The INITIAL position of the metacenter is most

The ship's METACENTRIC HEIGHT (GM) is not

useful in the study of stability, because it provides a

only a measure of the ship's RIGHTING ARM (GZ)

reference point when the ship is upright and most

but is also an indication of whether the ship is stable or

stable. In our discussion we will refer to initial position

unstable. If M is above G, the metacentric height is

of M. The distance from the center of buoyancy (B) to

positive, the moments which develop when the ship is

the metacenter (M) when the ship is on even keel is the

inclined are RIGHTING MOMENTS, and the ship is

METACENTRIC RADIUS.

stable, as shown in view A of figure 12-23. But if M is

below G, the metacentric height is negative, the

moments that develop are UPSETTING MOMENTS,

and the ship is unstable, as shown in view B of

The distance from the center of gravity (G) to the

figure 12-23.

metacenter is known as the ship's METACENTRIC

HEIGHT (GM). Figure 12-23, view A, shows a ship

heeled through a small angle (the angle is exaggerated

in the drawing), establishing a metacenter at M. The

If the metacentric height (GM) of a ship is large,

ship's righting arm is GZ, which is one side of the

the righting arms that develop, at small angles of heel,

triangle GZM. In this triangle GZM, the angle of heel is

will be large. Such a ship is "stiff" and will resist roll.

at M. The side GM is perpendicular to the waterline at

However, if the metacentric height of a ship is small,

even keel, and ZM is perpendicular to the waterline

the righting arms that develop will be small. Such a

when the ship is inclined.

ship is tender and will roll slowly.

M

In ships, large GM and large righting arms are

desirable for resistance to damage. However, a

M

ANGLE

OF

smaller GM is sometimes desirable for a slow, easy

HEEL

ANGLE OF HEEL

roll that allows for more accurate gunfire; therefore,

Z

G

the GM value for a naval ship is the result of

compromise.

Z

G

B

C

L

The ship designer uses calculations to determine

the vertical position of the center of gravity. From

available plans and data, the various items that go to

A

make up the ship and its load are tabulated. The ship

can be considered as consisting of the various parts of

C

L

the structure, machinery, and equipment. The load is

comprised of fuel, oil, water, ammunition, and sundry

stores aboard.

G

Z

Although the position of the center of gravity as

estimated by calculation is sufficient for design

M

purposes, an accurate determination is required to

B

establish the overall stability of the ship when it is

operating. Therefore, an inclining experiment is

performed to obtain accurately the vertical height of

B

the center of gravity above the keel (KG) when the ship

DCf1223

is completed. An inclining experiment consists of

moving one or more large weights across the ship and

measuring the angle of list produced. This angle of list

It is evident that for any given angle of heel, there

usually does not exceed 2°. The ship should be in the

will be a definite relationship between GM and GZ

best possible condition for the inclining. The naval

because GZ = GM sin θ. Thus GM acts as a measure of

shipyard or building yard at which the inclining

GZ, the righting arm.

experiment is to be performed issues a memorandum to

12-10