However, it is possible for conditions to exist which

If you study figure 12-20, you will notice that a

do not permit B to move far enough in the direction in

RIGHTING or RESTORING MOMENT is present.

which the ship rolls to place the buoyant force outboard

This righting moment is caused by the two equal and

of the force of gravity. The moment produced will tend

opposite forces, each of W tons (displacement)

to upset the ship, rendering it unstable. Figure 12-21

magnitude, separated by a distance GZ, which

shows an unstable ship in which the relative positions of

constitutes the LEVER ARM OF MOMENT. Figure

B and G produce an UPSETTING MOMENT. In this

12-20 shows that the ship is stable because the center of

illustration it is obvious that the cause of the upsetting

buoyancy (B) has shifted far enough to position the

moment is the high position of G (center of gravity) and

buoyant force where it tends to restore the ship to an

the GEOMETRIC CENTER OF THE UNDERWATER

even keel or an upright position.

BODY (B--the center of buoyancy).

DIRECTION OF

RIGHTING MOMENT

FORCE OF BUOYANCY

ANGLE

DIRECTION OF

OF

UPSETTING

HEEL

MOMENT

ANGLE

OF

G

Z

HEEL

Z

G

B

B

FORCE OF GRAVITY

FORCE OF GRAVITY

DCf1220

DCf1221

A moment is the product of a force tending to

produce a rotation about an axis times its distance from

the axis. If two equal and opposite forces are separated

A ship's METACENTER (M) is the intersection of

by a distance, the moment will become a couple which

two successive lines of action of the force of buoyancy,

is measured by ONE of the forces times the distance

as the ship heels through a very small angle.

that separates them. The RIGHTING MOMENT of a

Figure 12-22 shows two lines of buoyant force. One of

these represents the ship on even keel, the other at a

ship is therefore the product of the force of buoyancy

small angle of heel. The point where they intersect is

times the distance GZ (fig. 12-20) that separates the

the initial position of the metacenter. When the angle of

forces of buoyancy and gravity. It may also be

heel is greater than the angle used to compute the

expressed as the force of gravity (weight of the ship)

metacenter, M moves off the centerline and the path of

times GZ. The distance GZ is known as a ship's

movement is a curve.

RIGHTING ARM. Putting this into mathematical

terms, you have the following:

M

Righting moment = W x GZ (expressed in

ANGLE OF HEEL

IS EXAGGERATED

foot-tons)

C

L

Where:

WATERLINE

UPRIGHT

W = displacement in tons

WATERLINE

B2

B1

INCLINED

TO A VERY

GZ = righting arm in feet

SMALL

ANGLE

For example, if a ship displaces 10,000 tons and

has a 2-foot righting arm at 40° inclination, the righting

BUOYANT FORCE

BUOYANT FORCE

INCLINED

UPRIGHT

moment is 10,000 tons times 2 feet, or 20,000

foot-tons. These 20,000 foot-tons represent the force,

DCf1222

which tends to return the ship to an upright position.

12-9

Integrated Publishing, Inc. |