Emergency Position Fixing After GPS Failure
You are sailing a 12 m yacht 10 nm off the Wild Coast, South Africa, in clear weather but with a moderate swell. Your GPS fails suddenly. You have a paper chart, a hand-bearing compass, a depth sounder, and a sextant. You have been steering 240° true at 6 knots for the last 4 hours since your last known position, which was 5 nm east of a prominent headland. The chart shows a lighthouse on the headland with a characteristic of Fl(3) 10s, and a prominent peak inland. The depth sounder reads 45 m. The chart indicates the area has a sandy bottom with depth contours at 50 m and 100 m. You also have a trailing log that reads 24 nm since the last fix. The current is estimated to be setting NE at 1 knot. Your watchkeeper reports a bearing of the lighthouse at 300° true, and the peak at 330° true. The magnetic variation is 25° W, and deviation is 3° E.
1. Describe how you would obtain a position fix using the available aids, and what steps you would take to verify it.
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You can obtain a fix by taking bearings of the lighthouse and the peak using the hand-bearing compass. Convert these to true bearings by applying variation and deviation: True = Compass + Deviation + Variation (with signs: E is +, W is -). Here, variation is 25° W = -25°, deviation is 3° E = +3°, so total error = -22°. Thus, True = Compass - 22°. But the reported bearings are given as true? The problem states 'bearing of the lighthouse at 300° true' and 'peak at 330° true', so they are already true. So plot these from the charted positions of the lighthouse and peak. The intersection is your fix. Also, use the depth sounder: 45 m depth can be compared with the chart to confirm you are in the correct depth area. The trailing log reading of 24 nm can be used for dead reckoning (DR) from the last known position, but with current set NE at 1 knot for 4 hours, the current effect is 4 nm NE. Your course steered 240° at 6 knots for 4 hours gives 24 nm through the water; with current, your actual movement is the vector sum. The DR position should be close to the fix. Verify by comparing the fix with the DR and depth. Also, you can use the lighthouse characteristic to confirm identity: Fl(3) 10s means three flashes every 10 seconds; check the timing to ensure it's the correct light. If the fix and DR differ significantly, re-evaluate the current or your course/speed.
2. If the fix places you 2 nm north of your DR position, what does this indicate about the current, and how would you adjust your course to reach a waypoint 20 nm due west?
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If the fix is 2 nm north of the DR, it means the actual current has a stronger northward component than estimated, or your course made good was more northerly. Over 4 hours, a 2 nm displacement north implies an average current of 0.5 knots north. Your estimated current was NE at 1 knot, which has a north component of about 0.7 knots (if NE is 45°). So the actual north component is less than estimated, or perhaps the current is more easterly. To adjust, you need to determine the set and drift. You can compute the actual current vector by comparing the DR (which included the estimated current) with the fix. The difference is the error in your current estimate. To reach a waypoint 20 nm due west, you need to compute a course to steer that compensates for the actual current. If the current is setting you north, you need to steer south of west to counteract it. Use a vector triangle: desired course over ground is 270° at your speed. With a current of, say, 0.5 knots north, you need to steer a course that has a southward component to cancel the drift. You can use the one-in-sixty rule: for a 20 nm leg, a 2 nm offset requires a course alteration of about 6° (since 2/20 = 0.1, and 0.1 rad ≈ 6°). So steer about 264° true to make good 270°. Alternatively, compute precisely using a plotting sheet or calculator. Also, update your current estimate for future legs.