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┃          ┣━━━━━━┫
┃          ┃/~-- -,  J- ┃
┃C::~      ┃            ┃
┣━━━━━╋━━━━━━┫
┃          ┃            ┃
┗━━━━━┻━━━━━━┛
             
  l,    L    
┏━━┳━━┓
┃/   ┃    ┃
┃    ┃C-J ┃
┃    ┣━━┫
┃    ┃    ┃
┗━━┻━━┛
Fig. 3.67    Aircraft orientation in horizontal plane.
259
velocity VR in Fig. 3.67c. Now, the sideslip is zero but the aircraft orientation in
space has changed. Notice that in Fig. 3.67c the aircraft is still moving with the
same velocity  V with respect to the Earth as before. If the disturbance vanishes,
the aircraft orientation will also be restored.
    The angles of sideslip and yaw (Fig. 3.68) are two important parameters in the
study of directional stability. Both of these angles are measured in a horizontal
plane. The angle of sideslip is an aerodynamic angle defined as the angle between
the velocity vector and the airplane's plane of symmetry as shown in Fig. 3.68b.
The angle of sideslip is usually denoted by p and is given by
sin p
   v
=V
(3.237)
where v is the sideslip velocity and V is the fiight velocity.
   The usual sign convention is to assume B positive if the airplane sideslips to
starboard (right wing leading into sideslip) as shown in Fig. 3.68b and p negative
if the airplane sideslips towards port side (left wing leading into sideslip as shown
in Fig. 3.68c).
     The angle of yaw, usually denoted by ~, is a kinematic angle and is a measure
of the change in the heading or orientation of the aircraft relative t,o the Earth. It is
the angle between the airplane's plane of symmetry and a reference plane fixed in
space as shown in Fig. 3.68b. Usually, this reference plane is assumed to coincide
with the airplane's plane of symmetry when the airplane is in steady level flight
before it encounters the disturbance. In principle, the angles of sideslip and yaw
are independent of each other. However, in the special case when the direction
~
    . -.: r.
 ;t:j
260           PERFORMANCE, STABILITY, DYNAMICS, AND CONTROL
n
h_Reference
r Line
b)
D
U
Fig.3.68   Definitions of angles ofyaw and sideslip.
-p
3.5.1   Criterion of DirectionaIStabilffl]
     An airplane is said to be directionally stable if it has an inherent capability to
realign itself into the resultant wind whenever disturbed from steady level flight.
Mathematically, this requirement for directional stability can be expressed as fol-
lows:
or, in coefficient form,
Here, N is the yawing moment and
Np >O
Cnp > 0
Cn -
 (3.23 8)
(3.239)
(3.240)
(3.241)
The concept of directional stabilit3r is schematically illustrated in Fig. 3.69.
STATIC STABILITY AND CONTROL
                +                  
                                   
┏━━━━━━━━┳━━━━━━━┓
┃                ┃              ┃
┣━━━━━━━━╋━━━━━━━┫
┃\               ┃~~~r/ X N~t'  ┃
┃                ┃              ┃
┃  /             ┃              ┃
┗━━━━━━━━┻━━━━━━━┛
Fig. 3.69    Concept of static directional stability.
261
(Cnp)w = (C,,p)r.w + (cn~h.W
　
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