Creating a Running Fix
TL;DR: A running fix allows you to determine your current position by taking a single observation, waiting for your ship to travel a known distance, and then shifting your earlier line of position forward to meet your new one.
The Problem of Moving Targets
In our journey through celestial navigation, we have mastered the art of finding our longitude using a (Station 10). However, the ocean is rarely still, and neither is your vessel. If you take a star sight at dawn, your ship might travel twenty miles before you are ready to take a second observation. If you treat those two sightings as if they happened at the exact same moment, your math will be wrong, and your position on the chart will be drifting toward disaster. You are not a static point on a grid; you are a vector with speed and direction. To find your true location, you must account for the time and distance that pass between your measurements.
The Geometry of the Running Fix
Think of a as a snapshot of your reality at a specific moment. When you take a sight, you aren't finding a single point; you are finding a line. By the time you take a second sight, your first line of position is already 'stale'—it represents where you were, not where you are. To fix this, we use the technique of the running fix. You take your first line of position and draw it on your chart. Then, you calculate your ship’s movement—your and —during the interval between the two sights. You then shift that entire first line of position forward along your path of travel by the exact distance you covered. Where this 'advanced' line crosses your new, second line of position, you have found your current location. It is the geometric equivalent of catching up to your own shadow.
Putting It into Practice
Imagine you are sailing across the Atlantic. You sight a star and get a line of position at 04:00. You note your heading is 090° and your speed is 10 knots. By 05:00, you have traveled 10 nautical miles. Instead of ignoring that first sight, you simply slide that 04:00 line 10 miles to the east along your 090° path. When you take your second sight at 05:00 and plot it, the intersection of the shifted 04:00 line and the new 05:00 line provides your precise fix. This is a powerful tool because it allows a single navigator to build a reliable position using only one celestial object over time, rather than needing two stars to appear simultaneously.
This process relies entirely on your ability to track your movement accurately. If your speed estimate is off, your advanced line will be in the wrong place, and your final fix will be flawed. It turns the act of sailing into a continuous conversation between your instruments and the stars. You are no longer just looking at the sky; you are calculating the geometry of your own progress across the globe.
A running fix turns the passage of time into a navigational asset by advancing a previous line of position to intersect with a current one, effectively accounting for your ship's movement.
Now that you know how to bridge the gap between two separate observations, you are ready to handle the complexity of the sky at its most crowded. In our next station, we will move beyond single-star sightings to learn how to use multiple celestial bodies simultaneously to lock in your position with absolute certainty.