A boat moving through water that is itself moving has three motions worth naming. The water track is the boat's course and distance through the water: the heading you steered and the distance on the log. The tidal vector is the set (direction) and drift (distance) of the stream over the same period. The ground track is what results — where you actually went over the seabed. The three form a vector triangle, and the two classic chartwork problems are the same triangle solved for different unknowns.

Plotting conventions used on RYA-style chartwork
LineSymbolMeaning
Water trackOne arrowheadCourse steered, distance through the water
Tidal streamThree arrowheadsSet and drift for the period
Ground trackTwo arrowheadsCourse and distance made good over the ground
FixDot in a circle, with timeObserved position
DR positionShort cross-line on the track, with timeWater track only, no tide
Estimated positionDot in a triangle, with timeWater track plus tide (and leeway)

Estimated position: where am I?

You know what you did — the course you steered and the distance you logged — and you know what the tide did. Draw the water track from your last fix; apply leeway to it if the wind was pushing you sideways; then draw the tidal vector from its end. Where the tide vector ends is the estimated position. The line from the fix to the EP is the ground track, and its length divided by the time is your speed over the ground.

An estimated position plot. From the starting fix, the water track is drawn along the course steered for the distance sailed through the water in one hour, marked with a single arrowhead. From its end, the tidal stream vector for the same hour is drawn in the direction the stream sets, marked with three arrowheads. The end of the tide vector is the estimated position, drawn as a dot inside a triangle. The line from start to estimated position is the ground track, marked with two arrowheads.fix at 10:00water track: course steered, distance through water (1 h) ▷tidal stream, 1 h ▷▷▷ground track ▷▷ (start → EP)EP at 11:00Water track first, tide second, EP at the end. Leeway, if any, is applied to the water track before the tide is added.
What to notice: Water track first (one arrow), tide second (three arrows), EP at the end. The dashed line from fix to EP is the ground track (two arrows). The EP is marked with a dot in a triangle and the time.

Estimated-position triangle: water track from a fix, tidal vector added at the end, EP marked in a triangle.

Worked example

Fix at 10:00. You steer 090°T for an hour at 5 knots through the water, so the water track is 090° for 5 miles. The tidal diamond gives a set of 180° at 1.5 knots for that hour. From the end of the water track, draw 180° for 1.5 miles. The end of that line is the 11:00 EP: roughly 5.2 miles from the fix in a direction of about 107°. Your ground track was 107° and your speed over the ground about 5.2 knots — you were pushed south of where you were pointing.

Leeway

Leeway is the sideways drift caused by the wind pushing on the hull and rig; a sailing yacht hard on the wind might make 5° to 10°, much less when reaching. It is applied to the water track, downwind of the course steered, before the tide is added — because leeway is a property of the boat's movement through the water, while tide moves the water itself. In a course-to-steer problem it is applied the opposite way: once you have the course to steer through the water, you point upwind of it by the leeway angle.

Course to steer: where should I point?

Now you know where you want to go and what the tide will do, and you want the heading. Draw the ground track from your start point through the destination, extended past it. From the start point draw the tidal vector for the period you are planning — usually one hour — in the direction of the set. From the end of the tide vector, open the dividers to the distance your boat will travel through the water in that same period (its speed in knots, for one hour) and swing an arc to cut the ground track. The line from the end of the tide vector to that cut is the water track: measure its direction and that is your course to steer through the water. Apply leeway upwind, then convert true to compass.

A course-to-steer plot. The ground track is drawn from the start straight to the destination. From the start, the tidal stream vector for one hour is drawn in the direction the stream sets. From the end of the tide vector, an arc with radius equal to the boat's speed through the water for one hour is swung to cut the ground track. The line from the end of the tide vector to that intersection is the course to steer. The boat follows the ground track over the ground while pointing along the course to steer.startdestinationground track ▷▷ (where you want to go)tidal stream, 1 h ▷▷▷ (from the start)course to steer ▷ (boat speed × 1 h)arc: distance through water in 1 hTide from the start (opposite to the EP triangle). The arc cut is your position only if the plot period equals the time sailed.
What to notice: Ground track first (two arrows), then the tide from the start (three arrows), then the boat-speed arc from the end of the tide to the ground track. The line from the tide's end to the arc's cut is the course to steer (one arrow). Where the arc cuts the track is not your position after an hour unless the plot was exactly one hour long.

Course-to-steer triangle: ground track to destination, tidal vector from the start, and the boat-speed arc cutting the ground track to give the heading.

Worked example

You want to make good 000°T to a buoy 4 miles north. The stream for the next hour sets 090° at 2 knots and your boat makes 5 knots through the water. Draw the ground track north from the start. From the start, draw 090° for 2 miles (the tide). From the end of that line, swing a 5-mile arc to cut the ground track; it cuts it about 4.6 miles north of the start. The line from the tide's end to the cut points about 336°T: steer 336° and you will track north, making good about 4.6 knots. Note that the buoy at 4 miles is reached in a little under an hour — the arc cut is not the buoy.

Try it: course to steer with and without a stream

Course to steer plot: steer 336 degrees to make good north against a stream of 2 knots setting east.ground track 000° ▷▷stream 2 kn ▷▷▷course to steer 336° (5 kn) ▷One-hour plot. The boat points along the red line and travels along the green one.
Tidal streamTidal stream
Boat speed 5 kn, ground track wanted 000°. Stream 2.0 kn towards 090°: steer 336° (into the stream) to track north, making good 4.6 kn over the ground.
What to notice: Toggle the stream on and off, then push the rate up. The heading changes and the speed made good drops — and when the stream matches your boat speed, no heading works at all, which is what a foul tidal gate means.

Interactive: switch a tidal stream on and off and vary its rate to see the computed course to steer and speed made good change; at stream equal to boat speed there is no solution.

Passages longer than an hour

For a passage of two or three hours across a changing stream, add the hourly tidal vectors end to end from the start point (hour one's set and drift, then hour two's from its end, and so on), then swing the arc with the boat's distance through the water for the whole period from the end of the combined tide vector. This gives a single course to steer that averages the tide; it is accurate at the destination and approximate in between, which is fine for open water and not fine for passing close to a danger midway.

The common mistake

Drawing the tide on the wrong end. In an EP, the tide is added to the end of the water track; in a course to steer, it is drawn from the start. A second error is measuring the course to steer from the start point rather than from the end of the tide vector, which gives you the ground track direction back again. Say aloud what each line is as you draw it, and count the arrowheads.

Check yourselfYou have just finished a course-to-steer plot for one hour: ground track 045°, tide 135° at 1 knot, boat speed 4 knots. Your arc cut the ground track 3.7 miles from the start. Will you be at that point in one hour?Show answer

Yes — because the plot was for exactly one hour: one hour of tide and one hour of boat speed. In one hour you travel 4 miles through the water along the course to steer and the tide carries you 1 mile; the vector sum puts you at the arc cut, 3.7 miles along the ground track, so your speed made good is 3.7 knots. If the plot had used a different period, or you sail for a different time, the arc cut is not your position — it only defines the heading.

Key takeaways

  • Three vectors: water track (one arrow), tide (three arrows), ground track (two arrows).
  • Estimated position: water track first, leeway applied, tide added at the end. The EP is the end of the tide vector.
  • Course to steer: ground track first, tide from the start, boat-speed arc from the tide's end to the ground track. The line from the tide's end to the cut is the heading.
  • Leeway goes on the water track: downwind in an EP, upwind of the course to steer when helming.
  • The arc cut in a course-to-steer plot is your position only if the plot period equals the time you sail.