SHIP BUOYANCY AND STABILITY

23/11/2017 1Maria Acanfora Ship Buoyancy and Stability

SHIP BUOYANCY AND STABILITY

Lecture 08 – Damaged ship

stability


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)


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).


CollisionTitanic 1912

Cruise ship Explorer 2007


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


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


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



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


Longitudinal Subdivision & Cross-Flooding

Cross- Flooding: See Lecture #9


Permeability• Permeability m represents the percentage of empty space in a

compartment or tank that can be flooded

• Max flooded volume is:


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


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).


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


• Equilibrium floating condition after damage

• GM

• GZ-curve of the damaged ship


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)


0)(

0

WBG

W

Equilibrium equations GM and GZ curve

𝐺𝑀 =𝐼𝑥

𝛻− 𝐵𝐺

𝐺𝑍(𝜙) = 𝐾𝑁(𝜙) − 𝐾𝐺𝑠𝑖𝑛𝜙





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


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!!


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


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


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


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!


𝑀𝑠𝑡(𝜙) = Δ0𝐺𝑍𝐿𝐵(𝜙) 𝑀𝑠𝑡(𝜙) = Δ1𝐺𝑍𝐴𝑊(𝜙)Δ1 = Δ0 + 𝑄

Loss of buoyancy vs. Added Weight


Loss of buoyancy vs. Added Weight


Added water method Loss of Buoyancy method


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.


Water on deck problems


STOCKHOLM AGREEMENT

Water on vehicle deck due to ship damage in wave (or to firefighting water)


Stockholm Agreement


Stockholm Agreement


Stockholm Agreement

Documents

SHIP BUOYANCY AND STABILITY