Module 10 - Chartwork

Worked CTS: Complete Two-Hour Calculation

What you will learn

Solve and independently check a two-hour CTS from true vector construction through leeway assumptions, variation and deviation to a compass heading.

This worked example keeps every displacement and correction visible so the result can be checked by direction, components, distance and reverse conversion.

A fictional yacht must make good 090°T for two hours at 6 kn through the water. A steady stream sets 180°T at 2 kn. Leeway is ignored for this training example. The boat-distance arc is 2 × 6 = 12 M; tidal drift is 2 × 2 = 4 M south.

To finish on the eastbound ground track, the 12 M water vector needs 4 M of northing. Its eastward component is √(12² − 4²) = √128 = 11.31 M. The true water-track bearing is arctan(11.31 ÷ 4) = 70.5°T, read from the chart to appropriate precision and rounded here to 071°T. Ground distance is 11.31 M in two hours, so predicted SOG is 5.66 kn.

Now apply only the corrections specified. With no leeway in the example, true heading remains 071°T. With 2°W variation, add west to obtain 073°M. With 1°E deviation for the intended heading, subtract east to obtain 072°C. Real navigation uses the applicable place, date and deviation information, then monitors the actual track and position rather than treating the calculation as certainty.

Worked example

Desired ground track 090°T; boat speed 6 kn; duration two hours; stream 180°T at 2 kn; no leeway; variation 2°W; deviation 1°E.

1Plot 4 M on 180°T from the start for the two-hour stream displacement.
2Swing a 12 M boat-distance arc from the tidal endpoint to the 090°T ground-track line.
3Measure the water vector from tidal endpoint to intersection: 70.5°T, rounded to 071°T.
4Check components: 4 M north and 11.31 M east; √(4² + 11.31²) = 12 M.
5Convert 071°T + 2°W = 073°M; then 073°M − 1°E = 072°C.

Sense check: A south-setting stream demands a water track north of east, and converting 072°C forward through 1°E deviation and 2°W variation returns 071°T.

Worked CTS: Complete Two-Hour Calculation
Stage	Working	Result
Boat distance	6 kn × 2 h	12 M
Tidal drift	2 kn × 2 h south	4 M south
Water vector	√(12² − 4²)	11.31 M east; 071°T
Ground speed	11.31 M ÷ 2 h	5.66 kn
Compass	071°T + 2°W − 1°E	072°C

Keep calculated precision in proportion

A calculator displays 70.528779°, but the chart construction, stream estimate and steering cannot support six decimal places.

1. Retain exact working
Use the component calculation to check the plotted direction and ground distance.
2. Report realistic precision
Read and round in line with the chart, exercise and available inputs; here the teaching answer is 071°T.
3. Monitor the assumptions
Compare COG, SOG and fixes with the plan and revise when stream, speed or leeway differs materially.

Sense check: More displayed digits do not make an estimated tidal vector or hand-drawn plot more certain.

Common mistake or limitation

Measuring from the original start gives the ground track, not the required water track.
Applying west and east corrections as unsigned numbers loses their direction and can reverse the compass answer.

Recap

Use one two-hour interval for both boat distance and tidal drift.
Component arithmetic checks the chart construction.
Convert the true heading through signed variation and deviation only once.

Optional quick check

Section 7 of 11

After obtaining 071°T, variation is 2°W and deviation is 1°E. What compass heading follows?

Sources and factual review

Reviewed 2 September 2026 - Compass Revision editorial review.

Continue studying Chartwork

This public lesson is part of Revision Module 10. Full revision access adds the guided Learn, Practise and Test flow, flashcards and revision progress.

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