Course to steer — Navigation for Yachts, Lesson 29

In this lesson you will learn

Explain why steering straight at a destination in a cross-stream sets you off your track
Draw the one-hour vector triangle in the standard order and read off the course to steer and the speed over the ground
Use a tidal stream from a tidal diamond to work a course to steer for a real passage
Turn the course to steer into a compass course, and work out the passage time and ETA
Handle passages shorter or a little longer than an hour, and recognise when a stream is too strong and the passage needs re-timing

Why you need a course to steer

In Lesson 14 you worked forwards. You knew the course you had steered, the distance run and the tidal stream, and you found where the boat had got to: the estimated position. Planning a passage asks the opposite question. You know where you want to go — so which way should you steer to get there?

The obvious answer, pointing the boat at the destination, only works in still water. A tidal stream running across your track carries you sideways the whole time. Hold the destination’s bearing as your heading and an hour later you are well off the line, down-tide of it. Keep turning to point at the destination and you follow a curving path that sags down-tide: you sail further, arrive later, and may cross the very dangers you planned to avoid.

The course to steer (CTS) is the direction to steer through the water so that your own movement and the tidal stream, added together, carry you along the line you want over the ground.

The leg in this lesson’s worked example (310°T, two arrows). Steering 310°T for an hour, the stream from diamond A would leave you 0.9 M north-east of the line (grey EP) — the Lesson 14 calculation.

Both problems use the same vector triangle, worked in a different order:

	Estimated position (Lesson 14)	Course to steer (this lesson)
You know	Course steered, distance run, tidal stream	Where you are, where you want to go, the stream, your boat speed
You draw first	The water track, from the fix	The ground track, then the stream from the start
You find	The EP, and the course and speed over the ground	The course to steer and the speed over the ground

The one-hour vector triangle

Work the triangle for one hour. Stream rates and boat speeds are both in knots, so in one hour the stream carries you its rate in miles and the boat moves through the water its speed in miles. Both lines then cover the same hour — which they must. The standard order is:

Ground track. Draw a line from the start to the destination, with two arrows. Measure its direction (°T) and its length. If the passage will take less than an hour, extend the line beyond the destination.
One hour of tidal stream, from the start. Lay off the set from the start of the ground track, as long as one hour’s drift (the rate, in miles), with three arrows. The stream comes from the tidal diamonds or an atlas, exactly as in Lesson 28.
The arc. Open the dividers to one hour of your boat speed through the water — what you expect the log to show. Put one point on the end of the stream and swing an arc to cut the ground track.
The water track = the course to steer. Join the end of the stream to the cut, with one arrow. Measure its direction: that is the course to steer in °T. The distance from the start to the cut is how far you make good over the ground in the hour — your speed over the ground (SOG).

The triangle gives a true direction through the water. Before you hand it to the helm, allow for leeway (Lesson 30), then variation and deviation — see below.

InteractiveTriangle builder

Choose a leg, then take the stream from its diamond for any day and time (BST), or set it yourself. Change the boat speed and step through the construction. Tick “Compare” to see where steering straight at the destination would leave you after an hour. Try a strong stream with a slow boat, too.

Day (June 2027)

Leave at (BST)

HW Port Kerran 1232 BST. 1110 is 1 h 22 min before HW: row “1 hour before HW” (1102–1202). Diamond A, in the approach to Kerran Bay: 070°T; range 4.1 m, rate 0.6 + (1.2 − 0.6) × 0.71 = 1.02, about 1.0 kn.

Boat speed through the water5.0 kn

Compare: steer 310°T, straight at it, for an hour

Step 4: Join the end of the stream to the cut, with one arrow: its direction is the course to steer. Start to cut is your speed over the ground.

Course to steer

300°T

10° to port of the 310°T ground track — up-tide.

SOG 4.4 kn · 5.0 M takes 1 h 08 min · ETA 1218

To the helm (no leeway): 300°T → 303°M → 307°C (variation 3°W, deviation 4°W)

Over an hour (1 h 08 min): fine if the stream stays much the same; for longer passages, use each hour’s stream (Lesson 36).

Worked example: south of Brennan Bank to No 1 buoy

On Sun 13 Jun you plan to leave 49°40.6'N 004°05.1'W, south of Brennan Bank, at 1110 BST, bound for No 1 buoy at the start of the Port Kerran approach. You are motoring at 5.0 kn in a light breeze, so assume no leeway. The track passes close to tidal diamond A.

Worked example

1110 BST: from 49°40.6'N 004°05.1'W to No 1 buoy

1Ground track: the line from the start to No 1 buoy measures 310°T, 5.0 M.
2The stream at A: HW Port Kerran is 1132 UT, which is 1232 BST. 1110 is 1 h 22 min before HW, so use the row “1 hour before HW” (1102–1202): 070°T, springs 1.2 kn, neaps 0.6 kn.
3Range = 4.9 − 0.8 = 4.1 m; fraction (4.1 − 2.4) ÷ 2.4 = 0.71. Rate = 0.6 + (1.2 − 0.6) × 0.71 = 1.02, about 1.0 kn. So one hour of stream is 070°T, 1.0 M.
4From the start, lay off 070°T for 1.0 M, with three arrows.
5Open the dividers to 5.0 M. From the end of the stream, swing an arc to cut the ground track.
6Join the end of the stream to the cut. The water track measures 300°T: 10° to port of the ground track — up-tide, into a stream that comes at you from the port bow.
7From the start to the cut is 4.4 M: the SOG is 4.4 kn — less than 5.0 kn, because the stream is partly against you.
8Time = 60 × 5.0 ÷ 4.4 = 68 min, so the ETA at No 1 buoy is about 1218 BST.

CTS 300°T, SOG 4.4 kn, ETA 1218

The completed triangle: ground track (two arrows), one hour of stream from diamond A (three arrows), the 5.0 M arc and the water track (one arrow) — the course to steer.

Port Kerran — times UT (add 1 hour for BST), heights in metres above chart datum
Day	Time	m	HW/LW
Sun 13 Jun	0522	0.8	LW
	1132	4.9	HW
	1742	0.6	LW
	2352	5.0	HW

Tidal streams referred to HW Port Kerran — direction °T, rates in knots at springs and neaps
Hours	A49°43.1'N 004°08.6'W
Hours	DirSpNp
6 before	2450.80.4
5 before	2500.50.2
4 before	3300.20.1
3 before	0600.60.3
2 before	0651.00.5
1 before	0701.20.6
HW	0701.10.5
1 after	0700.90.4
2 after	0750.50.2
3 after	1500.20.1
4 after	2400.60.3
5 after	2451.00.5
6 after	2501.10.5

The passage takes a little over an hour, and its last 16 minutes fall in the next row of the table, “HW” (1202–1302). At A that gives 070°T at 0.9 kn: almost the same, so one hour’s triangle is all you need.

From the triangle to the helm

The water track is a true direction through the water. To turn it into something the helm can steer:

Leeway — a sailing yacht is pushed sideways by the wind. Lesson 30 shows how to allow for it by steering a few degrees up into the wind. Leeway is applied after the triangle and before variation; here there is none.
Variation — 2°44'W in 2027, rounded to 3°W for chart work (Lesson 9).
Deviation — from the deviation card for the ship’s head (Lesson 10).

CTS °T → leeway → °M → °C

T V M D C: coming down from true, westerly errors are added and easterly ones subtracted.

Worked example

Converting 300°T for the helm

1No leeway, so the heading to make good is still 300°T.
2Variation 3°W: coming down the ladder, add it. 300 + 3 = 303°M.
3The card is by compass heading, which will be close to 303°: that is between 270° (3°W) and 315° (4°W), so about 3.7°W, or 4°W.
4Westerly deviation is added too: 303 + 4 = 307°C. Check: the card at 307°C gives 4°W as well. ✓

Steer 307°C

Shorter and longer passages

The triangle is always one hour, however long the passage. If you will get there in less than an hour, the arc cuts the ground track beyond the destination — so extend the line past it before you swing the arc. Use only the direction of the water track; work out the time from the distance and the SOG.

Worked example

Wed 2 Jun, 1300 BST: No 1 buoy to the South Brennan buoy

1Ground track: 117°T, 4.0 M, again past diamond A. Boat speed 5.0 kn, no leeway.
2HW Port Kerran 1418 UT = 1518 BST. 1300 is 2 h 18 min before HW: row “2 hours before HW” (1248–1348), 065°T, springs 1.0, neaps 0.5. Range 5.0 − 0.6 = 4.4 m; rate = 0.5 + (1.0 − 0.5) × 0.83 = 0.92, about 0.9 kn.
3Lay off 065°T, 0.9 M from No 1 buoy. Extend the ground track beyond the South Brennan buoy, then swing a 5.0 M arc from the end of the stream.
4The arc cuts the extended track 1.5 M beyond the buoy. The water track measures 125°T, 8° to starboard of the track — up-tide again, because now the stream is coming from your starboard side.
5SOG 5.5 kn (fair stream). Time = 60 × 4.0 ÷ 5.5 = 44 min: ETA 1344, still inside the same tidal hour.
6Down the ladder: 125 + 3 = 128°M; the card near 128° gives 5°E (between 090° (4°E) and 135° (5°E)), and easterly deviation is subtracted: 128 − 5 = 123°C.

CTS 125°T (123°C), SOG 5.5 kn, ETA 1344

A passage of under an hour, leaving No 1 buoy at 1300: the ground track is extended (dashed) so the one-hour arc can cut it beyond the destination.

InteractivePlot it yourself

Use the chart’s dividers to build the triangle. First lay off one hour of stream from the start; then, from the end of the stream, find the point on the ground track exactly one hour of boat speed away. Each step is checked, and at the end the readout shows your course to steer. Try both examples, then as many new problems as you like.

From:: ⊙ 49°40.6'N 004°05.1'W at 1110
To:: No 1 buoy — ground track drawn: 310°T, 5.0 M
Tidal stream:: sets 070°T at 1.0 kn (diamond A, “1 hour before HW”, range 4.1 m)
Boat speed:: 5.0 kn through the water; no leeway

Step 1 of 2: one hour of stream from the start

A sits on the start. Move B until the readout shows the set and one hour’s drift.

Distance A→B: 0.60 MBearing A→B: 260°TDrag A and B, or Tab to them and use the arrow keysZoom with + / −, drag to pan

A little over an hour? As in the first example, one hour’s triangle is usually good enough, provided the stream does not change much during the extra time. Several hours? The stream changes from hour to hour, so you lay off each hour’s stream end to end from the start and swing an arc of the whole distance through the water. That is a Yachtmaster-level technique, covered in Lesson 36.

Check your understanding: your destination is 2 M away and you make 5 kn through the water, so you open the dividers to 5 M for the arc. How long should the stream line be?

Checks before you go

Does it point up-tide? The course to steer always aims into the stream, on the side it comes from. With the stream pushing you to starboard, you steer to port of the ground track, and the other way round. If yours points down-tide, check the stream: it goes from the start, in the direction the water flows towards.
Is the angle sensible? The stronger the stream across your track compared with your speed, the bigger the angle — and the slower your progress along the track.
Time and ETA. Time in minutes = 60 × distance ÷ SOG (Lesson 7’s 60D = ST). With a fair stream the SOG is more than your boat speed; with a foul stream, less. The ETA lets you work out the height of tide and the stream you will meet on arrival.
Does the arc reach the line at all? If the stream across the track is stronger than your speed through the water, no course keeps you on the line. You cannot make good that track at that time: re-time the passage for slack water or a fairer stream.

Stream straight across the track	Angle up-tide (5 kn boat)	SOG along the track
0.5 kn	6°	5.0 kn
1.0 kn	12°	4.9 kn
1.5 kn	17°	4.8 kn
2.0 kn	24°	4.6 kn
3.0 kn	37°	4.0 kn

Check your understanding: your ground track is 000°T, the stream sets 270°T at 1.5 kn, and you make 5 kn through the water. Which course to steer makes sense?

Ground track first; one hour of stream from the start; one hour of boat speed from the end of the stream; the water track is your course to steer — and it should point up-tide.

Key terms

Course to steer (CTS): The direction to steer through the water so that, with the stream, you make good the ground track you want.
Ground track: The line you intend to follow over the seabed, from start to destination: two arrows.
Water track: Your path through the water; in a CTS triangle its direction is the course to steer. One arrow.
One-hour vector triangle: Ground track, one hour of stream from the start, and one hour of boat speed from the end of the stream to the track.
Speed over the ground (SOG): Your speed along the ground track: the start-to-arc-cut distance of a one-hour triangle.
Up-tide: Towards the side the stream is coming from. A course to steer always aims up-tide of the ground track.
ETA: Estimated time of arrival: departure time plus 60 × distance ÷ SOG minutes.
Leeway: Sideways drift caused by the wind, allowed for after the triangle and before variation (Lesson 30).
Compass course: The course to steer converted from true with variation and deviation: what the helm steers.
Re-timing: Choosing another departure time when the stream would be too strong or foul for the passage.

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.

A tidal stream is running across your track. You simply point the bow at your destination and keep it there. What happens?

You have drawn the ground track from your start to your destination. What do you lay off next, and from where?

You leave 49°51.4'N 004°10.5'W at 0940 BST, bound for the Outfall buoy, at 5.0 kn through the water. Assume no leeway. The tidal stream sets 270°T at 1.2 kn. Work the one-hour vector triangle on the plotting sheet. What is the course to steer in °T?

Plotting sheet: the ground track is drawn, extended beyond the destination. A starts on the start. Move B to the end of one hour of stream and pencil it in; the dividers then start from there, so you can swing the boat-speed arc onto the track. The readout gives the bearing A→B.

Distance A→B: 0.60 MBearing A→B: 252°TDrag A and B, or Tab to them and use the arrow keysZoom with + / −, drag to pan

Your one-hour triangle from 49°44.8'N 004°08.7'W to the Kerran Approach buoy is plotted below (boat speed 4.5 kn, stream 245°T 1.0 kn). Use the dividers to find your speed over the ground.

Distance A→B: 0.80 MBearing A→B: 005°TDrag A and B, or Tab to them and use the arrow keysZoom with + / −, drag to pan

Your ground track to the Kerran Approach buoy measures 3.2 M, and your triangle gives a speed over the ground of 4.0 kn. You leave at 0950. How many minutes will the passage take?

On Sat 12 Jun you leave 49°44.6'N 004°22.0'W at 1030 BST, bound for a waypoint at 49°49.6'N 004°21.4'W, at 5.0 kn through the water. Assume no leeway. Find the tidal stream from the tide table and the stream table for diamond C, then work the one-hour vector triangle on the plotting sheet. What is the course to steer in °T?

Port Kerran — times UT (add 1 hour for BST), heights in metres above chart datum
Day	Time	m	HW/LW
Sat 12 Jun	0441	1.1	LW
	1052	4.6	HW
	1702	0.9	LW
	2312	4.8	HW

Tidal streams referred to HW Port Kerran — direction °T, rates in knots at springs and neaps
Hours	C49°46.4'N 004°20.4'W
Hours	DirSpNp
6 before	2501.40.7
5 before	2550.90.4
4 before	3400.30.1
3 before	0650.90.4
2 before	0701.70.8
1 before	0752.11.0
HW	0752.01.0
1 after	0751.60.8
2 after	0801.00.5
3 after	1600.30.1
4 after	2451.00.5
5 after	2501.80.9
6 after	2552.01.0

Distance A→B: 0.60 MBearing A→B: 124°TDrag A and B, or Tab to them and use the arrow keysZoom with + / −, drag to pan

Your triangle gives a course to steer of 208°T. Variation is 3°W (2°44'W in 2027, rounded). There is no leeway. What is the course to steer in degrees magnetic?

A triangle gives a course to steer of 306°T, with no leeway. Variation is 3°W. Using the deviation card below, what compass course do you give the helm?

Deviation card: deviation for each ship’s head by compass
Head °CShip’s head °C	000	045	090	135	180	225	270	315
DevDeviation	2°W	1°E	4°E	5°E	3°E	0°	3°W	4°W

Interpolate between entries for other headings. Variation in 2027: 2°44'W, rounded to 3°W for chart work.

Your ground track is 090°T. The stream sets 000°T at 1.2 kn and you make 4.0 kn through the water. Without plotting, which of these is the course to steer?

Off a headland the stream runs at 3 kn almost straight across your track, and in light winds you are making only 2.5 kn through the water. From the end of the stream line you swing an arc of 2.5 M, and it does not reach the ground track. What does that tell you?

0 of 10 answered · 0 correct

Course to steer drill

Five fresh questions each time: a course to steer to plot on a real leg (sometimes with the stream from a diamond), an SOG or passage time, a true-to-compass conversion, an up-tide sense check and a quick question on the method.