206 Ship Design for Efficiency and Economy

Appendix

A.1 Stability regulations

Historical perspective: Rahola's criterion

Rahola (1939) analysed statistically accidents caused by defects in stability and included the results in recommendations for `safe stability'. These recommendations are based on the criterion of a degree of dynamic stability up to 40° angle of heel. The dynamic stability can be represented by the area below the stability moment curve, i.e. as the integral of the stability moment over the range of inclination (Fig. A.1). (This quantity equals the mechanical work done, or energy used, in heeling the ship.) If the righting arm h is considered instead of the stability moment MSt, the area below the righting arm curve represents the dynamical lever e. This distance e is identical with the increase in the vertical distance between form and mass centres of gravity in heeled positions (Fig. A.2). e can be found by numerically evaluating the righting arm curve.

Rahola's investigation resulted in the standard requirements:

Other righting levers are seen as equivalent if

Z 40°

e D h d 0:08 m

0

for max 40°, where max is the upper limit of integration (Fig. A.3). Rahola's criterion disregards important characteristics (e.g. seakeeping

behaviour) and was derived for small cargo ships, especially coasters of a type which prevailed in the 1930s in the Baltic Sea. Nevertheless, Rahola's criterion became and still is widely popular with statutory bodies. The Germanischer

210 Ship Design for Efficiency and Economy

Z is the vertical distance from the centre of A to the centre of the underwater lateral area or approximately to a point at T=2 in [m].

1 is the displacement in [t].

The angle 1 [deg.] is calculated as

p

1 D 109 k X1 X2 rs

kfactor as follows:

k D 1:0 for a round-bilged ship having no bilge or bar keels k D 0:7 for a ship having sharp bilges

k according to Table A.1 for a ship having bilge keels, a bar keel or both. Ak is the total overall area of bilge keels, or area of the lateral

projection of the bar keel, or sum of these areas [m2]. X1 factor as shown in Table A.2.

Table A.1 Factor k

X2 factor as shown in Table A.3.

rD 0:73 0:6OG=T

OG is the distance between the centre of gravity and the waterline [m]

Appendix 211

For ships operating in areas where ice accretion is likely, icing allowances should be included in the stability calculations. This concerns particularly cargo ships carrying timber deck cargoes, fishing vessels and dynamically supported crafts.

SOLAS (1974)

The damaged stability characteristics of ships are largely defined in the SOLAS Convention (Safety of Life at Sea) (IMO, 1997). Damaged stability is required for nearly all seagoing ships, either on a deterministic or probabilistic basis. The probabilistic approach requires a subdivision index `A' to be greater than a required minimum value `R'. `A' is the total probability of the ship surviving all damages. A D 6pi si, where pi is the probability that a certain combination of subdivisions is damaged and si is the survivability factor ranging from 0 (no survival) to 1 (survival). In 99% of all damage cases of actual designs, s is either 1 or 0 (Bjorkman,¨ 1995). Sonnenschein and Yang (1993) point out some weaknesses in the SOLAS rules in comparison to U.S. Coast Guard rules. Further discussions of the SOLAS rules, sometimes with examples, are found in Abicht (1988, 1989, 1992) and Gilbert and Card (1990). All ships transporting bulk grain are subject to regulations as documented in Chapter VI of SOLAS (1974), amended in 1994.

MARPOL 73/78

Rule 25 of the MARPOL convention (IMO, 1992) imposes special requirements concerning damage stability for tankers. These requirements are, like some of the SOLAS requirements, probabilistic, but differ in detail; e.g. MARPOL assumes that damage location is as probable everywhere along the ship's length, while SOLAS assumes that damage is more likely in the foreship (Bjorkman,¨ 1995).

National regulations (Germany)

National regulations usually follow the above international regulations, but may impose additional requirements. German rules are given here as an example.

SBG regulations

In 1984 the SBG (Seeberufsgenossenschaft D German Mariners' Association) issued new regulations for intact stability which consider ship type and cargo type (SBG, 1984). These recommendations refer to the righting arm curve. Table A.5 gives the minimum required values.

F0=B 0:1, h30° 0:20 m for F0=B 0:2, linear interpolation in between. F0 is an ideal freeboard, the difference between ideal draught and available

mean draught.

212 Ship Design for Efficiency and Economy

Table A.5 Stability requirements of the SBG for cargo ships (summary)

Passenger ships:

Maximum heel angles are:

10° resulting from passengers crowding to one side

12° resulting from passengers crowding to one side and turning

12° resulting from lateral wind pressure.

The minimum residual freeboard to the bulkhead deck or openable windows must be 0.20 m when the ship is heeled by the above moments. Ships of over 12 m width must show that the lower edges of the windows above the bulkhead deck are not submerged under dynamic wind conditions.

The heeling moment due to passengers crowding on one side assumes 4 persons/m2 for open spaces, otherwise the `most realistic' assumptions, and 750 N per person plus 250 N luggage (50 N for day trips), centre of gravity 1 m above the deck at the side at L=2.

The heeling moment due to turning is as given for the IMO code of intact stability above.

Ships with large wind lateral area, except passenger ships: The heel angle under side wind is to be calculated.

T

MKr D p A lw C

2

p D 0:3 kN/m2 for coastal operation (Bft 9)

p D 0:6 kN/m2 for short-distance operation (Bft 10)

p D 1:0 kN/m2 for middleand long-distance operation (Bft 12)

The heel angle may not exceed 18°. The minimum residual freeboard under heel is 10% of the freeboard for the upright ship.

Further regulations concern tankers, hopper dredgers, ships with self-bailing cockpit or without hatch covers, offshore supply vessels, and heavy cargohandling.

German Navy stability review

All ships (except submarines) in the German navy are subject to a `stability review' in which the lever arm curves of righting and heeling moments are compared for smooth water conditions and in heavy seas (Vogt, 1988). The