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           (3.330)
          Cn8r
The pedal forces to maintain this rudder deflection can be calculated as follows.
   Assuming that the rudder has a balancing tab similar to the elevator trim tab,
we have
                                Ch = qipp + Ch8r8r + Ch8,8r                      (3.331)
where Ch8,  = ac,,]a8,.  nien, r.rie ~dal force Fp is given by
                . Fp = G2HM                                      (3.332)
           N
                            = G2qrlvSrcr(Chpp + Ch8r8r + Ch8,8t)              (3.333)
Here, G2 is the gearing ratio between the pedals and the rudder, Sr iS the rudder area,
and Cr iS the rudder mean aerodynamic chord. Substituting for 8r from Eq. (3.330),
we obtain
            Fp = G2qr7uSr r [C,pp - Ct,8r(CCp)  p + Ctr/Sr8,]            (3.334)

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286            PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Differentiating with respect to p and rearranging, we obtain the pedal force gra-
dient,
                    aF  = G2qOuSr r [Chp - (g   ) (C p),x]           (3.335)
        '  ap
A pedal force gradient of 5 lb or 22.28 N/deg sidesldpe:g T~peFeX~lp50c-fiph (ap-
proximately 240 km/h) is a comfortable minimum valu                                                  ications
require that the pedal force vary linearly with sideslip p or the pedal force gradient
be constant up to a sides ip angle ofl:15 deg.
3.5.8  Rudder Lock
      The floating angle of the rudder, as given by Eq. (3.322), depends on the hinge-
moment parameters Chp and Ch8r. As said earlier. with Chp > 0 and ChBr < 0,
the rudder fioating angle 8rf will be positive for positive sideslip. Furthermore,
the fioating angle increases with sideslip. Schematic variations of the required
rudder deflection and floating angle with sideslip are shown in Fig. 3.89. At high
 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
　
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