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the elevator, hence on the hinge-moment coefficient. Thus, a tab deflection affects
the stick force. The condition Cti - O corresponds to zero stjck force, and a tab
used to achieve this condition is called trim tab*
    Assuming that the hinge moment depends linearly on tail angle of attack, ele-
vator, and tab deflections,
                             Ch - Cho + ClurCts + Ch8,e8e + Ch8.t8r                 (3.139)
The floating angle of the elevator in the presence of the tab is given by
                                              Cho + Chaas + Ch8.,8t
                8ef =-_-   _-N_N_          (3.140)
          Ch8.e
      Usually,  Cho iS small and can be ignored. Then,
                                          Cmras + Ch8*,8t
                              N            (3*141)
         8ef=- Ch8e
From this relation, we note that the defiection of the tab modifies the floating
characteristics of the elevator. To see whether the deflection of the tab affects the
STATIC STABILITY AND CONTROL
Horizontal Tail        Elevator
       Scctlon A A
Fig.3 53   Schemabc diagram oftrim tab.
stick-free stability, consider the horizontal-tail term,
                        Cm.r = -CLt Vir7t
                              = a,(as + t8e[)Vi Or
                                              r(C~aG + Ch8.r8,
        -.ar t,-  C,. 8~]V,,7,
      .  dCm.t ar
                            d~ = -..(1 - ~) (1 -,g   ) V,,7,
229
(3.142)
(3.143)
(3.144)
(3.145)
Comparing this term with that in Eq. (3.134), we find that the deflection of the tab
does not alter the location of the stick-free neutral point- It only affects the hinge
moment as we have seen earlier.
    The tab defiection for zero hinge moment (Ch = O) iS given by
8, = _ Cja Cts + ChE.e8e
~8~
Note that Ch = 0 also corresponds to zero stick force,
(3.146)
230           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Substituting for cSe from Eq. (3.105), we obtrain
b,r = - Cl... (C,aCts + Ch&e [8e.o - (~),x CC.,])              (3.147)
Differentiating with respect to CL,
d8r
dC =-(CC,,.,)(.1.)(1-g )+(CC. )(C- )GC/ ),x
 =(g )(C.)(~g)-
      = (C/   )(C. )(-,8 - N/)
= - ( C/,,.,) (cl,) H:
(3.148)
(3.149)
(3.150)
(3.151)
Thus, we observe that d8r]dCL directly depends on the level of stick-free stabil-
ity or the stick-free margin. Usually, Cm8, Chu, CW.e, and Chai.r are all negative.
H; > O for a stick-free stable aircraft. Therefore, for a stick-free stable aircraft,
d8r]dCL > 0.
3.3.18   Determination of NeuttaJ Points in Flight
   The direct dependence of a stick-fixed neutral point on the elevator deflection
for pitch trim and that of stick-free neutral point on the trim-tab deflection enable
　
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