Celestial navigation on a moving vessel requires special measures to correct for the change in position between different observations unless the latter are performed in rapid succession or simultaneously, e. g., by a second observer.
If the navigator knows the speed of the vessel, v, and the true course, C (the angle formed by the motion vector and the local meridian), position line navigation provides a simple graphic solution.
Assuming that we make our first observation at the time T1 and our second observation at T2, the distance, d, traveled during the time interval T2-T1 is
d [nm] = [T 2 [h] –T1 [h]) * v [kn]
1 kn (knot) = 1 nm/h
Although we have no knowledge of our absolute position yet, we know our second position relative to the first one.
To find the absolute position, we plot both position lines in the usual manner, as illustrated in chapter 4. Then, we choose an arbitrary point of the first position line (resulting from the observation at T1) and advance this point according to the motion vector defined by d and C. Next, we draw a parallel of the first position line through the point thus located. The point where this advanced position line intersects the second line of position (resulting from the observation at T2) marks our position at T2. A position obtained in this fashion is called running fix (Fig. 5-1).
In a similar manner, we can obtain our position at T1 by retiring the second position line (Fig. 5-2)
Terrestrial lines of position may be advanced or retired in the same way as astronomical position lines. It is also possible to choose two different assumed positions. AP1 should be close to the estimated position at T1, AP2 close to the estimated position at T2 (Fig. 5-3).
A running fix is not as accurate as a stationary fix. For one thing, course and speed over ground can only be estimated since the effects of current and wind (drift) are not exactly known in most cases.
Further, there is a geometrical error inherent to the method. The latter is based on the assumption that each point of the circle of equal altitude, representing a possible position of the vessel, travels the same distance, d, along the rhumb line (see chapter 12) defined by the course, C. The result of such an operation, however, is a distorted circle. Consequently, the advanced (or retired) LOP is not exactly parallel to the original LOP. The resulting position error usually increases as the distance, d, increases . The procedure gives fairly accurate results when the distance traveled between the observations is smaller than approx. 50 nm.
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