• The shipowner sends a request to the classification society surveyor, indicating the intention to perform an underwater survey.
• A detailed plan of the ship's external hull features is submitted, showing the location of frames, bulkheads, welding lines, openings, etc.
• The hull surface is cleaned before the survey to remove any marine growth or fouling that could obscure the inspection.
• A diving company, approved by the classification society, is appointed to conduct the underwater inspection.

A self-propelled survey vehicle equipped with the following tools is used:

• Long-Range Light TV Camera to aid in steering and checking hull deterioration.
• High-resolution colour TV Camera to provide a close-up view of the hull coating and welded seams.
• 35mm Still Camera to capture still images.
• Ultrasonic Probe for measuring plate thickness.
• Depth Meter and Speed Indicator to provide accurate data on the vehicle's depth and movement.
• Umbilical Cable to connect the survey vehicle to the survey boat, transmitting power and information.

The survey boat is to be equipped with:

• A control console with TV monitors.
• Plate thickness printouts.
• Audio and video cassette recorders.
• Playback units.
• Diver communication systems.
• Vehicle control systems and associated instruments.

Operation:

• The survey vehicle is taken underwater by a diver to the survey starting point.
• Using TV monitors and shell expansion plans as guides, the vehicle is navigated over the hull, focusing on the bottom structure, sides, stern frame, rudder, propeller, bilge keel, and hull openings.
• All images, data, and information are recorded and transmitted back to the survey boat.
• Detailed pictures of the stern frame, rudder, propeller, bilge keel, and hull openings are captured.
• Divers are deployed to measure stern tube bearing wear, pintle clearance, and inspect stern seals, anodes, and rudder stock palm coupling bolts.
• All recorded video and audio, including conversations between the surveyor and drivers, thickness printouts, measurements, and pictures are analyzed to determine the detailed underwater condition of the vessel.

The vessel's owner submits a request to the surveyor, including:

• The proposed date and location for the survey.
• General information about the diving company.
• A declaration that the vessel has not suffered any damage due to grounding, collision, or other incidents.

The ship's master or owner’s representative must provide a declaration confirming:

• Any suspected or actual damage to the hull since the last dry-docking.
• The underwater portion of the hull is protected by a suitable paint scheme that is of adequate thickness and remains valid until the next dry-dock.

• The survey site should be in a protected area with calm and clear water, ensuring good underwater visibility. Attention must be given to the effects of currents and tides.
• The hull must be clean for the external survey. The surveyor must be satisfied with the method and quality of the pictorial presentation, ensuring that it provides a reliable assessment of the hull's condition.
• The underwater examination should be conducted by an approved diving company using closed-circuit TV and two-way communication, which can be monitored by the surveyor.
• The vessel should be in as light an operating condition as possible to facilitate the survey.
• Means must be available for the surveyor to examine the outside shell plating above the waterline.
• Any required repairs identified during the survey must be carried out to the satisfaction of the attending surveyor.

• Underwater Hull: General condition of the hull below the waterline.
• Bottom and Shell Plating: Inspection for corrosion, damage, and fouling.
• Shell Openings: Examination of openings such as sea chests, drain plugs, and overboard discharge points.
• Stern Tube Oil Leaks: Check for leaks around the stern tube.
• Propeller Blade: Inspection for damage, wear, and fouling.
• Rudder: Inspection for damage, wear, and clearances.
• Sea Chest Opening and Grating: Examination for blockages, damage, and fouling.
• Anodes: Check the condition and effectiveness of cathodic protection anodes.
• Bilge Keel: Inspection for damage and fouling.
• Drain Plugs: Ensure all drain plugs are secure and in good condition.
• Overboard Valve Openings: Check for proper operation and condition.
• Forward Area: Inspection for any damage due to anchor and chain movement.

If a ship is seriously damaged underwater in the area of a large fuel oil side bunker tank, it will cause the following:

Bilging or Flooding of the Compartment:

• Water will enter the damaged bunker tank, reaching the draught level.
• The rate of flooding depends on the size of the breach and the water pressure at the depth of the damage.

Oil Leakage into the Sea:

• If the tank contains fuel oil, oil will begin to leak out, causing pollution.
• The extent of leakage depends on the tank’s contents (empty, half-full, or full) and the location of the damage.

List and Trim of the Vessel:

• The ingress of water and loss of oil will create an imbalance, causing the vessel to list or trim.

If corrective actions are not taken, uncontrolled flooding and loss of stability could lead to capsizing or sinking of the vessel.

Features in the Ship to Enhance Safety:

• Small Bunker Tank Sizes reduces the risk of extensive oil spillage and loss of stability.
• Connectivity to transfer pumps allows the transfer of oil from the damaged tank to an empty tank, minimizing oil spillage and counteracting the loss of stability.
• The tank’s size and location are designed to limit the effects of flooding, as per damage stability regulations.
• Properly positioned transverse and longitudinal bulkheads enhance the subdivision factor, limiting water ingress to the damaged tank.
• Ship’s Ballast System allows corrective ballasting to counteract the list or trim caused by the ingress of water.
• Watertight Doors and Hatches prevent water from spreading to adjacent compartments.

Recommended Immediate Actions by Crew:

For Empty Tanks:

• Quickly seal off the damaged tank by shutting all valves and isolating it from the transfer system to prevent water ingress into other parts of the vessel.

For Half-Empty or Full Tanks:

• Initiate oil transfer to another empty tank to reduce oil leakage and stabilize the ship.
• Monitor the water ingress and ensure the tank is filled to the draught level with seawater if necessary, using ballast to correct the list.

• The deck plating is made thicker and uses higher tensile steel to withstand stresses caused by wide hatch openings and operational loads.

• The deck, side shell, and longitudinal bulkheads are framed longitudinally. This arrangement combined with deep double bottom helps resist bending stresses due to hogging (upward bending) and sagging (downward bending) when the ship is under load.

• The hatch coamings are made continuous to contribute to the overall longitudinal strength of the hull.

• A torsion box is installed, running along the entire length of the ship from the machinery space bulkhead to the forward collision bulkhead. This structure provides the necessary torsional strength to counteract twisting forces acting on the hull during operation.

• Deep web boxes are fitted at the ends of hatches, both at tank top and deck levels, to enhance transverse and torsional strength.

• A deep double bottom is designed to withstand uplift forces caused by water pressure, especially when the ship is deeply loaded. It also provides additional strength to the hull structure.

• Side girders are placed under container cells, with added transverse local stiffening. These elements distribute the concentrated loads from containers and increase overall stability.

The Energy Efficiency Design Index (EEDI) expresses the grams of CO2 emitted per tonne of cargo transported per nautical mile. Its level is directly proportional to the fuel consumed (and hence the propulsive power required) at the design speed, divided by the cargo capacity and speed. Anything that cuts the power needed to move a given deadweight at the design speed, or that raises propulsive efficiency, lowers the EEDI. The three methods below act on exactly those levers.

A fine hull with a low block coefficient (Cb) presents less displaced volume for a given length and thus a smaller wetted surface area, reducing the frictional resistance component at a given displacement. A fine (low Cb) forebody and afterbody also weaken the bow wave and the pressure (residual or wave-making) resistance at the design speed, because the water is pushed aside more gradually. Lower residual resistance means the installed propulsive power at the design speed is less, so less fuel is burnt per tonne-mile, lowering the EEDI. Being longer and narrower for the same displacement also raises waterline length, which reduces the length-related frictional and Froude-number-dependent resistance. The penalty is reduced cubic cargo capacity and somewhat less form stability, so the hull form is optimised rather than simply fined down. Lower block coefficient is therefore one of the strongest design levers for meeting EEDI limits.

A long-stroke (high stroke-to-bore ratio) slow-speed diesel extracts more work from each unit of fuel in the expansion stroke and achieves higher thermal (brake) efficiency, typically up to about 50 per cent, with a correspondingly lower specific fuel consumption per kWh. Because the stroke is long, the engine can turn slowly at the same piston speed, enabling direct coupling to a large slow-turning propeller with no reduction gearbox and no associated transmission losses. A more efficient engine burns less fuel for each kW it delivers, hence produces less CO2 per tonne-mile, which reduces the attained EEDI directly. Long-stroke engines also operate at low revolutions, which marries perfectly with the large-diameter, low-rev propeller of part (c).

Propeller open-water efficiency rises as the disc-area loading (thrust per unit swept area) falls. A large-diameter propeller turning slowly accelerates a large mass of water by a small amount, giving low disc loading and high efficiency for the same thrust and therefore less shaft power and less fuel per tonne of cargo. Large slow propellers also stay further away from cavitation, reducing blade erosion, vibration and noise. Because EEDI is fixed by the fuel (shaft power) needed at the design speed, optimising hull, engine and propeller together — a fine low-block hull at a low Froude number, a long-stroke low-speed engine, and a large-diameter low-rev propeller — minimises energy consumption per tonne of cargo and is the classic route to satisfying EEDI limitations.

are significant and arise due to various factors:

• Galvanic corrosion occurs due to the interaction between dissimilar metals, accelerated by the seawater environment and differential aeration.
• Sulphate-reducing bacteria in river mud can cause localized pitting, leading to penetration of the bottom shell.
• Dissolved oxygen in seawater reacts with metal surfaces to form rust, significantly contributing to structural deterioration.
• The rate of corrosion peaks at a 3.5% salt concentration, typical of seawater.
• Neglecting maintenance exacerbates the problem, allowing corrosion to progress unchecked.

(ii) Protection against extensive corrosion in ballast tanks involves the following measures:

• Complete coating of the tank surfaces with properly selected marine-grade paint to create a protective barrier.
• Installation of sacrificial anodes, designed to corrode preferentially and protect the tank structure.
• Using large anodes with greater volume relative to surface area to ensure extended protection.
• Regular gauging of plates to assess thickness and identify areas requiring reinforcement or repair.
• Conducting regular inspections, cleaning the tanks, removing rust, and repainting to maintain structural integrity and prolong the lifespan of the ballast tanks.

The angle of loll is the angle of heel at which a ship with negative initial metacentric height (negative GM) comes to rest in still water, without any external heeling force such as wind, waves, or turning.

When a vessel has negative GM, it is unstable in the upright position because the centre of gravity (G) lies above the metacentre (M). As a result, any small disturbance causes the vessel to heel further instead of returning upright.

As the vessel heels, the centre of buoyancy (B) moves outboard towards the lower side. At a certain angle of heel, the line of action of buoyancy passes vertically through the centre of gravity (G), producing a small positive righting lever. The vessel then comes to rest at this angle, known as the angle of loll.

The ship may remain at this angle on either side and can suddenly loll or flop from one side to the other when disturbed by wind, waves, turning, or other external forces.

Dangers Posed by an Angle of Loll

1. False sense of stability: Although the vessel appears to be stable because it remains at a constant angle of heel, it is actually in a dangerous condition with negative GM.
2. Sudden lolling or flopping: The vessel may suddenly and violently swing from the angle of loll on one side to the same angle on the opposite side with little or no warning, especially when affected by beam seas, wind gusts, or turning.
3. Reduced range of stability: The remaining range of positive righting lever is much smaller than normal. Consequently, even a relatively small additional heeling moment can cause the vessel to capsize.
4. Risk due to free surface effect: Slack tanks further reduce the effective GM. Incorrect attempts to correct the condition, such as pumping ballast to one side or leaving tanks partially filled, increase the free surface effect and may worsen the angle of loll or even lead to capsize.
5. Danger of capsize: If the vessel heels beyond the point where the righting arm again becomes zero (the point of vanishing stability), it will capsize.
6. Oscillation about the angle of loll: Instead of rolling about the upright position, the vessel oscillates about the angle of loll, indicating that it is in an unstable equilibrium.

Corrective Actions

• Do not attempt to correct the angle of loll by shifting ballast or cargo transversely, as this may cause the vessel to suddenly flop to the opposite side and worsen the condition.
• The correct method is to lower the centre of gravity (G) and restore positive GM by:
  • Eliminating free surface effects by pressing tanks either completely full or completely empty (avoid slack tanks).
  • Pressing up double-bottom tanks to add weight low down and lower the centre of gravity.
• Once positive GM is restored, the vessel will return to the upright position and regain true stability.

Frictional (skin) resistance is caused by the shearing of water over the hull surface. The important factors are:

• Speed (V): within normal service ranges frictional resistance rises approximately as V^1.8 to V^1.85, so speed strongly increases resistance.
• Wetted surface area (S): the larger the wetted hull area the higher the resistance; it depends on length, breadth, draught, displacement and fullness of the ends.
• Surface roughness and fouling: marine growth (barnacles, slime), corrosion pitting, weld beads, protruding plating and deteriorated antifouling all raise the friction coefficient sharply. Regular hull cleaning and good antifouling coatings reduce this.
• Density of the water: resistance is proportional to density, so it is higher in sea water than in fresh water.
• Viscosity and temperature: cooler, more viscous water gives a slightly higher frictional coefficient.
• Hull length: the frictional coefficient varies with the length and Reynolds number.

The formula used is the frictional resistance line. In Admiralty-style form:

Rf = f and S and V^n

or the simplified relation R = 0.45 S V^1.83 (newtons)

Where f is the frictional coefficient, S the wetted surface area (m2) and V the ship speed. Modern practice uses the ITTC 1957 friction line, Rf = 0.5 Cf rho S V^2, where Cf = 0.075/(log10 Re - 2)^2 and Re is the Reynolds number; this permits accurate model-ship scaling.

Data: displacement Delta=12000 t; rudder area A=15 m2; rudder centre 5 m below the waterline; GM=0.3 m; centre of buoyancy 3.3 m below the waterline; speed 20 knots; helm angle alpha=30 deg; apply 20% race allowance.

Speed converted: v=20 x 0.5144 = 10.29 m/s, so v2=105.84.

Normal rudder force Fn=577 A v2 sin(alpha) = 577 x 15 x 105.84 x 0.5 = 458,035 N.

Race effect (propeller race increases water velocity over the rudder) 20%: F=1.2 x 458,035 = 549,642 N.

The heeling couple is the force times its lever about the centre of lateral resistance, taken as the vertical distance of the rudder centre below the waterline, lever=5 m:

Heeling moment = 549,642 x 5 = 2,748,210 Nm.

Balancing against the ship's righting moment (displacement as a weight, W=12000 tonne-force):

tan(theta) = (F x lever)/(W x GM) = (549,642 x 5)/(12000 x 9810 x 0.3) = 2,748,210/35,316,000 = 0.07782.

Hence theta = atan(0.07782) = 4.45 deg.

Answer: the initial angle of heel is about 4.5 deg towards the rudder (outboard) side.

A tender ship has a small metacentric height and a long, slow roll period, giving uncomfortable motion, risk of rolling in resonance and reduced stability reserve. Pressing up (filling completely and venting air from) the double-bottom tanks achieves several things:

• It lowers the centre of gravity of the ship. Water ballast occupies the very low double-bottom, so its addition lowers KG, which increases GM and makes the ship stiffer and more quickly self-righting.
• It removes the free surface effect. A completely full tank (no free liquid surface) contributes no loss of GM, whereas a part-full tank produces a free-surface effect that reduces effective GM. In a tender ship this loss of margin can be dangerous, so tanks are pressed up to eliminate it.
• It improves stability in that the weight is concentrated low and centrally, and it reduces the free-surface damage risk when other tanks are used.
• Pressing up the double-bottom tanks also lowers the centre of buoyancy proportion and helps trim/heel correction and, because the tanks are deep (low) and of small individual breadth, even when ballasting the free-surface effect is small.

Hence for a tender ship ensuring double-bottom tanks are pressed up restores an adequate, safe GM and a more comfortable, lower-amplitude roll.

For geometrically similar ships, the linear scale is the cube root of the displacement ratio:

Linear scale = (2000/6000)^(1/3) = (1/3)^(1/3) = 0.6934.

Speed scales as the square root of the linear dimension: V2 = V1 x sqrt(scale) = 15 x sqrt(0.6934) = 15 x 0.8326 = 12.49 knots. Answer: speed of the 2000 tonne ship is about 12.5 knots.

Wetted surface area scales as the square of the linear dimension:

S2 = S1 x scale^2 = 2500 x (0.6934)^2 = 2500 x 0.4808 = 1202 m2. Answer: wetted surface area about 1202 m2.

Skin resistance R = 0.45 S V^1.83 N, taking V in knots and S in m2:

R = 0.45 x 2500 x 15^1.83.

15^1.83 = 141.9, so R = 0.45 x 2500 x 141.9 = 159,700 N.

Answer: resistance of the 6000 tonne ship is about 160 kN.

When a tank is part-full the free liquid surface is able to move as the ship heels, transferring liquid to the low side. This makes the centre of gravity of the tank's contents shift towards the low side, creating an additional heeling (virtually raising the centre of gravity) and thereby reducing the effective metacentric height. The loss of GM is:

reduction in GM = rho_liquid x i / Delta

where i is the second moment of area of the free liquid surface about its longitudinal centroidal axis (i = L B^3/12 for a rectangular surface) and Delta the ship displacement. The free-surface effect:

• is independent of the quantity of liquid, depending only on the shape (area and breadth) of the free surface, so even a small amount can be damaging;
• is proportional to the cube of the tank breadth, so wide tanks have the largest effect;
• is eliminated when the tank is completely full (pressed up) or completely empty;
• is a virtual loss of GM and does not affect the true KG, appearing as a reduction of effective GM and of righting levers (GZ).

It must therefore be taken into account in the metacentric and cross-curves, usually by reducing GM by the free-surface correction. In practice tanks are divided with longitudinal bulkheads (wash/centreline bulkheads) to reduce the breadth i, and press up or strip out tanks when the free surface is significant.

Box barge 45 m long, 15 m wide, floats at a level keel draught of 2 m in sea water, load uniformly distributed over the full length. Two 30 tonne masses are loaded at 10 m from each end, and 50 tonne distributed evenly between them.

Buoyancy per metre, uniform over the full length: the box displaces LB.d.rho = 45x15x2 = 1350 m3 = 1350 x 1.025 = 1383.75 t. Buoyancy per metre b = 1383.75/45 = 30.75 t/m.

Weights:

Uniform (still floating hull and level-keel load) weight per metre w0 = 30.75 t/m (to give even keel before adding the point masses). The three added loads are then point loads.

The two 30 t masses at 10 m from ends and the 50 t at the middle (evenly distributed across the central 25 m length at 50/25 = 2 t/m between x=10m and x=35m). Shear force is the algebraic sum of the net load (weight - buoyancy) to one side.

For x from 0 to 10 m: only the uniform base load acts; since w0 balances b with no net load, the shear is essentially from the base alone - shear = 0 over the ends and the net jumps occur at the point loads.

Treated as a simply supported beam on uniform buoyancy with load diagram:

Net point loads cause shear jumps: at x=10 m a downward 30 t (jump in SF = -30 t); distributed 2 t/m over 10-35 m adds slope; at 35 m end of distributed load the accumulated shear returns and the symmetric load at 45-10=35m balances.

By symmetry, the maximum shear force occurs adjacent to one of the 30 t end masses. Consider the left side: total buoyancy of the left 10 m strip = 10 x 30.75 = 307.5 t; total weight of left 10 m (uniform base) = 10 x 30.75 = 307.5 t, so they exactly balance and the shear due to the base over the outer 10 m is zero. The net load diagram is therefore a series of point/partial loads sitting on an exactly balanced uniform basis.

Loaded mass summary: base uniform load = buoyancy (balanced). Added: 30 t end loads and a 50 t uniform load over the middle 25 m at 2 t/m.

For the left half (symmetry axis at 22.5 m): total added weight left of mid = 30 (at x=10) + 2 x 12.5 (50 t spread to mid) = 30+25 = 55 t. The reaction portion of buoyancy on the left half = 1383.75/2 = 691.9 t, of which the base weight matches. The point 30 t at 10 m therefore creates a shear to its right of SF = -30 t, and the 2 t/m distributed load adds -2 per metre, so just left of midspan the shear is -30 - 2x12.5 = -55 t.

By symmetry the maximum shear force occurs at the ends of the distributed 50 t section, and equals 30 + 50/2 = 55 t. Hence maximum shear force = 55 tonnes (55 t). Sketch: the shear-force diagram shows a step of -30 t at x=10 m, then a linearly falling line over x=10 to 35 m at -2 t/m reaching -55 t at midspan, and a mirror image rising on the after half -50-?with symmetric positive values, maximum 55 t.

Centre of pressure on a deep tank bulkhead.

The bulkhead is a vertical plane whose top edge is 12 m wide and lies at a depth equal to the head, 2 m below the waterline. The vertical heights of the bulkhead at seven equidistant points across the 12 m breadth are 0, 3, 5, 6, 5, 3 and 0 m. With six equal intervals over 12 m the spacing is h=2 m.

For a submerged vertical plane surface, the centre of pressure lies at a depth below the waterline given by

depth of centre of pressure = (second moment of area about the waterline)/(first moment of area about the waterline), i.e. d = M2/M1.

For each station across the breadth the bulkhead bottom edge lies at depth (2 + height) below the waterline, while the top edge is at depth 2 m throughout.

First-moment integrand, element about the waterline (per unit breadth), integrating from depth 2 to (2+H):

M1_element = integral of z dz from 2 to (2+H) = [(z^2)/2] = 0.5[(2+H)^2 - 4] = 2H + 0.5H^2.

Second-moment integrand:

M2_element = integral of z^2 dz from 2 to (2+H) = [(z^3)/3] = (1/3)[(2+H)^3 - 8] = 4H + 2H^2 + H^3/3.

Values of H: 0,3,5,6,5,3,0:

For M1 (2H + 0.5 H2): 0,10.5,22.5,30,22.5,10.5,0.

For M2 (4H+2H2+H3/3): 0, 39, 111.67, 168, 111.67, 39, 0.

Using Simpson's rule with spacing 2 m and 7 ordinates:

M1 = (2/3)[ (0+0) + 4(10.5+30+10.5) + 2(22.5+22.5) ]

= (2/3)[0 + 4x51 + 2x45] = (2/3)[204+90] = (2/3)(294) = 196.

M2 = (2/3)[0 + 4(39+168+39) + 2(111.67+111.67)]

= (2/3)[4x246 + 2x223.33] = (2/3)[984+446.67] = (2/3)(1430.67) = 953.8.

Depth of centre of pressure below the waterline = M2/M1 = 953.8/196 = 4.87 m.

Answer: the centre of pressure is approximately 4.87 m below the waterline. (Since the top edge is 2 m below the waterline, the centre of pressure is about 2.87 m below the top edge of the bulkhead.)

Freeboard is the vertical distance from the waterline to the freeboard (upper) deck at side. It is required because it provides:

• Reserve buoyancy: the volume of the hull above the waterline that keeps the ship afloat when waves or damage raise the external waterline. Adequate reserve buoyancy is essential for floating headroom and survivability.
• Reduced shipping of water and deck wetness: a higher freeboard gives better watertight integrity against seas sweeping over the deck, protecting cargo, stability and the crew.
• Improved stability and reduced angle of heel by keeping the deck edge and openings (doors, hatches, air pipes, vents) well above water, and by providing a larger intact range of stability (area under the GZ curve).
• Comfort and safety in a seaway: better freeboard limits immersion in following/quartering seas and reduces green seas on deck, lowering risk of damage and of loss of stability.

The minimum freeboard is fixed by the International Load Line Convention, giving the load-line mark which must never be submerged.

The condition of assignment is the series of requirements that a ship must satisfy to receive its load line certificate, ensuring the hull strength, watertight integrity and the protection of openings are commensurate with the assigned freeboard. It covers the scantlings and weathertightness of the freeboard deck, the strength of the superstructure and hatch covers, the provision and closing of watertight and weathertight openings (doors, scuttles, vents, air pipes, sounding pipes, sill heights, freeing ports), and the availability of bulwark freeing arrangements. These are maintained by:

• keeping the hull structcuy sound and free from corrosion/defects;
• maintaining all weathertight and watertight closures, gaskets, coamings and securing arrangements in good order;
• ensuring proposed and deck fittings (gangways, cranes, lashings) do not open ill-hidden ports above the assigned deckline;
• carrying out planned and classification surveys (annual/periodical) and maintaining the load line certificate, the certificate being renewed at the load line survey;
• reporting any damage or alteration to the hull or openings so the surveyor can confirm the condition still satisfies the rules; unauthorised alterations that reduce the assigned freeboard are prohibited.

(Provide a diagram: a ship's side at midship with the freeboard deck line, and four waterlines at different heights.)

• Type A ships are designed to carry only liquid cargoes in bulk, with a closely guarded deck and high integrity (e.g. tankers). They get the lowest (smallest) freeboard because the spillover risk is small, giving maximum carrying capacity.
• Type B ships are general cargo ships not covered by type A; they require a greater freeboard.
• Type B60 and B100 are refined type B ships to which a reduced freeboard is permitted provided the ship satisfies additional strength and stability criteria - B60 allows 60% of the tabular difference between B and A freeboards to be taken off, B100 allows the full 100% reduction (i.e. the B freeboard may be reduced to the type A level) providing the prescribed additional conditions are met. Hence the freeboards order: Type A smallest, B100 next, B60 next, and plain Type B the largest freeboard.

Continuity of strength is ensured and maintained by gradually sloping the tank top height and internal structure to the required position. Additional support and stiffening is necessary for the main engines, boilers, etc., to provide a vibration-resistant solid platform capable of supporting the concentrated loads. On slow- speed diesel-engined ships, the tank top plating is increased to 40 mm thickness or thereabouts in way of the engine bedplate. This is achieved by using a special insert plate which is the length of the engine including the thrust block in size. Additional heavy girders are also fitted under this plate and in other positions under heavy machinery as required. Plating and girder material in the machinery spaces is of increased scantlings in the order of 10 per cent.

The method adopted.

A cellular void space within a ships structure is called a coffer dam. Like a bulkhead separates two spaces or divides a space into two, a coffer dam does the same with a larger degree of integrity since it incorporates a void which would contain any breach of either of the boundaries. This would contain the leakage and prevent it spreading into other areas. A cofferdam can be defined as an empty space separating compartments to prevent the contents of one compartment from entering another in case of leakage.

The thrust block is positioned close to the propulsion machinery (usually just aft of the main engine). Reasons are as follows:

• The axial thrust generated by the propeller could cause deformation and misalignment of the shafting system if the thrust block were positioned far from the engine. Placing it close to the engine minimizes the length of shafting subject to this thrust, thus reducing potential for misalignment. The strong double bottom structure directly beneath provides necessary support to mitigate any deformation.

• Differential expansion between the shaft and the hull due to temperature variations is a potential source of misalignment. Positioning the thrust block close to the engine helps to minimize the effect of this differential expansion.

• The weight of the propeller and the dynamic forces it creates can lead to whirling of the tailshaft and misalignment if not properly managed. Positioning the thrust block near the engine helps to stabilize the shafting system and reduce the risk of these issues.

• The substantial double-bottom structure under the main machinery provides an ideal, inherently strong foundation for the thrust block. This minimises the need for extensive additional reinforcement to support the thrust loads.

Fatigue is progressive and localised structural damage caused by cyclic loading, where the maximum stress is below the ultimate tensile strength. The relationship between stress level, cyclic frequency, and operating life depends on whether the fatigue is high-cycle/low-stress or low-cycle/high-stress.

High-cycle fatigue (low stress-high cycle):

• This occurs at lower stress levels over a high number of cycles, resulting in elastic deformation. The component can withstand more cycles at these lower stress levels, and its life expectancy is determined by the S-N curve, which predicts the number of cycles before failure at a given stress level. For example, fatigue in turbocharger blowers often results from prolonged vibration over numerous cycles.

Low-cycle fatigue (high stress-low cycle):

• This occurs at high-stress levels over fewer cycles, causing plastic deformation in the material. This type of fatigue is typically assessed by a strain curve. If the stress level increases, the component's operating life decreases, as higher stress accelerates the onset of failure. For example, air receivers filling automatically face high stress and experience fewer cycles before failure.

If stress levels or the number of cycles increase beyond the material’s capacity, failure will occur sooner. It is important to keep stress levels within allowable limits for extended component life.

• Surface roughness, porosity, inclusions, and abrupt section changes all create stress concentrations, lowering fatigue strength.
• Coarse grain size, specific chemical compositions, and cold working introduce residual stresses that reduce fatigue resistance.
• Corrosion, erosion, and decarbonisation weaken the material and accelerate fatigue crack initiation and propagation.
• Faulty workmanship during assembly or processing introduces defects that may significantly shorten the component's life.

• Cylinder overload due to excess power puts excessive stress on the girders.
• Incorrect crankshaft alignment induces uneven loading and stress concentrations.
• Material defects, high residual stresses in welds, heat-affected zone hardening, and the presence of dissolved oxygen all reduce fatigue resistance.
• Tank top deformation from pressurisation or overheating adds stress to the bedplate.

To minimise the risk of fatigue cracking:

(i) Constructional strength:

• Bed plates are made up of M.S. plates with four steel casting, which are assembled and welded together so that the bed plate is strong longitudinally & transversely with good resistance to twisting along its length.
• Longitudinal strength is obtained by fabricating each side of the bed plate in the form of a box girder.
• The cast steel cross girder in which the main bearing is placed contributes to the bed plate's transverse strength and resistance against twisting along its length.
• Resin cast chocks are used between the bedplate and the double bottom tank top to absorb the shocks & stress.

(ii) Maintenance:

• Monthly checks on the bolt tension.
• Monthly checks on engine load using power cards & measuring cylinder peak pressure.
• Regular checking of tension for main bearing jack bolts as recommended by engine manufacturers.
• Regular checks on crankshaft alignment by taking deflection & compare with recommended value.
• By maintaining engine operations at specified load, temperature, pressure, speed, etc.

Requirements for Unattended Machinery Space (UMS) Ship:

1. Fire Precaution

• Arrangements should be provided on the UMS ship to detect and give an alarm in case of fire.
• In the boiler, air supply casing and uptake.
• In scavenge space of propulsion machinery.
• In engines of power, 2250 kW and above or cylinders having bore more than 300mm should be provided with an oil mist detector for the crankcase or bearing temperature monitor or either of two.

2. Centralized control & instruments are required in Machinery Space

• UMS ships must have a centralised control room that is easily accessible and equipped with adequate instrumentation and equipment to monitor and operate all main and auxiliary machinery. A system must be provided to call the engineers to the machinery space in case of emergency

3. Protection against flooding:

• UMS ships must have bilge wells that are located and designed to detect the accumulation of liquid at a normal angle of heel and trim and to accommodate the drainage of liquid during an unattended period. If the bilge pump starts automatically, an alarm must indicate that the flow of liquid pumped is more than the capacity of the pump.

4. Automatic Fire Detection

• Alarms and detection should operate very rapidly and effectively. It should be placed at numerous well-sited places for quick response of the detectors.

5. Fire Extinguishing System

• There should be arrangements for a fire extinguishing system other than the conventional hand extinguishers, which can be operated remotely from machinery space. The station must give control of emergency fire pumps, generators, valves, extinguishing media, etc.

6. Alarm System

• A comprehensive alarm system must be provided for control & accommodation areas.

7. Automatic Start of Emergency Generator

• Arrangements for the starting of an emergency generator and automatic connection to the bus bar must be provided in case of a blackout condition, apart from that, the following points are also to be noted.

8. Local hand control of essential machinery like steering, emergency generator starting, emergency start for main engine, etc. 8. Adequate settling tank storage capacity. 9. Regular testing & maintenance of machinery alarms & instruments.

• Bilge wells in UMS ships should be located and provided in such a manner that the accumulation of liquid is detected at a normal angle of heel and trim and should also have enough space to accommodate the drainage of liquid during unattended periods.
• In the case of the automatic starting of the bilge pump, the alarm should be provided to indicate that the flow of liquid pumped is more than the capacity of the pump.

(ii) Control of Propulsion Machinery from Navigation Bridge:

• The ship should be able to be controlled from the bridge under all sailing conditions. The bridge should be able to control the speed and direction of thrust and should be able to change the pitch in case of a controllable pitch propeller.
• Emergency stops should be provided on navigating the bridge, independent of the bridge control system.
• The remote operation of the propulsion should be possible from one location at a time; at such connection, interconnected control positions are permitted.
• The number of consecutive automatic attempt which fails to start the propulsion machinery shall be limited to safeguard sufficient starting air pressure.

(i) Hammer Test: The hammer test, a method of non-destructive testing, would be carried out across all areas of the hull plating. The surveyor would gently tap the plating to assess its condition, listening for sounds indicating potential damage like cracking or delamination. Particular attention would be given to areas showing signs of corrosion or previous repairs. Areas such as welds, bilge keels, and around penetrations (e.g., sea chests) would require extra scrutiny.

(ii) Hose Test: The hose test checks the watertight integrity of the hull. This would be performed on new welds on the shell plating and other areas where watertightness is required. This is done using a nozzle with a 12.5 mm diameter and 2 bar water pressure at a distance of 1.5 m. Specific locations would include welds, sea chests, and around valve penetrations. The exact location will depend on areas of concern identified during the visual inspection.

• Welds: All weld joints, especially those in areas subject to stress or corrosion, must be carefully examined for cracks, porosity, and other defects.
• Angles and other structural members: These need inspection for corrosion, cracking and distortion.
• Bow: The bulbous bow, chain markings, and bow thruster area should be checked thoroughly.
• Stern: The stern frame is subjected to slamming and must be examined closely for cracking and buckling.
• Bilge Keel: This requires inspection for damage and proper attachment to the hull.
• Openings in shell plating: Sea chests and ship side valves (overboard valves) must be inspected for leaks, corrosion, and proper operation.
• Areas of previous damage or repair: These are especially susceptible to further corrosion or cracking and warrant close examination.
• Areas exposed during previous dry-docking: Any areas that were exposed to the elements during the previous dry-dock require close examination for damage or corrosion.
• Cathodic protection system: The effectiveness of the cathodic protection system and the condition of anodes need to be verified. Lack of anode consumption may indicate corrosion in other areas.
• Rudder and Propeller: The condition of the rudder and propeller, including the welds, should be examined for any signs of damage or corrosion.

is the amount, the ship can be flooded without the risk of sinking. i.e. the maximum length of the ship that can be flooded without submerging the margin line. The margin line is located 75mm below the bulkhead deck, providing a safety margin.

• A floodable length curve can be drawn for different permeability.
• It is used to test the after-bulkhead length so that the bulkhead length is sufficient to contain the flooding without sinking the vessel.
• Factor of subdivision = Permissible length / Floodable length

• Hose Test: This involves applying a high-pressure water jet (2 bar from a distance of 1.5 meters, nozzle diameter at least 12mm) to the bulkhead's surface. This test directly checks for leaks. The test is typically done from the side where the stiffeners are attached.
• Air Pressure Test: An air pressure test applies pressure (0.2 bar) for about an hour, detecting leaks that may not be apparent during the hose test. This usually happens prior to the application of protective coatings.
• Structural Test: Visual inspection, especially of welding joints, is carried out. Non-Destructive Testing (NDT) is done where necessary. Tanks designed to hold liquids, which form subdivisions of the ship, are tested for tightness with a water head up to the deepest subdivision load line or to a head of 2/3 the depth from the top of the tank to the margin line, whichever is greater.

Coefficient of Fineness of Waterplane Area (Cw)

This is the ratio of the ship's waterplane area to the area of a rectangle with the same length and breadth of the ship at the same waterline. It is given by:

$$C_{w}=\frac{WPA}{L\times B}$$

Where:

• Cw​ = Coefficient of fineness of waterplane area
• WPA = Waterplane area
• L = Length of the ship
• B = Breadth of the waterplane

Block Coefficient (Cb)

This is the ratio of the volume of displacement of a ship to that of a rectangular block having the same length, breadth, and draft as the ship. It is given by:

$$C_{b}=\frac{V}{L\times B\times D}$$

Where:

• Cb = Block coefficient
• V = Volume displaced by the ship
• L = Length of the waterline
• B = Breadth of the waterline
• D = Draft

Midship Coefficient (Cm)

This is the ratio of the cross-sectional area at the midship section to the product of the ship's beam (breadth) and draft. It is given by:

$$C_{m}=\frac{A_{m}}{B\times D}$$

Where:

• Cm​ = Midship coefficient
• Am​ = Cross-sectional area at midship
• B = Beam (breadth of the ship)
• D = Draft

• The concept compares the heeling moment energy (from external forces) and the righting moment energy (from the ship's stability).
• The ship will absorb the energy imparted by the heeling moment. If the righting energy is greater than the heeling energy, the ship will stabilize; otherwise, it may capsize.

Areas Under the Curve:

• Area A: Represents the region where the heeling moment exceeds the righting moment (external energy > ship's stability).
• Area B: Represents the region where the righting moment exceeds the heeling moment (ship's stability > external energy).
• The balance of these areas determines whether the ship will right itself or continue to heel.

When exposed to heeling forces such as wind or waves, the vessel inclines and may roll over to a certain angle of heel. If the external force is applied instantaneously, the ship must have enough reserve dynamic stability to absorb the energy and return to an upright position. If the external force is constant, the ship will remain at an equilibrium angle where the righting moment equals the heeling moment.

This refers to the remaining righting energy available to counteract additional external forces. A higher reserve dynamic stability ensures the vessel can handle greater heeling forces without capsizing.

The Admiralty coefficient is defined as C = Delta^(2/3) V^3 / P, where Delta is displacement (tonnes), V ship speed, and P shaft power.

Chosen the parent ship: Delta=12000 t. Compute C at each trial speed.

Speed V=10: numerator = 12000^(2/3) x 10^3. 12000^(2/3)=524, 10^3=1000, so 524,000/880 = 595.

V=11: 524x1331=697,444; /1155 = 604.

V=12: 524x1728=905,472; /1520 = 596.

V=13: 524x2197=1,151,228; /2010 = 573.

V=14: 524x2744=1,437,856; /2670 = 538.

V=15: 524x3375=1,768,500; /3600 = 491.

Plotting C against V gives a curve that is roughly flat (595-604) at low speed and falls progressively at higher speed (to about 490 at 15 kn), because wave-making resistance and other power terms rise faster than V^3 at high Froude numbers. The curve demonstrates that the constant-Admiralty-coefficient assumption holds only near moderate speeds.

For geometrically similar ships the displacement scales as the cube of length:

Delta140 = 12000 x (140/120)^3 = 12000 x 1.5876 = 19051 t.

So Delta140^(2/3) = 19051^(2/3) = 714.

Corresponding speed: for similarity, V2/V1 = sqrt(L2/L1) = sqrt(1.1667) = 1.0801. For the 140 m ship running at 14 knots, the corresponding speed of the parent (120 m) ship is 14/1.0801 = 12.96 knots, which lies between the 13-knot trial point (C=573) - read C is about 570 from the curve.

Using the Admiralty coefficient at that point, C=570:

P140 = Delta140^(2/3) x V^3 / C = 714 x 14^3 / 570 = 714 x 2744 / 570 = 1,959,216 / 570 = 3437 kW.

Answer: the shaft power required is about 3440 kW (approximately 3.4 MW).

(i) The Hull Roughness Analyzer (HRA) is a portable system designed to measure the roughness of a ship’s hull surface. It includes:

• A portable microprocessor with a digital display and printout capability.
• A handheld carriage equipped with a stylus measuring head. The stylus traces the hull surface, recording peaks and valleys to assess roughness.
• The system measures 10 sample lengths of 50 mm during a single traverse over the hull. For each 50 mm sample, the highest peak to lowest valley is recorded as Rt(50).
• Roughness surveys are conducted at approximately 100 locations on the hull, including the bow, stern, midship, and topping. Multiple traverses at each location provide numerous readings.
• Mean Hull Roughness (MHR) is calculated as:
• $$MHR\:=\:\frac{\sum Rt\left(50\right)}{n},\:where\:n\:is\:the\:number\:of\:readings\:at\:a\:station$$
• Average Hull Roughness (AHR) is calculated as:
• $$AHR\:\frac{\sum MHR}{m},\:where\:m\:is\:the\:total\:number\:of\:survey\:stations$$

(ii) Significance of Roughness Profile:

The roughness profile of the prepared hull surface impacts the performance of the applied coating and the overall operational efficiency of the vessel. A rough surface increases frictional resistance as the vessel moves through the water. This increased drag translates to higher power requirements for propulsion, leading to increased fuel consumption and operational costs. Furthermore, greater surface roughness contributes to increased carbon emissions, a concern under current MARPOL regulations. Therefore, a controlled and optimised roughness profile is essential for minimising frictional resistance, reducing fuel consumption and emissions, and maximising the longevity of the hull coating.

Typical Average Hull Roughness (AHR):

• New Ship: 120-200 µm (approx.).
• Eight-Year-Old Ship: 300-400 µm (approx.) due to annual deterioration of 20-40 µm.

Washing:

• The hull surface must be thoroughly cleaned to remove all marine growth (algae, slime, etc.), accumulated salts, dirt, grease, and oil. High-pressure freshwater washing is the standard method for this initial cleaning. The goal is to present a clean substrate for subsequent stages.

Blasting:

• Abrasive blasting is the preferred method for removing rust, defective paint, and any remaining contaminants. This process achieves a bare metal surface, essential for proper adhesion of the new coating. The extent of blasting (localized or full hull) depends on the condition of the existing surface. The intensity and type of abrasive used are carefully controlled to achieve the desired surface roughness profile.

Primer Application:

• After blasting, the surface is again cleaned to remove any blasting debris. A primer coat is then applied to provide corrosion protection and to create an ideal surface for the subsequent topcoat adhesion. This primer acts as an intermediary layer, enhancing the bond between the substrate and the long-life coating system.

(ii) Defects in Self-Polishing Paint Application:

• Blistering: Bubbles caused by trapped moisture.
• Curtaining/Sagging: Paint sagging due to its own weight.
• Dry Spray: Paint particles drying before reaching the surface.
• Peeling/Flaking: Caused by moisture, dust, excessive film thickness, or incompatible paints.
• Cissing/Crawling: Paint contracting immediately after application.

1. Primary Barrier: A thin membrane made of INVAR (36% Nickel, 64% Iron) with a thickness of 0.5 to 1.2 mm, forming the primary containment layer for the liquefied gas.
2. Primary Insulation box: A 200 mm thick layer of granulated Perlite insulation packed in plywood boxes, surrounding the primary barrier. Perlite is siliconised to make it impervious to moisture.
3. Secondary Barrier: A secondary membrane made of the same INVAR material is installed to prevent cargo leakage in case of primary barrier failure.
4. Secondary Insulation box: Another 200 mm thick layer of granulated Perlite is placed above the secondary barrier to provide additional insulation and prevent thermal transfer.

Invar (36% Ni, 64% Fe) is used for both the primary and secondary barriers. The reason for this choice is its exceptionally low coefficient of thermal expansion. This eliminates the need for expansion joints or corrugations in the membrane design. In addition, Invar remains strong and does not become brittle at the very low temperatures experienced by the liquefied gas. The thin and lightweight nature of Invar maximizes the cargo-carrying capacity of the tank.

, meaning they don't form part of the ship's hull and don't contribute to the ship's structural strength. They can be spherical, cylindrical, or prismatic (box-shaped). Prismatic tanks usually have internal stiffeners like bulkheads, webs, girders, and stiffeners for added structural integrity.

(i) Longitudinally:

Tanks are positioned longitudinally within the ship's cargo hold. The tanks are supported longitudinally by anti-roll chocks and anti-lift chocks that resist forces caused by ship motions. These chocks ensure the tank remains stable even in rough sea conditions. They also act as thermal barriers, preventing the transfer of heat between the hull and the tank.

The chocks also serve as thermal barriers between the hull and cargo and are often constructed of wood or plastic materials.

(ii) Transversely: Transverse support is provided by anti-pitch chocks and support chocks, which stabilize the tank against lateral forces. These chocks are typically made of plywood or plastic and help prevent thermal stress between the tank and the ship’s structure.

Sagging: Sagging deformation are caused by the uneven distribution of weight and buoyancy in the length of the hull. If a ship is supported on either end by the crest of a wave, the forces exerted by the waves on the buoyancy of the vessel would tend to lift the ends, whilst the center of the vessel would suffer a loss of buoyancy and tend to sag. This deformation is known as sagging.

Type of Stress: Compressive stress on deck, tensile stress on keel.

Hogging: When the wave passes the reverse situation of hogging results, i.e. the middle of the vessel is supported on the crest whilst the two ends hang over the crest on either side. This action is known as hogging.

Type of Stress: Tensile stress on deck, compressive stress on keel

Racking: When a vessel is rolling in a seaway the transverse section will try to distort at the corners due to racking stresses.

Type of Stress: Shear stress on transverse bulkheads and hull structure

Torsional forces: If a vessel is subjected to pitching and rolling at the same time, i.e. taking the wave on either bow, the vessel tends to twist longitudinally. These are known as torsional stresses or forces.

Slack tanks, or partially filled tanks, significantly impact a ship's stability due to the free surface effect

• When tanks are partially filled (slack), the liquid inside moves freely as the ship heels.
• This movement shifts the centre of gravity (G) laterally towards the heeling side.
• The righting lever (GZ) decreases, resulting in reduced metacentric height (GM) and overall stability.
• The virtual loss of GM is proportional to the breadth of the tank and the height of the free surface.

Consequences of Slack Tanks:

• Increased angle of heel.
• Reduced stability, making the ship tender and more prone to capsizing.

To Minimize the Effect:

• Avoid slack tanks where possible; either fill tanks completely or empty them.
• Design tanks with longitudinal divisions or swash bulkheads to limit liquid movement.
• Use sluice valves in tanks to control liquid transfer.
• Prioritize filling smaller tanks at the ship's bottom to lower G and improve stability.

Ice accumulating on the superstructure adds mass high up on the ship. This raises the centre of gravity (G), decreasing the metacentric height (GM). A lower GM reduces stability, making the ship more tender (more easily rolled) and increasing the period of roll. The ship becomes more susceptible to capsizing.

Wind:

• High freeboard or tall superstructures increase windage, leading to a greater rolling effect.
• Rolling caused by wind reduces stability, especially if the ship remains heeled for a prolonged period.

Waves:

• Large waves, especially when the ship is on the crest, can cause a significant loss of stability due to reduced underwater buoyant volume.
• The ship may develop excessive heeling or capsizing tendencies.
• Long ships are more vulnerable to wave action due to greater surface exposure, further reducing stability.

• Water Absorption by Deck Cargo:
  • Certain types of deck cargo, such as timber or other absorbent materials, can take up water during a voyage.
  • This absorbed water increases the weight of the cargo, raising the centre of gravity (G) of the ship.
  • As G moves higher, GM reduces, leading to decreased stability.
  • Retention of Water on Deck:
    • Water that accumulates on the deck, such as from heavy rain or seawater, adds additional weight to the ship's upper structure.
    • This shifts G upward, reducing GM and stability.
    • Retained water may also cause a list if it collects asymmetrically, further impacting the ship's balance.
    • Consequences:
      • Increased risk of capsizing in rough seas.
      • Increased rolling and reduced righting ability.
      • Mitigation Measures:
        1. Ensure proper drainage systems are in place to quickly remove water from the deck.
        2. Regularly monitor and secure deck cargo to prevent excessive water absorption.

The process begins with the removal of mill scale, a thin layer of iron oxide that forms during the steel rolling process.

1. Removal of Mill Scale:

• Weathering: Using wire brushes.
• Pickling: Immersing plates in a weak solution of H₂SO₄ or HCl.
• Shot Blasting: Abrasive blasting to remove rust and mill scale.
• Flame Cleaning: Heating and cleaning the surface.

Freshwater Washing and Drying: Ensures the surface is clean and ready for priming.

2. A primer is then applied. This acts as a base layer for subsequent coatings and improves adhesion. Common types include epoxy primers with corrosion-inhibiting pigments like iron oxide, zinc, and calcium phosphates (though zinc content is reduced due to safety concerns).

3. Next comes the anticorrosive coating, the main layer offering corrosion protection. Common choices are two-component epoxies, coal tar epoxies, and epoxy or polyester coatings with glass flakes for added strength and water impermeability.

4. Finally, an antifouling coating prevents marine organism attachment. While tin-based paints were once common, environmental regulations have led to their replacement with copper-based, silicone-based, or non-TBT (Tributyltin) self-polishing coatings. These utilize seawater-soluble polymers. The number of antifouling layers (two or three) depends on the chosen system and desired lifespan. The dry film thickness (DFT) of the primer is closely monitored to prevent cracking and ensure effective protection.

Corrosion prevention begins at the design stage:

• Avoid dissimilar metal joining to minimize galvanic corrosion.
• Use high-quality steel plates based on the galvanic series.
• Minimize areas where water can accumulate by ensuring proper drainage systems.
• Ensure sufficient anodes are installed in optimal positions.
• Consider installing Impressed Current Cathodic Protection (ICCP) and Marine Growth Prevention Systems (MGPS).

Maintenance:

• Regular checks and maintenance of ICCP and MGPS systems.
• Renewal of sacrificial anodes during dry-docking.
• Cleaning, repairing, and repainting surfaces to maintain the protective coatings.
• Ensuring proper drainage and inspecting for any areas of corrosion.

Sacrificial anodes are less noble metals (more electro-negative) than the hull material. When immersed in seawater, they corrode preferentially, protecting the hull. Common materials include zinc, aluminium, and magnesium. They are welded to the hull for good electrical contact.

• External surface: Large anodes provide complete protection until the next dry-docking.
• Internal surface: Anodes are fitted inside tanks, filters, and coolers to prevent internal corrosion.
• MGPS: These systems utilize sacrificial anodes to protect seawater lines and pumps, further preventing marine growth.
• ICCP: Impressed current systems offer an alternative, using an external DC power source and permanent anodes (typically titanium or platinum) for continuous protection. These systems are self-regulating and adjust current output based on hull coating condition. Regular monitoring (e.g., monthly data analysis) is important for both sacrificial and impressed current systems.

Masses at the bottom:

• The centre of gravity (G) moves down.
• Metacentric height (GM) increases, resulting in greater stability.
• Rolling period decreases.

Masses at the top:

• The centre of gravity (G) moves up.
• Metacentric height (GM) decreases, reducing stability.
• Rolling period increases.

Masses concentrated at the centre:

• The radius of gyration (K) decreases.
• Rolling period decreases.

Masses distributed away from the centre:

• The radius of gyration (K) increases.
• Rolling period increases.

The factor of subdivision introduces a safety measure by reducing the size of the compartments to limit the effects of flooding. It ensures that the ship's draft or trim has less chance of touching the margin line during flooding or heeling.

Permissible Length Formula:

$$Permissible\:length=\frac{Floodable\:length}{Factor\:of\:Subdivision}$$

A smaller factor of subdivision leads to a smaller permissible length, requiring more numerous and smaller compartments. This reduces the potential for catastrophic flooding, as a smaller flooded area is less likely to exceed the ship's reserve buoyancy and cause it to sink. The factor of subdivision is determined by the ship's length and its intended service. The nature of service is quantified by a "criterion of service" (Cs) number, which considers the proportion of passenger and machinery spaces to the total volume of the ship. A higher Cs number (indicating more passenger space) typically results in a lower factor of subdivision and therefore smaller compartments.

$$Excess\:moment=31000-16200=14800$$

$$LCG=\frac{\sum M}{\sum m}=\frac{14800}{16000}$$

$$LCG=0.925m\:fwd\:of\:midship$$

$$LCG=0.925m\:Fwd\:of\:midship$$

$$LCB=2.02m\:Fwd\:of\:midship$$

$$Trimming\:lever=LCB-LCG$$

$$2.02-0.925$$

$$=1.09m$$

$$Trimming\:moment=m\times d$$

$$=16000\times1.09$$

$$=17440tm$$

$$Change\:of\:trim=\frac{Trimming\:moment}{MCT_{1\operatorname{\mathrm{cm}}}}$$

$$=\frac{17440}{179}$$

$$97.43\operatorname{cm}$$

$$Draft\:fwd=8.25-\frac{97.43}{100\times120}\left(\frac{120}{2}+0.57\right)$$

$$=7.756m$$

$$Draft\:aft=8.25+\frac{97.43}{100\times120}\left(\frac{120}{2}-0.57\right)$$

$$=8.735m$$

If the ship is trimmed by the stern, the liquid will settle more toward the aft end, resulting in a higher sounding than if the ship were on an even keel. Conversely, if the ship is trimmed by the bow, the liquid shifts forward, and the sounding obtained will be less, potentially underestimating the actual volume.

To ensure accurate volume measurement despite varying trim conditions, tank calibrations are carried out for different trims, and the data is compiled into a sounding book or trim correction table. When taking soundings, the trim is noted, and the corrected volume is obtained using these calibration tables, ensuring reliable tank content assessment regardless of trim.

However, if the ship is heeled or trimmed during filling, the liquid inside the tank may collect on the lower side, causing both the center of gravity (G) and the center of buoyancy (B) to shift to that side. This results in a virtual loss of GM and a reduction in stability.

Once the DB tanks are fully pressed up, the liquid is evenly distributed, the ship returns to an upright position, and the center of gravity remains at its lowest point, resulting in maximum GM and optimal stability.

Maximum list during derrick operation.

Initial condition: displacement = 9900 t; KM = 7.3 m; KG = 6.4 m, so initial GM = KM - KG = 7.3 - 6.4 = 0.90 m.

The first 50 t lift is picked up off the quay (inshore side). While it is suspended at the derrick head, its position is above and outboard of the crane; as it swings, it acts as a weight at the head which is 15 m above the keel and 12 m out from the centreline. The maximum list occurs when the weight is suspended fully outboard (12 m out) before it is placed on deck at 6 m out, because the heeling moment is greatest then.

Effective heeling of the first lift. Treated the 50 t as suspended at (y=12 m outboard, z=15 m above keel):

• Transverse shift of the centre of gravity, GG' = w x y / Delta = 50 x 12 / 9900 = 0.0606 m outboard (about 6.06 cm).
• Vertical rise of the centre of gravity, since the load hangs at the derrick head above deck: compare to its final on-deck position at 6 m out, 9 m above keel. The movement from quay to head raises the effective load centre; the vertical rise of G = w x (rise)/(Delta). For the list the relevant GM is reduced by the raised KG.

A cleaner approach is to compute the moment. At maximum list the weight is fully outboard at 12 m; its KG contribution raises the centre of gravity by GGv = 50 x (15 - 9)/9900 = 50 x 6/9900 = 0.0303 m. New KG = 6.4 + 0.0303 = 6.4303 m; the effective GM falls to 7.3 - 6.4303 = 0.8697 m.

List, GGh = 50 x 12 / 9900 = 0.0606 m outboard.

tan(list) = GGh / GM = 0.0606 / 0.8697 = 0.0697.

So list = atan(0.0697) = 3.99 deg, about 4 deg.

Answer: the maximum list during the operation is about 4 degrees towards the outboard (derrick) side. (Note: after the first lift is placed on deck at 6 m out and the second lift is begun, the situation changes slightly; the critical maximum effect is when the suspended load is furthest outboard.)

are significant and arise due to various factors:

• Galvanic corrosion occurs due to the interaction between dissimilar metals, accelerated by the seawater environment and differential aeration.
• Sulphate-reducing bacteria in river mud can cause localized pitting, leading to penetration of the bottom shell.
• Dissolved oxygen in seawater reacts with metal surfaces to form rust, significantly contributing to structural deterioration.
• The rate of corrosion peaks at a 3.5% salt concentration, typical of seawater.
• Neglecting maintenance exacerbates the problem, allowing corrosion to progress unchecked.

(ii) Protection against extensive corrosion in ballast tanks involves the following measures:

• Complete coating of the tank surfaces with properly selected marine-grade paint to create a protective barrier.
• Installation of sacrificial anodes, designed to corrode preferentially and protect the tank structure.
• Using large anodes with greater volume relative to surface area to ensure extended protection.
• Regular gauging of plates to assess thickness and identify areas requiring reinforcement or repair.
• Conducting regular inspections, cleaning the tanks, removing rust, and repainting to maintain structural integrity and prolong the lifespan of the ballast tanks.

The purpose of the in-water survey is to obtain information on the condition of the hull and machinery of large vessels normally obtained from the Docking Survey. The survey may be carried out instead of any one of the two docking surveys, under the surveillance of a surveyor with the ship at a stable draught in sheltered waters, the in-water visibility is to be good and the underwater hull clean.

The survey requires a self-propelled, steerable survey vehicle fitted with a long-range TV camera to aid steering and check for hull distortion also a close-up high-resolution TV color camera to give a true picture of the state of coatings and for inspection of weld seams. In some cases a 35mm still camera is fitted. An ultrasonic probe is provided to measure plate thicknesses and other equipment includes a depth meter and speed indicator. Power is supplied and information is relayed using an umbilical from the vehicle to the survey boat

The survey boat usually houses a console containing TV monitors. plate thickness printout, audio cassette recorder, video recorder and playback unit, diver communication system, vehicle control system and associated instrumentation.

The survey vehicle is taken to the starting datum by a diver. With the aid of one of the TV monitors and using the shell expansion plan as a map, the vehicle may be guided, from the control console, over the bottom and sides of the hull by following weld runs and by reference to other features such as inlets and tank plugs. Pictures and navigational information are relayed back and video recorded along with plate thicknesses giving the surveyor an integrated visual record of all relevant information. In addition, a plate thickness print-out can be produced and/or an audio recording. The vehicle will also provide pictures of such items as the stern frame, rudder, propeller, bilge keels and hull openings although a diver may be used with a handheld camera for closer inspection of these items and also for inspection of plating on the turn of the bilge. Divers are used to measure stern bearing wear down and pintle clearances, and to inspect such things as stern seals, anodes, pintles and rudder stock couplings.

To facilitate underwater surveys plans must be submitted showing the external features of the hull below the sheer strake together with a key plan indicating the location of these features, also of reference points and the position of water-tight and oil-tight bulkheads. Notes are included on the proposed methods of marking and identifying plates. To assist divers color photographs should be provided of items such as shell openings, rudder closing plates and wear-down gauge plugs.

Provision should be made on the ship identifying bulkheads and frames above the waterline and also for establishing the identity and position of each propeller blade from inside the ship. The design of the ship must facilitate water inspection and repair, for example, sea inlets must be capable of being blanked off and drained to bilges, shell gratings hinged if practicable and anodes easily changed.

Construction and purpose of a bulbous bow.

Construction: The bulbous bow is a roughly pear-shaped or blunter solid forepeak projection from the stem, below the load waterline, formed by specially shaped shell plating. The bulb is built by a thick, heavily plated shell with internal framing made up of transverse webs (swash bulkheads/forepeak frames) and fore-and-aft stringers that connect it to the stem of the vessel and the side plating. It extends well below the waterline and often contains a forepeak collision-bulkhead behind it. The stanchion, stem bar and the bulb take the pounding and panting loads; the bulb shell plates are thicker at the leading edge and stiffened by the framing arrangement. The bulb usually joins the ship's side with a smooth radius, and the whole forepeak is subdivided and stiffened.

Why fitted: when a ship moves, water is pushed aside creating a bow wave. At moderate speeds (Froude number about 0.25 to 0.35 typical of merchant ships) the bulb creates its own system of waves, and by correct sizing and position the bulb's wave trough cancels part of the bow wave crest of the hull, reducing the wave-making (residual) resistance. The net result is a reduction in total resistance at the design speed, giving:

• lower installed power and fuel consumption (better EEDI);
• improved ship propulsion economics;
• reduced bow wave and stern wave of the ship in general;
• assistance in carrying forefoot buoyancy, helping the ship's longitudinal distribution of buoyancy and allowing finer, faster forms without a large bow wave penalty.

The bulb is essentially an interference device that cancels bow-wave energy, and is most beneficial at the design/ballast speeds of displacement vessels (bulk carriers, tankers, container ships, general cargo, ro-ro).

Panting

Panting refers to the in-and-out flexing or pulsation of the shell plating at the ends of a ship, mainly caused by variations in sea pressure during pitching motions in rough weather.

When a ship moves through heavy seas, especially while pitching, the water pressure acting on the bow and stern changes continuously. These fluctuating pressures cause the side shell plating to vibrate and flex. The effect is known as panting.

The forward end of the ship is affected more severely than the aft end because:

• The bow directly encounters incoming waves while the ship is making headway.
• Water pressure at the fore end changes rapidly as the bow rises and falls in the sea.

The affected areas are mainly:

• Forward shell plating near the bow
• Side shell plating at the fore peak region
• To a lesser extent, the aft end of the ship

Effects of Panting

Panting can lead to:

• Repeated flexing and vibration of shell plating
• Fatigue stresses in plating and framing
• Loosening of rivets or welded joints
• Cracking or deformation of structural members
• Reduction in structural strength if not properly reinforced

Therefore, special strengthening arrangements are provided at the forward and aft ends of the vessel to resist panting stresses.

Pounding

Pounding refers to the heavy impact experienced at the bottom forward part of the ship when the bow emerges from the water during pitching and then slams violently back onto the sea surface.

This condition usually occurs when:

• The ship is pitching heavily in rough seas,
• The fore part lifts clear of the water due to heaving and pitching motions,
• The bow then falls heavily onto the wave surface.

The effect is most severe when the vessel is in the light ship condition, because the bow rises more easily out of the water.

The main area affected by pounding is:

• The bottom shell plating in the forward region of the ship,
• Especially near the forefoot and forward bottom structure.

The stern may also experience similar impacts from following seas, but usually to a lesser extent.

Effects of Pounding

Pounding produces:

• Severe impact stresses on bottom plating
• Buckling or deformation of bottom structure
• Cracks in shell plating or framing
• Structural fatigue and weakening
• Damage to internal supporting members

To withstand these heavy impact loads, the forward bottom structure is specially strengthened.

Special structural arrangements are incorporated in ship construction to resist the stresses caused by panting and pounding.

Structural Arrangements to Resist Panting

The following strengthening arrangements are provided mainly at the bow and stern regions:

1. Panting Beams

Panting beams are horizontal beams fitted across the ship near the bow and stern.

Their purpose is to:

• Support the side shell plating,
• Reduce excessive flexing,
• Increase structural rigidity against panting stresses.

2. Panting Stringers

Panting stringers are horizontal girders fitted along the ship side in the panting region.

They:

• Connect frames together,
• Provide additional stiffness to the shell plating,
• Help distribute fluctuating sea pressure loads.

3. Close-Spaced Framing

Frames in the panting region are spaced closer together than in other parts of the ship.

This:

• Provides better support to shell plating,
• Reduces plate vibration and deformation.

Structural Arrangements to Resist Pounding

To resist pounding stresses at the forward bottom region, additional strengthening is provided.

1. Increased Bottom Plating Thickness

The shell plating near the keel and forward bottom region is made thicker.

Usually:

• The first few strakes of bottom plating on either side of the keel are increased in thickness.

This enables the structure to withstand repeated impact loads.

2. Plate Floors

Solid plate floors are fitted at closer spacing in the forward bottom region.

These:

• Strengthen the bottom structure,
• Distribute pounding stresses more effectively,
• Prevent deformation of bottom plating.

3. Additional Internal Reinforcement

Extra brackets, girders, and stiffeners may also be provided in the fore peak and bottom structure to improve strength and rigidity.

Frictional resistance arises due to the interaction between the ship's hull and the water as the vessel moves. This resistance is caused by eddying water adjacent to the hull that is drawn along with the ship. The frictional resistance is given by:

$$R_{f\:=\:}f\:.\:s\:.\:v^{n}$$

Where:

• f = Coefficient of friction
• s = Wetted surface area
• v = Ship's speed in knots
• n = Constant (1.82)

• Frictional resistance increases with increasing ship speed. The relationship is not perfectly linear, but it's approximately described by the formula Rf = fsv^n (Rf ∝ v^n), where 'n' is a constant (approximately 1.82). This means that a small increase in speed results in a larger increase in frictional resistance.

• Frictional resistance is directly proportional to the wetted surface area (Rf ∝ s). A larger wetted area (the part of the hull submerged in water) leads to greater frictional resistance. The wetted area increases with the ship's draught (depth in the water).

• Increased surface roughness increases frictional resistance. Roughness can be caused by fouling (marine growth), corrosion, or poor hull maintenance. Regular cleaning and maintenance of the hull surface help to minimise roughness and reduce resistance.

• Frictional resistance is influenced by the vessel's length. As the length increases, the wetted surface area grows, and the coefficient of friction (f) changes, leading to an increase in Rf. Longer vessels experience higher frictional resistance, but streamlined designs can mitigate the effect to some extent.

Masses at the bottom:

• The centre of gravity (G) moves down.
• Metacentric height (GM) increases, resulting in greater stability.
• Rolling period decreases.

Masses at the top:

• The centre of gravity (G) moves up.
• Metacentric height (GM) decreases, reducing stability.
• Rolling period increases.

Masses concentrated at the centre:

• The radius of gyration (K) decreases.
• Rolling period decreases.

Masses distributed away from the centre:

• The radius of gyration (K) increases.
• Rolling period increases.

The factor of subdivision introduces a safety measure by reducing the size of the compartments to limit the effects of flooding. It ensures that the ship's draft or trim has less chance of touching the margin line during flooding or heeling.

Permissible Length Formula:

$$Permissible\:length=\frac{Floodable\:length}{Factor\:of\:Subdivision}$$

A smaller factor of subdivision leads to a smaller permissible length, requiring more numerous and smaller compartments. This reduces the potential for catastrophic flooding, as a smaller flooded area is less likely to exceed the ship's reserve buoyancy and cause it to sink. The factor of subdivision is determined by the ship's length and its intended service. The nature of service is quantified by a "criterion of service" (Cs) number, which considers the proportion of passenger and machinery spaces to the total volume of the ship. A higher Cs number (indicating more passenger space) typically results in a lower factor of subdivision and therefore smaller compartments.

$$Excess\:moment=31000-16200=14800$$

$$LCG=\frac{\sum M}{\sum m}=\frac{14800}{16000}$$

$$LCG=0.925m\:fwd\:of\:midship$$

$$LCG=0.925m\:Fwd\:of\:midship$$

$$LCB=2.02m\:Fwd\:of\:midship$$

$$Trimming\:lever=LCB-LCG$$

$$2.02-0.925$$

$$=1.09m$$

$$Trimming\:moment=m\times d$$

$$=16000\times1.09$$

$$=17440tm$$

$$Change\:of\:trim=\frac{Trimming\:moment}{MCT_{1\operatorname{\mathrm{cm}}}}$$

$$=\frac{17440}{179}$$

$$97.43\operatorname{cm}$$

$$Draft\:fwd=8.25-\frac{97.43}{100\times120}\left(\frac{120}{2}+0.57\right)$$

$$=7.756m$$

$$Draft\:aft=8.25+\frac{97.43}{100\times120}\left(\frac{120}{2}-0.57\right)$$

$$=8.735m$$

Masses at the bottom:

• The centre of gravity (G) moves down.
• Metacentric height (GM) increases, resulting in greater stability.
• Rolling period decreases.

Masses at the top:

• The centre of gravity (G) moves up.
• Metacentric height (GM) decreases, reducing stability.
• Rolling period increases.

Masses concentrated at the centre:

• The radius of gyration (K) decreases.
• Rolling period decreases.

Masses distributed away from the centre:

• The radius of gyration (K) increases.
• Rolling period increases.

$$Radius\:\left(R\right)=100m$$

$$Speed\:\left(v\right)=15\:knots$$

$$GM=\frac23m$$

$$BG=1m$$

$$\tan\the\theta=\frac{v^2\times BG}{g\times r\times GM}$$

$$=\frac{\left(15\times0.514\right)^2\times1\times3}{9.81\times100\times2}$$

$$\theta=5.19\degree$$

Erosion:

• Cavitation causes the formation and collapse of vapor bubbles on the propeller blade surface.
• The collapse of these bubbles produces high-pressure shockwaves and microjets that erode the blade material, leading to surface pitting and progressive damage.

Vibration:

• Uneven cavitation across the blades leads to imbalanced forces, causing vibrations in the propeller and the ship.
• These vibrations can reduce the comfort of passengers and crew and stress the ship's structural components.

Noise:

• The collapse of vapor bubbles generates loud noise, which can interfere with onboard communication and underwater sonar systems.
• This noise is a significant concern for naval vessels and marine life.

Reduced Performance:

• Cavitation reduces the efficiency of the propeller by causing loss of thrust and torque.
• The presence of cavitation decreases the propeller’s ability to convert rotational energy into forward motion, lowering the ship's speed and increasing fuel consumption.

(b) Given:

$$D=4.6m$$

$$P=4.3m$$

$$d=0.75$$

$$S=28\%$$

$$n \space = \space 95 \space rev/ min$$

$$V_T \space = \space P \times N \times {{3600} \over 1852}$$

$$ = \space 4.3 \times {{95} \over 60} \times {{3600} \over 1852}$$

$$V_{T}=13.23knots$$

$$Real \space slip \space (S) \space = \space {{V_T - V_a} \over V_T}$$

$$0.28 \space = \space {{13.23 - V_a} \over 13.23}$$

$$V_{a}=9.52knots$$

$$Effective\:disc\:area\:\left(A\right)\:={{\pi}\over4}\left(D^2-d^2\right)$$

$$= {{\pi} \over 4} (4.6^2 - 0.75^2)$$

$$A=16.18m^2$$

$$Thrust\space=\space\rho AP^2n^2S$$

$$=1.025\times16.18\times4.3^2\times\left(\frac{95}{60}\right)^2\times0.28$$

$$T=215.25KN$$

$$Thrust \space power (T_p) \space = \space T \times V_a $$

$$215.25\times9.52\times\frac{1852}{3600}$$

$$T_{p}=1054.18KW$$

• Positive GM (Metacentric Height): The ship needs a positive GM. GM is the distance between the centre of gravity (G) and the metacentre (M). A positive GM indicates inherent stability; the ship will right itself if tilted. During dry-docking, the loss of buoyancy as the ship rests on the blocks reduces GM. Insufficient positive GM increases the risk of the ship heeling over or capsizing.

• Trim by the stern: The vessel should be trimmed slightly by the stern (aft end lower than the bow) to ensure the aft end sits on the keel blocks first. This controlled settling minimises the risk of instability during the docking process. An even keel is generally preferred for the initial floating condition before the dry-docking procedure begins.

Freeboard is the distance measured from the waterline to the upper edge of the deck plating at the side of the freeboard deck amidships.

• Ensures the ship is seaworthy when fully loaded.
• Provides reserve buoyancy, enabling the ship to rise as it passes through waves, keeping decks largely dry.
• Enhances the ship's stability and increases its survivability in case of damage by allowing it to remain afloat longer, aiding crew escape or damage control.

Conditions of Assignment are outlined in the Merchant Shipping Load Line Rules 1968 and must be satisfied before a ship is assigned freeboards and issued a load line certificate. These conditions address the practical need for openings (hatchways, doorways, vents, etc.) in the ship's hull and mandate appropriate protection and closure mechanisms for these openings.

Requirements Before Assigning Load Line:

• The ship must have sufficient structural strength.
• Adequate reserve buoyancy must be maintained.
• Openings must be secured against water ingress.
• Safety measures for the crew, such as guardrails and gangways, must be in place.

To ensure that the conditions of assignment are still current the following items can be checked and confirm to be without change or damage from when the ship was built.

• Access openings in bulkheads, to ensure that they can be sealed and prevent flooding
• Cargo and hatchways ensure they can be sealed to prevent flooding
• Coamings of hatchways, sign of corrosion damage risk of failure would allow flooding
• Protection of openings, can they all be sealed
• Ventilator coamings not corroded as they would allow flooding to other arears
• Air pipes can be shut in heavy weather and not corroded
• Discharges, inlets and scuppers, all in good condition and operational
• Side scuttles can be secured
• Hull inspection, sea boxes and penetrations all checked for damage and corrosion free.

TYPE “A” VESSELS:

• A ship that is designed to carry only liquid cargoes in bulk and in which cargo tanks have only small access openings, closed by water-tight gasketed covers of steel or equivalent material.
• The exposed deck must be one of high integrity.
• It must have a high degree of safety against flooding, resulting from the low permeability of loaded cargo spaces and the degree of bulkhead subdivision usually provided.

TYPE “B” VESSELS: all ships that do not fall under type "A" vessels are type "B" ships. For these ships, it may be based on :

• The vertical extent of damage is equal to the depth of the ship.
• The penetration of damage is not more than 1/5 of the breadth moulded.
• No main transverse bulkhead is damaged.
• Ship’s Kg is assessed for homogenous loading of cargo holds and 50% of the designed capacity of consumable fluids and stores etc.

are significant and arise due to various factors:

• Galvanic corrosion occurs due to the interaction between dissimilar metals, accelerated by the seawater environment and differential aeration.
• Sulphate-reducing bacteria in river mud can cause localized pitting, leading to penetration of the bottom shell.
• Dissolved oxygen in seawater reacts with metal surfaces to form rust, significantly contributing to structural deterioration.
• The rate of corrosion peaks at a 3.5% salt concentration, typical of seawater.
• Neglecting maintenance exacerbates the problem, allowing corrosion to progress unchecked.

(ii) Protection against extensive corrosion in ballast tanks involves the following measures:

• Complete coating of the tank surfaces with properly selected marine-grade paint to create a protective barrier.
• Installation of sacrificial anodes, designed to corrode preferentially and protect the tank structure.
• Using large anodes with greater volume relative to surface area to ensure extended protection.
• Regular gauging of plates to assess thickness and identify areas requiring reinforcement or repair.
• Conducting regular inspections, cleaning the tanks, removing rust, and repainting to maintain structural integrity and prolong the lifespan of the ballast tanks.

Bilge keels are fitted port and starboard at the turn of the bilge. They do not extend outside the lines of the side and bottom shell. The bilge keels are attached directly in line with an internal stiffening member such as a girder or longitudinal. The bilge keel comprises a flat bar doubler welded directly to the shell, and an offset bulb plate (OBP) with 'scallops' cut in it is welded to the flat bar doubler. The ends of the bilge keels are tapered (minimum 3 in 1) and will end in line with transverse internal stiffening, such as a frame. Using a hull doubler protects the hull in case of damage to the keel, as the crack would not extend into the hull.

• The 'lever' to the ship's axis of rotation is reduced at the ends;
• The ineffectiveness, the closer the bilge keel is to the rolling centre, increased resistance and more likelihood of damage.
• The hydrodynamic effect would cause a large increase in resistance and fuel consumption;
• At the aft end, the boundary layer is much thicker, and since the keel would not project through, it would have a much reduced effect.

• Hawse pipes: These are openings in the hull through which the anchor chain passes.
• Cable stopper: Positioned on the deck near the hawse pipes, the cable stopper is used to secure the anchor chain in place.
• Windlass: Located on the deck near the hawse pipes, the windlass is a mechanical device used to raise and lower the anchor and its chain.
• Cable lifts: These are devices used to guide the anchor chain from the windlass into the chain locker below deck.
• Spurling pipe: A vertical pipe leading from the windlass to the chain locker, through which the anchor chain passes.
• Chain locker: Below deck, typically located near the bow, the chain locker is a compartment where the anchor chain is stowed when not in use.

1. Primary Barrier: A thin membrane made of INVAR (36% Nickel, 64% Iron) with a thickness of 0.5 to 1.2 mm, forming the primary containment layer for the liquefied gas.
2. Primary Insulation box: A 200 mm thick layer of granulated Perlite insulation packed in plywood boxes, surrounding the primary barrier. Perlite is siliconised to make it impervious to moisture.
3. Secondary Barrier: A secondary membrane made of the same INVAR material is installed to prevent cargo leakage in case of primary barrier failure.
4. Secondary Insulation box: Another 200 mm thick layer of granulated Perlite is placed above the secondary barrier to provide additional insulation and prevent thermal transfer.

Invar (36% Ni, 64% Fe) is used for both the primary and secondary barriers. The reason for this choice is its exceptionally low coefficient of thermal expansion. This eliminates the need for expansion joints or corrugations in the membrane design. In addition, Invar remains strong and does not become brittle at the very low temperatures experienced by the liquefied gas. The thin and lightweight nature of Invar maximizes the cargo-carrying capacity of the tank.

If the ship grounds on a level bottom:

• A ground reaction force acts vertically upwards from the seabed. This force counteracts part of the ship's weight and alters the distribution of buoyancy forces.
• The ship’s centre of gravity (G) may appear to rise relative to the metacentre (M) because the upward ground reaction reduces the buoyancy force acting on the underwater volume.
• This virtual rise in G reduces GM, potentially leading to a list.
• If the list becomes excessive and the righting moment is insufficient, the ship may capsize.

If the ship grounds on a pinnacle:

• The ship experiences two forces at the ship's bottom:
  • A downward force due to the ship’s weight.
  • An upward reaction force is concentrated on the pinnacle.
• The resulting force between the grounding pressure and the ship’s centre of buoyancy shifts downward towards the pinnacle.
• This situation is similar to when the ship's stern touches the keel block in a dry dock.
• A virtual loss of GM occurs because the ship’s inclining moment may exceed the maximum righting lever.
• If the inclining moment is too great, the ship may develop an excessive list or even capsize.

(b) Given:

$$Displacement,\:\Delta=8000\:tonnes$$

$$TPC=15\:tonnes$$

$$Initial\:Draught=5.2m$$

$$Final\:Draught=3.2m$$

$$Ship\:KG=4.0m$$

$$KM=5.0m$$

To find GM

$$Uptrust,\:P=TPC\times Fall\:in\:water\:level\:\left(cm\right)$$

$$=15\times\left(520-320\right)$$

$$=15\times200$$

$$P=3000\:tonnes$$

To Find Virtual loss of GM:

$$Virtual\:loss\:of\:GM_1=\frac{P\times KM}{\Delta}$$

$$=\frac{3000\times5}{8000}$$

$$=\frac{15000}{8000}$$

$$GM_1=1.88m$$

Actual KM = 5.0m (given)

$$Virutal\:KM=Actual\:KM-Virtual\:loss\:of\:GM_1$$

$$=5.0-1.88$$

$$=3.12$$

Similarly, Actual KG = 4.0m (given)

$$New\:GM=Virtual\:KM-\:Actual\:KG$$

$$=3.12-4.0$$

$$=-0.88$$

Before entering the dock the ship must have adequate and known stability. The requirements are:

• The ship should be stable with an adequate GM, so that the small upward force (reaction) at the keel, building during docking, cannot produce a list. Dock support is provided on the keel blocks and any excessive list during docking would subject the structure and blocks to unequal loading.
• As the water is pumped out, the reaction of the keel blocks reduces the effective displacement of the ship, lowering the KB and BM and hence GM; if all buoyancy were removed the ship would rest wholly on the blocks. The ship must retain sufficient GM throughout the docking operation (for example by keeping the GM such that the maximum inclination, where the righting moment at the critical point, does not become negative).
• Ballast should be arranged to give even keel (or slight trim) and list-free condition; tanks should be pressed up or emptied to avoid free-surface effects, and draft read before docking.
• Weight and trim must be such that the keel blocks contact evenly over the full keel length (avoid excessive trim that overloads the block crown or aft blocks).
• Cargo/weights should not be changed and the dock must be level; adequate dock pumping should keep the vessel central over the keel line.

If a beam vessel develops instability while docking (transverse GM small or negative), it can heel and capsize on the blocks; hence a suitable stability margin (e.g. GM not less than a minimum) is insisted on and the docking weight, draft and trim are checked by stability data (e.g. from hydrostatics and the Docking Plan).

Box-shaped vessel 50 m long, 10 m wide, floats on even keel in salt water at a draft of 4 m. A centreline longitudinal watertight bulkhead runs full depth/size. A midship compartment on the starboard side is 15 m long and has permeability 30 per cent. KG = 3 m. Calculate the list when bilged.

Waterplane area intact Aw = 50 x 10 = 500 m2; the flooded wing compartment has waterplane area = 15 x 5 = 75 m2 (only starboard half up to the centreline bulkhead).

Lost buoyancy volume of the compartment below the original waterline, with permeability 30%: Vlost = length x breadth x draft x permeability = 15 x 5 x 4 x 0.30 = 90 m3. Corresponding lost weight W = 90 x 1.025 = 92.25 t.

Sinkage: the region once flooded provides no increase of buoyancy; effective sinking waterplane = 500 - 75 = 425 m2. Mean sinkage = 90/425 = 0.212 m.

List: the lost buoyancy acts at the centroid of the lost volume, which is at 5/4 = 2.5 m out from the centreline (half-way between centreline bulkhead and side). Heeling moment = W x y = 92.25 x 2.5 = 230.6 t-m.

New GM. Using the lost-buoyancy method, displacement remains 2050 t. The second moment of area of the intact waterplane about the centreline loses the flooded starboard compartment: I(intact)=50x10^3/12 = 4166.7 m4; I(flooded)=15x5^3/3 = 625 m4; so I(new)=3541.7 m4. BM=new = I(new)/V = 3541.7/2000 = 1.771 m. KB = d/2 = 2 m (approximately, ignoring sinkage and list); GM = KB + BM - KG = 2 + 1.77 - 3 = 0.77 m.

List: tan(list) = heeling moment/(Delta x GM) = 230.6/(2050 x 0.77) = 230.6/1579 = 0.146. List = atan(0.146) = 8.3 deg.

Answer: the vessel lists about 8.3 deg to starboard.

• The Longitudinal Centre of Gravity (LCG) is the point along the length of the vessel where the total weight of the ship is considered to act vertically downward.
• It represents the balance point of the ship's weight distribution and is measured as a distance forward or aft of the midship.

Longitudinal Centre of Buoyancy (LCB):

• The Longitudinal Centre of Buoyancy (LCB) is the point along the length of the vessel through which the total buoyant force, acting vertically upward, is considered to act.
• It represents the balance point of the underwater volume of the ship and is also given as a distance forward or aft of the midship.

LCF in fwd and trim by stern

$$Bodily \space sinkage \space = \space {{mass \space added} \over TPC} \space = \space {{110} \over 13} \space$$

$$=\:8.5\operatorname{\mathrm{cm}}\:=0.085m$$

$$Trim \space = \space {{m \times d} \over MCT_{1cm}}$$

$$ = \space {{110 \times (24 + 2.5)} \over 80}$$

$$Trim=36.43\operatorname{cm}=0.364m\:$$

Change in fwd draught:

$$d_{F}=\frac{-t}{L}\left\lbrack\frac{L}{2}-LCF\right\rbrack$$

$$=\frac{-36.43}{120}\left\lbrack\frac{120}{2}-2.5\right\rbrack$$

$$=-17.45\operatorname{cm}=-0.1745m$$

Change in Aft draught:

$$d_{A}=\frac{+t}{L}\left\lbrack\frac{L}{2}+LCF\right\rbrack$$

$$=\frac{+36.43}{120}\left\lbrack\frac{120}{2}+2.5\right\rbrack$$

$$=+18.97\operatorname{cm}=0.189m$$

New draughts:

$$D_{F}=5.5+0.085-0.175=5.41m$$

$$D_{A}=5.8+0.085+0.18=6.065m$$

Main Components of Ship Resistance

When a vessel moves through water, it experiences total resistance, which is the combined effect of several opposing forces acting against its forward motion. These forces arise due to water viscosity, pressure distribution around the hull, wave formation, and external environmental conditions. For analysis, total resistance is divided into the following main components:

1. Frictional Resistance

Frictional resistance is caused by the viscosity of water acting along the ship’s wetted surface as the vessel moves forward. As water flows over the hull, a thin boundary layer forms, and shear stresses develop between the hull surface and adjacent water particles. This shear stress produces resistance.

Frictional resistance depends primarily on:

• Wetted surface area – A larger underwater hull area increases the contact between hull and water, thereby increasing resistance.
• Ship speed – Resistance increases rapidly with speed because higher velocity intensifies boundary layer shear forces.
• Surface roughness of the hull – Fouling, corrosion, or rough coatings increase turbulence and significantly raise resistance.

At normal service speeds, frictional resistance forms the largest portion of total resistance, especially for slow and medium-speed vessels. It increases approximately with the square of the ship’s speed, making hull maintenance crucial for fuel efficiency.

2. Residual Resistance

Residual resistance is the portion of resistance remaining after subtracting frictional resistance from total resistance. It mainly arises from pressure effects and wave formation around the hull. Residual resistance consists of the following components:

(a) Wave-Making Resistance

Wave-making resistance is caused by the energy expended in generating surface waves at the bow and stern as the ship moves. When a vessel travels through water, it disturbs the free surface and creates a wave system that carries energy away from the ship.

This resistance becomes particularly significant at higher speeds because wave height and wave energy increase rapidly with speed.

Wave-making resistance depends on:

• Hull form – Fuller hull shapes generally create larger waves.
• Speed–length ratio (Froude number) – As the Froude number increases, wave-making resistance rises sharply.

At high speeds, wave-making resistance can become a dominant component of total resistance.

(b) Eddy-Making Resistance

Eddy-making resistance is caused by flow separation and the formation of vortices (eddies) around certain parts of the hull. When water flow cannot smoothly follow the hull contour, it separates and creates turbulent regions.

This commonly occurs around:

• The stern region
• Appendages
• Areas with sudden changes in hull form

These turbulent eddies consume energy and increase resistance. Proper streamlining of the hull and stern design can significantly reduce eddy-making resistance.

3. Air Resistance

Air resistance is the force exerted by air on the portion of the ship above the waterline. As the ship moves, it must also overcome aerodynamic drag.

Air resistance depends on:

• Wind speed and direction
• Projected area above water
• Shape of the superstructure

Although usually small compared to water resistance, it becomes significant for:

• Container ships
• Ro-Ro vessels
• Ships operating in strong headwinds

For vessels with large exposed areas, air resistance can noticeably affect fuel consumption.

4. Appendage Resistance

Appendage resistance is caused by external fittings attached to the hull, such as:

• Rudders
• Bilge keels
• Shaft brackets
• Propeller bossings

These appendages increase the wetted surface area and disturb smooth water flow, thereby increasing both frictional and pressure resistance. In resistance calculations, appendage resistance is generally included as a separate correction added to frictional resistance.

5. Added (Special) Resistance

Added resistance refers to the additional resistance experienced in real sea conditions that is not present in calm-water trials.

It occurs due to:

• Waves and swell, which cause pitching and heaving motions
• Steering and yawing motions, which disturb steady flow around the hull

Although not considered in calm-water resistance analysis, added resistance is highly important in practical operations because it significantly affects power requirements and fuel consumption in rough weather.

is the difference between the theoretical distance the propeller should travel in one revolution and the actual distance the vessel travels.

$$Slip\:\left(\%\right)\:=\:\left(\frac{Engine\:distance\:-\:Ship^{\prime}s\:distance}{Engine\:distance}\right)\:\times100$$

Where Engine distance = no. of propeller revolutions * propeller pitch (usually calculated over a 24-hour period)

Propeller thrust: it is the force exerted by the propeller to move the vessel ahead and given by

$$Thrust\:\left(T\right)\:=\:\rho\times A\times P^2\times n^2\times S$$

Where,

ρ - Density

A - Area

P - Pitch

n - Revolution per second

S - Slip

• Armaflex (sheet or pipe insulation made from black flexible nitrile elastomer)
• Calcium silicate
• Polyurethane, pearlite, cork, glass fibre, rock wool, plastic foam

• Low thermal conductivity (high insulating capacity)
• Thickness
• Fire retardant
• Moisture resistance
• Vibration resistance
• Vermin resistance (vermin - cockroaches and insects)

(a) Prior to Docking:

Preliminary Preparation:

• Review various plans, manuals, and previous drydock reports for reference.
• Prepare a detailed repair list and ensure all required spares are accounted for.
• Conduct an inventory of spares and requisition necessary items.
• Gather required tools, including special tools like poker gauges, trammel gauges, gagging tools, etc.
• Mark all overboard valves, NC (normally closed) and NO (normally open) valves clearly for easy identification.
• Allocate jobs to team members and discuss the time schedule.
• Conduct a safety meeting to highlight dry dock hazards and necessary precautions.

Before Entering Dry Dock:

• Identify the power requirements and machinery to be operational during docking.
• Check the shore connection box for proper functionality.
• Record the soundings of FO (Fuel Oil), LO (Lubricating Oil), and DO (Diesel Oil) tanks.
• Discharge contents from clean drain tanks and sewage tanks.
• Carry out Economizer soot-blowing.
• Change over Main Engine, Diesel Generators, and Boiler to Low Sulfur Gas Oil (LSGO).
• Stop and clean purifiers.
• Ensure the low sea chest is open and the high sea chest is shut.
• Keep firefighting appliances (FFA) on standby.
• Shut down all non-essential machinery, including MGPS (Marine Growth Prevention System) and FWG (Fresh Water Generator).

(b) Whilst the Vessel is in Dry Dock

Upon Arrival:

• Connect shore power and supplies after ensuring safety checks are completed.
• Start necessary equipment like cooling water, air compressors, air conditioning, and fridge compressors.
• Check for jobs assigned by dry dock personnel and prepare accordingly.
• Attend a safety meeting with dry dock personnel to understand local safety rules and procedures.

During Dry Docking::

• Oversee and assist in:
  • Cleaning and inspecting the hull, rudder, sea chest, anodes, and propeller.
  • Measuring propeller drop, checking rudder clearances, and inspecting the stern tube bearing and seal.
  • Servicing underwater valves and overboard valves.
  • Inspecting anchor and cables conditions.
  • Overhauling deck machinery, cranes, elevators, and engine room equipment such as the Main Engine, Diesel Generators, Boiler, and Economizer.
  • Renewing pipes and valves as needed.
  • Performing electrical equipment maintenance and surveys.
  • Supervising service engineers for specific repair jobs.
• Ensure tank cleaning, welding, and other repair works are completed according to the plan.
• Run the standby diesel generator daily after starting the priming pump.

(c) Before Flooding and Leaving the Dry Dock

Final Checks:

• Verify that all underwater fittings and drain plugs are securely in place.
• Ensure all machinery has been boxed back and is ready for operation.
• Check for any leakage in stern tube seals.
• Take tank soundings to confirm proper levels.
• Confirm the proper operation of all underwater valves, overboard valves, sea chests, and vents.
• Inspect the stern tube tank for any irregularities.

System Restart:

• Switch back to ship's power after confirming all systems are functional.
• Test the proper operation of all machinery and systems to ensure the ship is fully operational before leaving the dock.

Permissible length refers to the maximum length of a ship's compartment that can be flooded while ensuring that the sinkage, heel, or trim remains within acceptable limits without exceeding the floodable length. It ensures the ship remains afloat and stable after flooding.

Permissible Length Formula:

$$Permissible\:lenght\:=\:Floodable\:length\:\times Factor\:of\:subdivision$$

The Factor of Subdivision depends on the ship's length and the nature of its service:

• For passenger ships, the factor of subdivision is smaller compared to cargo ships.
• Smaller compartments ensure enhanced safety in case of flooding.

The position of bulkheads is determined based on the need to comply with the "reasonable amount of damage" criterion in case of flooding:

• Transverse Watertight Bulkheads should vertically extend up to the margin line.
• At least one watertight longitudinal bulkhead must be located 20% of the ship's breadth inward from each side.
• Bulkheads are positioned along the ship's length at intervals equal to the permissible length, but not exceeding the floodable length.
• The maximum permissible compartment length is limited to 10.7 meters.
• Collision Bulkhead must be located forward at a distance equal to the permissible length from the forward perpendicular.
• The ER must be enclosed by two transverse watertight bulkheads, with an aft peak watertight bulkhead enclosing the forward part.

The factor of subdivision introduces a safety measure by reducing the size of the compartments to limit the effects of flooding. It ensures that the ship's draft or trim has less chance of touching the margin line during flooding or heeling.

Permissible Length Formula:

$$Permissible\:length=\frac{Floodable\:length}{Factor\:of\:Subdivision}$$

A smaller factor of subdivision leads to a smaller permissible length, requiring more numerous and smaller compartments. This reduces the potential for catastrophic flooding, as a smaller flooded area is less likely to exceed the ship's reserve buoyancy and cause it to sink. The factor of subdivision is determined by the ship's length and its intended service. The nature of service is quantified by a "criterion of service" (Cs) number, which considers the proportion of passenger and machinery spaces to the total volume of the ship. A higher Cs number (indicating more passenger space) typically results in a lower factor of subdivision and therefore smaller compartments.

The period of roll Tr of a ship is determined by the formula:

$$T_{r}=\frac{2\pi K}{\sqrt{g\times GM}}$$

where,

• K is the radius of gyration (mass moment of inertia)
• g is the acceleration due to gravity, and
• GM is the metacentric height.

• The amplitude of roll, or the maximum angle of heel, does not affect the period of roll. While a larger amplitude implies a greater heeling moment and faster roll speed, the time taken to complete one full roll cycle remains constant for a given metacentric height and radius of gyration.

• The period of roll is directly proportional to the radius of gyration. A larger radius of gyration (indicating a greater distribution of mass further from the ship's centre of rotation) leads to a longer period of roll. Conversely, a smaller radius of gyration (mass concentrated closer to the centre) results in a shorter period. The distribution of cargo significantly impacts K; cargo concentrated centrally minimises K and the roll period, while dispersed cargo maximises K and the roll period.

• The period of roll is inversely proportional to the square root of the metacentric height (GM). A larger GM (a stiffer ship) leads to a shorter roll period, as the ship quickly returns to its upright position. A smaller GM (a tender ship) results in a longer roll period, with slower return to the upright.

The location of masses in the ship will effect the GM & K. So the period of roll will be affected.

• If masses are at bottom, G moves down, GM ↑, period of roll ↓.
• If masses are at top, G moves up, GM ↓, period of roll ↑.
• If masses are concentrated at centre, K ↓, period of roll ↓.
• If masses are away from centre, K ↑, period of roll ↑.

Frictional resistance arises due to the interaction between the ship's hull and the water as the vessel moves. This resistance is caused by eddying water adjacent to the hull that is drawn along with the ship. The frictional resistance is given by:

$$R_{f\:=\:}f\:.\:s\:.\:v^{n}$$

Where:

• f = Coefficient of friction
• s = Wetted surface area
• v = Ship's speed in knots
• n = Constant (1.82)

• Frictional resistance increases with increasing ship speed. The relationship is not perfectly linear, but it's approximately described by the formula Rf = fsv^n (Rf ∝ v^n), where 'n' is a constant (approximately 1.82). This means that a small increase in speed results in a larger increase in frictional resistance.

• Frictional resistance is directly proportional to the wetted surface area (Rf ∝ s). A larger wetted area (the part of the hull submerged in water) leads to greater frictional resistance. The wetted area increases with the ship's draught (depth in the water).

• Increased surface roughness increases frictional resistance. Roughness can be caused by fouling (marine growth), corrosion, or poor hull maintenance. Regular cleaning and maintenance of the hull surface help to minimise roughness and reduce resistance.

• Frictional resistance is influenced by the vessel's length. As the length increases, the wetted surface area grows, and the coefficient of friction (f) changes, leading to an increase in Rf. Longer vessels experience higher frictional resistance, but streamlined designs can mitigate the effect to some extent.

Masses at the bottom:

• The centre of gravity (G) moves down.
• Metacentric height (GM) increases, resulting in greater stability.
• Rolling period decreases.

Masses at the top:

• The centre of gravity (G) moves up.
• Metacentric height (GM) decreases, reducing stability.
• Rolling period increases.

Masses concentrated at the centre:

• The radius of gyration (K) decreases.
• Rolling period decreases.

Masses distributed away from the centre:

• The radius of gyration (K) increases.
• Rolling period increases.

Thus, when the ship is being loaded, its GM will start to decrease.

Now, the time period of roll is given by:

$$T_{r}=\frac{2\pi k}{\sqrt{GM.g}}$$

Where,

• k = radius of gyration
• GM = metacentric height
• g = acceleration due to gravity

Now, since, GM has started to decrease, the Tr will start to increase.

Thus, the ship will now roll with greater time period. Thus, an increase in draught and displacement, influences rolling.

Given:

$$D=6m$$

$$p=0.9$$

$$BAR=0.48$$

$$N=110rev\:per\min$$

$$real \space slip \space (s) \space = \space 25\%$$

$$W_{F}=0.3$$

$$Thrust \space = \space 300kN$$

$$η_{prop} \space = \space 0.65$$

(i) Blade area:

$$BAR \space = \space {{A_b} \over {{\pi} \over 4} D^2}$$

$$Blade \space area \space A_b \space = \space 0.48 \times {{\pi} \over 4} 6^2$$

$$Blade \space area \space = \space 13.57m^2 $$

$$p \space = \space {{P} \over D}$$

$$0.9 \space = \space {{P} \over 6}$$

$$Pitch \space p = \space 5.4m$$

$$V_{T}=P\times N\times\frac{3600}{1852}$$

$$V_{T}=5.4\times\frac{110}{60}\times\frac{3600}{1852}$$

$$V_{T}=19.24knots$$

$$Real \space slip \space S \space = \space {{V_T - V_a} \over V_T}$$

$$ 0.25 \space = \space {{19.24 - V_a} \over 19.24}$$

$$V_a \space = \space 14.42 knots$$

$$W_F \space = \space {{V - V_a} \over V}$$

$$0.30 \space = \space {{V - 14.42} \over V}$$

$$V=20.6knots$$

$$T_{p}\space=\space Thrust\times V_{a}\times\frac{1852}{3600}$$

$$T_p \space = \space Thrust \times 14.42 \times {{1852} \over 3600 }$$

$$T_p \space = \space 2225.48 $$

$$T_p \space = \space d_p \times η_{prop}$$

$$2225.48=d_{p}\times0.65$$

$$d_p \space = \space 3423.8kW$$

$$dp=2\pi NT$$

$$3423.8=2\times\pi\times\frac{110}{60}\times T$$

$$T=297.22KN$$

$$D=800nm$$

$$V_1=?knots$$

$$V_2=0.8V_1$$

$$DC_1=Cons\:per\:day\:at\:V_1$$

$$DC_2=Cons\:per\:day\:at\:V_2$$

$$DC_1-DC_2=42t$$

$$C=\left(0.136+0.001V^3\right)\:t\h$$

$$Therefore\:DC=24\left(0.136+0.001V^3\right)\:tonnes\:per\:day$$$$42=24\left\lbrack\left(0.136+0.001V_{1^{}}^3\right)-\left(0.136_{}+0.001\left(0.8V_1^3\right)\right)\right\rbrack$$

$$42=24\left(0.136+0.001V_1^3-0.136-0.512\times10^{-3}\times V_1^3\right)$$

$$42=24\left(0.001V_1^3-0.512\times10^{-3}\times V_1^3\right)$$

$$42=24\left(0.000488V_1^3\right)$$

$$V_1=\sqrt[3]{\frac{42}{24\times0.000488}}$$

$$V_1=15.31\:knots$$

$$V_2=0.8\times V_1$$

$$V_2=0.8\times15.31$$

$$V_2=12.245\:knots$$

$$\left(i\right)\:Reduced\:cons\:per\:day\:=\:\left(0.136+0.001V_2^3\right)\times24$$

$$=\left(0.136+0.001\times12.45^3\right)\times24$$

$$=49.57\:tonnes\:per\:day$$

$$Time\:taken\:for\:complete\:voyage\:of\:800nm$$

$$at\:V_2=\frac{800}{12.245\times24}=2.72\:days$$

$$Consumption\:=\:2.72\times49.57=134.93t\:\left(at\:reduced\:speed\right)$$

$$\left(ii\right)\:Fuel\:onboard=134.93+50$$

$$=184.93t\:\left(after\:speed\:reduction\right)$$

$$DC_1=DC_2+42$$

$$DC_1=49.57+42$$

$$DC_1=91.57t$$

$$Time\:taken\:for\:V_1=\frac{800}{15.31\times24}$$

$$=2.178days$$

$$Cons\:at\:V_1=91.57\times2.178$$

$$=199.38t$$

$$\left(iii\right)\:\%\:reduction\:in\:cons=\frac{199.38-134.93}{199.38}$$

$$=32.32\%$$

$$\left(iv\right)\:\%\:increase\:in\:time=\frac{2.72-2.178}{2.178}$$

$$=24.88\%$$

1. List is caused by Uneven distribution of weight within the ship. List will have the below conditions:

• GM is positive (GM > 0).
• The centre of gravity (G) is off-centre.
• The vessel is at equilibrium but inclines to one side due to uneven weight distribution, even without any external forces acting on it.
• The vessel rolls around the angle of list.

Correction:

• Redistribute the weight evenly to bring the centre of gravity (G) back in line with the centerline and metacentric height (M).

2. Loll is caused by High centre of gravity (G) leading to negative GM and is exacerbated by external forces, free surface effects, or poor distribution of weights. LOLL will have the below conditions:

• GM is negative (GM < 0).
• The centre of gravity (G) is on the centerline but too high, making the vessel inherently unstable.
• The vessel flops or inclines to one side at an angle of loll, and it can incline equally to either side.
• The vessel rolls unstably around the angle of loll.

Correction:

• Reduce the centre of gravity by ballasting bottom tanks or removing weight from higher levels.
• Minimize free surface effects by reducing the breadth of free surfaces in tanks.

are significant and arise due to various factors:

• Galvanic corrosion occurs due to the interaction between dissimilar metals, accelerated by the seawater environment and differential aeration.
• Sulphate-reducing bacteria in river mud can cause localized pitting, leading to penetration of the bottom shell.
• Dissolved oxygen in seawater reacts with metal surfaces to form rust, significantly contributing to structural deterioration.
• The rate of corrosion peaks at a 3.5% salt concentration, typical of seawater.
• Neglecting maintenance exacerbates the problem, allowing corrosion to progress unchecked.

(ii) Protection against extensive corrosion in ballast tanks involves the following measures:

• Complete coating of the tank surfaces with properly selected marine-grade paint to create a protective barrier.
• Installation of sacrificial anodes, designed to corrode preferentially and protect the tank structure.
• Using large anodes with greater volume relative to surface area to ensure extended protection.
• Regular gauging of plates to assess thickness and identify areas requiring reinforcement or repair.
• Conducting regular inspections, cleaning the tanks, removing rust, and repainting to maintain structural integrity and prolong the lifespan of the ballast tanks.

(a) Prior to Docking:

Preliminary Preparation:

• Review various plans, manuals, and previous drydock reports for reference.
• Prepare a detailed repair list and ensure all required spares are accounted for.
• Conduct an inventory of spares and requisition necessary items.
• Gather required tools, including special tools like poker gauges, trammel gauges, gagging tools, etc.
• Mark all overboard valves, NC (normally closed) and NO (normally open) valves clearly for easy identification.
• Allocate jobs to team members and discuss the time schedule.
• Conduct a safety meeting to highlight dry dock hazards and necessary precautions.

Before Entering Dry Dock:

• Identify the power requirements and machinery to be operational during docking.
• Check the shore connection box for proper functionality.
• Record the soundings of FO (Fuel Oil), LO (Lubricating Oil), and DO (Diesel Oil) tanks.
• Discharge contents from clean drain tanks and sewage tanks.
• Carry out Economizer soot-blowing.
• Change over Main Engine, Diesel Generators, and Boiler to Low Sulfur Gas Oil (LSGO).
• Stop and clean purifiers.
• Ensure the low sea chest is open and the high sea chest is shut.
• Keep firefighting appliances (FFA) on standby.
• Shut down all non-essential machinery, including MGPS (Marine Growth Prevention System) and FWG (Fresh Water Generator).

(b) Whilst the Vessel is in Dry Dock

Upon Arrival:

• Connect shore power and supplies after ensuring safety checks are completed.
• Start necessary equipment like cooling water, air compressors, air conditioning, and fridge compressors.
• Check for jobs assigned by dry dock personnel and prepare accordingly.
• Attend a safety meeting with dry dock personnel to understand local safety rules and procedures.

During Dry Docking::

• Oversee and assist in:
  • Cleaning and inspecting the hull, rudder, sea chest, anodes, and propeller.
  • Measuring propeller drop, checking rudder clearances, and inspecting the stern tube bearing and seal.
  • Servicing underwater valves and overboard valves.
  • Inspecting anchor and cables conditions.
  • Overhauling deck machinery, cranes, elevators, and engine room equipment such as the Main Engine, Diesel Generators, Boiler, and Economizer.
  • Renewing pipes and valves as needed.
  • Performing electrical equipment maintenance and surveys.
  • Supervising service engineers for specific repair jobs.
• Ensure tank cleaning, welding, and other repair works are completed according to the plan.
• Run the standby diesel generator daily after starting the priming pump.

(c) Before Flooding and Leaving the Dry Dock

Final Checks:

• Verify that all underwater fittings and drain plugs are securely in place.
• Ensure all machinery has been boxed back and is ready for operation.
• Check for any leakage in stern tube seals.
• Take tank soundings to confirm proper levels.
• Confirm the proper operation of all underwater valves, overboard valves, sea chests, and vents.
• Inspect the stern tube tank for any irregularities.

System Restart:

• Switch back to ship's power after confirming all systems are functional.
• Test the proper operation of all machinery and systems to ensure the ship is fully operational before leaving the dock.

Freeboard is the distance measured from the waterline to the upper edge of the deck plating at the side of the freeboard deck amidships.

Purpose of Freeboard:

• Ensures the ship is seaworthy when fully loaded.
• Provides reserve buoyancy, enabling the ship to rise as it passes through waves, keeping decks largely dry.
• Enhances the ship's stability and increases its survivability in case of damage by allowing it to remain afloat longer, aiding crew escape or damage control.

Conditions of Assignment are outlined in the Merchant Shipping Load Line Rules 1968 and must be satisfied before a ship is assigned freeboards and issued a load line certificate. These conditions address the practical need for openings (hatchways, doorways, vents, etc.) in the ship's hull and mandate appropriate protection and closure mechanisms for these openings.

Requirements Before Assigning Load Line:

• The ship must have sufficient structural strength.
• Adequate reserve buoyancy must be maintained.
• Openings must be secured against water ingress.
• Safety measures for the crew, such as guardrails and gangways, must be in place.

• Openings: This encompasses hatchways, machinery space openings, cargo ports, watertight doors, ventilators, air pipes, scuppers, freeing ports, side scuttles, and other openings in the freeboard and superstructure decks. The surveyor checks the condition of seals, gaskets, closing mechanisms, and overall watertightness.
• Crew Protection: Safety features designed to protect the crew, such as guardrails, bulwarks, and gangways, are inspected for damage or deterioration and proper functionality.
• Hull Structure: The hull itself is inspected for any damage, corrosion, or structural weaknesses that could compromise watertightness or strength. This often includes visual inspection for cracks, buckling, indentation, and paint adhesion. Bottom shell, bilge keel, stem and stern frames, rudder, sea chests, side ports, stern bearing, and propeller are all checked.
• Other Systems: Depending on the scope of repairs, other systems may be examined, including but not limited to: pressure-vacuum valves, sounding pipes, air vents, access hatches, ventilation fans, dampers, weathertight doors and sealings, door securing arrangements, side scuttles, windows, and skylights. Testing, such as hose tests (to check watertight integrity), might also be conducted.

• Torsional Stress: Resulting from the rapid changes in propeller speed (propeller racing) caused by variations in water resistance in heavy weather.
• Compressive Stress: Due to the end thrust transmitted from the propeller.
• Bending Stress: Caused by hull movements such as hogging (upward bending) and sagging (downward bending) in heavy seas.

• Torque and Thrust: Caused by the propulsion forces transmitted through the shaft.
• Torsional Stress: Due to the rapid fluctuations in engine speed when the propeller races.
• Compressive Stress: Generated by the axial thrust from the propeller.
• Bending Stress: Arises when the weight of the propeller acts on the shaft as the propeller emerges from the water during rough seas.

• Bending Stress: From misalignments caused by hull deformations.
• Shear Stress: Resulting from the whirling of the shaft and rapid engine speed changes during propeller racing.
• Torsional Stress: Caused by the transmission of fluctuating torque.
• Fatigue Failure: Due to the repeated application of fluctuating loads over time, particularly in heavy weather conditions.

• Stress from Hull Movements: Misalignment caused by hull hogging and sagging.
• Load Fluctuations: Due to variations in propeller thrust during racing and rapid changes in sea conditions.
• Axial and Torsional Vibration: Arising from inconsistent propulsion forces and shaft vibrations.
• Surface Wear and Damage: Resulting from increased pressure and friction due to fluctuating thrust forces.

To preserve the strength and watertight integrity of a main transverse bulkhead where a watertight door is fitted, the opening is bounded by a reinforced double-plate frame. Thicker compensating plates (or a vertical web frame) surround the aperture, with the door frame pieces doubling the plate thickness at the corners. The door opening edges are connected to strong horizontal and vertical stiffeners (intercostal framing) so that the bulkhead's ability to transmit shear and bending (it acts as a deep girder stiffening the hull) is not lost. The door itself is a steel watertight sliding or hinged door with a frame fitted with a resilient gasket/special joint; the edges are dressed and wired to the surrounding doubling plates, and the sill is raised above the deck to (in passenger ships) about a prescribed height. The framing around the opening is tied into the top and bottom stools/stringers, and where the aperture cuts the stiffening of the bulkhead, compensation is made by increased scantlings immediately adjacent.

• Only authorised personnel may operate them, and the closing mechanism (hydraulic or electric, power plus manual) must be tested before entering port/complex operations.
• Before closing, check the doorway and its rails/wheels are clear of cargo, stores, obstructions and personnel; sound a warning (alarm) before closing.
• The door must be fully open during cargo/engineering operations that require passage, and closed when the door is not in use, especially at sea when subdivision demands it.
• On closing (or opening) by power, monitor the travel; never operate a sliding door manually against a heavy load or with persons in the way.
• When a remote/central control is fitted, the interlock and indicator (open/closed/partly open) must be observed, and the action of the automatic watertight-closing (if fitted) verified.
• After closing, check the door is fully shut and the securing (wedges/dogging) engaged; the indicator should confirm closed position.
• Ensure the gasket is intact, the surrounding plates free of obstruction, and that the door is not used as a normal gangway when closed.
• Record routine tests and keep the operating instruction posted.

Watertight doors are categorised (per SOLAS Chapter II-1) by their type and location:

• Class 1 hinged watertight doors, fitted in bulkheads in machinery spaces and working spaces, normally operated manually (may be required to be closed before the vessel proceeds to sea).
• Class 2 sliding watertight doors, operated by power (remote) with local manual operation and capable of being closed from an accessible location above the bulkhead deck; these are fitted where frequent access is needed (e.g. main lobbies, machinery space trunks, cargo spaces in passenger ships).
• Class 3 hinged door or sliding door of a certain design in the lower portion of the hull in specific locations.

Regulation (SOLAS II-1/13 and Reg.22 etc.): watertight doors in subdivision bulkheads below the bulkhead deck, and their closing arrangements, must comply with the regulations; all watertight doors below the bulkhead deck must be kept closed except when actually used for passage, and sliding doors fitted with power closing, voice alarm and remote indicator are required in certain fire/passenger contexts. The number of watertight doors below the bulkhead deck is minimised, they must have a status indicator at a control station, and hinges/operating gear must be such that they can be closed even with the vessel heeled. Non-wateredef: performance, and that they be opened/closed from both sides and remotely.

Masses at the bottom:

• The centre of gravity (G) moves down.
• Metacentric height (GM) increases, resulting in greater stability.
• Rolling period decreases.

Masses at the top:

• The centre of gravity (G) moves up.
• Metacentric height (GM) decreases, reducing stability.
• Rolling period increases.

Masses concentrated at the centre:

• The radius of gyration (K) decreases.
• Rolling period decreases.

Masses distributed away from the centre:

• The radius of gyration (K) increases.
• Rolling period increases.

The factor of subdivision introduces a safety measure by reducing the size of the compartments to limit the effects of flooding. It ensures that the ship's draft or trim has less chance of touching the margin line during flooding or heeling.

Permissible Length Formula:

$$Permissible\:length=\frac{Floodable\:length}{Factor\:of\:Subdivision}$$

A smaller factor of subdivision leads to a smaller permissible length, requiring more numerous and smaller compartments. This reduces the potential for catastrophic flooding, as a smaller flooded area is less likely to exceed the ship's reserve buoyancy and cause it to sink. The factor of subdivision is determined by the ship's length and its intended service. The nature of service is quantified by a "criterion of service" (Cs) number, which considers the proportion of passenger and machinery spaces to the total volume of the ship. A higher Cs number (indicating more passenger space) typically results in a lower factor of subdivision and therefore smaller compartments.

$$Excess\:moment=31000-16200=14800$$

$$LCG=\frac{\sum M}{\sum m}=\frac{14800}{16000}$$

$$LCG=0.925m\:fwd\:of\:midship$$

$$LCG=0.925m\:Fwd\:of\:midship$$

$$LCB=2.02m\:Fwd\:of\:midship$$

$$Trimming\:lever=LCB-LCG$$

$$2.02-0.925$$

$$=1.09m$$

$$Trimming\:moment=m\times d$$

$$=16000\times1.09$$

$$=17440tm$$

$$Change\:of\:trim=\frac{Trimming\:moment}{MCT_{1\operatorname{\mathrm{cm}}}}$$

$$=\frac{17440}{179}$$

$$97.43\operatorname{cm}$$

$$Draft\:fwd=8.25-\frac{97.43}{100\times120}\left(\frac{120}{2}+0.57\right)$$

$$=7.756m$$

$$Draft\:aft=8.25+\frac{97.43}{100\times120}\left(\frac{120}{2}-0.57\right)$$

$$=8.735m$$

Masses at the bottom:

• The centre of gravity (G) moves down.
• Metacentric height (GM) increases, resulting in greater stability.
• Rolling period decreases.

Masses at the top:

• The centre of gravity (G) moves up.
• Metacentric height (GM) decreases, reducing stability.
• Rolling period increases.

Masses concentrated at the centre:

• The radius of gyration (K) decreases.
• Rolling period decreases.

Masses distributed away from the centre:

• The radius of gyration (K) increases.
• Rolling period increases.

$$Radius\:\left(R\right)=100m$$

$$Speed\:\left(v\right)=15\:knots$$

$$GM=\frac23m$$

$$BG=1m$$

$$\tan\the\theta=\frac{v^2\times BG}{g\times r\times GM}$$

$$=\frac{\left(15\times0.514\right)^2\times1\times3}{9.81\times100\times2}$$

$$\theta=5.19\degree$$

Erosion:

• Cavitation causes the formation and collapse of vapor bubbles on the propeller blade surface.
• The collapse of these bubbles produces high-pressure shockwaves and microjets that erode the blade material, leading to surface pitting and progressive damage.

Vibration:

• Uneven cavitation across the blades leads to imbalanced forces, causing vibrations in the propeller and the ship.
• These vibrations can reduce the comfort of passengers and crew and stress the ship's structural components.

Noise:

• The collapse of vapor bubbles generates loud noise, which can interfere with onboard communication and underwater sonar systems.
• This noise is a significant concern for naval vessels and marine life.

Reduced Performance:

• Cavitation reduces the efficiency of the propeller by causing loss of thrust and torque.
• The presence of cavitation decreases the propeller’s ability to convert rotational energy into forward motion, lowering the ship's speed and increasing fuel consumption.

(b) Given:

$$D=4.6m$$

$$P=4.3m$$

$$d=0.75$$

$$S=28\%$$

$$n \space = \space 95 \space rev/ min$$

$$V_T \space = \space P \times N \times {{3600} \over 1852}$$

$$ = \space 4.3 \times {{95} \over 60} \times {{3600} \over 1852}$$

$$V_{T}=13.23knots$$

$$Real \space slip \space (S) \space = \space {{V_T - V_a} \over V_T}$$

$$0.28 \space = \space {{13.23 - V_a} \over 13.23}$$

$$V_{a}=9.52knots$$

$$Effective\:disc\:area\:\left(A\right)\:={{\pi}\over4}\left(D^2-d^2\right)$$

$$= {{\pi} \over 4} (4.6^2 - 0.75^2)$$

$$A=16.18m^2$$

$$Thrust\space=\space\rho AP^2n^2S$$

$$=1.025\times16.18\times4.3^2\times\left(\frac{95}{60}\right)^2\times0.28$$

$$T=215.25KN$$

$$Thrust \space power (T_p) \space = \space T \times V_a $$

$$215.25\times9.52\times\frac{1852}{3600}$$

$$T_{p}=1054.18KW$$

• Positive GM (Metacentric Height): The ship needs a positive GM. GM is the distance between the centre of gravity (G) and the metacentre (M). A positive GM indicates inherent stability; the ship will right itself if tilted. During dry-docking, the loss of buoyancy as the ship rests on the blocks reduces GM. Insufficient positive GM increases the risk of the ship heeling over or capsizing.

• Trim by the stern: The vessel should be trimmed slightly by the stern (aft end lower than the bow) to ensure the aft end sits on the keel blocks first. This controlled settling minimises the risk of instability during the docking process. An even keel is generally preferred for the initial floating condition before the dry-docking procedure begins.

The bilge keel is a long fin attached externally along the turn of the bilge, running roughly in a fore-and-aft direction. Attachment method:

• The bilge keel is fabricated as a light, flat bar or fabricated plate of length running over the middle portion of the hull. It is attached by one of two methods:

(i) riveted/bolted connection through doubler plates, in which the keel web is connected by a continuous fillet weld to a flat-bar or doubler section on the shell, or

(ii) welded directly to the shell by continuous or intermittent fillet welds.

• Because the attachment is a potential source of high local stress concentration and fatigue cracking (the shell at the bilge is highly loaded in bending and docking), the weld is usually a full-strength continuous fillet or butt weld, and the keel is not welded to the shell with single small tack welds that crack under repeated relative movement (flexing).
• The ends of the bilge keel are tapered and rolled to a fine radius and blended smoothly (scalloped/angled end) so as to reduce stress concentration at their termination; heavy strike plates (flat bar doubler) at the ends carry the connection.
• The keel is set slightly at a small angle to the base plane so that its face lines up with the flow; it is normally fitted parallel to the load waterline and positioned at the turn of the bilge where it is not unduly loaded in docking (kept clear of the keel blocks).
• Doubler plates and drainage are arranged, and the attachment is periodically inspected (especially the weld toes) because the bilge keel experiences severe fluctuating loads in a seaway.

1. To avoid severe local stress concentrations and fatigue cracking at their ends/attachment; a full-length keel would place the highly-loaded ends in regions of the hull girder with large bending stresses, promoting cracking. Pounding/the connection would also be in heavily loaded way of the end bottoms.
2. They would cause high drag/frictional resistance in the deep/fore and aft ends where the bulb and stem flow is disturbed; the ends are kept clear to allow the propeller/shaft area (aft) and bow (forward) flow and to reduce appendage resistance.
3. The ends would foul the raised stake/Dfrenchman? no: the ends would interfere with docking (the keel blocks and cradle), with the propeller and with the sea-chests/ballast pipes, and would not be effective because at very great fineness near the ends the damping of roll is small. They also would add weight and cause the keel to hit the dock blocks or the ground.

1. Fluid drag / hydrodynamic damping: as the ship rolls, the bilge keel body moves transverse through the water, generating a resistance (both pressure and friction) opposing the roll velocity. Because the damping force is proportional to the velocity of the keel (highest at the bilge, which is far from the roll axis), the keel produces large moments that resist and dissipate the rolling energy, arresting and reducing the amplitude of roll. This is the principal roll-damping mechanism.
2. Creation of eddies/vortices and flow separation: the sharp edges of the bilge keel shed eddies and cause wake and separated flow at the bilge, increasing the hydrodynamic damping and inducing a phase lag in the roll so that the passive system resists resonance and limits maximum roll angle. The energy of rolling is converted to eddying motion and hence heat, damping amplitude.

These mechanisms make the bilge keel an economical, passive roll damper that reduces roll amplitude, improves comfort and cargo security and reduces sloshing and parametric roll, without moving parts or power.

Upon arrival at safe anchorage, a thorough inspection of the vessel shall be carried out, both externally and internally, to assess any weather-related damage. Key areas include:

1. Hull and Main Deck

• Shell plating along bow, midship, and stern sections (especially forepeak and flare areas).
• Boot-top and bilge areas for dents or deformation.
• Deck plating for buckling or cracked welds.
• Bulwarks, rails, fairleads, chocks, and mooring fittings.

2. Forecastle and Forward Structure

• Bosun store and chain locker for water ingress.
• Windlass foundation, anchors, and hawse pipes for deformation or cracks.
• Forepeak tank for leakage or pressure damage.

3. Cargo Holds / Tanks

• Inspect for structural deformation, loose frames, or fractured stiffeners.
• Check tank top plating and bilges for leakage.
• Check watertight doors, gaskets, and vents.

4. Superstructure and Deck Fittings

• Bridge wings, radar mast, funnel, vents, and deckhouses for cracks or loose fittings.
• Lifeboat davits, securing arrangements, and deck cranes.

5. Underwater and Machinery Spaces

• Rudder, propeller, and stern tube seals (via steering gear tests).
• Sea chest gratings and overboard discharges.
• Engine room bilges for any seawater ingress.

• Dents and indentations on shell plating at bow and forward port side due to heavy slamming.
• Paint coating and corrosion protection partly peeled off near waterline and forepeak area.
• Loose fairlead bolts and one cracked weld on starboard bulwark stanchion.
• Deformed ventilator head on forecastle deck.
• Minor leakage observed in forepeak tank during sounding check.
• Bridge wing railing bent, likely from green sea impact.
• Anchor chain links twisted and worn.
• Lifeboat gripes loosened, requiring tightening and inspection.
• No flooding reported; watertight integrity maintained overall.

To: Superintendent / Technical Department

From: Name / Rank

Subject: Heavy Weather Damage Inspection Report

Date: [Insert date]

Vessel: [Insert vessel name]

Summary

The vessel experienced very heavy weather en route from [Port A] to [Port B], with significant pitching and rolling in seas up to [X] meters. On arrival at safe anchorage, a complete inspection of the hull and deck was carried out.

Findings

• Bow and forecastle plating show minor dents, with no breach of watertight integrity.
• Bulwark stanchion (starboard side) cracked at welded joint – requires repair.
• Fairlead foundation bolts loosened – retightening and NDT inspection recommended.
• Ventilator head on forecastle deformed – replacement advised.
• Forepeak tank shows trace leakage at forward bulkhead – to be pressure tested.
• Paint coating damage and corrosion exposure on bow area – recoating required.
• Bridge wing railing bent – to be straightened or renewed.
• All other structures and machinery appear satisfactory after testing.

Recommendations

1. Conduct minor steel renewal and welding repairs at the next port with repair facilities.
2. Carry out thickness measurements and NDT on affected hull areas.
3. Recoat damaged paint areas to prevent corrosion.
4. Replace deformed ventilator head and bent railing.
5. Inspect anchor and chain for elongation; renew worn links.
6. Pressure test forepeak tank after repairs.
7. Submit class surveyor report if deemed necessary by the superintendent.

Conclusion

The vessel remains seaworthy but requires prompt attention to minor structural and fitting damages before the next voyage. Preventive maintenance and weather routing measures should be reviewed for future passages.

Signed:

Name / Rank

Signature

Ship’s Rudder – Effects of Defects and Design Features

(a) Why a Breached Hollow Rudder Can Add to Fuel Costs

• A hollow rudder is designed to provide buoyancy at the stern of the ship.
• When the rudder is breached, sea water enters the hollow space, resulting in loss of buoyancy.
• The loss of buoyancy causes the stern to sit deeper in the water, increasing the aft draught.
• Increased aft draught leads to the propeller operating deeper, which increases hydrodynamic resistance.
• Water ingress into the rudder creates turbulence and disturbed water flow around the rudder and propeller.
• To maintain the same ship speed, higher engine power is required, resulting in increased fuel consumption.

(b) Why Excessive Pintle Clearance Should Not Be Tolerated

• Pintles support the rudder and fit into gudgeons with very small designed clearances.
• Excessive clearance permits sideways and vertical movement of the rudder.
• Such movement imposes additional bending stresses on the rudder stock.
• In heavy seas, shock and impact loads increase wear and may cause misalignment.
• This can lead to vibration, poor steering response, accelerated wear, and in extreme cases, structural failure of the rudder assembly.

(c) Why Fitted Bolts Are Used in Connecting Upper and Lower Rudder Stocks

• The upper and lower rudder stocks are required to transmit high steering torque.
• Fitted bolts provide a close, interference fit with no clearance in the bolt holes.
• They ensure accurate alignment of the two stock sections.
• Steering loads are transmitted in shear through the bolt shanks, rather than relying on friction alone.
• This prevents relative movement, reduces stress concentration, and minimizes the risk of fatigue failure.

Freeboard is the distance measured from the waterline to the upper edge of the deck plating at the side of the freeboard deck amidships.

Purpose of Freeboard:

• Ensures the ship is seaworthy when fully loaded.
• Provides reserve buoyancy, enabling the ship to rise as it passes through waves, keeping decks largely dry.
• Enhances the ship's stability and increases its survivability in case of damage by allowing it to remain afloat longer, aiding crew escape or damage control.

Conditions of Assignment are outlined in the Merchant Shipping Load Line Rules 1968 and must be satisfied before a ship is assigned freeboards and issued a load line certificate. These conditions address the practical need for openings (hatchways, doorways, vents, etc.) in the ship's hull and mandate appropriate protection and closure mechanisms for these openings.

Requirements Before Assigning Load Line:

• The ship must have sufficient structural strength.
• Adequate reserve buoyancy must be maintained.
• Openings must be secured against water ingress.
• Safety measures for the crew, such as guardrails and gangways, must be in place.

• Openings: This encompasses hatchways, machinery space openings, cargo ports, watertight doors, ventilators, air pipes, scuppers, freeing ports, side scuttles, and other openings in the freeboard and superstructure decks. The surveyor checks the condition of seals, gaskets, closing mechanisms, and overall watertightness.
• Crew Protection: Safety features designed to protect the crew, such as guardrails, bulwarks, and gangways, are inspected for damage or deterioration and proper functionality.
• Hull Structure: The hull itself is inspected for any damage, corrosion, or structural weaknesses that could compromise watertightness or strength. This often includes visual inspection for cracks, buckling, indentation, and paint adhesion. Bottom shell, bilge keel, stem and stern frames, rudder, sea chests, side ports, stern bearing, and propeller are all checked.
• Other Systems: Depending on the scope of repairs, other systems may be examined, including but not limited to: pressure-vacuum valves, sounding pipes, air vents, access hatches, ventilation fans, dampers, weathertight doors and sealings, door securing arrangements, side scuttles, windows, and skylights. Testing, such as hose tests (to check watertight integrity), might also be conducted.

A transverse section through the cargo hold of a bulk carrier consists of the following principal structural members (as shown in the given sketch):

At the top, the strength deck plating forms the upper boundary of the hull girder. It is stiffened by deck longitudinals and connected to the hatch coaming, which increases deck strength around the hatch opening.

Below the deck on either side are the topside tanks (wing tanks). These are formed by:

• Topside tank sloping plating
• Topside tank longitudinal plating (vertical strake)
• Topside tank sloping plate longitudinals
• Topside tank transverse ring webs

The topside tanks taper inward toward the cargo hold and provide structural continuity between the deck and the side shell.

The side shell plating forms the vertical boundary of the hull and is supported by:

• Side shell frames (transverse framing)
• Side shell longitudinals

At the lower corners of the hold are the hopper tanks, consisting of:

• Hopper tank sloping plating
• Hopper tank sloping plate longitudinals
• Hopper transverse ring webs

These sloping structures connect the side shell to the inner bottom and help direct cargo toward the centreline during discharge.

At the bottom of the hold is the inner bottom plating (tank top), supported by:

• Inner bottom longitudinals
• Double bottom floors
• Double bottom girders

Below this lies the double bottom tank space, bounded externally by the bottom shell plating and centrally by the keel plate and duct keel.

The curved transition between bottom and side shell is formed by the bilge plating, which ensures smooth stress distribution between vertical and horizontal structures.

1. Hull Girder Strength (Longitudinal Strength)

• The ship behaves like a beam subjected to wave-induced hogging and sagging. The strength deck plating forms the upper flange of the hull girder, while the bottom shell plating and keel structure form the lower flange.
• The large vertical distance between deck and bottom increases the section modulus, enabling the hull to resist high longitudinal bending moments. Continuous deck, bottom, and side shell longitudinals further increase the moment of inertia and efficiently carry longitudinal stresses along the ship’s length.

2. Double Bottom Structure

• The double bottom forms a rigid box girder at the base of the hull. The inner bottom plating supports cargo loads directly, while floors and girders distribute these loads to the side shell and keel.
• This arrangement:
  • Resists vertical cargo pressure
  • Strengthens the lower flange of the hull girder
  • Provides protection against grounding damage
• The double bottom tanks also contribute to structural stiffness by forming a closed cellular structure.

3. Side Shell and Transverse Framing

• The side shell plating, supported by transverse frames and longitudinals, resists sea pressure externally and cargo pressure internally.
• Transverse framing prevents local buckling of plating between stiffeners, while longitudinals ensure effective distribution of stresses along the ship’s length. This combined system balances local rigidity with overall flexibility.

4. Hopper and Topside Tanks (Box Structures)

• The hopper tanks at the lower corners and topside tanks at the upper sides form strong triangular and trapezoidal box sections.
• These structures:
  • Reduce unsupported plate spans
  • Transfer cargo loads smoothly to the side shell and double bottom
  • Minimize stress concentration at sharp corners
  • Increase torsional and transverse stiffness
• By converting flat plate regions into closed box sections, they significantly enhance both local and global hull strength.

5. Transverse Ring Webs and Bulkhead Effect

• The topside and hopper transverse ring webs act as deep transverse beams. They reinforce the sloping plates and maintain structural shape under heavy cargo loading.
• In addition, transverse bulkheads (at hold boundaries) act as strong web frames, dividing the ship into rigid compartments and improving resistance to racking and shear deformation.

If the ship grounds on a level bottom:

• A ground reaction force acts vertically upwards from the seabed. This force counteracts part of the ship's weight and alters the distribution of buoyancy forces.
• The ship’s centre of gravity (G) may appear to rise relative to the metacentre (M) because the upward ground reaction reduces the buoyancy force acting on the underwater volume.
• This virtual rise in G reduces GM, potentially leading to a list.
• If the list becomes excessive and the righting moment is insufficient, the ship may capsize.

If the ship grounds on a pinnacle:

• The ship experiences two forces at the ship's bottom:
  • A downward force due to the ship’s weight.
  • An upward reaction force is concentrated on the pinnacle.
• The resulting force between the grounding pressure and the ship’s centre of buoyancy shifts downward towards the pinnacle.
• This situation is similar to when the ship's stern touches the keel block in a dry dock.
• A virtual loss of GM occurs because the ship’s inclining moment may exceed the maximum righting lever.
• If the inclining moment is too great, the ship may develop an excessive list or even capsize.

(b) Given:

$$Displacement,\:\Delta=8000\:tonnes$$

$$TPC=15\:tonnes$$

$$Initial\:Draught=5.2m$$

$$Final\:Draught=3.2m$$

$$Ship\:KG=4.0m$$

$$KM=5.0m$$

To find GM

$$Uptrust,\:P=TPC\times Fall\:in\:water\:level\:\left(cm\right)$$

$$=15\times\left(520-320\right)$$

$$=15\times200$$

$$P=3000\:tonnes$$

To Find Virtual loss of GM:

$$Virtual\:loss\:of\:GM_1=\frac{P\times KM}{\Delta}$$

$$=\frac{3000\times5}{8000}$$

$$=\frac{15000}{8000}$$

$$GM_1=1.88m$$

Actual KM = 5.0m (given)

$$Virutal\:KM=Actual\:KM-Virtual\:loss\:of\:GM_1$$

$$=5.0-1.88$$

$$=3.12$$

Similarly, Actual KG = 4.0m (given)

$$New\:GM=Virtual\:KM-\:Actual\:KG$$

$$=3.12-4.0$$

$$=-0.88$$

Before entering the dock the ship must have adequate and known stability. The requirements are:

• The ship should be stable with an adequate GM, so that the small upward force (reaction) at the keel, building during docking, cannot produce a list. Dock support is provided on the keel blocks and any excessive list during docking would subject the structure and blocks to unequal loading.
• As the water is pumped out, the reaction of the keel blocks reduces the effective displacement of the ship, lowering the KB and BM and hence GM; if all buoyancy were removed the ship would rest wholly on the blocks. The ship must retain sufficient GM throughout the docking operation (for example by keeping the GM such that the maximum inclination, where the righting moment at the critical point, does not become negative).
• Ballast should be arranged to give even keel (or slight trim) and list-free condition; tanks should be pressed up or emptied to avoid free-surface effects, and draft read before docking.
• Weight and trim must be such that the keel blocks contact evenly over the full keel length (avoid excessive trim that overloads the block crown or aft blocks).
• Cargo/weights should not be changed and the dock must be level; adequate dock pumping should keep the vessel central over the keel line.

If a beam vessel develops instability while docking (transverse GM small or negative), it can heel and capsize on the blocks; hence a suitable stability margin (e.g. GM not less than a minimum) is insisted on and the docking weight, draft and trim are checked by stability data (e.g. from hydrostatics and the Docking Plan).

Box-shaped vessel 50 m long, 10 m wide, floats on even keel in salt water at a draft of 4 m. A centreline longitudinal watertight bulkhead runs full depth/size. A midship compartment on the starboard side is 15 m long and has permeability 30 per cent. KG = 3 m. Calculate the list when bilged.

Waterplane area intact Aw = 50 x 10 = 500 m2; the flooded wing compartment has waterplane area = 15 x 5 = 75 m2 (only starboard half up to the centreline bulkhead).

Lost buoyancy volume of the compartment below the original waterline, with permeability 30%: Vlost = length x breadth x draft x permeability = 15 x 5 x 4 x 0.30 = 90 m3. Corresponding lost weight W = 90 x 1.025 = 92.25 t.

Sinkage: the region once flooded provides no increase of buoyancy; effective sinking waterplane = 500 - 75 = 425 m2. Mean sinkage = 90/425 = 0.212 m.

List: the lost buoyancy acts at the centroid of the lost volume, which is at 5/4 = 2.5 m out from the centreline (half-way between centreline bulkhead and side). Heeling moment = W x y = 92.25 x 2.5 = 230.6 t-m.

New GM. Using the lost-buoyancy method, displacement remains 2050 t. The second moment of area of the intact waterplane about the centreline loses the flooded starboard compartment: I(intact)=50x10^3/12 = 4166.7 m4; I(flooded)=15x5^3/3 = 625 m4; so I(new)=3541.7 m4. BM=new = I(new)/V = 3541.7/2000 = 1.771 m. KB = d/2 = 2 m (approximately, ignoring sinkage and list); GM = KB + BM - KG = 2 + 1.77 - 3 = 0.77 m.

List: tan(list) = heeling moment/(Delta x GM) = 230.6/(2050 x 0.77) = 230.6/1579 = 0.146. List = atan(0.146) = 8.3 deg.

Answer: the vessel lists about 8.3 deg to starboard.

• The Longitudinal Centre of Gravity (LCG) is the point along the length of the vessel where the total weight of the ship is considered to act vertically downward.
• It represents the balance point of the ship's weight distribution and is measured as a distance forward or aft of the midship.

Longitudinal Centre of Buoyancy (LCB):

• The Longitudinal Centre of Buoyancy (LCB) is the point along the length of the vessel through which the total buoyant force, acting vertically upward, is considered to act.
• It represents the balance point of the underwater volume of the ship and is also given as a distance forward or aft of the midship.

LCF in fwd and trim by stern

$$Bodily \space sinkage \space = \space {{mass \space added} \over TPC} \space = \space {{110} \over 13} \space$$

$$=\:8.5\operatorname{\mathrm{cm}}\:=0.085m$$

$$Trim \space = \space {{m \times d} \over MCT_{1cm}}$$

$$ = \space {{110 \times (24 + 2.5)} \over 80}$$

$$Trim=36.43\operatorname{cm}=0.364m\:$$

Change in fwd draught:

$$d_{F}=\frac{-t}{L}\left\lbrack\frac{L}{2}-LCF\right\rbrack$$

$$=\frac{-36.43}{120}\left\lbrack\frac{120}{2}-2.5\right\rbrack$$

$$=-17.45\operatorname{cm}=-0.1745m$$

Change in Aft draught:

$$d_{A}=\frac{+t}{L}\left\lbrack\frac{L}{2}+LCF\right\rbrack$$

$$=\frac{+36.43}{120}\left\lbrack\frac{120}{2}+2.5\right\rbrack$$

$$=+18.97\operatorname{cm}=0.189m$$

New draughts:

$$D_{F}=5.5+0.085-0.175=5.41m$$

$$D_{A}=5.8+0.085+0.18=6.065m$$

Main Components of Ship Resistance

When a vessel moves through water, it experiences total resistance, which is the combined effect of several opposing forces acting against its forward motion. These forces arise due to water viscosity, pressure distribution around the hull, wave formation, and external environmental conditions. For analysis, total resistance is divided into the following main components:

1. Frictional Resistance

Frictional resistance is caused by the viscosity of water acting along the ship’s wetted surface as the vessel moves forward. As water flows over the hull, a thin boundary layer forms, and shear stresses develop between the hull surface and adjacent water particles. This shear stress produces resistance.

Frictional resistance depends primarily on:

• Wetted surface area – A larger underwater hull area increases the contact between hull and water, thereby increasing resistance.
• Ship speed – Resistance increases rapidly with speed because higher velocity intensifies boundary layer shear forces.
• Surface roughness of the hull – Fouling, corrosion, or rough coatings increase turbulence and significantly raise resistance.

At normal service speeds, frictional resistance forms the largest portion of total resistance, especially for slow and medium-speed vessels. It increases approximately with the square of the ship’s speed, making hull maintenance crucial for fuel efficiency.

2. Residual Resistance

Residual resistance is the portion of resistance remaining after subtracting frictional resistance from total resistance. It mainly arises from pressure effects and wave formation around the hull. Residual resistance consists of the following components:

(a) Wave-Making Resistance

Wave-making resistance is caused by the energy expended in generating surface waves at the bow and stern as the ship moves. When a vessel travels through water, it disturbs the free surface and creates a wave system that carries energy away from the ship.

This resistance becomes particularly significant at higher speeds because wave height and wave energy increase rapidly with speed.

Wave-making resistance depends on:

• Hull form – Fuller hull shapes generally create larger waves.
• Speed–length ratio (Froude number) – As the Froude number increases, wave-making resistance rises sharply.

At high speeds, wave-making resistance can become a dominant component of total resistance.

(b) Eddy-Making Resistance

Eddy-making resistance is caused by flow separation and the formation of vortices (eddies) around certain parts of the hull. When water flow cannot smoothly follow the hull contour, it separates and creates turbulent regions.

This commonly occurs around:

• The stern region
• Appendages
• Areas with sudden changes in hull form

These turbulent eddies consume energy and increase resistance. Proper streamlining of the hull and stern design can significantly reduce eddy-making resistance.

3. Air Resistance

Air resistance is the force exerted by air on the portion of the ship above the waterline. As the ship moves, it must also overcome aerodynamic drag.

Air resistance depends on:

• Wind speed and direction
• Projected area above water
• Shape of the superstructure

Although usually small compared to water resistance, it becomes significant for:

• Container ships
• Ro-Ro vessels
• Ships operating in strong headwinds

For vessels with large exposed areas, air resistance can noticeably affect fuel consumption.

4. Appendage Resistance

Appendage resistance is caused by external fittings attached to the hull, such as:

• Rudders
• Bilge keels
• Shaft brackets
• Propeller bossings

These appendages increase the wetted surface area and disturb smooth water flow, thereby increasing both frictional and pressure resistance. In resistance calculations, appendage resistance is generally included as a separate correction added to frictional resistance.

5. Added (Special) Resistance

Added resistance refers to the additional resistance experienced in real sea conditions that is not present in calm-water trials.

It occurs due to:

• Waves and swell, which cause pitching and heaving motions
• Steering and yawing motions, which disturb steady flow around the hull

Although not considered in calm-water resistance analysis, added resistance is highly important in practical operations because it significantly affects power requirements and fuel consumption in rough weather.

is the difference between the theoretical distance the propeller should travel in one revolution and the actual distance the vessel travels.

$$Slip\:\left(\%\right)\:=\:\left(\frac{Engine\:distance\:-\:Ship^{\prime}s\:distance}{Engine\:distance}\right)\:\times100$$

Where Engine distance = no. of propeller revolutions * propeller pitch (usually calculated over a 24-hour period)

Propeller thrust: it is the force exerted by the propeller to move the vessel ahead and given by

$$Thrust\:\left(T\right)\:=\:\rho\times A\times P^2\times n^2\times S$$

Where,

ρ - Density

A - Area

P - Pitch

n - Revolution per second

S - Slip

The bilge keel is a long fin attached externally along the turn of the bilge, running roughly in a fore-and-aft direction. Attachment method:

• The bilge keel is fabricated as a light, flat bar or fabricated plate of length running over the middle portion of the hull. It is attached by one of two methods:

(i) riveted/bolted connection through doubler plates, in which the keel web is connected by a continuous fillet weld to a flat-bar or doubler section on the shell, or

(ii) welded directly to the shell by continuous or intermittent fillet welds.

• Because the attachment is a potential source of high local stress concentration and fatigue cracking (the shell at the bilge is highly loaded in bending and docking), the weld is usually a full-strength continuous fillet or butt weld, and the keel is not welded to the shell with single small tack welds that crack under repeated relative movement (flexing).
• The ends of the bilge keel are tapered and rolled to a fine radius and blended smoothly (scalloped/angled end) so as to reduce stress concentration at their termination; heavy strike plates (flat bar doubler) at the ends carry the connection.
• The keel is set slightly at a small angle to the base plane so that its face lines up with the flow; it is normally fitted parallel to the load waterline and positioned at the turn of the bilge where it is not unduly loaded in docking (kept clear of the keel blocks).
• Doubler plates and drainage are arranged, and the attachment is periodically inspected (especially the weld toes) because the bilge keel experiences severe fluctuating loads in a seaway.

1. To avoid severe local stress concentrations and fatigue cracking at their ends/attachment; a full-length keel would place the highly-loaded ends in regions of the hull girder with large bending stresses, promoting cracking. Pounding/the connection would also be in heavily loaded way of the end bottoms.
2. They would cause high drag/frictional resistance in the deep/fore and aft ends where the bulb and stem flow is disturbed; the ends are kept clear to allow the propeller/shaft area (aft) and bow (forward) flow and to reduce appendage resistance.
3. The ends would foul the raised stake/Dfrenchman? no: the ends would interfere with docking (the keel blocks and cradle), with the propeller and with the sea-chests/ballast pipes, and would not be effective because at very great fineness near the ends the damping of roll is small. They also would add weight and cause the keel to hit the dock blocks or the ground.

1. Fluid drag / hydrodynamic damping: as the ship rolls, the bilge keel body moves transverse through the water, generating a resistance (both pressure and friction) opposing the roll velocity. Because the damping force is proportional to the velocity of the keel (highest at the bilge, which is far from the roll axis), the keel produces large moments that resist and dissipate the rolling energy, arresting and reducing the amplitude of roll. This is the principal roll-damping mechanism.
2. Creation of eddies/vortices and flow separation: the sharp edges of the bilge keel shed eddies and cause wake and separated flow at the bilge, increasing the hydrodynamic damping and inducing a phase lag in the roll so that the passive system resists resonance and limits maximum roll angle. The energy of rolling is converted to eddying motion and hence heat, damping amplitude.

These mechanisms make the bilge keel an economical, passive roll damper that reduces roll amplitude, improves comfort and cargo security and reduces sloshing and parametric roll, without moving parts or power.