Page 50 - Introduction to Naval Architecture

FLOTATION AND STABILITY 37

Figure 4.7 Transverse metacentre

ordinate of the original waterline at the cross-section the emerged or
immersed section area is:

for small angles, and the total volume of each wedge is:

integrated along the length of the ship.
This volume is effectively moved from one side to the other and for
triangular sections the transverse movement will be 4j/3 giving a total
transverse shift of buoyancy of:

since <f) is constant along the length of the ship.
The expression within the integral sign is the second moment of
area, or the moment of inertia, of a waterplane about its centreline. It
may be denoted by /, whence the transverse movement of buoyancy
is:

so that BBi = I<p/V where V is the total volume of displacement.