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224           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
surface span and is defined as
                           .  Kcr _ (Kcy\,(l - th) - (Ka).,o(l - 17o)
                                                 7o - r,/                              (3.125)
 where O = 2y/b, O:  = 2yr/b, and ?7o  = 2Yolb. Here, r7,  and rlo are the inboard and
outboard span locations of the control surface, which in this case is the elevator.
Note that the y coordinate is measured from the fuselage centerline and is positive
towards the right wing. Data presented in Fig. 3.48b can be used to estimate the
parameters (Ka),U and (Ka)rro.
Estimation of Ch8,e at subsonic speeds.   We havel
                          2cosAc/4 '
Ch8.e=cosAc/4cosAHL[(C,,.e)baj+U8(C,urXal A+2  A_, ,., .,)l+ACh8.e
            (3.126)
where AHL is the hingeline sweep and
        . (Ch8.e)bal
       (3.127)
(Ch8:e)bal = Ch8.,  C/_,.
CY8= Cl8
    ao
(3.128)
                     q
     ch8e=cc,C,. (Ch8.e)theory   (3.129)
The parameter CL8 can be obtained from the data given in Fig. 3.3 7. Data to eval-
uate the parameters (Ch8.e)btd/C;8.e, cL8.e/cch8.e)theory, (Cht.e)rr,eory, and ACh8.e
are presented in Figs. 3.49~3.51. The variable aol(ao)U eory can be obtained from
Fig. 3.13. The parameter K8 is defined as
                                     K8 - (K J)o,(l - ll:) - (K8X1o(l - Oo)
                                                 rlo - 0,                              (3.130)
The parameters (K8)", and (Ka)oo can be obtained using data given in Fig. 3.48b.
Note that the parameters c} and d correspond to values ofcf and c resolved normal
to the quarter chordline of the control surface.
3.3.I5 Stick-FreeNeutraIPoint
We have
Cm = CLXa + CmaC.*n + Cmf - CL.i Vl Tit                (3.131)
STATIC STABIUTY AND CONTROL
Fig.3.49    Effect ofnose balance on control hinge moment I
225
 The floating elevator affects the tail contribution as follows:
                                                   CL.t = a,(as + r8ef )                                           (3.132)
           =arcys(l-.C,C )     . (3.133)
 Here, we have ignored Cho as it is small. Substituting for CL.t in Eq. (3.131) and
differentiating with respect to CL, we get
  ~~ ),, = a+(~g)f _:.V,,7,(l_dd ) 1-,CC,,.,)  (3.134)
It can be easily shown that the relation between stick-free and stick-fixed stabilities
is given by
   :f:),.=(:g),x-CcC,,.(i-2) (3.135)
The stick-free neutral point is that location of the center of gravity when
(dCm/dCL)free = 0 and is given by
NL = xac        Ci
　
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