A running fix can be obtained by using mathematical relationships involved. A ship steams past a landmark. At any point a bearing of a LIGHT is observed and expressed as degrees right or left of the course (a relative bearing if the ship is on a course). At some later time, at a second bearing of the LIGHT is observed and expressed as before, when the LIGHT is broad on the beam. The various triangles could be solved by trigonometry to find the distance from any bearing. Distance and bearing provide a fix.
Example: A ship is steaming on course 315°, speed 12 knots. At 1230 a lighthouse bears 340°, and at 1300 it bears 000°
Required:
1. Distance from the light at 1300 (2nd bearing).
2. Distance form the light when it is broad on the starboard beam.
Table 7 (Green - Bowditch) or Table 18 (Red - Bowditch) provides a quick and easy solution. The table is entered with the difference between the course and first bearing along the top of the table, and the difference between the course and 2nd bearing on the left side of the table. For each pair of angles listed, two numbers are given:
To find the distance from the LIGHT at the time of the 2nd bearing multiply the distance run between bearings by the first number on the left side of each column from Table 7.
To find the distance when the LIGHT is abeam, multiply the distance run by the second number on the right side of each column from the Table 7.
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