The Geometry of Ships

THE GEOMETRY OF SHIPS 53
Section 12
Decks, Bulkheads, Superstructures, and Appendages
Although the hull of a ship accounts for its largest surfaces,
and often the most complex and demanding surfaces
in terms of shape requirements, other parts of the
ship also present many geometric challenges. Decks and
bulkheads are typically relatively simple surfaces (planar
in most cases), but need complex outlines in order to
meet the hull accurately. Superstructures are often complex
assemblages of many large and small surface elements,
with important aesthetic and functional requirements.
Hull appendages — for example, stern tube
bossings, bow bulbs, sonar domes, and sailing yacht
keels — must be shaped to perform critical hydrodynamic
functions, and require accurate, usually smooth,
connection to the hull surfaces.
12.1 Interior Decks and Bulkheads. Interior decks
and bulkheads are typically horizontal or vertical planes,
trimmed by intersection with the hull. The longitudinal
subdivision by watertight bulkheads has to meet hydrostatic
requirements for damaged flotation and stability.
The bulkheads and/or interior decks also form the principal
compartmentation of the ship’s interior, so their locations
interact with requirements for locating machinery
and cargo. It is highly beneficial in the early stages of
design for the bulkhead and deck positions to be parametrically
variable, to support optimal resolution of
these space and volume requirements.
12.2 Weather Deck. Weather deck surfaces are
occasionally planes — horizontal or with some fore-andaft
inclination — but are much more commonly given
camber (transverse shape) in order to encourage shedding
of water, to gain structural stiffness, and to gain interior
volume without increase of freeboard. In small
craft, it is common for the deck camber to be specified
as a circular arc having a constant ratio of crown to
breadth, typically 6 to 8 percent. The relationship between
radius R, crown h, and chord c (i.e., breadth for a
deck) for a circular arc is
2Rh h 2 c 2 /4 (135)
This shows that for constant h/c, R is directly proportional
to c:
R/c (c/h)/8 (h/c)/2 (136)
If the weather deck is required to be developable, this
imposes substantial constraints on the design. A general
cylinder swept by translation of a camber profile along a
longitudinal straight line is the simplest solution; however,
this tends to make a very flat deck forward, where
it becomes narrow. A shallow cone made from the deck
perimeter curves, with its apex inside the superstructure,
is often an advantageous construction.
Large commercial ships usually have planar deck surfaces,
the outboard portions slanted a few degrees, combined
with some width of flat deck near the centerline.
12.3 Superstructures. In merchant and military
ships, superstructures usually consist of flat surfaces,
making for relatively easy geometric constructions from
trimmed planes and flat quadrilateral or triangular
patches. Where the superstructure meets the deck, some
plane intersections with deck surfaces, or projections
onto the deck, will be required.
An interesting recent trend in military ship design is
the “stealth” concept for reducing detectability by radar.
Since its invention during World War II, radar has been an
extremely important military technology. The basic concept
of radar is to scan a region of interest with a focused
beam of pulsed high-frequency radio waves (wavelength
of a few mm or cm) and listen for reflected pulses
(echoes) at the same or nearby wavelengths. The orientation
of the antenna at the time reflection is received gives
the direction of the reflecting object, and the time delay
between emission and reception of the pulse provides the
range (distance). In addition, measuring the frequency
shift of the returned signal indicates the target’s velocity
component along the beam direction.
“Radar cross-section,” a quantity with units of area, is a
standard way to express the radar reflectivity of an object.
Essentially, it is the area of a perfect reflector oriented exactly
normal to the radar beam, that would return a signal
of the same strength as the object. Radar cross-section is
highly dependent on the exterior geometry of the object,
and on its orientation with respect to the radar beam.
One component of stealth technology is naturally the
development of materials and coatings that are effective
absorbers of electromagnetic radiation at radar frequencies.
Another important component is purely geometric:
the use, insofar as possible, of flat faces for the ship’s exterior
surface, angled so as to reflect radar away from
the transmitter’s direction (Fig. 39). Whereas a curved
surface presents a moderate cross-section over a range
of angular directions, a flat face produces a comparatively
very high cross-section, but only in one very specific
direction — the direction of the normal to the face.
The use of flat faces trades off very large cross-sections
in a few particular directions against near-total invisibility
from all other directions. Since the majority of radar
sources directed at a ship will be close to sea level, the
horizontal directions are most important; this consideration
promotes use of faces that are inclined inboard 10°
to 15° from vertical, allowing for moderate roll angles.
This inclination also avoids 90° concave corners, e.g., between
the superstructure and the deck, where double reflections
provide a strong return in any direction normal
to the line of intersection between the two planes.
(A concave corner where three mutually orthogonal
planes meet is particularly to be avoided; this makes the
well-known “corner reflector” configuration used, for
example, on navigational buoys. Triple reflection of a ray