
Ch13-H6927.tex 30/6/2007 11: 47 Page 382
382 Flight Dynamics Principles
Equating equivalent terms in equation (13.219), expressions for the normalised
pitching moment derivatives, referred to aircraft wind axes, may be derived as
follows:
M
u
=
ρS
c
2I
y
∂(V
2
C
m
)
∂U
=
ρVS
c
2I
y
V
∂C
m
∂V
+2C
m
≡
ρVS
c
2I
y
M
∂C
m
∂M
+2C
m
=
ρVS
c
2I
y
(MC
m
M
+2C
m
) (13.220)
Again, remembering that for a wind axes reference U =U
e
+u ≡ V and Mach
number M =V /a. To define the derivative M
u
at the flight condition of interest, let the
perturbation become vanishingly small such that u →0, hence V →V
0
and M →M
0
.
Further, since the perturbation is a disturbance about trim and when the aircraft is in
trim the pitching ...