Fundamentals of Stability

8/12/2019 Fundamentals of Stability

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DISPLACEMENT

The weight of the volume of water that is displaced by the

underwater portion of the hull is equal to the weight of the ship.

This is known as a ship's displacement. The unit of measurement

for displacement is the Long Ton (1 LT = 2240 LBS).

GRAVITY

The force of gravity acts vertically downward through the ship's

center of gravity. The magnitude of the force depends on the

ship's total weight.

UNITS OF MEASURE

Force:A push or pull that tends to produce

motion or a change in motion. Units: tons,

pounds, Newtons, etc.

Parallel forces may be mathematically summed to

produce one "Net Force" considered to act

through one point.

Weight:The force of gravity acting on a body.

This force acts towards the center of the earth.

Units: tons, pounds, kilograms, etc.

Moment:The tendency of a force to produce a

rotation about a pivot point. This works like a

torque wrench acting on a bolt. Units: foot

tons, Newton meters, etc.

Volume:The number of cubic units in an object.

Units: Cubic feet (FT3), cubic inches, etc. The

volume of any compartment onboard a ship can be

found using the equation:

SpecificThe specific volume of a fluid is its volume per unit.

Volume:weight. Units: cubic feet per ton (FT3/LT). The specific

volume of liquids (NSTM 096 Table 096-1) used most frequently in

this unit are:


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Salt Water = 35 FT3/LT

Fresh Water = 36 FT3/LT

Diesel Fuel = 43 FT3/LT

CALCULATING THE WEIGHT OF FLOODING WATER

A compartment has the following dimensions:

Length = 20 FT Flooded with salt

Breadth = 20 FT water to a depth

Height = 8 FT of 6 FT

1. First, calculate the volume of water that has been added to

the compartment.

Volume = Length x Breadth x Depth of Flooding Water

= 20 FT x 20 FT x 6 FT

= 2400 FT3

2. Second, divide the volume of water by its specific volume.

STABILITY REFERENCE POINTS

M - Metacenter

G - Center of Gravity


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B - Center of Buoyancy

K - Keel

K - Keel:The base line reference point from which all other

reference point measurements are compared.

B - Center of Buoyancy:The

geometric center of the ship's

underwater hull body. It is

the point at which all the

forces of buoyancy may be

considered to act in a

vertically upward direction.

The Center of Buoyancy will move as the shape of the underwater

portion of the hull body changes. When the ship rolls to

starboard, "B" moves to starboard, and when the ship rolls toport, "B" moves to port.

When the ship's hull is made heavier, the drafts increase as the

ship sits deeper in the water. "B" will move up.

When the ship's hull is lightened, the drafts decrease as the ship

sits shallower in the water. "B" will move down.


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** The Center of Buoyancy moves

in the same direction as the

ships waterline. **

G - Center of Gravity:The

point at which all forces of

gravity acting on the ship

can be considered to act. "G"

is the center of mass of the

vessel. The position of "G"

is dependent upon the

distribution of weights

within the ship. As thedistribution of weights is

altered, the position of "G"

will react as follows:

M - Metacenter:As the ship

is inclined through small

angles of heel, the lines of

buoyant force intersect at a

point called the metacenter.

As the ship is inclined, thecenter of buoyancy moves in

an arc as it continues to

seek the geometric center of

the underwater hull body.

This arc describes the

metacentric radius.

1. "G"moves towards a weight addition

2. "G"moves away from a weight removal

3. "G"moves in the same direction as a weight shift


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As the ship continues to heel

in excess of 7-10 degrees,

the metacenter will move as

shown.

The position of the metacenter is a function of the position of

the center of buoyancy, thus a function of the displacement of the

ship. The position of "M" moves as follows:

As the Center of Buoyancy moves up, the Metacenter moves down.

As the Center of Buoyancy moves down, the Metacenter moves up.

LINEAR MEASUREMENTS IN STABILITY

KG- Height of the ships Center of Gravity the above Keel:Thismeasurement is found in section II(a) of the DC Book for several

conditions of loading. To find "KG" for loading conditions other

than those in the DC Book, calculations must be performed.


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KM- Height of Metacenter above the Keel:This measurement isfound by using the Draft Diagram and Functions of Form Curves

located in section II(a) of the DC Book.

GM- Metacentric Height:This measurement is calculated bysubtracting KG from KM (GM = KM - KG). GM is a measure of the

ship's initial stability.

BM- Metacentric Radius:The distance between the Center ofBuoyancy and the Metacenter. It is actually the radius of the

circle for the movements of "B" at small angles of heel.

THE STABILITY TRIANGLE

When a ship is inclined, the center of buoyancy shifts off

centerline while the center of gravity remains in the same

location. Since the forces of buoyancy and gravity are equal andact along parallel lines, but in opposite directions, a rotation

is developed. This is called a couple, two moments acting

simultaneously to produce rotation. This rotation returns the ship

to where the forces of buoyancy and gravity balance out.

The distance between the forces of buoyancy and gravity is knownas the ships righting arm. As shown above, the righting arm is a

perpendicular line drawn from the center of gravity to the point

of intersection on the force of buoyancy line.

For small angles of heel (0othrough 7oto 10o, metacenter doesnt

move), the value for the ships righting arm (GZ) may be found by

using trigonometry:


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Using the Sine function to solve for the righting arm:

With initial stability (0oto 7o-10o) the metacenter does not move,

and the Sine function is almost linear (a straight line.)

Therefore, the size of the ships Righting Arm, GZ, is directly

proportional to the size of the ships Metacentric Height, GM.

Thus, GM is a good measure of the ships initial stability.

RIGHTING MOMENT (RM)

The Righting Moment is the best measure of a ship's overall

stability. It describes the ship's true tendency to resist

inclination and return to equilibrium. The Righting Moment is

equal to the ships Righting Arm multiplied by the ships

displacement.

Example:

A destroyer displaces 6000 LT and has a righting arm of 2.4 FT

when inclined to 40 degrees. What is the ships Righting Moment?

RM = 2.4 FT x 6000 LT

RM = 14,400 FT-Tons (pronounced "foot tons")

STABILITY CONDITIONS


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curve is produced. This curve is a "snapshot" of the ship's

stability at that particular loading condition.

Much information can be obtained from this curve, including:

Range of Stability:This ship will generate Righting Arms wheninclined from 0oto approximately 74o. (This curve usually assumes

that the entire superstructure is watertight.)

Maximum Righting Arm:The largest separation between the forces of

buoyancy and gravity. This is where the ship exerts the most

energy to right itself.

Angle of Maximum Righting Arm: The angle of inclination where the

maximum Righting Arm occurs.

Danger Angle:One half the angle of the maximum Righting Arm.

SHIP'S HULL MARKINGS

Calculative Draft Marks Used for determining displacement and

other properties of the ship for stability and damage control.

These draft marks indicate the depth of the keel (baseline) below

the waterline.


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Two possible marking systems:

a. Roman numerals 3" in height (prior to 1972)

b. Arabic numerals 6" in height

Navigational Draft Marks

Ships operating drafts. These draft marks include the depth of

any projections below the keel of the ship.

a. Arabic numerals 6" in height

Limiting Draft Marks

"...installed on those ships whose limiting displacements are

known. As limiting displacements are determined, such markings

will be installed. If such drafts are exceeded, it means

jeopardizing the ship's ability to survive damage or heavyweather." (NSTM 079 - 14.26)

Limiting drafts are assigned to maintain reserve buoyancy

(freeboard) prior to damage, and to prevent excessive hull

stresses as a result of overloading.

Plimsoll Marks (Load lines)

Markings of minimum allowable freeboard for registered cargo-

carrying ships. Located amidships on both the port and starboardsides the ship.

Since the required minimum freeboard varies with water density and

severity of weather, different markings are used for:

- TF - Tropical Fresh Water

- F - Fresh Water

- T - Tropical Water (sea water)

- S - Standard Summer

- W - Winter

- WNA - Winter North Atlantic


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DRAFT DIAGRAM AND FUNCTIONS OF FORM

The Draft Diagram is a nomogram located in section II(a) of the

Damage Control Book. Each ship platform will have its own Draft

Diagram and it may vary between individual ships. It is used for

determining the ships displacement, as well as other properties

of the ship, including:

- Moment to Trim One Inch (MT1")

- Tons per Inch Immersion (TPI)

- Height of Metacenter (KM)

- Longitudinal Center of Flotation (LCF)

- Longitudinal Center of Buoyancy (LCB)

Instructions for use:

1. Draw a straight line (LINE #1) between the

ship's forward and aft draft readings (use

calculative drafts)

2. Where LINE #1 intersects the Displacement

Curve is the ship's displacement at those given

drafts.

3. Draw a horizontal line (LINE #2) through the

ship's displacement. (Hint: When the forward and

aft drafts are equal, the line is horizontal)

4. MT1", TPI, KM, and LCB are determined using LINE #2.

5. Draw a vertical line (LINE #3) through the

ship's displacement (There is no way to ensure

this line is vertical - just eyeball it.)

6. Where LINE #3 intersects the LCF Curve is theship's LCF for the given drafts.


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Example:

FFG-21 has the following drafts: Forward: 14'0"Aft: 15'6"

Find:1. Ship's Displacement: 3600 LT

2. KM: 22.37 FT

3. MT1": 758 FT-Ton per Inch

4. TPI: 32.2 LT per Inch

5. LCB: 2.1 FT Aft of Midships

6. LCF: 24 FT Aft of Midships


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Fundamentals of Stability