Module 10 - Chartwork
Worked DR to EP: Coordinates and Assumptions
What you will learn
Advance a two-hour DR and tidal EP in latitude and longitude, check every intermediate value and state why the result remains an estimate.
Coordinate arithmetic can check a plot when the local scale and assumptions are explicit. It cannot turn estimated course, speed and stream into an observed fix.
Start from the fictional fix 50°00.0′N 001°00.0′W. The yacht travels on 090°T through the water at 6 kn for two hours with no leeway, so its DR displacement is 12 M east. Near 50°N, one minute of longitude spans approximately cos 50° = 0.643 M. The longitude change is therefore 12 ÷ 0.643 = 18.7′ east.
Moving 18.7′ east from 001°00.0′W reduces the west longitude to 000°41.3′W. The 1400 DR is 50°00.0′N 000°41.3′W. Apply a steady stream setting 180°T at 2 kn for two hours: drift is 4 M south, equal to 4.0′ of latitude. The 1400 EP is 49°56.0′N 000°41.3′W.
The calculation assumes the start was accepted, 090°T and 6 kn were maintained, leeway was negligible, the stream remained representative and the short east-west conversion used an appropriate latitude. Mark and time DR and EP, retain an uncertainty area and compare with depth, visual, radar or checked GNSS evidence before using the result near danger.
Worked example
From 50°00.0′N 001°00.0′W, travel 12 M east through the water, then apply 4 M of south-setting stream.
- 1Longitude scale at 50°N: cos 50° = 0.643 M per minute of longitude.
- 2Eastward longitude change: 12 ÷ 0.643 = 18.7′.
- 3DR: 001°00.0′W − 18.7′ = 000°41.3′W at unchanged 50°00.0′N.
- 4Southward latitude change: 4 M = 4.0′ of latitude.
- 5EP: 50°00.0′N − 4.0′ = 49°56.0′N, longitude 000°41.3′W.
Sense check: Eastward travel must reduce a west longitude, while a 180°T stream must reduce north latitude.
| Position | Latitude | Longitude | Status |
|---|---|---|---|
| Start | 50°00.0′N | 001°00.0′W | Accepted fix at 1200 |
| DR | 50°00.0′N | 000°41.3′W | 12 M east through water |
| EP | 49°56.0′N | 000°41.3′W | Adds 4 M south stream |
Challenge the coordinate signs
A worksheet gives 50°04.0′N 001°18.7′W for an eastbound vessel in a south-setting stream.
1. Predict before calculating
Eastbound movement should make west longitude smaller; southward movement should make north latitude smaller.
2. Check the two scales
Latitude uses 1 M per minute; longitude needs the nearby latitude scale or an appropriate chart measurement.
3. Retain position status
Even correct coordinates remain an EP until supported by an observation-derived fix.
Sense check: The quadrant and direction should be right before the decimal arithmetic is trusted.
Common mistake or limitation
- Using one minute of longitude as one nautical mile away from the equator gives the wrong east-west coordinate change.
- Adding eastward movement to a west longitude moves the plotted point in the wrong direction.
Recap
- Use the local latitude scale for north-south distance.
- Convert east-west distance with the nearby longitude scale or cosine approximation.
- Check signs, assumptions and position status separately.
Optional quick check
Section 8 of 11
Why is 12 M east at 50°N more than 12 minutes of longitude?
Sources and factual review
Reviewed 2 September 2026 - Compass Revision editorial review.
- RYA Coastal Skipper/Yachtmaster Offshore Theory Course
- MCA MGN 610 Amendment 1 — navigation and SOLAS Chapter V
- MCA MGN 379 Amendment 1 — use of electronic navigational aids
- IHO S-4 chart specifications, edition 4.10.0
- RIN guidance for safe use of electronic navigation on leisure vessels
- USCG Boat Crew Handbook — Navigation and Piloting
- GPS Standard Positioning Service Performance Standard, fifth edition
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.