The Geometry of Ships

Section 1
Geometric Modeling for Marine Design
Geometry is the branch of mathematics dealing with the
properties, measurements, and relationships of points
and point sets in space. Geometric definition of shape
and size is an essential step in the manufacture or production
of any physical object. Ships and marine structures
are among the largest and most complex objects
produced by human enterprise. Their successful planning
and production depends intimately on geometric
descriptions of their many components, and the positional
relationships between components.
Traditionally, a “model” is a three-dimensional (3-D)
representation of an object, usually at a different scale
and a lesser level of detail than the actual object.
Producing a real product, especially one on the scale of
a ship, consumes huge quantities of materials, time, and
labor, which may be wasted if the product does not
function as required for its purpose. A physical scale
model of an object can serve an important role in planning
and evaluation; it may use negligible quantities
of materials, but still requires potentially large amounts
of skilled labor and time. Representations of ships in the
form of physical scale models have been in use since ancient
times. The 3-D form of a ship hull would be defined
by carving and refining a wood model of one side
of the hull, shaped by eye with the experience and intuitive
skills of the designer, and the “half-model” would
become the primary definition of the vessel’s shape.
Tank testing of scale ship models has been an important
design tool since Froude’s discovery of the relevant dynamic
scaling laws in 1868. Maritime museums contain
many examples of detailed ship models whose primary
purpose was evidently to work out at least the exterior
appearance and arrangements of the vessel in advance
of construction. One can easily imagine that these models
served a marketing function as well; showing a
prospective owner or operator a realistic model might
well allow them to relate to, understand, and embrace
the concept of a proposed vessel to a degree impossible
with two-dimensional (2-D) drawings.
From at least the 1700s, when the great Swedish naval
architect F. H. Chapman undertook systematic quantitative
studies of ship lines and their relationship to performance,
until the latter decades of the 20th century,
the principal geometric definition of a vessel was in the
form of 2-D scale drawings, prepared by draftsmen,
copied, and sent to the shop floor for production. The
lines drawing, representing the curved surfaces of the
hull by means of orthographic views of horizontal and
vertical plane sections, was a primary focus of the design
process, and the basis of most other drawings. An
intricate drafting procedure was required to address the
simultaneous requirements of (1) agreement and consistency
of the three orthogonal views, (2) “fairness” or
quality of the curves in all views, and (3) meeting the
design objectives of stability, capacity, performance,
seaworthiness, etc. The first step in construction was
lofting: expanding the lines drawing, usually to full size,
and refining its accuracy, to serve as a basis for fabrication
of actual components.
Geometric modeling is a term that came into use
around 1970 to embrace a set of activities applying
geometry to design and manufacturing, especially with
computer assistance. The fundamental concept of geometric
modeling is the creation and manipulation of a
computer-based representation or simulation of an existing
or hypothetical object, in place of the real object.
Mortenson (1995) identifies three important categories
of geometric modeling:
(1) Representation of an existing object
(2) Ab initio design: creation of a new object to meet
functional and/or aesthetic requirements
(3) Rendering: generating an image of the model for
visual interpretation.
Compared with physical model construction, one
profound advantage of geometric modeling is that it requires
no materials and no manufacturing processes;
therefore, it can take place relatively quickly and at
relatively small expense. Geometric modeling is essentially
full-scale, so does not have the accuracy limitations
of scale drawings and models. Already existing in
a computer environment, a geometric model can be
readily subjected to computational evaluation, analysis,
and testing. Changes and refinements can be made and
evaluated relatively easily and quickly in the fundamentally
mutable domain of computer memory. When 2-D
drawings are needed to communicate shape information
and other manufacturing instructions, these can be
extracted from the 3-D geometric model and drawn by
an automatic plotter. The precision and completeness
of a geometric model can be much higher than that of either
a physical scale model or a design on paper, and
this leads to opportunities for automated production
and assembly of the full-scale physical product. With
these advantages, geometric modeling has today assumed
a central role in the manufacture of ships and
offshore structures, and is also being widely adopted for
the production of boats, yachts, and small craft of essentially
all sizes and types.
1.1 Uses of Geometric Data. It is important to realize
that geometric information about a ship can be put to
many uses, which impose various requirements for precision,
completeness, and level of detail. In this section,
we briefly introduce the major applications of geometric
data. In later sections, more detail is given on most of
these topics.