Damage Control TrainingStability and Buoyancy Lessons

LESSON TOPIC: 4.1 TITLE: PRINCIPLES OF STABILITY

Contact periods allotted this LESSON TOPIC:

Classroom: 2.5 Test: 0.0

Trainer: 0.5 Total: 3.0

MEDIA: Classroom lecture with visual media, FFG-7 StabilityTrainer

TERMINAL OBJECTIVES:

6.0 EVALUATE shipboard stability by analyzing weight and momentconsiderations. (JTI 3.2.1, 6.0, 6.1, 6.2)

ENABLING OBJECTIVES:

6.1 DESCRIBE the reference points, forces, and linear measurementsused in stability calculations.

6.2 DESCRIBE the movement of stability reference points as a functionof changes in displacement and inclination.

6.3 DIFFERENTIATE between indicators of initial stability andmeasures of overall stability as a function of ships displacement.

6.4 IDENTIFY and DESCRIBE the uses of various types of external hullmarkings.

6.5 Given a draft diagram/functions of form and a set of draftreadings, CALCULATE displacement (WF), tons per inch immersion (TPI),and moment to trim one inch (MT1").

6.6 Given cross curves of stability and the ship's displacement,CONSTRUCT an uncorrected, statical stability curve.

FUNDAMENTALS OF STABILITYStability is the tendency of a vessel to rotate one way or the other whenforcibly inclined. Stability can be broken down into several categories, eachof which are alternatively emphasized in designing and operating Navy andCoast Guard ships.

STABILITY

INITIAL STABILITY - The stability of a ship in the range from 0 to7/10 of inclination.

OVERALL STABILITY - A general measure of a ship's ability to resistcapsizing in a given condition of loading.

DYNAMIC STABILITY - The work done in heeling a ship to a given angleof heel.

THE LAWS OF BUOYANCY1. Floating objects possess the property of buoyancy.

2. A floating body displaces a volume of water equal inweight to the weight of the body.

3. A body immersed (or floating) in water will be buoyed upby a force equal to the weight of the water displaced.

EXAMPLE OF GRAVITY -VS- BUOYANCY

1 ton of steel 1 ton of steel

If the cube of steel is placed in water it sinks. There is not enoughdisplaced volume for the forces of buoyancy to act upon. If the ships hullis placed in the water it will float. The larger volume of the ship's hullallows the forces of buoyancy to support the hull's weight.

The ship's hull will sink to a draft where the forces of buoyancy and theforces of gravity are equal.

DISPLACEMENT

The weight of the volume of water that is displaced by the underwater portionof the hull is equal to the weight of the ship. This is known as a ship'sdisplacement. The unit of measurement for displacement is the Long Ton (1 LT= 2240 LBS).

GRAVITYThe force of gravity acts vertically downward through the ship's center ofgravity. The magnitude of the force depends on the ship's total weight.

UNITS OF MEASUREForce: A push or pull that tends to produce motion or achange 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 forceacts towards the center of the earth. Units: tons, pounds,kilograms, etc.

Moment: The tendency of a force to produce a rotation about apivot point. This works like a torque wrench acting on abolt. Units: foot tons, Newton meters, etc.

Volume: The number of cubic units in an object. Units: Cubicfeet (FT3), cubic inches, etc. The volume of any compartmentonboard a ship can be found using the equation:

Specific The specific volume of a fluid is its volume per unitVolume: weight. Units: cubic feet per ton (FT3/LT). Thespecific volume of liquids (NSTM 096 Table 096-1) used mostfrequently in this unit are:

Salt Water = 35 FT3/LT

Fresh Water = 36 FT3/LT

Diesel Fuel = 43 FT3/LT

CALCULATING THE WEIGHT OF FLOODING WATERA 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 thecompartment.

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

B - Center of Buoyancy

K - Keel

K - Keel: The base line reference point from which all otherreference point measurements are compared.

B - Center of Buoyancy: Thegeometric center of the ship'sunderwater hull body. It is thepoint at which all the forces ofbuoyancy may be considered toact in a vertically upwarddirection.

The Center of Buoyancy will move as the shape of the underwater portion ofthe hull body changes. When the ship rolls to starboard, "B" moves tostarboard, and when the ship rolls to port, "B" moves to port.

When the ship's hull is made heavier, the drafts increase as the ship sitsdeeper in the water. "B" will move up.

When the ship's hull is lightened, the drafts decrease as the ship sitsshallower in the water. "B" will move down.

** The Center of Buoyancy movesin the same direction as theships waterline. **

G - Center of Gravity: Thepoint at which all forces ofgravity acting on the ship canbe considered to act. "G" isthe center of mass of thevessel. The position of "G" isdependent upon thedistribution of weights withinthe ship. As the distributionof weights is altered, theposition of "G" will react asfollows:

1. "G" moves towards a weight addition2. "G" moves away from a weight removal3. "G" moves in the same direction as a weight shift

M - Metacenter: As the ship isinclined through small angles

of heel, the lines of buoyantforce intersect at a pointcalled the metacenter.

As the ship is inclined, thecenter of buoyancy moves in anarc as it continues to seekthe geometric center of theunderwater hull body. This arcdescribes the metacentricradius.

As the ship continues to heelin excess of 7-10 degrees, themetacenter will move as shown.

The position of the metacenter is a function of the position of the center ofbuoyancy, thus a function of the displacement of the ship. The position of"M" moves as follows:

As the Center of Buoyancy moves up, theMetacenter moves down.As the Center of Buoyancy moves down, theMetacenter 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 severalconditions of loading. To find "KG" for loading conditions other thanthose in the DC Book, calculations must be performed.

KM - Height of Metacenter above the Keel: This measurement is foundby using the Draft Diagram and Functions of Form Curves located insection 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'sinitial stability.

BM - Metacentric Radius: The distance between the Center of Buoyancyand the Metacenter. It is actually the radius of the circle for themovements of "B" at small angles of heel.

THE STABILITY TRIANGLEWhen a ship is inclined, the center of buoyancy shifts off centerline whilethe center of gravity remains in the same location. Since the forces ofbuoyancy and gravity are equal and act along parallel lines, but in oppositedirections, a rotation is developed. This is called a couple, two momentsacting simultaneously to produce rotation. This rotation returns the ship towhere the forces of buoyancy and gravity balance out.

The distance between the forces of buoyancy and gravity is known as theships righting arm. As shown above, the righting arm is a perpendicular linedrawn from the center of gravity to the point of intersection on the force ofbuoyancy line.

For small angles of heel (0o through 7o to 10o, metacenter doesnt move), thevalue for the ships righting arm (GZ) may be found by using trigonometry:

Using the Sine function to solve for the righting arm:

With initial stability (0o to 7o-10o) the metacenter does not move, and theSine function is almost linear (a straight line.) Therefore, the size of theships Righting Arm, GZ, is directly proportional to the size of the shipsMetacentric Height, GM. Thus, GM is a good measure of the ships initialstability.

RIGHTING MOMENT (RM)The Righting Moment is the best measure of a ship's overall stability. Itdescribes the ship's true tendency to resist inclination and return toequilibrium. The Righting Moment is equal to the ships Righting Armmultiplied by the ships displacement.

Example:A destroyer displaces 6000 LT and has a righting arm of 2.4 FT when inclinedto 40 degrees. What is the ships Righting Moment?

RM = 2.4 FT x 6000 LT

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

STABILITY CONDITIONSThe positions of Gravity and the Metacenter will indicate the initialstability of a ship. Following damage, the ship will assume one of thefollowing three stability conditions:

POSITIVE STABILITYThe metacenter is located abovethe ships center of gravity. Asthe ship is inclined, RightingArms are created which tend toreturn the ship to its original,vertical position.

NEUTRAL STABILITYThe metacenter and the shipscenter of gravity are in the samelocation. As the ship is inclined,no Righting Arms are created.(until the metacenter starts tomove after the ship is inclinedpast 7o-10o)

NEGATIVE STABILITYThe ships center of gravity islocated above the metacenter. Asthe ship is inclined, negativeRighting Arms (called upsettingarms) are created which tend tocapsize the ship.

STATICAL STABILITY CURVE (RIGHTING ARM CURVE)When a ship is inclined through all angles of heel, and the righting arm foreach angle is measured, the statical stability curve is produced. This curveis 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 when inclined from0o to approximately 74o. (This curve usually assumes that the entiresuperstructure is watertight.)

Maximum Righting Arm: The largest separation between the forces of buoyancyand gravity. This is where the ship exerts the most energy to right itself.

Angle of Maximum Righting Arm: The angle of inclination where the maximumRighting Arm occurs.

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

SHIP'S HULL MARKINGS

Calculative Draft MarksUsed for determining displacement and other properties of the ship forstability and damage control. These draft marks indicate the depth of thekeel (baseline) below the waterline.

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 anyprojections below the keel of the ship.

a. Arabic numerals 6" in height

Limiting Draft Marks"...installed on those ships whose limiting displacements are known. Aslimiting displacements are determined, such markings will be installed. Ifsuch drafts are exceeded, it means jeopardizing the ship's ability to survivedamage or heavy weather." (NSTM 079 - 14.26)

Limiting drafts are assigned to maintain reserve buoyancy (freeboard) priorto 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 starboard sides the ship.

Since the required minimum freeboard varies with water density and severityof 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

DRAFT DIAGRAM AND FUNCTIONS OF FORMThe Draft Diagram is a nomogram located in section II(a) of the DamageControl Book. Each ship platform will have its own Draft Diagram and it mayvary between individual ships. It is used for determining the shipsdisplacement, 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 forwardand aft draft readings (use calculative drafts)

2. Where LINE #1 intersects the Displacement Curve is theship's displacement at those given drafts.

3. Draw a horizontal line (LINE #2) through the ship'sdisplacement. (Hint: When the forward and aft drafts areequal, 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'sdisplacement (There is no way to ensure this line is vertical- just eyeball it.)

6. Where LINE #3 intersects the LCF Curve is the ship's LCFfor the given drafts.

Example:FFG-21 has the following drafts: Forward: 14'0" Aft: 15'6"Find: 1. Ship's Displacement: 3600 LT2. KM: 22.37 FT3. MT1": 758 FT-Ton per Inch4. TPI: 32.2 LT per Inch5. LCB: 2.1 FT Aft of Midships6. LCF: 24 FT Aft of Midships

CROSS CURVES OF STABILITYThe Cross Curves Of Stability are used to determine the length of therighting arm at any angle of inclination for a given displacement. Using theship's displacement (from the Draft Diagram and Functions of Form) a staticalstability curve for the ship can be constructed.

Instructions for use:1. Enter the ships displacement along the horizontal axis.

2. Draw a vertical line at the ship's displacement. (Hint:"tick marks" are located along the top of the curve to assistin drawing this vertical line)

3. The displacement line will cross each "angle ofinclination" curve at various points.

4. The righting arm for each angle of inclination is readalong the vertical axis (left side).

5. Each righting arm is plotted at the corresponding angle ofinclination on the "Statical Stability Curve Plotting Sheet"or on regular graph paper.