# Damage stability calculations

Calculations of stability of damaged ship are complicated and tedious. At present, two different analysis concepts are applied: the deterministic concept and the probabilistic concept. For both concepts, the damage stability calculation shall be made according to the method of lost buoyancy. Unfortunately, the collision resistance is not considered when assessing damage stability and vessels with strengthened side structures are treated in the same way as single-hulled ships.

The damage stability legislation is contained in the following Conventions or related mandatory Codes.

- **Deterministic concept **– This method is based on damage assumptions such as damage length, transverse extent and vertical extent. Depending on the ship type or potential risk to the environment resulting from the type of cargo carried, compliance with a required compartment status must be proved. The deterministic concept applies to chemical and liquefied gas tankers, bulk carriers, offshore supply vessels, high-speed crafts and special-purpose ships.

- **Probabilistic concept** – The new SOLAS 2009 regulations applies for dry cargo ships of 80m in length (L) and upwards and to all passenger vessels with a keel laying date on or after 01.01.2009 respectively for vessels which undergo a major conversion on or after that date. The harmonized regulations on subdivision and damage stability are contained in SOLAS chapter II –1 in parts B-1 through B-4. These regulations use the probability of survival after damage as a measure of ships’ safety in a damaged condition. They are intended to provide ships with a minimum standard of subdivision determined by the required subdivision index R which depends on the ship length and number of passengers. Any assumed damage of arbitrary extent can make a contribution towards establishing of the required subdivision index R. The probability to survive in each case of damage is assessed and the summation of all positive probabilities of survival provides an attained subdivision index A. The attained subdivision index A is to be not less than the required subdivision index R.

Calculations are to be carried out for three initial draughts:

- a deepest subdivision draught without trim,

- a partial subdivision draught without trim,

- a light service draught with a trim level corresponding to that condition.

For each of the three considered draughts the calculated partial index AS, AP and AL shall meet a percentage of the total attained index A. For dry cargo vessels that percentage shall be not less than 0.5R, for passenger vessel 0.9R.

A = 0.4 AS + 0.4AP + 0.2AL