The document discusses vessel stability management for ship officers, covering essential concepts like hydrostatics, static stability, and the implications of stability on safety and capital investment. It includes an analysis of the Sewol ferry accident to highlight the importance of understanding stability manuals and the consequences of inadequate cargo handling. Additionally, it provides detailed explanations of related terms and principles, emphasizing the relationship between weight, buoyancy, and vessel stability throughout various conditions.

1. Ac#ve
Management
of
Vessel
Stability
Promo#ng
understanding
of
Vessel
Stability
for
the
Ship’s
Officer:
Implica#ons
for
Capital
Investment
Series
of
“Ac#ve
Safety”
lectures
for
Vessel
Officers,
Capt.
Philip
Corsano
2014
©
Philip
Corsano
2014

2. Index
• Accident
analysis;
• What
a
Trim
&
Stability
booklet
includes;
• Back
to
the
Greeks,
Eureka!
• Hydrosta#c
Terminology;
• Explana#on
of
Newtonian
moments;
• Metacenter;
• Stability
curves;
• Density
and
displacement;
• Sta#c
stability;
• Free
Surface
Effects
• Transverse
Stability
• Longitudinal
Stability
• Stability
Formula’s
• Instruments
for
Dra
Survey
©
Philip
Corsano
2014

3. Problems
Understanding
Stability
• Stability,
Trim,
&
Hull
Strength
=
standalone
calcula#ons,
limited
to
LOADING-­‐UNLOADING
vessel;
• Very
li`le
means
for
checking
stability
in
transit……….
Cri#cal
for
vessel
safety….
Yet
not
simple…
©
Philip
Corsano
2014

4. Korean
“Sewol”
Ferry
Accident
Analysis
• April
16,
2014,
304
dead,
“Sewol”
capsizes;
• Sharp
turn
to
Stb,
<140°,
10
°/sec,
[safe
turn
for
ship
5°
/2
mins.
Turn
to
avoid
other
ship…
AIS
not
working,
“Jindo”
VTS
lost
vital
seconds
of
ship
data.
Ship
caught
by
undercurrent
@
08:49,
ship
not
turning,
steering
failure?…
Helm
misunderstood
check
to
port,
as
“hard”
port….
• Effect
of
stability
of
vessel
of
45°
turn,
was
22°
list
for
20/secs
on
one
spot.
Cargo
spilled,
was
not
secured,
so
restoring
buoyant
force
not
sufficient
to
right
ship.
©
Philip
Corsano
2014

5. Accident
Analysis
• MCA
US
CG
and
Ship-­‐owner
Protec#on
Ltd
inves#ga#ons
shown
that
in
many
cases
the
officers
responsible
for
cargo
handling
were
not
familiar
with
onboard
vessel
stability
manuals,
computer
programs;
• Monitor
vessel
dra
readings,
rolling
period,
trim,
and
co-­‐ordinates
for
center
of
gravity;
• Proper
observa#on
[dra
readings]
can
determine
displacement
of
vessel
[weight]
to
½%
[tho
not
trivial
during
sailing];
• Comprehension
of
stability
will
mean
an
increased
understanding
of
hull
strength,
reduc#on
in
Cap
Ex
and
maintenance,
reduc#on
in
catastrophic
accidents.
©
Philip
Corsano
2014

6. Extract
from
Loading,
Trim
&
Stability
booklet
for
a
Ro-­‐Ro
vessel
•
Principal
sources
of
danger:
Some
important
sources
of
danger
which
can
affect
the
safety
of
roll
on/roll
off
ships
and
of
persons
on
them
include:
• 1.
Cargo
badly
stowed
or
inadequately
secured
inside
or
on
cargo
units.
• 2.
Free
surface
effects
in
tank
vehicles,
tank
containers
or
other
bulk
units
which
are
slack.
• 3.
Poorly
maintained
ramps,
lis
and
stern
doors.
• 4.
Poorly
maintained
or
inadequately
illuminated
decks.
• 5.
Wet
decks,
Freezing
spray
esp
in
Alasakan
waters.
• 6.
Failure
to
apply
brakes
correctly.
• 7.
Insufficient
or
incorrectly
applied
lashings
or
the
use
of
lashing
equipment
of
the
wrong
type
or
of
inadequate
strength
with
respect
to
mass
and
centre
of
gravity
of
the
cargo
unit
and
the
weather
condi#ons
likely
to
be
encountered
during
the
voyage.
©
Philip
Corsano
2014

7. Archimedes
Principle
• Ship
sinks
un#l
weight
of
water
displaced
by
the
underwater
volume
is
equal
to
the
weight
of
the
ship
– Forces
of
gravity:
G
=
mshipg
=Wship
– Forces
of
buoyancy:
B
=
ρwaterVdisplaced
Wship
=
ρwaterVdisplaced
©
Philip
Corsano
2014

8. Archimedes
Principle
• Center
of
Gravity
(G):
all
gravity
forces
as
one
force
ac#ng
downward
through
ship’s
geometric
center
• Center
of
Buoyancy
(B):
all
buoyancy
forces
as
one
force
ac#ng
upward
through
underwater
geometric
center
©
Philip
Corsano
2014

9. LAW
OF
FLOATATION
• THE
WEIGHT
OF
ANY
SHAPE
IS
ACTING
ONLY
AT
A
CERTAIN
POINT
WHICH
IS
CALLED
CENTRE
OF
GRAVITY
CENTRE
OF
GRAVITY
:
IS
DEFINED
AS
A
POINT
WHERE
THE
SHIPS
WEIGHT
IS
CONCENTRATED
,
THIS
FORCE
IS
ACTING
DOWNWARD
&
THE
POINT
ALWAYS
LIES
AT
½
THE
DEPTH
OF
THE
SHAPE
KG
=
½
DEPTH
EXAMPLE
DEPTH
=
4m
SO
KG
=
2m
DEPTH
W
G
₀
©
Philip
Corsano
2014

10. LAW
OF
FLOATATION
• THE
CENTRE
OF
BOUYANCY
• IS
DEFINED
AS
A
POINT
WHERE
THE
SHIP’S
BOUYANCY
IS
CONCENTRATED,
THIS
FORCE
IS
ACTING
UPWARD,
AND
ALWAYS
CENTERED
AT
½
THE
DRAFT
.
KB
=
½
DRAFT
,e.g;
DRAFT
=
4m
,
SO
KB
=
2m
B’
W
L
B
DRAFT
₀
©
Philip
Corsano
2014

11. RESERVE
BOUYANCY
DEFINED
AS
THE
SPACE
THAT
LIES
BETWEEN
THE
WATER
SURFACE
AND
THE
FIRST
WATER
TIGHT
INTEGRITY
(
MAIN
DECK).
RESERVE BOUYANCY = DEPTH - DRAFT
OR
RESERVE BOUYANCY = VOLUME OF SHIP - VOLUME UNDER WATER
OR
RESERVE BOUYANCY = AREA OF THE SHIP - AREA UNDER WATER
Volume under water
Area under water
Reserve bouyancy
depth
draft
©
Philip
Corsano
2014

12. Hydrosta#cs
Terminology
• Displacement:
total
weight
of
ship
=
total
submerged
volume
of
ship
(measured
in
tons)
• Dra:
ver#cal
distance
from
waterline
to
keel
at
deepest
point
(measured
in
feet)
• Reserve
Buoyancy:
volume
of
water#ght
por#on
of
ship
above
waterline
(important
factor
in
ship’s
ability
to
survive
flooding)
• Freeboard:
ver#cal
distance
from
waterline
to
main
deck
(rough
indica#on
of
reserve
buoyancy)
©
Philip
Corsano
2014

13. Hydrosta#cs
Terminology
• As
dra
&
displacement
increase,
freeboard
and
reserve
buoyancy
decrease
©
Philip
Corsano
2014

14. Moments
• Depending
on
loca#on
of
G
and
B,
two
types
of
moments:
– Righ#ng
moment:
tends
to
return
ship
to
upright
posi#on
– Upse|ng
moment:
tends
to
overturn
ship
• Magnitude
of
righ#ng
moment:
– RM
=
W
*
GZ
(-­‐tons)
– GZ:
moment
arm
()
©
Philip
Corsano
2014

15. Metacenter
• Metacentric
Height
(GM)
– Determines
size
of
righ#ng/upse|ng
arm
(for
angles
<
7o)
GZ
=
GM*sinφ
– Large
GM
-­‐>
large
righ#ng
arm
(s#ff)
– Small
GM
-­‐>
small
righ#ng
arm
(tender)
©
Philip
Corsano
2014

16. Metacenter
• Rela#onship
between
G
and
M
– G
under
M:
ship
is
stable
– G
=
M:
ship
neutral
– G
over
M:
ship
unstable
STABLE
UNSTABLE
©
Philip
Corsano
2014

17. Stability
Curve
©
Philip
Corsano
2014

18. Stability
Curve
• Plot
GZ
(righ#ng
arm)
vs.
angle
of
heel
– Ship’s
G
does
not
change
as
angle
changes
– Ship’s
B
always
at
center
of
underwater
por#on
of
hull
– Ship’s
underwater
por#on
of
hull
changes
as
heel
angle
changes
– GZ
changes
as
angle
changes
©
Philip
Corsano
2014

19. EFFECT
OF
DENSITY
ON
SHIP’S
VOLUME
&
DISPLACEMENT
• ANY
BOX
SHAPED
VESSEL
SAILS
FROM
ONE
PORT
TO
ANOTHER
CERTAIN
CHANGES
OCCURES
OVER
THE
SHIP,
AS
A
RESULT
OF
THE
EFFECT
OF
DENSITY
ON
SHIP’S
VOLUME
&
DISPLACEMENT
AS
WE
KNOW
THAT
THE
DENSITY = MASS kg
VOLUME
A
RELATION
BETWEEN
THE
DENSITY
&
MASS
WOULD
BE
;
DIRECT
PROPORTION
DENSITY
∞
MASS
( DIRECT PROPORTION ) WHICH
MEANS
THAT
WHEN
DENSITY
DECREASES
THE
MASS
DECREASES
WHEN
DENSITY
INCREASES
THE
MASS
INCREASES
©
Philip
Corsano
2014

20. EFFECT
OF
DENSITY
ON
SHIP’S
VOLUME
&
DISPLACEMENT
• A
RELATION
BETWEEN
THE
DENSITY
&
VOLUME
WOULD
BE
;
INV.
PROPORTION
DENSITY
1
/
∞
VOLUME
( INV. PROPORTION ) WHICH
MEANS
THAT
WHEN
DENSITY
DECREASES
THE
VOLUME
INCREASES
WHEN
DENSITY
INCREASES
THE
VOLUME
DECREASES
THE
VOLUME
IS
THE
SUM
OF
L
*
B
*
DRAFT
,
THE
L
&
B
NEVER
CHANGE
FROM
PORT
TO
ANOTHER
SO
THE
ONLY
PARAMETER
THAT
CHANGES
IS
THE
DRAFT
,THERFORE
THE
VOLUME
CHANGES
AS
WELL
©
Philip
Corsano
2014

21. EFFECT
OF
DENSITY
ON
VOLUME
• A
BOX
SHAPED
VESSEL
DISPLACES
20,000
TONS
IN
1
ATMOSPHERE
SAILED:
FROM
PORT
A
HAS
WATER
DENSITY
1.OOO
TO
PORT
B
HAS
WATER
DENSITY
1.025
,
ACCORDING
TO
THE
RELATION
BETWEEN
DENSITY
AND
VOLUME
“INV.PROPORTIONS” ,
WE
DETERMINE
THAT
@
PORT
B,
THE
VOLUME
WILL
DECREASES
AS
THE
WATER
DENSITY
INCREASES
(
1.000
PORT
A
TO
1.025
PORT
B
)
,
WHILE
THE
SHIP
STILL
DISPLACES
THE
SAME
20,000TONS
SINCE
THE
VOLUME
=
L
*
B
*
DRAFT
,
SO
THE
CHANGE
IN
THE
VOLUME
COMES
FROM
THE
CHANGE
IN
THE
DRAFT
©
Philip
Corsano
2014

22. EFFECT
OF
DENSITY
ON
DISPLACEMENT
•
SHIP’S
VOLUME
AT
PORT
A
=
SHIP’S
VOLUME
AT
PORT
B
THE
SHIP
DISPLACES
THE
SAME
VOLUME
OF
WATER
IN
BOTH
PORTS
A
&
B
WHERE
THE
VOLUME
=
OLD
MASS
NEW
MASS
-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐
=
-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐
OLD
DENSITY
NEW
DENSITY
©
Philip
Corsano
2014

23. EFFECT
OF
DENSITY
ON
VOLUME
&
DISPLACEMENT
• EFFECT
OF
DENSITY:
TH
E
PLYMSOL
MARK
(DRAFT
MEASURES)
FREE
BOARD
(RESERVE
BOUYANCY
)
54
FWA Fresh
Summer
Winter
WNA
Tropical
Tropical F
230mm
300mm
540mm
©
Philip
Corsano
2014

24. EFFECT
OF
DENSITY
ON
VOLUME
&
DISPLACEMENT
• FWA
(
FRESH
WATER
ALLOWANCE
)
DEFINED
AS
THE
NUMBER
OF
MM
THAT
INCREASES
OR
DECREASES
IN
SHIPS
MEAN
DRAFT
WHEN
THE
SHIP
SAILS
FROM
SALT
WATER
TO
FRESH
WATER
&
VISE
VERSA
• T
FWA = DISPLACEMENT
4 * TPC
P
C
(
TONS
PER
CENTIMETRE)
DEFINED
AS
THE
NUMBER
OF
TONS
LOADED
OR
DISCHARGED
INORDER
TO
CHANGE
SHIPS
DRAFT
1
CM
IN
SALT
WATER
©
Philip
Corsano
2014

25. EFFECT
OF
DENSITY
ON
VOLUME
&
DISPLACEMENT
• IF
THE
SHIP
SAILS
FROM
PORT
A
WHOSE
WATER
DENSITY
IS
1.000
TO
PORT
B
WHOSE
WATER
DENSITY
IS
1.025
(
THE
DENSITY
INCREASED)
,
SO
ACCORDING
TO
THE
RELATION
BETWEEN
DENSITY
&
VOLUME.
DENSITY
1
/
∞
VOLUME
(
INV.
PROPORTION
)
WHICH
MEANS
THAT
WHEN
DENSITY
DECREASES
THE
VOLUME
INCREASES
WHEN
DENSITY
INCREASES
THE
VOLUME
DECREASES
THE
SHIPS
DRAFT
WILL
DECREASES
,
THE
VALUE
OF
DRAFT
DECREASING
EQUALS
THE
FWA.
Eg.
SHIP
SHAPE
V/L
SAILED
FROM
PORT
A
WITH
DENSITY
1.000
TO
PORT
B
WITH
DENSITY
1.025
FWA
200MM
.OLD
DRAFT
7.0mtrs
so
the
new
dra
will
decrease
to
7.0
mt
-­‐
FWA
200MM
(
20CM,
0.2mt
)
7
-­‐
0.2
=
6.8
mt
(
NEW
DRAFT
)
©
Philip
Corsano
2014

26. EFFECT
OF
DENSITY
ON
VOLUME
&
DISPLACEMENT
• EXAMPLE
SHIP
SHAPE
V/L
SAILED
FROM
PORT
A
WITH
DENSITY
1.025
TO
PORT
B
WITH
DENSITY
1.015
FWA
200MM
.OLD
DRAFT
7.0mtrs
,
DWA
200MM
,
SO
THE
NEW
DRAFT
WILL
INCREASE
“ACCORDING TO THE INV. RELATION
“ BY
THE
VALUE
OF
THE
DWA
(
FROM
SALT
WATER
DENSITY
TO
DOCK
WATER
DENSITY
)
,
OLD
DRAFT
+
DWA
=
NEW
DRAFT
7.0
+
200mm(
0.2mtrs)
=
7.2mtrs
©
Philip
Corsano
2014

27. STATIC
STABILITY
• HEELING
,
IS
THE
ANGLE
OCCURES
WHEN
IN
THE
SHIP
WHEN
HEELS
TO
ONE
SIDE
DUE
TO
EXTERNAL
FORCES
(WIND,WAVES)
• LIST,
IS
THE
ANGLE
OCCURES
IN
THE
SHIP
WHEN
HEELS
TO
ONE
SIDE
DUE
TO
INTERNAL
FORCES
,
LIST
PORTSIDE
OR
LIST
STRB
SIDE.
(
BALLAST,CARGO)
• TRIM,
IS
THE
DIFFRENCE
BETWEEN
THE
FORWARD
DRAFT
&
THE
AFT
DRAFT.
TRIM
COULD
BE
BY
FORE
(
FORWARD
DRAFT
LARGER
THAN
AFT
DRAFT)
10
M
FORE
-­‐
8.0
M
AFT
=
2.0
M
BY
FORE
(
TRIM
)
TRIM
COULD
BE
BY
AFT
(
AFT
DRAFT
LARGER
THAN
FORE
DRAFT)
10
M
FORE
-­‐
15
M
AFT
=
5.0
M
BY
AFT
(
TRIM
)
©
Philip
Corsano
2014

28. STATIC
STABILITY
KG
M
KM
G.M
K
G
M
K
G
K
B B B
©
Philip
Corsano
2014

29. STATIC
STABILITY
• KM
=
KG
+
GM
• KM
=
KB
+
BM
• KG
=
KB
+
BG
• KG
=
KM
-­‐
GM
• GM
=
KM
-­‐
KG
KB
=
½
DRAFT
,
KG
=
½
DEPTHKB
=
½
DRAFT
,
KG
=
½
DEPTH
• KB
=
½
DRAFT
,
KG
=
½
DEPTH
CENTRE
OF
BOUYANCY
ALWAYS
MOVES
TO
THE
HEELED
SIDE
TO
BE
CENTERED
IN
½
THE
UNDER
WATER
VOLUME
©
Philip
Corsano
2014

30. STATIC
STABILITY
• KG
DEFINED
AS
THE
HEIGHT
BETWEEN
THE
KEEL
&
CENTRE
OF
GRAVITY
• KM
DEFINED
AS
THE
HEIGHT
BETWEEN
THE
KEEL
&
METACENTRE
.THE
HEIGHT
OF
METACENTRE
• GM
DEFINED
AS
THE
HEIGHT
BETWEEN
CENTRE
OF
GRAVITY
&
METACENTRE
.
CALLED
(
METACENTRIC
HEIGHT)•
GM
COULD
BE
+VE
(
G
BELOW
M
)
STABLE
SHIP
GM
COULD
BE
-­‐VE
(
G
ABOVE
M
)
UNSTABLE
SHIP
M
•
•
W G
• L
G
M
•
+ VEGM -VE GM
©
Philip
Corsano
2014

31. STATIC
STABILITY
• METACENTRE
POINT
DEFINED
AS
THE
POINT
THAT
EXISTS
WHEN
THE
SHIP
HEELS
OR
LISTS
TO
A
SIDE
,
THIS
POINT
OCCURS
WHEN
THE
LINE
OF
BOUYANCY
THAT
ACTS
UPWARD
INTERSECT
WITH
THE
CENTRE
LINE.
B
M
B’
K
W
L
G
B
W
•
©
Philip
Corsano
2014

32. STATIC
STABILITY
EQUILIBRIUM
• STABLE
SHIP
STABLE
SHIP
MEANS
THAT
THE
SHIP
HAS
A
+VE
GM
.
AND
WHEN
HEELS
OR
LISTS
A
RIGHTING
LEVER
APPEARS
,
THE
LEVER
HAS
A
MOMENT
TO
RIGHTEN
THE
SHIP
&
BRINGS
HER
BACK
TO
THE
UPRIGHT
CONDOTION
.
THE
STATICAL
RIGHTENING
MOMENT
IS
THE
SUM
OF
THE
RIGHTENIG
LEVER
&
THE
SHIPS
DISPLACEMENT.
STATICAL
RIGHTENIG
MOMENT
=
RIGHTENING
LEVER
*
DISPLACEMENT
RM
(
TON
METER)
=
GZ
(mtrs)
*
Δ
(
tons
)
THE
RIGHTENING
LEVER
IS
REPRESENTED
BY
GZ.
THE
GZ
THAT
APPEARS
,
STARTS
FROM
THE
G
POINT
TO
THE
LINE
OF
BOUANCY
MAKING
A
RIGHT
ANGLE.
©
Philip
Corsano
2014

33. STATIC
STABILITY
STABLE
SHIP
• STABLE
SHIP
B
W
B
M
G
B
k
w
M
G
W
B
B B’
K
Z
G
•
•
•
•
•
•
STATICAL RIGHTENING MOMENT = GZ * DISPLACEMENT
A COUPLING IS SET TO BRING THE SHIP BACK TO UP RIGHT CONDOTION
©
Philip
Corsano
2014

34. STATIC
STABILITY
UNSTABLE
SHIP
• UNSTABLE
SHIP
MEANS
THAT
THE
SHIP
HAS
A
-­‐VE
GM
,THERFORE
A
CAPSIZING
LEVER
WILL
APPEARS
,WITH
THE
SHIP’S
DISPLACEMENT
A
CAPSIZING
MOMENT
OCCURES;
WHICH
HEELS
THE
SHIP
EVEN
MORE
TO
THE
HEELED
OR
THE
LISTED
SIDE.
STATICAL
CAPSIZING
MOMENT
=
-­‐
GZ
*
DISPLACEMENT
-­‐
RM
=
-­‐
GZ
*
Δ
©
Philip
Corsano
2014

35. STATIC
STABILITY
UNSTABLE
SHIP
• UNSTABLE
SHIP
B
G
•
M
•
B
K
W
B
Z G
W
K
M
B B’
B
Z G
W
•
•
•
•
•
STATIC CAPSIZING MOMENT = - GZ * DISPLACEMENT
A COUPLING IS SET & INCREASES THE SHIPS HEEL OR LIST
©
Philip
Corsano
2014

36. STATIC
STABILITY
NEUTRAL
SHIP
• NEUTRAL
SHIP
DEFINED
AS
A
SHIP
HAS
HER
G
POINT
COINSIDE
WITH
THE
M
POINT
AS
A
RESULT
NO
LEVER
APPEARS
THERFORE
NO
MOMENT
OCCURS
,&
NO
COUPLING
ARISES
.THE
SHIP
STAYES
HEELED
.
UNABLE
TO
BE
UPRIGHT.
THE
B
M G
B
K
W
B
G M
B B’
K
W
B
W
•
• •
©
Philip
Corsano
2014

37. STATIC
STABILITY
TENDER
&
STIFF
SHIPS
• TENDER
SHIP
A
SHIP
SAID
TO
BE
TENDER
WHEN
SHE
HAS
A
SMALL
GM
,
WHEN
SHE
HEELS
GZ
SMALL
CONSEQUNTLY
STATICAL
RIGHTENING
MOMENT
IS
ALSO
SMALL.
THERFORE
PERIOD
OF
ROLLING
IS
LONG
EXAMPLE
:
PASSENGER
SHIPS
,
CARGO
SHIPS
M
G
K
©
Philip
Corsano
2014

38. STATIC
STABILITY
TENDER
&
STIFF
SHIPS
• STIFF
SHIP
A
SHIP
SAID
TO
BE
STIFF
WHEN
SHE
HAS
A
LARGE
GM
,
WHEN
SHE
HEELS
GZ
LARGE
CONSEQUNTLY
STATICAL
RIGHTENING
MOMENT
IS
ALSO
LARGE.
THERFORE
PERIODE
OF
ROLLING
IS
SHORT
EXAMPLE
:
WAR
SHIPS,
OLYMPIC
SAILING
BOATS,
eg.
DRAGON
K
M
G
©
Philip
Corsano
2014

39. STATIC
STABILITY
ANGLE
OF
LOLL
• ANGLE
OF
LOLL
THE
ANGLE
THAT
APPEARS
WHEN
THE
SHIP
HEELS
TO
A
SIDE
WHILE
THE
SHIP
HAS
A
–VE
GM
.
A
CAPSIZING
MOMENT
CREATED
INCREASES
THE
HEELING
,
BY
THAT
TIME
THE
CENTRE
OF
BOUYANCY
B
STARTS
TO
MOVE
TO
THE
HEELED
SIDE
UNTILL
B
REACHES
A
POINT
JUST
BELOW
THE
LINE
OF
GRAVITY.
THE
ANGLE
WHERE
THAT
HAPPENS
IS
CALLED
ANGLE
OF
LOLL
.
WE
NOTICE
THAT
THE
SHIP
AT
THE
ANGLE
OF
LOLL
,
HAS
NO
GZ,
NO
GM,
NO
MOMENT
AT
ALL.AS
A
RESULT
THE
SHIP
STAYES
ON
THIS
CONDITION
(
HEELED)
©
Philip
Corsano
2014

40. STATIC
STABILITY
ANGLE
OF
LOLL
IF
THE
SHIP
HEELED
AS
RESULT
OF…
(WIND),
THE
CENTRE
OF
BOUYANCY
B
MOVES
FAR
FURTHER
AWAY
IN
THE
HEELED
SIDE,
AS
A
RESULT
B
IS
NO
MORE
ACTING
BELOW
THE
SAME
LINE
OF
GRAVITY,
AND
A
RIGHTING
MOMENT
IS
CREATED
TO
BRING
BACK
THE
SHIP
[NOT
TO
THE
UPRIGHT
CONDITION]
BUT
TO
THE
ANGLE
OF
LOLL
AGAIN.
THE
SHIP
KEEPPS
ROLLING
AROUND
THE
ANGLE
OF
LOLL
,
TILL
STATIC
STABILITY
IS
REACHED
AGAIN
©
Philip
Corsano
2014

41. STATIC
STABILITY
ANGLE
OF
LOLL
F
Z G
M
B
B’
K
B
M G
B’
Fig.1 Fig.2
M
•
•
G Z
B B’
B
W
B
W
B
W
WIND
CAPSIZING
MOMENT
WIND
WIND
RIGHTING MOMENT
LOLL
•
•
•
•
•
•
•
• •
•
Fig.
3
©
Philip
Corsano
2014

42. STATIC
STABILITY
CORRECTING
ANGLE
OF
LOLL
IN
ORDER
TO
CORRECT
<
OF
LOLL
WE
MUST
LOWER
THE
G
BELOW
M.
CONSIDER
THIS
SEQUENCE:
1. FILLING
THE
½
FULL
BALLAST
TANKS
(TO
REMOVE
FREE
SURFACE)
2. LOWER
ANY
UPPER
LOADS
(
CRANES
,
TOPSIDES
TO
DOUBLE
BOTTOM
TANKS)
3. FILLING
THE
TANKS
IN
THE
HEELED
SIDE
4. THEN
FILL
THE
TANKS
IN
THE
OTHER
SIDE
TO
THE
HEELED
SIDE
&
THAT
SHOULD
BE
GRADUAL
SO
AS
TO
RESTABLISH
+VE
STABILITY.
WHY
THE
HEELED
SIDE
FIRST
?
FILLING
THE
TANKS
IN
THE
HEELED
SIDE
THE
G
WILL
MOVE
UP
SLOWLY
&
INCREASE
LOLL
ANGLE:
DUE
TO
FREE
SURFACE
EFFECT.
EVENTUALLY
WHILE
THE
G
STARTS
TO
MOVE
DOWN,
ANGLE
OF
LOLL
IS
GRADUALLY
REDUCED
UNTIL
IT
REDUCED
=
0.
G
RETURNS
BELOW
M,
{+VE
CONDITION}
-­‐
CREATING
A
RIGHTING
MOMENT,
MAKES
THE
SHIP
BACK
TO
THE
UPRIGHT
CONDITION.
©
Philip
Corsano
2014

43. STATIC
STABILITY
CORRECTING
ANGLE
OF
LOLL
• IF
WE
FILL
TANKS
ON
THE
HIGH
SIDE
,
THE
TANKS
GETS
FILLED
GRADUALLY
….
FREE
SURFACE
WILL
MAKES
THE
G
MOVE
MORE
UP
,INCREASING
THE
HEEL
&
ANGLE
OF
LOLL;
EVENTUALLY
FREE
SURFACE
EFFECT
DISSIPATES
&
THE
SHIP
STARTS
TO
BE
ADJUSTED
&
RETURNS
TO
THE
UPRIGHT
CONDITION.
G
STARTS
TO
MOVE
DOWN
,
ANGLE
OF
LOLL
DECREASES
GRADUALLY
,
THEN
CEASES,
&
G
TURNS
TO
BE
BELOW
THE
M
(+VE
GM),
A
RIGHTING
MOMENT
IS
CREATED
BUT
MAY
BE
VERY
STRONG
ONE.
• IF
THE
GZ
CREATED
IS
VERY
LARGE
,
THE
RETURN
WILL
BE
VERY
SEVERE,
STIFF
AND
IN
A
MATTER
OF
SECONDS;
&
MAY
LEAD
TO
A
VERY
DANGEROUS
SITUATION
TO
THE
SHIP.
©
Philip
Corsano
2014

44. FINAL
KG
• ANY
SHIP
DURING
LOADING
/
DISCHARGING
CARGO;
THE
CENTRE
OF
GRAVITY
G
STARTS
TO
MOVE
EITHER
TOWARD
OR
AWAY
FROM
THE
CENTRE
OF
GRAVITY
g
OF
THE
WEIGHTS
LOADED
/
DISCHARGED
.
• (fig.1)
G
MOVED
TO
G’ RELATED
TO
g
of
the
weight
• (fig.2)
G
MOVED
TO
G’ RELATED
TO
g
of
the
weight
G’
G G
»
g
K K
g
G’
Fig. 1 ©
Philip
Corsano
2014
Fig.2

45. FINAL
KG
• ACCORDING
TO
THE
ILLUSTRATION
,
WE
DISCOVER
THAT
THE
G
OF
THE
SHIP
KEEPS
MOVING
UP
AND
DOWN
WITH
THE
g
OF
THE
WEIGHTS
LOADED
/
DISCHARGED,
UNTIL
IT
IS
SET
IN
A
FINAL
POSITION
AFTER
FINISHING
THE
LOADING/DISCHARGING
PROCESS.
• WE
HAVE
AN
INITIAL
KG
,
LEADS
TO
FINAL
KG
.
• THE
FINAL
KG
LEADS
TO
THE
FINAL
GM.
FINAL GM =
FINAL
GM
K=
M
K M -
-­‐F
IFNINAALL
KKGG
©
Philip
Corsano
2014

46. FINAL
KG
• TO
CALCULATE
FINAL
KG,
EVERY
WEIGHT
HAS
ITS
Kg
,
THE
G
CHANGES
BY
THE
EFFECT
OF
THE
MOMENT
OCCURRED
FROM
THE
Kg
&
w
,TILL
G
REACHES
A
FINAL
POSITION
(
KG
)
w/tons
Kg/m
MOMENT/
ton
m
100
10
1000
200
5.0
1000
Total
w
Total
M
300
2000
FINAL
KG’ =
TOTAL
MOMENT
2000
=
FINAL
KG’
TOTAL
W
300
IF
THE
SHIP’S
ORIGINAL
KM
=
8
m
The
final
G’.M
=
ORIGINAL
KM
-­‐
FINAL
KG’
8
-­‐
6.6
=
final
G’M
6.6m
1.4m
©
Philip
Corsano
2014

47. FINAL
KG
• GG’IS
THE
MOVE
OF
G
TO
G’
DURING
LOAD/DISCH
LEADING
TO
THE
FINAL
KG,
&
FINAL
GM
G’
K
100 T
g
k
10m (kg)
200 T
g
k
5m (kg)
G
Initial KG
FINAL KG
M
Final G’M
INITIAL GM
©
Philip
Corsano
2014

48. GZ
CURVES
• GZ
IS
THE
“LEVER”
THAT
OCCURES
WHEN
THE
SHIP
HEELS
,THE
GZ
LEVER
IS
RESPONSIBLE
FOR
RETURNING
THE
SHIP
BACK
TO
THE
UP
RIGHT
CONDITION.
• THE
LENGTH
OF
GZ
LEVER
DEPENDS
ON
TWO
PARAMETERS
,
GM
&
ANGLE
OF
HEEL,
or
Ѳ
M B’
Ѳ
heel
GZ = GM * SIN Ѳ
B
M
K
G
Z
B’
G Z
W
•
•
•
©
Philip
Corsano
2014

49. GZ
CURVES
GM
• AS
THE
Ѳ
INCREASES
,
GZ
INCREASES
UNTILL
REACHES
THE
MAX
THEN
DROPS
DOWN
AGAIN
TO
REACH
THE
VANISHING
ANGLE.
• THE
RED
LINE
CALLED
ARCHI
.
LINE
,FROM
THIS
LINE
WE
GET
THE
INITIAL
GM
OF
THE
SHIP.
FROM
Ѳ
57.3
⁰
EXTEND
UP
A
LINE
TO
CUT
THE
ARCHI
.LINE
AT
A
POINT.
FROM
THIS
POINT
WE
EXTEND
A
HORIZONTAL
LINE
TO
READ
THE
GM,
ON
THE
GZ
SCALE
.THE
ARCHI
LINE
DRAWN
AS
A
TANGENT
FROM
0
AND
SLOPE
OF
THE
CURVE
AS
SHOWN
BELOW.
3.9m
57.3
Vanishing angle
91 ⁰
Max GZ
Ѳ 40⁰
Max
GZ
GZ ARCHI LINE
GM 1.1 m
10 20 30 40 50 60 70 80 90
4
3
2
1
0
©
Philip
Corsano
2014

50. GZ
CURVES
STABLE
SHIP
• MAX
GZ
=
4.0
m
AT
Ѳ
39.0⁰
RANGE
OF
STABILITY
=
0—90
⁰
• INITIAL
GM
=
1.3
m
AT
Ѳ
57.3⁰
VANISHING
ANGLE
=
90⁰
GZ
GM
GM
57,3
STABLE SHIP +VE GZ
10 20 30 40 50 60 70 80 90
4
3
2
1.3
1
0
©
Philip
Corsano
2014

51. GZ
CURVES
STATIC
MOMENT
• IF
THE
SHIP
DISPLACEMENT
=
5000T
THE
MOMENT
AT
25⁰
WOULD
BE
•
GZ
*
W
=
MOMENT
3.0
*
5000
=
15000
Tm
(
at
25⁰
)
GZ
4
3
2
GM
1
10 20 2 5 30 40 50 5 7 , 3 6 0 70 80 90
©
Philip
Corsano
2014

52. GZ
CURVES
UNSTABLE
SHIP
GZ
RANGE
OF
STABILITY
17
⁰-­‐-­‐-­‐
83⁰
Ѳ
LOLL
17⁰
MAX
GZ
3.8m
at
Ѳ
43⁰
VANISHING
Ѳ
83⁰
4.0
MAX
GZ
AT
43⁰
Ѳ LOLL
17⁰
43⁰
UNSTABLE SHIP –VE GZ CURVE
83⁰
RANGE OF UNSTABILITY 0⁰
-­‐-­‐-­‐
17⁰
< LOLL
GZ
10 20 30 40 50 60 70 80 90
3
2
1
0
-1
-2
©
Philip
Corsano
2014

53. GZ
CURVES
UNSTABLE
SHIP
4_
3_
2_
1_
UNSTABLE SHIP -VE GZ
57.3
0
|
|
|
|
|
|
|
|
|
|
-­‐1
-2
-3
Ѳ LOLL
22⁰
GM – 3m
RANGE OF UNSTABILITY 0⁰-­‐-­‐-­‐
22⁰
RANGE
OF
STABILITY
22⁰
-­‐-­‐
92⁰
INITIAL
GM
-­‐
3
m
GZ
10 20 30 40 50 60 70 80 90 100
©
Philip
Corsano
2014

54. FREE
SURFACE
• FREE
SURFACE
IS
DEFINED
AS
THE
SURFACE
THAT
CAN
MOVE
FREELY
FROM
ONE
SIDE
TO
ANOTHER
FREELY
,
EXAMPLE
A
TANK
½
FULL
OF
BALLAST
.
THE
FREE
SURFACE
HAS
A
NEGATIVE
EFFECT
OVER
THE
SHIP’S
STABLE
CONDITION
THE
FREE
SURFACE
LEADS
TO
LOSS
IN
THE
G
M
,
WHICH
MEANS
THAT
IT
COULD
REDUCES
THE
GM
TO
THE
EXTENT
OF
CONVERTING
THE
+VE
GM
TO
-­‐VE
GM
(
STABLE
SHIP
TO
UNSTABLE
SHIP
),SPECIALLY
IF
THE
SHIP
STARTED
HER
VOYAGE
WITH
A
SMALL
INITIAL
G.M
,
AS
A
RESULT
THE
SHIP
CAN
EASILY
CAPSIZE
&
SINKS.
©
Philip
Corsano
2014

55. FREE
SURFACE
• THE
FREE
SURFACE
REDUCES
THE
SHIP
RIGHTING
MOMENT
BY
REDUCING
THE
GZ
LEVER,
THE
LEVER
WHICH
USED
TO
BRING
THE
SHIP
BACK
TO
THE
UPRIGHT
CONDITION
.
• THE
FREE
SURFACE
PRODUCES
AN
EXTRA
CAPSIZING
MOMENT
OVER
THE
SHIP,
AS
A
RESULT
OF
THE
EXTRA
WEIGHT
ADDED
FROM
THE
LIQUID
IN
THE
½
FULL
TANK
IN
THE
HEELED
SIDE.
g
moved
to
g1
ALSO
//
G
MOVED
TO
G’
AS
LIQUID
HEELED
G’Z
<
GZ
M
NEW
MOMENT
<
OLD
MOMENT
NEW
G’M
<
OLD
GM
GG1
=
LOSS
IN
GM
G1
Z1
G
Z
B
B’
G’
©
Philip
Corsano
2014

56. FREE
SURFACE
• THE
EFFECT
OF
THE
FREE
SURFACE
ON
THE
SHIP’S
STABILITY
IS
SIMILAR
TO
SHIFTING
A
LOAD
VERTICALLY
UP.
THE
RIGHTING
MOMENT
IS
AFFECTED
FROM
THE
FREE
SURFACE,
AS
THE
G
MOVES
HORIZONTALLY
TO
G’ &
PARALLEL
TO
g
g1
,
THE
GZ
WILL
BE
REDUCED
TO
G’Z
AND
CONSEQUENTLY
THE
RIGHTING
MOMENT
WILL
ALSO
BE
REDUCED
.
RM
=
GZ
*
W
IN
PRESENCE
OF
FREE
SURFACE
,THE
EFFECT
RM
=
G’Z
*W
• AS
THE
G
ALSO
MOVES
UP
VERTICALLY
TO
G1
,
GM
REDUCED
BY
THE
VALUE
OF
THE
MOVE
OF
G
TO
G1
&
THAT
IS
CALLED
THE
LOSS
IN
GM
(LOSS
IN
STABILITY)
,
THE
NEW
IS
G1M
©
Philip
Corsano
2014

57. FREE
SURFACE
• SUMMARY
1. FREE
SURFACE
COMES
FROM
½
FULL
TANKS
2. FREE
SURFACE
LEADS
TO
LOSS
IN
SHIPS
STABILITY
(LOSS
IN
GM)
3. FREE
SURFACE
REDUCES
THE
SHIPS
RIGHTING
MOMENT
4. FREE
SURFACE
REDUCES
THE
GZ
5. FREE
SURFACE
EFFECT
ON
SHIPS
STABILITY
IS
EQUIVALENT
TO
THE
EFFECT
OF
SHIFTING
A
LOAD
VERTICALLY
UPWARD
.
6. FREE
SURFACE
MAKES
THE
LIQUID
IN
TANK
TO
LEAN
TO
THE
HEELED
SIDE
,
&
ADDS
AN
EXTRA
HEELING
MOMENT
(CAPSIZING)
,I.E” REDUCES THE
RIGHTING MOMENT “WHICH
MAKES
THE
SHIP
TO
HEEL
WITH
A
LARGER
Ѳ”
©
Philip
Corsano
2014

58. TRANSVERSE
STABILITY
LIST
• LIST
IS
THE
ANGLE
THAT
OCCURES
WHEN
THE
SHIP
LEAN
TO
EITHER
SIDE
PORT
OR
STRB
AS
A
RESULT
OF
THE
EFFECT
OF
AN
INTERNAL
FORCE
SUCH
AS
BALLAST
TANKS
,
CARGO
DISTRIBUTION
/
SHIFTING
.
• DURING
LOADING
/DISCHARGING
A
SHIP,
THE
WEIGHTS
ADDED/REMOVED
FROM
THE
SHIPS
SIDES
LEADS
TO
LIST
HER
TO
EITHER
SIDE.
• THE
LIST
THAT
OCCURES
DEPENDS
ON
THE
MOMENT
THAT
EXISTS
FROM
THE
SUM
OF
WEIGHTS
ADDED
/REMOVED
&
THERE
DISTANCE
FROM
THE
CENTRE
LINE.
LIST
MOMENT
=
W
*
d
(
distance
from
centre-­‐line)
©
Philip
Corsano
2014

59. TRANSVERSE
STABILITY
-­‐
LIST
• EQUIVALENT
TO
A
SIMPLE
BALANCE.
2OO
100
1OO
3OO
3OO
5O
d d
Fig .1
• AS THE Fig . 1 SHOWS, EVERY WEIGHT IS FAR FROM THE CENTRE BY ‘d ‘ ,
IN ORDER TO DETERMINE WHICH SIDE IS HEAVIER AND LEADS THE BALANCE TO
LEAN ,WE SHOULD GET THE TOTAL MOMENT PORT & TOTAL MOMENT STRB ,
MOMENT = W * D
©
Philip
Corsano
2014

60. TRANSVERSE
STABILITY
-­‐
LIST
• The
SHIP
LIST
IS
VERY
SIMILLAR
TO
THE
LAST
EXAMPLE
CONCEPT.
PORT STB
100 50
d d
d d
d d
d
d
d d
200
100
150
300
200
150
50
300
EACH WEIGHT ON THE SHIP IS MOVED FROM THE CENTRE LINE BY DISTANCE “d”
SHIP WILL LEAN TO ONE SIDE ACCORDING TO THE MOMENT OF EACH SIDE.
MOMENT = W * D
©
Philip
Corsano
2014

61. TRANSVERSE
STABILITY
-­‐
LIST
DEEPER
VIEW
OF
THE
EFFECT
OVER
THE
SHIP’S
STBILITY
“GM”
G
MOVES
TO
THE
WEIGHT
g
THE
SHIP’S
G
IS
NOW
OUT
OF
THE
CENTRE
LINE:
NAMELY
THE
SIDE
WHICH
HAS
THE
BIGGER
MOMENT;
RESULT
-­‐
SHIP
NOW
LEANS
TO
THAT
SIDE,
&
STOPS
WHEN
THE
B’
IS
UNDER
THE
G‘.
ACTS
ON
THE
SAME
“FORCE”
LINE.
THEREFORE
THE
SHIP’S
G
,
SETTLES
AT
G’ ,
TAN
Ѳ
=
GG
‘
GM
Ѳ
IS
THE
LISTING
ANGLE
G G’
K
M
Ѳ
B
B’
W
B
M
Ѳ
G G’
©
Philip
Corsano
2014

62. TRANSVERSE
STABILITY
-­‐
LIST
Moment
Strb
Moment
port
D
(
gg’)
Distance
from
centre
line
w
50
10
500
200
20
4000
150
10
1500
300
5
1500
100
5
500
100
10
1000
200
5
1000
150
10
1500
50
5
250
300
10
3000
1600
6750
8000
1600ton
FINAL
GG’
1250
strb
©
Philip
Corsano
2014

63. TRANSVERSE
STABILITY
-­‐
LIST
• LISTING
MOMENT
=
1250
STRB
• TOTAL
WEIGHT
=
1600
TON
• FINAL
GG’
=
TOTAL
MOMENT
1250
=
0.781
mtrs.
•
TOTAL
WEIGHT
1600
• IF
THE
FINAL
GM
=
5.5
mtrs
TAN
Ѳ
=
GG’ 0.781
=
8⁰
strb
GM
5.50
M
G G’
0.781
5.5
8⁰
©
Philip
Corsano
2014

64. LONGITUDINAL
STABILITY
-­‐
TRIM
• TRIM
IS
THE
DIFFERENCE
BETWEEN
THE
AFT
DRAFT
&
THE
FORE
DRAFT.
TRIM
COULD
BE
BY
AFT
OR
BY
FORE.
• IF
THE
FOR
&
AFT
DRAFT
WERE
EQUAL
&
HAD
NO
DIFFERENCE
,THEN
THE
SHIP
SAID
TO
BE
ON
AN
EVEN
KEEL.
LBP
ф
L2 L1
LBP IS THE LENGTH BETWEEN “PERPENDICULARS” ф MIDSHIP
L1 DISTANCE FROM AFT B. TO MID SHIP ,CF
L2 DISTANCE FROM FORE B. TO MID SHIP,CF
©
Philip
Corsano
2014

65. LONGITUDINAL
STABILITY
-­‐
TRIM
• IF
LOADS
ARE
ADDED
OR
REMOVED
FROM
THE
SHIP,
THERE
WILL
BE
AN
EFFECT
ON
THE
SHIPS
DRAFTS
&
CONSEQUENTLY
ON
THE
TRIM.
• IF
THE
LOADS
WILL
CHANGE
THE
DRAFTS
AFT
&
FORE
BY
THE
SAME
VALUE,
THIS
ONLY
HAPPENS
IF
THE
CENTRE
OF
FLOATATION
IS
AMIDSHIP.
IF
NOT
,THE
CHANGE
WILL
DEPEND
ON
THE
CHANGE
IN
TRIM
OCCURRED:
L1
&
L2.
L
LBP
L2 ф L1
DRAFT
FORE
DRAFT
CF AFT
©
Philip
Corsano
2014

66. LONGITUDINAL
STABILITY
-­‐
TRIM
• WHEN
A
LOAD
IS
ADDED
FORWARDS
,THE
G
WILL
MOVE
TOWARD
THE
g
of
the
weight
,making
SHIP
LEAN
FORWARD
.
THE
SHIP
STOPS
LEANING
FORWARD
ONCE
B
MOVES
&
REACH
JUST
BELOW
THE
G’ ,
WHICH
MEANS
BOTH
G
‘&
B’
ACT
AGAIN
ON
THE
SAME
FORCE
LINE.
THE
FINAL
GG’ (
DISTANCE
BETWEEN
G
&G’)
IS
CALCULATED
FROM
THE
FINAL
MOMENTS
OF
THE
WEIGHTS
&
TOTAL
WEIGHTS.
GML
ф
W
G G’
B B
’
©
Philip
Corsano
2014

67. LONGITUDINAL
STABILITY
-­‐
TRIM
• CENTRE
OF
FLOATATION
IS
THE
CENTRE
WHERE
THE
LINES
OF
WATER
INTERSECTS
.
THE
SHIP
TRIM
LONGITUDINALY
AROUND
THIS
POINT.
THE
DRAFT
AT
THIS
POINT
IS
CONSTANT.
LBP
L2 L1
ф
CF
NEW
DRAFT
NEW AFT
DRAFT
FORE
©
Philip
Corsano
2014

68. LONGITUDINAL
STABILITY
-­‐
TRIM
• IF
A
LOAD
IS
ADDED
AFT
,THE
SHIPS
DRAFT
AFT
WILL
BE
INCREASED
WHILE
THE
SHIPS
DRAFT
FORE
DECREASES,
AS
SHOWN
IN
THE
fig.
1
BELOW.
THE
EFFECT
OF
THE
WEIGHT
OVER
THE
SHIP’S
TRIM
COMES
FROM
THE
MOMENT
IT
MAKES.
• TRIMMING
MOMENT
IS
THE
MOMENT
TO
CHANGE
THE
SHIP’S
TRIM
,&
IT
IS
THE
SUM
OF
THE
W
&
DISTANCE
OF
W
FROM
CF.
•
trimming
moment
=
_w
*
d
MEASURED
IN
TON
METER
W
LBP
L2 L1
ф
CF
NEW
DRAFT
W
NEW AFT
DRAFT
FORE
Fig.1
d
©
Philip
Corsano
2014

69. LONGITUDINAL
STABILITY
-­‐
TRIM
• TRIMMING
MOMENT
=
w
*
d
MEASURED
IN
TON
METER
W
MCTC
:
IS
THE
MOMENT
THAT
CHANGE
THE
TRIM
BY
1
CM
.
CHANGE
OF
TRIM
IS
THE
TOTAL
CHANGE
IN
THE
SHIPS
TRIM
FROM
THE
RATIO
BETWEEN
THE
MOMENTS
OCCURRED
&
THE
TRIMMING
MOMENT.
MEASURED
IN
CM
=
TRIMMING
MOMENT
MCTC
LBP
L2 L1
ф
CF
NEW
DRAFT
W
NEW AFT
DRAFT
FORE
Fig.1
d
©
Philip
Corsano
2014

70. LONGITUDINAL
STABILITY
-­‐
TRIM
• THE
TOTAL
CHANGE
IN
TRIM
IN
CM
,WILL
BE
DISTRIBUTED
BETWEEN
THE
DRAFTS
FORE
&
AFT.
IF
THE
CF
OF
THE
SHIP
IS
COINSIDE
WITH
THE
MID
SHIP
POINT
,THE
CHANGE
IN
TRIM
WILL
BE
DIVIDED
EQUALLY
ON
BOTH
DRAFTS.
• EXAMPLE
.
CHANGE
IN
TRIM
=
6
CM
CF
MID
SHIP
• SO
DRAFT
AFT
=
+3
CM
DRAFT
FORE
=
-­‐
3
CM
LBP
L2 ф L1
CF
W
Fig.1
d
©
Philip
Corsano
2014

71. LONGITUDINAL
STABILITY-­‐
TRIM
• THE
TOTAL
CHANGE
IN
TRIM
IN
CM
,WILL
BE
DISTRIBUTED
BETWEEN
THE
DRAFTS
FORE
&
AFT.
IF
THE
CF
OF
THE
SHIP
IS
NOT
IN
THE
MID
,THE
CHANGE
IN
TRIM
WILL
BE
DISTRIBUTED
BETWEEN
THE
DRAFTS
BY
THE
FOLLOWING.
• DRAFT
FORE
=
L2
*
CHANGE
OF
TRIM
(L2
DIST
FROM
CF
TO
FORE
B
)
L
(
L1
DIST
FROM
CF
TO
AFT
B
)
DRAFT
AFT
=
L1_
*
CHANGE
OF
TRIM
(
L
IS
THE
LBP
)
L
L
L2 L1
ф
CF
NEW
DRAFT
W
NEW AFT
DRAFT
FORE
Fig.1
d
©
Philip
Corsano
2014

72. LONGITUDINAL
STABILITY
-­‐TRIM
THE
ADDED
/DISCHARGED
WEIGHT
ALSO
HAS
AN
EFFECT
OVER
THE
SHIP
,
THE
EFFECT
APPEARS
OVER
THE
SHIPS
MEAN
DRAFT
CALLED
BODILY
SINKAGE/RISE
,THIS
CHANGE
ADDED
OR
REMOVED
TO
BOTH
DRAFTS
FORE
&
AFT.
IF
A
WEIGHT
ADDED
THE
EFFECT
CALLED
BODILY
SINKAGE
=
_W
_
IF
A
WEIGHT
DISCH.
THE
EFFECT
CALLED
BODILY
RISE
TPC
L
L2 L1
ф
CF
NEW
DRAFT
W
NEW AFT
DRAFT
FORE
Fig.1
d
©
Philip
Corsano
2014

73. Stability
Formula’s
• Change
in
Dra
result
of
H2O
density:
Old
Dra
x
New
Stowage
F/Old
Stowage
F
• Block
Coeff
b=
V/LxBxD
• Water
Plane
[WP]
Coeff
p
=
Area
of
WP/L
x
B
• Tons/inch
immersion
[TPI]
=
Area
of
Waterplane/420
• KG=
Total
Ver#cal
Moments/
Total
Weights
• G
G’
=
(w
x
d)/Displacement
• GM=
KM-­‐KG
• Free
Surface
Effect
=
G
G”
=
rlb3/12
V
• Rolling
period
=
0.44B/√
GM
• Right
moment
=
GZ
x
displacement
• GZ=
GM
x
sine
Θ
[for
small
angles
of
inclina#on]
• Trim
=
Trim
moment/MTI
• MTI
=
k
x
(TPI)
2
Where
k
=
constant
~
value
of
block
coeff
• MTI
=
GM
L
x
Dsipl/12L
©
Philip
Corsano
2014

74. Instruc#ons
for
Dra
Survey
• Accuracy
0.998
–
1.040
kg,
range
of
Fresh
to
Sea-­‐water;
• Scale
graduated
in
density
kg/l
air;
• Use
clean
water,
samples
around
vessel;
• Take
hydrometer
reading
where
the
level
liquid
meets
the
graduated
scale.
©
Philip
Corsano
2014

75. CONCLUSION
• Stability
can
and
should
be
ac#vely
managed
through
a
cap-­‐ex
investment
programme;
• As
ships
get
bigger,
the
risks
of
misunderstanding
Stability,
{Newtonian
Physics}
increases;
• Aligning
economic
incen#ves
with
ac#ve
stability
management
and
training
will
be
a
cost
effec#ve
training
programme.
©
Philip
Corsano
2014

76. Acknowledgements
• Stability
and
Trim
for
Ship’s
Officer,
William
E.
George;
• Accident
analysis
of
MV
“Sewol”,
Korean
Coast
Guard;
• Lack
of
understanding
of
Stability,
“Ship-­‐
owners
Protec#on
Ltd”.
London
UK;
• US
Coast
Guard
Casualty
reports,
www.uscg.mil/hq/g-­‐m/moa/
repor#ndexcas.htm
©
Philip
Corsano
2014