Running with the sun

by Cameron Bright

When using the sun for celestial navigation, a running fix is the best method for a navigator to determine a vessel’s position. Running fixes are the traditional technique by which seamen have navigated the oceans. Indeed many today disdain star sights in favor of the ease of sun navigation using running fixes.

When using celestial navigation during daylight hours, there is most commonly only one celestial body available to the navigatorandmdash;the sun. A sextant sight taken on the sun will yield one line of position (LOP). By itself, an LOP contains only certain information about a vessel’s position, namely that the vessel is somewhere on that LOP. Theoretically speaking, an LOP is long line. Like a parallel of latitude, it extends far beyond the boundaries of a plotting sheet. A navigator needs another reference to help determine his vessel’s position on this line.

A DR position, plotted for the same time as the LOP, is the critical reference for focussing the navigator’s attention to the appropriate segment of his line. The DR is where the vessel should be – provided there is no poorly logged information or other external factors. Without DR, a navigator would be left to admire the handiwork of his LOP without being capable of assessing his position on it. The navigator’s best guess of a position on the LOP is typically the point that is closest to the DR position. This point on the LOP is called an estimated position, or EP.

An EP, then, is the best guess when a navigator has only one LOP and a DR position. Naturally, a navigator would prefer to fix his position, but this is an elusive goal so long as there is only one celestial body available. A fix occurs at the intersection of two or more LOPs taken at the same time. This approach will not work for the sun, since the bearing to the sun does not change quickly enough. LOPs from two sun sights taken within a few minutes of each other will be virtually parallel. In fact, two such lines form the worst combination for constructing a fix. It is still possible to create a good approximation of a fix from two sun sights, but these cannot be taken one immediately after the other. They must be separated by several hours. This approximation is called a “running fix” to distinguish it from a regular fix.

Any time a navigator has taken one sight and then taken another a couple of hours later, he has two options: 1) create a new EP; or, 2) create a running fix. Constructing an EP would be most sensible if the DR information was suspect, or if the presence of a strong ocean current was possible. Only if DR information is believed accurate, should a running fix give a navigator the best position.

The technique for creating a running fix requires some imagination on the part of the navigator. To begin, a navigator must pretend that the first sun sight was actually taken at the time of the second sun sight. There is more to the technique than mere pretense. To create this effect, a navigator must physically move an entire LOP across his chart to take into account the vessel’s movement between the two sights. This presents the first LOP as it would be if it had been taken at the time of the second LOP.

How can this sleight of hand be rationalized? Consider an LOP not as a line, but rather a series of points arranged side by side. The EP is one of these points. It is the point that the navigator thinks most likely to be the vessel’s position. But, the vessel could easily be on an adjoining point, or maybe one a mile away, or even five miles away. Plotting a DR track from the EP effectively moves one of these points forward, presenting its position at the time of the second sight. If the navigator’s original DR was skillfully arrived at, the second LOP may plot through this DR position. This would confirm that the vessel’s position on the first LOP was the point selected as the EP. All too often, the second LOP does not intersect the DR position plotted from the EP. This indicates that the EP was not the correct position on the first LOP. The navigator should have advanced a different point. One solution to this mistake would be to select another point on the first LOP and plot a DR track from it. As this process is somewhat random, this could lead to plotting numerous DR tracks. Even if the track is straight and easily plotted, this is time-consuming and clutters the chart with extraneous lines. However, to do this once is instructive. If one were to plot a number of these extra points, they would form a straight line. This straight line would be parallel to the first LOP from which the points originated.

There is a simpler method for achieving this same line and guaranteeing that the correct point is moved. Plot the DR track, as before, out from the EP to the time of the second sight and mark the DR position. Draw a line through this DR position that is parallel to the original LOP. That is the andquot;advancedandquot; LOP. For clarity’s sake, it should be labeled with the time of the first sight, then a hyphen and the time of the DR that it was drawn through. This clearly shows where the line came from as well as the time to which it has been advanced. The intersection of this advanced LOP and the second LOP is the running fix.

Because accurate DR information is essential, a navigator will never be able to produce an accurate running fix unless the necessary information is available. When the navigator is on watch, this is a simple task of monitoring the vessel’s heading via the compass and its progress through the water as determined by a log. When the navigator is not on watch, it is essential that DR information is scrupulously noted in the logbook. The captain must make this a matter of almost religious importance to each crewmember. The requirements are quite simple. At the end of each hour, write down time, vessel’s heading over the past hour and log reading or average speed in the logbook. In addition, if the vessel changes course, the time and log reading of that should also be noted. This provides a clear record of the vessel’s progress across the ocean. It also allows a navigator to plot a DR track.

Constructing a DR track requires only two pieces of information: A vessel’s speed through the water and its heading. By accurately plotting these, a navigator is able to determine where his vessel should be in the absence of external forces.

The EP is a combination of two discrete pieces of navigational information. The EP represents the navigator’s best estimate of a vessel’s position. However, a navigator will use the discrepancy between an LOP and a DR for more than just creating an EP. If a DR track has accurately portrayed a vessel’s progress, the LOP should run through the DR position for the same time. The difference in the location of the LOP and the DR must be accounted for by some other factor. This is often the result of ocean currents, compass error, poorly logged steering, poor speed estimates or the effects of wave action or leeway. Without a DR position, there is no signal to the navigator that his vessel is not performing as he expects.

From the EP, the navigator continues to plot the DR track, effectively abandoning the old DR position. An EP is the best analysis of a vessel’s position combining all information that the navigator has at hand. It makes sense to restart the DR from the best position available, even if it means abandoning the old DR. Otherwise, positional information from the LOP would not be incorporated into any subsequent DR position.

It is typically necessary to wait at least a couple of hours after the time of the first LOP before the bearing to the sun has changed sufficiently to obtain a good crossing angle. This time period is variable, depending on the time of day, latitude of the vessel and declination of the sun. Bearings to the sun typically change most rapidly near local apparent noon. If the boat’s latitude and sun’s declination are similar, the bearing to the sun will remain fairly constant all morning and afternoon. There will be a rapid change of bearing close to noon. When latitude and declination are far apart, the sun’s bearing changes slowly and steadily throughout the daylight hours.

To find a specific change rate, look in an inspection sight reduction table like Pub. No. 229 or Pub. No. 249. (Other tables can also be used but require more steps and a clearer sense of the processes involved to accomplish the same tasks.) Enter the table with the information used in the first sight reduction. Next decide what the minimum crossing angle will be. Using Z from the first sight, determine what the new Z should be in order to have the desired crossing angle with the Z from the first sight. Track through the sight reduction table, increasing the LHA while keeping declination and latitude constant, until locating the sought-after new Z. Note the LHA at that Z. Find the difference between the LHA of the first sight and the new LHA, then multiply this difference by four. (LHA changes 1 degree every four minutes.) The result gives the number of minutes between sights to get the desired crossing angle.

The crossing angle is important to the navigator because an ideal crossing angle of two lines is 90 degrees However, it’s not necessary to wait until the LOPs cross at 90 degrees. Smaller angles will work effectively, particularly if the navigator can be confident of the accuracy of his sights. Except for a special circumstance, the crossing angle should be greater than 25 degrees or 30 degrees. There is no magic to 30 degrees, but that is where the amount of error in the sight is doubled in the resulting fix. A sight with one minute of arc error will cause the resulting fix to be off by: a) one mile given a 90 degree angle; b) 1.4 miles at 45 degrees c) two miles at 30 degrees and d) 2.9 miles at 20 degrees. This progression gets much worse at smaller angles, so that the fix error is five times as large when the crossing angle is 11.5anddeg;.

Any two lines that are not parallel will cross – somewhere. Effective navigation is designed so that the fix resulting from two LOPs will be trustworthy. When navigating using only the sun, there is the added difficulty that a significant amount of time separates the two sights. This accounting for the vessel’s travels is the essence of the running fix. The most important discipline is to plot appropriately (see accompanying diagrams). This is no place for sloppily drawn lines, worn pencil points, or missing labels. Slipshod plotting will easily cause misleading results. An excellent set of sights and good, reliable DR information are of little use to a navigator who plots poorly.

A fix is most desirable, and a running fix most closely approximates a fix when there is only one celestial body available. A running fix starts with the disadvantage of having two LOPs taken at different times. Its accuracy can be diminished by poor DR information or by ignorance of the external factors between the two sights.

By Ocean Navigator