Page 58 - Introduction to Naval Architecture

FLOTATION AND STABILITY 45

A, then the increase in displaced volume for unit increase in draught at
that waterplane is 1 X A. The increase in displacement will be pgA. In
3 2
SI units forp = 1025 kg/m and g= 9.81 m/s increase in displacement
per metre increase in draught is:

1025 X 9.81 X 1 X A = 10055Anewtons,

In imperial units the value quoted was usually the added tons per inch
3
immersion, TPI. As it was assumed that 35 ft of sea water weighed 1 ton,
2
for A in ft :

The increase in displacement per unit increase in draught is useful in
approximate calculations when weights are added to a ship. Since its
value varies with draught it should be applied with care.
Hydrostatic curves are useful for working out the draughts and the
initial stability, as represented by GM, in various conditions of loading.
This is done for all normal working conditions of the ship and the
results supplied to the master.

Fully submerged bodies

A fully submerged body presents a special case. Firstly there is no
waterplane and therefore no metacentre. The forces of weight and
displacement will always act vertically through G and B respectively.
Stability then will be the same for inclination about any axis. It will
be positive if B is above G. Secondly a submarine or submersible is
an elastic body and will compress as the depth of submergence
increases. Since water is effectively incompressible, there will be a
reducing buoyancy force. Thus the body will experience a net
downward force that will cause it to sink further so that the body is
unstable in depth variation. In practice the decrease in buoyancy
must be compensated for by pumping water out from internal tanks
or by forces generated by the control surfaces, the hydroplanes. Care
is needed when first submerging to arrange that weight and buoyancy
are very nearly the same. If the submersible moves into water of a
different density there will again be an imbalance in forces due to the
changed buoyancy force. There is no 'automatic' compensation such
as a surface vessel experiences when the draught adjusts in response
to density changes.