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vertical tail itself. DatcomJ gives an approximate engineering method to evaluate
the vertical tail contribution for s}imple configurations. The interested reader may
refer to Datcomi for more information.
    However, to get a crude estimate for preliminary design purposes, Eq. (3.311)
may be used with the lift-curve slope au  of the venical tail evaluated at supersonic
speeds using the methods presented in Section 3.3.
3.5.3   Effect of Power
       For a propeller-driven aircraft, the effect of power on static directional stability
consists of two parts: 1) the direct effect due to forces developed by or acting on
the propulsion unit and 2) indirect effect caused by propeller slipstream passing
over the wing or tail surfaces.
    The direct effect includes thrust developed by the propulsion unit and the side
force (drag) acting on the propulsion unit because of sideslip. Because the resultant
thrust vector is usually contained in the plane of symmetry, the contribution of
the thrust to directional stability can be ignored. The situation, however, is different
if there is an engine failure, which we will discuss a little later. The effect of side
force depends on the location of the propulsion unit. This effect is destabilizing
for a propeller air)lane and stabilizing for a pusher aurl[,lane as shown Figs. 3.81
and 3.82. .  '

278           PERFORMANCE, STABILITY, DYNAMICS, AND COBITROL
Fig. 3.81     Schematic illustration of power effects: propeller airplane.
   The indirect effects arise mainly because of the slipstream effect on wing as
shownin Fig. 3.83.The sections ofthe wing coming under theinfluence ofpropeller
slipstream experience higher dynamic pressuresleading to higherlocallift and drag
forces. The asymmetry in lift gives a destabilizing effect in roll. The asymmetry
in drag as represented by AD produces a destabilizing yawing moment AN as
shown in Fig. 3.83.
    For a jet aircraft, the direct effects due to side forces on the intake are sirrular
to that of a propeller airplane. The indirect effects caused by the jet-induced flow
field affect the vertical tails in a manner similar to that shown for horizontal tails
in Fig. 3.28.
    In general, the evaluation of power effects is quite complex and configuration
dependent. For simplicity, we ignore the power effects. The interested reader may
refer to Datcoml  for additional information.
Fig. 3.82    Schematic illustration of power effects: pusher airplane.
STATIC STABILITY AND CONTROL
mg. 3.83    Schematic illustration of propeUer slipstream effects.
279
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
　
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