Module 10 - Chartwork

Multi-Hour CTS with Changing Tidal Streams

What you will learn

Combine changing hourly tidal vectors into one declared planning interval, solve an average true water track and recognise when the assumed duration must be iterated.

A single long-leg CTS can represent several different streams only when their timed displacements, the boat's distance and the intended ground track all cover the same interval.

Choose the proposed passage interval and identify the tidal stream for each relevant hour from the correct source and reference-port time. Convert every rate into a displacement for the part of the hour actually used. Plot the hourly vectors head to tail; their final endpoint represents the cumulative estimated movement of the water during the interval.

Multiply speed through the water by the same total time. From the cumulative tidal endpoint, swing one arc of that total boat distance to the intended ground-track line. The vector from the cumulative endpoint to the intersection gives one average true water track for the interval. Label every hourly vector so a wrong tidal hour or direction remains visible.

For a fixed destination, elapsed time may not be known at the first attempt. Compare the ground distance produced by the construction with the destination distance, estimate a revised time and repeat with the tidal hours that revised passage would use. One averaged heading is unsuitable when speed, route, tidal regime, leeway or safety constraints change materially; split the leg or recalculate instead.

Worked example

For a fictional three-hour eastbound leg at 5 kn, the hourly tidal displacements are 1.0 M south, 1.0 M east and 0.5 M north.

1Stack the vectors to obtain a cumulative tidal displacement of 1.0 M east and 0.5 M south.
2The boat covers 3 × 5 = 15.0 M through the water in the same interval.
3From the cumulative tidal endpoint, swing a 15.0 M arc to the eastbound ground-track line.
4The required boat vector contains 0.5 M northing and about 14.99 M easting, giving approximately 088°T.
5The ground distance is about 15.99 M, so predicted SOG is about 5.33 kn; compare that distance with the intended destination and iterate if necessary.

Sense check: The small net southerly set requires a small northerly correction, while the net eastward tide slightly increases ground distance.

Multi-Hour CTS with Changing Tidal Streams
Hour	Stream displacement	Cumulative effect
1	1.0 M south	1.0 M south
2	1.0 M east	1.0 M east, 1.0 M south
3	0.5 M north	1.0 M east, 0.5 M south

Reject an answer built from mismatched hours

A three-hour plot uses three hourly stream vectors but a 20 M boat-distance arc for a yacht expected to average 5 kn.

1. Check common time
Three hours at 5 kn gives 15 M, so the boat arc and tidal sequence describe different durations.
2. Correct the interval
Rebuild both the stream displacement and boat distance for one declared elapsed time.
3. Test the destination
If the resulting ground distance does not reach the destination, revise time and repeat rather than stretching the arc.

Sense check: Every movement vector in the construction must describe the same clock interval.

Common mistake or limitation

A simple arithmetic average of stream directions can be wrong; combine vector displacements instead.
Choosing tidal hours from the first time estimate and then changing passage duration without recalculating creates a circular error.

Recap

Cumulative tidal displacement is the vector sum of the timed hourly streams.
Boat distance and tidal displacement must cover the same interval.
A destination problem may require iteration or a split leg.

Optional quick check

Section 6 of 13

Why may a fixed-destination multi-hour CTS need a second calculation?

Sources and factual review

Reviewed 2 September 2026 - Compass Revision editorial review.

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