The Geometry of Ships

THE GEOMETRY OF SHIPS 51
11.2 Bonjean Curves. Bonjean curves are a graphical
presentation of transverse section areas as a function of
draft. For a monohull hull form, with the transverse offset
expressed explicitly as y y(x, z), and with the base
plane at the keel (z 0), the data for Bonjean curves are
the values of
S (x, Z) 2 Z 0 y(x, z) dz (133)
For more general hull forms, S(x, Z) is simply the section
area at station x, up to the z Z waterplane. The
Bonjean curves result from plotting these values vs. Z
for a series of stations x, usually the same set of stations
used in the lines drawing. These are presented in two alternative
formats:
(a) plotted from a common vertical axis (Fig. 37)
(b) plotted from individual vertical axes, each corresponding
to the station x (Fig. 38).
In both cases, the Bonjean curves are superimposed
on a (usually stretched) profile view of the ship.
In the days of manual hydrostatic calculations, Bonjean
curves were a useful intermediate form of the displacement
calculation, streamlining the figuring of displacement
and LCB for an arbitrarily trimmed waterplane (or
variable water surface), which was required for launching
calculations, damaged stability, and longitudinal strength.
With the help of Bonjean curves, the displaced volume and
longitudinal moment of volume up to the arbitrary waterline
Z(x) can be figured by the single integrals:
V S[x, Z(x)] dx, M x S[x, Z(x)] x dx (134)
where the integrals are taken over the undamaged
lengths of the ship.
Today, with almost all advanced hydrostatic calculations
performed by computer, Bonjean curves have little
practical role (unless used internally by the program to
accelerate calculations). However, they remain a requirement
among the deliverables in many instances of
design contract language, so the naval architect must be
prepared to supply them.
Fig. 37
Bonjean curves plotted from a common vertical axis.