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A great circle is the line traced on a sphere's surface by a plane passing through its centre and the two positions concerned. Because it is the shortest path between them, it is the natural choice for any long ocean passage — but the saving comes at a cost. Unlike a rhumb line, a great circle track crosses every meridian at a different angle, so the true course to steer is constantly changing. In practice this means either re-plotting the course at intervals (turning the great circle into a series of rhumb-line legs, close enough for the purpose) or using an integrated bridge system that steers the curve directly.

The highest (or lowest) latitude reached on a great circle track is called the vertex. Meridians converge toward the poles, so a great circle between two points at similar latitude often bulges well polewards of either of them to shorten the distance — sometimes far enough to run into ice, heavy weather, or simply latitudes the ship, her ice class or her charter party have no business being in. This is the single most common error examiners see: a candidate quotes a great-circle distance without first checking where its vertex actually lies.

Composite great circle sailing is the practical fix. Instead of letting the track run all the way to its natural vertex, a limiting latitude is chosen — set by ice season, company policy, or simple prudence — and the track is built in three parts: great circle from the start up to the limiting parallel, a stretch of parallel sailing along that latitude to cover the required change of longitude, then great circle down to the destination. The parallel-sailing leg is plain departure, and costs a little extra distance in exchange for staying clear of what lies beyond the limit.

Ocean routeing in its simplest form is climatological: pilot charts and seasonal current and wind atlases show where gales, calms, ice limits and favourable currents typically lie for the month of the passage, and the track is chosen to work with them rather than against them. It is planning information, fixed well in advance and blind to what is actually happening on the day.

Weather routeing is the live version of the same idea. A routeing service combines the current forecast with the ship's own performance curves — how much speed she loses, and how much motion and stress she takes on, in a given sea state on a given heading — and proposes a track, updated as the forecast changes, intended to minimise passage time, fuel, or damage to ship and cargo. The output is usually a recommended track and a set of waypoints, sometimes with an alternative ranked by a different priority.

The trade-off examiners want articulated is straightforward: a longer track through calmer water can beat a shorter track through heavy weather, both on arrival time and on the condition of the cargo, because speed loss and heaving-to in a seaway cost far more than the extra miles. But routeing advice remains advice. The service does not know the ship's current stability condition, her actual cargo securing, or a defect the crew are nursing, and it carries no authority over the vessel. However good the advice, the decision to accept, adapt or reject the recommended track — and the responsibility that goes with it — stays with the master.

Ice discipline starts with speed. A vessel making way through ice at a speed judged for open water risks hull and propeller damage long before the bridge team registers a problem; reduced speed buys the time to see and react to what is ahead. The second discipline is following leads — the open water channels between floes — rather than forcing a direct track through heavier ice, which a vessel without the structure or power for it should not attempt regardless of the distance saved. Where ice concentration and type exceed what the ship's ice class permits, the answer is not caution, it is a different route.

Ice accretion is a stability problem disguised as a seamanship one. Spray freezing on the mast, rigging, rails and upperworks adds weight high above the keel, exactly where it does the most damage to GM — a relatively modest tonnage of ice, acting well above the vessel's existing centre of gravity, can shift KG and erode stability faster than most officers expect (worked through numerically later in this chapter). Anti-icing measures and, where practicable, altering course or speed to reduce spray are stability decisions as much as comfort ones.

• Ice class — sets which ice regimes and seasons the vessel may legally enter; it is a limit on the ship, not a target to sail up to.
• Lookout and lighting — extra lookouts and searchlight use at night, since radar alone under-reports low, wet ice.
• Ice reporting — passing and receiving ice information keeps the picture ahead current for other traffic as well as for the ship.

The Polar Code adds a layer of formal requirement on top of ordinary good practice for ships operating in polar waters. It calls for a Polar Water Operational Manual specific to the vessel, setting out her operational limitations and the procedures for working within them; for equipment and structural standards appropriate to the ice and cold expected; and for crew holding recognised polar training appropriate to their role, on top of their ordinary certification. None of this replaces ordinary ice seamanship — it formalises the planning and the qualifications behind it.

Restricted visibility is handled as a procedure, not a reaction, because that is exactly how examiners mark it: as a checklist run in full, every time, whether the fog is patchy or solid. The moment visibility starts to close in, speed is reduced to what is safe for the conditions — not a fixed number, but a speed that allows the vessel to be stopped within a distance appropriate to the circumstances, taking account of traffic density, the ship's manoeuvring characteristics and the effectiveness of her radar picture. Engines are brought to immediate manoeuvring readiness, so a sudden close-quarters situation is met with an available engine movement, not a delay while the engine room is called up.

An additional lookout is posted, because a lone watchkeeper managing radar, sound signals and the con at once will miss something. Radar is worked properly rather than glanced at — contacts plotted or their vectors read, ranges and bearings tracked over time so that a developing close- quarters situation is recognised early, in line with the general duty under Rule 19 to take early and substantial action and, so far as possible, to avoid altering course toward a vessel forward of the beam, or toward one abeam or abaft the beam that is being overtaken. Appropriate sound signals are sounded at the required intervals — a single prolonged blast at intervals of not more than two minutes for a power-driven vessel making way is the one every candidate should have cold, with the different signals for not under command, restricted in ability to manoeuvre, at anchor and so on sitting alongside it. Throughout, the master is kept informed, watertight doors are closed as the ship's procedures require, and every action taken is logged.

A traffic separation scheme exists to put opposing traffic into separate lanes so that the main risk becomes overtaking within a lane rather than head-on meetings across it. The governing obligation, under Rule 10, is to use the appropriate lane and proceed in the general direction of traffic flow shown for it, keeping clear of the separation zone or line that divides the lanes except when crossing. Vessels joining or leaving a lane do so, so far as practicable, at its terminations; where a vessel must join or leave from the side, it is done at as small an angle to the general traffic flow as practicable, so the vessel merges rather than cuts across.

Crossing a lane is the one manoeuvre within a scheme that is meant to be quick rather than gradual: it is to be done on a heading as near to 90° to the general direction of traffic flow as practicable. The reasoning is exposure time — a vessel crossing obliquely spends longer inside the lane, for longer in the path of traffic she has no priority over, than one that crosses at right angles (quantified numerically in the worked example that follows). A current setting across the intended track complicates this: the heading that looks like 90° on the compass is not necessarily the heading that makes good a 90° track over the ground, and it is the track that Rule 10 is concerned with.

• Inshore traffic zone — reserved mainly for vessels under 20 m, sailing vessels and fishing vessels; other vessels use it only to avoid immediate danger.
• Vessels of restricted manoeuvrability — engaged in an operation for the maintenance of safety within a scheme are exempted from complying with the scheme so far as needed for that operation.
• Avoiding the scheme — a vessel not using a scheme should avoid it, or the line/zone bordering it, by as wide a margin as is practicable.

Three fully stepped problems: costing a latitude cap on a composite great circle track, the stability effect of ice accretion, and the course correction needed to cross a TSS at a true 90° track under set.

Worked example 1

Composite great circle sailing — costing the latitude cap

A passage's unrestricted great-circle vertex would reach 66°S, well inside the ice-season limit the company has set at 60°S. The plan is capped: great circle out to 60°S, a run along that parallel, then great circle back down to the destination. The two points where the track meets the 60°S limiting parallel are 40° 00′ of longitude apart. For the same change of longitude, the unrestricted great-circle track (plotted on the gnomonic chart) measures 1000 nm. At the vessel's service speed of 10 kn, how much extra distance and time does capping the track at 60°S cost?

Given

Limiting latitude = 60°S, cos 60° = 0.5000 DLo between the two points on the limiting parallel = 40° 00′ = 2400′ Unrestricted great-circle distance for the same DLo (from the gnomonic chart) = 1000 nm Service speed = 10 kn

1. Along the limiting parallel the ship is no longer on a great circle.

   Dep=DLo(′) × cos(Lat) =2400 × 0.5000 =1200 nm

   She is parallel sailing, so the distance made good is the departure for that change of longitude at that latitude.

2. That parallel-sailing distance replaces what would otherwise have been the corresponding stretch of the unrestricted great circle, so the two are compared directly to find the cost of the cap.

   Extra distance=1200 − 1000 =200 nm

3. Convert the extra distance to steaming time.

   t=distance / speed =200 / 10 =20 h

   The cost is expressed in something the master can weigh against the ice and swell risk further south.

AnswerCapping the track at 60°S costs about 200 nm and roughly 20 hours over the unrestricted great circle — accepted, given what lies south of the limit.

The trap: quoting the great-circle distance for the whole passage without first checking whether its vertex breaches the latitude the ship is permitted, or willing, to reach.

Worked example 2

Ice accretion — the hidden stability cost

A vessel bound through an area forecast for icing has a departure displacement of 7900 t, KG 6.00 m and KM 7.20 m. Over several hours, 100 t of ice accretes high on the mast, rigging and upperworks, estimated to act at a height of 22.00 m above the keel. Find the GM before and after the icing, and state whether the vessel still meets the 0.30 m minimum GM her stability book requires for this condition.

Given

Displacement before icing, W₁ = 7900 t, KG₁ = 6.00 m KM = 7.20 m (treated as constant over this small draught change) Ice accretion, w = 100 t at Kg = 22.00 m Minimum GM required by the stability book for this condition = 0.30 m

Required

Find the GM before and after the icing, and state whether the vessel still meets the 0.30 m minimum GM her stability book requires for this condition

1. Before doing anything with the ice, fix the starting point.

   GM(before)=KM − KG₁ =7.20 − 6.00 =1.20 m

2. Ice is added weight at a height well above the current KG.

   Rise in KG=w × (Kg_ice − KG₁) / (W₁ + w) =100 × (22.00 − 6.00) / 8000 =100 × 16.00 / 8000 =0.20 m

   So it raises KG. The rise is found from the moment the ice adds, spread over the new total displacement — the same shortcut used for any weight added high up.

3. Apply the rise to get the new KG.

   KG(after)=6.00 + 0.20 = 6.20 m GM(after)=KM − KG(after) =7.20 − 6.20 =1.00 m

   Then the new GM, and check it against the stability book's minimum for the condition.

AnswerGM falls from 1.20 m to 1.00 m — a drop of exactly the KG rise, 0.20 m. Still above the 0.30 m minimum, but the margin has shrunk by a sixth from one spell of icing, and it will keep shrinking if accretion continues.

The trap: reading GM off the departure stability condition and treating it as still valid — ice accretion keeps raising KG for as long as it keeps forming, so GM has to be recalculated for the accreted condition, not assumed from before.

Worked example 3

Crossing a TSS at 90° in reduced visibility — allowing for the set

Visibility has closed in and a vessel must cross a traffic separation scheme. The lane is 4.0 nm wide, measured across the direction of traffic flow. Speed has already been reduced to 5.0 kn for the restricted visibility. A current of 3.0 kn sets along the lane — that is, directly across the vessel's intended crossing track, which is to be as near 90° to the flow as practicable. Find the course correction needed to hold that 90° track, the speed made good across the lane, and how long the vessel will be inside it.

Given

Lane width (crossing distance) = 4.0 nm Desired track = 90° to the traffic flow Current sets along the lane (i.e. at 90° to the desired track) at 3.0 kn Speed through the water, reduced for restricted visibility = 5.0 kn

Required

Find the course correction needed to hold that 90° track, the speed made good across the lane, and how long the vessel will be inside it

1. The current runs parallel to the lane.

   SMG=√(V² − drift²) =√(5.0² − 3.0²) =√(25 − 9) =√16 =4.0 kn

   So relative to the desired track it acts entirely sideways. The velocity triangle is therefore right-angled: own speed is the hypotenuse, the current is one leg, and the speed actually made good along the track is the other.

2. To hold the track at exactly 90° against a current pushing along the lane.

   sin θ=drift / V =3.0 / 5.0 =0.600 θ≈37°

   The heading must be angled up into the current by an angle found from the same triangle.

3. Time inside the lane depends on the speed made good across it.

   t=width / SMG =4.0 / 4.0 =1.0 h

   Not on the speed through the water — the heading correction has already been spent holding the current off.

AnswerSteer about 37° up-current of the 90° track; speed made good across the lane ≈ 4.0 kn; about one hour inside the lane.

The trap: steering the 90° heading itself and letting the current carry the ship diagonally through the lane — the compass shows the right number, but the track made good is oblique, exactly what crossing as near 90° as practicable is meant to prevent.