Module 6 - Position, Course & Speed
Worked DR and EP from Course, Log, and Tide
What you will learn
Build a time-labelled dead-reckoning position from course and distance, add a tidal vector to form an estimated position, and state the uncertainty that remains.
A DR advances the last established position using course steered and distance through the water. An EP modifies that estimate with relevant external information such as tidal stream or leeway; neither is a fresh observed fix.
Start the DR from the last established position. For the chosen interval, plot the true course steered and the distance run through the water. In the convention used for this lesson, wind and current are not included in the DR; record the time and assumptions so another navigator can reconstruct it.
An EP modifies the DR with additional estimated information that is insufficient by itself to establish a fix. For a supplied tidal stream, calculate drift from rate × time and plot it in the direction of set from the DR endpoint. If leeway is also supplied, represent it consistently in the water-track or vector construction rather than adding the same effect twice.
Plotting symbols differ between training and operational conventions. The USCG handbook, for example, uses a semicircle for DR and a square for EP, while other schemes use different marks for electronic fixes or estimates. Use the convention specified by the course, chart or organisation, and label time and method rather than relying on shape alone.
A neat EP is still an estimate. Steering error, log error, changing stream, leeway and the quality of the starting position all travel with the construction. Near danger, shorten the interval and seek independent position evidence instead of allowing the plot to create false confidence.
Worked example
Find the net displacement of the worked 1030 EP from the 1000 fix as an independent numerical sense check.
- 1The 2.5 M vector on 045°T has components about 1.768 M east and 1.768 M north.
- 2The 1.0 M vector on 120°T has components about 0.866 M east and 0.500 M south.
- 3Net components are about 2.634 M east and 1.268 M north.
- 4The resulting displacement is about 2.92 M on 064.3°T from the 1000 fix.
Sense check: A 1.0 M south-easterly tide turns the 045°T DR displacement towards the east and increases total displacement only modestly; it cannot produce 3.5 M on 165°T.
| Stage | Calculation | Result and label |
|---|---|---|
| Time | 30 ÷ 60 | 0.5 h |
| Distance through water | 5 kn × 0.5 h | 2.5 M |
| DR | 2.5 M on 045°T from the fix | 1030 DR |
| Tidal drift | 2 kn × 0.5 h | 1.0 M on set 120°T |
| EP | Add the tidal vector from the DR | 1030 EP; about 2.92 M on 064.3°T from start |
Carry a 1000 fix forward to 1030
From the 1000 fix you steer 045°T at 5 kn through the water for 30 minutes. The supplied tidal stream sets 120°T at 2 kn for the same interval.
1. Convert time
30 minutes = 0.5 hours.
2. Plot the DR
Distance through water = 5 × 0.5 = 2.5 M. Plot 2.5 M on 045°T and label the 1030 DR.
3. Plot tidal drift
Drift = 2 × 0.5 = 1.0 M. From the DR plot 1.0 M on the supplied set of 120°T.
4. Label and monitor
The vector endpoint is the 1030 EP. Record its assumptions, then compare it with the next independent position evidence.
Sense check: The tide sets south-east, so the EP should lie south-east of the DR. If the vector points 300°T, set has been plotted reciprocally.
Common mistake or limitation
- Adding tide to the course line before first establishing the DR endpoint required by the exercise method.
- Plotting tidal set in the reciprocal direction or using the rate as a distance without multiplying by time.
- Calling the EP a fix or assuming its exact-looking mark removes uncertainty in course, speed, stream, leeway and start position.
- Applying leeway once to the course and then again as a separate vector.
Recap
- DR advances the last established position using course and distance through the water.
- EP modifies the DR with additional estimated information such as tide or leeway.
- Set is direction; drift is distance for the chosen interval.
- Use the stated plotting convention, label time and assumptions, and seek independent position evidence.
Optional quick check
Section 6 of 6
A stream sets 120°T at 2 kn for 30 minutes. Which vector belongs from the DR endpoint?
Sources and factual review
Continue studying Position, Course & Speed
This public lesson is part of Revision Module 6. Full revision access adds the guided Learn, Practise and Test flow, flashcards and revision progress.