曝光台 注意防骗
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Note that the spin axis is also vertical.
In a steady-state spin, when viewed from the top,the airplane's center of gravity
appears to be moving in a circular path with a constant angular velocity. Let S2
denote this constant angular velociojr. Let us assume that the airplane is spuuung
to its right, i.e., it is rotating in a clockwise direction when viewed from the top.
Because of this angular velocity, the airplane will have a component of velocity
along the y-body axis. At the center of gravity, the velocity component along the
y-body axis is given by
V - -QR
(7.82)
where R is the radius ofthe helix or the spin radius.As said earlier, the spin radius is
usually about one-halfofthe wing span for steep spins and still smaller for flat spins.
Because in a steady-statc spin U, V , and W arc constants
U - V - W -0 (7.83)
In spin, the angle of attack is well above the stalling angle.At such angles of attack,
the resultant aerodynamic force is approximately normal to the wing chordline.
Note that the lift acts in the horizontal plane and drag is directed in the vertical
plane opposite to the gravity as shown in Fig. 7.12.
Spin
INERTIA COUPLING AND SPIN
Fig. 7.13 Angular velocity components in spin.
651
The angular velocity vector S2 can be resolved along the x- and z-body axes (see
Fig. 7.13) as
p = g? cos (y
r - S-2 sin a
If the wings are in the horizontal plane,
q-0
(7.84)
(7.85)
(7.86)
Because of the helical motion, the spinning airplane experiences a sideslip. For
example, in a positive spin (spin to the right), the sideslip is towards the lefi or port
wing, which is also the leading wing. In right spin, the right or starboard wing is
the trailing wing. As shown in Fig. 7.14, the sideslip angle is related to the helix
angle by the following relation:
where the helix angle y is given by
tr - -Y
(7,87)
y = t .' ('2UR) (7.88)
Now consider a more general case where the wings are tilted out of the horizontal
plane. Let Oy denote the wing tilt. We assume that Oy is positive when the right
wing is tilted down and the left wing is raised with respect to the horizontal plane
as shown in Fig. 7.15. The sideslip is now given by
f3 = Oy - y
(7.89)
652 PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
Velocity
thg. 7.14 Schematic iLlustration of sideslip in spin.
q-b
I /HelicaIPathofc.g
SpinAxis -- I
fc.g
Fig. 7.15 Schematicillustration of the effect of wing ffltin spin.
INERTIA COUPLING AND SPIN
~t.
I
SpinA,as -4
"
f
Fig. 7.16 Schematic illustration ofrotation about normal-to-wing chord.
653
We observe that a positive wing tilt Oy reduces the sideslip. When ey = y, the
sideslip is zero.
The sideslip plays animportant rolein the balance ofmoments. Usually, a certain
amount ofsideslip is always necessary to achieve a balance of all three components
of the moment Because the centrifugal force acting on all the components ofthe
airplane is directed radially outward and passes through the spin axis, it cannot
gena:ate any moment about the spin axis. Therefore, the resultant aerodynanuc
force must also pass through the spin axis as indicated in Fig. 7.12. Therefore,
the only way in which an airplane can have the right amount of wing tilt to adjust
the sideslip to the required value is through a rotation about the normal to the
chordline as shown in Fig. 7.16. Note that the normal to the wing chordline is
along the negative z-body axis. Hence, the airplane essentially rotates about its
z-body axis to gene:rate the required amount of wing tilt. Let X denote the angle
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