Sample Question and Answers

Part 1: Submarine Design, Metallurgy & Stability

1. Metallurgy of Submarine Hulls: Why the Inner Hull Must Be Stronger

A submarine has a double-hull or partial double-hull construction:

• Inner hull (pressure hull): Withstands external hydrostatic pressure at depth. Must resist elastic buckling and plastic collapse.
• Outer hull (light hull): Provides hydrodynamic shape, protects internal systems, and houses ballast tanks. It is not pressure-tight and experiences minimal stress.

Why the inner hull is stronger:

At depth $h$, external pressure is:

where $\rho \approx 1025 \, \text{kg/m}^3$ (seawater), $g = 9.81 \, \text{m/s}^2$.

At 300 m depth:

This pressure acts uniformly on the inner hull, creating compressive hoop stress:

where $r$ = hull radius, $t$ = hull thickness.

If $\sigma_{\theta}$ exceeds yield strength or causes buckling, catastrophic implosion occurs. Hence, the inner hull uses high-yield, low-alloy steels with excellent toughness at low temperatures.

Materials Used:

Stress-Strain Diagram Insight:

• Inner hull steel (HY-100): High yield plateau, large plastic region before necking → absorbs energy without brittle fracture.
• Outer hull steel (A36): Lower yield, earlier plastic deformation → acceptable since it doesn’t bear pressure.

Stress (σ)
  |
  |        HY-100 (Inner Hull)
  |       /¯¯¯¯¯¯¯¯¯¯¯\
  |      /             \______
  |     /
  |    /   A36 (Outer Hull)
  |   /   /¯¯¯¯¯\_____
  |  /   /
  | /   /
  |/___/______________ Strain (ε)

The inner hull must remain elastic up to design depth; plastic deformation = failure.

2. Ballast Tanks: Functions & Locations

Submarines use ballast tanks to control buoyancy and trim. Key types:

Diagram: Ballast Tank Layout (Simplified)

         [Outer Hull]
   ┌─────────────────────────┐
   │ MBT │ MBT │ MBT │ MBT   │ ← Main Ballast (floodable)
   │─────┴─────┴─────┴───────│
   │ [Pressure Hull Interior]│
   │ Neg │ Trim F │ Trim A   │ ← Negative + Trim Tanks
   └─────────────────────────┘

• MBTs: Always vented at top; flood from bottom → air escapes, water enters → submarine loses buoyancy.
• Trim/Negative: Pump-controlled; used for precise depth/angle control.

3. How a Submarine Surfaces & Submerges

Submerging:

1. Open MBT vents → air escapes, seawater floods tanks.
2. Buoyancy decreases → submarine becomes negatively buoyant.
3. Use diving planes (bow/stern) to control descent angle.
4. Trim tanks adjusted to maintain level dive.

Surfacing:

1. Close MBT vents, inject high-pressure air → forces water out.
2. Buoyancy increases → submarine rises.
3. Blow negative tank early for positive lift.
4. Trim tanks compensate for shifting center of gravity.

Submerging:          Surfacing:
  Air out              Air in (HP)
  Water in → ⬇         Water out → ⬆
  Negative buoyancy    Positive buoyancy

4. Role of Negative & Trim Tanks

• Negative Tank: Provides instant negative buoyancy for emergency dives. During surfacing, it’s blown first to initiate ascent.
• Trim Tanks: Maintain zero trim angle (level). When flooding MBTs, water distribution may shift G (center of gravity); trim tanks pump water fore/aft to realign G with B (center of buoyancy).

Without trim control, the submarine would pitch uncontrollably during depth changes.

5. Intact Stability: Transverse vs. Longitudinal (Surfaced vs. Submerged)

Surfaced Condition:

• Behaves like a surface ship.
• Transverse stability: Depends on waterplane area → large BMₜ (metacentric radius).
• Longitudinal stability: Much larger BMₗ due to elongated waterplane.

Submerged Condition:

• No waterplane → BM = 0 (no buoyancy shift with heel).
• B (center of buoyancy) is fixed relative to hull.
• Stability depends entirely on G-B separation:
  • G below B → stable (like a pendulum).
  • G above B → unstable.

Surfaced:          Submerged:
   M                   B
   |                   |
   B                   |
   |                   G (must be < B)
   G

• Transverse GM (submerged): $GM_t = KB - KG$ (since BM = 0)
• Longitudinal GM (submerged): Same formula, but G-B alignment is critical for pitch control.

6. Righting Moment: Mono-hull Ship vs. Submerged Submarine

Surface Ship:

• Heel → B shifts outward → creates righting arm GZ.
• M (metacenter) is above G → positive GM.
• Righting Moment: $RM = \Delta \cdot GZ = \Delta \cdot GM \cdot \sin\theta$

Submerged Submarine:

• B does not shift (fully submerged, no waterplane).
• No metacenter (M) → stability from G below B.
• Righting Moment: $RM = \Delta \cdot (KB - KG) \cdot \sin\theta$

Surface Ship:       Submarine (Submerged):
     M                    B
     |                    |
     B                    |
     |                    G
     G
   GZ = GM·sinθ         GZ = (KB-KG)·sinθ

Submarines have much smaller righting moments when submerged → rely on active control (planes, trim) rather than passive stability.

7. GM Longitudinal vs. Transverse in Submarines

Key Insight: In submerged condition, GMₗ ≈ GMₜ (both depend only on vertical G-B separation), unlike surface ships where GMₗ » GMₜ.

Part 2: Wave Mechanics for Ship Stability & Safety

1. Trochoidal Waves: Definition & Geometry

A trochoidal wave models real ocean waves more accurately than sinusoidal waves. It describes the path of a water particle as a trochoid curve—generated by a point on a rolling circle.

Definition:

A trochoid is the curve traced by a point at distance $r$ from the center of a circle of radius $R$ rolling along a straight line.

• If $r = R$: Cycloid (sharp crest, flat trough)
• If $r < R$: Prolate trochoid (realistic ocean wave)
• If $r > R$: Curtate trochoid (not physical for waves)

Key Parameters:

• $R$: Radius of rolling circle = $\frac{L}{2\pi}$, where $L$ = wavelength
• $r$: Radius of particle orbit = decreases with depth
• Still Water Line (SWL): Datum at mean water level
• Particle P: Moves in circular orbit; radius $r$ at surface, decays exponentially with depth

Trochoidal Wave Diagram:

        Crest
          *
         / \
        /   \      Particle P at crest:
       /     \     → Moving forward (→)
------*-------*---- Still Water Line (SWL)
     /         \
    /           \   Particle P at trough:
   /             \  → Moving backward (←)
  *               *
 Trough         Crest

Circle radius R = L/2π
Particle orbit radius r (≤ R)

Particle Motion:

• At crest: P moves forward (in wave direction)
• At trough: P moves backward
• At SWL (rising): P moves upward
• At SWL (falling): P moves downward

Orbit radius at depth $z$:

2. Significant Wave Height ($H_s$ or $H_{1/3}$)

Definition:

The average height of the highest one-third of waves in a record. It approximates what an experienced observer would report as “significant” wave height.

Calculation Example:

Given 12 wave heights (m):

1. Sort descending:
   

   $$6.1, 5.5, 5.0, 4.8, 4.5, 4.2, 3.9, 3.7, 3.5, 3.2, 2.8, 2.1$$

2. Top 1/3 = 4 waves: 6.1, 5.5, 5.0, 4.8

3. $H_s = \frac{6.1 + 5.5 + 5.0 + 4.8}{4} = 5.35 \, \text{m}$

Extreme Waves:

• $H_{max}$: Typically \approx 1.8–2.0 \times H_s in fully developed seas
• North Atlantic: Design H_s \approx 14–16 , \text{m} ; H_{max} can exceed 25 m → influences hull scantlings, hatch cover loads, freeboard assignment .

3. Natural Period of Roll ($T_\phi$)

Derived from simple harmonic motion analogy:

Restoring moment for small heel $\phi$:

Moment of inertia about roll axis:

where $k$ = radius of gyration in roll \approx 0.35–0.45 \times B .

Equation of motion:

Natural period:

Simplified empirical formula (Derrett’s):

T_\phi \approx \frac{C \cdot B}{\sqrt{GM}}, \quad C \approx 0.75–0.85

Example (Bulk Carrier from your data):

• $B = 32.6 \, \text{m}$, $GM = 0.885 \, \text{m}$, assume $C = 0.8$

This is dangerously long → risk of synchronous rolling with typical ocean wave periods (8–15 s).

4. Synchronous Rolling & Parametric Rolling

Synchronous Rolling:

Occurs when wave encounter period $T_E$ matches ship’s natural roll period $T_\phi$.

Encounter period (for heading angle $\mu$):

where $L_w$ = wavelength, $V_w$ = wave celerity, $V_s$ = ship speed.

Danger: Even moderate waves can cause resonant roll amplification → capsizing (e.g., APL CHINA, 1988) .

APL CHINA Case:

• Container ship in North Pacific storm
• Large roll angles (>30°) → container losses
• Cause: Synchronous rolling in beam seas + low GM
• Solution: Increase GM (counterintuitive: usually mariners reduce GM for comfort) .

Parametric Rolling:

Occurs in head or following seas when wave passage modulates GM periodically.

Conditions:

• Fine bow, wide stern (container ships, cruise vessels)
• Wave length ≈ ship length
• Ship speed such that pitch period ≈ ½ × roll period

Mechanism:

• Crest amidships → waterplane narrows → GM decreases
• Trough amidships → waterplane widens → GM increases
• If GM variation frequency ≈ 2× roll frequency → parametric resonance → roll angles >40° possible.

Avoidance Strategies:

1. Change speed → alter encounter period
2. Alter course → move away from head/following seas
3. Adjust GM (ballast transfer)
4. Activate anti-roll tanks/fins

5. Virtual Gravity & Virtual Upright (Trochoidal Waves)

On a trochoidal wave, the effective gravity vector tilts due to centrifugal acceleration of water particles.

Virtual Gravity ($g'$):

where $\omega$ = wave angular frequency, $r$ = particle orbit radius.

Virtual Upright:

The direction perpendicular to the local wave slope (not horizontal). A ship on a wave crest “feels” upright relative to the sloped surface.

Danger to Small Craft:

• Fishing vessels on steep waves → virtual upright misaligns with true vertical
• Crew perceives stability when actually GZ is reduced
• Sudden wave trough → loss of righting moment → capsize

True Vertical      Virtual Upright
     ↓                  ↖
     |                   \
     |                    \  Wave slope
-----*---------------------*---- SWL
     |                   /
     |                  /
     ↓                 ↙
  Gravity           Virtual Gravity

6. MSC Circular 1228: Avoiding Dangerous Situations

Core Assumptions:

1. Waves are trochoidal, not sinusoidal.
2. Ship motions are linear (small angles) — limitation in extreme seas.
3. Resonant interactions dominate risk (synchronous roll, parametric roll, surf-riding).

Key Parameters:

Limitations:

• Assumes regular waves — real seas are irregular (spectral).
• Does not account for wind drift, current, or loading changes.
• Masters must observe actual $T_w$, $H_w$, and adjust speed/course proactively.

7. Surfing, Broaching, and Pooping

Surfing (Following Seas):

• Ship speed ≈ wave celerity → vessel “surfs” down wave face.
• Risk: Loss of steerage, broaching (sudden yaw to beam seas).

Broaching:

• Stern lifted by wave → rudder/propeller emerge → loss of control.
• Ship turns beam-to-sea → large roll moment → capsize.

Pooping (Stern Seas):

• Wave breaks over stern → flooding, structural damage.

Avoidance:

• Reduce speed in following seas > 0.7 × wave celerity.
• Alter course to 30–45° off wave direction.

8. Resonant vs. Non-Resonant Ship-Wave Interactions

Flowchart:
Start
  ↓
Measure Tw, Hw, Ship Speed, Heading
  ↓
Calculate TE (Encounter Period)
  ↓
Is TE ≈ Tϕ? ───Yes───> Synchronous Rolling (Resonant) → Change course/speed
  ↓ No
Is TE ≈ 0.5 Tϕ? ─Yes───> Parametric Rolling (Resonant) → Adjust GM/speed
  ↓ No
Is Vs ≈ Vw·cosμ? ─Yes───> Surf-riding/Broaching (Non-resonant) → Slow down
  ↓ No
Safe Zone (Non-resonant) → Monitor continuously

Examples:

• Resonant: APL CHINA (synchronous), modern container ships (parametric)
• Non-resonant: RoPax in quartering seas (broaching), fishing vessel pooping

9. Guidance Note to Masters (Safety Superintendent)

Subject: Avoiding Synchronous Rolling & Pooping in Adverse Weather

Observations Required:

1. Wave Period ($T_w$): Time between 5 consecutive crests → average.
2. Wave Height ($H_w$): Visual estimate or radar.
3. Ship’s Roll Period ($T_\phi$): Measure 5 rolls → average.

Actions:

• If $T_w \approx T_\phi$: Alter course by 20–30° or change speed by 20%.
• If following seas: Ensure $V_s < 0.7 V_w$ to avoid surf-riding.
• Log all observations in deck logbook + report to shore.

Diagram: Wave Observation:

Creast:  *     *     *     *
         |<--Tw-->|
         |<------ 5Tw ------>| → Average for accuracy

10. Rolling & Pitching Estimation (Your Bulk Carrier Data)

Given:

• $L = 217 \, \text{m}$, $B = 32.6 \, \text{m}$, $T = 12.2 \, \text{m}$, $GM = 0.885 \, \text{m}$

Roll Period (as above): $T_\phi \approx 27.7 \, \text{s}$

Pitch Period (empirical):

T_\theta \approx \frac{L}{\sqrt{g \cdot GM_L}}, \quad GM_L \approx 100\text{~}300 , \text{m}

Assume $GM_L = 200 \, \text{m}$:

Risk: $T_\phi$ is too long → high synchronous roll risk in beam seas of 12–15 s waves (common in North Atlantic).

Part 3: Tanker vs. Bulk Carrier Design & Safety

1. Inherent Strength: Tanker vs. Dry Cargo Ship

Tanker Advantages:

• Continuous longitudinal strength: Cargo tanks act as integral part of hull girder → no large hatch openings.
• Smaller hatchways: Only for inspection → minimal stress concentration.
• Double bottom + double sides (post-MARPOL): Redundant protection, improved torsional rigidity.
• Uniform cargo density: Liquid cargo distributes evenly → predictable shear/bending.

Bulk Carrier Disadvantages:

• Large hatch openings (for grab/crane access) → reduce deck section modulus by 30–40%.
• Stress concentrations at hatch corners → fatigue cracks.
• Variable cargo density: Ore vs. grain → unpredictable loading, risk of hold flooding.
• Single-skin construction (pre-2000s): Vulnerable to corrosion, grounding.

Tanker Hull:          Bulk Carrier Hull:
┌──────────────┐      ┌──────────────────┐
│  Small Hatches│      │  LARGE HATCHES   │ ← Weakens deck
├──────────────┤      ├──────────────────┤
│  Integral Tanks│      │  Topside/Hopper  │ ← Stress risers
└──────────────┘      └──────────────────┘

2. Freeboard Assignment: Why Tankers Get Less Freeboard

ILLC (International Load Line Convention) Objectives:

1. Reserve buoyancy for wave immersion
2. Limit deck edge immersion angle
3. Ensure watertight integrity of openings
4. Account for hull form (sheer, camber)
5. Consider cargo type (permeability, shift risk)
6. Structural strength (hull girder, hatch covers)
7. Survivability after damage

Tanker vs. Bulk Carrier Freeboard:

Result: For same L, B, D → tanker assigned 0.5–1.5 m less freeboard than bulk carrier.

3. Pump Room Double Bottom: Survivability Enhancement

Regulatory Requirement (SOLAS II-1/12):

• Cargo pumps in tankers must be in pump rooms with double bottom height ≥ 0.76 m (or equivalent protection).

Safety Benefits:

1. Grounding protection: Double bottom absorbs impact → prevents cargo tank rupture.
2. Flooding isolation: Pump room flooding ≠ cargo tank flooding → limits free surface effect.
3. Fire safety: Pump room is gas-tight, separate from engine room → reduces explosion risk.

Tanker Midship Section:
┌─────────────────────┐
│  Cargo Tanks        │
├─────────────────────┤
│  Pump Room (Double Bottom)│ ← 0.76m+ protection
├─────────────────────┤
│  Engine Room        │
└─────────────────────┘

Without this, grounding could flood pump room + adjacent cargo tanks → loss of stability + fire hazard.

4. Corrosion in Tankers: Problems & Regulatory Solutions

Corrosion Mechanisms:

• Cargo tank coating breakdown → seawater + oil residue → accelerated wastage.
• Ballast tank corrosion: Poor coating, inadequate cathodic protection.
• Stress corrosion cracking: High-tensile steel + residual stress + seawater.

Notable Losses:

1. MV Sea Star (1997): ULCC, structural failure due to corroded deck plating → broke in two.
2. MV Erika (1999): Single-hull tanker, corroded bottom plating → grounding → spill.
3. MV Prestige (2002): Age + corrosion → hull fracture in storm.

Regulatory Solutions:

• MARPOL Annex I, Reg. 13: Mandatory double hulls for tankers >5,000 DWT (phased out single hull by 2010).
• IACS CSR (Common Structural Rules): Enhanced corrosion margins, coating standards.
• ESP (Enhanced Survey Programme): Annual thickness measurements for tankers >10 years.

5. Bulk Carrier Design: Topside & Hopper Tanks

Why Included?

1. Strength: Triangular structure → resists racking (transverse distortion).
2. Stability: Lowers VCG (vertical center of gravity) → improves GM.
3. Flooding control: Limits cargo shift + free surface in hold flooding.
4. Ballast management: Dedicated tanks for trim/draft control.

Bulk Carrier Hold:
     Topside Tank
    /¯¯¯¯¯¯¯¯¯¯¯¯\
   │              │
   │   CARGO      │
   │              │
    \____________/
     Hopper Tank

Safety Impact: After flooding of one hold, topside/hopper tanks prevent progressive flooding to adjacent holds → survivability.

6. Granular Sulphur Ban (Post-Arcadia, 1998)

Incident:

• MV Arcadia: Bulk carrier, granular sulphur cargo → shifted like grain → angle of loll → capsized near Mumbai.

Why Banned?

• Twindex behavior: Sulphur fines fluidize under vibration → acts like Bingham plastic (solid at rest, liquid when disturbed).
• Angle of repose: ~35° → exceeds safe heel angle for many bulk carriers.
• IMO MSC/Circ. 664: Prohibited carriage unless treated as grain (shifting boards, trimming).

Lesson: Cargo classification must account for dynamic behavior, not just static density.

7. Single-Skin Bulk Carrier Sinking Scenario

Typical Failure Sequence:

1. Hatch cover failure (corrosion + overpressure) → seawater ingress.
2. Hold flooding → free surface effect → GM reduces.
3. Bulkhead collapse (designed for cargo, not water pressure) → progressive flooding.
4. Loss of longitudinal strength → hull girder fails → rapid sinking.

Progressive Flooding:
Hold 1 → Bulkhead → Hold 2 → Bulkhead → Hold 3
  ↓        ↓         ↓        ↓         ↓
Flooded  Failed    Flooded  Failed    Flooded → Sinking

Survivability Issue: Single-skin bulk carriers cannot survive two adjacent holds flooded.

8. IMO/IACS Formal Safety Assessment (1995–2000)

Main Failures Identified:

1. Design: Hatch covers under-designed for wave loads.
2. Construction: Poor welding, corrosion allowances insufficient.
3. Operation: Overloading, improper ballasting, delayed maintenance.
4. Survey: Inadequate thickness measurements.

Solutions:

Result: Bulk carrier losses dropped >70% post-2005.

9. Numerical: Hatch Cover Design Load (LLC 2005)

Given:

• Ship length $L = 300 \, \text{m}$
• Hatch cover at forepeak (0% L) and 15% L from FP
• Stiffener spacing $s = 700 \, \text{mm}$

Wave Load Formula (IACS UR S21):

Simplified for forepeak:

Assume design wave height $H_w = 12 \, \text{m}$ (North Atlantic):

At 15% L:

Minimum Plating Thickness:

Assume $\sigma_{allow} = 235 \, \text{MPa}$, $k = 0.9$:

Note: Actual design uses stiffened panels → thickness ~20–30 mm with stiffeners.

10. Kinetic & Potential Energy of Waves on Hatches (Type B Ships)

Type B Ships:

• Dry cargo ships with large hatch openings → reduced deck strength.

Wave Energy Effects:

1. Potential Energy: Wave elevation → hydrostatic pressure on hatch cover.
2. Kinetic Energy: Wave impact (slamming) → dynamic pressure spike.

Wave Impact on Hatch:
      Crest
        *
       /|\
      / | \  → Kinetic (impact)
     /  |  \
----*---|---*---- Hatch Cover
        |
        ↓
    Potential (static)

Design Implication: Hatch covers must withstand both static + dynamic loads → LLC 2005 increased requirements.

Part 5: ROPAX Stability & SOLAS 90/90+50 Standards

1. Case Studies: Al Salaam & Boccaccio 98

MV Al Salaam (2006, Red Sea)

• Loss: 950+ lives
• Cause: Fire in vehicle deck → water accumulation from firefighting → free surface effect → capsized.
• Stability Failure:
  • Firefighting water not pumped out → GM reduced to negative.
  • Passengers ran to one side → heeling moment exceeded righting moment.
  • No damage stability compliance (pre-SOLAS 90).

MV Boccaccio 98 (1992, Baltic Sea)

• Loss: 140+ lives
• Cause: Bow door failure → seawater ingress on vehicle deck → free surface + free communication → capsized in 30 min.
• Stability Failure:
  • Large undivided vehicle deck → water spread across beam.
  • Insufficient reserve buoyancy → rapid downflooding.

Common Factor: Both lacked SOLAS 90 damage stability → could not survive one-compartment flooding.

2. SOLAS 90 Standard for ROPAX Ships

Definition:

SOLAS 90 (1990 amendments) requires ROPAX ships to survive flooding of any one compartment with:

• Residual GM ≥ 0.05 m
• Righting lever GZ ≥ 0.1 m over 30° range
• Equilibrium heel ≤ 15°

Key Requirements:

1. Subdivision: Vehicle decks divided by watertight bulkheads.
2. Damage stability calculations: Probabilistic method (not deterministic).
3. Free surface correction: Account for water accumulation on car decks.

Impact: Pre-1990 ROPAX ships failed this standard → required retrofits or phase-out.

3. SOLAS 90+50 (Stockholm Agreement, 1996)

Background:

After Estonia disaster (1994), IMO adopted Stockholm Agreement (1996), enhancing SOLAS 90.

Key Provisions:

• Additional 50 cm freeboard (hence “+50”) for ROPAX ships.
• Higher damage stability: Survive flooding with 50 cm water on vehicle deck.
• Mandatory bow door locks + CCTV monitoring.
• Phased compliance: Existing ships to comply by 2010.

A and Amax Parameters:

• A: Actual subdivision index (probability of surviving damage).
• Amax: Minimum required index (function of ship length, N passengers).

Compliance Rule:

Where $L_s$ = subdivision length, $N$ = passenger capacity.

Effect: Larger ships with more passengers → higher Amax → stricter subdivision.

4. Stability Failures in Al Salaam/Boccaccio 98 (with Diagrams)

(a) Firefighting Operations (Al Salaam)

Vehicle Deck:
┌─────────────────────┐
│  Fire → Water Spray │ ← Accumulates on deck
│  ~500 tons water    │
└─────────────────────┘
Effect: Free surface → GM ↓ → Negative → Capsize

Lesson: ROPAX must have scuppers + pumps to remove firefighting water immediately.

(b) Passengers Running to One Side

Passenger Movement:
   Left Side: 200 pax → Right Side: 800 pax
         ↓                  ↑
   Heeling Moment = 600 pax × 10m (beam) ≈ 6,000 ton-m
   Righting Moment < 6,000 → Capsize

Lesson: Crowd control + stability margins for heeling moments.

(c) Vessel Making Wide Turn at Speed

Turning Maneuver:
   Centrifugal Force = (Δ × V²) / R
   Heeling Angle ≈ 10–15° at 20 knots
   + Water on deck → GM ↓ → Capsize risk

Lesson: Speed restrictions in adverse weather + anti-rolling systems.

5. Structural Alterations for SOLAS 90/90+50 Compliance

Retrofit Options for Existing ROPAX:

Sketch: Watertight Subdivision:

Pre-SOLAS 90:      Post-SOLAS 90:
┌──────────────┐   ┌───┼───┼───┐
│ Undivided    │   │ W │ W │ W │ ← Watertight bulkheads
│ Vehicle Deck │   │ T │ T │ T │
└──────────────┘   └───┴───┴───┘

Sketch: Buoyancy Boxes:

Original:        Retrofitted:
┌──────┐        ┌──┬──┬──┐
│ Ship │        │S │S │S │ ← Sponsons (buoyancy)
└──────┘        └──┴──┴──┘

6. Ro-Ro Ship Fire Safety: SOLAS Definitions

SOLAS Definitions:

• Ro-Ro Space: Space intended for cargo vehicles with fuel in tanks (SOLAS II-2/3).
• Special Category Space: Enclosed Ro-Ro space extending >25% of ship length (SOLAS II-2/3.14).

Fire Safety Measures:

1. Fixed foam/water spray systems (mandatory for special category spaces).
2. Smoke extraction: 10 air changes/hour.
3. Fire detection: Heat/smoke sensors every 50 m².
4. Separation: Engine rooms, accommodation separated by A-60 bulkheads.

Goal: Prevent fire spread + maintain stability during firefighting.

7. Numerical: A/Amax Compliance Example

Given:

• ROPAX ship: $L_s = 150 \, \text{m}$, $N = 1000$ passengers

Calculate Amax:

Required: Subdivision index $A \geq 0.623$

If actual A = 0.58 → Non-compliant → must add bulkheads or buoyancy.

8. Comparison: Pre-SOLAS 90 vs. SOLAS 90+50 ROPAX

Part 6: Stability Formulas & Numericals

1. Wall-Sided Formula (Large Angle Heel)

Derivation:

For a wall-sided vessel (vertical sides at waterline), the righting lever $GZ$ at large heel $\theta$ is:

Assumptions:

• Hull sides are vertical near waterline (valid for box barges, some tankers).
• Waterplane area remains constant with heel.
• Valid up to θ ≈ 25° (before deck edge immersion).

Diagram:

Heeled Wall-Sided Hull:
       Original WL
         ____
        /    \
       /      \   Heeled WL
      /        \ /
     /__________\
    B → B₁ (shifts outward)
    G fixed
    GZ = GM·sinθ + ½·BM·sinθ·tan²θ

Why “Wall-Sided”?
Because the formula assumes the hull behaves like a vertical-walled box → waterplane breadth unchanged with heel.

2. Atwood’s Formula (General Large Angle)

For any hull form (not just wall-sided):

Where:

• $v$: Volume of wedge immersed (or emerged)
• $h$: Horizontal shift of wedge centroid
• $V$: Total displacement volume
• $BG$: Distance between B and G

Derivation Insight:

• Accounts for actual hull geometry (not just vertical sides).
• More accurate than wall-sided for flared or tumblehome hulls.

3. Limitations of $GZ = GM \sin\theta$

Validity Range:

• θ < 6°: Accurate (small-angle approximation).
• θ > 6°: Underestimates GZ for wall-sided ships, overestimates for flared hulls.

Why?

• $GM$ is initial metacentric height (at θ = 0°).
• At large angles, M moves (prometacentre concept) → GM is no longer constant.

Comparison:

4. Prometacentre (M_θ)

Definition:

The prometacentre $M_\theta$ is the instantaneous metacentre at heel angle $\theta$. Unlike M (at θ = 0°), $M_\theta$ moves as the hull heels.

Diagram:

Upright:          Heeled (θ):
   M₀                M_θ
   |                 /
   |                /
   B₀              B_θ
   |               |
   G               G
GM₀ = M₀B₀ - BG   GM_θ = M_θB_θ - BG (varies with θ)

Why Calculate Restoring Moments at Large Angles?

• GM₀ is irrelevant beyond 6°.
• GZ curve (from Atwood’s or hydrostatics) determines dynamic stability (area under curve).
• Angle of vanishing stability (GZ = 0) → capsize risk.

5. Angle of Loll (Unstable Equilibrium)

Definition:

An angle of loll occurs when:

• GM < 0 (unstable upright)
• Ship finds stable equilibrium at heel angle $\theta_{loll}$ where $GZ = 0$ again.

Formula (Wall-Sided):

Example (Derrett’s Q9a): Given: $GM = -0.3 \, \text{m}$, $BM = 4.8 \, \text{m}$

Danger: Ship may loll suddenly to 20° → cargo shift → capsize.

6. Derrett’s Numerical: Example 2 (Page 140)

Problem: Box-shaped barge, L = 60m, B = 10m, D = 5m, draft = 3m, KG = 4m. Find GZ at 20° heel.

Step 1: Calculate KB, BM, GM

• $KB = \frac{T}{2} = 1.5 \, \text{m}$
• $BM = \frac{B^2}{12T} = \frac{10^2}{12 \times 3} = \frac{100}{36} \approx 2.78 \, \text{m}$
• $KM = KB + BM = 1.5 + 2.78 = 4.28 \, \text{m}$
• $GM = KM - KG = 4.28 - 4.0 = 0.28 \, \text{m}$

Step 2: Wall-Sided GZ at 20°

Compare with $GM \sin\theta$:

7. Derrett’s Q9b: Box-Shaped Barge Angle of Loll

Given: L = 50m, B = 8m, draft = 4m, KG = 5m, KB = 2m, BM = 1.33m.

Step 1: Calculate GM

• $KM = KB + BM = 2 + 1.33 = 3.33 \, \text{m}$
• $GM = KM - KG = 3.33 - 5.0 = -1.67 \, \text{m}$ (unstable)

Step 2: Angle of Loll

Interpretation: Ship will loll to ~58° → likely capsize if cargo shifts.

8. GZ Curve & Dynamic Stability

GZ Curve Components:

1. Initial slope: $\frac{dGZ}{d\theta} = GM$ at θ = 0°.
2. Maximum GZ: At θ ≈ 30–40° (varies by hull).
3. Angle of vanishing stability: GZ = 0 → capsize threshold.
4. Area under curve: Dynamic stability (energy to capsize).

Diagram:

GZ (m)
  |
  |     Max GZ
  |      *
  |     / \
  |    /   \
  |   /     \
  |  /       \
  | /         \
  |/___________\______ θ (°)
  0   30   60   90
       Angle of Vanishing Stability

Regulatory Minimums (IMO A.749):

• Area under GZ curve ≥ 0.055 m·rad (up to 30°)
• Max GZ ≥ 0.20 m at θ ≥ 25°

9. Rolling Period & GM Relationship

From earlier:

Rearranged for GM:

Rolling Test Procedure:

1. Displace ship slightly (tug push).
2. Measure time for 5 complete rolls → average $T_\phi$.
3. Assume $k \approx 0.4B$ → calculate GM.

Example:

• $B = 20 \, \text{m}$, $T_\phi = 12 \, \text{s}$, $k = 0.4 \times 20 = 8 \, \text{m}$ $$GM = \frac{4\pi^2 \times 8^2}{9.81 \times 12^2} = \frac{4 \times 9.87 \times 64}{9.81 \times 144} \approx \frac{2527}{1413} \approx 1.79 \, \text{m}$$

10. Summary Table: Stability Formulas

Part 7: High-Speed Craft & Hydrofoils

1. SOLAS Definition of High-Speed Craft

SOLAS Chapter X (High-Speed Craft):

A High-Speed Craft is defined as (SOLAS Reg. X/1.2):

“A craft capable of a maximum speed in metres per second (m/s) satisfying:

$$> V \geq 3.7 \cdot \nabla^{0.1667} >$$

where $\nabla$ = volume of displacement at design waterline (m³).”

Simplified: For most vessels, this translates to:

• ≥ 25 knots for displacement hulls
• ≥ 35 knots for planing/semi-planing hulls

HSC Code (IMO Resolution A.373):

Mandatory for all HSC engaged on international voyages:

• Construction: Lightweight materials (aluminum, composites).
• Stability: Enhanced damage stability (flooding of one compartment).
• Fire safety: Automatic sprinklers, smoke extraction.
• Navigation: Redundant systems, weather restrictions.

2. Hydrofoils: How High Speed is Achieved

Principle:

Hydrofoils lift the hull out of water at speed → dramatically reduces drag.

Drag Components:

• Frictional drag (hull wetted surface) → eliminated when hull clears water.
• Wave-making drag (hull pushing water) → minimized.
• Foil drag (small submerged foils) → much lower than full hull drag.

Speed Regimes:

Power Requirement:

Where $D$ = drag. By reducing $D$ by 70–80% (foil-borne), speed increases 2–3× for same power.

Diagram:

Displacement Mode:     Foil-Borne Mode:
   ____                  ____
  /    \                /    \
 /______\  ← Hull      /______\  ← Hull (clear of water)
 ~~~~~~~~  Water          ||||
                          ||||  ← Foils submerged

3. Transverse & Longitudinal Stability (Hydrofoils)

Transverse Stability (Roll):

• Foil-borne: Stability from dihedral angle of foils (like airplane wings).
  • Heel → lower foil generates more lift → righting moment.
• Hull-borne: Conventional waterplane stability (GM-based).

Key Parameter: Dihedral angle $\gamma$:

Where $L_{foil}$ = foil span, $\Delta V$ = lift change.

Longitudinal Stability (Pitch):

• Canard configuration (forward foil + aft foil):
  • Forward foil: Controls pitch, provides lift.
  • Aft foil: Stabilizes, trims.
• Automatic control systems: Adjust foil angles to maintain level flight.

Diagram:

Side View (Canard Hydrofoil):
      Forward Foil (adjustable)
           /
          /
         /
        /___________ Hull (clear)
                 \
                  \
                   \ Aft Foil (stabilizer)

Risk: Pitch-poling (bow dives) if forward foil stalls → automated systems prevent this.

4. Seakeeping (Hydrofoils)

Advantages:

• Hull clear of waves → minimal motion sickness.
• Active foil control → adjusts to wave slope → smooth ride.

Limitations:

• Foil ventilation (air drawn into foil) → loss of lift → sudden drop.
• Wave height limit: Typically Hs ≤ 2.5 m for safe foil-borne operation.
• Speed restrictions: Reduce to hull-borne in rough seas.

Comparison with Monohull:

5. Propulsion Arrangement (Hydrofoils)

Common Systems:

1. Waterjets (most common):
   • High efficiency at 30–50 knots.
   • No exposed propellers → safe for passengers.
2. Surface-piercing propellers:
   • Reduced drag (partially out of water).
   • Risk: Ventilation, cavitation.
3. Gas turbines (military hydrofoils):
   • High power-to-weight ratio.
   • Fuel consumption: Very high.

Diagram:

Hydrofoil Propulsion:
   Hull (clear)
      ||
      ||  ← Struts (house driveshafts)
      ||
   Foils + Waterjets (submerged)

Advantage: Waterjets allow rapid reversal → excellent maneuverability.

6. HSC Code: Key Safety Requirements

Structural:

• Lightweight materials: Aluminum alloys (5083, 6061), carbon fiber composites.
• Collision protection: Double bottom, watertight compartments.

Stability:

• Damage stability: Survive flooding of one compartment (similar to SOLAS 90).
• Intact stability: GM ≥ 0.15 m (hull-borne), positive righting energy (foil-borne).

Fire Safety:

• Automatic sprinklers in passenger spaces.
• Smoke extraction: 20 air changes/hour.
• Fire-resistant bulkheads: A-60 class.

Operational Restrictions:

• Weather limits: Hs ≤ 2.5 m (typical).
• Speed limits: Reduce in restricted visibility.
• Mandatory reporting: Position, weather, passenger count.

7. Comparison: Monohull vs. Multihull vs. Hydrofoil

Power/Speed Ratio:

Hydrofoils achieve 2–3× speed for same power → ideal for fast ferries.

8. Numerical: HSC Speed Threshold

Given: HSC with displacement volume $\nabla = 500 \, \text{m}^3$

Calculate minimum speed for HSC classification:

Interpretation: This vessel must exceed 20.2 knots to be classified as HSC → likely a planing hull or hydrofoil.

9. HSC Operational Challenges

1. Weather sensitivity: Must reduce speed/stop in Hs > 2.5 m.
2. Foil strike risk: Submerged foils can hit debris → inspection mandatory.
3. Passenger comfort: Sudden transitions (hull-borne ↔ foil-borne) → motion sickness.
4. Regulatory compliance: HSC Code requires annual surveys, crew training.