SHIP BUOYANCY AND STABILITY
Transcript of SHIP BUOYANCY AND STABILITY
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SHIP BUOYANCY AND STABILITY
Lecture 08 – Damaged ship
stability
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Following lecturers
• Preparation for the laboratory test
• Dynamic stability
• Second generation of intact stability criteria
• Ship Damage Stability I
General
Loss of buoyancy method
Added weight method
Water on deck (Stockholm agreement)
• Stability special topics
• Introduction
• Ship equilibrium and introduction to hydrostatics
• Ship initial Stability
• The stability curve (GZ curve)
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Damaged ship
A ship is said to be damaged when due to external causes it has a breach in the hull and water can flood in.
• Flooding can be caused by:
- Collision (with another ship, structure or iceberg);
- Grounding;
- Damage to hull (bow door, sea chest, etc.);
- Explosions (navy ships mainly).
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CollisionTitanic 1912
Cruise ship Explorer 2007
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GroundingSally Albatros 1994
Costa Concordia 2012
Exxon Valdez 1989
Oil spill disaster after grounding. The tanker leakeda devasting amount of toxic crude oil in the water.Improvement to the subdivisions of crude oilcarrier MARPOL 73/78
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Damage to hullHerald of Free Enterprise 1987
MV Estonia 1994
• SOLAS convention started in 1929, after Titanic sinking.
• In 1960 it was updated after Andrea Doria sank
• SOLAS 1974 – Major Revision
• SOLAS 90/95 – ”Stockholm Agreement introduction”, after Estonia andEnterprice accidents
• SOLAS 2009 – Probabilistic Damage stability rules
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ExplosionUSS Cole 2000
These are just few examples of damaged ships. Damage stability rules and damagestability research aim to reduce the risk of damage and to minimize the consequences
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Compartment Subdivision• Subdivision means subdividing the ship into compartments with watertight bulkheads.
• Watertight bulkheads are limited to the bulkhead deck
• Subdivision is mainly transversal, but also longitudinal
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Longitudinal Subdivision & Cross-Flooding
Cross- Flooding: See Lecture #9
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Permeability• Permeability m represents the percentage of empty space in a
compartment or tank that can be flooded
• Max flooded volume is:
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Permeability
• When liquid loads are considered for the intact ship, the steel reduction (typically 2%) isaccounted
• However in damage calculation, the permeability (0.95 for tanks i.e. 5% of reduction) isused
• Thus when a full ballast tank is damaged, the draft will decrease and trim will change
• NOTE: damage stability calculations are normally performed for a dry ship
• In case of cargo hold of bulk carrier is it possible to use a variable permeability aboveand below the cargo level
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Margin Line• An imaginary line 76 mm below the bulkhead deck
• It was required that at the final equilibrium condition after damage the margin line was not submerged
• Nowadays margin line verification is obsolete due to the new SOLAS rules (2009).
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Floodable Length• It is the maximum length that a damage can have, without immerging the
margin line. This is carried out at any point of the ship. The vertical extent of the damage is limited to the margin line
• In other words: how long a damage can extend without compromising the floatability of a ship?
• The largest allowed length of the flooded compartment is referred to as floodable length
• As for the margin line, also this approach is obsolete. However floodable length curves are still useful sometimes at the initial design stage
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• Equilibrium floating condition after damage
• GM
• GZ-curve of the damaged ship
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The calculation of ship equilibrium and stability parameters can be carriedout according to two different approaches. The loss of buoyancy method(i.e. constant weight/displacement method) or the added weight method(i.e. adding the amount of flooded water to the displacement)
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0)(
0
WBG
W
Equilibrium equations GM and GZ curve
𝐺𝑀 =𝐼𝑥
𝛻− 𝐵𝐺
𝐺𝑍(𝜙) = 𝐾𝑁(𝜙) − 𝐾𝐺𝑠𝑖𝑛𝜙
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Loss of buoyancy method
In general it is an
iterative procedure to
find the final equilibrium
after damage! There are:
• an increase in draft,
• a change in buoyancy
• a change in trim
They are linked together
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Metacentric radius L. o. B.• The main problem in evaluating the metacentric radius is in calculating the
new moment of the inertia of the waterplane area!
The moments of inertia modify. If 𝐼𝑥𝑦1 ≠ 0 we
need to rotate the axis (by means of a), since they are not central axis of inertia!!
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Center of buoyancy L. o. B.
The metacentric height changes because of the change of the waterplane area and because of the change in center of buoyancy
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Added weight method• Floodwater is treated as liquid cargo!
• Remember that:
Ship displacement increase due to the flooded water
Center of gravity will change as well
Ship draft will increase due to the larger displacement (but the waterplanearea is equal to the intact ship)
Center of buoyancy will change accordingly
Δ1 = Δ0 + 𝑄
(G1−O)Δ1 = (G0 − O)Δ0+(𝐺𝑤 − 𝑂)𝑄
𝐺1
𝐺0
𝐺𝑤
𝑂
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Added weight method- equilibrium iteration
Initial condition before damage (f0; q0; 0 T0 B0=(xb0, yb0, zb0)
Calculate the flooded volume of the
compartment Vwi
Calculate the variation in draftof the ship dTi (assuming notrim change) due to thechange in the displacementdue to added water (subroutine to
adjust the draft to the properdisplacement)
Calculate the new center of buoyancy (xb(i), yb(i), zb(i))
If the longitudinal and thetransversal coordinate ofthe center of buoyancydon’t change (xb(i)=xb(i-1);yb(i)=yb(i-1)) then the newequilibrium is found
If the transversal and/or thelongitudinal coordinate thecenter of buoyancy change thenthe ship will modify her heeland/or trim. Then calculate thenew heel and or/trim.
fi-1 qi-1 i 0 +gVwi
Ti=Ti-1 dTi
Bi=(xb(i-1), yb(i-1), zb(i))
If the flooded volume of thecompartment doesn’t changeVwi=Vwi-1, then the newequilibrium is found
f1 q1 i 0
Ti=Ti-1 dTi
Bi=(xb(i), yb(i), zb(i))
If the flooded volume changes Vwi≠Vwi-1, then
restart the routine!
damage
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Metacentric height (A.W)
𝐺𝑀0 = 𝐾𝐵0 + 𝐵𝑀0 − 𝐾𝐺0
𝛿𝐺𝑀 = 𝛿𝐾𝐵 + 𝛿𝐾𝐺 + 𝛿𝐵𝑀
The waterplane area remain as intact,and it modifies according to the finalequilibrium after damage.The metacentric radius changeaccordingly
The center of buoyancy changesdue to the change in finalequilibrium condition (draft, heeltrim). But is carried out on theintact hull
The center of gravitychanges due to the loadedflooded water
Since a liquid cargo is loaded, the
metacentric height has to be
reduced by freesurface effects!
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𝑀𝑠𝑡(𝜙) = Δ0𝐺𝑍𝐿𝐵(𝜙) 𝑀𝑠𝑡(𝜙) = Δ1𝐺𝑍𝐴𝑊(𝜙)Δ1 = Δ0 + 𝑄
Loss of buoyancy vs. Added Weight
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Deterministic Damage stability• It is generally required to carry out verification on the GZ curve and on the
GM after damage, for several loading conditions and for several damagescenarios.
• The deterministic damage stability approach is based on standarddimensions of damage extending anywhere along the ship's length orbetween transverse bulkheads.
• Although it has been replaced by the probabilistic damage stability in manycases, it is still possible to apply it.
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STOCKHOLM AGREEMENT
Water on vehicle deck due to ship damage in wave (or to firefighting water)