Running Fix from a Single Object

What the rule requires

The trigger is availability. When only one charted object can be observed, the running fix is the method that gets a position out of it: take a bearing, run a timed distance on a steady course, take a second bearing, advance the first line of position along the DR track by the distance run, and lay it across the second bearing Bowditch Ch. 7 §708. The same construction covers any case where LOPs cannot be taken simultaneously, and the advance always runs to the time of the second observation Bowditch Ch. 7 §702.

Two quantities govern the advance, and only two: direction is the course steered, distance is the distance run. The advanced LOP is drawn parallel to the original, offset by that vector. Because the advance rides on the DR track, it inherits what DR knows and nothing more — course steered and distance run through the water, with current and leeway left out of the reckoning Bowditch Ch. 8 §801.

The bearing has to move. Bearings on a single object produce a usable running fix only when the relative bearing changes substantially Bowditch Ch. 7 §703, and the reason shows on the chart: the angle at which the advanced LOP cuts the second bearing is the change in the object's bearing between the two observations. Strong fixes cross their LOPs near 90 degrees Bowditch Ch. 7 §707, so a bearing that has swung 15 degrees gives a shallow, ambiguous cut, and one that has swung 60 to 90 degrees gives a positive one.

When the relative bearing has run out to exactly twice its first value, the geometry hands you a range for free. This is the doubling-the-angle technique, and it is the one shortcut on this topic worth having cold: the distance run between the two relative bearings equals the distance to the object at the second bearing . At the second bearing, not the first, and it is the slant distance to the object along the bearing line, not the distance the object will be off the track when abeam.

Plot the DR position for the time of the second bearing before you advance anything, because that DR position is what measures the run. A new DR position belongs at every course change, every speed change, at the time of each fix, and at least once each hour, more often in pilot waters . Symbols carry the distinction the exam tests: a fix is a dot inside a circle, a DR position a dot with a semicircle, and an estimated position a dot inside a square, each labelled with the 24-hour time Bowditch Ch. 8 §802. Label the advanced LOP with both times so the plot reads unambiguously to the next watchstander.

You take a bearing on a light at 1000, hold course and speed, and take a second bearing at 1030. In what direction and for what distance do you advance the 1000 LOP?

In the direction of the course steered, for the distance run in the 30 minutes — the vector from the 1000 DR position to the 1030 DR position. Not along the bearing to the light, and not along the LOP itself. The advanced line stays parallel to the 1000 LOP .

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Telling it apart

Four positions get confused here, and one criterion separates all four: what the position is built from.

• Fix — two or more LOPs observed at the same moment Bowditch Ch. 7 §701; dot inside a circle. Most often misfiled: two bearings taken several minutes apart on different objects, called a fix. If the vessel ran between them, one LOP must be advanced and the result is a running fix.
• Running fix — LOPs observed at different times, the earlier advanced along the DR track to the time of the later Bowditch Ch. 7 §702. Most often misfiled: the point where the second bearing crosses the DR track. That uses one observation, and a fix is the intersection of LOPs.
• DR position — no observation at all; course steered and distance run from the last fix, current and leeway ignored Bowditch Ch. 8 §801; dot with a semicircle. Most often misfiled: assumed to include the current because the vessel was obviously being set.
• Estimated position — the DR position with the estimated set and drift laid off for the elapsed time Bowditch Ch. 8 §803; dot inside a square. Most often misfiled: a candidate corrects the run between the two bearings for estimated current and still calls the answer a running fix. Once an estimate of current is in the position, it is an EP.

Set is the direction toward which the current flows and drift is its speed, and the EP is the best position available between fixes when only the current can be estimated .

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Working a question

You are steering 090°T at 8 knots in clear weather off a featureless coast. One charted object is in sight, a light on a headland. At 0900 it bears 040°T. You hold course and speed. At 0930 it bears 350°T. Required: the 0930 position.

1. Establish which method applies. One object, two bearings, thirty minutes apart, with the vessel running between them. LOPs cannot be taken simultaneously, so this is a running fix, not a fix Bowditch Ch. 7 §702.
2. Check that the bearing moved enough to be worth plotting. Relative bearing at 0900 is 50° off the port bow; at 0930 it is 100° off the port bow. The bearing swung 50°, so the two LOPs will cut at 50° — short of the ideal 90° Bowditch Ch. 7 §707 but a positive intersection, and a substantial change as the method requires Bowditch Ch. 7 §703.
3. Plot both LOPs from the light. Draw 040°/220° through the light and label it 0900; draw 350°/170° and label it 0930. Each is a line along which the vessel was known to lie at that moment Bowditch Ch. 7 §701.
4. Compute the run and plot the 0930 DR. 8 knots for 0.5 h is 4.0 nautical miles, laid off along 090°T from the 0900 DR position Bowditch Ch. 8 §801.
5. Advance the 0900 LOP. Set the dividers to 4.0 nm. From the point where the 0900 LOP crosses the course line, step 4.0 nm along the course line in the direction of travel and mark it. Lay the parallel rulers on the 0900 LOP, slide to that mark, and draw the advanced line. Label it with both times, 0900–0930.
6. Take the intersection. Where the advanced LOP cuts the 0930 bearing is the running fix. Plot it as a dot inside a circle and label it with the time of the second bearing Bowditch Ch. 8 §802.
7. Check it with the doubling-the-angle relation. The relative bearing went 50° to 100° — it doubled — so the distance from the light to the vessel at 0930 equals the distance run, 4.0 nm . Measure the plotted running fix from the light along 170°. If it is not 4.0 nm, the error is in the plot, not in the arithmetic.
8. Restart the DR from the running fix, since a new DR position belongs at the time of each fix .

Had a current been running across the track and gone unallowed-for, the advance would be wrong by the set and drift over those 30 minutes, and the running fix wrong with it. That is exactly the assumption the method rests on: that course and speed were held as recorded Bowditch Ch. 7 §708.

Same problem, but the second bearing is taken at 0906 instead of 0930. Is the resulting running fix better or worse?

Worse. The run is only 0.8 nm and the bearing has barely changed, so the advanced LOP and the second bearing cut at a shallow angle and the intersection slides a long way for a small bearing error. The method needs a substantial change in relative bearing , and LOPs crossing near 90° give the strongest position . A shorter run does not buy accuracy.

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Where candidates lose the point

Advancing the wrong line, or advancing it the wrong way. The distractor is the position found by carrying the second bearing backward to the time of the first. Only the earlier LOP moves, and it moves forward to the time of the later observation Bowditch Ch. 7 §702.

Advancing along the bearing instead of along the track. A candidate who has plotted the LOP from the light slides it toward or away from the light, because the light is what they were just working with. The offset direction is the course steered Bowditch Ch. 7 §708.

Crossing the second bearing with the DR track and calling that the running fix. It looks like a fix because two lines cross. It uses one observation, and a fix is the intersection of two or more LOPs Bowditch Ch. 7 §701.

Putting estimated current into the advance and keeping the word "fix." Applying set and drift produces an estimated position, plotted as a dot inside a square Bowditch Ch. 8 §803. The DR track the LOP is advanced along ignores current and leeway by definition Bowditch Ch. 8 §801.

Trusting a running fix as though it were a fix from two objects. On a question asking which position to work from when a hazard is close aboard, the running fix attracts because it is the most recent observation. It is less accurate than a fix from simultaneous LOPs and less reliable than a simultaneous two-object fix, because it assumes the course and speed were held exactly .

Applying the doubling-the-angle distance to the first bearing. The distance run equals the distance to the object at the second bearing Bowditch Ch. 7 §703. Candidates also read it as the distance the object will pass abeam, which it is not.

Mislabelling the plotted result. A running fix drawn with a semicircle reads as a DR position to the next watchstander, and consistent labelling is the whole point of the symbol scheme Bowditch Ch. 8 §802.

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Check yourself

You are on course 000°T at 10 knots. At 1400 a lighthouse bears 045°T; at 1424 it bears 090°T. What is your distance from the lighthouse at 1424, and how do you know without measuring the plot?

4.0 nm. The run is 10 knots for 24 minutes, or 4.0 nm. The relative bearing went from 45° off the starboard bow to 90° off — it doubled — so the distance run equals the distance to the object at the second bearing Bowditch Ch. 7 §703.

Only one aid to navigation is visible. You take a bearing at 1100, alter course 20° to starboard at 1115 to clear a fish trawler, and take a second bearing at 1130. Can you advance the 1100 LOP with a single vector?

No. The advance must reflect the track actually run, which now has two legs. Carry the DR forward with a new DR position at the 1115 course change Bowditch Ch. 8 §801, then advance the 1100 LOP by the direction and distance from the 1100 DR position to the 1130 DR position. A single 1100-to-1130 vector on the original course would place the fix off by the whole effect of the alteration, and the method already assumes course and speed were held exactly Bowditch Ch. 7 §708.

At 0800 you fix by bearings on two charted towers. At 0830 only one tower is still visible and you take a bearing on it. What position can you plot for 0830, and with what symbol?

A running fix, plotted as a dot inside a circle. The 0800 fix gave you a bearing on the tower that is still visible, so advance that 0800 LOP along the DR track to 0830 and cross it with the 0830 bearing on the same tower. Had there been no earlier LOP on that object, the 0830 bearing alone would give a single LOP, and your best position would be the 0830 DR (dot with a semicircle), or an EP (dot inside a square) if set and drift can be estimated Bowditch Ch. 8 §802, Bowditch Ch. 8 §803.

Two bearings on a single object, 8 minutes apart, differ by 6°. Your plotted running fix lands 1.5 nm from where you expected. What is the most likely cause?

The cut. With a 6° change in bearing the advanced LOP crosses the second bearing at 6°, so a one-degree bearing error moves the intersection a long way. The method requires a substantial change in relative bearing , and LOPs crossing near 90° give the strongest result Bowditch Ch. 7 §707. Run longer between bearings.

You advance the first LOP using the distance run through the water, then shift the resulting position 0.6 nm in the direction of a known set of 210° before labelling it. What have you plotted?

An estimated position, not a running fix. Laying off set and drift from a reckoned position produces an EP, plotted as a dot inside a square .

You are 2 nm off a charted shoal and have both a 1200 running fix on a single light and a 1200 fix from three simultaneous bearings. Which do you navigate from?

The three-bearing fix. A running fix is less accurate than a fix from simultaneous LOPs Bowditch Ch. 7 §702. Where the three LOPs form a cocked hat near a hazard, assume the corner nearest the danger Bowditch Ch. 7 §705.