# SHIP S STABILITY

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```					   Principles of Ship’s
Stability

PETRAS PIKSRYS
SHIP’S STABILITY

• SHIP’S STABILITY IS
THE TENDENCY OF
SHIP TO ROTARE ONE
WAY OR THE OTHER
WHEN FORCIBLY
INCLINED
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
FUNDAMENTALS OF STABILITY

STABILITY is the tendency of vessel to rotate one way or the
other when forcibly inclined.

IMPORTENT !!

Ship’s stability can’t catch directly

Stability can define only by calculating
HOW CALCULATING SHIP‖S
STABILITY AND CARCO PLAN ?

• 1.By previous similar cargo plan.
• 2.By standard cargo plan according
―STABILITY 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
SHIP’S STABILITY CRITERIAS

• THERE ARE TWO SHIP’S STABILITY
CRITERIAS:
• 1 h>0 ship’s metacenter height always
positive.
• 2 Zg < Zcritical
•   h = Zm – Zg
•   Zg defined by calculating
•   Zm define according hydrostatic curves
• Zg critical define according special
diagram.
SHIP’S STABILITY CALCULATING
• SHIP’S STABILITY CALCULATING BY
MOMENT FORMULAS.
• MAIN OBJECT OF CALCULATING TO
DEFINE SHIP’S STABILITY CRITERIAS:
• GM=h METACENTER HEIGHT
• Zg    SHIP’S GRAVITY HEIGHT
• MOMENT FORMULA:

•      D0Z0+P1Z1+P2Z2+…….+PnZn
• Zg =
•       D0 + P1 +P2 + …….. + Pn
SHIP’S STABILITY CALCULATING

• Zg critical CURVE
6.60
6.50

6.40

Zg critical
6.30

6.20

6.10

8000 10000 12000   14000   16000 18000   20000
WHO CALCULATING SHIP’S
CARGO PLAN AND STABILITY?
• 1.CARGO OFFICER (ch.mate)
• 2.PORT CARGO OFFICER (supercargo)
• 3.SHIP’S MASTER
SHIP’S STABILITY

STABILITY

INITIAL   OVERALL     DYNAMIC
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

DYNAMIC STABILITY - The work done in heeling
a ship to a given angle of heel.
INITIAL SHIP’S STABILITY

• Initial ship’s stability when ship inclinating
from 7 till12 degrees. Ship’s underwater
body did not change volume
•         V0=V1                          V1
m                        L1
V0
w                       G                          L

W1                                  C1
C
INITIAL METACENTRIC
FORMULA
M=D lst                 Qst
m
lst=hsinQ                           h
M=D h sin Q       lst

G    D
Vg

C1

C
SHIP’S STABILITY
CALCULATING
• Initial stability calculating by ship’s
stability triangle
• Calculating formula lst= h sinQ
• Overall stability calculating by
hydrostatic ship’s body formula lf
• Dynamic stability is the area under
the static stability curve
• Dynamic stability also potential
energy available to return the ship to
the upringing
STABILITY TRIANGLE
m
lst =hsin Q
l   f
h           Q
l   st

G                 Vg
D
C1
lf

C
PHANTACORENS

SHIP’S BADY FORM STABILITY ARMS lf

lf
2.8
80    90
2.4       70
60
1.6
50
40
1.2
30
0.8
20

0.4       10

4000 6000    8000   10000   12000 14000 16000       20000
18000
DISPLACEMENT
METACENTRIC HEIGHT
Metacentric height GM is calculated by subtracting KG
From KM (GM=KM-KG), GM is a measure of the ship.s
stability. 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, is
directly prportional to the size of the ship’s Metacentric
Height, GM.

IMPORTENT !

Thus , GM is a good measure of the ship’s
initial stability.
METACENTRIC HEIGHT

m
h     L
W           G
a
a
C
MAIN STABILITY POINTS

• There are three main stability
points:
• m- metacenter is the end of
hydrostatic force when ship
listing.
• G- centre of ship gravity
• C- centre of ship underwater
body.
SHIP’S STABILITY

• STABILITY REFERENCE POINTS
m
h
Zm
G
WO                              r   Lo
ZG
a
Zc   C
MAIN STABILITY POINTS
•         m metacenter
•         G center of gravity
•         C center of buoyancy
m
Q
L1
h

Q
Wo                                LO
a     G

W1          C             C1
SHIP’S STABILITY

METACENTER

m

C0
SHIP’S STABILITY

• METACENTRIC HEIGHT FORMULAS
• h=r-a
• h=zm –   zG
• h=zc - ro -   zG
METACENTRIC HEIGHT
•   METACENTRIC HEIGHT MEENS SHIP’S INITIAL STABILITY

m

h
W                         G
r0
a

C
Three states of static equilibrium

(a) Positive stability - m above G
(b) Neutral stability – m and   G in
the same position
( c )Negative stability –m below G

m                                G

h>O     m       G h=O          h<O

G                                 m
a               b                 c
POSITIVE SHIP’S STABILITY

• Positive ship’s stability when m above G
•                    h>0

h
m                          L1

W                  G                              L

W1
C          C1
SHIP’S STABILITY CURVE

POSITIVE SHIP’S STABILITY
L
l st
h>0

h
57, 3
Q   Q
NEUTRAL SHIP’S STABILITY

• Neutral ship’s stability when m and
G in the same position
•                  h=0

Gm                  L
W

C          C1
SHIP’S STABILITY

• NEUTRAL SHIP’S STABILITY
lst
h=0

Q
NEGATIVE SHIP’S STABILITY

• Negative ship’s stability when m
below G
•                  h<0

G                 L1
h
W              m                      L
C1
W1             C
NEGATIVE   SHIP’S    STABILITY

h=-0
Mst

Qst
57.3

-h
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 ship’s center of gravity.
As the ship is inclined, Righting Arm are created which tend
to return the ship to it’s original, vertical position.
2. NEUTRAL STABILITY. The metacenter and the ship’s
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.
OVERALL
METACENTRIC FORMULA
M
M=( lf —lst)D
• h=Zm - ZG      m                         L1

h

G   lst
W0                                              L0
Vg

C1       Zm
lf                         ZG
W1                   C

M- UPSERTING MOMENT
METACENTRIC HIGHT
METACENTRIC HIGHT IS FIRST DERIVATIVE SHIP‖S
STABILITY CURVE
Mst
lst

h
Q
57,3
METACENTER HEIGHT
Metacenter height GM is a determine of ship’s
stability curve
•                    m                  L1

W            h                             L
G

C1
W1
C

METACENTER MOMENT IS UPSERTING MOMENT
M= D h sin Q
DYNAMIC STABILITY

W                       L
SHIP’S DYNAMIC STABILITY

• DYMAMIC MOMENT
M

MDYNAMIC
MOMENT

Q
SHIP’S STABILITY

• STATIC MOMENT CURVE

M

Q
SHIP’S DYNAMIC STABILITY

• MAXIMUM DYNAMIC ANGLE
M                                Qdyn WHEN S1= S2
S2

S1

Q   static   Q   dyn       Q dyn max Q
SHIP’S DYNAMIC CURVE

• SHIP’S DYNAMIC STABILITY CURVES APPLICATES
IS EQUVALENT STATIC CURVES AREA

S=Mdyn
Mdyn

Mdyn

Q
DYNAMIC STABILITY
The dynamic stability is the area under the curve in metre-radians
Multiplated by the ship,s displacement in tonnes. It is areas under
the GZ
Curve which are required for checking stability criteria which
depending
Upon the ship,s data may be expressed in metre-degrees or
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.
DYNAMIC STABILITY
Mst         CURVE

Mst             Mdin

Md

Q                Q
max
STABILITY   ELEMENTS
THE LAW OF BUOYANCY
THE LAW OF GRAVITY
STABILITY REFERENCE POINTS
LINEAR MESURMENTS IN STABILITY
THE STABILITY TRIANGLE
RIGHTING MOMENT
STATIC STABILITY CURVE
DYNAMIC STABILITY CURVE
ROLLING PERIOD
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 buoyancy
to righting arms and stability
• Comprehend and identify positive, negative and
neutral conditions of stability
• Comprehend the effects of movements of the centers of
gravity and buoyancy on vessel stability
• Know how ship's stability curves are derived and
comprehend their use in determining stability condition
Definitions

•   Draft
•   Freeboard
•   Depth of hull
•   Reserve buoyancy
•   List / Trim
SHIP’S HULL    MARKINGS

At 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.
PLIMSOL DISC

• PLIMSOL DISC DIVAIDING SHIP‖S
BODY IN TWO PARTS:
• 1. RESERVE BUOYANCY
• 2. DISPLACEMENT

W        L        RESERVE BOYANCY

DISPLACEMENT
FREE BOARD

• SHIP’S MAIN FREE BOARD MEENS SHIP’S
RESERVE BUOYANCY

•          DRAFT

• SHIP’S MAIN DRAFT MEENS SHIP’S
DISPLACEMENT
RESERVE BUOYANCY

• MAINTAIN FREEBOARD – RASERVE
BUOYANCY PRIOR TO PREVENT
LIMITING DRAFTS ARE ASSIGNED
TO EXCESIVE HULL STRESS AS A
FREE BOARD
FREE BOARD MEENS RESERVE BUOYANCY

TF
FREE BOARD
F         S
WL

W

WNA
DRAFT

• MAIN DRAFT MEENS SHIP‖S DISPLACEMENT

W                                 L

DRAFT
Buoyancy

• Archimedes' principle
• Calculations of displacement (W)
• The effect of salt water and fresh water
on displacement (relate to draft)
[1/35 vs 1/36]
Archimede’s principle

A body immersed (or floating) in water will
buoyed

ARCHIMEDE’S FORCE

By a force equal to the weight of the water
displaced.
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
D=Vg

D
W         G
L

C

Vg
SHIP’S BUOYANCY
• D=V*g

L
W             G
D

V*g
C

ARCHIMEDES FORCE

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      TF
- F - Fresh Water                F
- T - Tropical Water (sea water) T
- S - Standard Summer                               S
- W - Winter
W
- WNA-Winter North Atlantic
WNA
SHIP’S 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
DRAFT IN FEETS
• 1 ft = 0.3048 m

XVII
XVI
XV
XIV
XIII
DRAFT IN METRES

• 1 ft = 0.3048 m
44

42

40
38

36
SHIP’S HULL MARKINGS

Ship’s 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 stresses
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

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.

MOMENT
The endency of a force to produce a rotation about a pivot point.
This works like a torque wrench acting on a bolt.
DISPLACEMENT

•   D=DLS + DS + DC
•   D – Displacement
•   DLS – Weight light ship
•   DS - Weight supply
•   DC - Weight cargo
GRAVITY
• THE FORCE OF GRAVITY ACTS VERTICALY
DOWNWARD THROUGHT THE SHIP‖S CENTER OF
GRAVITY

W                 G
D= DL+DC+DS   L
SHIP’S STABILITY

• METACENTER MOMENT
=UPSERTING MOMENT
M = D h sin O
RIGHTING MOMENT

• THE TENDENY OF A FORCE TO
A PIVOT POINT

m
h         M=Dh   sinQ
G        Vg
D
C1
C0
GRAVITY

• The force of gravity acts vertically downward throught
the ship’s center of gravity.

•                        D=Vg
D
W                                      L
G

C

Vg
Application of following terms to
overall stability

(a)Couple

(b)Righting arm (GZ)

(c)Righting moment (RM) - RM= GZ (W)

(d)Upsertting moment
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 ship’s righting arm.

Righting moment. The righting moment is equal to the ship’s
Righting arm multiplied by the ship’s displacement.

Metacentric height. The distance between center of gravity G and
Metacener M .
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
SHIP’S STABILITY CURVE

Using curves,find
(a) Maximum rigting
arm (GZ) GZ=h
(b) Angle of heel where
maximum GZ arm ocurs
l static maximum
(c) Range of critical
stability Q critical
SHIP’S STABILITY

• STABILITY CURVES ELEMENTS
lst

l static max

h                                      Q

57.3
Q   critical
STATIC STABILITY CURVE
When a ship is inclined through all angles of
heel,and the
righting arm for each angle is measured, the
statical stability curve is produced. This
curve is a “snapshot‖of the ship’s stability at
information can be obtained 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:One half the angle of the maximum
Righting Arms.
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 ship’s 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
DRAFT NOMOGRAM
8.2     18000   17900   19900    26.5
7.8     17000   16860   18800     26
7.2     16000   15845   17600    25.5
6.8     15000   14840   16600     25
6.4     14000   13840   15500    24.5
6.0     13000   12820   15000     24
5.6     12000   11820   14600    23.5
5.2     11000   10820   14400     23
4.8     10000   9820    14200    22.5
4.4     9000    8820    14000     22
Tm      Dt      Vm3     M t/cm   P t/cm
HYDROSTATIC CURVES

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

• SHIP’S FLOATING BODY FUNCTION CURVES
DRAFT

V
Zc           r

Xf
D
S

FUNCTIONS
COUPLE
m
M=D h sin Q
h           Q
l   st

G            Vg
D
C1

C
PLIMSOL DISC
TF
F      T

S

W

WNA
LIST

Q      L1

Q Lo
WO
W1
ROLLING PERIOD
CB
• SHIP‖S STABILITY AND ROLLING PERIOD
T=
h

W                                       L
ROLLING PERIOD
The rolling period of the ship’s dependenced from ship’s stability. The formula
Between ship,s stability and rolling :

T = c*B/sqr GM

In this formula:
T – rolling period in sec.
c - constanta
B – the ship’s beam to outside of hull.

Note: the constanta c dependenced from ship’s 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 Lloyd’s Register of shipping and the 1991 HMSO
Code of Practice for Ro-Ro ships use c= 0.7
SHIP’S STABILITY VARIATIONS

m0

h0
G0

C0

SHIP’S STABILITY VARIATIONS
h0 < h1
m1
m0
h1
h0
G0
G1
C1
C0
p

SHIP’S STABILITY VARIATIONS
h0 >h1
m1
P1   m0             P2
h1
G1         h0

G0
C1
C0

SHIP’S STABILITY VARIATIONS

• MOVING CARGO
m0

h0
G0

C0

STABILITY REFERENCES POINTS BEFORE MOVING
SHIP’S STABILITY VARIATIONS

• MOVING CARGO
P2
P1     m0

h0
G0

C0

STABILITY REFERENCES POINTS BEFORE MOVING DOWN
SHIP’S STABILITY VARIATIONS
h1 > h0
• MOVING CARGO
m0

h0      h1
G0

G1
C0
P1                    P2

STABILITY REFERENCES POINTS AFTER MOVING DOWN
SHIP’S STABILITY VARIATIONS

• MOVING CARGO
m0

h0
G0

C0
P1           P2

STABILITY REFERENCES POINTS BEFORE MOVING UPWARD
SHIP’S STABILITY VARIATIONS
h0 > h1

• MOVING CARGO                      P2
P1      m0
h1
G1                 h0
G0

C0

STABILITY REFERENCES POINTS AFTER MOVING UPVARD
SHIP’S STABILITY VARIATIONS

m
h0
h1
G0   G1     L0
W0

C0
SHIP’S STABILITY VARIATIONS

•         FREE LIQUID AREA

G0
W0                           L0

C0

P0
M Moment liquid

SHIP’S STABILITY VARIATIONS
M Moment upserting
•         FREE LIQUID AREA
m

L1
G0
Q
W0                                    L0
C1
W1            C0

P1
P1
SHIP’S STABILITY VARIATIONS
M1
• FREE LIQUID AREA

Y1

Q1                P1          M2

Y2

P2
M2>M1              Q2>Q1
Mcargo

SHIP’S STABILITY VARIATIONS

•         HANGING CARGO                     Q

lz

W0                             L1
L0
P

W1

Mcargo= Pcargo lz sin Q
TRIM
Trim means different between draft fore TF and draft aft TAF

W1

W                                                               L

TAF                                                     L1
TF
TAf
SHIP’S TRIM DIAGRAM
m
9
8

7

6

5

4

3

2

1                                         Tf
2    3   4   5   6   7    8   9 m
SHIP’S TRIM DIAGRAM
Dt

4000

3600

3200
2800
2400

1600
1200

3
-5   -4    -3   -2   -1    0   1   2   Xc m
0
SHIP’S STABILITY VARIATIONS

TRIM
Trim means different between draft fore TF and draft aft TAF

W1

W                                                               L
lx
TAF                                                     L1
P
TF

SHIP’S TRIM BEFORE SHIFTING CARGO
Mdif

DH
SHIP’S STABILITY VARIATIONS

TRIM
Trim means different between draft fore TF and draft aft TAF

P lx
d=            L
DH
W1

W                                                               L

TAF0      P                    P                        L1
TAF1                             lx                                   d

TF0     TF1
L

SHIP’S TRIM AFTER SHIFTING CARGO
LIST

Q      L1

Q Lo
WO
W1
SHIP’S STABILITY VARIATIONS

LIST

P

Lo
WO

SHIP’S LIST BEFORE SHIFTING CARGO
SHIP’S STABILITY VARIATIONS

LIST

ly
P                        P
L1

WO                                 Q         Lo

W1

tg Q =   P ly
Dh
SHIP’S LIST AFTER SHIFTING CARGO

```
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