5.3 Dead-Reckoning Plots & Estimated Positions
Key Takeaways
- A DR plot projects position from the last fix using only course steered and speed; it ignores current, wind, and steering error and must be checked against fixes.
- Label the true course above the line and speed below, and mark a DR position (semicircle + time) at every course change, speed change, fix, and hour.
- Advance or retard a DR with 60 D = S T: at 10 knots a 30-minute leg is 5.0 nm, laid off along the new course from the turn point.
- Correct a DR for a known current to get an estimated position (square): shift the DR by set (direction) a distance of drift times time.
- With only one line of position, the best estimate is the foot of the perpendicular from the DR to that LOP, marked as an EP.
What a DR Plot Shows
A dead-reckoning (DR) plot projects your position forward from your last fix using only the course steered and the speed (or distance run). It deliberately ignores current, wind, and steering error, so it answers "where should I be?" — an estimate to be checked against the next fix. The engine is the same 60 × D = S × T relationship from Chapter 2; here we focus on drawing and labeling the track.
Building the Track
- Start at your last fix (circle + time).
- Draw the course line in the true direction steered; label C 075°T above the line and S 10 below it.
- Wherever anything changes — a new course, a new speed, a fix, or simply the top of the hour — mark a DR position with a semicircle and the four-digit time.
Worked example — plotting DR positions. You take a 0800 fix, then steer C 075°T at S 10. Where are the 0900 and 0930 DR positions?
- To 0900 (60 min): D = (S × T)/60 = (10 × 60)/60 = 10.0 nm.
- To 0930 (90 min): D = (10 × 90)/60 = 15.0 nm.
Step off 10.0 nm and 15.0 nm along the 075°T line with your dividers and mark each with a semicircle and time.
Advancing (and Retarding) a Position
Because DR is time-based you can advance a position forward or retard it back with the same arithmetic.
Worked example — a course change. At 0930 you alter course to C 120°T, still at 10 knots. Where is the 1000 DR? That is 30 minutes: D = (10 × 30)/60 = 5.0 nm. From the 0930 DR position, lay off 5.0 nm along 120°T and mark the 1000 DR. The track now has a "kink" at 0930 where you turned — DR always follows the actual sequence of courses and speeds.
Retarding a position works the same arithmetic backward. If you want the DR for 1000 but only plotted a position at 1015, back off the distance run in those 15 minutes — at 10 knots, (10 × 15)/60 = 2.5 nm — along the reverse of the course to find the earlier point.
The Three Positions Compared
| Position | Built from | Symbol |
|---|---|---|
| DR | Course steered + speed/time only | Semicircle |
| EP | DR corrected for known current | Square |
| Fix | Two or more crossing LOPs | Circle |
Each is a better estimate than the one above it: a fix beats an EP, which beats a bare DR.
When to Plot a DR Position
Prudent practice — and the convention the exam expects — is to lay down a new DR position at four moments: every time you change course, every time you change speed, every time you take a fix, and at every whole hour. Plotting on these events keeps the track honest and gives you ready reference points if a question asks "where were you at 0930?" A DR carried too far without a checkpoint invites arithmetic slips and leaves nothing to reset against when the next fix arrives. On a timed plotting problem, marking the hourly and turn positions also earns the partial-credit checkpoints graders look for.
From DR to Estimated Position
A DR position ignores current. When you know a current is running, apply it to the DR to get an estimated position (EP), marked with a square. You shift the DR by the current's set (direction) a distance equal to drift × time.
Worked example — DR corrected for current. From the 0900 DR position you know a current has been setting 180°T (due south) at 1.5 knots for the past hour. Over 1 hour the current carries you 1.5 nm in direction 180°T. Shift the 0900 DR 1.5 nm due south and mark that point with a square — that is your 0900 EP, a better estimate of where you truly are than the raw DR.
Estimated Position From a Single LOP
If you get only one bearing — a single line of position — you cannot fix your position, but you can improve the DR. The best estimate is the point on the LOP nearest the DR position: drop a perpendicular from the DR to the LOP, and mark the foot of that perpendicular as an EP (square) with the time. It uses the one piece of real information you have (you are somewhere on that line) without pretending to a full fix.
Symbol and Method Traps
- Mixing the symbols. DR = semicircle, fix = circle, EP = square. Graders check these.
- Not restarting DR from each new fix. Every fix resets the accumulated DR error; carry the DR forward from the fix, not from the old DR.
- Applying current twice — once as an EP and again as a "corrected DR." The current adjustment turns a DR into an EP; it is applied once.
- Forgetting the hourly/turn marks, which leaves the plot unreadable and costs partial-credit checkpoints.
On a plotting sheet, which symbol marks a dead-reckoning position?
You take a known current and apply it to a DR position to account for how far it has carried you. The resulting marked position is called and drawn as:
What does a dead-reckoning plot deliberately leave out?