· GM, metacentric height, is the distance from G

Righting moments are measured in foot-tons. Since

the righting arm (GZ) is equal to GM times sin θ, for

to M; it is measured in feet. Z is the point at

small values of θ, you can say that the righting

which a line, through G, parallel to the waterline,

intersects the vertical line through B.

moment is equal to W times GM times sin θ. Because

· GZ, the distance from G to Z, is the ship's righting

of the relationship between righting arms and righting

moments, it is obvious that stability may be expressed

arm; it is measured in feet. For small angles of

either in terms of GZ or in righting moments.

heel, GZ may be expressed by the equation

However, you must be very careful not to confuse

· GZ = GM sin θ

righting arms with righting moments; they are NOT

· W is the weight (displacement) of the ship; it is

identical.

measured in long tons.

· K is a point at the bottom of the keel, at the

midship section, from which all vertical

When a series of values for GZ (the ship's righting

measurements are made.

arm) at successive angles of heel are plotted on a graph,

· KB is the vertical distance from K to the center of

the result is a STABILITY CURVE. The stability

buoyancy when the ship is upright. KB is

curve, as shown in figure 12-24, is called the CURVE

measured in feet.

OF STATIC STABILITY. The word *static *indicates

· KG is the vertical distance from K to the ship's

that it is not necessary for the ship to be in motion for

the curve to apply. If the ship is momentarily stopped at

center of gravity when the ship is upright. KG is

any angle during its roll, the value of GZ given by the

measured in feet.

curve will still apply.

· KM is the vertical distance from K to the

metacenter when the ship is upright. KM is

measured in feet.

The stability curve is calculated

The RIGHTING MOMENT of a ship is W times

graphically by design engineers for values

GZ, that is, the displacement times the righting arm.

indicated by angles of heel above 7°.

3

2

1

10

20

50

60

30

80

90

40

70

0

ANGLE OF HEEL, IN DEGREES

G

Z

Z

G

G

G

Z

G

WATERLINE

B

B

B

B

B

o

ANGLE OF HEEL = 20

o

o

ANGLE OF HEEL = 40

ANGLE OF HEEL = 0

ANGLE OF HEEL = 60o

o

ANGLE OF HEEL = 70

GZ = 1.33 FEET

GZ = 2.13 FEET

GZ = 0

GZ = 1 FOOT

GZ = 0

DCf1224

12-12