Running Fix
Advancing a Line of Position to Fix Your Position with a Single Landmark
When You Need a Running Fix
A running fix is used when only one object is visible for bearings. In ideal conditions you would take simultaneous bearings to two or three landmarks, but coastal navigation is rarely ideal. Fog may obscure all but one lighthouse; the coastline may be featureless except for a single identifiable headland; or the vessel may be too far offshore for multiple objects to be visible. In these situations, the running fix allows you to obtain a position from two bearings taken at different times to the same object.
The principle is straightforward: take a bearing to the object and record the time. Continue sailing on a known course at a known speed. After a suitable interval — long enough for the bearing to change significantly — take a second bearing to the same object. The first bearing gives an LOP valid at the time it was taken; by advancing that LOP along the vessel's track for the distance traveled, you bring it forward to the time of the second bearing. The intersection of the advanced LOP with the second bearing is your running fix.
The accuracy depends on how precisely you know your course and speed made good between the two observations. Any error in course, speed, or current estimation translates directly into an error in the advanced LOP, and therefore in the fix. A running fix is inherently less accurate than a simultaneous fix from multiple landmarks, but it is far better than no fix at all, and in many coastal situations it is the only fix available.
Choose your timing so that the angle between the two bearings is at least 30 degrees and ideally 60-90 degrees. A larger angle change produces a stronger cut and a more reliable fix.
A running fix is used when:
What determines the accuracy of a running fix?
Step-by-Step Procedure
Step 1: Take the first bearing. Sight the object with your hand-bearing compass and record the compass bearing, the exact time (to the nearest minute using 24-hour format), the vessel's compass heading, and the log reading. Apply variation and deviation to convert the compass bearing to a true bearing. Plot the first LOP on the chart by drawing a line through the object on the corrected bearing.
Step 2: Maintain course and record. Continue sailing on a steady course. Note your compass heading continuously and record your speed (from the log, knotmeter, or GPS speed over ground). If you suspect a current, estimate or measure the set and drift. You need to know not just your course and speed through the water but your course and speed made good over the ground, which includes the effect of current.
Step 3: Take the second bearing. When the bearing to the object has changed by at least 30 degrees (ideally 60-90 degrees), take a second bearing. Record the same data as before: compass bearing, time, heading, and log reading. Convert to a true bearing and plot the second LOP on the chart. Step 4: Advance the first LOP. Calculate the distance traveled between the two bearings using speed multiplied by time (or the difference in log readings). From any convenient point on the first LOP, lay off the course made good for the distance traveled, and draw a new line through that point parallel to the original first LOP. This is the advanced LOP. Where it crosses the second LOP is your running fix. Label it with the time of the second bearing and the notation 'R Fix.'
Label your advanced LOP with double arrows to distinguish it from the original LOPs. Write both times beside it (e.g., '1030-1055') to show it has been advanced.
Advancing the LOP Correctly
The key to a reliable running fix is correctly advancing the first LOP. The advanced line must be moved in the direction of the course made good (not necessarily the compass course) for the distance made good (not necessarily the log distance). If there is a current, your course made good differs from your heading, and your speed made good differs from your speed through the water. Failure to account for current is the most common error in running fixes.
To advance the LOP, pick any point on the first LOP — it does not have to be a special point, any point will do. From that point, plot the course made good and measure along it the distance made good. Mark the new point. Now draw a line through this new point exactly parallel to the original first LOP. You can use parallel rulers, a rolling plotter, or a pair of triangles to transfer the line accurately. This new parallel line is the advanced LOP.
A useful cross-check is to advance two points on the first LOP independently and confirm that the resulting advanced line is parallel to the original. If you have a drafting error, the two advanced points will not produce a line parallel to the original. In practice, most navigators advance a single point and use parallel rulers to ensure the line is parallel, which is faster and sufficiently accurate.
Always use course and speed made good (over the ground), not course and speed through the water. In areas with strong current, the difference can be significant and will produce a dangerously incorrect fix if ignored.
Sources of Error
The running fix is subject to all the errors of a visual bearing fix — compass errors, landmark misidentification, plotting mistakes — plus additional errors unique to the advancement of the LOP. The most significant source of error is unknown or poorly estimated current. If the actual set and drift differ from your estimate, the advanced LOP will be displaced from its correct position, and the resulting fix will be wrong.
Leeway is another source of error. If the vessel is sailing to windward and making leeway, the actual track over the ground is downwind of the heading. If you advance the LOP along the compass course without correcting for leeway, the fix will be displaced. Estimate leeway from experience, the vessel's polar data, or by comparing the wake angle to the heading, and apply it to the course made good before advancing the LOP.
Speed error affects the distance used to advance the LOP. If your knotmeter is inaccurate, or if you are using GPS speed over ground without accounting for current changes during the interval, the distance made good will be wrong. Whenever possible, use the log (distance through the water) corrected for current, or compare log distance with GPS distance to calibrate. The longer the time between bearings, the more these errors accumulate, so avoid excessively long intervals — 15 to 30 minutes is typically a good range for coastal work.
If you suspect significant current but cannot measure it precisely, take a third bearing and compute two running fixes. Compare them to see if the positions are consistent — if they diverge, your current estimate needs revision.
The Special Case: Doubling the Angle on the Bow
Doubling the angle on the bow is a special application of the running fix that simplifies the calculation. Take the first bearing when the object is at some angle on the bow — say 30 degrees off the bow. Continue on course and take the second bearing when the angle on the bow has exactly doubled to 60 degrees. In this configuration, the geometry creates an isosceles triangle in which the distance run between the two bearings equals the distance from the object at the time of the second bearing.
The best-known special case is the bow-and-beam bearing (45-90 degrees), but other pairs work equally well: 22-44, 25-50, 30-60, and 35-70 are all commonly used. The advantage is that you do not need to plot the advanced LOP at all — you simply measure the distance run and know immediately how far off the object you are. Combined with the second bearing, this gives a complete fix without the usual chart work of advancing an LOP.
However, the same sources of error apply. The distance run must be the distance made good over the ground, not just the log reading. If there is a cross-current pushing you sideways, the isosceles-triangle assumption breaks down and the distance off will be incorrect. Always correct for current, and treat the result as a good approximation rather than an exact fix when conditions are uncertain.
When doubling the angle on the bow, what geometric shape is formed by the vessel's track and the two bearing lines?
Summary
A running fix uses two bearings to the same object taken at different times, advancing the first LOP to the time of the second bearing to find the intersection.
The first LOP is advanced along the course made good for the distance made good — always account for current and leeway.
Choose a time interval that produces at least 30 degrees of bearing change, ideally 60-90 degrees, for a strong cut.
Sources of error include unknown current, leeway, speed inaccuracy, and compass errors — all accumulate over the interval between bearings.
Doubling the angle on the bow is a special case that simplifies the running fix: the distance run equals the distance off at the second bearing.
A running fix is less accurate than a simultaneous multi-landmark fix but is invaluable when only one landmark is available.
Key Terms
- Running Fix
- A position fix obtained by advancing a line of position from an earlier observation along the vessel's course and speed made good to the time of a later observation.
- Advanced LOP
- A line of position that has been moved forward in the direction and distance of the vessel's travel to make it valid at a later time.
- Course Made Good (CMG)
- The actual track of the vessel over the ground, accounting for current, leeway, and steering error, as opposed to the compass heading.
- Speed Made Good (SMG)
- The actual speed of the vessel over the ground, which may differ from the speed through the water due to current.
- Leeway
- The sideways drift of a vessel downwind, causing the actual track to differ from the heading. It is expressed as an angle between the heading and the course made good.
- Set and Drift
- The direction (set) and speed (drift) of the current affecting the vessel. Set is given as the direction toward which the current flows.