# Damage stability Deterministic method

Deterministic Damage Stability

This is a traditional method of assessment of the stability of a ship when it is flooded. In this process, the ship is divided into several subdivisions along its length with the help of transverse watertight bulkheads. Now the stability of the ship is calculated when one or more compartments get flooded due to a breach of hull.

The changes in draft and stability when a compartment becomes flooded due to damage can be investigated by either of two methods:

• Lost Buoyancy method
• Added weight method

Lost Buoyancy method:

The damaged compartment(s) is considered open to the sea and therefore, does not contribute to the buoyancy of the ship. So, the lost buoyancy must be compensated by sinkage of the vessel and the moment due to change in LCB of the vessel is manifested through the heel or trim of the vessel.

The assumptions considered in this method are that the flooded compartment does not provide buoyancy anymore and hence, there is no change in displacement or KG of the vessel and no free surface effect is observed.

This method considers that water ingresses in the damaged compartments up to the new water level and the weight of the ingressed water augments the displacement of the vessel that is compensated by the sinkage of the vessel. Consequently, the KG of the vessel changes due to the weight of ingressed water and Free Surface Effects has to be taken into account, if the compartment is partially filled with water.

The weight added shifts the CG of the vessel that might lead to list or trim of the vessel.

Thus, the two methods act as a twofold assessment of the damaged condition of a vessel. It is actually a good practice to verify the result of the assessment of the damaged condition of the vessel by the complementary method.

Both methods will give identical answers for final draughts, trim and righting moments, despite different values for GM. However, IMO/SOLAS recommends the use of Lost buoyancy method for all calculations.

Deterministic damage stability– An insight to floodable length concept

As we discussed, in deterministic approach the hull is internally subdivided to increase the factor of safety of the vessel in case of hull damage. Now, this subdivision is not arbitrary. It takes a lot of study and analysis balancing both economic and safety needs of the vessel before the designer fixes the subdivision of the vessel. In this approach, the length of this compartment is to be calculated such that if this compartment is flooded, the ship will sink to a point where margin line is just submerged. This is the floodable length at a point along the length of the ship.

The subdivisions accordingly resist flooding in damaged conditions to the safest limits. Floodable Length is an important parameter that is taken into account here. It is defined as the maximum length of the compartment that can be flooded such that the draft of the ship remains below the margin line. Thus, the maximum division of bulkheads is the best solution. But, other factors such as minimum required size of hold, improper cargo stowage, and the number of required outfitting or increased steel weight hinders the possibility to some extent. Thus, optimizing the safe limits of floodable length to the minimum required length of the watertight compartment is done in most cases