liquid above GCB - weight of real liquid above GA = weight of imaginary liquid in cylin-
drical sector AOBG and in prismoid, AOBF. Volume of sector AOBG =
(17r/6)/(2Tf) = 1.833/?^2 ; volume of prismoid AOBF = l/2(Q.5R)(R + \M6K) =
0.711R^2 ; PV= wR^2 (l.833 + 0.717) = 2.55QwR^2.
STABILITYOFA VESSEL
The boat in Fig. 4 is initially floating upright in freshwater. The total weight of the boat
and cargo is 182 long tons (1813 IcN); the center of gravity lies on the longitudinal (i.e.,
the fore-and-aft) axis of the boat and 8.6 ft (262.13 cm) above the bottom. A wind causes
the boat to list through an angle of 6° while the cargo remains stationary relative to the
boat. Compute the righting or upsetting moment (a) without applying any set equation;
(b) by applying the equation for metacentric height.
Calculation Procedure:
- Compute the displacement volume and draft when the boat
is upright
The buoyant force passes through the center of gravity of the displaced liquid; this point
is termed the center of buoyancy. Figure 5 shows the cross section of a boat rotated
through an angle. The center of buoyancy for the upright position is B; B' is the center
of buoyancy for the position shown, and G is the center of gravity of the boat and cargo.
In the position indicated in Fig. 5, the weight W and buoyant force R constitute a cou-
ple that tends to restore the boat to its upright position when the disturbing force is re-
moved; their moment is therefore termed righting. When these forces constitute a couple
that increases the rotation, their moment is said to be upsetting. The wedges 614 C and
OA 'C are termed the wedge of emersion and wedge of immersion, respectively. Let h =
horizontal displacement of center of buoyancy caused by rotation; h' = horizontal dis-
tance between centroids of wedge of emersion and wedge of immersion; V = volume of
FIGURE 4