Three-bearing fix and cocked-hat triangle

Bowditch Ch. 7 §701

Bearings and Lines of Position A line of position (LOP) is a line along which the vessel is known to lie at a given moment based on a single observation. A fix is the intersection of two or more LOPs taken simultaneously.

Bowditch Ch. 7 §702

Bearings and Lines of Position A running fix is a fix 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 is the running fix, less accurate than a fix from simultaneous LOPs.

Bowditch Ch. 7 §703

Bearings and Lines of Position Bearings to a single object can produce a running fix when the relative bearing changes substantially. The 'doubling-the-angle' technique uses two relative bearings; the distance run between them equals the distance to the object at the second bearing.

Bowditch Ch. 7 §704

Bearings and Lines of Position Compass bearings of an approaching vessel are the canonical method of detecting risk of collision. If the bearing remains constant and the range is decreasing (CBDR), risk of collision exists.

Bowditch Ch. 7 §705

Bearings and Lines of Position A three-bearing fix takes three simultaneous lines of position to well-separated charted objects. The three LOPs rarely cross at a single point; the small triangle they form is the "cocked hat". A small cocked hat indicates a good fix, taken at its centre; a large one signals bearing or plotting error. Where the triangle lies near a hazard, the corner nearest the danger is assumed for safety.

Bowditch Ch. 7 §706

Bearings and Lines of Position A danger bearing keeps a vessel clear of an off-lying hazard using a single charted object. A line is drawn from the object tangent to the edge of the hazard — or to a danger circle scribed at a safe distance around it — and labelled NMT (not more than) or NLT (not less than) that bearing. So long as the object's observed bearing stays on the safe side of the danger bearing, the vessel remains in safe water.