
Ch02-H6927.tex 10/7/2007 14: 22 Page 24
24 Flight Dynamics Principles
The time to complete one turn is given by
t =
2πR
V
0
=
2πV
0
g tan φ
(2.25)
therefore the rate of turn is given by
˙
ψ =
2π
t
=
g tan φ
V
0
(2.26)
Thus,
˙
ψ =0.068 rad/s. For the conditions applying to the turn,
˙
φ =
˙
θ =θ =0 and thus
equation (2.21) may now be used to find the values of r and q:
⎡
⎢
⎣
p
q
r
⎤
⎥
⎦
=
⎡
⎢
⎣
10 0
0 cos 60
◦
sin 60
◦
0 −sin 60
◦
cos 60
◦
⎤
⎥
⎦
⎡
⎢
⎣
0
0
˙
ψ
⎤
⎥
⎦
Therefore, p =0, q =0.059 rad/s and r =0.034 rad/s. Note that p, q and r are the
angular velocities that would be measured by rate gyros fixed in the aircraft with their
sensitive axes aligned with the ox, oy and oz aircraft axes respectively.
2.5