Page 51 - Introduction to Naval Architecture

38 FLOTATION AND STABILITY

Referring to Figure 4.7 for the small angles being considered BBi =
BM<f> and BM= //?. Thus the height of the metacentre above the centre
of buoyancy is found by dividing the second moment of area of the
waterplane about its centreline by the volume of displacement. The
height of the centre of buoyancy above the keel, KB, is the height of the
centroid of the underwater volume above the keel, and hence the
height of the metacentre above the keel is:

KM. = KB + BM

The difference between KM and .KG gives the rnetacentric height,
GM.

Transverse metacentre for simple geometrical forms
Vessel of rectangular cross section
Consider the form in Figure 4.8 of breadth B and length L floating at
draught T. If the cross section is uniform throughout its length, the
volume of displacement = LBT.
The second moment of area of waterplane about the centreline =
LBV 12. Hence:

Height of centre of buoyancy above keel, KB = 7/2 and the height of
metacentre above the keel is:

Figure 4.8 Rectangular section vessel