In this lesson you will learn
- Explain why you plot a position regularly, even with GPS on board
- Plot a DR from a fix, using the course steered converted to true and the distance run from the log
- Turn a DR into an EP by adding the tidal stream’s set and drift for the same time
- Draw the vector triangle with the standard symbols and arrows, and find the COG and SOG
- Check an EP against depth, landmarks and GPS, and keep an hourly plotting routine
Where am I between fixes?
In the last few lessons you fixed your position from bearings and transits. A fix is the best answer to “where am I?” — but it is only true for the moment you took it. Half an hour later the boat is somewhere else, and you cannot always get another fix: the coast may be out of sight, it may be dark or foggy, or there may be nothing suitable to take a bearing of.
So between fixes, navigators work out their position from what they know: the course they have steered, the distance the log says they have run, the time, and the tidal stream. There are two levels of answer.
DR = last fix + course steered + distance run. EP = DR + the tidal stream for the same time.
Why bother, when the GPS shows your position all the time?
- Electronics fail. If the power or the GPS goes, a recent position on the paper chart — and the course and log readings since — is what you navigate from. Without it you are guessing.
- An EP is an independent check. If your EP and the GPS agree, you can trust both. If they don’t, something is wrong: a mistyped waypoint, a GPS fault, a compass error or a stream you did not expect.
- It shows where the water is taking you. The EP tells you not just where the bow points but where you are really going, and so which dangers lie ahead.
Dead reckoning: course steered and distance run
Dead reckoning (DR) starts from your last fix and carries it forward using two things you have measured on board:
- The course steered. The average heading the helm has held on the steering compass since the fix. The chart is drawn in true, so convert it: apply the deviation from the deviation card (Lesson 10) to get magnetic, then the variation (Lesson 9) to get true. On the practice chart, variation in 2027 is 2°44'W, which you round to 3°W for chart work.
- The distance run. The log measures distance through the water (Lesson 7). Note its reading at the fix and again now: the difference is the distance run. If you only have a speed, use 60D = ST.
- Lay it off. From the fix, draw a line in the direction of the true course steered and step off the distance run along it with the dividers. This line is the water track, marked with one arrow. Its end is your DR position: a small cross, labelled with the time.
Worked example
The 1100 DR
- 1At 1000 a fix puts you 0.9 M from the Kerran Approach buoy, bearing 257°T from it (49°42.0'N 004°12.8'W). The log reads 1246.3.
- 2You steer 315°C for an hour. The deviation card gives 4°W for that heading: 315 − 4 = 311°M.
- 3Variation 2°44'W, rounded to 3°W: 311 − 3 = 308°T. Both errors are west, so both come off on the way to true.
- 4At 1100 the log reads 1251.3: distance run = 1251.3 − 1246.3 = 5.0 M.
- 5From the 1000 fix, lay off 308°T and step off 5.0 M with the dividers. Mark a cross and write 1100 beside it.
1100 DR: 49°45.1'N 004°18.9'W
Estimated position: adding the tidal stream
A tidal stream is the horizontal movement of the water as the tide rises and falls. The whole body of water moves over the seabed and carries the boat with it, whatever she is doing through the water. A stream is described by:
- Set — the direction the water flows towards, in °T. (A wind is the other way round: it is named by where it blows from.)
- Rate — its speed, in knots.
- Drift — the distance it carries you in a given time.
drift = rate × time
Or use 60D = ST with the time in minutes: 1.5 kn for 40 min gives 1.5 × 40 ÷ 60 = 1.0 M.
From the DR, draw the tidal stream for the same period: a line in the direction of the set, as long as the drift, marked with three arrows. Its end is your estimated position (EP): a triangle with a dot, labelled with the time.
Worked example
The 1100 EP
- 1The tidal stream for 1000–1100 sets 240°T at 1.2 kn.
- 2Drift = 1.2 kn × 1 h = 1.2 M.
- 3From the 1100 DR, lay off 240°T and step off 1.2 M. Draw a triangle and write 1100 beside it.
1100 EP: 49°44.5'N 004°20.5'W — 1.2 M from the DR
The vector triangle: course and speed over the ground
Join the fix to the EP and you have a triangle of three lines, each with its own arrows:
| Line | Arrows | Direction | Length |
|---|---|---|---|
| Water track | One | Course steered (°T) | Distance run, from the log |
| Tidal stream | Three | Set | Drift = rate × time |
| Ground track | Two | Course over the ground | Distance over the ground |
The ground track is how the yacht has really moved over the seabed. Its direction is the course over the ground (COG); measure its length and divide by the time to get the speed over the ground (SOG). In the example the ground track measures 5.6 M on 296°T in one hour, so the SOG is 5.6 kn — although the log showed 5.0 kn through the water. These are the COG and SOG your GPS displays; the compass and log give your heading and speed through the water.
InteractiveEP builder
Plot it yourself with the chart’s dividers. Work out the distance run and the drift, lay off the water track from the fix, then the tidal stream from your DR. Each step is checked (within 0.2 M), and at the end you can read off the COG and SOG. Try the two examples, then as many new problems as you like.
- 1000 fix:
- ⊙ on the chart, 49°42.0'N 004°12.8'W
- Course steered:
- 315°C → 308°T (deviation 4°W, variation 3°W)
- Log:
- 1000 1246.3 · 1100 1251.3
- Tidal stream 1000–1100:
- sets 240°T, rate 1.2 kn
Step 1 of 2: plot the 1100 DR
A sits on the fix. Work out the distance run from the log, then move B until the readout shows the course in °T and that distance.
The order makes no difference to where the EP ends up — stream first and water track second gives the same point — but the usual habit is the water track first, so that the DR is on the chart as well.
Why the tide matters
A stream of a knot or two may not sound much, but it never stops. Steer 090°T at 5 kn for two hours across a 2 kn stream and you end up 4 M from your DR — enough to put you on the wrong side of a headland or a shoal.
- Fair stream (flowing the way you are going): your SOG is higher than your speed through the water.
- Foul stream (flowing against you): your SOG is lower, and the passage takes longer.
- Cross stream: you are carried sideways, so your COG differs from the course steered.
InteractiveTide matters
The yacht steers 090°T at 5 kn. Change the stream’s set and rate, and the time since the fix, and watch the EP move away from the DR. Try the four example streams first.
Steering 090°T at 5 kn
Water track 5 M
Tidal drift 2 M
COG 112°T · SOG 5.4 kn
If you trusted the DR you would be 2 M out — that is 20 cables.
Times other than an hour
Every part of the triangle must cover the same interval: the log distance, the stream and the clock. If you have run for 40 minutes, the stream line is 40 minutes’ worth of drift.
Worked example
1420 to 1500
- 1At 1420, leaving the harbour approach, a fix puts you 0.6 M from No 1 buoy, bearing 175°T from it. Log 3871.6. You steer 135°C until 1500, when the log reads 3875.0. The stream sets 030°T at 1.5 kn.
- 2Deviation 5°E: 135 + 5 = 140°M. Variation 3°W: 140 − 3 = 137°T. (East deviation is added: Compass ADd East → True.)
- 3Distance run = 3875.0 − 3871.6 = 3.4 M. Lay it off on 137°T: the 1500 DR.
- 4Drift = 1.5 × 40 ÷ 60 = 1.0 M. Lay it off from the DR towards 030°T: the 1500 EP.
- 5The ground track measures 3.3 M on 120°T. SOG = 60 × 3.3 ÷ 40 = 4.95, about 5.0 kn.
1500 EP 49°41.6'N 004°06.6'W; COG 120°T, SOG about 5.0 kn
Checking the EP
An EP is only as good as what went into it: a course the helm did not quite hold, a log that reads a little low, a stream stronger than predicted. Check it at every opportunity:
- Depth. Compare the depth sounder with the charted depth at your EP. The height of tide normally adds water over chart datum (Module 4 shows how much), so the sounder will usually read a little more than the chart — but if the chart shows 30 m and the sounder 8 m, you are not where you think you are. Contours and shoals, such as Brennan Bank, make the best checks.
- Landmarks. A quick hand-bearing of a landmark, converted to true, should be close to the bearing you measure from your EP to it on the chart. Better still, take a fix.
- GPS. If the EP and the GPS agree to within a few cables, you can trust both. If they don’t, find out why: a wrong course in the log, the wrong stream, an error in the deviation, or a GPS problem.
When you get a fix, the plot starts again from it: never carry an old EP forward once you have something better. And the longer it has been since your last fix, the less you should trust your EP, because small errors in course, distance and stream all grow with time.
A fix beats an EP, and an EP beats a DR. Always work from the best position you have.
An hourly routine
- On the hour, and whenever you alter course, note the time, the log reading and the course steered. The next lesson turns this into a proper logbook.
- Plot the EP from your last fix or EP, using that hour’s tidal stream.
- Check it against the GPS, the depth and anything you can see — and take a fix when you can.
- Look ahead: lay off the next hour’s likely track and check it for dangers.
If you alter course in the middle of an hour, work out the EP for the time of the alteration first, then start the new course from that EP.
Key terms
- Fix
- A position found from observations, such as bearings: ⊙ on the chart, labelled with the time.
- Dead reckoning (DR)
- Position from the last fix, course steered and distance run, ignoring the tidal stream: a small cross.
- Estimated position (EP)
- The DR plus the effect of the tidal stream for the same time: a triangle with a dot.
- Course steered
- The average compass heading held since the fix; converted to °T before it is laid off.
- Distance run
- Distance through the water: the difference between two log readings.
- Water track
- The line of the course steered and distance run: one arrow.
- Tidal stream
- The horizontal movement of the water: three arrows on the plot.
- Set
- The direction a tidal stream flows towards, in °T.
- Rate and drift
- The stream’s speed in knots, and the distance it carries you: drift = rate × time.
- Ground track
- From the fix to the EP: how the boat really moved over the seabed. Two arrows.
- COG
- Course over the ground: the direction of the ground track.
- SOG
- Speed over the ground: the ground track’s length divided by the time.
Exercises
Check your understanding. You get a second try at each question, then the worked answer. Score 70% or more to complete the lesson — your progress is saved in this browser.
Plotting sheet: A starts on the 0815 fix. Move B until the readout shows the direction and distance you need, then pencil in a mark. The dividers then start from your mark for the next vector.
Plotting sheet: A starts on the 0730 fix. Move B until the readout shows the direction and distance you need, then pencil in a mark. The dividers then start from your mark for the next vector.
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DR and EP drill
Five fresh questions each time: a log or drift sum, a compass-to-true conversion, a DR or EP to plot from a random fix, a COG or SOG and a quick check on the conventions.