The Geometry of Ships

56 THE PRINCIPLES OF NAVAL ARCHITECTURE SERIES
these spaces is an important aspect of the design of any
ship, so that it meets its capacity objectives with respect
to both mass and volume of each type of cargo as well as
overall mass and center of gravity when fully loaded. The
subdivision also plays a major role during loading and unloading,
to ensure that freeboard and longitudinal
strength criteria are met throughout the operations.
In practice, a large majority of partitions lie on planes
parallel to the principal coordinate planes of the ship:
• decks on horizontal planes
• transverse bulkheads (often referred to simply as
“bulkheads”) on transverse planes
• longitudinal bulkheads on planes parallel to the
centerplane.
Most compartments are therefore bounded by orthogonal
planes on most of their sides; but most have at least
one face that is a portion of the curved hull surface. In
rare cases, curved surfaces are involved as interior partitions;
for example, in some liquefied natural gas (LNG)
carriers, the cargo is contained in spherical insulated
tanks.
Subdivision is fundamentally a solid modeling problem:
taking a solid region (the interior of the ship) and
subdividing it into smaller solids (the compartments). In
almost all cases, a compartment can be defined as the
Boolean intersection of the ship’s interior volume with a
simple rectangular solid aligned with the axes. (A different
form of subdivision is breaking a ship down into
units or modules for construction purposes.)
13.3 Compartment Volumes and Centroids. In the
analysis of capacity, the primary geometric quantities of
interest are the volumes and centroids of the individual
compartments. Values are most often required for the
compartment filled to capacity, but there may be a need
to evaluate them for partially filled compartments, up to
an arbitrary waterline level Z. These quantities are calculated
by any of the volume calculation methods discussed
in Section 9.4.
13.4 Dry Cargo Capacity. Dry cargo spaces have capacities
that depend somewhat on the nature of the
cargo. Such spaces are usually fitted with battens (ceiling)
on the inside of frames, and are also restricted somewhat
by the intrusion of other structural members; for example,
beams under the overhead deck, or stiffeners on a
bulkhead partition. Such encroachments have slight impact
on the volume available for a granular bulk cargo,
but interfere significantly with stowage of cargo packed
in crates, bags, bundles, and bales. Consequently, a distinction
is made between:
grain capacity: the molded volume of the compartment,
less a small deduction for volume of included
structure
bale capacity: the volume of the compartment inside the
batten line, and below the deck beams
Dry cargo capacities are often calculated in terms of
the stowage factors of various cargoes. Stowage factor is
an inverse effective density (cubic meters per ton), taking
into account packing fraction as well as the inherent
solid or liquid density of the material.
13.5 Tank Capacity and Contents. Tanks are compartments
used for carrying fluid consumables (fuel oil
and fresh water), fluid cargoes, and waste water. A
tank’s full capacity is basically its volume, less the volume
of any structure, piping, etc., interior to the tank.
A tank that has significant interior obstructions can be
assigned a “permeability,” usable volume / total volume
of the space. For any contents besides water, allowance
must be made for thermal expansion. For oil,
this is a deduction of typically 2 to 3 percent of the tank
volume. (Of course, water expands too, but the difference
is that an overflow of water is relatively
harmless.)
During loading and operation, it is necessary to know
the fullness of each tank. Various devices are used to
measure the location of the free surface in a tank. A pressure
gauge at the bottom of the tank is the simplest
method; this provides a direct indication of the height of
the free surface above the gauge. The hydrostatic pressure
in the tank is g(Z z g ), where is the density of the
tank contents, g is acceleration due to gravity, Z is the
free surface level, and z g is the vertical coordinate of the
pressure gauge. Other methods involve sonic sensing of
the free surface height, or lowering a float until it reaches
the surface. In some cases, there may not be an accessible
location that allows a vertical measurement for all
possible levels in the tank. In that case, a tube may be
provided inside the tank to guide a sounding chain. Tank
capacity tables or charts must be developed that relate
the volume and centroid of the tank contents to the measurement
method.
Ullage is a term for the empty space in a tank, above
the surface of the fluid, or the vertical extent of this
space. Ullage tables express the tank capacity as a function
of ullage rather than depth of fluid.
13.6 Tank Stability Effects. When a vessel changes
attitude (heel and trim), the liquid in a partially filled
tank shifts to a new equilibrium position, taking a new
shape (while maintaining its volume and mass).
Therefore, its center of gravity shifts in a complex way
depending on the shape of the tank. This shift of center
of gravity has important stability effects that go under
the name of free surface effects. For large attitude
changes, calculation of free surface effects requires
treating the complete tank as a solid at a specified attitude,
and solving for the free surface height that makes
the solid volume below the free surface equal to the current
volume contents of the tank.
For small attitude changes, there is a useful linearized
approximation similar to initial stability (equation 106).
Free surface effects are properly accounted for by treating
the liquid mass as if its vertical center is at a metacenter
located above the center of gravity of the liquid at
a distance (metacentric radius) I/V, where V is the volume
of liquid and I is the moment of inertia of the free