MARINA Chief Mate / Master Theoretical Exam cheat sheet

Mercator sailing: departure = D.Long × cos(mean latitude); great-circle distance from cos D = sin φ1 sin φ2 + cos φ1 cos φ2 cos D.Long.

Mid-latitude sailing uses mean latitude for departure; use it only when D.Long is small or latitudes are low, otherwise switch to great-circle or Mercator.

Great-circle initial course: tan C = sin D.Long / (cos φ1 tan φ2 − sin φ1 cos D.Long); verify quadrant against the direction of D.Long.

Composite great-circle: vertex latitude limits the track; waypoints where track reaches limiting latitude are found from cos D.Long(vertex) = cos(limit)/... use cos φv = cos φ1 sin C1.

Current triangle: set and drift vector added to course and speed through water gives course and speed made good; SMG = distance run / elapsed time.

Tidal stream: use the appropriate tidal diamond or atlas page for the hour relative to HW at the standard port, interpolate between springs and neaps by range ratio.

Running fix: advance the earlier LOP by the course and distance run, then plot the transferred LOP with the later LOP; error grows with the advance distance.

Position fixing accuracy: fix quality depends on angle of cut; 90° is ideal, avoid cuts below 30° or above 150°, and prefer three or more position lines.

Stowage factor (SF) = volume in m³ / mass in tonnes; broken stowage = (space occupied − cargo volume) / space occupied, expressed as a percentage.

Deadweight available for cargo = summer deadweight − bunkers − fresh water − stores − ballast − constants; always confirm with the ship's loading manual.

IMO grain code: list of grain-laden ships requires either the ship to be trimmed/filled to the required standard or to have documented stability calculations; heeling moments from grain shift must be included.

Dangerous goods segregation table: 'away from' = 3 m horizontally; 'separated from' = 6 m; 'separated by a complete compartment or hold from' = one bulkhead or deck between; 'separated longitudinally by an intervening complete compartment' = one hold length.

IMDG class 1 (explosives) and class 7 (radioactive) require special stowage and competent authority approval; class 2.3 and 6.1 toxic gases/liquids must not be stowed in accommodation or under it.

Container lashing: check stack weight limits, corner casting SWL, and the lashing plan for the actual stow; excessive stack weight or uneven distribution causes racking and lashing failure.

Bulk cargo liquefaction risk: group A cargoes (e.g., mineral concentrates) may liquefy if moisture content exceeds the transportable moisture limit (TML); require a certificate of moisture content and TML.

Timber deck cargo: lashings and stanchions must be checked, and the ship's stability must account for water absorption and ice accretion; check the timber load line if assigned.

Fire triangle: fuel, oxygen, heat; removing any one side extinguishes combustion. Class A = solids, B = liquids, C = gases, D = metals, F/K = cooking oils.

CO₂ extinguishes by oxygen displacement; never use in a confined space with people, and cool boundaries after discharge to prevent re-ignition.

Man overboard: shout 'Man overboard', release the lifebuoy with smoke/light, note position/time, helm to turn the stern away from the person, and initiate the Williamson or Anderson turn.

Abandon ship: Mayday with position, nature of distress, number of persons, and intention; account for all persons at the muster station and take the SART and EPIRB if time permits.

Collision: assess damage and flooding, close watertight doors, sound the general alarm, broadcast safety message, and exchange vessel details as required by SOLAS V/31.

Grounding: stop engines, sound the general alarm, take soundings around the hull, check for pollution, and do not refloat until stability, tide, and damage are assessed.

Emergency generator: must start automatically and supply emergency loads within 45 s; test weekly and run under load monthly per SOLAS II-1.

Fire drills and abandon-ship drills: every crew member participates at least monthly; drills must be recorded in the official logbook with date, time, and remarks.

GM = KM − KG; positive GM gives a righting moment. GZ = GM × sin θ for small angles; the GZ curve gives the actual righting lever at large angles.

Initial transverse metacentric height: BM = I / V, where I is the waterplane second moment of area and V is the displaced volume.

Free surface effect: FSC = i × ρ / (Δ), where i is the free surface second moment of area; reduce by pressing up or dividing tanks.

Angle of vanishing stability is where GZ returns to zero; the area under the GZ curve to 30° and to 40° is checked against the applicable intact stability criteria.

Damage stability: flooding a compartment raises KG and may reduce GM; the margin line and permissible length rules are checked in the ship's damage stability booklet.

Load line marks: the summer load line is at the assigned freeboard; the deck line and load line disc are marked amidships on both sides.

Strength: still-water shear force and bending moment are combined with wave-induced components; the loadicator must stay within the permissible still-water limits.

Bulkhead and watertight integrity: watertight doors must be operable locally and from the bridge; indicators show open/closed status on the bridge panel.

Buys Ballot's law (Northern Hemisphere): with your back to the wind, low pressure lies to your left; in the Southern Hemisphere it lies to the right.

In the Northern Hemisphere, wind blows counter-clockwise around a low and clockwise around a high; surface friction causes inflow toward the low.

Beaufort scale: force 0 = calm (<1 kn), force 6 = strong breeze (22–27 kn), force 8 = gale (34–40 kn), force 12 = hurricane (≥64 kn).

Tropical revolving storm: in the Northern Hemisphere the dangerous semicircle is the right-hand side of the track; the navigable semicircle is the left-hand side.

Fog forms when the dew point is close to the air temperature; radiation fog forms on clear calm nights, advection fog when warm moist air moves over a cold surface.

Swell travels beyond the generating area and can arrive before the storm; long-period swell indicates a distant or intense system.

Sea state: significant wave height is the average of the highest one-third of waves; the maximum individual wave may be about twice the significant height.

Ocean currents: the Gulf Stream and Kuroshio are western boundary currents; the Antarctic Circumpolar Current is driven by the prevailing westerlies and is unobstructed by land.

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

Watchkeeping: the OOW is responsible for the safe navigation of the ship and must not leave the bridge unattended; a lookout must be maintained at all times.

Muster list: assigns each crew member to a station and duty; posted in conspicuous places and updated when the crew changes.

Permit to work: required for hot work, enclosed space entry, working aloft or over the side, and other high-risk tasks; the permit specifies precautions and validity.

Enclosed space entry: atmosphere must be tested for oxygen (≥20.9% is normal air; entry typically requires ~21%), hydrocarbons, and toxic gases before entry; a standby person remains at the entrance.

Toolbox talk: pre-task briefing covering hazards, controls, and roles; documented for high-risk operations.

Fatigue management: consider cumulative rest, circadian rhythm, and workload; the master may adjust schedules but must maintain minimum rest.

Safety management system (ISM Code): requires documented procedures, designated person ashore, master's overriding authority, and internal audits.

SOLAS: minimum safety construction, fire protection, life-saving appliances, and radio equipment standards; chapter V covers navigation and voyage planning.

MARPOL Annex I (oil), II (noxious liquid substances), III (harmful packaged substances), IV (sewage), V (garbage), VI (air pollution); special areas have stricter discharge rules.

MARPOL Annex V: discharge of garbage is generally prohibited; food waste may be discharged outside special areas beyond 12 nm (comminuted, ≥25 mm) or 3 nm if comminuted.

MARPOL Annex VI: global sulphur limit 0.50% m/m since 1 January 2020; 0.10% in ECAs; NOx Tier limits apply to new engines; EEDI/EEXI and CII apply to ships.

COLREG Rule 13: an overtaking vessel keeps out of the way until finally past and clear; Rule 14 head-on: both alter course to starboard; Rule 15 crossing: the vessel with the other on her starboard side gives way.

COLREG Rule 19: in restricted visibility, reduce speed to a safe speed, and if a risk of collision exists, take avoiding action; a vessel hearing a fog signal forward of the beam must reduce speed to the minimum.

STCW: certificates of competency, endorsements, and watchkeeping standards; the 2010 Manila Amendments added rest hours, ECDIS, and leadership requirements.

UNCLOS: territorial sea 12 nm, contiguous zone 24 nm, EEZ 200 nm, and the right of innocent passage; the flag state has jurisdiction over its ships on the high seas.

Two-stroke slow-speed diesel: uniflow scavenging, one power stroke per revolution; typical efficiency ~50% for large low-speed engines.

Four-stroke medium-speed diesel: one power stroke every two revolutions; used for auxiliary generators and medium-speed propulsion.

Turbocharger: exhaust gas drives a turbine that drives a compressor; it increases charge air density and power output; surging indicates a mismatch between engine and turbocharger.

Fuel oil: viscosity is controlled by heating before injection; the viscosity at the injector is typically 10–15 cSt; water and cat fines must be removed by purifiers.

Cooling systems: jacket water and central cooling; high-temperature alarms indicate scale, low flow, or a faulty pump; never open a hot system under pressure.

Steering gear: SOLAS requires two independent power units; the main and auxiliary steering gear must be tested before departure, and emergency steering drills are held every three months.

Bilge and ballast systems: bilge wells, oily water separator (15 ppm alarm), and ballast water management per the BWM Convention.

Propulsion shafting: stern tube bearings and seals; monitor temperatures and leakage; a controllable-pitch propeller can be set to zero pitch for emergency running.

GMDSS sea areas: A1 (VHF coverage), A2 (MF), A3 (Inmarsat), A4 (HF); the ship's equipment must match the area of operation.

DSC distress alert: VHF channel 70 or MF/HF DSC; after sending, follow with a Mayday on radiotelephony or radiotelephony distress frequency; do not use channel 70 for voice.

EPIRB: 406 MHz COSPAS-SARSAT; float-free mounting, registration with the national authority, and battery expiry date checked monthly.

SART: radar transponder, 9 GHz, range about 5–10 nm from a ship's radar; test according to the manufacturer's instructions.

ECDIS: must use official ENC or an approved RCDS; safety settings, alarms, and route monitoring; the ECDIS must not be used as the sole means of navigation unless the ship complies with SOLAS V/19.

GPS/GNSS: position accuracy depends on HDOP and satellite geometry; RAIM detects faults; GNSS is vulnerable to jamming and spoofing, so cross-check with other fixes.

AIS: transmits identity, position, course, speed, and heading; class A for SOLAS ships; AIS is not a collision-avoidance system and does not replace radar or visual lookout.

NAVTEX: receives MSI on 518 kHz (English international), 490 kHz (national), and 4209.5 kHz (HF); messages categorized as vital, important, or routine.