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Ship's Transverse Stability

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Mohammud Hanif Dewan M.Phil.
Mohammud Hanif Dewan M.Phil.

This document provides definitions and explanations of key concepts related to a ship's transverse stability. It discusses heel and list, stability reference points like the metacenter, center of buoyancy, and center of gravity. It introduces the stability triangle and explains positive, neutral, and negative stability. Key terms are defined, such as displacement, draft, and the laws of buoyancy. Graphs demonstrate concepts like the righting arm curve and how stability changes with angle of heel. The roles of factors like GM, GZ, and the angle of loll in capsizing are also summarized.

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Ship’s Transverse Stability
DEFINITIONS 1. Heel. A ship is said to be heeled when she is inclined by an external force. For example, when the ship is inclined by the action of the waves or wind. 2. List. A ship is said to be listed when she is inclined by forces within the ship. For example, when the ship is inclined by shifting a weight transversely within the ship. This is a fixed angle of heel.
Introduction to Stability CL M G B K BM KM DISPLACEMENT TONS W EIGHT TON S W EIGHT B G
STABILITY The tendency of a ship to rotate one way or the other (to right itself or overturn) INITIAL STABILITY The stability of a ship in the range from 0° to 7°/10° 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.
LAWS OF BUOYANCY  A floating object has the property of buoyancy  A floating body displaces a volume of water equal in weight to the weight of the body.
LAWS OF BUOYANCY • A floating object has the property of buoyancy • A floating body displaces a volume of water equal in weight to the weight of the body. • A body immersed (or floating) in water will be buoyed up by a force equal to the weight of the water displaced.
DISPLACEMENT • The weight of the volume of water that the ship hull is displacing • Units of displacement is metric ton / ton.
DISPLACEMENT 00 G DISPLACEMENT
DISPLACEMENT 04 G B DISPLACEMENT
DISPLACEMENT 09 G B DISPLACEMENT
DISPLACEMENT 16 G B DISPLACEMENT
DISPLACEMENT 20 G B DISPLACEMENT
 Weight : - Gravitational force which direction towards the centre of the earth. Units : tons, pounds, etc • Moment: The tendency of a force to produce rotation about an axis Moment = F x d a d F
2. Stability Reference Points  Metacentre  Gravity  Buoyancy  Keel
STABILITY REFERENCE POINTS CL M G B K etacenter ravity uoyancy eel
STABILITY REFERENCE POINTS CL otherM ooseG eatsB idsK
B WATERLINE RESERVE BUOYANCY B THE CENTER OF BUOYANCY B1
WATERLINE B RESERVE BUOYANCY RESERVE BUOYANCY, FREEBOARD, DRAFT AND DEPTH OF HULL DRAFT FREEBOARD DEPTH
CENTER OF BUOYANCY B WLWL B WL B WL B WL B
CENTER OF BUOYANCY B BB B BB B B B
CENTER OF GRAVITY • Point at which all weights could be concentrated. • Center of gravity of a system of weights is found by taking moments about an assumed center of gravity, moments are summed and divided by the total weight of the system.
G G1 KGo KG1 THE CENTER OF GRAVITY G G1 KGo KG1
MOVEMENTS IN THE CENTER OF GRAVITY G moves towards a weight addition  G moves away from a weight removal G moves in the direction of a weight shift
MOVEMENTS IN THE CENTER OF GRAVITY •G MOVES TOWARDS A WEIGHT ADDITION G G1 KGo KG1
G KGo G1 KG1
MOVEMENTS IN THE CENTER OF GRAVITY  G moves away from a weight removal G G1 KGo KG1
G G G G G G G1 KG1 KGo G
MOVEMENTS IN THE CENTER OF GRAVITY  G moves in the direction of a weight shift G G
G2 G
THE METACENTER CL B B20 B45 M M20 M45 M70 B70 METACENTER M B B1 B2
METACENTER BBBBBBBBB
METACENTER B SHIFTS M
MOVEMENTS OF THE METACENTER The metacenter will change positions in the vertical plane when the ship's displacement changes. the metacenter moves law these two rules: 1. When B moves up M moves down. 2. When B moves down M moves up.
M G B M G B G M B M1 B1 G M B M1 B1 G M B M1 B1 G M B M1 B1 MOVEMENT OF THE METACENTRE
CL B M 0o -7/10o MOVEMENT OF THE METACENTRE
CL B B20 M M20 MOVEMENT OF THE METACENTRE
C L M M20 M45 B B20 B45 MOVEMENT OF THE METACENTRE
CL B B20 B45 M M20 M45 M70 B70 MOVEMENT OF THE METACENTRE
CL M20M45 M70 M90 B B20 B45 B70 B90 M MOVEMENT OF THE METACENTRE
MOVEMENTS OF THE METACENTER The metacenter will change positions in the vertical plane when the ship's displacement changes The metacenter moves law these two rules: 1. when B moves up M moves down. 2. when B moves down M moves up.
G B G M B M1 B1 MOVEMENT OF THE METACENTRE G WHEN BMOVES UPMMOVES DOWN.
GM KG CLK M G B BM KM LINEAR MEASUREMENTS IN STABILITY KB
RECAPITULATION 1. The centre of gravity of a body `G' is the point through which the force of gravity is considered to act vertically downwards with a force equal to the weight of the body. KG is VCG of the ship. 4. KM = KB + BM Also KM = KG + GM 3. To float at rest in still water, a vessel must displace her own weight of water, and the centre of gravity must be in the same vertical line as the centre of buoyancy. 2. The centre of buoyancy `B' is the point through which the force of buoyancy is considered to act vertically upwards with a force equal to the weight of water displaced. It is the centre of gravity of the underwater volume. KB is VCB of the ship.
3. Stability Triangle M G Z
M G Z CL K B G M THE STABILITY TRIANGLE CL K B G M
CL K B G MM CL G B K B1 CL M G B K B1 CL M G B K B1 CL K B G M B1 Z THE STABILITY TRIANGLE
M G Z Sin θ = opp / hyp Where : opposite = GZ hypotenuse = GM Sin θ = GZ / GM GZ = GM x Sin θ Growth of GZ α GM
CL K B G M G1
G M Z G1 Z1  As GM decreases righting arm also decreases Growth of GZ α GM
INITIAL STABILITY G B M 0 - 7°CL
M ZG B B1 CL OVERALL STABILITY RM = GZ x Wf
G B1 M Z G B1 M B G B1 M B THE THREE CONDITIONS OF STABILITY POSITIVE NEUTRAL NEGATIVE
CL K B G M POSITIVE STABILITY
CL K B G M B1 Z POSITIVE STABILITY
CL K B GM NEUTRAL STABILITY
CL K B B1 NEUTRAL STABILITY GM
CL K B G M NEGATIVE STABILITY
CL K B G M B1 NEGATIVE STABILITY
EQUILIBRIUM Stable equilibrium  A ship is said to be in stable equilibrium if, when inclined, she tends to return to the initial position. For this to occur the centre of gravity must be below the metacentre, that is, the ship must have positive initial metacentric height.  The lever GZ is referred to as the righting lever and is the perpendicular distance between the centre of gravity and the vertical through the centre of buoyancy. At a small angle of heel (less than 150 ). GZ = GM sin θ and Moment of Statical Stability = W x GM sin θ  If moments are taken about G there is a moment to return the ship to the upright. This moment is referred to as the Moment of Statical Stability and is equal to the product of the force 'W' and the length of the lever GZ. i.e. Moment of Statical Stability = W x GZ (tonnes-metres).
 When a ship which is inclined to a small angle tends to heel over still further, she is said to be in unstable equilibrium. For this to occur the ship must have a negative GM. Note how G is above M. Figure a shows a ship in unstable equilibrium which has been inclined to a small angle. The moment of statical stability, WGZ, is clearly a capsizing moment which will tend to heel the ship still further. UNSTABLE EQUILIBRIUM Note. A ship having a very small negative initial metacentric height GM need not necessarily capsize. This point will be examined and explained later. This situation produces an angle of loll.
NEUTRAL EQUILIBRIUM  When G coincides with M as shown in Figure a, the ship is said to be in neutral equilibrium, and if inclined to a small angle she will tend to remain at that angle of heel until another external force is applied. The ship has zero GM. Note that KG = KM.  Moment of Statical Stability = W x GZ, but in this case GZ = 0; Moment of Statical Stability = 0 see Figure b. Therefore there is no moment to bring the ship back to the upright or to heel her over still further. The ship will move vertically up and down in the water at the fixed angle of heel until further external or internal forces are applied.
CORRECTING UNSTABLE AND NEUTRAL EQUILIBRIUM When a ship in unstable or neutral equilibrium is to be made stable, the effective centre of gravity of the ship should be lowered. To do this one or more of the following methods may be employed: 1. weights already in the ship may be lowered, 2. weights may be loaded below the centre of gravity of the ship, 3. weights may be discharged from positions above the centre of gravity, or4. free surfaces within the ship may be removed
STIFF AND TENDER SHIPS o The time period of a ship is the time taken by the ship to roll from one side to the other and back again to the initial position. o When a ship has a comparatively large GM, it will thus require larger moments to incline the ship. When inclined she will tend to return more quickly to the initial position. The result is that the ship will have a comparatively short time period, and will roll quickly - and perhaps violently - from side to side. A ship in this condition is said to be `stiff', and such a condition is not desirable. The time period could be as low as 8 seconds. The effective centre of gravity of the ship should be raised within that ship. o When the GM is comparatively small, The ship will thus be much easier to incline and will not tend to return so quickly to the initial position. The time period will be comparatively long and a ship, for example 30 to 35 seconds, in this condition is said to be `tender'. As before, this condition is not desirable and steps should be taken to increase the GM by lowering the effective centre of gravity of the ship.
The officer responsible for loading a ship should aim at a happy medium between these two conditions whereby the ship is neither too stiff nor too tender. A time period of 20 to 25 seconds would generally be acceptable for those on board a ship at sea. WHAT SHOULD THE OFFICER DO?
NEGATIVE GM AND ANGLE OF LOLL It has been shown previously that a ship having a negative initial metacentric height will be unstable when inclined to a small angle. As the angle of heel increases, the centre of buoyancy will move out still further to the low side.
If the centre of buoyancy moves out to a position vertically under G, the capsizing moment will have disappeared as shown in Figure b. The angle of heel at which this occurs is called the angle of loll. It will be noticed that at the angle of loll, the GZ is zero. G remains on the centre line. If the ship is heeled beyond the angle of loll from θ1 to θ2, the centre of buoyancy will move out still further to the low side and there will be a moment to return her to the angle of loll as shown in Figure c.
From this it can be seen that the ship will oscillate about the angle of loll instead of about the vertical. If the centre of buoyancy does not move out far enough to get vertically under G, the ship will capsize. The angle of loll will be to port or starboard and back to port depending on external forces such as wind and waves. There is always the danger that G will rise above M and create a situation of unstable equilibrium. This will cause capsizing of the ship.
GM is crucial to ship stability. The table below shows typical working values for GM for several ship-types all at fully-loaded drafts. The GM value At drafts below the fully-loaded draft, due to KM tending to be larger in value it will be found that corresponding GM values will be higher than those listed in the table above. For all conditions of loading the Tp stipulate that the GM must never be less than 0.15 m.
Body Axis
Curve of Statical Stability
RIGHTINGARMS(FT) ANGLE OF HEEL (DEGREES) 9060300 10 20 40 50 70 80 WL 20° G B Z W L 40° G B Z WL 60° G B Z GZ = 1.4 FT GZ = 2.0 FT GZ = 1 FT RIGHTING ARM CURVE
RIGHTINGARMS(FT) ANGLE OF HEEL (DEGREES) 9060300 10 20 40 50 70 80 WL WL 20° G B Z W L 40° G B Z 60° G B Z GZ = 1.4 FT GZ = 2.0 FT GZ = 1 FT MAXIMUM RIGHTING ARM ANGLE OF MAXIMUM RIGHTING ARM DANGER ANGLE MAXIMUM RANGE OF STABILITY
DRAFT DIAGRAM AND FUNCTIONS OF FORM 17 16 15 14 13 12 11 800 4000 3500 3000 2550 750 700 650 600 550 AFTER DRAFT MARKS (FT) MOMENT TO ALTER TRIM ONE INCH (FOOT-TONS) DISPLACEMENT (TONS) 22.2 22.3 22.4 22.5 22.6 22.7 22.8 TRANSERSE METACENTER ABOVE BOTTOM OF KEEL (FT) 28 29 30 31 32 33 5 4 3 2 1 1 2 3 4 5 11 12 13 14 15 16 17 TONS PER INCH (TONS/IN) LONGITUDINAL CENTER OF BUOYANCY (FEET) FORWARD DRAFT MARKS (FT) CURVE OF CENTER OF FLOTATION 30 20 10 Length Between Draft Marks 397' 0" DRAFT FWD = 14 FT 6 IN DRAFT AFT = 16 FT 3 IN Wo Wo = 3850 TONS KM = TPI = LCB = LCF =MT1" = MT1" 778 FT-TONS/IN KM 22.28 FTTPI 32.7 TONS/IN LCB 3.5 FT AFT LCF 24 FT AFT
FFG 7 CROSS CURVES OF STABILITY CENTER OF GRAVITY ASSUMED 19.0 FT ABOVE THE BASELINE DISPLACEMENT (TONS) RIGHTINGARMS(FT) 3000 3500 4000 4500 40 30 20 15 10 60 5545 50 3.0 2.5 2.0 1.5 1.0 0.5 10o = 15o = 20o = 30o = 40o = 45o = 50o = 55o = 60o = .55 FT .85 FT 1.1 FT 1.73 FT 2.35 FT 2.55 FT 2.6 FT 2.5 FT 2.3 FT
0 1 2 3 4 5 STATICAL STABILITY CURVE PLOTTING SHEET RIGHTINGARMS(FT) 10o = 15o = 20o = 30o = 40o = 45o = 50o = 55o = 60o = .55 FT .85 FT 1.1 FT 1.73 FT 2.35 FT 2.55 FT 2.6 FT 2.5 FT 2.3 FT X X X X X X X X X X 10 20 30 40 50 57.3 60 70 80 90 ANGLE OF INCLINATION - DEGREES

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Ship's Transverse Stability

  • 2. DEFINITIONS 1. Heel. A ship is said to be heeled when she is inclined by an external force. For example, when the ship is inclined by the action of the waves or wind. 2. List. A ship is said to be listed when she is inclined by forces within the ship. For example, when the ship is inclined by shifting a weight transversely within the ship. This is a fixed angle of heel.
  • 4. STABILITY The tendency of a ship to rotate one way or the other (to right itself or overturn) INITIAL STABILITY The stability of a ship in the range from 0° to 7°/10° 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.
  • 5. LAWS OF BUOYANCY  A floating object has the property of buoyancy  A floating body displaces a volume of water equal in weight to the weight of the body.
  • 6. LAWS OF BUOYANCY • A floating object has the property of buoyancy • A floating body displaces a volume of water equal in weight to the weight of the body. • A body immersed (or floating) in water will be buoyed up by a force equal to the weight of the water displaced.
  • 7. DISPLACEMENT • The weight of the volume of water that the ship hull is displacing • Units of displacement is metric ton / ton.
  • 13.  Weight : - Gravitational force which direction towards the centre of the earth. Units : tons, pounds, etc • Moment: The tendency of a force to produce rotation about an axis Moment = F x d a d F
  • 14. 2. Stability Reference Points  Metacentre  Gravity  Buoyancy  Keel
  • 18. WATERLINE B RESERVE BUOYANCY RESERVE BUOYANCY, FREEBOARD, DRAFT AND DEPTH OF HULL DRAFT FREEBOARD DEPTH
  • 21. CENTER OF GRAVITY • Point at which all weights could be concentrated. • Center of gravity of a system of weights is found by taking moments about an assumed center of gravity, moments are summed and divided by the total weight of the system.
  • 22. G G1 KGo KG1 THE CENTER OF GRAVITY G G1 KGo KG1
  • 23. MOVEMENTS IN THE CENTER OF GRAVITY G moves towards a weight addition  G moves away from a weight removal G moves in the direction of a weight shift
  • 24. MOVEMENTS IN THE CENTER OF GRAVITY •G MOVES TOWARDS A WEIGHT ADDITION G G1 KGo KG1
  • 26. MOVEMENTS IN THE CENTER OF GRAVITY  G moves away from a weight removal G G1 KGo KG1
  • 28. MOVEMENTS IN THE CENTER OF GRAVITY  G moves in the direction of a weight shift G G
  • 29. G2 G
  • 33. MOVEMENTS OF THE METACENTER The metacenter will change positions in the vertical plane when the ship's displacement changes. the metacenter moves law these two rules: 1. When B moves up M moves down. 2. When B moves down M moves up.
  • 37. C L M M20 M45 B B20 B45 MOVEMENT OF THE METACENTRE
  • 40. MOVEMENTS OF THE METACENTER The metacenter will change positions in the vertical plane when the ship's displacement changes The metacenter moves law these two rules: 1. when B moves up M moves down. 2. when B moves down M moves up.
  • 41. G B G M B M1 B1 MOVEMENT OF THE METACENTRE G WHEN BMOVES UPMMOVES DOWN.
  • 43. RECAPITULATION 1. The centre of gravity of a body `G' is the point through which the force of gravity is considered to act vertically downwards with a force equal to the weight of the body. KG is VCG of the ship. 4. KM = KB + BM Also KM = KG + GM 3. To float at rest in still water, a vessel must displace her own weight of water, and the centre of gravity must be in the same vertical line as the centre of buoyancy. 2. The centre of buoyancy `B' is the point through which the force of buoyancy is considered to act vertically upwards with a force equal to the weight of water displaced. It is the centre of gravity of the underwater volume. KB is VCB of the ship.
  • 45. M G Z CL K B G M THE STABILITY TRIANGLE CL K B G M
  • 47. M G Z Sin θ = opp / hyp Where : opposite = GZ hypotenuse = GM Sin θ = GZ / GM GZ = GM x Sin θ Growth of GZ α GM
  • 49. G M Z G1 Z1  As GM decreases righting arm also decreases Growth of GZ α GM
  • 52. G B1 M Z G B1 M B G B1 M B THE THREE CONDITIONS OF STABILITY POSITIVE NEUTRAL NEGATIVE
  • 59. EQUILIBRIUM Stable equilibrium  A ship is said to be in stable equilibrium if, when inclined, she tends to return to the initial position. For this to occur the centre of gravity must be below the metacentre, that is, the ship must have positive initial metacentric height.  The lever GZ is referred to as the righting lever and is the perpendicular distance between the centre of gravity and the vertical through the centre of buoyancy. At a small angle of heel (less than 150 ). GZ = GM sin θ and Moment of Statical Stability = W x GM sin θ  If moments are taken about G there is a moment to return the ship to the upright. This moment is referred to as the Moment of Statical Stability and is equal to the product of the force 'W' and the length of the lever GZ. i.e. Moment of Statical Stability = W x GZ (tonnes-metres).
  • 60.  When a ship which is inclined to a small angle tends to heel over still further, she is said to be in unstable equilibrium. For this to occur the ship must have a negative GM. Note how G is above M. Figure a shows a ship in unstable equilibrium which has been inclined to a small angle. The moment of statical stability, WGZ, is clearly a capsizing moment which will tend to heel the ship still further. UNSTABLE EQUILIBRIUM Note. A ship having a very small negative initial metacentric height GM need not necessarily capsize. This point will be examined and explained later. This situation produces an angle of loll.
  • 61. NEUTRAL EQUILIBRIUM  When G coincides with M as shown in Figure a, the ship is said to be in neutral equilibrium, and if inclined to a small angle she will tend to remain at that angle of heel until another external force is applied. The ship has zero GM. Note that KG = KM.  Moment of Statical Stability = W x GZ, but in this case GZ = 0; Moment of Statical Stability = 0 see Figure b. Therefore there is no moment to bring the ship back to the upright or to heel her over still further. The ship will move vertically up and down in the water at the fixed angle of heel until further external or internal forces are applied.
  • 62. CORRECTING UNSTABLE AND NEUTRAL EQUILIBRIUM When a ship in unstable or neutral equilibrium is to be made stable, the effective centre of gravity of the ship should be lowered. To do this one or more of the following methods may be employed: 1. weights already in the ship may be lowered, 2. weights may be loaded below the centre of gravity of the ship, 3. weights may be discharged from positions above the centre of gravity, or4. free surfaces within the ship may be removed
  • 63. STIFF AND TENDER SHIPS o The time period of a ship is the time taken by the ship to roll from one side to the other and back again to the initial position. o When a ship has a comparatively large GM, it will thus require larger moments to incline the ship. When inclined she will tend to return more quickly to the initial position. The result is that the ship will have a comparatively short time period, and will roll quickly - and perhaps violently - from side to side. A ship in this condition is said to be `stiff', and such a condition is not desirable. The time period could be as low as 8 seconds. The effective centre of gravity of the ship should be raised within that ship. o When the GM is comparatively small, The ship will thus be much easier to incline and will not tend to return so quickly to the initial position. The time period will be comparatively long and a ship, for example 30 to 35 seconds, in this condition is said to be `tender'. As before, this condition is not desirable and steps should be taken to increase the GM by lowering the effective centre of gravity of the ship.
  • 64. The officer responsible for loading a ship should aim at a happy medium between these two conditions whereby the ship is neither too stiff nor too tender. A time period of 20 to 25 seconds would generally be acceptable for those on board a ship at sea. WHAT SHOULD THE OFFICER DO?
  • 65. NEGATIVE GM AND ANGLE OF LOLL It has been shown previously that a ship having a negative initial metacentric height will be unstable when inclined to a small angle. As the angle of heel increases, the centre of buoyancy will move out still further to the low side.
  • 66. If the centre of buoyancy moves out to a position vertically under G, the capsizing moment will have disappeared as shown in Figure b. The angle of heel at which this occurs is called the angle of loll. It will be noticed that at the angle of loll, the GZ is zero. G remains on the centre line. If the ship is heeled beyond the angle of loll from θ1 to θ2, the centre of buoyancy will move out still further to the low side and there will be a moment to return her to the angle of loll as shown in Figure c.
  • 67. From this it can be seen that the ship will oscillate about the angle of loll instead of about the vertical. If the centre of buoyancy does not move out far enough to get vertically under G, the ship will capsize. The angle of loll will be to port or starboard and back to port depending on external forces such as wind and waves. There is always the danger that G will rise above M and create a situation of unstable equilibrium. This will cause capsizing of the ship.
  • 68. GM is crucial to ship stability. The table below shows typical working values for GM for several ship-types all at fully-loaded drafts. The GM value At drafts below the fully-loaded draft, due to KM tending to be larger in value it will be found that corresponding GM values will be higher than those listed in the table above. For all conditions of loading the Tp stipulate that the GM must never be less than 0.15 m.
  • 70. Curve of Statical Stability
  • 71. RIGHTINGARMS(FT) ANGLE OF HEEL (DEGREES) 9060300 10 20 40 50 70 80 WL 20° G B Z W L 40° G B Z WL 60° G B Z GZ = 1.4 FT GZ = 2.0 FT GZ = 1 FT RIGHTING ARM CURVE
  • 72. RIGHTINGARMS(FT) ANGLE OF HEEL (DEGREES) 9060300 10 20 40 50 70 80 WL WL 20° G B Z W L 40° G B Z 60° G B Z GZ = 1.4 FT GZ = 2.0 FT GZ = 1 FT MAXIMUM RIGHTING ARM ANGLE OF MAXIMUM RIGHTING ARM DANGER ANGLE MAXIMUM RANGE OF STABILITY
  • 73. DRAFT DIAGRAM AND FUNCTIONS OF FORM 17 16 15 14 13 12 11 800 4000 3500 3000 2550 750 700 650 600 550 AFTER DRAFT MARKS (FT) MOMENT TO ALTER TRIM ONE INCH (FOOT-TONS) DISPLACEMENT (TONS) 22.2 22.3 22.4 22.5 22.6 22.7 22.8 TRANSERSE METACENTER ABOVE BOTTOM OF KEEL (FT) 28 29 30 31 32 33 5 4 3 2 1 1 2 3 4 5 11 12 13 14 15 16 17 TONS PER INCH (TONS/IN) LONGITUDINAL CENTER OF BUOYANCY (FEET) FORWARD DRAFT MARKS (FT) CURVE OF CENTER OF FLOTATION 30 20 10 Length Between Draft Marks 397' 0" DRAFT FWD = 14 FT 6 IN DRAFT AFT = 16 FT 3 IN Wo Wo = 3850 TONS KM = TPI = LCB = LCF =MT1" = MT1" 778 FT-TONS/IN KM 22.28 FTTPI 32.7 TONS/IN LCB 3.5 FT AFT LCF 24 FT AFT
  • 74. FFG 7 CROSS CURVES OF STABILITY CENTER OF GRAVITY ASSUMED 19.0 FT ABOVE THE BASELINE DISPLACEMENT (TONS) RIGHTINGARMS(FT) 3000 3500 4000 4500 40 30 20 15 10 60 5545 50 3.0 2.5 2.0 1.5 1.0 0.5 10o = 15o = 20o = 30o = 40o = 45o = 50o = 55o = 60o = .55 FT .85 FT 1.1 FT 1.73 FT 2.35 FT 2.55 FT 2.6 FT 2.5 FT 2.3 FT
  • 75. 0 1 2 3 4 5 STATICAL STABILITY CURVE PLOTTING SHEET RIGHTINGARMS(FT) 10o = 15o = 20o = 30o = 40o = 45o = 50o = 55o = 60o = .55 FT .85 FT 1.1 FT 1.73 FT 2.35 FT 2.55 FT 2.6 FT 2.5 FT 2.3 FT X X X X X X X X X X 10 20 30 40 50 57.3 60 70 80 90 ANGLE OF INCLINATION - DEGREES