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AFy = m(AV + r Uo) (4.381)
AFz = m(A W - qUo) (4,382)
AL = plr - rlrz
AM = q Iy
AN = r Iz - p Ixz
(4.383)
(4.384)
(4.385)
EQUATIONS OF MOTION AND ESTIMATION OF STABILITY DERIVATIVES 375
Define
AU
u= U
AV
v : --
Uo
AW
w - - (4.386)
Uo
AFx AFy AFz
ACx= pUS' ACy= US ACz=2pUS (4.387)
ACi=TAL AM AN
2~pUo2S7 ACrrt=~_pU2S ACn:- JSb (4.388)
: = ;-p U2S
so that
AW
Act ~ ~
Uo -w
Ap ~ AUV =v
Then, Eqs. (4.380-4.385) take the following form:
mUo .
ACx - ~-p U2Su
Z\Cy = pUU ScAB + r)
ACz= UUS(Ad-_q)
AC,= p+Sb(PIx -r Ixz)
l),
ACm= pU S q
AC" = pU~Sb(r Iz - plxz)
(4.389)
(4.390)
(4.391)
(4.392)
(4.393)
(4.394)
(4.395)
(4.396)
(4.397)
(4.398)
W
tana ~ Aa - -
Uo
sinp ~ Ap = jt
376 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
4.3.5 Estimation of Aerodynamic Forces and Moments
Our next task is to estimate the aerodynamic coefficients ACx, ACz, ACm,
A/, AM, and AN in the disturbed motion. For this purpose, we use Bryan's
method,i which, as said- in section 4.1, is based on two principal assumptions:
1) the instantaneous aerodynamic forces and moments depend on the instaneous
values of the motion variables and 2) the aerodynamic forces and moments varjr
linearly with motion variables. Furthermore, we introduce another important as-
sumption that the longitudinal aerodynamic forces and moment (Fx,'$~ and M)
are infiuenced only by the longitudinal variables u, a, and q. In other words, we
assume that the lateral- directional variables p, p, and r do not infiuence the lon-
gitudinal aerodynamic forces Fx and Fz and the pitching moment M. Similarly,
we assume that the side force Fy, the rolling moment L, and the yawing mo-
ment N depend only on the lateral-directional variables p, p, and r and are not
influenced by the longitudinal variables u, a, and q. In other words, we assume
that there is no aerodynamic coupling between longitudinal and lateral-directional
variables, forces, and moments. These assumptions are usually valid for small
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