A ship may be damaged at sea due to various reasons such as grounding, collision, acci- dental opening of a sea water inlet valve or an underwater explosion. This causes water entry into compartments which have been damaged occupying spaces which do not hold cargo and replaces the liquids that may be there in such compartments. The unwanted entry of water has the following consequences:
• Sinkage and trim in the final equilibrium condition with loss of freeboard and reserve buoyancy. Could be severe enough causing capsize due to loss of complete reserve buoyancy or progressive flooding through openings on upper deck. • Loss of transverse stability causing loss of static and dynamic stability leading to
capsize.
• Loss of longitudinal stability and excessive trim leading to plunge. • Damage to cargo.
For this reason, it is necessary to contain the extent of water entry due to damage to outer hull. Therefore, a ship is divided into a number of compartments by providing transverse water-tight bulkheads so that the water entry is only in the volume enclosed within the fore and aft bulkheads of the damaged area. If the complete damaged com- partment is at a level below the intact waterline, the entrained water would occupy the entire space of the compartment and this may be treated as an added weight to the ship. There is no free-surface effect of the stability of the ship since the compartment
Wave trough amidships
Calm water
Wave crest amidships
Angle of inclination
Righ
ting ar
m
FIGURE 6.14
would be full of water. However, in a partially flooded compartment, free-surface effect of a flooded compartment needs to be taken into account only if one uses the added weight method of calculation as shown later in this section. For this reason, ships are often provided with water-tight longitudinal bulkhead limiting water entry and free- surface effects. In modern ships there are vertical side tanks as in container ships, tank- ers and bulk carriers or sloping side tanks as in bulk carriers and double bottom tanks. In loaded condition, the ballast tanks are empty and are the first casualty of damage. On the other hand, in ballast voyage the hold space may be flooded. Further, the posi- tion and longitudinal extent of damage determines whether longitudinally one or more compartments have been damaged and also how much unsymmetrical flooding takes place. Thus, the extent and location of damage plays a major role in determining equi- librium and stability in damaged condition. Figure 6.15 shows a damaged ship section indicating unsymmetrical flooding with assumed permeability of various compart- ments which are empty. There is a shift of the transverse centre of gravity (TCG) due to unsymmetrical flooding.
For doing stability calculations in damaged condition, the loading (Δ,LCB,LCF etc.) in the original intact condition and the corresponding equilibrium draught and trim must be known. Then a particular compartment or a group of adjacent compartments may be damaged based on the extent and location of damage. The final equilibrium waterline inside the damaged compartment and outside is the same. There are two alternative methods of calculation of final damaged equilibrium position and stability (Comstock 1967). In lost buoyancy method, damaged compartment(s) is considered open to the sea and, therefore, does not contribute to the total buoyancy of the ship and ship’s weight (or displacement) and CG remains constant. In added weight method, water entering into the damaged compartment is considered as a weight added to the ship, the body remaining intact. Therefore, weight and CG position change and so do buoyancy and CB. For stability
μ = 0.95 φ T2 tcg μ = 0.85 μ = 0.95 μ=0 .95 k9 FIGURE 6.15
calculation, in this procedure, free-surface effects of the damaged compartment have to be considered since this compartment remains a part of the ship.
When a compartment is damaged, the rate of water entry into the damaged compart- ment depends on the amount of tear of the outer hull. So the vessel may take some time to come to final equilibrium position when the water levels outside and inside the com- partment will be the same. During this period, there is only partial water entry into the compartment. In this condition, water level inside the damaged compartment is parallel to but below the outside water level. The stability in this condition may be even worse than in the final equilibrium position. It is necessary to investigate damage stability in partially flooded condition also.
There is a loss of stability due to damage and Figure 6.16 shows a typical intact GZ curve and damaged GZ curve due to flooding and loss of freeboard. It can be seen easily that dynamic stability is greatly impaired and the vessel’s capability to withstand external heeling moment reduces. In some cases, the initial metacentric height may be negative giv- ing an angle of loll (Figure 6.5c) when the vessel heels to an angle for stable equilibrium. Even then both static and dynamic stability are greatly reduced. In extreme cases of exces- sive flooding, such as car deck in a RORO ship, the loss of stability may be total leading to capsize (Figure 6.16 – case of 75 mm freeboard).
If there is unsymmetrical flooding due to damage of side compartments on one side, the vessel attains an initial heel along with loss of stability (Figures 6.5c and 6.15). If the com- partment is far away from midship, there is also large trim. Thus, in trimmed and heeled condition, deck (particularly forward deck) may come under water when openings on deck may take in water causing progressive flooding and ultimately the vessel may cap- size. To avoid such a situation, side tanks are very often cross-connected so that damage of one side may flood both the port and starboard compartments leading to symmetric flood- ing leading to higher sinkage and trim, but less heel. Of course, the intermediate stages of flooding may be critical in such cases since flooding of the cross-connected compartment will have a time lag depending on the cross section of the connecting pipe.
Variation of righting arm with freeboard
amidship For 3.0 m freeboard For 1.6 m freeboard For 75 mm freeboard Degrees heel GZ FIGURE 6.16