Inbound to Aldenham River on a falling tide with a degraded GPS fix
MV Kestrel Trader, a 12,400 dwt general cargo ship, is inbound to the Aldenham river entrance on a falling tide. Draught is 7.5 m even keel. The dredged channel has a charted depth of 6.2 m, the height of tide at the entrance is 2.4 m and it is falling at about 0.3 m per hour. The ship is steering 090°T at 10.0 knots through the water. The GPS has been intermittent since 0600 and the master has ordered positions by terrestrial means. At 0910 a fix places the ship 1.6 NM south-west of Fairlight Buoy; at 0930 a second fix places her 3.0 NM from the first, bearing 105°T. Rain reduces visibility to about 1.5 NM and the buoy is lost from sight between fixes. Wind is SW force 4, the ebb sets across the dredged channel, and there is a north-going eddy close to the training wall. The pilot boards at 1000 and the echo sounder reads 0.9 m below the keel.
1. From the two fixes, determine the set and drift, then the course to steer to make good 090°T and the speed made good.
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Both fixes are ground positions, so the vector between them is the ground track, not the water track.
- Interval 20 min = 0.333 h. Ground run 3.0 NM gives 3.0 ÷ 0.333 = 9.0 kn along 105°T.
- Water run in the same 20 min at 10.0 kn on 090°T = 3.33 NM.
- Resolve east/north: water = 3.33 E, 0 N. Ground = 3.0 sin15° = 0.78 N, 3.0 cos15° = 2.90 E.
- Set/drift vector = ground minus water = (2.90 − 3.33) = −0.43 E, that is 0.43 W, and +0.78 N. Magnitude √(0.43² + 0.78²) = 0.89 NM in 20 min, so 2.67 kn. Direction: atan(0.43/0.78) = 29° west of north, i.e. 119°T.
Set about 119°T, drift 2.7 kn.
The tide carries the ship south-east, so the water track must be aimed north of 090°T. Needed northerly component of the water track = 2.67 cos61° = 1.29 kn, cancelling the southerly drift. Easterly component = √(10² − 1.29²) = 9.92 kn. Course = atan(9.92/1.29) = 083°T. Speed made good = 9.92 + 2.67 sin61° = 9.92 + 2.33 = 12.3 kn.
Steer about 083°T. At 12.3 kn the ship will reach the boarding ground early, so speed must be reduced or the passage slowed; the drift must be re-checked against a fresh fix, because the eddy near the wall makes the set non-uniform across the channel.
2. The buoy is no longer visible. Explain how you would fix and monitor position in the last 30 minutes, and what the limitations of each method are.
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With the buoy lost, build the fix from independent lines of position rather than trusting one:
- Radar range and bearing to a charted corner of the training wall or a radar-conspicuous buoy. Ranges are markedly more accurate than bearings; two ranges, or a range and a bearing, give a fix. Plot at 5-minute intervals in confined water, not 20.
- A running fix, if only one object can be seen: take a bearing, run for a set interval, take a second bearing and transfer the first along the water track. In a 2.7 kn cross-set the transferred line is only as good as the assumed drift, so treat the result as an estimated position with a large error ellipse.
- Soundings as a line of position: echo sounder reading plus height of tide gives a depth contour. Cross it with a bearing. A ±0.5 m sounding error translates into a wide band, so this confirms rather than fixes.
- Parallel indexing the wall on radar gives continuous cross-track guidance without a full fix.
Plot DR and EP each time, allow for the cross-set deliberately, keep speed down to reduce the consequence of error, station a lookout forward and have the anchor ready. Never let a single line of position become the sole basis for a turn.
3. Calculate the under-keel clearance at 0930 and at 1000 and reconcile it with the echo sounder reading of 0.9 m below the keel. What do you do?
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Available depth = charted 6.2 + tide. At 0930 tide is 2.4 m, so 8.6 m. At 1000, with the tide falling 0.3 m/h, it is about 2.25 m, so 8.45 m.
Static UKC at 0930 = 8.6 − 7.5 = 1.1 m. Squat at 10 kn in a restricted channel is of the order of 0.5–0.6 m, so net UKC is about 0.5 m, dropping to roughly 0.35 m by 1000. That is already thin for a soft or uneven bottom.
The echo sounder shows 0.9 m below the keel, about 0.4 m more than the calculation. Do not simply accept the better number. Possible causes: the tide height is higher than predicted (barometric pressure, wind setup); the echo sounder zero is set at the transducer, which is not at the point of maximum draught, and the ship is trimmed; squat is under-estimated; or the charted sounding is a soft-mud depth (CATZOC quality). Investigate, then act on the pessimistic figure: reduce to minimum steerage speed to cut squat and sinkage, keep to the centre of the dredged channel, station a lookout forward, ring standby anchor, and if the margin falls below policy, hold off and wait for the next tide rather than pressing on.