6

At 70°, the corrected GZ = 0.5412

At 80°, the corrected GZ = minus 0.4392

5

(e)

(d)

(f)

It is not necessary to figure the corrected GZ at 90°,

(g)

(c)

4

since the value is already negative at 80°. When the

(h)

values from 10° through 80° are plotted on the grid and

3

(b)

joined with a smooth curve, the CORRECTED

A

(i)

stability curve (B) shown in figure 12-27 results. As

2

you can see, the corrected curve shows maximum

(a)

1

stability to be at 40°; it also shows that an upsetting

arm, rather than a righting arm, generally exists at

angles of heel in excess of 75°.

0

80 90

60

50

30

20

40

70

10

B

ANGLE OF HEEL IN DEGREES

DCf1227

When a tank or a compartment in a ship is partially

full of liquid that is free to move as the ship heels, the

surface of the liquid tends to remain level. The surface

of the free liquid is referred to as FREE SURFACE.

The tendency of the liquid to remain level as the ship

Suppose that the cross curves are made up on the

heels is referred to as FREE SURFACE EFFECT. The

basis of an assumed KG of 20 feet and that you

term *LOOSE WATER *is used to describe liquid that has

determine that the actual KG is 24 feet for the particular

a free surface; it is NOT used to describe water or other

condition of loading. This means that the true G is 4 feet

liquid that completely fills a tank or compartment and

higher than the assumed G and that the righting arm

thus has no free surface.

(GZ) at each angle of inclination will be SMALLER

than the righting arm shown in figure 12-27 (curve A)

for the same angle. To find the new value of GZ for each

Free surface in a ship causes a reduction in GM, due

angle of inclination, multiply the increase in KG (4 feet)

to a change in the center of gravity, and a consequent

by the sine of the angle of inclination, and SUBTRACT

reduction in stability. The free surface effect is separate

this product from the value of GZ shown on the cross

from and independent of any effect that may result

curves or on the uncorrected stability curve. In order to

merely from the addition of the weight of the liquid.

facilitate the correction of the stability curves, a table

When free surface exists, a free surface correction must

showing the necessary sines of the angles of inclination

be included in stability calculations. However, when a

is included on the cross curves form.

tank is completely filled so that there is no free surface,

Next, find the corrected values of GZ for the

the liquid in the tank may be treated as a solid; that is, the

various angles of heel shown on the stability curve (A)

only effect of the liquid on stability is the effect of its

in figure 12-27, and plot them on the same grid to make

weight at its particular location.

the corrected stability curve (B) shown in figure 12-27.

To understand the actions that occur because of

free surface effect, use a centerline compartment that is

At 10°, the uncorrected value of GZ is 1.4;

partially full of water, as shown in figure 12-28, as an

therefore, the corrected GZ at 10° is 1.4 minus

example.

(4 x 0.1736), or 0.7056.

At 20°, the uncorrected value of GZ is 2.8;

L4

therefore, the corrected GZ at 20° is 2.8 minus

L3

(4 x 0.3420), or 1.4320.

L2

L1

W1

Repeating this process at 30°, 40°, 50°, 60°, 70°,

W

L

W2

and 80°, the following values are obtained:

l4

W3

w

l

F

W4

w

At 30°, the corrected GZ = 2.2000

E

4

D

At 40°, the corrected GZ = 2.3288

At 50°, the corrected GZ = 2.2360

DCf1228

At 60°, the corrected GZ = 1.4360

12-15