Chief Mate CoC cheat sheet

Great circle distance: D = 60 × arccos(sin φ1 sin φ2 + cos φ1 cos φ2 cos Δλ), φ in degrees, Δλ the smaller longitude difference.

Initial great circle course: C = atan2(sin Δλ cos φ2, cos φ1 sin φ2 − sin φ1 cos φ2 cos Δλ); convert to 000–360°T.

Mercator sailing: DMP = 7915.7 × log10[tan(45° + φ/2)] minutes; course angle C = atan(Δλ / DMP); distance = Δφ / cos C.

Plane sailing for short legs: departure = distance × sin course; difference of latitude = distance × cos course; DLAT in minutes equals nautical miles.

Current vector: set = direction current flows toward (true); drift = speed in knots. Course to steer = course made good − current effect, solved by vector triangle or set/drift table.

Under keel clearance (UKC) minimum = static draft + squat + heel + wave-induced rise + chart datum allowance; squat ≈ Cb × V² / 100 (m) for open water, doubled in confined channels.

ECDIS route safety: XTD must not exceed the safety contour buffer; check safety depth, safety contour, and isolated danger symbol against UKC plan; verify all route waypoints are on the safe side of the safety contour.

IALA Region A: red can buoys mark port hand, green conical buoys mark starboard hand when entering from sea; Region B reverses colours. Cardinal marks: N = two cones up, E = cones base-to-base, S = two cones down, W = cones point-to-point.

Passage plan appraisal (IMO Res. A.893(21)): all pertinent information - charts, publications, weather, traffic, no-go areas, abort points, contingency anchorages - must be gathered and evaluated before execution.

GM = KM − KG. Positive GM = stable; negative GM = unstable and will capsize. GM = 0 is neutral equilibrium.

GZ curve: area under the curve to 30° ≥ 0.055 m·rad, to 40° ≥ 0.09 m·rad, to 40° or flooding angle ≥ 0.09 m·rad; maximum GZ ≥ 0.20 m at angle ≥ 25° (IS Code 2008).

Free surface effect: FSC = (i × ρ_liquid) / (Δ × ρ_water), where i = second moment of free surface area about its centreline; reduce GM by FSC.

Angle of loll: cos θ = √(2 GM / BM) for negative GM; ship lists to port or starboard unpredictably; correct by lowering KG (ballast in double bottoms) before attempting to right.

List due to off-centre weight: tan θ = (w × d) / (Δ × GM), where w = weight shifted, d = transverse distance shifted.

Cargo securing: MSL (maximum securing load) = breaking strength / safety factor (1.5 for web lashings, 2.0 for chain, 2.0 for wire). Required lashing strength per CSS Code Annex 13.

Bulk cargo liquefaction: TML (transportable moisture limit) = 90% of flow moisture point; cargo with moisture above TML must not be loaded (IMSBC Code).

Draft survey: displacement = f(mean of forward, aft, and midship drafts corrected for deflection); apply first and second trim corrections and density correction.

Timber deck cargo: GM must remain positive; account for water absorption (up to 15% weight increase) and ice accretion in winter zones.

Buys Ballot's Law (Northern Hemisphere): with back to wind, low pressure is to your left; in Southern Hemisphere, low is to your right.

Geostrophic wind: parallel to isobars, speed inversely proportional to pressure gradient; surface friction turns wind 10–20° over sea, 30–45° over land, toward low pressure.

Tropical revolving storm (TRS) avoidance (Northern Hemisphere): in the dangerous semicircle (right of track), steer to bring wind on starboard bow and move away from the storm centre; in the navigable semicircle, keep wind on starboard quarter.

Fog formation: radiation fog requires clear sky, light wind, and high relative humidity; advection fog forms when warm moist air moves over a cold surface (sea fog).

Swell: generated by distant weather; period increases and height decreases with distance from fetch; swell direction indicates source storm bearing.

Ocean currents: western boundary currents (Gulf Stream, Kuroshio) are warm, fast, and narrow; eastern boundary currents (Canary, Benguela) are cold, slow, and broad; upwelling occurs on the equatorward side of eastern boundary currents.

Beaufort scale: force 6 = 22–27 kn (strong breeze); force 8 = 34–40 kn (gale); force 10 = 48–55 kn (storm); force 12 = ≥64 kn (hurricane).

Barometer: falling rapidly at >1 hPa/hour indicates approaching low; rise after fall indicates passing of centre; diurnal variation ~3 hPa in tropics.

Iceberg limits: in North Atlantic, icebergs may be encountered south of 40°N in spring; growlers and bergy bits are radar-poor targets; keep speed ≤ 10 kn in ice-infested waters.

Collision bulkhead: located at not less than 0.05L and not more than 0.08L (or 0.05L + 3 m, whichever is greater) from the forward perpendicular (SOLAS II-1).

Double bottom height: not less than B/20 or 760 mm, whichever is greater (SOLAS II-1/9); minimum 600 mm at the keel.

Watertight subdivision: damage stability must satisfy SOLAS II-1 probabilistic requirements (A-index) for passenger ships; cargo ships use deterministic criteria (SOLAS II-1/6).

Bulkhead deck: the uppermost deck to which transverse watertight bulkheads are carried; defines extent of flooding.

Permeability: engine room 0.85, cargo spaces 0.70–0.95 depending on cargo, stores 0.60, accommodation 0.95.

Tonnage: gross tonnage (GT) = K1 × V (V = total enclosed volume in m³, K1 = 0.2 + 0.02 log10 V); net tonnage derived from cargo volume (ITC 1969).

Load line marks: S = summer, W = winter, T = tropical, F = fresh water, TF = tropical fresh, WNA = winter North Atlantic; freeboard decreases from W to T to S.

Corrosion control: impressed current cathodic protection (ICCP) and sacrificial anodes; coating breakdown accelerates in ballast tanks; survey intervals per ESP for bulk carriers and oil tankers.

Hull stress: hogging (wave amidships, buoyancy ends) causes deck tension and keel compression; sagging (wave at ends) reverses. Avoid excessive ballast transfer during heavy weather.

UNCLOS: territorial sea 12 nm from baseline; contiguous zone 24 nm; exclusive economic zone 200 nm; high seas beyond.

Innocent passage: continuous and expeditious; no threat or use of force; submarines must navigate on surface and show flag (UNCLOS Art. 20).

Hague-Visby Rules: carrier must exercise due diligence to make ship seaworthy before and at beginning of voyage; 1-year time bar for suit.

Hamburg Rules: carrier liable for loss/damage unless proves took reasonable measures to avoid occurrence; 2-year time bar; applies to live animals and deck cargo if agreed.

Rotterdam Rules (2009): door-to-door coverage; 3-year time bar; not yet in force for major trading nations as of 2024.

General average (York-Antwerp Rules): sacrifice or expenditure intentionally and reasonably made for common safety; contribution by all cargo interests in proportion to arrived values.

Salvage (Lloyd's Open Form 2020): no cure, no pay, with SCOPIC clause for environmental protection; Article 13 (property) and Article 14 (environment) awards under Salvage Convention 1989.

Limitation of liability (LLMC 1976/1996 Protocol): 2 million SDR for loss of life, 1 million SDR for property (for ships ≤ 2,000 GT); increases with tonnage.

Bill of lading: prima facie evidence of quantity and condition; clean vs. claused; a clean B/L estops carrier from denying condition against a bona fide third-party holder.

SOLAS Chapter V: voyage data recorder (VDR) mandatory for passenger ships and cargo ships ≥ 3,000 GT; annual performance test.

MARPOL Annex I: oil discharge ≤ 15 ppm from machinery space; ≤ 30 L/nm for cargo area; outside special areas; 50 nm from land.

MARPOL Annex VI: global sulphur cap 0.50% m/m from 1 Jan 2020; 0.10% in ECAs (Baltic, North Sea, North American, US Caribbean, Mediterranean from 1 May 2025).

MARPOL Annex IV: sewage discharge beyond 12 nm (comminuted and disinfected) or 3 nm (treated); no discharge in special areas except treated.

STCW 2010 Manila Amendments: rest hours minimum 10 hours in any 24-hour period and 77 hours in any 7-day period; maximum 14 hours on duty in any 24-hour period.

ISM Code: safety management system (SMS) with functional requirements; company must designate a person ashore (DPA); internal audits annually, external audit by flag State.

ISPS Code: ship security plan (SSP), ship security officer (SSO), company security officer (CSO), port facility security officer (PFSO); three security levels.

MLC 2006: minimum age 16 (18 for hazardous work); hours of work 14/77; repatriation; accommodation standards; complaint procedures.

COLREG Rule 10: traffic separation schemes - cross at right angles, avoid crossing lanes, do not anchor in TSS.

Rule 5: proper lookout by sight and hearing and by all available means; no relaxation of this duty.

Rule 6: safe speed determined by visibility, traffic density, manoeuvrability, background light, state of sea, draft, and stopping distance.

Rule 7: risk of collision deemed to exist if compass bearing of approaching vessel does not appreciably change; if in doubt, assume risk exists.

Rule 8: action to avoid collision must be positive, made in ample time, large enough to be readily apparent; alteration of course alone is preferred.

Rule 13: overtaking vessel keeps clear; overtaking persists until finally past and clear.

Rule 14: head-on - both vessels alter course to starboard and pass port-to-port.

Rule 15: crossing - vessel with other on her starboard side gives way; avoid crossing ahead.

Rule 19: restricted visibility - reduce speed to minimum steerage way; no right of way; avoid altering course to port for vessel forward of beam.

Rule 21: masthead light 225°, sidelights 112.5° each, sternlight 135°; towing light yellow 135°; all-round lights 360°.

Muster list: must be posted before sailing; drills - abandon ship and fire drill monthly for crew; passenger ships weekly.

SOLAS III/19: fire and abandon ship drills within 24 hours of leaving port if more than 25% of crew has not participated in prior month.

Man overboard (MOB): immediate helm hard over toward the person, release lifebuoy with light/smoke, sound three long blasts, initiate Williamson or Anderson turn.

Fire triangle: fuel, heat, oxygen; extinguishing by cooling, smothering, starving, or chemical inhibition. Class A = solids, B = liquids, C = gases, D = metals, F = cooking oils.

Fixed CO2 system: release requires all personnel accounted for; CO2 displaces oxygen; do not enter space until ventilated and atmosphere tested.

Emergency generator: must start automatically and supply emergency switchboard within 45 seconds (SOLAS II-1/43).

GMDSS: distress alert via DSC (VHF Ch 70, MF/HF), Inmarsat, or EPIRB; follow with distress message on radiotelephony Ch 16 or MF 2182 kHz.

Damage control: set material condition (X-ray, Yoke, Zebra); Zebra = all watertight closures secured; report to bridge; prepare damage control parties.

Safety management: near-miss reporting, risk assessment (5×5 matrix), permit-to-work for hot work and enclosed space entry (SOLAS III/19, ISM).

Two-stroke slow-speed diesel: uniflow scavenging, exhaust valve, crosshead; typical BMEP 18–20 bar; specific fuel consumption ~165–175 g/kWh.

Four-stroke medium-speed: trunk piston, inlet valve in cylinder head; used for auxiliary generators and medium-speed propulsion.

Turbocharger: exhaust gas drives turbine which drives compressor; air cooler reduces intake temperature to increase density.

Fuel oil: HFO requires heating to ~130–150°C at injectors for viscosity 10–15 cSt; MGO/MDO viscosity 2–6 cSt at 40°C; sulphur limits per MARPOL Annex VI.

Boiler: water-tube for high pressure; fire-tube for auxiliary; safety valve set at 1.1 × design pressure; gauge glass blow-through daily.

Steering gear: SOLAS II-1/29 requires two independent power units; main and auxiliary; test before departure; emergency steering drill every 3 months.

Pumping: bilge system must be capable of draining any watertight compartment; emergency bilge suction direct to main engine cooling pump.

Electrical: 440 V 60 Hz or 380 V 50 Hz typical; insulation resistance ≥ 1 MΩ; earth fault detection; emergency switchboard supplied by emergency generator.

Refrigeration: compressor, condenser, expansion valve, evaporator; refrigerant R404A/R134a; leak detection required; no CFCs (Montreal Protocol).

Situational leadership: directing (high task/low relationship), coaching (high task/high relationship), supporting (low task/high relationship), delegating (low task/low relationship).

Bridge resource management (BRM): closed-loop communication, challenge and response, assertiveness with respect, shared mental model, fatigue management.

STCW rest hours: minimum 10 hours in any 24-hour period and 77 hours in any 7-day period; maximum 14 hours on duty in any 24-hour period; rest may be divided into no more than two periods, one of at least 6 hours.

Fatigue: performance degrades after 17 hours awake equivalent to 0.05% BAC; circadian low 02:00–06:00; mitigate with strategic napping (20–30 min).

Just culture: distinguishes human error (console), at-risk behaviour (coach), reckless behaviour (sanction); encourages reporting without fear.

Safety culture (Reason): pathological, reactive, calculative, proactive, generative.

Conflict resolution: separate people from problem, focus on interests not positions, generate options, use objective criteria (Fisher & Ury).

Cross-cultural communication: high-context (Asian, Arab) vs. low-context (Northern European, North American); use explicit standard phrases to avoid ambiguity.

Training: onboard familiarisation before assignment; STCW competence requirements; drills and exercises recorded in official logbook.

MARPOL Annex I: oil record book Part I (machinery space) and Part II (cargo); entries for ballasting, cleaning, discharge; retained 3 years.

Oil discharge criteria (Annex I Reg. 15): outside special areas, en route, instantaneous rate ≤ 30 L/nm, total ≤ 1/30,000 of cargo carried, ≥ 50 nm from land, oil content meter and slop tank arrangement.

Special areas (Annex I): Mediterranean, Baltic, Black Sea, Red Sea, Gulf, Gulf of Aden, Antarctic, North West European waters, Oman area, Southern South African waters.

Garbage (Annex V): no discharge of plastics anywhere; food waste ≥ 12 nm (comminuted ≥ 3 nm); cargo residues ≥ 12 nm; garbage record book retained 2 years.

Sewage (Annex IV): discharge of comminuted/disinfected sewage ≥ 3 nm; untreated ≥ 12 nm; special areas stricter.

Air pollution (Annex VI): SOx ECA 0.10%; global 0.50%; NOx Tier III for ships built after 1 Jan 2016 in NOx ECAs; ODS prohibited; incinerator restrictions.

Ballast water management (BWM Convention 2004): D-1 exchange (sequential or flow-through, 95% volumetric) or D-2 treatment; BWRB retained 2 years; IOPP certificate.

Anti-fouling (AFS Convention 2001): prohibits organotin compounds; ships ≥ 400 GT require IAFS certificate; apply before 60 months.

Oil spill response: SOPEP (Shipboard Oil Pollution Emergency Plan) required for oil tankers ≥ 150 GT and other ships ≥ 400 GT; SMCP for communications.