discuss with respect to positional errors in fixes position line and in fixes,

Excellent topic. Understanding positional errors is the foundation of safe and effective navigation. It’s the difference between thinking you are at a single point and knowing you are somewhere inside an area of probability.

Let’s break this down by first discussing the fundamental building block—the Position Line—and then how its errors combine to create errors in a Fix.

1. The Position Line (LOP) and its Errors

A Position Line (or Line of Position - LOP) is a line on a chart on which the observer is known to be located. It can be a straight line or an arc.

Examples of LOPs:

• A visual bearing to a known landmark (e.g., a lighthouse).
• A radar range from a coastline or buoy.
• A celestial Line of Position from an observation of the sun, moon, or a star.
• A line of constant depth from an echo sounder (a depth contour).

No LOP is ever perfect. It is always subject to errors, which can be categorized as follows:

A) Sources of Error in an LOP:

1. Systematic Errors: These are constant or predictable errors that can, in theory, be corrected.

   • Example: A magnetic compass has a known deviation that hasn’t been applied. A sextant has a known index error. A radar has a fixed range error. If you know the error, you can correct for it. Uncorrected systematic errors will consistently shift your LOP in one direction.

2. Random Errors: These are unpredictable, small, fluctuating errors that cannot be eliminated, only minimized. They are the primary source of uncertainty in good navigation.

   • Example: The slight unsteadiness of the hand holding a bearing compass. The difficulty in perfectly aligning a radar cursor with the edge of a fuzzy target. Atmospheric shimmer when taking a visual bearing. The small, unavoidable inaccuracies in timing a celestial sight.

3. Gross Errors (Blunders): These are major mistakes that must be identified and discarded.

   • Example: Misidentifying a lighthouse. Reading the wrong side of a compass card (e.g., 170° instead of 350°). A major calculation mistake. Plotting the LOP from the wrong starting point.

B) Representing the Error on a Chart:

Because of these inherent random errors, a single LOP should not be thought of as an infinitely thin line. Instead, it is the centerline of a “band of uncertainty.”

• The navigator’s true position is not on the line, but somewhere within this band.
• The width of the band depends on the confidence level (e.g., 95% confidence) and the estimated accuracy of the observation. A very clear, sharp radar range will produce a much thinner band of uncertainty than a hazy visual bearing to a distant mountain.