Ship Stability

Ship Stability prepared by: Guided by:

WHAT IS SHIP STABILITY ? 

The ability of the object or vessel to float free on the water surface without sinking and gravitational force acting on it is grater than that of buoyancy force acting on it is called stability of the ship.

Objectives 

Archimedes Principle

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Terminology of ship’s hydrostatics

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Metacenter, Center of Gravity, Center of Buoyancy, couple etc.

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Stability curves

Archimedes Principle 

Law: A body floating or submerged in a fluid is buoyed up by a force equal to the weight of the water it displaces

Archimedes Principle 

Ship sinks until weight of water displaced by the underwater volume is less to the weight of the ship. 

Forces of gravity:

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Forces of buoyancy: B = ρ

Wship = ρ

Vdisplaced

water

G = mshipg =Wship Vdisplaced

water

Archimedes Principle 

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Forces act everywhere on ship -> too tough to analyze Center of Gravity (G): all gravity forces as one force acting downward through ship’s geometric center Center of Buoyancy (B): all buoyancy forces as one force acting upward through underwater geometric center

Archimedes Principle 

Center of Gravity (G): Changes position only by change/shift in mass of ship  Does not change position with movement of ship 

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Center of Buoyancy (B): Changes position G with movement of ship -> underwater geometric center moves  Also affected by displacement 

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Hydrostatics Terminology Displacement: total weight of ship = total

submerged volume of ship (measured in tons) Draft: vertical distance from waterline to keel at deepest point (measured in feet) Reserve Buoyancy: volume of watertight portion of ship above waterline (important factor in ship’s ability to survive flooding) Freeboard: vertical distance from waterline to main deck (rough indication of reserve buoyancy)

Hydrostatics Terminology

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As draft & displacement increase, freeboard and reserve buoyancy decrease

Moments 

Def’n: tendency of a force to produce rotation or to move an object about an axis 

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Distance between the force and axis of rotation is the moment arm

Couple: two forces of equal magnitude in opposite and parallel directions, separated by a perpendicular distance 

G and B are a couple

Moments 

Depending on location of G and B, two types of moments: 

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Righting moment: tends to return ship to upright position Upsetting moment: tends to overturn ship

Magnitude of righting moment:  

RM = W * GZ (ft-tons) GZ: moment arm (ft)

Metacenter 

Define as the intersection of two successive lines of action of the force of buoyancy as ship heels through small angles (M) 

If angle too large, M moves off centerline

Metacentric height 

Ship’s Metacentric height is define as distance from center of gravity (G) to the metacenter is known as the ship’s METACENTRIC HEIGHT(GM)

Metacenter 

Relationship between G and M G under M: ship is stable  G = M: ship neutral  G over M: ship unstable 

STABLE

UNSTABLE

Metacenter v. Stability Curves 

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At this point, we could use lots of trigonometry to determine exact values of forces, etc for all angles -> too much work GM used as a measure of stability up to 7°, after that values of GZ are plotted at successive angles to create the stability curve

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Stability Curve Plot GZ (righting arm) vs. angle of heel

Plot GZ (righting arm) vs. angle of heel

When a series of values for GZ at successive angles of heel are plotted on a graph which result in STABILITY CURVE    

Ship’s G does not change as angle changes Ship’s B always at center of underwater portion of hull Ship’s underwater portion of hull changes as heel angle changes GZ changes as angle changes

Stability Curve

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Conclusi on

Ship stability normally refers to the ability of a floating vessel to resists the overturning forces encountered in the course of its operations. Which is arise from weather, wind, waves etc. Stability calculations solves this forces and apply them in a practical way to a mathematical model of the ship so that the response of the vessel can be examined for various magnitudes of overturning.

Questions ?