Cross-track control with a strong beam stream, and a not-under-command contact on the bow
M/V Anselm Bay, a 152 m geared bulk carrier of 17,500 dwt, is on passage north through a coastal traffic area. At 0300 the OOW plots a fix 36 nm south of waypoint NORTH ROCK; the ship is steering 000°T at 12.0 kn through the water on a planned track that runs due north. The tidal stream is forecast to set 090°T at 3.0 kn and to hold steady for the next four hours, and the previous three fixes have confirmed it. A charted shoal with 6.5 m least depth lies 2.5 nm east of the planned track; the ship is at 6.8 m draught and the master has told the OOW that no easterly cross-track error is acceptable. At 0305 the ARPA acquires a contact bearing 040°T at 8.0 nm, showing two all-round red lights in a vertical line, making good 300°T at 13.0 kn. Visibility is good, sea slight, wind NE force 3, and the rest of the traffic picture is clear.
1. Calculate the course to steer and the speed made good, and give the ETA at NORTH ROCK. Show the vector reasoning.
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Vector triangle over one hour
Through-water speed 12.0 kn along the course steered; stream 3.0 kn setting 090°T; required track 000°T.
Let θ be the angle by which the heading must be offset to port of the track. For the resultant to lie along 000°T, the easterly component of the ship's own velocity must exactly cancel the stream:
- 12.0 × sin θ = 3.0 → sin θ = 0.250 → θ = 14.5°
- Course to steer = 000° − 14.5° = 345.5°T (apply compass error to get the course to steer by standard compass)
- Speed made good = 12.0 × cos 14.5° = 11.62 kn (the stream has no component along 000°T)
- Time for 36 nm = 36 ÷ 11.62 = 3.10 h = 3 h 06 min, ETA 0606
Sanity check: in 3.1 h the ship's own velocity alone would carry her about 9.3 nm west of the ground track (37.2 × sin 14.5°), while the stream carries her about 9.3 nm east; the residuals cancel.
Judgement points the examiner is looking for: never aim the heading at the waypoint; always steer on the track, not on the mark. The error budget is one-sided because the shoal is east, so a stream stronger than forecast must be detected early by fixing at 0400 and 0500 and re-working the triangle. If the stream is found to be setting harder, increase the offset to port rather than accepting easterly cross-track error, and be ready to reduce speed or ask the master.
2. The contact showing two all-round red lights is now 8 nm away on the starboard bow. State what it is, who must keep out of the way, and set out your manoeuvring options given the shoal.
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Identification: two all-round red lights in a vertical line at night means a vessel not under command (Rule 27); by day she would show two balls. She is the stand-on vessel for the purposes of Rule 17, but Rule 18(a) requires a power-driven vessel underway to keep out of her way, because a NUC cannot manoeuvre as required by the Rules.
Geometry: relative bearing about 40° on the starboard bow, target course 300°T at 13 kn, own course 000°T at 12 kn. Relative velocity is roughly west-south-west at about 12.5 kn, so TCPA is about 38 minutes and the target will cross ahead from starboard to port. This is a crossing situation with own ship as give-way vessel.
Options and the constraint: Rule 16 requires early and substantial action, and Rule 8 requires the alteration to be large enough to be obvious on the radar. Turning to port would take the ship across the target's bow and is wrong. Turning to starboard is correct in principle, but 2.5 nm east lies a 6.5 m shoal against a 6.8 m draught. At 12 kn a 40° starboard alteration held for 20 minutes produces about 1.5 nm of easting, so the alteration must be timed and monitored, not left open-ended.
Practical plan: make a bold starboard alteration of at least 30–40° now, while 8 nm of range remains, and combine it with a reduction in speed so the target passes ahead quickly; monitor the cross-track error to the shoal continuously and plan to take all way off rather than hold the turn. Confirm the target's aspect and lights have not changed, keep the VHF silent for collision avoidance, and call the master.
3. At 0400 the fix puts the ship 0.8 nm east of track. Determine the actual stream and the new course to steer.
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What the fix tells you
Over one hour the ship was set 0.8 nm east of track while steering 345.5°T. Her own velocity had an intended westerly component of 12 × sin 14.5° = 3.0 kn. A residual 0.8 kn of easterly drift means the stream is actually setting east at:
3.0 + 0.8 = 3.8 kn, setting 090°T
New course
- 12.0 × sin θ = 3.8 → sin θ = 0.3167 → θ = 18.5°
- Course to steer = 000° − 18.5° = 341.5°T
- Speed made good = 12.0 × cos 18.5° = 11.38 kn
Remaining distance is about 36 − 11.6 = 24.4 nm, giving about 2.14 h, ETA approximately 0610.
Assessment: the ship has already used 0.8 nm of a 2.5 nm margin, but the new heading holds her on track and gives roughly 1.7 nm of clearance to the 6.5 m contour. That is acceptable in good visibility with a fix every hour; it is not acceptable if the stream is still strengthening. The correct response is to apply the new heading, shorten the fixing interval to 30 minutes while abeam of the shoal, inform the master, and be prepared to slow down or turn away if a further easterly set appears. Do not correct by aiming at the waypoint.