Stability Criteria of different Types of vessels

Type of vessel	Code reference	Minimum GM₀	Area under GZ curve up to 40° (or φf)	Area / GZ requirement at heel ≥ 30°	Area 30°–40° (or 30°–φf)	Righting lever (GZ) at specified angles	Range of stability / other limits
Cargo ships ≥ 24 m	Part A, 2.2	≥ 0.15 m	≥ 0.09 m·rad	GZ ≥ 0.20 m at ≥ 30°	≥ 0.03 m·rad	GZmax at angle ≥ 25°	Positive GZ up to φf; weather criterion (2.3) also applies (φ₀ ≤ 16°, area b ≥ area a)
Passenger ships	Part A, 3.1	≥ 0.15 m (per 2.2)	≥ 0.09 m·rad	GZ ≥ 0.20 m at ≥ 30°	≥ 0.03 m·rad	GZmax at ≥ 25°	Heel ≤ 10° from passenger crowding (75 kg/passenger, 4 persons/m²) and ≤ 10° from turning
Oil tankers ≥ 5,000 t dwt	Part A, 3.2	Per MARPOL Annex I reg. 27 (i.e. 2.2 criteria incl. GM ≥ 0.15 m)	≥ 0.09 m·rad	GZ ≥ 0.20 m at ≥ 30°	≥ 0.03 m·rad	GZmax at ≥ 25°	Comply with regulation 27 of Annex I, MARPOL 73/78
Timber deck cargo ships – standard	Part A, 3.3	≥ 0.15 m (per 2.2)	≥ 0.09 m·rad	GZ ≥ 0.20 m at ≥ 30°	≥ 0.03 m·rad	GZmax at ≥ 25°	Weather criterion; 16° steady-wind heel limit (80% deck-edge immersion may be ignored, 3.3.2.4)
Timber deck cargo ships – alternative	Part A, 3.3.2	≥ 0.10 m at all times (incl. water absorption/icing)	≥ 0.08 m·rad (to 40° or flooding angle)	–	–	GZmax ≥ 0.25 m	Cargo full beam, secured at large heel; weather criterion with 16° limit applies
Grain carriers	Part A, 3.4	Per Grain Code (MSC.23(59)): GM ≥ 0.30 m	Per Grain Code: ≥ 0.075 m·rad	–	–	GZmax ≥ 0.12 m at ≥ 12° heel (Grain Code)	Intact stability per International Grain Code
High-speed craft	Part A, 3.5	Per 1994 or 2000 HSC Code	Per HSC Code	Per HSC Code	Per HSC Code	Per HSC Code	1994 HSC Code (built 1996–2002); 2000 HSC Code (built after 1 Jul 2002)
Fishing vessels ≥ 24 m	Part B, 2.1.3	≥ 0.35 m single-deck; ≥ 0.15 m with complete superstructure or L ≥ 70 m	≥ 0.09 m·rad (per A, 2.2.1)	GZ ≥ 0.20 m at ≥ 30° (per A, 2.2.2)	≥ 0.03 m·rad	GZmax at ≥ 25° (per A, 2.2.3); weather criterion optional (45 m+ or reduced P for 24–45 m)	Decked vessels < 30 m: GM_min formula 2.1.5.1
Pontoons	Part B, 2.2	– (no GM criterion)	≥ 0.08 m·rad up to angle of GZmax	–	–	Area measured up to angle of maximum righting lever	Range ≥ 20° (L ≤ 100 m), ≥ 15° (L ≥ 150 m), interpolated between; wind heel (540 Pa) ≤ half freeboard
Containerships > 100 m	Part B, 2.3.2	– (no GM criterion; form factor C governs)	≥ 0.016/C m·rad (to 40° or φf)	GZ ≥ 0.033/C m at ≥ 30°; area to 30° ≥ 0.009/C m·rad	≥ 0.006/C m·rad	GZmax ≥ 0.042/C m; total area to φf ≥ 0.029/C m·rad	May replace Part A, 2.2 criteria
Offshore supply vessels	Part B, 2.4	≥ 0.15 m (per A, 2.2)	≥ 0.09 m·rad	GZ ≥ 0.20 m at ≥ 30°	≥ 0.03 m·rad	GZmax at ≥ 25°	Alternative (2.4.5, ≤ 100 m): area to 15°/30° ≥ 0.07/0.055 m·rad; GZmax at ≥ 15°; min freeboard at stern 0.005 L
Special purpose ships ≥ 500 gt	Part B, 2.5	≥ 0.15 m (per A, 2.2)	≥ 0.09 m·rad	GZ ≥ 0.20 m at ≥ 30°	≥ 0.03 m·rad	GZmax at ≥ 25°	OSV alternative criteria (B, 2.4.5) may be used if < 100 m and similar design
MODUs – surface & self-elevating units	Part B, 2.6.3.1	– (righting moment based)	–	–	–	Righting moment curve positive from upright to second intercept	Area under righting moment curve to 2nd intercept or φf ≥ 1.4 × area under wind heeling curve to same angle (40% excess)
MODUs – column-stabilized units	Part B, 2.6.3.1	– (righting moment based)	–	–	–	Righting moment curve positive from upright to second intercept	Area under righting moment curve to φf ≥ 1.3 × area under wind heeling curve to same angle (30% excess)

Form Factor C for Container Ships

From Part B, 2.3.2.6 of the IS Code:

Formula

$$C = \frac{d \cdot D'}{B_m^2} \sqrt{\frac{d}{KG}} \left( \frac{C_B}{C_W} \right)^2 \sqrt{\frac{100}{L}}$$

Definitions of terms

• d = mean draught (m)
• D′ = moulded depth corrected for volumes within the hatch coamings: $$D' = D + h \left( \frac{2b - B_D}{B_D} \right) \left( \frac{2\, \Sigma l_H}{L} \right)$$
• D = moulded depth of the ship (m)
• B_D = moulded breadth of the ship (m)
• KG = height of the centre of mass above the baseline, corrected for free-surface effect, and not to be taken as less than d (m)
• C_B = block coefficient
• C_W = waterplane coefficient
• l_H = length of each hatch coaming within L/4 forward and aft of amidships (m)
• b = mean width of hatch coamings within L/4 forward and aft of amidships (m)
• h = mean height of hatch coamings within L/4 forward and aft of amidships (m)
• L = length of the ship (m)
• B = breadth of the ship at the waterline (m)
• B_m = breadth of the ship at the waterline at half the mean draught (m)

Purpose:

C accounts for hull form characteristics — draught, depth, beam, fullness (C_B/C_W) and size — that affect resistance to capsizing at large heel angles. It scales the five alternative criteria for containerships > 100 m (e.g. area ≥ 0.016/C m·rad to 40°, GZ ≥ 0.033/C m at 30°, GZmax ≥ 0.042/C m). The shaded volumes in the Code’s figure 2.3-1 represent partial volumes within hatch coamings that contribute righting energy when the ship is on a wave crest.