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left when the aircraft sideslips to starboard and vice versa.
STATfC STABIUTY AND CONTROL
285
   The effective sideslip angle Pv of the vertical tail with rudder free to :float is
given by
Then,
pv N p + Cr + -C28rf
(3.325)
(Cn.V)free=ka,,[p+o- C
 .   U-T2gt}3]V217u  (3.326)
                         (Cnp.VXtee = ka,[(1+ ~p) - ,2g   ] V2?7v             (3.327)
 Using Eq. (3.317), we get
                      (Cnp.V)free =(Cnp.v)fix+C,p (g   )             (3.328)
and
                        (Cnp)free = (Cnp)W + (Cnp)B(W) + (Cnp.V)frree              (3.329)
For positive rudder-free directional stability, (Cnp)fn:e > O.
3.5.7 PedaIForces
    Suppose that the aircraft is required to maintain a given sideslip [3. Then, the
required rudder deflectrion is given by
            8r- (Cnp)rixP
           (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)

 :{
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
　
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