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Old 06-03-2003
Jim Sexton Jim Sexton is offline
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Running Fixes

When there's only one reference in view, a running fix is a good option for dead reckoning.
When you are in the coastal phase of navigation, there are usually many different types of objects that you can use for visual bearings or radar fixes. Buoys are plentiful and there are towers, steeples, and prominent landmarks that you can use for visual LOP bearings. Even so, there will be times when it is impossible to get more than one LOP at approximately the same time, or there may only be a single object that is usable. In this type of situation you will want to use a type of piloting procedure called a running fix.

When two or more LOPs are taken at different times, their intersection does not constitute a fix because the boat moved some distance between the times of the observations. To compensate for this movement, the LOPs must be adjusted to a common time by using the speed of the vessel multiplied by the time between the LOP and the fix time. For two LOPs, the usual method is to adjust the first LOP to the time of the last LOP by moving it down course for the distance traveled. This new advanced LOP is plotted parallel to the old LOP and labeled with both the time of the initial observation and the time to which it was advanced. These two times are separated by a dash. For example you take a bearing on a buoy that is slightly ahead of the vessel at 1103 and then take a beam bearing on a tower at 1115. The time between LOPs is 12 minutes, and for a boat speed of six knots, you would advance the first LOP for a distance of 1.2 nm (D= S x T / 60, or 6 x 12 / 60 = 1.2) down the track and plot it parallel to itself or just plot it at the true bearing initially observed.

The advanced LOP would be labeled 1103-1115 on top of the LOP and the magnetic bearing observed is annotated underneath the LOP (see illustration).

Advancing the older LOP to the time of the newest LOP is the key to a running fix.
The second LOP would be plotted and labeled with the time of 1115 on top of the LOP and the magnetic bearing underneath. The intersection of these two LOPs is considered a fix and it would be labeled with the time of 1115 parallel to the bottom of the chart. Obviously a beam LOP (speed line) would be moved considerably more down the track than one taken slightly ahead of the vessel (a course line), and for this reason it is best to take the ahead or aft bearings first and beam bearings last. However, it is far easier to advance the plot of a beam bearing, because you simply move it down course the appropriate distance and plot it perpendicular to the course.

There are as many different ways of taking LOPs and combining them as there are ways of tying a knot. A bearing LOP can be advanced to a distance-off LOP just as easily as to a depth sounding or celestial LOP. The important point to remember is that you need to advance the older LOP to the time of the newest LOP no matter the source of the LOPs.

All the bearings you take are usually magnetic and you must convert them to true bearings to plot them. Although you can use the magnetic compass rose for plotting, it is standard practice to convert to and plot true bearings. Do you remember the memory aid "Can Dead Men Vote Twice?" The first letter of each word is used to convert from Compass to Magnetic by applying Deviation and then Variation to arrive at True. Did you also recall the "East is Least and West is Best" mnemonic for applying the correct plus or minus value to west or east variation and deviation? These plus or minus values are also applied when going from true to compass, but are reversed when converting from compass to true.

Transfering your bearing from a range object to the chart will allow you to avoid the conversion process.
If the conversion process is not to your liking, you may want to utilize range bearings as much as possible. To take a range bearing, simply line up two identifiable objects and note the time. Then you lay the plotter on the chart, align it with the two objects, and draw the LOP on the chart in the direction of your boat. Do this a second and a third time with different objects and advance the older LOPs to the time of the last one and you will have a running fix plotted without worrying about the conversion process from magnetic to true.

It is possible and easy to take a series of bearings on the same object and thus obtain what is called a running fix (R Fix). For the best accuracy, these relative bearings are taken when the object is approximately 45, 90, and 135 degrees from the boat. You then either advance the first two LOPs to the time of the last LOP, or you retard the last two LOPs to the time of the first LOP. An alternate method is to use the time of the beam bearing as the fix time and then advance the first LOP and retard the last LOP to that time. Usually the first method of advancing the first two LOPs to the time of the last one is the preferred method.

Keep in mind that variables like current and wind will affect the accuracy of your DR.
The accuracy of a running fix is based on the distance of the boat from the object and the amount of time it takes to go from the first bearing to the last one. A critical assumption in all of this is that the wind and tidal current both remain fairly constant for the whole time. In the real world that is seldom the case since it might take up to 30 minutes to get all three bearings. Because it is difficult to record and plot all the relevant information, we usually take the easy way out and assume that the variables do in fact remain constant. Any errors are usually small. However, if you know the predicted set and drift, you can adjust each LOP for the effect of set and drift for the time of advance and achieve a bit more accuracy. This technique is explained in Bowditch, Chapmans, and The Annapolis Book of Seamanship. If you are interested you may want to read up on it.

Sometimes it is necessary to change course between LOPs, and the advancement of the first LOP will thus be a bit different, but this is relatively easy to do. Simply draw a dashed line between the two DRs (you will need to plot a DR position for the time of each bearing) and advance the first LOP along this dashed line for the time of advance. Again, this procedure is explained in detail in the sources mentioned above.