Page 53 - Introduction to Naval Architecture

40 FLOTATION AND STABILITY

minimum at T given by:

In the example KM is a minimum when the draught is 6.12m.

Vessel of constant triangular section

Consider a vessel of triangular cross section floating apex down, the
breadth at the top being B and the depth D. The breadth of the
waterline at draught T is given by:

In this case the curves of both KM and KB against draught are straight
lines starting from zero at zero draught.

Vessel of circular cross section
Consider a circular cylinder of radius R and centre of section O,
floating with its axis horizontal. For any waterline, above or below O,
and for any inclination, the buoyancy force always acts through O. That
is, KM is independent of draught and equal to R The vessel will be
stable or unstable depending upon whether KG is less than or greater
than R

Metacentric diagrams

The positions of B and M have been seen to depend only upon the
geometry of the ship and the draughts at which it is floating. They can
therefore be determined without knowledge of the loading of the ship
that causes it to float at those draughts. A metacmtric diagram, in which
KB and KM are plotted against draught, is a convenient way of defining
the positions of B and M for a range of waterplanes parallel to the
design or load waterplane.