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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.
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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
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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:
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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
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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.
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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. **
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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
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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
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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.
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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:
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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:
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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)
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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:
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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.
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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
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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:
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- 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
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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.
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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.