The Geometry of Ships

4 THE PRINCIPLES OF NAVAL ARCHITECTURE SERIES
vessel will operate at varying loadings, so the plane of
flotation is at least somewhat variable, and LWL is
hardly a geometric constant. Further, if an appendage
(commonly a rudder) intersects the waterplane, it is
sometimes unclear whether it can fairly be included in
LWL; the consensus would seem to be to exclude such
an appendage, and base LWL on the “canoe hull,” but
that may be a difficult judgment if the appendage is
faired into the hull. Nevertheless, LWL is almost universally
represented amongst the particulars.
Design Waterline (DWL): a vessel such as a yacht which
has minimal variations in loading will have a planned
flotation condition, usually “half-load,” i.e., the mean
between empty and full tanks, stores, and provisions.
DWL alternatively sometimes represents a maximumload
condition.
Length Between Perpendiculars (LBP or LPP): a common
length measure for cargo and military ships,
which may have relatively large variations in loading.
This is length between two fixed longitudinal locations
designated as the forward perpendicular (FP)
and the aft perpendicular (AP). FP is conventionally
the forward face of the stem on the vessel’s summer
load line, the deepest waterline to which she can
legally be loaded. For cargo ships, AP is customarily
the centerline of the rudder stock. For military ships,
AP is customarily taken at the aft end of DWL, so
there is no distinction between LBP and DWL.
Beam: the maximum lateral extent of the molded hull
(excluding trim, guards, and strakes).
Draft: the maximum vertical extent of any part of the vessel
below waterline; therefore, the minimum depth of
water in which the vessel can float. Draft, of course, is
variable with loading, so the loading condition should
be specified in conjunction with draft; if not, the DWL
loading would be assumed.
Displacement: the entire mass of the vessel and contents
in some specified loading condition, presumably that
corresponding to the DWL and draft particulars.
Tonnage: measures of cargo capacity. See Section 13 for
discussion of tonnage measures.
Form coefficients, such as block and prismatic coefficient,
are often included in particulars. See Section
10 for definition and discussion of common form
coefficients.
Obviously, the particulars furnish no detail about the
actual shape of the vessel. However, they serve (much
better, in fact, than a more detailed description of shape)
to convey the gross characteristics of the vessel in a very
compact and understandable form.
1.2.2 Offsets. Offsets represent a ship hull by
means of a tabulation or sampling of points from the hull
surface (their coordinates with respect to certain reference
planes). Being a purely numerical form of shape
representation, offsets are readily stored on paper or in
computer files, and they are a relatively transparent
form, i.e., they are easily interpreted by anyone familiar
with the basics of cartesian analytic geometry. The completeness
with which the hull is represented depends, of
course, on how many points are sampled. A few hundred
to a thousand points would be typical, and would generally
be adequate for making hydrostatic calculations
within accuracy levels on the order of 1 percent. On the
other hand, offsets do not normally contain enough information
to build the boat, because they provide only 2-
D descriptions of particular transverse and longitudinal
sections, and there are some aspects of most hulls that
are difficult or impossible to describe in that form
(mainly information about how the hull ends at bow
and stern).
An offsets-level description of a hull can take two
forms: (1) the offset table, a document or drawing presenting
the numerical values, and (2) the offset file, a
computer-readable form.
The offset table and its role in the traditional fairing
and lofting process are described later in Section 8. It is
a tabulation of coordinates of points, usually on a regular
grid of station, waterline, and buttock planes. The offset
table has little relevance to most current construction
methods and is often now omitted from the process
of design.
An offset file represents the hull by points which are
located on transverse sections, but generally not on any
particular waterline or buttock planes. In sequence, the
points representing each station comprise a 2-D polyline
which is taken to be, for purposes of hydrostatic calculations,
an adequate approximation of the actual curved
section. Various hydrostatics program packages require
different formats for the offset data, but the essential file
contents tend to be very similar in each case.
1.2.3 Wireframe. Wireframes represent a ship hull
or other geometry by means of 2-D and 3-D polylines or
curves. For example, the lines drawing is a 2-D wireframe
showing curves along the surface boundaries,
and curves of intersection of the hull surface with specified
planes. The lines drawing can also be thought of as
a 3-D representation (three orthogonal projections of a
3-D wireframe). Such a wireframe can contain all the information
of an offsets table or file (as points in the
wireframe), but since it is not limited to transverse sections,
it can conveniently represent much more; for example,
the important curves that bound the hull surface
at bow and stern.
Of course, a wireframe is far from a complete surface
definition. It shows only a finite number (usually a very
small number) of the possible plane sections, and only a
sampling of points from those and the boundary curves.
To locate points on the surface that do not lie on any
wires requires further interpolation steps, which are
hard to define in such a way that they yield an unequivocal
answer for the surface location. Also, there are many
possibilities for the three independent 2-D views to be
inconsistent with each other, yielding conflicting or ambiguous
information even about the points they do presume
to locate. Despite these limitations, lines drawings