3.3 Visual Position Lines, Three-Bearing Fixes & Cocked Hats
Key Takeaways
A Position Line (Line of Position or LOP) is a line plotted on the chart representing an observed bearing or other position constraint, subject to measurement and plotting error; two intersecting LOPs provide a fix, but three LOPs provide vital verification and error detection.
A Hand-Bearing Compass (HBC) operated on the open deck away from vessel magnetic anomalies requires correction only for magnetic variation, not the ship's steering compass deviation card.
Transits (leading marks) occur when two charted landmarks align visually; they provide the single most accurate visual position line afloat, requiring zero compass correction and serving as an ideal check on compass deviation.
Optimal geometry for a three-bearing fix requires bearings intersecting at angles of approximately 60° (or 120°), preventing shallow cut angles (less than 30°) that introduce massive spatial uncertainty.
A cocked hat does not bound the yacht's possible position. Assess observation errors and allow an uncertainty area extending outside the triangle; keep that whole area clear of danger and obtain an independent check.
3.3 Visual Position Lines, Three-Bearing Fixes & Cocked Hats
Note
Core Principle: A Position Line (or Line of Position, LOP) is a line plotted on a nautical chart representing an observation of the vessel's position at a specific time, subject to error. Intersecting multiple independent LOPs produces a Fix. The three-bearing visual fix remains the benchmark standard for independent, un-spoofable coastal positioning.
Electronic chartplotters can suffer satellite signal loss, power interruption, antenna failure, or software freeze. Visual position fixing provides an instantaneous, independent check against the physical landscape. Mastery of the hand-bearing compass, charted transits, and geometric cut angles is a fundamental competency tested in Coastal Skipper and Yachtmaster examinations.
Types of Visual Position Lines
Navigators utilize four distinct forms of visual position lines:
- Compass Bearings: Sighting a charted object (lighthouse, daymark, spire, headland) with a hand-bearing compass and plotting the reciprocal bearing out to sea.
- Transits (Leading Lines): Observing two charted objects in exact optical alignment. Transits require no instrument, have zero magnetic error, and provide an exceptionally precise position line.
- Clearing Bearings: A pre-computed limit bearing drawn from a charted mark. Keeping on the safe side clears underwater hazards or reefs.
- Horizontal Sextant Angles: Measuring horizontal angles between landmark pairs with a sextant to yield circular position lines independent of compass error.
The Hand-Bearing Compass (HBC) and Deviation
A Hand-Bearing Compass (HBC) is a portable magnetic compass equipped with a prism or sight vane. Because it is hand-held and moved around deck, specific rules govern its use:
The Magnetic Clean Spot
The HBC must be sighted from a pre-identified "clean spot" on deck—typically on the centerline, well clear of large ferrous metal masses (steel pulpits, engine blocks, anchor winches, and steering pedestals) and personal electronics (smartphones, handheld radios, sunglasses with magnetic clips).
HBC and Deviation Cards
Important
Critical Exam Rule: The vessel's published Deviation Card applies strictly and exclusively to the fixed steering compass mounted at the helm. You must NEVER apply the steering compass deviation card to a bearing taken with a hand-bearing compass. Sighted from a clean spot on deck, deviation is treated as zero, and you correct the observed bearing solely for Magnetic Variation:
Transits: The Gold Standard of Coastal Fixing
A Transit (also called a range or leading line) occurs when two charted objects align in one optical plane:
- Zero Compass Error: Because transits rely purely on line of sight, they are completely immune to variation, deviation, electrical failure, or parallax error.
- Checking Deviation Afloat: If a charted transit has a true direction of 245°(T), and local variation is 2°W, the magnetic bearing is . If the helmsman steers along this transit and the steering compass reads 251°(C), the steering compass deviation on that heading is revealed as ().
Geometry of Three-Bearing Fixes
While two intersecting position lines produce a fix, any observational error will displace the intersection without warning. Navigators observe three bearings on three widely separated charted objects. The third bearing acts as an independent audit.
Optimal Cut Angles
- Two Bearings: An intersection angle of 90° provides maximum geometric strength.
- Three Bearings: Sights should ideally be separated by approx 60° (or 120° if distributed around the horizon). This equilateral distribution ensures that sighting errors produce a symmetrical, detectable triangle.
- Unacceptable Geometry: If bearing lines intersect at an acute angle of less than 30° or an obtuse angle of greater than 150°, minor sighting errors create massive spatial elongation along the cut line, rendering the fix unreliable.
Observation Sequence
Sight the three objects in rapid succession (within 30 to 60 seconds) to minimize vessel movement between sights:
- Sight objects dead ahead or dead astern first: Bearings change most slowly as the vessel moves forward.
- Sight objects on the beam last: Bearings of objects abeam change at the fastest rate. Record the exact log reading and UTC time when the final bearing is taken.
The "Cocked Hat" and Its Causes
In practical navigation, three plotted position lines rarely intersect at a single point, forming a triangle known as a Cocked Hat (or triangle of error).
Physical Causes
- Personal Observation Error: Difficulty steadying the HBC card on a rolling yacht in sea chop (typically ±1° to ±2°).
- Vessel Movement: Distance run between the first and third sights.
- Unaccounted Compass Deviation: An unnoticed metallic item near the HBC.
- Chart or Plotting Errors: Minor parallel rule slip or paper stretch.
- Landmark Misidentification: Sighting the wrong tower or daymark.
Sizing and Assessing the Cocked Hat
A small triangle shows that the plotted observations agree closely; it does not prove they are accurate. A common compass error or misidentified landmark can displace the whole fix. A large triangle calls for investigation, but no single width in nautical miles establishes whether a fix is usable.
Check landmark identification, compass corrections, plotting, time between observations and cut angles. Compare with an independent position line, soundings or another reliable method. If observations disagree materially, retake them while using the best available position estimate and safe clearances.
Position Uncertainty Near Danger
Caution
The yacht may be outside the cocked hat. Neither its centre nor the corner nearest danger is a guaranteed position or an outer limit of error.
When plotting near shallow water, rocks or other hazards:
- Assess a plausible position area from the bearing accuracy, range to the marks, geometry and possible common errors. This area may extend beyond the triangle.
- Check clearance from the danger-side extent of that area, allowing an additional safety margin.
- If the area could overlap danger, take safe action and obtain further observations. Do not rely on selecting a corner to guarantee clearance.
Summary Table: Visual Fixing Techniques & Geometry
| Technique | Instrument Used | Compass Correction Required | Optimal Geometry / Angle | Inherent Error Risk |
|---|---|---|---|---|
| Transit (Leading Line) | Naked eye / Binoculars | None (pure line of sight) | N/A (linear LOP) | Misidentifying distant background mark |
| Two-Bearing Fix | Hand-Bearing Compass | Variation only | 90° intersection angle | No check against undetected error |
| Three-Bearing Fix | Hand-Bearing Compass | Variation only | 60° or 120° separation | Cocked hat if sights delayed or distorted |
| Clearing Bearing | Hand-Bearing Compass | Variation only | Angular limit relative to hazard | Sighting wrong mark or misreading card |
When taking visual bearings with a hand-bearing compass (HBC) on the open deck of a fiberglass yacht, how should the navigator correct the observed compass bearing to plot it on the nautical chart?
Apply only magnetic variation (from the chart's compass rose), assuming the observer is standing in a magnetically clean position free from vessel deviation
Apply both the main steering compass deviation card values and the charted variation
Apply neither, because hand-bearing compasses automatically align with True North using internal gyroscopes
Add 10° for standard deck ironwork interference, then subtract variation
A three-bearing fix produces a small cocked hat near a shallow reef. Which assessment best supports safe navigation?
Assume the vessel's true position is exactly at the geometric center (centroid) of the triangle
The yacht may lie outside the triangle; assess the full plausible position area, keep it clear of the reef and obtain an independent check
Erase the fix entirely and steer dead reckoning until GPS signal is regained
Average the longest two sides of the triangle and plot the midpoint along the track line
Which of the following angular distributions provides the optimal geometry for a three-bearing visual position fix?
All three objects situated on the same side of the vessel within a 30° arc of the beam
Two objects directly ahead and one directly astern
Three charted objects spaced approximately 60° (or 120°) apart around the vessel to provide wide, well-balanced cuts
Two objects at 15° separation and one at 180° separation
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