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d6e
dCL
o
+
d6t
dCL
231
┏━━━━━━━━━━━┓
┃Xcgl lcg2 )icg3 No ┃
┃J~rapo;"t:,-- Icc ┃
┣━━━━━━━━━━━┫
┃ ┃
┗━━━━━━━━━━━┛
E
┏━┳━━━━━━━━┓
┃xcgi xcg2/xcg3'ati ┃
┣━┻━━━━━━━━┫
┃ ┃
┗━━━━━━━━━━┛
Fig. 3 54 Deternunation of neutral points in flighL
Let the stick force Fs be given by
Fs - -Gi Mh
= -Gi Chq,Se Ce
(3.152)
(3.153)
where Gi is the constant ofproportionality between the elevator hinge moment and
the stick force or the gearing ratio, Mh is the hinge moment, Se iS the elevator area,
and Ce iS the mean aerodynamic chord of the elevator. The units of Gi are N/Nm or
rad/m. The hinge-moment coefficient Ch in the presence of a trim tab is given by
Ch = Cho + ChaCLs + Ch8.e8e + Ch8.18r (3.154)
The negative sign is chosen in Eq. (3.152) so that, for a stable aircraft, the push
force has a positive sign and the pull force has a negative sign. For a stable aircraft,
the pilot usually applies a pull force to deflect the elevator upward (trailing edge
up). Note that, according to our sign convention, downward elevator deflection is
positive and upward defiection is negative. With elevator deflected upwards, the
232 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Pull Force
a)
~v Ele~ratorRotates
Down
Elcvzrtor Rotates
Up
b)
Fig.3.55 Schematic diagram ofstick-elevatorlinkage.
hinge moment is usually positive and Eq. (3.154) gives a negative (pull) force as
desired.
Substituting for 8e from Eq. (3.105), we have
Ch -. Cho + ChaCts + Ch8.e 8.o - (dc,)r,xq
-.., l+Ch8r8r (3.155)
where
ces - Ctvr, - /rn +it - 6 (3.156)
Let
. Ki - -.Gi,SeCer7t (3.157)
and
K2 = Cho + Cha(aw.oL - iw + /r) + Ch8.e8eo (3.158)
Then,
Fs -,pV2K, [K2 + -. (1- : ) - CC.C (,:,),x + Ch8r8;]
(3.159)
] . Chi.el
=~pVl-K,[K2- '.,c GC~ ).e+Ch8.t8,] (3.160)
, 2- Cm, ree
J
. (3.161)
= ~p V2KI(K7.+ ChS.r/Sr) - K,CC., g GC~ ),,_
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