Page 116 - Introduction to Naval Architecture

SEAKEEPING 103

Figure 6.2 Heaving

Heaving
If z is the downward displacement at any instant there will be a net
upward force on the ship, that is one tending to reduce z, which has a
magnitude of pgA^z and the resulting motion is defined by:

where A w is the waterplane area.
Again the motion is simple harmonic, this time of period:

T =

Added mass

In practice the motion of the ship disturbs the water around its hull and
the overall effect is to appear to increase the mass and inertia of the
1
ship . 'Added mass' values vary with the frequency of motion but, to a
first order, this variation can be ignored. Typically the effect for rolling
is to increase the radius of gyration by about 5 per cent. In heaving its
influence is greater and may amount to as much as an apparent
doubling of the mass of the ship.

Damping
2
The other factor affecting the motion in still water is the damping . In
a viscous fluid the ship experiences a resistance to motion and damping
represents the energy absorbed in overcoming this resistance. Damping
is also felt because of the energy that goes into the wave system created
by the ship. The simplest allowance for damping, taking rolling as a
typical motion, is to assume that the damping moment varies linearly