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3.5.4  Rudder-Fixed Directional Stability
    Ignoring the power effects, the rudder-fixed directional stability of the airplane
is given by the sum of the individual contributions as follows:
                                      (C i,a)rix = (Cnp)w + (Cnp)B(W) + (Cnp.v)fix                      (3.313)
   For static directional stability, (Cnp)nx must be positive over the desired angle
of attack and speed range. Ge;:erally, a value of C~~ between 0.0010 and 0.0025
would be considered satisfactory. However, an upper limit on the value of Cn~ may
arise from directional control requirements as discussed below.
3.5.5 DirectionaIControl
     The rudder is the primary directional control and its effectiveness is measured
by the parameter Cn8r, which is equal to the yawing-moment coefficient per unit
rudder deflection. The sign convention for the rudder defiection is as follows: the
rudder deflection is said to be positive if the rudder is deflected to the left side
and that towards the right side is negative as shown in Fig. 3.84. Thus, a positive
rudder deflection produces a positive side force and a negative yawing moment,
and a negative rudder deflection produces a negative side force and a positive
yawing moment. As a result, Cn~r iS usually negative.
Let
'02 = ~2f3
(3.314)
Nr = -kq 7u Syau(r28r + u)/y
(3.315)
280           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
ng 3.84   Sign convention for rudder deflection.
or, in coefficient form,
so that
where
Cnr = -k,7u V2av(T2br + cr)
Cn8r ~ -kr1u V2aur2
(3.316)
(3.317)
Cnr = qAl~b                        (3.318)
                       a cn                                                                      (3.319)
C"8r = a8r
We assume that r7y -  7r   :he method to evaluate r7r was presentedin Section 3.3.
    The rudder deflection to generate a sideslip t3 is given by
(cnp)rxP + Cn8r8r = 0
(3.320)
                                                                          (C tp)fixP
            (3.321)
           8r=- ,8
 From this relation, we observe that the higher thelevel of static directional stability,
the higher the rudder deflection to generate a given sideslip will be. Typically, a
value of q.iBr of --O.OOl is considered satisfactory
      The rudder effectiveness, Jike that of any other aerodynamic control surface,is
 nearly constant at low and moderate sideslip but falls off rapidly at high values of
 sideslip because of flow separation and stall.
STATIC STABILITY AND CONTROL
281
   Rudder requirements.   An airplane having an adequate level of static di-
rectional stability and symmetric power generally tends to maintain zero sideslip
condition and, as such, the defiection of the rudder may not be usually warranted.
However, under some critical conditions, it is possible that the static directional
sta'oility alone may not be sufficient to maintain zero sideslip, and the operation of
the rudder becomes absolutely essential. The rudder should be designed to provide
sufficient control authority under such circumstances as discussed in the following
sections.
   Crosswind takeoff and landing.   During the ground run, if the aircraft en-
　
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