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 sideslip, the floating angle increases beyond the linear rate indicated by Eq. (3.322)
 because the center of pressure moves aft because of flow separation and stall. This
accentuates the floating tendency of the rudder. At one point, the floating angle
 may catch up with the required rudder deflection. This condition is usually known
 as rudder lock. Beyond this point, the floating angle may overshoot and opposite
pedal forces are required to operate the rudder. Such a situation is undesirable
 because it may take considerable effort for the pilot to break the rudder lock.
   Aerodynamic balancing to prevent rudder /ock.  As we have discussed
before, aerodynamic balancing helps to alter hinge-moment coefficients and the
 floating characteristics of a control surface. Therefore, with proper aerodynamic
E
STATIC STABILITY AND CONTROL
Fuselage
Rudder
Horizontal
Tail
287
balancing, the floating tendency of the rudder can be so adjusted that the rudder
lock phenomenon is avoided.
     Dorsal fin use to preventrudder Jock.    Anothermethod ofpreventing rudder
 lock is the use of a device called a dorsal fin. As we know, the stall angle of a given
lifting surface increases as the aspect ratio is reduced (see Chapter 1). Extending
the chord of inboard sections adds area without extending the span so that the
aspect ratio decreases. This form of extension is known as a dorsal fin as shown
in Fig. 3.90. Addition of a suitably sized dorsal fin helps to delay the vertical tail
stall to higher sideslip (Fig. 3.91a) and minimizes the possibility of rudder lock.
Also, the dorsal fin makes the pedal forces vary monotonically with sideslip as
indicated in Fig. 3.91b.
                                      Example 3.8
      For the tailless'aircraft of Example 3.2, determine the static directional stability
parameter Cnp at M -0.7 and altitude of 8500 m (c   = 0.3881) and at M = 2.0
and 18,000 m (cr = 0.094).
    Solution.   Let us calculate Cnp for M = 0.7 (subsonic) at 8500 m altitude.
    The aspect ratio of the given wing is 2.6893. Hence, the strip theory cannot be
used. We use the empirical relation in Eq. (3.271) to determine approximately the
wing contribution due to dihedral as follows:
                              (C,,p)r.w = -0.075 FCL/rad
where F is in radians. We have F = 3.5 deg so that
                       (C,p)r.w = -0.075 (53753) C~/rad
                              - -0.0046CLlrad
                              - -O.OOOICL/deg
      ' ' :':
:r,
;:-.:"i.
{
288           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
With Dorsal
a)
  Fp    :oucdkd "            
┏━━┳━━━━━━━━━━┓
┃    ┃                    ┃
┣━━╋━━━━━━━━━━┫
┃ O  ┃~--..-   -------- - ┃
┃    ┣━━━━━━━━━━┫
┃    ┃              -     ┃
┗━━┻━━━━━━━━━━┛
in VertiCal
I
,stall
ain Verticat
il
ith Dorsal
Fig.3.91    Effect ofdorsal f/n.
The wing contribution caused by sweep is given by the Eq. (3.299):
      (C,,ph.w  1     tanAc/4
                 CZ - = 47rA   ~A~A+4cosA/4~
        A A2 +6-a~/)
                     x  cosAc/4 - 2 -  8cosA~4+
　
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