Ship construction and stability

In short

Ship construction covers how a steel hull is built up from keel, frames, plating, bulkheads and decks so it carries cargo and resists the sea; stability covers whether that hull returns upright after being heeled by wind, waves, cargo shift or flooding. The two are inseparable: subdivision, double bottoms and tank arrangement are construction features whose whole purpose is stability and watertight integrity. For marine engineers this is examined in university Ship Construction and Ship Stability papers, in DG Shipping / MMD Class IV and Class II oral and written examinations, and in GATE-NA type questions on hydrostatics. It is used daily by engineers on board (ballasting, tank soundings, free surface control), by shipyard and design offices (Cochin Shipyard, Mazagon Dock, GRSE, L&T Kattupalli) and by classification surveyors (Indian Register of Shipping, Lloyd's, DNV).

Explained

Hull form, main dimensions and coefficients

• LOA (length overall), LBP (length between perpendiculars, forward perpendicular at the waterline intersection of the stem to the after perpendicular at the rudder stock), beam (B), depth (D) to the uppermost continuous deck, draught (d) keel to waterline, freeboard = D − d measured at the deck line.
• Camber (transverse rise of deck for drainage), sheer (longitudinal rise of deck towards the ends), rise of floor, tumblehome (inward slope of side plating), flare (outward slope forward), bilge radius, parallel middle body.
• Displacement (Δ) = mass of water displaced = mass of ship. Lightship = ship as built with machinery, spares and liquids in systems but no cargo, fuel, stores or crew. Deadweight (DWT) = displacement at load draught − lightship = cargo + fuel + fresh water + ballast + stores + crew.
• Form coefficients at a given draught: block coefficient Cb, midship area coefficient Cm, prismatic coefficient Cp, waterplane coefficient Cw. Full forms (Cb ≈ 0.80-0.85) are tankers and bulk carriers; fine forms (Cb ≈ 0.55-0.65) are container ships and warships.
• TPC (tonnes per centimetre immersion) and MCTC (moment to change trim by one centimetre) are read from hydrostatic curves or the hydrostatic table in the ship's stability booklet.

Structural members and framing systems

• Keel: flat plate keel (common in merchant ships), bar keel or duct keel (a narrow longitudinal passage in the double bottom carrying piping). The centre girder sits on the keel plate; side girders (intercostal) run either side.
• Bottom structure: inner bottom (tank top) plating over a double bottom of floors and girders. Solid plate floors at every frame in way of machinery and bulkheads; bracket floors elsewhere; watertight floors divide double bottom tanks.
• Side structure: shell plating in strakes - garboard strake next to the keel, bilge strake at the turn of the bilge, sheer strake at the deck edge (thickest side strake, highly stressed, rounded or welded gunwale). Frames, tween-deck frames, side stringers, web frames (deep frames at intervals) and panting arrangements forward (panting beams, stringers, deep floors) resist wave pulsation.
• Deck structure: deck plating with stringer plate at the edge, deck beams, deck longitudinals, deck girders and pillars; hatch coamings with stiffeners and deck openings compensated by insert plates and rounded corners to avoid stress concentration.
• Transverse framing: closely spaced transverse frames with few longitudinals - good transverse strength, simple, used in short ships and in the ends of larger ships.
• Longitudinal framing: closely spaced longitudinals supported by widely spaced deep web frames - resists longitudinal bending far better per tonne of steel, so it is used in tankers and bulk carriers.
• Combined (mixed) system: longitudinal framing in deck and bottom (where bending stress is highest) and transverse framing in the sides - the usual arrangement in large ships.
• Stresses the structure must take: longitudinal bending (hogging - crest amidships, deck in tension; sagging - crests at the ends, deck in compression), shear, racking (transverse distortion in a beam sea, resisted by bulkheads and brackets), panting, pounding/slamming forward, torsion (severe in open-deck container ships, resisted by a torsion box), local loads, vibration.
• Welding and materials: mild steel and higher-tensile steel to class rules; butt and fillet welds; crack arrestors, brackets, and the rule that discontinuities (hatch corners, superstructure ends) are rounded and tapered.

Watertight subdivision, tanks and closing appliances

• Collision bulkhead: the foremost watertight bulkhead, taken to the freeboard deck, located within a rule band aft of the forward perpendicular (SOLAS Ch. II-1 limits - typically not less than about 5% of length and not more than about 5% plus 3 m, with variants for bulbous bows).
• After peak bulkhead encloses the stern tube; machinery space bulkheads fore and aft of the engine room. Minimum number of watertight bulkheads increases with ship length and machinery position.
• Double bottom tanks for fuel, fresh water, ballast and lubricating oil; deep tanks, wing tanks, topside tanks (bulk carriers, for grain and trim control), hopper tanks. Cofferdams separate oil from fresh water or cargo.
• Double hull requirement for oil tankers (MARPOL Annex I Regulation 19) and segregated ballast tanks so ballast never touches cargo oil.
• Closing appliances: watertight doors, weathertight hatch covers, air pipes with automatic closing heads, sounding pipes with striker plates, scuppers, non-return valves, and the load line survey items.
• Bulkhead deck / freeboard deck and the margin line (76 mm below the upper surface of the bulkhead deck at side) are reference planes for floodable length and permissible length calculations; permeability (μ) accounts for the volume a flooded space can actually take (about 0.85 for machinery, 0.95 for empty spaces, 0.60 for stores/cargo as a typical set - the booklet values govern).

Statical stability: the fundamentals

• Centre of gravity G: acts down, with weight Δ; position KG above keel and LCG fore-and-aft. Centre of buoyancy B: centroid of the underwater volume, buoyancy acts up; KB, LCB.
• Metacentre M: the point where successive lines of buoyancy action intersect for small angles; KM = KB + BM from hydrostatics, BM = I/V where I is the second moment of area of the waterplane about the centreline and V the displaced volume.
• GM = KM − KG is the metacentric height - the single most important stability number.
  • GM positive → stable, ship returns upright.
  • GM zero → neutral, ship stays at whatever small angle it is pushed to.
  • GM negative → unstable, ship takes an angle of loll until the shifted B gives a righting moment (an unstable ship with symmetrical loading lolls to either side; correction is to lower G, not to add weight on the high side).
• Righting lever GZ = GM sin θ for small angles (up to roughly 7-10°); righting moment = Δ × GZ (t·m).
• Stiff ship: large GM - short rolling period, quick jerky rolls, high accelerations, cargo damage risk. Tender ship: small GM - long easy period, comfortable but slow to right.
• Rolling period T = 2·k/√GM approximately (k = radius of gyration ≈ 0.35-0.40 B) - the basis of the rolling period test to estimate GM on board, valid only in calm water with free rolling.
• Large-angle stability: GZ no longer equals GM sin θ; it is read from cross curves of stability (KN curves) for the displacement, then GZ = KN − KG sin θ. Plotting GZ against θ gives the curve of statical stability, from which are read: initial slope (= GM at 1 radian = 57.3°), maximum GZ and its angle, range of stability, and angle of vanishing stability. The area under the curve is dynamical stability (energy, in t·m·radian).

Effects of loading, free surface and trim

• Shift of weight: loading a mass w at a height d above G shifts G up by GG′ = w·d/(Δ + w); discharging has the opposite sign; a transverse shift gives GG′ = w·d/Δ and heel tan θ = GG′/GM.
• Suspended weight: a load on a crane acts at the head of the derrick/crane, not at its physical position - lifting a weight from the deck instantly raises G to the suspension point and reduces GM.
• Free surface effect (FSE): a partly filled tank lets liquid move; the virtual rise of G is FSC = i·ρ_liquid/(V·ρ_water) or in mass terms FSM/Δ, where i = b³l/12 for a rectangular tank. Key facts: it depends on the cube of the tank breadth, not on the depth of liquid; longitudinal divisions (two divisions reduce FSE to about one-ninth) are the cure; a pressed-up or empty tank has no free surface; GM_fluid (effective GM) = GM_solid − FSC. Ships always quote fluid GM.
• Trim: difference between after and forward draughts. Change of trim = trimming moment / MCTC = w × d / MCTC (cm); the change is apportioned between the ends about the centre of flotation F (centroid of the waterplane): change forward = (distance of F from FP / LBP) × total trim, remainder aft, with the signs set by whether the weight moved forward or aft.
• Loading on or discharging from F changes draught only (by w/TPC) and not trim; this is why the engineer chooses ballast tanks near F for parallel sinkage and tanks at the ends for trim correction.
• Bilging: a holed compartment can be treated by lost buoyancy (preferred - displacement and KG unchanged, waterplane area reduced, so BM and GM fall) or added weight (treat flood water as cargo with a free surface). Bilging an end compartment also changes trim sharply.
• Density and dock water allowance: moving from sea water (1.025 t/m³) to fresh water (1.000 t/m³) the ship sinks; FWA (mm) = Δ/(4 × TPC_sw) and DWA is pro-rated for intermediate dock-water density. Dock water allowance is why a ship may legally submerge its load line in a river berth.

Rules, criteria and Indian practice

• Intact stability criteria (IMO 2008 IS Code, Part A, Chapter 2 - mandatory through SOLAS and the Load Line Convention): area under GZ curve up to 30° ≥ 0.055 m·rad; up to 40° or the angle of flooding (whichever is less) ≥ 0.090 m·rad; between 30° and 40° (or flooding angle) ≥ 0.030 m·rad; GZ at 30° ≥ 0.20 m; maximum GZ at an angle preferably ≥ 30° (not less than 25° in the Code's wording); initial fluid GM ≥ 0.15 m. A severe wind and rolling (weather) criterion applies in addition, and special criteria apply to grain carriage (International Grain Code), timber deck cargoes, passenger ships (crowding and turning heel) and offshore vessels.
• Inclining experiment: required by SOLAS on completion for a new ship and after major alteration; small known weights are shifted transversely in still water with minimal moorings and tanks either empty or pressed up, the heel measured by pendulums or a U-tube, GM found from GM = w·d/(Δ tan θ), then KG = KM − GM and the lightship KG and LCG deduced. A lightweight survey alone may be accepted for a sister ship.
• Damage stability: older deterministic floodable length / factor of subdivision approach; current SOLAS Ch. II-1 (as amended, harmonised from 2009) uses the probabilistic method requiring the attained subdivision index A ≥ required index R, with partial indices for the deepest, partial and light service draughts.
• Load line: the Plimsoll mark and deck line, with seasonal marks TF, F, T, S, W and WNA, assigned under the International Convention on Load Lines 1966 (Protocol 1988) and, in India, the merchant shipping law - the Merchant Shipping Act, 2025, in force from 15 March 2026 and repealing the 1958 Act - with the Merchant Shipping (Load Line) Rules, 2026 made under it (submersion of load lines is an offence under section 122); minimum freeboard ensures reserve buoyancy and adequate stability range.
• Indian regulators and bodies: Directorate General of Shipping (renamed the Directorate General of Maritime Administration, DGMA, in 2026; flag administration, MMD examinations and surveys through Mercantile Marine Departments), Indian Register of Shipping (IRS) as the Indian classification society and an IACS member, Indian Ports Act, 2025 (which replaced the Indian Ports Act, 1908) and the Major Port Authorities Act, 2021 for port matters, and the Indian Maritime University syllabus for the academic coverage. Every ship must carry an approved trim and stability booklet and (since the 2016 SOLAS amendment, with phase-in by ship type) suitable stability information for the master, many ships using approved loading instruments.

Key points

• Displacement - mass of water displaced, equal to the mass of the ship; deadweight is displacement minus lightship.
• Block coefficient Cb - Δ/(L·B·d·ρ); high for tankers and bulkers, low for container ships and warships.
• KM = KB + BM, BM = I/V - purely a function of hull form and draught, independent of loading.
• GM = KM − KG - positive for stability; fluid GM subtracts free surface correction.
• GZ = GM sin θ small angles only; at large angles GZ = KN − KG sin θ from cross curves.
• Righting moment = Δ × GZ; dynamical stability = area under the GZ curve × Δ.
• Free surface effect depends on the cube of tank breadth and not on the amount of liquid; longitudinal subdivision is the remedy.
• Angle of loll - the steady angle of a ship with negative initial GM and symmetrical loading; corrected by lowering G, filling low tanks on the centreline.
• Stiff vs tender - large GM gives short quick rolls; small GM gives long easy rolls.
• TPC - tonnes needed to change mean draught by 1 cm; MCTC - moment to change trim 1 cm.
• Centre of flotation F - weight added at F changes draught only, not trim.
• Transverse framing gives transverse strength; longitudinal framing gives longitudinal strength with less steel; large ships use the combined system.
• Hogging and sagging - the two longitudinal bending conditions; the deck and keel plating carry the highest stress, hence the thick sheer strake and keel.
• Collision bulkhead and after peak bulkhead - mandatory watertight boundaries; double bottom and double hull give flooding and pollution protection.
• IMO 2008 IS Code minima - 0.055, 0.090 and 0.030 m·rad areas, GZ30 ≥ 0.20 m, GM ≥ 0.15 m.
• Inclining experiment - determines the lightship KG and LCG, the base of every later loading calculation.
• Load line marks - TF, F, T, S, W, WNA; FWA = Δ/(4 TPC) mm; dock water allowance is pro-rated.
• Lost buoyancy method - preferred for bilging; GM falls because waterplane inertia falls, not because weight is added.

Formulas and examples

Example 1 - displacement, TPC and KM of a box-shaped barge. A box barge is L = 60 m, B = 12 m, floating at even keel draught 3 m in sea water (1.025 t/m³). KG = 2.8 m.

• V = 60 × 12 × 3 = 2,160 m³ → Δ = 2,160 × 1.025 = 2,214 t.
• A_w = 60 × 12 = 720 m² → TPC = 720 × 1.025/100 = 7.38 t/cm.
• KB = d/2 = 1.5 m; BM = B²/(12d) = 144/36 = 4.0 m; KM = 1.5 + 4.0 = 5.5 m.
• GM = 5.5 − 2.8 = 2.7 m (solid). Rolling period with k = 0.35 × 12 = 4.2 m: T ≈ 2 × 4.2/√2.7 = 8.4/1.643 = 5.1 s - a stiff barge.

Example 2 - free surface effect and heel from a shifted weight. Same barge (Δ = 2,214 t, GM_solid = 2.7 m). A rectangular ballast tank 10 m long × 6 m wide is partly filled with sea water.

• i = l·b³/12 = 10 × 216/12 = 180 m⁴; FSC = i·ρ_l/(V·ρ_w) = 180 × 1.025/(2,160 × 1.025) = 180/2,160 = 0.083 m.
• Fluid GM = 2.7 − 0.083 = 2.617 m.
• Now a 30 t container is shifted 5 m to starboard: GG′ = 30 × 5/2,214 = 0.0678 m.
• tan θ = 0.0678/2.617 = 0.0259 → θ = 1.48° to starboard.
• If instead the tank had been divided by one longitudinal centreline bulkhead, b = 3 m, i = 2 × (10 × 27/12) = 45 m⁴ → FSC = 45/2,160 = 0.021 m, one quarter of the original.

Example 3 - loading a weight: new draught and new KG. A ship displaces 8,000 t at draught 6.40 m, KG = 7.20 m, TPC = 20 t/cm. 400 t of fuel is loaded into a double bottom tank at Kg = 0.80 m.

• Increase in draught = 400/20 = 20 cm → new draught = 6.60 m (TPC taken constant over this small change).
• New Δ = 8,400 t. Moments about the keel: (8,000 × 7.20) + (400 × 0.80) = 57,600 + 320 = 57,920 t·m.
• New KG = 57,920/8,400 = 6.895 m - G has fallen 0.305 m, so GM improves (less any free surface while the tank is being filled).

Example 4 - change of trim. A ship of LBP 120 m has forward draught 5.20 m, aft draught 5.80 m, MCTC = 150 t·m/cm, centre of flotation 54 m forward of the after perpendicular. 120 t of ballast is moved 40 m forward.

• Trimming moment = 120 × 40 = 4,800 t·m → change of trim = 4,800/150 = 32 cm by the head.
• Change forward = 32 × 66/120 = 17.6 cm (increase), using the distance of F from the FP (120 − 54 = 66 m); change aft = 32 × 54/120 = 14.4 cm (decrease). Check: 17.6 + 14.4 = 32 cm.
• New draughts: forward 5.20 + 0.176 = 5.376 m; aft 5.80 − 0.144 = 5.656 m. Trim is now 0.28 m by the stern (was 0.60 m).

Example 5 - GZ curve point and the IS Code check. At Δ = 10,000 t the cross curves give KN = 3.20 m at 30°. The ship's fluid KG = 6.00 m and KM = 7.10 m at this displacement.

• GM = 7.10 − 6.00 = 1.10 m (above the 0.15 m minimum).
• GZ at 30° = KN − KG sin 30° = 3.20 − 6.00 × 0.5 = 3.20 − 3.00 = 0.20 m - exactly the Code minimum of 0.20 m, so the condition is marginal and any extra free surface would fail it.
• Righting moment at 30° = 10,000 × 0.20 = 2,000 t·m.

Where it is used

• Shipbuilding and repair yards: Cochin Shipyard, Mazagon Dock Shipbuilders, Garden Reach Shipbuilders & Engineers, Hindustan Shipyard, L&T Kattupalli - structural drawings, block construction, weld inspection, launching and inclining experiments.
• On board as an engineer officer: ballast and bunker transfer planning to keep fluid GM and trim within the booklet, pressing up tanks before heavy weather, sounding and ullage records, tank top and double bottom inspection for corrosion.
• Deck and cargo operations: loading computers on tankers and bulk carriers checking GM, trim, shear force and bending moment limits; grain stability calculations; container lashing and GM for parametric roll.
• Classification and statutory survey: IRS, Lloyd's Register, DNV, ABS plan approval and survey; DG Shipping / MMD load line and safety construction surveys, special surveys and thickness measurement.
• Design and consultancy: naval architecture offices and the Indian Navy's Directorate of Naval Design - subdivision, damage stability indices A and R, structural scantling to class rules.
• Offshore and inland craft: jack-ups, barges and dredgers (free surface and tow stability), Inland Vessels Act, 2021 vessels on the national waterways.

Interview questions

• Q: What exactly is metacentric height and why does a ship need a positive value? A: GM is the vertical distance from G to the initial metacentre M, GM = KM − KG; if positive, heeling shifts B outboard of G so a righting moment restores the ship upright.
• Q: A ship has a list and a ship has a loll - what is the difference? A: A list is a steady heel from an off-centre G with positive GM and is corrected by shifting weight; a loll is the angle a ship with negative GM settles at under symmetrical loading and is corrected by lowering G.
• Q: Does free surface effect depend on how much liquid is in the tank? A: No - the virtual rise of G depends on the free surface moment, i = l·b³/12, so on tank breadth cubed; a tank 10% full and 90% full give almost the same effect, while empty or pressed-up gives none.
• Q: How would you reduce free surface effect on board? A: Press tanks up or empty them, use as few slack tanks as possible, and rely on the longitudinal subdivisions and swash bulkheads built into the tanks.
• Q: Where would you load a weight if you want to increase draught without changing trim? A: At the centre of flotation - the centroid of the waterplane - since the trimming lever about F is then zero.
• Q: Why is the sheer strake the thickest side plating? A: It lies farthest from the neutral axis at the deck edge, so it carries the highest longitudinal bending stress in hogging and sagging, and it is a point of stress concentration at the deck-side junction.
• Q: Explain hogging and sagging. A: Hogging is a wave crest amidships with the ends unsupported, putting the deck in tension and the keel in compression; sagging is crests at the ends, reversing the stresses.
• Q: Why do large tankers use longitudinal framing in the deck and bottom? A: Longitudinals run in the direction of the bending stress, so they contribute directly to the section modulus and give the required strength with less steel than closely spaced transverse frames.
• Q: What is an inclining experiment and what does it give you? A: Known weights are shifted transversely in still water and the heel measured; GM = w·d/(Δ tan θ), and from KM the lightship KG and LCG are deduced for the stability booklet.
• Q: A ship is stable but rolls very sharply with cargo shifting - what is happening? A: It is stiff, with excessive GM and a short rolling period; raising G sensibly (ballast in higher tanks, heavier cargo up) lengthens the period and reduces accelerations.
• Q: Why is a double bottom fitted and what are the risks it brings? A: It protects against grounding damage and provides ballast and fuel tanks that lower G; the risks are free surface while filling, and corrosion or cracking of the tank top that is hard to inspect.
• Q: What is the lost buoyancy method and why is it preferred for bilging? A: The flooded space is treated as outside the hull, so displacement and KG stay the same and only the waterplane changes; it avoids the free surface and KG bookkeeping that the added weight method requires.
• Q: Give the main IMO intact stability criteria. A: Area under GZ to 30° ≥ 0.055 m·rad, to 40° or the flooding angle ≥ 0.090 m·rad, between 30° and 40° ≥ 0.030 m·rad, GZ at 30° ≥ 0.20 m, maximum GZ preferably beyond 30°, and initial fluid GM ≥ 0.15 m.

Common mistakes

• Using GZ = GM sin θ beyond small angles instead of KN − KG sin θ from the cross curves - it overstates stability badly past about 10°.
• Quoting solid GM when the ship has slack tanks; the figure that matters, and that the booklet and surveyor want, is the fluid GM after the free surface correction.
• Thinking free surface effect grows with the depth of liquid, or that a nearly full tank is safe - it is the breadth cubed that counts.
• Correcting an angle of loll by adding weight on the high side - that can capsize the ship; fill a low centreline tank to lower G first.
• Forgetting that a suspended weight acts at the crane head the instant it leaves the deck, so GM drops immediately.
• Apportioning trim equally forward and aft instead of about the centre of flotation, and losing track of the sign convention for trim by head or stern.
• Mixing up KM (hull form, fixed by draught) with GM (depends on loading), and using an inconsistent displacement when dividing by Δ in shift-of-G or free surface formulas.
• Treating freeboard as a comfort margin rather than as assigned reserve buoyancy under the Load Line rules, and ignoring dock water allowance when loading in a river port.

Related topics

Naval architecture basics · Engine room watchkeeping · Ship safety and fire fighting · Marine hydrodynamics and resistance · Ship design and classification society rules · Cargo handling and ballast water management