Navigation Direction Simulator

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Navigation Practice Hub STCW // TABLE-A-II/1 • COMPASS-LAB

True Course, True Bearing & Relative Bearing: Maritime Trigonometry & Training Simulator

Resolving directional angular relationships accurately is a core competency required of every watchkeeping officer under STCW Code (Table A-II/1) and the International Regulations for Preventing Collisions at Sea (COLREGs)[cite: 1]. The mathematical interdependence between True Course (TC), True Bearing (TB), and Relative Bearing (RB) governs visual lookouts, collision risk assessment, terrestrial position fixing from charted lighthouses, and radar plotting[cite: 1].

The NavLib Navigation Simulator resolves spatial ambiguity between semicircular (0°–180° Port/Starboard) and circular (0°–360°) notation systems[cite: 1]. Featuring an interactive azimuth compass rose with draggable course and bearing vectors, live algebraic sign breakdown (+ for Starboard, - for Port), and a dedicated cadet examination quiz engine, the platform enables navigators to master mental course calculations instinctively[cite: 1].

Dynamic Compass Rose
Interactive Azimuth Lab
Drag-and-drop course and target bearing needles via mouse or touch with automated port/starboard color coding (Green Stbd / Red Port).
Complete Trigonometry
Modular Angular Outputs
Real-time derivation: semicircular RB (0°–180°), circular RB (0°–360°), reciprocal back-bearing (TB ± 180°), and verbal aspect classification[cite: 1].
Watchkeeper Exam
Self-Testing Drill Engine
Generate dynamic navigation problems solving for Relative Bearing or True Bearing with instant scoring, feedback, and solution steps.

Frequently Asked Questions: Courses, Bearings & Relative Angles (FAQ)

What primary formula connects True Course, True Bearing, and Relative Bearing?
The primary maritime navigation equations are[cite: 1]:

TB = TC + RB_stbd (for targets on the starboard side, plus sign)
TB = TC - RB_port (for targets on the port side, minus sign)

Standard 0°–360° circular normalization rules apply[cite: 1]:
  • If the resulting sum exceeds 360°, subtract 360°[cite: 1].
  • If the difference is negative, add 360°[cite: 1].
How do you determine Relative Bearing (RB) from known Course and Bearing?
Relative bearing is calculated by subtracting course from bearing[cite: 1]:
Difference = TB - TC
  • If the difference is positive and under 180°: target is on Starboard (RB_stbd)[cite: 1].
  • If the difference is negative (0° to -180°): target is on Port (RB_port)[cite: 1].
  • If the difference exceeds +180°, subtract 360° to assign it to Port (e.g., +240° - 360° = -120° = 120° Port)[cite: 1].
  • If the difference is less than -180°, add 360° to assign it to Starboard[cite: 1].
What is the difference between semicircular and 360° circular relative bearing?
Semicircular System (0°–180°): measured from the ship's head towards Starboard (positive) or Port (negative)[cite: 1]. Used for lookouts and oral bridge reports ("Light 40 degrees on starboard bow")[cite: 1].
Circular System (0°–360°): measured strictly clockwise from the ship's head from 0° through 360°[cite: 1]. Standard in ARPA/radar repeaters: TB = (TC + RB_360) mod 360[cite: 1].
What is a reciprocal bearing and why is it used on nautical charts?
A reciprocal bearing (back-bearing) is the direction from the observed target back to the vessel[cite: 1]. It differs from the true bearing by exactly 180 degrees[cite: 1]:
Reciprocal = TB + 180° (if TB < 180°)
Reciprocal = TB - 180° (if TB ≥ 180°)
Navigators plot the reciprocal bearing directly from a lighthouse or landmark onto paper or ECDIS charts to construct a Line of Position (LOP)[cite: 1].
What relative bearing corresponds to an object being "abeam"?
An object is said to be abeam when its direction lies perpendicular to the ship's fore-and-aft centerline (keel line)[cite: 1, 2]. This corresponds to a relative bearing of exactly 90° Starboard or 90° Port (or 090° / 270° circular)[cite: 1]. Passing abeam indicates the point of closest approach (CPA) to a stationary landmark.
Standard: STCW Code Table A-II/1, IMO Model Course 7.03, COLREGs Rule 5
Formulas: TB = TC + RB (Stbd), TB = TC - RB (Port), Reciprocal Bearing
Features: Retina Canvas, Drag & Drop Control, Self-Testing Exam

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