Running Fix from a Single Object
TL;DR — A running fix is obtained by advancing the first LOP along the DR track to the time of the second observation; when only one charted object is available, the doubling-the-angle technique yields both a running fix and the distance off at the second bearing.
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What the Rule Says
Line of Position and the Fix — the Foundation
A line of position (LOP) is a line along which the vessel is known to lie at a given moment, derived from a single observation. A fix is the intersection of two or more LOPs taken simultaneously. Bowditch Ch. 7 §701
When two or more objects suitable for simultaneous observation are not available, the navigator must work with what is at hand. The technique that bridges this gap is the running fix. Bowditch Ch. 7 §702
The Running Fix — Mechanics
A running fix is obtained when LOPs cannot be taken simultaneously. The procedure is:
1. Take a bearing to the available object and plot the first LOP at Time 1. 2. Maintain the DR track — recording course and speed carefully. 3. Take a second bearing to the same object (or a different one) at Time 2. 4. Advance the first LOP along the DR track by the distance run between the two observations, keeping it parallel to its original direction. 5. The intersection of the advanced LOP with the second LOP is the running fix.
The running fix is inherently less accurate than a fix from simultaneous LOPs because it depends on the assumption that the vessel has maintained the planned course and speed between observations. Bowditch Ch. 7 §702
Running Fix from a Single Object — Doubling the Angle on the Bow
When only one charted object is visible, successive bearings to that object can still produce a running fix, provided the relative bearing changes substantially between observations. Bowditch Ch. 7 §703
The most exam-tested special case is the doubling-the-angle technique (also called "doubling the angle on the bow"):
- Take the first relative bearing to the object (Bearing 1) and note the distance run.
- Continue on course until the relative bearing to the same object is exactly twice the first relative bearing (Bearing 2).
- At that moment, the distance run between the two bearings equals the distance from the vessel to the object at the time of the second bearing. Bowditch Ch. 7 §703
This relationship is a consequence of the isosceles triangle formed by the vessel's track and the two bearing lines. The two equal sides of that triangle are (1) the distance run and (2) the distance off at the second bearing.
Radar as a Source of LOPs
Marine radar processes echoes to display a plan-view picture of surrounding targets. Range and bearing to a radar target give a direct fix. Bowditch Ch. 13 §1301 A radar range arc and a visual bearing to the same object can be combined as two simultaneous LOPs, producing a fix without the need for a running fix at all — a point worth remembering when radar is available.
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Why It Matters on the Exam
The Core Tested Concept
OUPV and Master 100 GT written exams routinely present scenarios in which the candidate must identify the correct procedure when only one charted object is visible. The examiners test whether the candidate understands:
1. What makes a running fix different from a fix — the time separation between LOPs and the requirement to advance the first LOP. Bowditch Ch. 7 §702 2. The doubling-the-angle rule — specifically, that the distance run between the first and second bearings equals the distance off at the second bearing. Bowditch Ch. 7 §703 3. The accuracy limitation — a running fix is less accurate than a simultaneous fix because it rests on the assumption that course and speed were held constant. Bowditch Ch. 7 §702 Navigational errors accumulate from instrument error, observation error, plotting error, computation error, and precisely this assumption of a maintained course. Bowditch Ch. 23 §2301
Typical Exam Question Formats
Exam questions on this topic tend to appear in three forms:
Procedural: "You have a single lighthouse in sight. You take a bearing of 045° relative at 0800 and a bearing of 090° relative at 0820. Your speed is 10 knots. What is your distance off the lighthouse at 0820?" The answer is the distance run in 20 minutes at 10 knots = 3.3 nautical miles, because the angle doubled (045° to 090°) and the distance run equals the distance off. Bowditch Ch. 7 §703
Definitional: "A running fix differs from a fix in that ___." The answer: the LOPs are not taken simultaneously; the first LOP must be advanced along the DR track. Bowditch Ch. 7 §702
Accuracy: "Which position is more accurate — a running fix or a fix from simultaneous bearings?" The answer is always the simultaneous fix. Bowditch Ch. 7 §702
Plotting Procedure Step by Step
Understanding the plotting steps prevents errors under exam time pressure:
1. Plot the first LOP (a bearing line from the charted object through the DR position at Time 1). 2. Determine the distance run between Time 1 and Time 2 using speed × time. 3. Advance the first LOP: move every point on that line in the direction of the vessel's course by the distance run. The advanced LOP is drawn parallel to the original, labeled with both times (e.g., "0800–0820"). 4. Plot the second LOP at Time 2. 5. Mark the intersection of the advanced first LOP and the second LOP as the running fix, labeled with the time of the second observation.
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Common Pitfalls
1. Forgetting to Advance the First LOP — Not the DR Position
A frequent error is advancing the DR position rather than the LOP itself. The entire first LOP must be translated parallel to itself along the course line by the distance run. Moving only the DR point and re-drawing the bearing from there is incorrect and will produce a wrong intersection. Bowditch Ch. 7 §702
2. Misapplying the Doubling-the-Angle Rule
The rule states that the distance run between the two bearings equals the distance off at the second bearing — not at the first, and not at some midpoint. Candidates sometimes apply the distance to the wrong moment. Bowditch Ch. 7 §703
Additionally, the rule requires the relative bearing to double — not merely change. If the first relative bearing is 30° and the second is 50°, the angle has not doubled and the isosceles-triangle relationship does not hold.
3. Treating a Running Fix as Equivalent to a Simultaneous Fix
A running fix is explicitly less accurate than a fix from simultaneous LOPs. Bowditch Ch. 7 §702 The accuracy of a running fix degrades with any error in course steered, speed made good, or current not accounted for. Navigational errors from instrument error, observation error, plotting error, computation error, and the assumption of a maintained course all compound over the interval between observations. Bowditch Ch. 23 §2301 On the exam, never select "running fix" as the more accurate option when a simultaneous fix is offered as an alternative.
4. Ignoring Radar as an Alternative
When radar is available, a range arc from radar combined with a visual bearing to the same object produces two simultaneous LOPs and therefore a direct fix — no advancement required, no running fix degradation. Bowditch Ch. 13 §1301 Bowditch Ch. 7 §701 Exam questions sometimes offer radar range as a distractor; recognize that it eliminates the need for a running fix entirely.
5. Mislabeling the Advanced LOP
The advanced LOP must be labeled with both the original time and the time of advancement (e.g., "0800–0820"). Labeling it only with the second time, or failing to label it at all, is a plotting error that can cause confusion and is penalized on practical exams. Bowditch Ch. 7 §702
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Quick Check
Q1 — What is a running fix, and how does it differ from a standard fix?
A running fix is obtained when LOPs cannot be taken simultaneously. The first LOP is advanced along the DR track to the time of the second observation; the intersection of the advanced LOP and the second LOP is the running fix. A standard fix is the intersection of two or more LOPs taken simultaneously. The running fix is less accurate because it depends on the vessel having maintained the planned course and speed between observations. Bowditch Ch. 7 §702
Q2 — You observe a lighthouse at a relative bearing of 030° at 1000. At 1030 the relative bearing is 060°. Your speed is 12 knots. What is your distance off the lighthouse at 1030, and why?
Distance run in 30 minutes at 12 knots = 6.0 nautical miles. Because the relative bearing doubled (030° to 060°), the doubling-the-angle rule applies: the distance run between the two bearings equals the distance off at the second bearing. Distance off at 1030 = 6.0 nautical miles. Bowditch Ch. 7 §703
Q3 — Which is more accurate: a running fix or a fix from simultaneous bearings? What sources of error affect a running fix?
A fix from simultaneous bearings is more accurate. Bowditch Ch. 7 §702 A running fix is degraded by instrument error, observation error, plotting error, computation error, and the assumption that the vessel held the planned course between observations. Bowditch Ch. 23 §2301
Q4 — When advancing the first LOP to obtain a running fix, what must be done to the LOP, and how is it labeled?
The entire first LOP is translated parallel to itself in the direction of the vessel's course by the distance run between the two observations. It is labeled with both the time of the original observation and the time to which it has been advanced — for example, "0800–0820." Bowditch Ch. 7 §702
Q5 — Radar shows a range of 4.0 nm to a lighthouse. You simultaneously take a visual bearing of 270°T to the same lighthouse. What type of position does this produce, and is a running fix required?
The radar range arc and the visual bearing are two simultaneous LOPs. Their intersection is a direct fix. Bowditch Ch. 7 §701 Bowditch Ch. 13 §1301 No running fix is required because the LOPs are taken simultaneously; no LOP advancement is needed.