Active management of vessel stability

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

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

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…


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.


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.


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, li\s 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.


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


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


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


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


RESERVE BOUYANCY

DEFINED AS THE SPACE THAT LIES BETWEEN THE WATER SURFACE AND THE FIRST WATER TIGHT INTEGRITY ( MAIN DECK).

Volume under water Area under water

Reserve bouyancy

draft

depth

RESERVE BOUYANCY = DEPTH - DRAFT OR RESERVE BOUYANCY = VOLUME OF SHIP - VOLUME UNDER WATER OR RESERVE BOUYANCY = AREA OF THE SHIP - AREA UNDER WATER


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)


Hydrosta#cs Terminology

•  As dra\ & displacement increase, freeboard and reserve buoyancy decrease


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 (\)


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)


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

Stability Curve


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


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

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

DENSITY = MASS kg VOLUME


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


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


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


EFFECT OF DENSITY ON VOLUME & DISPLACEMENT

•  EFFECT OF DENSITY: THE PLYMSOL MARK

(DRAFT MEASURES)

FREE BOARD

(RESERVE BOUYANCY )

54

WNA Winter

Summer FWA Fresh

Tropical F

Tropical

230mm

300mm

540mm © Philip Corsano 2014


•  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 P C ( TONS PER CENTIMETRE) DEFINED AS THE NUMBER OF TONS LOADED OR DISCHARGED INORDER TO

CHANGE SHIPS DRAFT 1 CM IN SALT WATER

FWA = DISPLACEMENT

4 * TPC



•  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 )



•  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


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 )


STATIC STABILITY

G.M KM KG K

G

K

M

G

M

K

B B B


STATIC STABILITY •  KM = KG + GM •  KM = KB + BM •  KG = KB + BG •  KG = KM -‐ GM •  GM = KM -‐ KG

•  KB = ½ DRAFT , KG = ½ DEPTH CENTRE OF BOUYANCY ALWAYS MOVES TO THE HEELED SIDE TO BE CENTERED IN ½ THE UNDER

WATER VOLUME

KB = ½ DRAFT , KG = ½ DEPTHKB = ½ DRAFT , KG = ½ DEPTH


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

G

M

M

+ VEGM -VE GM

G W L •

•

•

•


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

•


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.

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.

STATICAL RIGHTENIG MOMENT = RIGHTENING LEVER * DISPLACEMENT RM ( TON METER) = GZ (mtrs) * ∆ ( tons )


STATIC STABILITY

STABLE SHIP •  STABLE SHIP B

W

w

k

B

G

M

B

W

B

B B’

G

M

K

Z

G

•

•

•

•

•

•

STATICAL RIGHTENING MOMENT = GZ * DISPLACEMENT A COUPLING IS SET TO BRING THE SHIP BACK TO UP RIGHT CONDOTION


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 * ∆


STATIC STABILITY UNSTABLE SHIP

•  UNSTABLE SHIP

W

K

B

M

G

B

W

K

B B’

M

G Z

B

B

W

G Z

•

•

•

•

•

• •

STATIC CAPSIZING MOMENT = - GZ * DISPLACEMENT A COUPLING IS SET & INCREASES THE SHIPS HEEL OR LIST


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

K

B

M G

B

W

B B’

K

G M

W

B B

W

•

• •


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

K

G

M


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

G

M


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)


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


STATIC STABILITY ANGLE OF LOLL F

M

G Z

BB’

K

B B’

M G

B B’

G Z

M

B

W

B

W

B

W

CAPSIZING MOMENT

WIND WIND

WIND

RIGHTING MOMENT

Fig.1 Fig.2

LOLL

•

• •

•

•

•

•

• •

• •

•

Fig. 3


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.


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.


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

» 

K K

G G

G’

g

g

G’

Fig. 1 Fig.2 © Philip Corsano 2014

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 = KM -‐ FINAL KG FINAL GM = KM - FINAL KG


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 )

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

w/tons Kg/m MOMENT/ ton m

100 10 1000

200 5.0 1000

Total w Total M

300 2000

6.6m

1.4m © Philip Corsano 2014

FINAL KG

•  GG’IS THE MOVE OF G TO G’ DURING LOAD/DISCH

LEADING TO THE FINAL KG, & FINAL GM

K

100 T

g

k

10m (kg)

200 T

g

k

5m (kg)

G

G’

Initial KG

FINAL KG

M Final G’M

INITIAL GM


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

Ѳ heel

GZ = GM * SIN Ѳ

B

M

K

G

B’

Z

G Z

M B’

W

•

•

•


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

ARCHI LINE GZ

10 20 30 40 50 60 70 80 90

GM 1.1 m

4

3

2

1

0


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

1

2

0

3

1.3


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

57,3 25 10 20 30 40 50 60 70 80 90 © Philip Corsano 2014

GZ CURVES UNSTABLE SHIP

GZ RANGE OF STABILITY 17 ⁰-‐-‐-‐ 83⁰ Ѳ LOLL 17⁰ MAX GZ 3.8m at Ѳ 43⁰ VANISHING Ѳ 83⁰

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 0

-1

-2

1

2

3

4.0


GZ CURVES UNSTABLE SHIP

4_ 3_ 2_ 1_ 0 | | | | | | | | | | -‐1

UNSTABLE SHIP -VE GZ

57.3

-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


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.


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 NEW MOMENT < OLD MOMENT NEW G’M < OLD GM GG1 = LOSS IN GM

M

G1 Z1

G Z

B B’

G’


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


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”


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)


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


TRANSVERSE STABILITY -‐ LIST •  The SHIP LIST IS VERY SIMILLAR TO THE LAST EXAMPLE CONCEPT.

STB PORT

d d

d d

d d

d d

d d

100 50

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


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

K

G G’

M

Ѳ

B B’

W

B

G G’

M Ѳ


TRANSVERSE STABILITY -‐ LIST Moment Strb

Moment port

D ( gg’) Distance from centre line

w

500 10 50

4000 20 200

1500 10 150

1500 5 300

500 5 100

1000 10 100

1000 5 200

1500 10 150

250 5 50

3000 10 300

8000 6750 1600

1250 strb FINAL GG’ 1600ton © Philip Corsano 2014

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

G G’

M

0.781

5.5

8⁰


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 L1 L2

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



•  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.

LBP

ф L1 L2

DRAFT FORE

DRAFT AFT CF

L



•  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.

ф W

G G’ B B’

GML



•  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

ф

L1 L2

CF NEW DRAFT AFT NEW

DRAFT FORE



•  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

ф

L1 L2


DRAFT FORE

W

Fig.1

d



•  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

ф

L1 L2


DRAFT FORE

W

Fig.1

d



•  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

ф L1 L2

CF W

Fig.1

d


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

ф

L1 L2


DRAFT FORE

W

Fig.1

d


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

ф

L1 L2


DRAFT FORE

W

Fig.1

d


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


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.


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.


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


Science

Active management of vessel stability