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the flight velocity is constant. With the assumptions of constant flight velocity and
constant roll rate, Eqs. (7.1) and (7.4) reduce to two algebraic equations. These
equations can be used to derive control settings, which is not the main issue here.
Hence, we ignore these two equations from our analysis. With these assumptions,
we can express the remauung four equations as (see Section 4.3.4)
AFy = m Uo(Ap +r - Po Aa)
AFz - mUo(Aa + Po At3 - q)
AM =qIy +rPo(lx - /z)
AN = r Iz + poq(ly - Ix)
(7.7)
(7.8)
(7.9)
(7.10)
    Notice that the longitudinal and lateral-directional motions of the aircrafi are
now coupled because of the nonzero steady-state rolling velocity Po. However,
Eqs. (7.7-7.10) are still linear because we have retained the assumption of small
disturbances in all the disturbance variables. For a nonrolling aircraft (Po = 0),
the above equations reduce to two sets of uncoupled, linear equations, one set of
two equations for the longitudinal motion (short-period oscillation) and another
set of two equations for the Iateral-directional motion (Dutch-roll oscillation) as
we have studied in Chapter 6.
     Divide both sides.of Eqs. (7.7) and (7.8) by qS, those of Eq. (7.9) by qSc, and
those of Eq. (7.10) by qSb so that we can express them in the nondimensional
form as follows:
where
ACy = micAB +r - PoAa)
ACz - mi(Act + Po AP - q)
ACm = qIyl +rPo(lxi - /zl)
ACn = rl;i + Poq(l;i - cl)
(7.11)
(7.12)
(7.13)
(7.14)
(7.15)
(7.16)
(7.17)
(7.18)
(7.19)
Ix, = q~S
Iy, = q~S
Iz, = q~S
cl = qLSb
632           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
(7.20)
(7.21)
Here,it may be noted that some of the above nomenclature involving the moments
ofinertia terms differ from those used in Chapter 4.
Let
             ACy = Cyp Ap
               A'Cz - Cza Atr
ACm - Cmcr Ace + Cmq (2qU
(7.22)
(7.23)
(7.24)
                                     ACn = Cnp Ap + Cnr (23,)                          (7.25)
                           ty, we have ignored the acceleration derivatives like CyB, Cmdr, and
~c\Fgj (:Is'mg_":;r 5)tary derivatives like Cyp, Cyr, and C,,p. With these assumptions,
                     5) can be expressed as follows:
                              miPoAa-+   Cyp - midd )Ap - mir - 0                  (7.26)
                            (Cza - midd)A   - m,PoAB+miq - 0                 (7.27)
                      CmaAa+ (C, qCl _Iy,dd ) q - (IJcl - Izi) Por = 0           (7.28)
                                                                                                                                                                                    .
　
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