Crossing Traffic in a Channel with a Beam Current
You are the officer of the deck of a power-driven ship making 8.0 kt through the water on heading 000° in a buoyed channel. The tidal current sets 090° at 2.0 kt. Radar gives a power-driven contact, 'C,' bearing 045° true at 3.0 nm, making good 10 kt on course 270° over the ground. C is not constrained by her draft and there is deep water outside the buoy line on her side. Shoal water limits you to the starboard edge of the channel; a turn to port would put you aground. Visibility is good, sea state moderate, no other traffic. Your radars are working and the contact is in sight.
1. Compute your course and speed made good. Determine C's relative bearing from your heading, and state which vessel must keep out of the way and why.
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Ground vector of own ship:
- Heading 000 at 8.0 kt through the water → north component 8.0
- Current 090 at 2.0 kt → east component 2.0
- Course made good = arctan(2.0 ÷ 8.0) = 014° true
- Speed made good = √(8.0² + 2.0²) = √68 = 8.25 kt
Relative bearing of C:
- From heading 000: 045 − 000 = 45° on the starboard bow
- From course made good 014: 045 − 014 = 31° on the starboard bow
- Both give the same answer qualitatively, which is the point: small current-induced differences do not change the rule.
Responsibility: C is on your starboard side on a crossing course with risk of collision, so under the crossing rule you are the give-way vessel. Rule 9(b) - a vessel that can safely navigate outside the channel must not impede you - may also apply to C, but it is a duty placed on C; it does not relieve you of your own obligation to take action. Assume C does not see you or will not act.
2. Compute the closest point of approach and the time to it. Is there a risk of collision? Show the geometry rather than asserting an answer.
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Positions (nm, east/north): C is at 3.0 nm on 045° → (2.12, 2.12). Own ship at (0, 0).
Ground velocities: own ship (2.0, 8.0); C on 270° at 10 kt → (−10, 0).
Relative velocity of C with respect to own ship: (−10 − 2.0, 0 − 8.0) = (−12, −8); |v|² = 144 + 64 = 208
Time to CPA: t = −(r · v) ÷ |v|² = −[(2.12)(−12) + (2.12)(−8)] ÷ 208 = 42.4 ÷ 208 = 0.204 hr ≈ 12.2 minutes
CPA position: r + v·t = (2.12 − 2.45, 2.12 − 1.63) = (−0.33, 0.49) → range = 0.59 nm
Interpretation: the bearing is not perfectly steady - it is slowly drawing aft - but the range is closing fast and the predicted CPA of about 0.6 nm in a narrow channel is far inside what a prudent watchstander accepts for a crossing vessel. Rule 7 settles it: when in doubt, risk of collision is deemed to exist. Treat this as a risk-of-collision case and act early rather than waiting to see whether the plot tightens.
Useful cross-check: C needs 2.12 nm ÷ 10 kt = 12.7 min to cross your track; you need 2.12 nm ÷ 8 kt = 15.9 min to reach hers. C crosses ahead of you by about 3 minutes. That single number drives the maneuver.
3. State the action you take in the next minute, justify it against the two constraints (shoal water to port; C crossing ahead), and explain what you must recompute after the maneuver.
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Action:
- Take the way off - reduce speed substantially, and be ready to stop. Because C crosses ahead of you by only ~3 minutes, slowing immediately opens the CPA faster than any helm change and cannot put you aground.
- Simultaneously make a bold alteration to starboard toward the starboard edge of the channel - the only side the water allows. A large, unmistakable change (not 5–10°) is required so C can read your intentions; small increments are prohibited by the rules and dangerous in practice.
- Signal one short blast if altering to starboard, and use the bridge-to-bridge radio to agree on intentions if there is any doubt.
Why the alternatives are wrong:
- Turn to port: puts you across C's bow, increases the crossing rate, and grounds you.
- Hold course and speed: you are the give-way vessel; standing on transfers the entire burden to C and to luck.
- Small starboard nudge: too little to be seen and too little to change the CPA.
Recompute after the turn: the current sets 090 at 2 kt, so your heading must lead your intended ground track by roughly 14°. After any course change, re-derive course and speed made good - a heading of 045° does not produce a track of 045° here, and a watchstander who steers headings while thinking tracks will drift toward the shoal. Re-plot C's CPA within a minute of the maneuver and confirm the range is opening.