Page 268 - Introduction to Naval Architecture

MANOEUVRING 255

DIRECTIONAL STABILITY AND CONTROL

It was seen in an earlier chapter that when a ship at rest in still water is
disturbed in the horizontal plane there are no hydrostatic forces to
return it to its original position or to increase the movement. The ship
is in neutral equilibrium. When a moving ship is disturbed in yaw it is
acted upon by hydrodynamic forces which may be stabilizing or
destabilizing. If stabilizing, the ship will take up a new steady line of
advance but unless some corrective action is applied, by using the
rudder for example, this will not be the original line of advance. The
vessel is said to be directionality stable in these conditions but clearly this
stability differs from that discussed in considering inclinations from the
vertical. A ship is said to be directionaily stable if, after being disturbed
in yaw, it takes up a new straight line path.
An arrow is an example of a directionaily very stable body. If gravity
is ignored the flight of an arrow is a straight line. If it is disturbed, say
by a gust of wind, causing it to take up an angle of attack relative to its
line of motion, the aerodynamic forces on its tail feathers will be much
greater than those on the shank. The disturbing force will push the
arrow sideways and the moment from the force on the tail will reduce
the angle of attack. The arrow will oscillate a little and then settle on a
new straight line path. The arrow, like a weathercock, has a high degree
of directional stability.
For a ship form it is not clear from the lines whether it will be stable
or not. By analogy with the arrow, good stability requires that the
resultant hydrodynamic moment following a disturbance should tend
to reduce yaw. The disturbing force is said to act at the hull's centre of
lateral resistance. For stability this must be aft of the centre of gravity and
it is to be expected that a cut away bow, a large skeg aft and trim by the
stern would all tend to improve stability. That is about as much as one
can deduce from the general shape at this stage. A degree of directional
stability is desirable otherwise excessive rudder movements will be
needed to maintain a straight course. Too much stability makes a ship
difficult to turn.
Ignoring any longitudinal components, a disturbing force on a ship
will lead to a small sideways velocity, 14 an angular velocity in yaw, r, and
linear and angular accelerations. In addition, in the general case, there
will be forces and moments due to the use of the rudder. For small
deviations second order terms in the equations of motion can be
ignored and the equations become:

(m - Y v)v = Y vv + (Y r - m)r + Y d