Page 286 - Introduction to Naval Architecture

MANOEUVRING 271

7
A simplified formula for open water is:

8
Other approximate approaches are to take squat as 10 per cent of
the draught or as 0.3 metres for every five knots of speed.

DYNAMIC STABILITY AND CONTROL OF SUBMARINES

Modern submarines can travel at high speed although sometimes their
function requires them to move very slowly. These two speed regimes
pose quite different situations as regards their dynamic stability and
control in the vertical plane. The submarine's static stability dominates
the low speed performance but has negligible influence at high speed.
For motions in the horizontal plane the submarine's problems are
similar to those of a surface ship except that the submarine, when deep,
experiences no free surface effects. At periscope depth the free surface
becomes important as it affects the forces and moments the submarine
experiences, but again mainly in the vertical plane.
A submarine must avoid hitting the sea bed or exceeding its safe
diving depth and, to remain covert, must not break surface. It has a
layer of water in which to manoeuvre which is only about two or three
ship lengths deep. At high speed there is little time to take corrective
action should anything go wrong. By convention submarines use the
term pitch angle for inclinations about a transverse horizontal axis (the
trim for surface ships) and the term trim is used to denote the state of
equilibrium when submerged. To trim a submarine it is brought to
neutral buoyancy with the centres of gravity and buoyancy in line.
The approach to the problem is like that used for the directional
stability of surface ships but bearing in mind that:

(1) The submarine is positively stable in pitch angle. So if it is
disturbed in pitch while at rest it will return to its original trim
angle.
(2) The submarine is unstable for depth changes due to the
compressibility of the hull.
(3) It is not possible to maintain a precise balance between weight
and buoyancy as fuel and stores are used up.

The last two considerations mean that the control surfaces must be able
to provide a vertical force to counter any out of balance force and
moment in the vertical plane. To control depth and pitch separately