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        with a frequency content.The bandwidth ofthe human pilotis about 4rad/s (Ref. 3).
    Therefore, it is reasonable to expect that a human pilot can control any lateral-
        directional flight path variable using aileron/rudder mputs within this range of f. r3eV'
     quency. The autopilots ha've much higher bandwidths, up to 20-25 rad/s (Ref. 3).
             As an example of the lateral_directional frequency response, we have presented
     the frequency responses for sideslip, roll angle, roll rate, yaw angle, and yaw rate
          to aileron input in Figs. 6.26-6.30 for the general aviation airplane. Here, G p, G,r,,
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL          589
                      .                                              Dutch Roll
flg. 6.26
input.
co
o
 -
o
Frequency response of the general aviation airplane: sideslip to aileron
                                                                                                     Dutch Roll
q
b
'o
..-
o
~
Fig. 617    Frequency response of the general aviation airplane: roll angle to aileron
inpuL
m
o
.l\
o
PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
       Fraquency, racVs
Frequency response: roll rate
Fig. 6.28   Frequency response of the general aviation airplane: roll rate to aileron
inpuL
G4, G p, and Gr are thelateral-directional transfer functions ofthe general aviation
airplane given in Eqs. (6.258-6.262). These frequency-response (Bode magnitude
and phase) plots were drawn using MATLAB.I Similar frequency responses can be
obtained for rudder input using the transfer functions given in Eqs. (6.263-6.265).
    For the general aviation airplane, the Dutch-roll frequency is 2.3973 rad/s, and
the damping ratio is 0.2043. Thus, the Dutch roll is lightly damped. In view of
this, the magnitude responses of all the variables display a peak value around this
frequency.
   The n:agnitude crossover frequency for sideslip is around 0.09 rad/s, which
 means that the aileron inputs of frequencies of 0.09 rad/s and higher will have little
or no effect on the sideslip. Only aileron inputs of frequencies much lower than
 0.09 rad/s will have some effect on the sideslip. Around the Dutch-roll frequency,
the phase angle of IGpl is close to 90deg, which is a characteristic of lightly
damped systems.
    The magnitude crossover frequency for roll angle is about 4 rad/s. Hence, the
human pilot can have good roll control using the aileron inputs. We observe that
 the magnitude of the crossover frequency for yaw rate is quite low and is about
0.5 rad/s. Thus, it is not possible to have good yaw control using the aileron
inputs.
AIRPLANE RESPONSE AND CLOSED-LOOP CONTROL          591
    Frequency, rad/s
Frequency respanse: psi
Fig. 6.29    Frequency response of the general aviation airplane: yaw angle to aileron
input
6.4 FlyingQualities
   The subject of flying qualities attempts to quantify the ease or difficulty with
which a pilot can fly an airplane in a given category of flight. Besides the dynamic
behavior of the airplane, pilot opinion is also infiuenced by such factors like stick
force gradients, design and layout of the cockpit controls, visibility, weather con-
ditions, physical and emotional condition of the pilot, etc. In view of such widely
varying factors that can affect pilot opinion, it is usual to conduct several tests and
　
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