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)
　
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