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b) Positive wing tilt, O  > oN < o
Fig.7.20 Schematicillustrationofinertia-yawingmomentinspin.
INERTIA COUPLING AND SPIN
661
prospin yawing moment, whereas fuselage masses produce antispin yawing mo-
ment  Ifly  >  Ix, then theinertia yawing couple will be antispin and,iflx  >  Iy,it
will be prospin.
    This simple concept oflumped masses helps us understand how important the
wing tilt is in the establishment of equilibrium spin modes. Generally, in a right
spin, the majority ofthe airplanes have a smallpositive wing tilt (Oy > 0, X  < O)
and a small outward sideslip (sideslip to port wing, P  < 0).
     The contribution to aerodynamic yawing moment mainly comes :ffom the fuse-
Iage and vertical tail. The cross-scctional shape of the fuselage has a strong influ-
ence on the fuselage contribution.18,19 In particular, the aft cross sections have a
stronger influence owing to their large moment arm with respect to the center of
 gravity. The cross sections with flat-bottom surfaces contribute to prospir/yawing
moment, whereas those with 7rounded-bottom surfaces generate antispin yawing
moments.
        The effectiveness of the vertical tail and the rudder in spin depend on the extent
of sluelding of these components due to the wake of the horizontal tail as shown
 in Fig. 7.21. A deflection of the elevator also has an effect on the shielding of the
 vertical tail and rudder surfaces. A downward defiection of the elevator increases
the shielded area, whereas an upward deflection alleviates the shielding effect.
    The nature and extent of shielding of the vertical tail and rudder surfaces also
depend on the relative placement of the horizontal tail with respect to the vertical
tail as shown in Fig. 7.22. In Fig. 7.22a the aft-body part A and the part B of
the body below the horizontal tail contribute to the yawing moment developed
by the fuselage. The unshielded part C of the rudder contr:ibutes to the rudder
effectiveness in generating yawing moments. We observe that the tail design of
Fig. 7.22a results in substantial shielding of the rudder. By moving the horizontal
tail further aft as in Fig. 7.22b, the shielding of the vertical tail and the rudder
      -
    /
-o
/
 ~  J
         ()
    o
)-t"
Fig. 7.21   SchematiciHustration ofshielding effect on vertical taiJ and rudder.
662            PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
a)
  /
-
 n
/
/
/
 /
-t
      V
  n
/
/
--
   .
,
Fig. 7.22    Effect of'vertical tail design on sluelding effect.
INERTIA COUPLING AND SPIN
663
can be reduced. Also, extending the rudder below the horizontal tail as shown in
Fig. 7.22c improves rudder effectiveness.
7.6  Spin Recovery
      The FAR Part 2320 requires that, for a normal recovery, a single-engine airplane
be capable of recovering from one turn spin or from a 3-s spin, whichever takes
longer, in no more than an additional turn using normal recovery controls.
  The standard method of spin reco'very as given in so-called "NACA Recov-
ery Procedure" for conventional single-engine light air)lanes21,22 is as follows:
move the rudder briskly against the spin, followed by forward stick about one-half
turn later while maintaining neutral ailerons. It has been found that this recovery
technique is effective in majority of the test cases NASA has evaluated over the
years on a variety of single-engine light gener    aviation airplanes.ll
   The role of ailerons as recovery controls depends on the mass and inertia dis-
tribution of the airplane. For an airplane that has most of its mass concentrated
into along fuselage and has relatively lighter wings with a short span (Iy]lx  >  1),
then the aileron applied in the direction of the spin (or direction of rolling) tends to
assist the recovery. The longer the fuselage and greater the weight concentrated in
nose and tail, the larger will be the numerical value of the ratio /y//x and greater
will be the effect of in-spin ailerons in aiding the recovery. For an airplane that
has heavy wings and a large wing span giving Iy/lx < 1, then out-spin ailerons
or ailerons applied against the direction of spin (or the direction of roll) is most
　
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