GPS, Doppler Log and the Autopilot
On a 90 m coaster in a tidal estuary, the GPS receiver displays speed over ground 12.4 knots and course over ground 102°T. The Doppler speed log, set to give speed through water, displays 10.1 knots. The gyro heading is 090°T and the autopilot is steering in heading mode. The master is preparing a blind pilotage plan for a narrow channel and asks whether to use the log speed or GPS speed for the next leg. The echo sounder shows 22.5 m below the keel; the vessel’s draught is 6.2 m and the charted depth in the channel is 15.0 m at chart datum. There is a strong cross-current and the tidal stream is expected to set roughly southeast. You must decide what the instrument readings imply, calculate the set and drift, and advise which speed source to use for the pilotage plan and why.
1. Calculate the set and drift from the GPS and Doppler log readings. Show the vector reasoning.
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The readings are not inconsistent: GPS gives motion over the ground, while the Doppler log gives motion through the water. The difference is the current. Resolve the vectors using ground = water + current, so current = ground − water.
- Ground: 12.4 kn at 102°T → east 12.4 sin 102° = 12.13 kn; north 12.4 cos 102° = −2.58 kn.
- Water: 10.1 kn at 090°T → east 10.1 kn; north 0.
- Current: east 2.03 kn; north −2.58 kn. Speed = √(2.03² + 2.58²) ≈ 3.3 kn. Direction = atan2(2.03, −2.58) gives a bearing of about 142°T. So the set is about 142°T and the drift about 3.3 kn-southeast, as expected.
2. Which speed source should be used for the blind pilotage plan and which for other purposes? Explain the autopilot’s behaviour.
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For the blind pilotage plan, use GPS SOG/COG for the ground track, because the plan is drawn over the ground and the cross-current is already included. Use the Doppler log for speed through water, engine performance, and as a check that the current is as predicted. Do not feed a through-water speed into a ground-referenced ECDIS/autopilot track mode and expect it to follow the charted ground track; conversely, do not use GPS SOG alone to judge true wind or propulsive efficiency. The autopilot is in heading mode, so it holds 090°T heading while the vessel crabs along 102°T COG. Cross-check both against a visual transit or radar, and keep the log running to detect changes in current.
3. The echo sounder reads 22.5 m below the keel. What tide height is implied, and does this change your advice?
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Depth below keel 22.5 m plus draught 6.2 m gives 28.7 m of water. If the charted depth is 15.0 m at chart datum, implied tide height = 28.7 − 15.0 = 13.7 m. That is a very large tide and should first prompt a check of the echo sounder’s draught/keel offset, chart datum, and whether the 15.0 m is a least depth or a spot sounding; if the offsets are correct, the arithmetic stands. It does not change the speed-source advice: use GPS for ground track and log for through-water/current check, and use the echo sounder for under-keel clearance with the same offset verification.