing root chord, positive for center of gravity above the root chord. The data to estimate (pqp/k)cL =o are presented in Fig. 4.25 for typical wing planforms. The vertical tail contribution, (CLp)V is given by where (Clp)V=l2(b)( b )fcyp,v z - zv cos a - lv sina (4.579) (4.580) Here, zy is the vertical distance between the aerodynamic center of the vertical tail and the center of gravity and is measured perpendicular to the fuselage centerline, lv is the horizontal distance between the aerodynamic center of the vertical tail and the center of gravity and is measured parallel to the fuselage centerline. The parameter C),p,v can be obtained using Eq. (4.547). For supersonic speeds, no general method suitable for engineering purposes is available for estimating the contributions of the wing and the vertical tail to damping-in-roll derivative. Datcod presents data for some selected wing plan- forms.lnterested readers may refer to Datcom] EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 411 Estimation of Cnp. This derivativeis a measure oftheyawing momentinduced due to a roll rate experienced by the aircraft. The contributions of the fuselage and horizontal t,ail to Cnp are usually small and can be ignored. The contr:ibutions mainly come from the wing and the vertical tail so that Cnp = (Cnp)W + (Cnp)-V (4.581) For low subsonic speeds, an approximate estimation of the wing conLribution can be done using the strip theory as follows. Consider once again the strip RT on right wing (Fig. 4.27a). The force in the Ox direction is given by dF - dL sin Cep - dD cos ap where (4.582) = ~:pUo2[ao(y)(a + ap)ap - (CDO,l + CDa,l(cy +ap))lc(y)dy (4.583) = ;: p Uo2[_CD.I + (ao(y)ct - CDa.I)CX plc(y) dy CD.1 = CDO,I + CDa,.lCL (4.584) (4.585) Substituting ap = py/Uo, the yawing moment developed by the elemental strip RT is given by dYM=-gpUo2[-CD.l+[ao(y)a-CDa.,lZrYlc(y)ydy (4.586) The total yawing moment due to the right wing is given by YMR = _: pUo2l,' [-CD.I + [ao(y)a - CDcr,L]7jY].(y)ydy (4.587) Similarly, the yawing moment developed by the left wing (change +y to -y) is given by YM, = -,pU,~[,' [-CDJ - [ao(y)a - CD j]ZY]c(y)ydy (4.588) The total or net yawing moment, which is the sum of the right and left wing yawing moments, is given by We have YM=-pUo2['[ao(y)a-CD..,]GjY),(y)ydy (4.589) (4.590) (4.591) Cn= pYUMS7 Cnp = -,(:C:: ) 412 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL so that -4 z (C"p)W = Sb4 f,b/2Lao(Y)a _ CDa.j]c(y)y2dy (4.592) www.aero.cn 航空翻译 www.aviation.cn 本文链接地址：PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL3
