Chapter 8: Piloting

Lines of position and fixes

A visual bearing to a charted object gives a line of position; two crossing LOPs give a fix, three give a fix with an error triangle that reveals bad data. Radar gives range circles, which are generally more accurate than radar bearings because beam width degrades bearing accuracy. A range (two objects in line) is the most accurate LOP available and needs no instrument. Depth contours give a rough LOP from the echo sounder.

• Prefer ranges, then visual bearings, then radar ranges, then radar bearings
• Cut LOPs as near 90° as possible; avoid angles under 30°
• Take the most rapidly changing bearing last

Running fix and special cases

A running fix advances an earlier LOP by the DR run to cross a later LOP from the same or another object, and carries all the DR's uncertainty. Doubling the angle on the bow, and the special-case bearings 22.5°/45° ('bow and beam'), give distance off equal to the run between bearings. Distance off by vertical sextant angle of a charted elevation is quick and precise.

Danger bearings, angles and clearing ranges

A danger bearing is a single limiting bearing on a charted object that keeps the vessel clear if the observed bearing stays on the safe side of it. A horizontal danger angle between two objects, measured with a sextant, keeps the vessel outside a circle through both objects. A clearing range or clearing depth provides the same protection using radar or the echo sounder. These pre-planned limits are the piloting equivalent of a guard rail.