A Lambert conformal conic chart with standard parallels at 54°N and 59°N is used for navigation. The straight line between A 55° 00.0’N 165° 00.0’E and B 58° 00.0’N ’E is drawn on this chart. The True track along the straight line at A is 301° and at is B 292°.
Calculate the longitude of position B.
In a Lambert conformal conic chart a a great circle at the parallel of origin is almost a straight line and we know that chart convergence is the angle of inclination between meridians on the chart, (or the change in direction of a straight line), between 2 longitudes.
Chart convergence for a Lambert conformal conic chart is constant across the chart:
Chart convergence = ch.long. × sine parallel of origin
The parallel of origin is halfway between the standard parallels, (54º + 59º) / 2 = 56,5º and the change in direction of the straight line will give us chart convergence:
Chart convergence = 301º - 292º = 9º
ch.long. = 9º / sine (56,5º) = 10,8º
Flying in westerly direction:
165º - 10,8º = 154,2º
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