Why a Fix Requires Two Independent Lines of Position
A single bearing or range places the vessel somewhere along a line; it does not tell you where on that line. Two or more lines of position (LOPs) that cross at a usable angle give an intersection — a fix. The quality of that fix depends on the accuracy of each LOP and the angle at which they cross. Cuts less than roughly 30° or greater than 150° produce elongated cocked hats and large position uncertainty; aim for cuts close to 90° where possible.
Magnetic Compass Bearings as LOPs
On a yacht, bearings are commonly taken with a hand-bearing compass, which gives compass bearings. To plot these on a chart, you must convert to true bearings:
- Compass bearing → Magnetic bearing: apply deviation for the hand-bearing compass (if known; on many yachts a separate deviation card exists for the hand-bearing compass)
- Magnetic bearing → True bearing: apply variation (from the chart compass rose, corrected for annual change)
Mnemonic: Cadet Delivers More Very True — Compass → apply Deviation → Magnetic → apply Variation → True. Error applied incorrectly produces a systematic position error that compounds with every LOP.
Plot each true bearing as a back bearing from the charted object through the vessel's estimated position. Take bearings of at least two — preferably three — objects, noting the time. Three bearings give a cocked hat; the vessel's most probable position is inside it, biased toward danger.
Radar Ranges as LOPs
A radar range from a charted object produces a circular LOP centred on that object. On the chart, set dividers to the measured range (converted from nautical miles using the chart scale), and scribe an arc centred on the object. A radar range is generally more accurate than a radar bearing because it is less affected by beam width distortion.
Practical considerations:
- Identify the correct target; radar returns can shift from the actual charted position, particularly for sloping coastlines — the return arrives from the highest reflecting point, not necessarily the charted position.
- Use variable range marker (VRM) rather than cursor for accuracy.
Combining Both Methods
A magnetic bearing and a radar range from the same object gives a rapid two-LOP fix — a straight LOP crossed by a circular arc. This is particularly useful in restricted visibility where visual bearings of a second object are unavailable. The two methods are independent in nature (compass error does not affect the range; radar index error does not affect the bearing), making the combination robust for cross-checking.
Record the fix with time, method, and COG/SOG for the passage log.