Page 44 - Introduction to Naval Architecture

32 FLOTATION AND STABILITY

Since the buoyancy force is equal to the weight of the body, m -
pV
In other words the mass of the body is equal to the mass of the water
displaced by the body. This can be visualized in simple physical terms.
Consider the underwater portion of the floating body to be replaced by
a weightless membrane filled to the level of the free surface with water
of the same density as that in which the body is floating. As far as the
water is concerned the membrane need not exist, there is a state of
equilibrium and the forces on the skin must balance out.

Underwater volume
Once the ship form is defined the underwater volume can be
calculated by the rules discussed in Chapter 3. If the immersed areas of
a number of sections throughout the length of a ship are calculated a

sectional area curve can be drawn as in Figure 4.2. The underwater
volume is:

If immersed cross-sectional areas are calculated to a number of
waterlines parallel to the design waterline, then the volume up to each
can be determined and plotted against draught as in Figure 4.3. The
volume corresponding to any given draught T can be picked off,
provided the waterline at T is parallel to those used in deriving the
curve.
A more general method of finding the underwater volume, known as
the volume of displacement, is to make use of Bonjean curves. These are
curves of immersed cross-sectional areas plotted against draught for
each transverse section. They are usually drawn on the ship profile as in