
Ch06-H6927.tex 20/6/2007 16: 34 Page 152
152 Flight Dynamics Principles
In the initial steady trim state the lift and weight are in balance thus
L
e
=
1
2
ρV
2
0
SC
L
= mg (6.24)
and in disturbed flight the lift is given by
L =
1
2
ρV
2
SC
L
(6.25)
As a consequence of assumption (iii) the lift coefficient C
L
also remains constant and
equations (6.23)–(6.25) may be combined to give
L = mg −ρghSC
L
(6.26)
Since simple undamped oscillatory motion is assumed, a consequence of assumption
(ii), the single degree of freedom equation of motion in height may be written:
m
¨
h = L cos θ − mg
∼
=
L − mg (6.27)
since, by definition, θ is a small angle. Substituting for lift L from equation