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causing a roll reversal. Therefore, the rudder should have sufficient control power
to prevent the development of adverse yaw during a tum.
      Asymmetric power.      On multiengined furcraft, either partial or total failure of
one or more engines grves rise to an asymmetric power situation that can generate
a significant yawing moment as schematically shown in Fig. 3.87. If this yawing
moment is not countered by the rudder, the aircraft will develop a sideslip and, in
 some cases, may go out ofcontrol because of aerodynamic roll-yaw coupling. The
rudder must be designed to have sufficient control"authority to maintain controlled
flight under such conditions.
    Spin recove,)r.   Generally, in spin, the airplane is operating at high angles
of attack with wings and horizontal tail surfaces more or less completely stalled.
Quite often, the rudder may be the only control that has some effectiveness under

282
PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
a) Zero rudder deflection
b) With rudder deflection
R
U
n
w
a
y
R
U
n
w
a
y
ng.3.8s   Schematic diagramofcrosswind takeoffflamLing
;/
  . .':
STATIC STABILITY AND CONTROL
r:
       \
        \
        \
                         
                         
          \V .d          
                         
                         
┏━━━┳━━━━━━━┓
┃      ┃        \     ┃
┃      ┃L             ┃
┃      ┣━━━━━━━┫
┃----  ┃              ┃
┃(,    ┃           I  ┃
┗━━━┻━━━━━━━┛
Fig.3.86   Adverse yaw during a coordinated turn.
283
these conditions. To break out of an established spin, the rudder must be capable of
producing sufficient yawing moment to slow the spin rate and initiate a successful
recovery. We will learn more about'spin recovery when we discuss the spinning
motion in Chapter 7.
3.5.6  Rudder-Fr€e Directional Stallu7ity
8r f
~g p ,8
T2 <Ti
Fig.3.87   Asymmetric power effects.
(3.322)
  In sideslipping motion, if the rudder is left free to float (pilot's foot off the
rudder pedal), it will assume a condition such that the net hinge moment is zero.
This position is called the floating angle of the rudder and is grven by
284           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
where
a) Cr,p > 0
b) CA6 < 0
Fig.3.88    Sign convention for rudderlunge-moment coefficient
Clp = aac~
C,,8r = aag-
(3.323)
(3.324)
The hinge-moment coefficients Chp and q,ar can be estimated using the methods
given in Section 3.3.14 using the variable p instead of cr and 8r instead of 8e.
     Recall that the elevator hinge moment was assumed positive if it rotated the
elevator trailing edge down or in a direction to increase the elevator deflection.
In a similar way, we assume rudder hinge moment to be positive if it rotates the
rudder such that rudder deflection increases,i.e., it makes the rudder deflect to the
left. With this understanding, we observe that a positive sideslip causes a positive
hinge moment so that Chp > 0. Similarly, a positive rudder deflection generates
a negative hinge moment so that Ch8r < O. These concepts are schematically
illustrated in F~g  3.88.
    With Chp > 0 and'ChSr < 0 for positive sideslip, we observe from Eq. (3.322)
that the floating angle of the rudder will be positive, i.e., the rudder floats to the
　
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