principles of ship’s stability
TRANSCRIPT

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Principles of ShipsStability
PETRAS PIKSRYS

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SHIPS STABILITY
SHIPS STABILITY IS
THE TENDENCY OFSHIP TO ROTARE ONE
WAY OR THE OTHER
WHEN FORCIBLY
INCLINED

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WHAY IS STABILITY IS SO
IMPORTENT ?
IF THE SHIP LOST STABILITY WHAT
WILL BE HAPPENED:
1. LOST OF MOBILE
2. LOST THE HUMANS LIFES
3. LOST THE SHIP
4. LOST THE CARGO
5. OIL POLLUTION

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FUNDAMENTALS OF STABILITY
STABI LI TY is the tendency of vessel to rotate one way or the
other when forcibly incl ined.
IMPORTENT !!
Ships stability cant catch directly
Stability can define only by calculating

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HOW CALCULATING SHIPS
STABILITY AND CARCO PLAN ?
1.By previous similar cargo plan.
2.By standard cargo plan accordingSTABILITY BOOKLET
3.By standard cargo plan forms
4.By special cargo plan computer
5.By standard PC with special cargo
plan program 6.By special or standard hand
calculator

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SHIPS STABILITY CRITERIAS
THERE ARE TWO SHIPS STABILITYCRITERIAS:
1 h>0 ships metacenter height alwayspositive.
2 Zg < Zcritical
h = ZmZg
Zg defined by calculating
Zm define according hydrostatic curves
Zg critical define according specialdiagram.

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SHIPS STABILITY CALCULATING
SHIPS STABILITY CALCULATING BYMOMENT FORMULAS.
MAIN OBJECT OF CALCULATING TO
DEFINE SHIPS STABILITY CRITERIAS:
GM=h METACENTER HEIGHT Zg SHIPS GRAVITY HEIGHT
MOMENT FORMULA:
D0Z0+P1Z1+P2Z2+.+PnZn
Zg=
D0 + P1 +P2 + .. + Pn

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SHIPS STABILITY CALCULATING
Zg critical CURVE
8000 10000 12000 14000 16000 18000 20000
6.10
6.20
6.30
6.40
6.50
6.60
Zg critical

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WHO CALCULATING SHIPS
CARGO PLAN AND STABILITY? 1.CARGO OFFICER (ch.mate)
2.PORT CARGO OFFICER (supercargo)
3.SHIP
S MASTER

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SHIPS STABILITY
STABILITY
INITIAL OVERALL DYNAMIC

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STABILITY
INITIAL STABILITY The stability of a ship
in the range from 0
to 7
/10
of
inclination.
OVERALL STABILITY A general measure of a
ship's ability to resist capsizing in a
given condition of loading.
DYNAMIC STABILITY The work done in heeling
a ship to a given angle of heel.

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INITIAL SHIPS STABILITY
Initial ships stability when ship inclinating
from 7 till12 degrees. Ships underwaterbody did not change volume
V0=V1
C
C1G
m
V0
V1
w L
W1
L1

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INITIAL METACENTRIC
FORMULA
m
G
C
M=D h sin Q
Qst
h
DVg
C1
lst
M=D lst
lst=hsinQ

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SHIPS STABILITY
CALCULATING Initial stability calculating by ships
stability triangle
Calculating formula lst= h sinQ
Overall stability calculating byhydrostatic ships body formulalf
Dynamic stability is the area underthe static stability curve
Dynamic stability also potentialenergy available to return the ship tothe upringing

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STABILITY TRIANGLE
Q
m
C
G
C1
lst=hsin Q
l sth
D
Vg
lf
l f

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4000 6000 8000 10000 1200014000
1600018000
2000
0.4
0.8
1.2
1.6
2.4
2.8
10
20
30
40
50
60
70
80 90
PHANTACORENS
SHIPS BADY FORM STABILITY ARMS lf
lf
DISPLACEMENT

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METACENTRIC HEIGHT
Metacentric height GM is calculated by subtracting KG
From KM (GM=KMKG), GM is a measure of the ship.sstability. KM=h.
With initial stability(0 10 deg.) the metacenter does not
move, and Sine function is almost linear(a straight line).
Therefore, the size of the ship,s Righting Arm, GZ, isdirectly prportional to the size of the ships Metacentric
Height, GM.
IMPORTENT !
Thus , GM is a good measure of the ships
initial stability.

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METACENTRIC HEIGHT
m
G
C
h
a
WL
a

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MAIN STABILITY POINTS
There are three main stabilitypoints:
m metacenter is the end ofhydrostatic force when shiplisting.
G centre of ship gravity
C centre of ship underwaterbody.

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SHIPS STABILITY
STABILITY REFERENCE POINTS
G
h
a
r
C
WO Lo
m
Zc
ZG
Zm

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MAIN STABILITY POINTS
m metacenter G center of gravity
C center of buoyancy
m
G
h
a
C1
Q
Wo LO
W1
L1
Q
C

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SHIPS STABILITY
METACENTER
m
C0

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SHIPS STABILITY
METACENTRIC HEIGHT FORMULAS
h=ra
h=zmzG
h=zc  ro  zG

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METACENTRIC HEIGHT METACENTRIC HEIGHT MEENS SHIPS INITIAL STABILITY
m
G
C
h
a
Wr0

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Three statesof static equilibrium
(a) Positive stability  m above G
(b) Neutral stability m and G in
the same position
( c )Negative stabilitym below G
m
a
m G
b
G
mG
h>O h=O h

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POSITIVE SHIPS STABILITY
Positive ships stability when m above G
h>0
C C1
G
mh
W L
W1
L1

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SHIPS STABILITY CURVE
L
l st
Q
h57, 3
Q
POSITIVE SHIPS STABILITY
h>0

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NEUTRAL SHIPS STABILITY
Neutral ships stability when m and
G in the same position
h=0
C C1
G m
WL

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SHIPS STABILITY
NEUTRAL SHIPS STABILITY
lst
Q
h=0

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NEGATIVE SHIPS STABILITY
Negative ships stability when m
below G
h

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h=0
NEGATIVE SHIP S STABILITY
57.3
h
Mst
Qst

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STABILITY CONDITIONS
The positions of Gravity and the Metacenter will indicate the initial stability
of a ship.Following damage, the ship will assume one of the following three stability
conditions:
1. POSITIVE STABILITY. The metacenter is located above
the ships center of gravity.
As the ship is inclined, Righting Arm are created which tendto return the ship to its original, vertical position.
2. NEUTRAL STABILITY. The metacenter and the ships
center of gravity are in the same location. As the ship is inclined,
. there are no returing moment.
3. NEGATIVE STABILITY.The ship,s center of gravity is
above the metacenter.
As the ship is inclined, negative Righting Arms (called upsetting
arms) are created which tend to capsize the ship.

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METACENTRIC FORMULA
h=Zm ZG
CC1
m
h
lst
M=( lflst)D
OVERALL
Vg
W0 L0
W1
L1
lf
G
Zm ZG
M UPSERTING MOMENT
M

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METACENTRIC HIGHT
METACENTRIC HIGHT IS FIRST DERIVATIVE SHIPS
STABILITY CURVE
h
57,3
Mst
Q
lst
METACENTER HEIGHT

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METACENTER HEIGHT
W L
W1
L1
C
C1
G
m
h
Metacenter height GM is a determine of shipstability curve
METACENTER MOMENT IS UPSERTING MOMENT
M= D h sin Q

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W L
DYNAMIC STABILITY

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SHIPS DYNAMIC STABILITY
DYMAMIC MOMENT
Q
M
M DYNAMIC
MOMENT

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SHIPS STABILITY
STATIC MOMENT CURVE
Q
M

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SHIPS DYNAMIC STABILITY
MAXIMUM DYNAMIC ANGLE
Q dynQ static Q
M
Qdyn max
S1
S2
Qdyn WHEN S1= S2

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SHIPS DYNAMIC CURVE
SHIPS DYNAMIC STABILITY CURVES APPLICATES
IS EQUVALENT STATIC CURVES AREA
Mdyn
S=Mdyn
Q
Mdyn

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DYNAMIC STABILITY
The dynamic stability is the area under the curve in metreradians
Multiplated by the ship,s displacement in tonnes. It is areas underthe GZ
Curve which are required for checking stability criteria which
depending
Upon the ship,s data may be expressed in metredegrees or
metreradians.
The area unde GZ curve also the potential energy available to
return the
Ship to the upringht.
Principle of conservation of energy, the potential energy
in converted into
Rotation energy as the ship moves towards the upright.

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Md
Mst
Q max
DYNAMIC STABILITY
Mst
Q
Mdin
CURVE

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STABILITY ELEMENTS
THE LAW OF BUOYANCY
THE LAW OF GRAVITYSTABILITY REFERENCE POINTS
LINEAR MESURMENTS IN STABILITY
THE STABILITY TRIANGLE
RIGHTING MOMENT
STATIC STABILITY CURVE
DYNAMIC STABILITY CURVE
ROLLING PERIOD

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Learning Objectives
Comprehend the concepts of hydrostatics, buoyancy,
and Archimedes' principle
Comprehend static equilibrium of a floating vessel and
the relationship of the centers of gravity and buoyancyto righting arms and stability
Comprehend and identify positive, negative and
neutral conditions of stability
Comprehend the effects of movements of the centers ofgravity and buoyancy on vessel stability
Know how ship's stability curves are derived and
comprehend their use in determining stability condition

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Draft
Freeboard
Depth of hull Reserve buoyancy
List / Trim
Definitions

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SHIPS HULL MARKINGS
t XVIII hundred one Englishman called
PLIMSOL in Great Britan Parlament filds
for marcks on the hull to for Safe shipping.
Now thats marks called PLIMSOL MARKS.

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PLIMSOL DISC
PLIMSOL DISC DIVAIDING SHIPS
BODY IN TWO PARTS:
1. RESERVE BUOYANCY
2. DISPLACEMENT
W L RESERVE BOYANCY
DISPLACEMENT

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FREE BOARD
SHIPS MAIN FREE BOARD MEENS SHIPSRESERVE BUOYANCY
DRAFT
SHIPS MAIN DRAFT MEENS SHIPS
DISPLACEMENT

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RESERVE BUOYANCY
MAINTAIN FREEBOARDRASERVE
BUOYANCY PRIOR TO PREVENT
LIMITING DRAFTS ARE ASSIGNED
TOEXCESIVE HULL STRESS AS A
RESULTOF OVERLOADING

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FREE BOARD
WL
FREE BOARD
WNA
W
SF
TF
FREE BOARD MEENS RESERVE BUOYANCY

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DRAFT
MAIN DRAFT MEENS SHIPS DISPLACEMENT
W L
DRAFT
B

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Archimedes' principle
Calculations of displacement (W)
The effect of salt water and fresh wateron displacement (relate to draft)
[1/35 vs 1/36]
Buoyancy

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Archimedes principle
BOY D
A body immersed (or floating) in water will
buoyed
ARCHIMEDES FORCE
By a force equal to the weight of the water
displaced.

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THE LAWS OF BUOYANCY
1. Floatating objects posses the property of buoyancy.
2. A floatating body displaces a volume of water equal in
a body immersed (or floating) in water will be duoyed
up by a force equal to the weight of the water displaced
W L
C
Vg
D
G
D=Vg

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SHIPS BUOYANCY D=V*g
V*g
DG
C
WL
ARCHIMEDES FORCE
PLIMSOL MARKS (Load lines)

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WNAW
ST
F
TF
Markings of minimum allowable freeboard for registred cargo
Carryng ships.Located amidships on both the port and starboard
sides 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
 WNAWinter North Atlantic

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SHIPS HULL MARKINGS
Calculative Draft Marks
Used for determining displacement and other properties
of the ship for stability and damage control.
Those draft marks indicate the depth of the keel (baseline)
below the waterline.
TWO POSIBLE MARKING SYSTEMS:
1. Roman numerals in height
2. Arabic numerals in height

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DRAFT IN FEETS
1 ft = 0.3048 m
XIII
XIV
XV
XVIXVII

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DRAFT IN METRES
1 ft = 0.3048 m
36
38
40
42
44
SHIPS HULL MARKINGS

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SHIPS HULL MARKINGS
Navigational Draft MarksShips operational drafts.
These draft marks include the depth of any
projections below the keel of the ship.
Limiting Draft Marks
Limiting drafts are assigned to maintain
reserve buoyancy (freeboard) prior to
damage, and to prevent excessive hull stressesas a result of overloading.
DISPLACEMENT

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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 ships
GRAVITYThe force of gravity acts vertically downward through the ships centerOf gravity. The magnitude of the force depends on the ships total weight.
MOMENTThe endency of a force to produce a rotation about a pivot point.This works like a torque wrench acting on a bolt.

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DISPLACEMENT
D=DLS + DS + DC
D Displacement
DLSWeight light ship
DS  Weight supply
DC  Weight cargo

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GRAVITY
THE FORCE OF GRAVITY ACTS VERTICALY
DOWNWARD THROUGHT THE SHIPS CENTER OF
GRAVITY
WL
GD= DL+DC+DS

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SHIPS STABILITY
METACENTER MOMENT=UPSERTING MOMENT
M = D h sin O

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RIGHTING MOMENT
THE TENDENY OF A FORCE TO
PRODUCE A ROTATION ABOUT
A PIVOT POINT
C0
G
m
C1
M = D h sinQ
DVg
h

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GRAVITY
The force of gravity acts vertically downward throught
the ships center of gravity.
D=Vg
W L
Vg
D
C
G
Application of following terms to

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pp g
overall stability
(a)Couple
(b)Righting arm (GZ)
(c)Righting moment (RM)  RM= GZ (W)
(d)Upsertting moment

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DEFINITIONS
Couple. Since the forces of buoyancy and gravity are equal and act
along parallel lines, but in opposite directions, a rotation is developed
Righting arm.The distance between the forces of buoyancy and
gravity is know as the ships righting arm.
Righting moment. The righting moment is equal to the ships
Righting arm multiplied by the ships displacement.
Metacentric height. The distance between center of gravity G and
Metacener M .

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The development of the static stability curve from the
cross
curves of stability
Foctors involed:
G does not change position as heeling angle
changes
 C is always at the geometric center of the volume
of the underwater hull
 the shape of the underwater hull changes as
heeling angle changes

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Using curves,find
(a) Maximum rigting
arm (GZ) GZ=h(b) Angle of heel where
maximum GZ arm ocurs
l staticmaximum(c) Range of critical
stability Qcritical
SHIPS STABILITY CURVE

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SHIPS STABILITY
STABILITY CURVES ELEMENTS
lst
Qh
57.3
l static max
Q critical
STATIC STABILITY CURVE

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When a ship is inclined through all angles of
heel,and the
righting arm for each angle is measured, the
statical stabilitycurve is produced. This
curve is asnapshotof the ships stability at
thatparticular loading condition.Much
information can beobtained from this curve,
including:
1. Range of Stability:
This ship will generate Righting
Arms when inclined from 0 deg. Till to approximately 74 dg.
2. Maximum Righting Arm:The angle of inclination
where the maximum Righting Arm occurs
3. Danger Angle:Onehalf the angle of the maximum
Righting Arms.
DRAFT DIAGRAM AND FUNCTIONS

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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.
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)
Displacement (D)VOLUME V m
Weight, drafting per 1 cm

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HYDROSTATIC CURVES
SHIPS FLOATING BODY FUNCTIONS CAN CALCULATING
BY HYDROSTATIC CURVES. THIS CURVES IS FUNCTIONS
FLOATING SHIPS BODY STABILITY AND UNDERSEA
SHIPS BODY CAPITICY.
ARGUMENT FOR CALCULATING IS SHIPS DRAFT
FUNCTIONS FOR CALCULATING:
a) DISPLACEMENT D
b) VOLUME V
c) FLOATING CENTER Xf
d) BOYAD CENTER XC Zc
e METACENTER RADIUS r
f) SQUERE OF WATERLINE S

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HYDROSTATIC CURVES
SHIPS FLOATING BODY FUNCTION CURVESDRAFT
FUNCTIONS
V
D
S
Xf
Zc r

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COUPLE
Q
m
C
G
C1
M=D h sin Q
l st
h
D
Vg

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PLIMSOL DISC
WNA
W
S
TF
TF

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LIST
Q
Q
W1
L1
WO Lo

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ROLLING PERIOD
SHIPS STABILITY AND ROLLING PERIOD
W L
T= C B
h
ROLLING PERIODTh lli i d f h hi d d d f hi bili Th f l

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The rolling period of the ships dependenced from ships stability. The formula
Between ship,s stability and rolling :
T = c*B/sqr GM
I n this formula:
T rolling period in sec.
c  constanta
B the ships beam to outside of hull.
Note: the constanta c dependenced from ships displacements.
There are the followings meanings:
c=0.88 when ship is empty or ballast;
c=0.78  when the ship has on board amout 20 %
c=0.75 when liquids on board 10%
c=0.73 when all liquids on board amout 5%
HOWEVER, for all lagers ships Lloyds Register of shipping and the 1991 HMSO
Code of Practice for RoRo ships use c= 0.7

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SHIPS STABILITY VARIATIONS
LOADING CARGO
C0
G0
m0
h0
STABILITY REFERENCES POINTS BEFORE LOADING

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SHIPS STABILITY VARIATIONS
LOADING CARGO IN HOLD
C0
G0
m0
h0
STABILITY REFERENCES POINTS AFTER LOADING
p
C1G1
m1
h1
h0 < h1

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SHIPS STABILITY VARIATIONS
LOADING CARGO AT DECK
C0
G0
m0
h0
STABILITY REFERENCES POINTS AFTER LOADING
P1 P2
G1
m1
h1
h0 >h1
C1

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SHIPS STABILITY VARIATIONS
MOVING CARGO
C0
G0
m0
h0
STABILITY REFERENCES POINTS BEFORE MOVING

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SHIPS STABILITY VARIATIONS
MOVING CARGO
C0
G0
m0
h0
STABILITY REFERENCES POINTS BEFORE MOVING DOWN
P1
P2

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SHIPS STABILITY VARIATIONS
MOVING CARGO
C0
G0
m0
h0
STABILITY REFERENCES POINTS AFTER MOVING DOWN
P1 P2
G1
h1
h1 > h0

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SHIPS STABILITY VARIATIONS
MOVING CARGO
C0
G0
m0
h0
STABILITY REFERENCES POINTS BEFORE MOVING UPWARD
P1 P2

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SHIPS STABILITY VARIATIONS
MOVING CARGO
C0
G0
m0
h0
STABILITY REFERENCES POINTS AFTER MOVING UPVARD
P1
P2
G1h1
h0 > h1

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SHIPS STABILITY VARIATIONS
LOADING CARGO
G0
C0
W0L0G1
m
h0
h1

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SHIPS STABILITY VARIATIONS
FREE LIQUID AREA
P0
W0L0
C0
G0

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SHIPS STABILITY VARIATIONS
FREE LIQUID AREA
Q1 P1
P2
M1
M2
Y1
Y2
M2>M1 Q2>
Q1
Mcargo

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SHIPS STABILITY VARIATIONS
HANGING CARGO Q
lz
P
Mcargo= Pcargo lz sin Q
W0
L0
W1
L1

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TRIM
Trim means different between draft fore TF and draft aft TAF
TF
TAF
W L
W1
L1

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SHIPS TRIM DIAGRAM
Tf
TAf
m
m
12 3 4 5 6 7 8 9
2
3
4
5
6
7
8
9

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SHIPS TRIM DIAGRAMDt
Xc m01 02345 1 2
3
200
600
400
800
200
600
4000
SHIPS STABILITY VARIATIONS

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TRIM
Trim means different between draft fore TF and draft aft TAF
TF
TAF
W L
W1
L1P
SHIPS TRIM BEFORE SHIFTING CARGO
lx
Mdif
D H
SHIPS STABILITY VARIATIONS

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TRIM
Trim means different between draft fore TF and draft aft TAF
TF0
TAF0
W L
W1
L1P
TF1
AF1
SHIPS TRIM AFTER SHIFTING CARGO
Plx
d =P lx
D HL
L
d

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LIST
Q
Q
W1
L1
WOLo
SHIPS STABILITY VARIATIONS

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LIST
WOLo
P
SHIPS LIST BEFORE SHIFTING CARGO
SHIPS STABILITY VARIATIONS

8/10/2019 Principles of Ships Stability
102/102
LIST
WO Lo
P Ply
W1
L1
Q
tg Q = P ly
D h